Sample records for modified mode-i cracked

  1. Microscopic study of mode I crack tip deformation

    Deshun Fan; Caifu Qian; Zhongjun Jiang


    By simulating edge dislocation emissions from a mode I crack tip along multiple inclined slip planes, the plastic zone and dislocation-free zone around the crack tip are obtained. It is found that the shape of the mode I plastic zone consists of two leaning forward loops which is better agreement with experimental observations. Except at the crack tip there are also stress peaks in front of the crack tip. A formula of the maximum peak stress as a function of the applied stress intensity factor and the friction stress has been regressed.

  2. Mode I stress intensity factors of slanted cracks in plates

    Ismail, Al Emran; Ghazali, Mohd Zubir Mohd; Nor, Nik Hisyamudin Muhd


    This paper presents the roles of slanted cracks on the stress intensity factors (SIF) under mode I tension and bending loading. Based on the literature survey, lack of solution of SIFs of slanted cracks in plain strain plates are available. In this work, the cracks are modelled numerically using ANSYS finite element program. There are two important parameters such as slanted angles and relative crack length. SIFs at the crack tips are calculated according to domain integral method. Before the model is further used, it is validated with the existing model. It is found that the present model is well agreed with the previous model. According to finite element analysis, there are not only mode I SIFs produced but also mode II. As expected the SIFs increased as the relative crack length increased. However, when slanted angles are introduced (slightly higher than normal crack), the SIFs increased. Once the angles are further increased, the SIFs decreased gradually however they are still higher than the SIFs of normal cracks. For mode II SIFs, higher the slanted angels higher the SIFs. This is due to the fact that when the cracks are slanted, the cracked plates are not only failed due to mode I but a combination between both modes I and II.

  3. Assisted crack tip flipping under Mode I thin sheet tearing

    Felter, Christian Lotz; Nielsen, Kim Lau


    such as slanting, cup-cone (rooftop), or cup-cup (bathtub) the flipping crack never settles in a steady-state as the near tip stress/strain field continuously change when the flip successively initiates and develops shear-lips. A recent experimental investigation has revealed new insight by exploiting 3D X...... type loading) on the tip of a slant Mode I crack can provoke it to flip to the opposite side. Both experiments and micro-mechanics based modeling support this hypothesis....

  4. Crack tip fields in elastic-plastic and mixed mode I+II+III conditions, finite elements simulations and modeling

    F. Fremy,


    Full Text Available This paper is devoted to the analysis of the load path effect on I+II+III mixed mode fatigue crack propagation in a 316L stainless steel. Experiments were conducted in mode I+II and in mode I+II+III. The same maximum, minimum and mean values of the stress intensity factors were used for each loading path in the experiments. The main result of this set of experiments is that very different crack growth rates and crack paths are observed for load paths that are however considered as equivalent in most fatigue criteria. The experiments conducted in mode I+II and in mode I+II+III, also allowed to show that the addition of mode III loading steps to a mode I+II loading sequence is increasing the fatigue crack growth rate, even when the crack path is not significantly modified.

  5. Combined mode I stress intensity factors of slanted cracks

    Ismail, A. E.; Rahman, M. Q. Abdul; Ghazali, M. Z. Mohd; Zulafif Rahim, M.; Rasidi Ibrahim, M.; Fahrul Hassan, Mohd; Nor, Nik Hisyamudin Muhd; Ariffin, A. M. T.; Zaini Yunos, Muhamad


    The solutions of stress intensity factors (SIFs) for slanted cracks in plain strain plate are hard to find in open literature. There are some previous solutions of SIFs available, however the studies are not completed except for the case of plain stress. The slanted cracks are modelled numerically using ANSYS finite element program. There are ten slanted angles and seven relative crack depths are used and the plate contains cracks which is assumed to fulfil the plain strain condition. The plate is then stressed under tension and bending loading and the SIFs are determined according to the displacement extrapolation method. Based on the numerical analysis, both slanted angles and relative crack length, a/L played an important role in determining the modes I and II SIFs. As expected the SIFs increased when a/L is increased. Under tension force, the introduction of slanted angles increased the SIFs. Further increment of angles reduced the SIFs however they are still higher than the SIFs obtained using normal cracks. Under bending moment, the present of slanted angles are significantly reduced the SIFs compared with the normal cracks. Under similar loading, mode II SIFs increased as function of a/L and slanted angles where increasing such parameters increasing the mode II SIFs.

  6. New theory for Mode I crack-tip dislocation emission

    Andric, Predrag; Curtin, W. A.


    A material is intrinsically ductile under Mode I loading when the critical stress intensity KIe for dislocation emission is lower than the critical stress intensity KIc for cleavage. KIe is usually evaluated using the approximate Rice theory, which predicts a dependence on the elastic constants and the unstable stacking fault energy γusf for slip along the plane of dislocation emission. Here, atomistic simulations across a wide range of fcc metals show that KIe is systematically larger (10-30%) than predicted. However, the critical (crack tip) shear displacement is up to 40% smaller than predicted. The discrepancy arises because Mode I emission is accompanied by the formation of a surface step that is not considered in the Rice theory. A new theory for Mode I emission is presented based on the ideas that (i) the stress resisting step formation at the crack tip creates ;lattice trapping; against dislocation emission such that (ii) emission is due to a mechanical instability at the crack tip. The new theory is formulated using a Peierls-type model, naturally includes the energy to form the step, and reduces to the Rice theory (no trapping) when the step energy is small. The new theory predicts a higher KIe at a smaller critical shear displacement, rationalizing deviations of simulations from the Rice theory. Specific predictions of KIe for the simulated materials, usually requiring use of the measured critical crack tip shear displacement due to complex material non-linearity, show very good agreement with simulations. An analytic model involving only γusf, the surface energy γs, and anisotropic elastic constants is shown to be quite accurate, serves as a replacement for the analytical Rice theory, and is used to understand differences between Rice theory and simulation in recent literature. The new theory highlights the role of surface steps created by dislocation emission in Mode I, which has implications not only for intrinsic ductility but also for crack tip

  7. Reconsidering the boundary conditions for a dynamic, transient mode I crack problem

    Leise, Tanya


    A careful examination of a dynamic mode I crack problem leads to the conclusion that the commonly used boundary conditions do not always hold in the case of an applied crack face loading, so that a modification is required to satisfy the equations. In particular, a transient compressive stress wave travels along the crack faces, moving outward from the loading region on the crack face. This does not occur in the quasistatic or steady state problems, and is a special feature of the transient dynamic problem that is important during the time interval immediately following the application of crack face loading. We demonstrate why the usual boundary conditions lead to a prediction of crack face interpenetration, and then examine how to modify the boundary condition for a semi-infinite crack with a cohesive zone. Numerical simulations illustrate the resulting approach.

  8. Mode I and mixed I/III crack initiation and propagation behavior of V-4Cr-4Ti alloy at 25{degrees}C

    Li, H.X.; Kurtz, R.J.; Jones, R.H. [Pacific Northwest National Lab., Richland, WA (United States)


    The mode I and mixed-mode I/III fracture behavior of the production-scale heat (No. 832665) of V-4Cr-4Ti has been investigated at 25{degrees}C using compact tension (CT) specimens for a mode I crack and modified CT specimens for a mixed-mode I/III crack. The mode III to mode I load ratio was 0.47. Test specimens were vacuum annealed at 1000{degrees}C for 1 h after final machining. Both mode I and mixed-mode I/III specimens were fatigue cracked prior to J-integral testing. It was noticed that the mixed-mode I/III crack angle decreased from an initial 25 degrees to approximately 23 degrees due to crack plane rotation during fatigue cracking. No crack plane rotation occurred in the mode I specimen. The crack initiation and propagation behavior was evaluated by generating J-R curves. Due to the high ductility of this alloy and the limited specimen thickness (6.35 mm), plane strain requirements were not met so valid critical J-integral values were not obtained. However, it was found that the crack initiation and propagation behavior was significantly different between the mode I and the mixed-mode I/III specimens. In the mode I specimen crack initiation did not occur, only extensive crack tip blunting due to plastic deformation. During J-integral testing the mixed-mode crack rotated to an increased crack angle (in contrast to fatigue precracking) by crack blunting. When the crack initiated, the crack angle was about 30 degrees. After crack initiation the crack plane remained at 30 degrees until the test was completed. Mixed-mode crack initiation was difficult, but propagation was easy. The fracture surface of the mixed-mode specimen was characterized by microvoid coalescence.

  9. A boundary integral method for a dynamic, transient mode I crack problem with viscoelastic cohesive zone

    Leise, Tanya L.


    We consider the problem of the dynamic, transient propagation of a semi-infinite, mode I crack in an infinite elastic body with a nonlinear, viscoelastic cohesize zone. Our problem formulation includes boundary conditions that preclude crack face interpenetration, in contrast to the usual mode I boundary conditions that assume all unloaded crack faces are stress-free. The nonlinear viscoelastic cohesive zone behavior is motivated by dynamic fracture in brittle polymers in which crack propagation is preceeded by significant crazing in a thin region surrounding the crack tip. We present a combined analytical/numerical solution method that involves reducing the problem to a Dirichlet-to-Neumann map along the crack face plane, resulting in a differo-integral equation relating the displacement and stress along the crack faces and within the cohesive zone. © 2009 Springer Science+Business Media B.V.

  10. Out-of-plane deviation of a mode I+III crack encountering a tougher obstacle

    Leblond, Jean-Baptiste; Ponson, Laurent


    One possible explanation of out-of-plane deviations of cracks loaded in mode I+III was suggested by Gao and Rice in 1986. These authors noted that small in-plane undulations of the crack front, arising from fluctuations of the fracture toughness, should generate a small local mode-II component, causing the crack to depart from planarity. Their analysis is completed here by explicitly calculating the evolution in time of the out-of-plane deviation of a mode-I+III crack encountering a tougher obstacle. The calculation is based on (i) first-order formulae for the stress intensity factors of a crack slightly perturbed within and out of its plane; and (ii) a "double" propagation criterion combining a Griffith condition on the local energy-release rate and a Goldstein-Salganik condition on the local stress intensity factor of mode II. It is predicted that the crack must evolve toward a stationary state, wherein the orthogonal distance from the average fracture plane to the perturbed crack front is constant outside the obstacle and varies linearly across it. We hope that this theoretical prediction will encourage comparison with experiments, and propose a fracture test involving propagation of a mode-I+III crack through a 3D-printed specimen containing some designed obstacle. xml:lang="fr"

  11. Mode I and mixed mode crack-tip fields in strain gradient plasticity

    Goutianos, Stergios


    Strain gradients develop near the crack-tip of Mode I or mixed mode cracks. A finite strain version of the phenomenological strain gradient plasticity theory of Fleck–Hutchinson (2001) is used here to quantify the effect of the material length scales on the crack-tip stress field for a sharp...... stationary crack under Mode I and mixed mode loading. It is found that for material length scales much smaller than the scale of the deformation gradients, the predictions converge to conventional elastic–plastic solutions. For length scales sufficiently large, the predictions converge to elastic solutions....... Thus, the range of length scales over which a strain gradient plasticity model is necessary is identified. The role of each of the three material length scales, incorporated in the multiple length scale theory, in altering the near-tip stress field is systematically studied in order to quantify...

  12. Stress intensity factors of eccentric cracks in bi-materials plate under mode I loading

    Ismail, A. E. [Faculty of Mechanical and Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia, 86400 Batu Pahat, Johor (Malaysia)


    Bi-material plates were generally used to joint electronic devices or mechanical components requiring dissimilar materials to be attached. During services, mechanical failure can be occurred due to the formation of cracks at the interfacial joint or away from the centre. Generally, linear elastic fracture mechanics approach is used to characterize these cracks based on stress intensity factors (SIF). Based on the literature survey, the SIFs for the central cracks were easily available. However, the SIFs for eccentric cracks were difficult to obtain. Therefore, this paper presented the SIFs for eccentric cracks subjected to mode I tension loading. Three important parameters were used such as relative crack depth, a/L, relative offset distance, b/L and elastic mismatch, E{sub 1}/E{sub 2} or α. It was found that such parameters significantly affected the characteristic of SIFs and it was depend on the location of cracks.

  13. Subcritical crack growth under mode I, II, and III loading for Coconino sandstone

    Ko, Tae Young

    In systems subjected to long-term loading, subcritical crack growth is the principal mechanism causing the time-dependent deformation and failure of rocks. Subcritical crack growth is environmentally-assisted crack growth, which can allow cracks to grow over a long period of time at stresses far smaller than their failure strength and at tectonic strain rates. The characteristics of subcritical crack growth can be described by a relationship between the stress intensity factor and the crack velocity. This study presents the results of studies conducted to validate the constant stress-rate test for determining subcritical crack growth parameters in Coconino sandstone, compared with the conventional testing method, the double torsion test. The results of the constant stress-rate test are in good agreement with the results of double torsion test. More importantly, the stress-rate tests can determine the parameter A with a much smaller standard deviation than the double torsion test. Thus the constant stress-rate test seems to be both a valid and preferred test method for determining the subcritical crack growth parameters in rocks. We investigated statistical aspects of the constant stress-rate test. The effects of the number of tests conducted on the subcritical crack growth parameters were examined and minimum specimen numbers were determined. The mean and standard deviation of the subcritical crack growth parameters were obtained by randomly selecting subsets from the original strength data. In addition, the distribution form of the subcritical crack growth parameters and the relation between the parameter n and A were determined. We extended the constant stress-rate test technique to modes II and III subcritical crack growth in rocks. The experimental results of the modes I, II and III tests show that the values of the subcritical crack growth parameters are similar to each other. The subcritical crack growth parameter n value for Coconino sandstone has the range


    陈少华; 王自强


    The strain gradient effect becomes significant when the size of fracture process zone around a crack tip is comparable to the intrinsic material length l,typically of the order of microns. Using the new strain gradient deformation theory given by Chen and Wang, the asymptotic fields near a crack tip in an elastic-plastic material with strain gradient effects are investigated. It is established that the dominant strain field is irrotational. For mode I plane stress crack tip asymptotic field,the stress asymptotic field and the couple stress asymptotic field can not exist simultaneously. In the stress dominated asymptotic field, the angular distributions of stresses are consistent with the classical plane stress HRR field; In the couple stress dominated asymptotic field, the angular distributions of couple stresses are consistent with that obtained by Huang et al. For mode II plane stress and plane strain crack tip asymptotic fields, only the stress-dominated asymptotic fields exist. The couple stress asymptotic field is less singular than the stress asymptotic fields. The stress asymptotic fields are the same as mode II plane stress and plane strain HRR fields,respectively. The increase in stresses is not observed in strain gradient plasticity for mode I and mode II, because the present theory is based only on the rotational gradient of deformation and the crack tip asymptotic fields are irrotational and dominated by the stretching gradient.

  15. The nonlocal theory solution of a Mode-I crack in functionally graded materials

    LIANG Jun


    The behavior of a Mode-I finite crack in functionally graded materials is investigated using the non-local theory. To make the analysis tractable, it is assumed that the shear modulus varies exponentially with coordinate vertical to the crack. The problem in this paper can be solved through the Fourier transform with the help of two pairs of dual integral equations, in which the unknown variables are jumps of displacements across crack surfaces. To solve dual integral equations, the jumps of displacements across crack surfaces are directly expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularities are present at crack tips. The non-local elastic solutions yield a finite stress at crack tips, thus allowing us to use the maximum stress as a fracture criterion. Numerical examples are provided to show the effects of the crack length, the parameter describing the functionally graded materials, the lattice parameter of materials and the materials constants upon the stress fields near crack tips.

  16. The nonlocal theory solution of a Mode-I crack in functionally graded materials


    The behavior of a Mode-I finite crack in functionally graded materials is investigated using the non-local theory. To make the analysis tractable, it is assumed that the shear modulus varies exponentially with coordinate vertical to the crack. The problem in this paper can be solved through the Fourier transform with the help of two pairs of dual integral equations, in which the unknown variables are jumps of dis- placements across crack surfaces. To solve dual integral equations, the jumps of displacements across crack surfaces are directly expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularities are present at crack tips. The non-local elastic solu- tions yield a finite stress at crack tips, thus allowing us to use the maximum stress as a fracture crite- rion. Numerical examples are provided to show the effects of the crack length, the parameter describ- ing the functionally graded materials, the lattice parameter of materials and the materials constants upon the stress fields near crack tips.

  17. Steady-state crack growth in single crystals under Mode I loading

    Juul, Kristian Jørgensen; Nielsen, Kim Lau; Niordson, Christian Frithiof


    The active plastic zone that surrounds the tip of a sharp crack growing under plane strain Mode I loading conditions at a constant velocity in a single crystal is studied. Both the characteristics of the plastic zone and its effect on the macroscopic toughness is investigated in terms of crack ti...... monotonically increases the crack tip shielding, whereas the opposite behaviour is observed at high velocities. This observation leads to the existence of a characteristic velocity at which the crack tip shielding becomes independent of the rate-sensitivity....... shielding due to plasticity (quantified by employing the Suo, Shih, and Varias set-up). Three single crystals (FCC, BCC, HCP) are modelled in a steady-state elastic visco-plastic framework, with emphasis on the influence of rate-sensitivity and crystal structures. Distinct velocity discontinuities...... that the largest shielding effect develops in HCP crystals, while the lowest shielding exists for FCC crystals. Rate-sensitivity is found to affect the plastic zone size, but the characteristics overall remain similar for each individual crystal structure. An increasing rate-sensitivity at low crack velocities...

  18. FEM solutions for plane stress mode-I and mode-II cracks in strain gradient plasticity

    邱信明; 郭田福; 黄克智


    The strain gradient plasticity theory is used to investigate the crack-tip field in a power law hardening material. Numerical solutions are presented for plane-stress mode I and mode II cracks under small scale yielding conditions. A comparison is made with the existing asymptotic fields. It is found that the size of the dominance zone for the near-tip asymptotic field, recently obtained by Chen et al., is on the order 5% of the intrinsic material length I. Remote from the dominance zone, the computed stress field tends to be the classical HRR field. Within the plastic zone only force-stress dominated solution is found for either mode I or mode II crack.

  19. Basic solution of two parallel Mode-I cracks in functionally graded materials

    LIANG Jun


    The solution of two parallel cracks in functionally graded materials subjected to a tensile stress loading is derived in this paper. To make the analysis tractable, it is assumed that the shear modulus varies exponentially with coordinate parallel to the crack. The problem is formulated through Fourier transform into four pairs of dual integral equations, in which the unknown variables are jumps of displace- ments across crack surfaces. To solve the dual integral equations, the jumps of displacements across crack surfaces are directly expanded as s series of Jacobi polynomials to obtain the shielding effects of the two parallel cracks in functionally graded materials.

  20. Basic solution of two parallel Mode-I cracks in functionally graded materials


    The solution of two parallel cracks in functionally graded materials subjected to a tensile stress loading is derived in this paper. To make the analysis tractable, it is assumed that the shear modulus varies exponentially with coordinate parallel to the crack. The problem is formulated through Fourier transform into four pairs of dual integral equations, in which the unknown variables are jumps of displace-ments across crack surfaces. To solve the dual integral equations, the jumps of displacements across crack surfaces are directly expanded as a series of Jacobi polynomials to obtain the shielding effects of the two parallel cracks in functionally graded materials.

  1. Mode-I-crack compression modeling and numerical simulation for evaluation of in-situ stress around advancing coal workfaces

    LIU Wei-qun; ZHU Li


    The relatively high stress probably leads to generation of a fractured or even instable area around a working coalface. Also, the generated weak area often evolves into an easy-infiltrating field of water/gas to greatly increase probability of accident occurrence. To reveal the distribution of high stress around working faces, we put forward the mode-I-crack compression model. In this model, the goaf following a working face is regarded as a mode-I crack in an infinite plate, and the self-gravity of overlaying strata is transformed into an uniform pressure applied normal to the upper edge of the model crack. Solving this problem is based on the Westergaard complex stress function. For comparison, the software RFPA-2D is also employed to simulate the same mining problem, and furthermore extendedly to calculate the stress interference induced by the simultaneous advances of two different working faces. The results show that, the area close to a working face or the goaf tail has the maximum stress, and the stress is distributed directly proportional to the square root of the advance and inversely proportional to the square root of the distance to the working face. The simultaneous advances of two neighboring working faces in different horizontals can lead to extremely high resultant stress in an interference area.

  2. Mode I Cohesive Law Characterization of Through-Crack Propagation in a Multidirectional Laminate

    Bergan, Andrew C.; Davila, Carlos G.; Leone, Frank A.; Awerbuch, Jonathan; Tan, Tein-Min


    A method is proposed and assessed for the experimental characterization of through-the-thickness crack propagation in multidirectional composite laminates with a cohesive law. The fracture toughness and crack opening displacement are measured and used to determine a cohesive law. Two methods of computing fracture toughness are assessed and compared. While previously proposed cohesive characterizations based on the R-curve exhibit size effects, the proposed approach results in a cohesive law that is a material property. The compact tension specimen configuration is used to propagate damage while load and full-field displacements are recorded. These measurements are used to compute the fracture toughness and crack opening displacement from which the cohesive law is characterized. The experimental results show that a steady-state fracture toughness is not reached. However, the proposed method extrapolates to steady-state and is demonstrated capable of predicting the structural behavior of geometrically-scaled specimens.

  3. Mode I and Mode II Interlaminar Crack Growth Resistances of Ceramic Matrix Composites at Ambient Temperature


    polymer matrix composite , used as comparison, showed R-curve behavior and typically 2-3 and 8 times greater in GI and GII, respectively, than the CMCs. Experimental error analysis concerning the effect of the off-the-center of a crack plane on GI and GII was also

  4. Modified Dugdale cracks and Fictitious cracks

    Nielsen, Lauge Fuglsang


    (displacement) respectively of material considered. The practical applicability of the two models is limited such that predicted strength sigma_CR must be less than sigma_L/3, which corresponds to an assumption that fictitious cracks are much smaller than real crack lengths considered. The reason......A number of theories are presented in the literature on crack mechanics by which the strength of damaged materials can be predicted. Among these are theories based on the well-known Dugdale model of a crack prevented from spreading by self-created constant cohesive flow stressed acting in local...... Dugdale crack is the same as if it has been weakened by the well-known Griffith crack, namely sigma_CR = (EG_CR/phi)^1/2 where E and 1 are Young's modulus and crack half-length respectively, and G_CR is the so-called critical energy release rate. The physical significance of G_CR, however, is different...

  5. Development of fracture facets from a crack loaded in mode I+III: Solution and application of a model 2D problem

    Leblond, Jean-Baptiste; Frelat, Joël


    It is experimentally well-known that a crack loaded in mode I+III propagates through formation of discrete fracture facets inclined at a certain tilt angle on the original crack plane, depending on the ratio of the mode III to mode I initial stress intensity factors. Pollard et al. (1982) have proposed to calculate this angle by considering the tractions on all possible future infinitesimal facets and assuming shear tractions to be zero on that which will actually develop. In this paper we consider the opposite case of well-developed facets; the stress field near the lateral fronts of such facets becomes independent of the initial crack and essentially 2D in a plane perpendicular to the main direction of crack propagation. To determine this stress field, we solve the model 2D problem of an infinite plate containing an infinite periodic array of cracks inclined at some angle on a straight line, and loaded through uniform stresses at infinity. This is done first analytically, for small values of this angle, by combining Muskhelishvili's (1953) formalism and a first-order perturbation procedure. The formulae found for the 2D stress intensity factors are then extended in an approximate way to larger angles by using another reference solution, and finally assessed through comparison with some finite element results. To finally illustrate the possible future application of these formulae to the prediction of the stationary tilt angle, we introduce the tentative assumption that the 2D mode II stress intensity factor is zero on the lateral fronts of the facets. An approximate formula providing the tilt angle as a function of the ratio of the mode III to mode I stress intensity factors of the initial crack is deduced from there. This formula, which slightly depends on the type of loading imposed, predicts somewhat smaller angles than that of Pollard et al. (1982).

  6. 各向异性复合材料周期性I型裂纹尖端应力分析%Analysis of stress for mode I periodic cracks near crack tip of anisotropic composite materials

    谢秀峰; 李俊林; 杨维阳


    对各向异性复合材料板的周期性I型裂纹尖端应力场进行了力学分析.通过求解一类线性偏微分方程的边值问题,引入Westergaard应力函数,采用复变函数方法及待定系数法,给出在无穷远处受对称载荷σ作用下,周期性Ⅰ型裂纹尖端的应力强度因子,推出了各向异性复合材料板周期性Ⅰ型裂纹尖端附近应力场的理论计算公式.%Mode-I stress fields near periodic cracks tip of anisotropic composite materials were analyzed. The boundary value problem of one kind of partial differential equation was solved. By introducing Westergaard' s stress function, using complex function method and approach of undetermined coefficients, the stress intensity factors at the crack tip for mode I periodic cracks were presented under symmetrical loading a. The stress field theoretical computing formulae of mode I periodic cracks near crack tip were obtained.

  7. Some relationships between the peak stresses and the local strain energy density for cracks subjected to mixed-mode (I+II loading

    G. Meneghetti


    Full Text Available In this work, a link between the averaged strain energy density (SED approach and the peak stress method in the case of cracks subjected to mixed mode (I+II loading has been investigated. Some closed-form expressions of the strain energy density, averaged in a volume of radius R0, as function of the Stress Intensity Factors are provided for plane strain conditions under mixed mode I+II loadings, the material being thought of as isotropic and linear elastic. On the basis of the peak stress method (PSM some expressions useful to estimate the mode I and mode II stress intensity factors (SIFs have been recently derived. These relationships take advantage of the elastic peak stresses from FE analyses carried out by using a given mesh pattern where the element size and type are kept constants. The evaluation of the SIFs from a numerical analysis of the local stress field usually requires very refined meshes and then large computational effort. The usefulness of the PSM-based expressions is that (i only the elastic peak stresses numerically evaluated at the crack tip are needed and not a set of stress–distance data; (ii the employed meshes are rather coarse if compared to those necessary for the evaluation of the whole local stress field. By substituting the PSM-based relationships in the closed-form expressions of the averaged SED it appears that the latter can be directly estimated by means of the elastic peak stresses evaluated at the crack tip. Several FE analyses have been carried out on cracked plates subjected to tension loading considering different geometrical combinations, varying the length 2a and the inclination ϕ of the crack (i.e. the mode mixity as well as the size d of the adopted finite elements, with the aim to evaluate the local SED and the elastic peak stress components σpeak and τpeak. In all cases the numerical values of the SED derived from the FE analyses have been compared with those analytically obtained by using the

  8. Modified Dugdale crack models - some easy crack relations

    Nielsen, Lauge Fuglsang


    are assumed to be self created by local materials flow. The strength sigma_CR predictid by the Dugdale model is sigma_CR =(E Gamma_CR/phi1)^½ where E and 1 are Young’s modulus and crack half-length respectively of the material considered. The so-called critical strain energy rate is Gamma_CR = sigma......_Ldelta_CR where sigma_L is strength, and at the same time constant flow stress, of the uncracked material while delta_CR is flow limit (displacement).Obviously predictions by the Dugdale model are most reliable for materials with stress-strain relations where flow can actually be described (or well approximated......) by a constant flow stress (sigma_L). A number of materials, however, do not at all exhibit this kind of flow. Such materials are considered in this paper by Modified Dugdale crack models which apply for any cohesive stress distribution in crack front areas. Formally modified Dugdale crack models exhibit...

  9. From mode I cracking to dilatancy, shear, and compaction banding: Constraints from axisymmetric and poly-axial experiments and numerical models

    Chemenda, A. I.; Jorand, C.; Petit, J.; Nguyen, S.


    Dilatancy bands were recently obtained in conventional axisymmetric extension tests on a synthetic physical rock analogue (granular, frictional, cohesive and dilatant) material GRAM1 at a relatively low mean stress σ within range σd material within the band, which have a complex 3-D structure. At σ σs , the bands become inclined to σ1 , resulting in dilatant shear and then in compactive shear bands that have an irregular structure and geometry at a micro-scale. Pure compaction bands were not obtained (at least not evidenced) in the extension tests, but they were generated in the GRAM1 compression tests as previously in the porous rocks. At lower pressure in the compression tests were obtained compactive shear and dilatant shear bands as well as axial splitting fractures that could be originated as dilatancy bands. We also present results from poly-axial tests conducted with material GRAM2 that have slightly different properties than GRAM1. The parallelepiped GRAM2 samples are first subject to the isotropic stress σ0 and then to the uniaxial unloading under plane-strain conditions. At some stage of this process, the sample loses stability and is affected by regular networks of localization bands/fractures whose spacing depends on the loading conditions. The band type changes with the initial mean stress σ0 in the same way as in the above axisymmetric tests where normally only one band is formed. The angle ψ between the bands and σ1 direction continuously increases with σ0 . At sufficiently low σ0 , ψ = 0, which corresponds to the dilatancy bands. Their borders bear plumose features very similar to those on natural joint surfaces. Different-type tests thus show generally similar change of failure/localization structure with pressure, but under axisymmetric conditions some end-member structures are missing (the compaction bands in the extension tests and the dilatancy bands/mode I fractures in the compression tests). Deformation bifurcation is commonly

  10. Effect of Modified Polymer on Crack Resistance of Mortar


    At present, the basic technical principle in China is to adopt polymers to modifying the properties of mortar so as to improve the crack-resistance of construction structures and to strengthen their water-resisting and climate-resisting properties as well. However, how polymer acts on anti-crack mortar is short of systematic research. Theoretical exposition of polymer mortar is basically explained by Ohama Model, which is cement slaking and polymer coating are carried on together and mutually-cross web structure interweaved with liquid and polymer coating. But anti-crack mortar has its own special characteristics because of fewer polymers mixed in it and its high viscosity. So this paper is to showing how different polymers affect its crack-resistance cannot be reflected from this theory. Vinyl-acetate ethylene (VAC/E) has been selected as representation of polymerization, whose property is modified by compounding it from some inorganic components, such as talc, CaCO3 and so on. And then the mechanics property and shrinkage of anti-crack polymer mortar is tested when different amount of polymers is added as admixture of mortar. The result indicates that, the working performance and mechanics property of the polymer mortar are worse mixed VAC/E only. It basically meets the demands for mechanics strength and working performance when mixed both VAC/E and CaCO3. While it achieves much better mechanical property and working performance than the two former when mixed VAC/E,talc and CaCO3; the result of corresponding scanning electron microscopy (SEM) of sample indicates that the internal result of the polymer mortar, compared with classical Ohama Model, has a particularity that its structure is formed by polymer coating instead of filling up the intervals among cement grains.

  11. Modified boundary layer analysis for a mode III crack problem

    Beom, Hyeon Gyu; Kim, Yu Hwan; Cho, Chong Du; Kim, Chang Boo [Inha University, Incheon (Korea, Republic of)


    A modified boundary layer problem of a semi-infinite crack in an elastic-perfectly plastic material under a Mode III load is analyzed. The analytic solution of elastic fields is derived by using complex function theory. It is found that the size and the shape of the plastic zone near the crack tip depend on the elastic T-stress given on the remote boundary. A method for determining higher order singular solutions of elastic fields is also proposed. In order to determine the higher order singular solutions of the elastic fields, Williams expansion of the solution is used. Higher order terms in the Williams expansion are obtained through simple mathematical manipulation. The coefficients of each term in the Williams expansion are also calculated numerically with the J-based mutual integral

  12. Determination of mode-I cohesive strength for interfaces

    Jørgensen, J. B.; Thouless, M. D.; Sørensen, Bent F.


    The cohesive strength is one of the governing parameters controlling crack deflection at interfaces, but measuring its magnitude is challenging. In this paper, we demonstrate a novel approach to determine the mode-I cohesive strength of an interface by using a 4-point single-edge-notch beam...... in response to this stress, before the main crack starts to grow. Observations using 2D digital-image correlation showed that an ''apparent" strain across the interface initially increases linearly with the applied load, but becomes nonlinear upon the initiation of the interface crack. The cohesive strength...

  13. Determination of mode-I cohesive strength for interfaces

    Jørgensen, J. B.; Thouless, M. D.; Sørensen, Bent F.


    The cohesive strength is one of the governing parameters controlling crack deflection at interfaces, but measuring its magnitude is challenging. In this paper, we demonstrate a novel approach to determine the mode-I cohesive strength of an interface by using a 4-point single-edge-notch beam...... in response to this stress, before the main crack starts to grow. Observations using 2D digital-image correlation showed that an ''apparent" strain across the interface initially increases linearly with the applied load, but becomes nonlinear upon the initiation of the interface crack. The cohesive strength...

  14. A Modified Constant-Stress Coupon for Enhanced Natural Crack Start during Fatigue Testing


    UNCLASSIFIED UNCLASSIFIED A Modified Constant- Stress Coupon for Enhanced Natural Crack Start during Fatigue Testing Witold Waldman, Robert...modified constant- stress coupon for use in fatigue testing . This novel coupon design has a significantly greater surface area along the notch boundary...modified constant- stress coupon for use in fatigue testing . A constant- stress coupon is a novel design that has a significantly greater surface area along

  15. Observations on Mode I ductile tearing in sheet metals

    El-Naaman, Salim Abdallah; Nielsen, Kim Lau


    testing and comparison with published results. A series of crack propagation tests have been carried out, where cracks are driven many plate thicknesses under global Mode I loading. The current study employs both the edge crack specimen (ECS) loaded in combined in-plane bending and extension......, and the double edge notched tension (DENT) specimen loaded in extension. Clear evidence of the alternating slant failure is observed for a normal strength steel and details on the phenomenon are brought out by grinding and polishing cross-sections in successive steps along the crack growth direction. Moreover...... of void growth (thus severe thinning in the process zone), whereas slanting is typical in high strength materials that rapidly nucleate large populations of smaller voids. © 2013 Elsevier Masson SAS. All rights reserved....

  16. Cumene cracking on modified mesoporous material type MCM-41

    Ahmed Belhakem


    Full Text Available The effect of ionic exchange degree of aluminated mesoporous materials H(X-AlMCM-41 materials, the method of its exchange mode and its grains form were investigated for the mesoporous catalytic activity in the cumene (i.e. isopropylbenzene cracking reaction. Benzene, propylene and xylene derivatives are the main products of this reaction. Olefins like butene and pentene appeared as the products of secondary reactions. No saturated hydrocarbons, except traces of butane, nor ethylbenzene and toluene were formed and seemed to be typical products of secondary reactions obtained with HNaY zeolites. Generally the exchanged H(X-AlMCM-41 materials by the substitution of Na+ by NH4+ are more active than those exchanged directly with acid solution (substitution of Na+ by H+ even if both the two methods used exhibit a comparable content of acid sites within catalysts at a low exchange degrees. However, the first method of exchange has exhibited an important acidity for mesoporous materials when the ionic exchange degree was increased up to 90%; it was probably due not only to the percentage of exchanged degree but also to the distribution of acid sites within the materials.

  17. Dependence of mode I and mixed mode I/III fracture toughness on temperature for a ferritic/martensitic stainless steel

    Li, H.; Jones, R.H.; Gelles, D.S. [Pacific Northwest Lab., Richland, WA (United States)] [and others


    The objective is to investigate the dependence of mode I and mixed mode I/III fracture toughness on temperature in the range of {minus}95{degrees}C to 25{degrees}C for a low activation ferritic/martensitic stainless steel (F82-H). Mode I and mixed Mode I/III fracture toughnesses were investigated in the range of {minus}95 to 25{degree}C for a F82-H steel heat-treated in the following way; 1000{degree}C/20 h/air-cooled (AC), 1100{degree}C/7 min/AC, and 700{degree}C/2 h/AC. The results indicate that crack tip plasticity was increased by mixed mode loading, and suggest that at low temperature, mode I fracture toughness is the critical design parameter, but at temperatures above room temperature, expecially concerning fatigure and creep-fatigue crack growth rate, a mixed mode loading may be more harmful than a mode I loading for this steel because a mixed mode loading results in lower fracture toughness and higher crack tip plasticity (or dislocation activity).

  18. Mode I fracture of sheet metal

    Pardoen, T.; Hachez, F.; Marchioni, B.; Blyth, P. H.; Atkins, A. G.


    The perceived wisdom about thin sheet fracture is that (i) the crack propagates under mixed mode I & III giving rise to a slant through-thickness fracture profile and (ii) the fracture toughness remains constant at low thickness and eventually decreases with increasing thickness. In the present study, fracture tests performed on thin DENT plates of various thicknesses made of stainless steel, mild steel, 6082-O and NS4 aluminium alloys, brass, bronze, lead, and zinc systematically exhibit (i) mode I "bath-tub", i.e. "cup & cup", fracture profiles with limited shear lips and significant localized necking (more than 50% thickness reduction), (ii) a fracture toughness that linearly increases with increasing thickness (in the range of 0.5- 5 mm). The different contributions to the work expended during fracture of these materials are separated based on dimensional considerations. The paper emphasises the two parts of the work spent in the fracture process zone: the necking work and the "fracture" work. Experiments show that, as expected, the work of necking per unit area linearly increases with thickness. For a typical thickness of 1 mm, both fracture and necking contributions have the same order of magnitude in most of the metals investigated. A model is developed in order to independently evaluate the work of necking, which successfully predicts the experimental values. Furthermore, it enables the fracture energy to be derived from tests performed with only one specimen thickness. In a second modelling step, the work of fracture is computed using an enhanced void growth model valid in the quasi plane stress regime. The fracture energy varies linearly with the yield stress and void spacing and is a strong function of the hardening exponent and initial void volume fraction. The coupling of the two models allows the relative contributions of necking versus fracture to be quantified with respect to (i) the two length scales involved in this problem, i.e. the void spacing

  19. Evaluation of HAZ liquation cracking susceptibility and HAZ softening behavior in modified 800H

    Lundin, C.D.; Qiao, C.Y.P. (Tennessee Univ., Knoxville, TN (United States). Dept. of Materials Science and Engineering)


    A modified 800H alloy, developed at Oak Ridge National Laboratory (ORNL), is one of the candidate materials designed for high temperature applications. Extensive mechanical and corrosion investigations have been completed and it has been proven that modified 800 has excellent high temperature mechanical and metallurgical behavior. Weldability studies of modified 800H are being carried out at the University of Tennessee, Knoxville. A series of modified 800H alloys and two similar commercial high temperature materials (310Ta and HR3C) were used to conduct this investigation. A preliminary weldability evaluation has been accomplished and the major part of the results (HAZ liquation cracking resistance and HAZ softening behavior in modified 800H) is addressed in this report. The basic conclusion of this investigation is that modified 800H material possesses good resistance to HAZ liquation cracking especially with a grain size control (thermo-mechanical treatment). The information from this study is important to the further modification of the material in order to extend its applications.

  20. Constitutive mixed mode model for cracks in concrete

    Jacobsen, J.S.; Poulsen, P.N.; Olesen, J.F.;


    The scope of the paper is to set up a constitutive mixed mode model for cracks in concrete. The model is formulated at macro level and includes the most important micro scale effects. An associated plasticity model inspired by the modified Cam clay model is established. The hardening parameters...... is determined from the topographic information and the constitutive model is thereby purely mechanically based. Using the actual topographic description the model is validated against experimental results for mixed mode crack openings....... are based on the standard Mode I tensile softening response and the response for Mode I crushing. The roughness of the crack is included through a topographic description of the crack surface. The constitutive behavior is based on the integration of local contributions. The local mixed mode ratio...

  1. Rutting and Fatigue Cracking Resistance of Waste Cooking Oil Modified Trinidad Asphaltic Materials

    Rean Maharaj


    Full Text Available The influence of waste cooking oil (WCO on the performance characteristics of asphaltic materials indigenous to Trinidad, namely, Trinidad Lake Asphalt (TLA, Trinidad Petroleum Bitumen (TPB, and TLA : TPB (50 : 50 blend, was investigated to deduce the applicability of the WCO as a performance enhancer for the base asphalt. The rheological properties of complex modulus (G∗ and phase angle (δ were measured for modified base asphalt blends containing up to 10% WCO. The results of rheology studies demonstrated that the incremental addition of WCO to the three parent binders resulted in incremental decreases in the rutting resistance (decrease in G∗/sinδ values and increases in the fatigue cracking resistance (decrease in G∗sinδ value. The fatigue cracking resistance and rutting resistance for the TLA : TPB (50 : 50 blends were between those of the blends containing pure TLA and TPB. As operating temperature increased, an increase in the resistance to fatigue cracking and a decrease in the rutting resistance were observed for all of the WCO modified asphaltic blends. This study demonstrated the capability to create customized asphalt-WCO blends to suit special applications and highlights the potential for WCO to be used as an environmentally attractive option for improving the use of Trinidad asphaltic materials.

  2. Effects of Forming Process on Composite mode I Interlaminar Fracture Toughness

    CHEN Xingyi


    Full Text Available In order to compare and analyse the effect of two different kinds of forming process on composite mode I interlaminar fracture toughness, the DCB specimens were tested by using hypothesis inspeetion method.A finite element model was also used to simulate the crack propagation process.The results demonstrate that the average of mode I interlaminar fracture toughness from silicon rubber flexible mold forming is a bit higher than that from metal rigid mold forming.Howevers the variance of mode I interlaminar fracture toughness from the two groups shows no significant difference.The crack propagation process of the two forming process is similar. The established finite element model, which is identical to the test results, can predict the process of the crack expansion effectively.

  3. Finite element modeling and experimental studies on mixed mode-I/III fracture specimens

    M. Bozkurt


    Full Text Available In this study, finite element modeling and experimental studies on a mode-I/III specimen similar to the compact tension specimen are presented. By using bolts, the specimen is attached to two loading apparatus that allow different levels of mode-I/III loading by changing the loading holes. Specimens having two different thicknesses are analyzed and tested. Modeling, meshing and the solution of the problem involving the whole assembly, i.e., loading devices, bolts and the specimen, with contact mechanics are performed using ANSYSTM. Then, the mode-I/III specimen is analyzed separately using a submodeling approach, in which threedimensional enriched finite elements are used in FRAC3D solver to calculate the resulting stress intensity factors along the crack front. In all of the analyses, it is clearly shown that although the loading is in the mode-I and III directions, mode-II stress intensity factors coupled with mode-III are also generated due to rotational relative deformations of crack surfaces. The results show that the mode-II stress intensity factors change sign along the crack front and their magnitudes are close to the mode-III stress intensity factors. It is also seen that magnitudes of the mode-III stress intensity factors do not vary much along the crack front. Fracture experiments also performed and, using the stress intensity factors from the analyses and crack paths and surfaces are shown.

  4. Effects of geometry and temperature on mode I interlaminar fracture of filled polypropylene–elastomer nanocomposite

    Bishnu P Panda; Smita Mohanty; S K Nayak


    In this study, organically modified Na-MMT clay was used for the preparation of blend nanocomposites containing different ratios of polypropylene (PP) and ethylene propylene diene monomer (EPDM) elastomer in a twin screw extruder. Maleic-grafted PP (MAPP) was used as compatibilizer for making PP hydrophilic. Surface modification of Na–MMT was made by using amino propyl trimethoxy silane (APS) and trimethyl amine as coupling agent with surface grafting catalyst, respectively. A fracture mechanics approach has been adopted by mode I test and the effects of specimen geometry have been investigated. Increase in interlaminar fracture energy value, c, was observed as the crack propagated through the composite, i.e. a rising ‘R-curve’ for both blend and nanocomposites. Deep fracture studies were carried out at different temperatures (–60 °C to 60 °C) using Izod impact and SENT tests. Fracture energy, fracture stress and brittle ductile transition were determined from crack initiation and propagation process, which showed significant improvement in impact and fracture energy at positive temperature. The wide-angle X-ray diffraction (XRD) patterns showed increased -spacing of clay layers, indicating enhanced compatibility between PP and clay with the addition of maleated polypropylene (MAPP). Morphology/impact property relationships and an explanation of the toughening mechanisms were made by comparing the impact properties with scanning electron micrographs (SEMs) of fracture surfaces. The transmission electron microscopy (TEM) photomicrographs illustrated the intercalated and partially exfoliated structures of the hybrids with clay, MAPP and elastomer.

  5. Effect of Organophilic Montmorillonite on Ther-mal-oxidative Aging Behavior of SBS Modified Bitumen Crack Filling Material

    YU Jianying; WANG Xilin; KUANG Dongliang; ZHANG Henglong


    Styrene-butadiene-styrene(SBS)modified bitumen crack filling material with or-ganophilic montmorillonite(OCFM)was prepared by melt blending.X-ray diffraction analysis shows that the interlayer spacing of organophilic montmorillonite(OMMT)in OCFM is widened and an exfoliated structure may be formed.Thermal-oxidative aging behavior of OCFM and SBS modified bitumen crack filling material(SCFM)was investigated.The experimental results indicate that the rate of thermal-oxidative aging of OCFM is much slower than that of SCFM,which can be attributed to barrier of exfoliated structure of OCFM to oxygen.

  6. Catalytic cracking of 1-butene to propylene by Ag modified HZSM-5

    Rongrong Zhang; Zhengbao Wang


    Silver modified HZSM-5 (AgHZ) zeolite catalysts were prepared by ion exchange method and their catalytic properties in the 1-butene cracking reaction were measured. The catalysts were characterized by infrared spec-troscopy with pyridine adsorption (Py-IR), N2 adsorption and X-ray diffraction (XRD). The effects of Ag loading and steaming treatment on catalytic performances were studied. It is found that the activity of HZSM-5 (HZ) cat-alyst significantly decreases with the steaming time, whereas AgHZ catalysts show stable activity in the steaming time of 24–48 h and their activities increase with the Ag loading. When the steaming time is 24–48 h, the yield of propylene over HZ catalyst significantly decreases, whereas it is stable over AgHZ catalysts. The AgHZ catalysts with Ag loadings of 0.28%–0.43%(by mass) show similar propylene yields (~30%), which are higher than that over the AgHZ catalyst with a Ag loading of 0.55%(by mass). These results indicate that the steam-treated AgHZ catalysts with optimum Ag loadings have higher yield of propylene and are more stable than the steam-treated HZ catalyst. The regeneration stability measurement in butene cracking also shows that the AgHZ catalyst steam-treated under a suitable condition has better stability than the HZ catalyst.

  7. Determining mode I cohesive law of Pinus pinaster by coupling double cantilever beam test with digital image correlation

    J. Xavier


    Full Text Available The direct identification of the cohesive law in pure mode I of Pinus pinaster is addressed. The approach couples the double cantilever beam (DCB test with digital image correlation (DIC. Wooden beam specimens loaded in the radial-longitudinal (RL fracture propagation system are used. The strain energy release rate in mode I ( is uniquely determined from the load-displacement ( curve by means of the compliance-based beam method (CBBM. This method relies on the concept of equivalent elastic crack length ( and therefore does not require the monitoring of crack propagation during test. The crack tip opening displacement in mode I is determined from the displacement field at the initial crack tip. The cohesive law in mode I is then identified by numerical differentiation of the relationship. Moreover, the proposed procedure is validated by finite element analyses including cohesive zone modelling. It is concluded that the proposed data reduction scheme is adequate for assessing the cohesive law in pure mode I of P. pinaster

  8. Development of Modified 304 Stainless Steel Resistant to Stress Corrosion Cracking in Chloride Environment


    This was a feasibility study for a modified 304 steel resistant to stress corrosion cracking (SCC) in aqueous environment containing chloride. SCC tests were conducted potentiostaticaly with spot-welded specimens, which had both crevice and residual stress, mainly in 3 % NaCl solution at various temperatures to determine the critical temperature for SCC at and below which the steel would not suffer from SCC. The effects of individual alloying element of silicon, manganese and copper on SCC of 18Cr-14Ni steels which phosphor content is 0.002 % and molybdenum content is 0.01 % were examined. Addition of 1 or 2 % of copper has beneficial effect on resistance to SCC, while increasing silicon or manganese content has no significant effect. Critical temperature of the steel with 0.002 % of phosphor and 2 % of copper is 150 ℃, which is markedly higher than 50 ℃ of 304L steel. However, the beneficial effect of copper is reduced with increasing phosphor content. From practical viewpoint, the modified steel with good SCC resistance should have 0.01 %-0.015 % of phosphor and 0.3 % or more of molybdenum, because it is very difficult to reduce phosphor content below 0.008 % industrially and such molybdenum content is inevitably introduced through cost-saving melting process using return steel. Aluminium is to be added as another alloying element and 3 % of aluminium combined with 2 % of copper has been found to negate the deleterious effects of increased phosphor and molybdenum content. As a candidate steel at this stage, 14Cr-16Ni-0.013P-2Cu-1Al-(0.3-1)Mo steel has critical temperature of 110 ℃.

  9. Performance of various modified binders in road trials and under simulated crack movement in the laboratory

    Rust, FC


    Full Text Available crack movement from a knowledge of block sizes and structural parameters such as basin of deflection and an example of this is shown. It is also shown that these models can be used to predict the decrease in crack movement due to the overlaying of a...


    Józef DREWNIAK


    Full Text Available Versatile hypotheses of fatigue damage accumulation are utilized in order to determine the fatigue life of particular mechanical elements. Such an approach to an analysis of fatigue processes is recognized as being phenomenological. In the present paper, modifications to the Paris and Foreman laws of fracture mechanics have been proposed. The goal of these modifications is an explicit formulation of crack propagation velocity as a function of crack length. Additionally, the process of crack growth was simulated according to the Palmgren-Miner and Pugno-Ciavarella-Cornetti-Carpinteri fatigue hypotheses. The results of simulation were verified based upon test stand experiments.

  11. Mode I Critical Stress Intensity Factor of Medium - Density Fiberboard Obtained by Single-Edge - Notched Bending Test

    Hiroshi Yoshihara


    Full Text Available The Mode I critical stress intensity factor (KIc obtained by single-edge-notched bending (SENB tests of medium-density fiberboard (MDF was experimentally analyzed. In the SENB test, the critical load for crack propagation (Pc was determined from the relationship between load/loading-line displacement and load/crack opening displacement (COD. A double cantilever beam (DCB test was also conducted and the results were compared with those of SENB tests. The value of Mode I critical stress intensity factor was obtained by introducing an additional crack length, when the crack length ranged from 0.5 to 0.7 times the depth of the specimen. This range coincided well with that used to derive the appropriate KIc value in the single-edge-notched tension (SENT test, which was conducted using the specimens with a similar confi guration cut from the MDF panel used in this study.

  12. Rock Fracture Toughness Study Under Mixed Mode I/III Loading

    Aliha, M. R. M.; Bahmani, A.


    Fracture growth in underground rock structures occurs under complex stress states, which typically include the in- and out-of-plane sliding deformation of jointed rock masses before catastrophic failure. However, the lack of a comprehensive theoretical and experimental fracture toughness study for rocks under contributions of out-of plane deformations (i.e. mode III) is one of the shortcomings of this field. Therefore, in this research the mixed mode I/III fracture toughness of a typical rock material is investigated experimentally by means of a novel cracked disc specimen subjected to bend loading. It was shown that the specimen can provide full combinations of modes I and III and consequently a complete set of mixed mode I/III fracture toughness data were determined for the tested marble rock. By moving from pure mode I towards pure mode III, fracture load was increased; however, the corresponding fracture toughness value became smaller. The obtained experimental fracture toughness results were finally predicted using theoretical and empirical fracture models.

  13. Studies on effect of pre-crack length variation on Inter-laminar fracture toughness of a Glass Epoxy laminated composite

    Huddhar, Arun; Desai, Abilash; Sharanaprabhu, C. M.; Kudari, Shashidhar K.; Shivakumar Gouda, P. S.


    Laminates of fiber reinforced polymer composites are good in in-plane properties and inherently weak in through thickness direction. To address this through thickness properties, the inter-laminar fracture toughness (GIc and GIIc) of a unidirectional (UD) Glass epoxy composite laminates were subjected to Mode-I and Mode-II loadings. Experiments were conducted using Double cantilever beam (DCB) and End notch flexure (ENF) specimens with varying pre-crack lengths. Mode I energy release rate (GIc) were also evaluated with modified beam and modified compliance theories. The experimental results reveal that, GIc fracture toughness increases with increasing in pre-crack length, where as in GIIc the effect of increase in pre-crack length exhibits reduced fracture toughness.

  14. Application of modified-alginate encapsulated carbonate producing bacteria in concrete: a promising strategy for crack self-healing

    Jianyun eWang


    Full Text Available Self-healing concrete holds promising benefits to reduce the cost for concrete maintenance and repair as cracks are autonomously repaired without any human intervention. In this study, the application of a carbonate precipitating bacterium Bacillus sphaericus was explored. Regarding the harsh condition in concrete, B. sphaericus spores were first encapsulated into a modified-alginate based hydrogel (AM-H which was proven to have a good compatibility with the bacteria and concrete regarding the influence on bacterial viability and concrete strength. Experimental results show that the spores were still viable after encapsulation. Encapsulated spores can precipitate a large amount of CaCO3 in/on the hydrogel matrix (around 70% by weight. Encapsulated B. sphaericus spores were added into mortar specimens and bacterial in-situ activity was demonstrated by the oxygen consumption on the mimicked crack surface. Specimens with free spores added showed no oxygen consumption. This indicates the efficient protection of the hydrogel for spores in concrete. To conclude, the AM-H encapsulated carbonate precipitating bacteria have great potential to be used for crack self-healing in concrete applications.

  15. Application of modified-alginate encapsulated carbonate producing bacteria in concrete: a promising strategy for crack self-healing.

    Wang, Jianyun; Mignon, Arn; Snoeck, Didier; Wiktor, Virginie; Van Vliergerghe, Sandra; Boon, Nico; De Belie, Nele


    Self-healing concrete holds promising benefits to reduce the cost for concrete maintenance and repair as cracks are autonomously repaired without any human intervention. In this study, the application of a carbonate precipitating bacterium Bacillus sphaericus was explored. Regarding the harsh condition in concrete, B. sphaericus spores were first encapsulated into a modified-alginate based hydrogel (AM-H) which was proven to have a good compatibility with the bacteria and concrete regarding the influence on bacterial viability and concrete strength. Experimental results show that the spores were still viable after encapsulation. Encapsulated spores can precipitate a large amount of CaCO3 in/on the hydrogel matrix (around 70% by weight). Encapsulated B. sphaericus spores were added into mortar specimens and bacterial in situ activity was demonstrated by the oxygen consumption on the mimicked crack surface. While specimens with free spores added showed no oxygen consumption. This indicates the efficient protection of the hydrogel for spores in concrete. To conclude, the AM-H encapsulated carbonate precipitating bacteria have great potential to be used for crack self-healing in concrete applications.

  16. Motion compensated image processing and optimal parameters for egg crack detection using modified pressure

    Shell eggs with microcracks are often undetected during egg grading processes. In the past, a modified pressure imaging system was developed to detect eggs with microcracks without adversely affecting the quality of normal intact eggs. The basic idea of the modified pressure imaging system was to ap...

  17. An Effective Fem-Based Approach for Discrete 3D Crack Growth

    Nielsen, Morten Eggert; Lambertsen, Søren Heide; Pedersen, Erik B.


    A new geometric approach for discrete crack growth modeling is proposed and implemented in a commercial FEM software. The basic idea is to model the crack growth by removing volumes of material as the crack front advances. Thereby, adaptive meshing techniques, found in commercial software, is well......-suited for relatively fast and reasonable meshing of the updated geometry. Influence on structural stiffness is negligible, as the amount of removed material is kept insignificant. The approach is automatized in ANSYS APDL and demonstrated by means of energy-based mixed mode stress intensity factors and the crack...... growth direction criterion by Richard. The applicability of the implemented approach is validated against a previously published experimental result, which tests a mixed mode I + III fatigue loading of a modified CT specimen. The proposed approach may be used as a computational framework for modeling...


    XUYou-hao; ZHANGJiu-shun; LONGJun; HEMing-yuan; XUhui


    A concept of two different reaction zones was proposed based on the FCC reaction mechanism.The concept was used to design a novel reactor with corresponding operation measures.Experiments were conducted on the newly designed pilot-plant riser reactor.In comparison with the conventional FCC at relatively equivalent conversion,the pilot-plant test results showed that the olefin content in the cracked naphtha dropped by 12.4% ,and both cintents of iso-paraffin and aromatic increased by 6%,and its MON increased by 1.3 units while maintaining the RON of the naphtha unchanged,and its sulfur content reduced by 15% with a significant extension of its induction period for Shengli VGO+VR.The run test results of commercial trial were conformable with the results of pilot -plant test.

  19. Equivalent elastic compliance tensor for rock mass with multiple persistent joint sets:Exact derivation via modified crack tensor

    崔洁; 江权; 冯夏庭; 李邵军; 高红; 李帅军


    Discontinuities constitute an integral part of rock mass and inherently affect its anisotropic deformation behavior. This work focuses on the equivalent elastic deformation of rock mass with multiple persistent joint sets. A new method based on the space geometric and mechanical properties of the modified crack tensor is proposed, providing an analytical solution for the equivalent elastic compliance tensor of rock mass. A series of experiments validate the capability of the compliance tensor to accurately represent the deformation of rock mass with multiple persistent joint sets, based on conditions set by the basic hypothesis. The spatially varying rules of the equivalent elastic parameters of rock mass with a single joint set are analyzed to reveal the universal law of the stratified rock mass.

  20. Microbranching in mode-I fracture in a randomly perturbed lattice

    Heizler, Shay I.; Kessler, David A.; Elbaz, Yonatan S.


    We study mode-I fracture in lattices using atomistic simulations with randomly distributed bond lengths. By using a small parameter that measures the variation of the bond length between the atoms in perfect lattices and using a three-body force law, simulations reproduce the qualitative behavior of the beyond-steady-state cracks in the high-velocity regime, including reasonable microbranching. In particular, the effect of the lattice structure on the crack appears minimal, even though in terms of the physical properties such as the structure factor g(r) and the radial or angular distributions, these lattices share the physical properties of perfect lattices rather than those of an amorphous material (e.g., the continuous random network model). A clear transition can be seen between steady-state cracks, where a single crack propagates in the midline of the sample, and the regime of unstable cracks, where microbranches start to appear near the main crack, in line with previous experimental results. This is seen in both a honeycomb lattice and a fully hexagonal lattice. This model reproduces the main physical features of propagating cracks in brittle materials, including the total length of microbranches as a function of driving displacement and the increasing amplitude of oscillations of the electrical resistance. In addition, preliminary indications of power-law behavior of the microbranch shapes can be seen, potentially reproducing one of the most intriguing experimental results of brittle fracture. There was found to exist a critical degree of disorder, i.e., a sharp threshold between the cleaving behavior characterizing perfect lattices and the microbranching behavior that characterizes amorphous materials.

  1. Evaluation of six modified binders for retardation of crack reflection through laboratory studies and field work.

    Rust, FC


    Full Text Available the road networks are ageing (and available funds are often decreasing) it is becoming increasingly important to apply successful and cost-effective rehabilitative measures. Even though materials such as bitumen-rubbers, geofabrics and polymer-modified...

  2. Mode Ⅰ Plane Crack Interacting with an Interfacial Crack Along a Circular Inhomogeneity

    WANG Rui; MA Jian-jun; LIU Zheng-guang


    The elastic interaction of the mode Ⅰ plane crack with an interfacial crack along a circular inhomogeneity is dealt with. The dislocation density and the stress intensity factors (SIFs) of the mode I plane crack are obtained numerically. A new kind of dislocation equilibrium equation about the plane crack is applied. The influence of some material parameters on the dislocation density and SIFs are analyzed.

  3. Double noding technique for mixed mode crack propagation studies

    Liaw, B. M.; Kobayashi, A. S.; Emergy, A. F.


    A simple dynamic finite element algorithm for analyzing a propagating mixed mode crack tip is presented. A double noding technique, which can be easily incorporated into existing dynamic finite element codes, is used together with a corrected J integral to extract modes I and II dynamic stress intensity factors of a propagating crack. The utility of the procedure is demonstrated by analyzing test problems involving a mode I central crack propagating in a plate subjected to uniaxial tension, a mixed mode I and II stationary, slanted central crack in a plate subjected to uniaxial impact loading, and a mixed mode I and II extending, slanted single edge crack in a plate subjected to uniaxial tension.

  4. Analysis of Mixed Mode I/II/III Fracture in Foam Core Sandwich Structures Using Imposed Displacement Split Cantilever Beams

    Rizov V.


    Full Text Available Static fracture in foam core sandwich structures under mixed mode I/II/III loading conditions was studied theoretically. In order to generate such loading conditions, a thread guide was used to impose in- plane displacements of the lower crack arm of a sandwich Split Cantilever Beam (SCB. The upper crack arm was loaded by a transverse force. A three-dimensional finite element model of the imposed displacement sandwich SCB configuration was developed. The fracture was studied applying the concepts of linear-elastic fracture mechanics. The strain energy release rate mode components distribution along the crack front was analyzed using the virtual crack closure technique. The influence of the imposed displacement magnitude and the crack length on the fracture was evaluated. The effect of the sandwich core material on the mixed-mode I/II/III fracture was studied. For this purpose, finite element simulations were carried-out assuming that the core is made by different rigid cellular foams. It was found that the strain energy release rate decreases when the foam density increases.

  5. Study of matrix micro-cracking in nano clay and acrylic tri-block-copolymer modified epoxy/basalt fiber-reinforced pressure-retaining structures


    Full Text Available In fiber-reinforced polymer pressure-retaining structures, such as pipes and vessels, micro-level failure commonly causes fluid permeation due to matrix cracking. This study explores the effect of nano-reinforcements on matrix cracking in filament-wound basalt fiber/epoxy composite structures. The microstructure and mechanical properties of bulk epoxy nanocomposites and hybrid fiber-reinforced composite pipes modified with acrylic tri-block-copolymer and organophilic layered silicate clay were investigated. In cured epoxy, the tri-block-copolymer phase separated into disordered spherical micelle inclusions; an exfoliated and intercalated structure was observed for the nano-clay. Block-copolymer addition significantly enhanced epoxy fracture toughness by a mechanism of particle cavitation and matrix shear yielding, whereas toughness remained unchanged in nano-clay filled nanocomposites due to the occurrence of lower energy resistance phenomena such as crack deflection and branching.Tensile stiffness increased with nano-clay content, while it decreased slightly for block-copolymer modified epoxy. Composite pipes modified with either the organic and inorganic nanoparticles exhibited moderate improvements in leakage failure strain (i.e. matrix cracking strain; however, reductions in functional and structural failure strength were observed.

  6. The effect of mixed mode I/II on the fracture toughness and fracture behavior of nano-structured metal matrix composites

    Hassan, Hala A., E-mail: [Dept. of Design and Prod. Eng., Faculty of Eng., Ain Shams University, Cairo (Egypt); Dept. of Mat. Sci. and Eng., Case Western Reserve University, Cleveland, OH (United States); El-Shabasy, Adel B. [Dept. of Design and Prod. Eng., Faculty of Eng., Ain Shams University, Cairo (Egypt); Dept. of Mat. Sci. and Eng., Case Western Reserve University, Cleveland, OH (United States); Lewandowski, John J. [Dept. of Mat. Sci. and Eng., Case Western Reserve University, Cleveland, OH (United States)


    A nano-structured Al{sub 89}Gd{sub 7}Ni{sub 3}Fe{sub 1} composite alloy was made from extruding its atomized amorphous powder at different extrusion ratios (ER). The effects of changing the notch radius from fatigue pre-crack to 100 {mu}m on mode I fracture toughness were studied at different test temperatures (e.g., 298 K and 498 K). The effects of mixed mode (I/II) loading using different offset ratios were also studied at these temperatures. Increasing the test temperature showed a significant effect on the fracture toughness for mode I and mixed mode I/II conditions. Fracture surfaces were examined to reveal the nature of failure of such nano-structured Al composite materials at these loading conditions.

  7. Comparison of creep crack growth rates on the base and welded metals of modified 9Cr-1Mo steel

    Kim, Woo Gon; Yun, Song Nam; Kim, Yong Wan; Kim, Sung Ho [KAERI, Daejeon (Korea, Republic of); Park, Jae Young; Kim, Seon Jin [Pukyong National Univ., Busan (Korea, Republic of)


    This paper is to compare Creep Crack Growth Rates (CCGR) on the Base Metal (BM) and Welded Metal (WM) of modified 9Cr-1Mo steel for Gen-IV reactors. Welded specimens were prepared by Shielded Metal Arc Weld (SMAW) method. To obtain material properties for the BM and welded metal, a series of creep and tensile tests was conducted at 600 .deg. C, and CCG tests was also performed using 1/2'' compact tension specimens under different applied loads at 600 .deg. C. Their CCGR behaviors were analyzed by using the empirical equation of the da/dt vs. C{sup *} parameter and compared, respectively. It appeared that, for a given value of C{sup *}, the rate of creep propagation was about 2.0 times faster than in the WM than the BM. This reason is that a creep rate in the WM was largely attributed when compared with that in the BM. From this result, it can be utilized for assessing the rate of creep propagation on the BM and WM of the G91 steel.

  8. Investigation of mixed mode - I/II fracture problems - Part 1: computational and experimental analyses

    O. Demir


    Full Text Available In this study, to investigate and understand the nature of fracture behavior properly under in-plane mixed mode (Mode-I/II loading, three-dimensional fracture analyses and experiments of compact tension shear (CTS specimen are performed under different mixed mode loading conditions. Al 7075-T651 aluminum machined from rolled plates in the L-T rolling direction (crack plane is perpendicular to the rolling direction is used in this study. Results from finite element analyses and fracture loads, crack deflection angles obtained from the experiments are presented. To simulate the real conditions in the experiments, contacts are defined between the contact surfaces of the loading devices, specimen and loading pins. Modeling, meshing and the solution of the problem involving the whole assembly, i.e., loading devices, pins and the specimen, with contact mechanics are performed using ANSYSTM. Then, CTS specimen is analyzed separately using a submodeling approach, in which three-dimensional enriched finite elements are used in FRAC3D solver to calculate the resulting stress intensity factors along the crack front. Having performed the detailed computational and experimental studies on the CTS specimen, a new specimen type together with its loading device is also proposed that has smaller dimensions compared to the regular CTS specimen. Experimental results for the new specimen are also presented.

  9. Mode-I fracture and durability of FRP-concrete bonded interfaces

    Qiao Pizhong


    Full Text Available In this study, a work-of-fracture method using a three-point bend beam (3PBB specimen, which is commonly used to determine the fracture energy of concrete, was adapted to evaluate the mode-I fracture and durability of fiber-reinforced polymer (FRP composite-concrete bonded interfaces. Interface fracture properties were evaluated with established data reduction procedures. The proposed test method is primarily for use in evaluating the effects of freeze-thaw (F-T and wet-dry (W-D cycles that are the accelerated aging protocols on the mode-I fracture of carbon FRP-concrete bonded interfaces. The results of the mode-I fracture tests of F-T and W-D cycle-conditioned specimens show that both the critical load and fracture energy decrease as the number of cycles increases, and their degradation pattern has a nearly linear relationship with the number of cycles. However, compared with the effect of the F-T cycles, the critical load and fracture energy degrade at a slower rate with W-D cycles, which suggests that F-T cyclic conditioning causes more deterioration of carbon fiber-reinforced polymer (CFRP-concrete bonded interface. After 50 and 100 conditioning cycles, scaling of concrete was observed in all the specimens subjected to F-T cycles, but not in those subjected to W-D cycles. The examination of interface fracture surfaces along the bonded interfaces with varying numbers of F-T and W-D conditioning cycles shows that (1 cohesive failure of CFRP composites is not observed in all fractured surfaces; (2 for the control specimens that have not been exposed to any conditioning cycles, the majority of interface failure is a result of cohesive fracture of concrete (peeling of concrete from the concrete substrate, which means that the cracks mostly propagate within the concrete; and (3 as the number of F-T or W-D conditioning cycles increases, adhesive failure along the interface begins to emerge and gradually increases. It is thus concluded that the

  10. Effect of fracture surface roughness on shear crack growth

    Gross, T.S.; Watt, D.W. (New Hampshire Univ., Durham, NH (United States). Dept. of Mechanical Engineering); Mendelsohn, D.A. (Ohio State Univ., Columbus, OH (United States). Dept. of Engineering Mechanics)


    A model of fracture surface interference for Mode I fatigue crack profiles was developed and evaluated. Force required to open the crack faces is estimated from point contact expressions for Mode I stress intensity factor. Force transfer across contacting asperities is estimated and used to calculate Mode II resistance stress intensity factor (applied factor is sum of effective and resistance factors). Electro-optic holographic interferometry was used to measure 3-D displacement field around a Mode I fatigue pre-crack in Al loaded in Mode II shear. Induced Mode I crack face displacements were greater than Mode II displacements. Plane stress shear lip caused displacement normal to surface as the crack faces are displaced. Algorithms are being developed to track the displacements associated with the original coordinate system in the camera. A 2-D boundary element method code for mixed mode I and II loading of a rough crack (sawtooth asperity model) has been completed. Addition of small-scale crack tip yielding and a wear model are completed and underway, respectively.

  11. Crack propagation in fracture mechanical graded structures

    B. Schramm


    Full Text Available The focus of manufacturing is more and more on innovative and application-oriented products considering lightweight construction. Hence, especially functional graded materials come to the fore. Due to the application-matched functional material gradation different local demands such as absorbability, abrasion and fatigue of structures are met. However, the material gradation can also have a remarkable influence on the crack propagation behavior. Therefore, this paper examines how the crack propagation behavior changes when a crack grows through regions which are characterized by different fracture mechanical material properties (e.g. different threshold values KI,th, different fracture toughness KIC. In particular, the emphasis of this paper is on the beginning of stable crack propagation, the crack velocity, the crack propagation direction as well as on the occurrence of unstable crack growth under static as well as cyclic loading. In this context, the developed TSSR-concept is presented which allows the prediction of crack propagation in fracture mechanical graded structures considering the loading situation (Mode I, Mode II and plane Mixed Mode and the material gradation. In addition, results of experimental investigations for a mode I loading situation and numerical simulations of crack growth in such graded structures confirm the theoretical findings and clarify the influence of the material gradation on the crack propagation behavior.

  12. Mixed Mode I and II Fully Plastic Crack Growth from Simulated Weld Defects.


    steel 281 348 105 61.1 hot rolled 0.29% C max, 0.60-0.90% Mn HY80 steel 587 692 175 69.9 0.18% C, 2-3.25% Ni, 0.10-0.40...8217S MN/rn Alloy *1018 steel 796 0.05152 0.10 cold finished 1018 steel 818 0.01718 0.23 normalized A36 steel 697 0.02628 0.24 hot rolled * HY80 steel 1107...0.00702 0.12 *HY100 steel 1180 0.00488 0.10 5088-Hlll 589 0.00554 0.19 - aluminum 47 TABLE 3 - TEST RESULTS (Ligament 10=2.54 mm) Alloy 1018 CF HY80

  13. Comparison of Intralaminar and Interlaminar Mode-I Fracture Toughness of Unidirectional IM7/8552 Graphite/Epoxy Composite

    Czabaj, Michael W.; Ratcliffe, James


    The intralaminar and interlaminar mode-I fracture-toughness of a unidirectional IM7/8552 graphite/epoxy composite were measured using compact tension (CT) and double cantilever beam (DCB) test specimens, respectively. Two starter crack geometries were considered for both the CT and DCB specimen configurations. In the first case, starter cracks were produced by 12.5 micron thick, Teflon film inserts. In the second case, considerably sharper starter cracks were produced by fatigue precracking. For each specimen configuration, use of the Teflon film starter cracks resulted in initially unstable crack growth and artificially high initiation fracture-toughness values. Conversely, specimens with fatigue precracks exhibited stable growth onset and lower initiation fracture toughness. For CT and DCB specimens with fatigue precracks, the intralaminar and interlaminar initiation fracture toughnesses were approximately equal. However, during propagation, the CT specimens exhibited more extensive fiber bridging, and rapidly increasing R-curve behavior as compared to the DCB specimens. Observations of initiation and propagation of intralaminar and interlaminar fracture, and the measurements of fracture toughness, were supported by fractographic analysis using scanning electron microscopy.

  14. Fracture toughness in Mode I (GIC) for ductile adhesives

    Gálvez, P.; Carbas, RJC; Campilho, RDSG; Abenojar, J.; Martínez, MA; Silva LFM, da


    Works carried out in this publication belong to a project that seeks the replacement of welded joints by adhesive joints at stress concentration nodes in bus structures. Fracture toughness in Mode I (GIC) has been measured for two different ductile adhesives, SikaTack Drive and SikaForce 7720. SikaTack Drive is a single-component polyurethane adhesive with high viscoelasticity (more than 100%), whose main use is the car-glass joining and SikaForce 7720 is double-component structural polyurethane adhesive. Experimental works have been carried out from the test called Double Cantilever Beam (DCB), using two steel beams as adherents and an adhesive thickness according to the problem posed in the Project, of 2 and 3 mm for SikaForce 7720 and SikaTack Drive, respectively. Three different methods have been used for measuring the fracture toughness in mode I (GIC) from the values obtained in the experimental DCB procedure for each adhesive: Corrected Beam Theory (CBT), Compliance Calibration Method (CCM) and Compliance Based Beam Method (CBBM). Four DCB specimens have been tested for each adhesive. Dispersion of each GIC calculation method for each adhesive has been studied. Likewise variations between the three different methods have been also studied for each adhesive.

  15. Asymptotic analysis of mode Ⅰ propagating crack-tip field in a creeping material

    WANG Zhen-qing; ZHAO Qi-cheng; LIANG Wen-yan; FU Zhang-jian


    Adopting an elastic-viscoplastic, the asymptotic problem of mode I propagating crack-tip field is investigated. Various asymptotic solutions resulting from the analysis of crack growing programs are presented. The analysis results show that the quasi-statically growing crack solutions are the special case of the dynamic propagating solutions. Therefore these two asymptotic solutions can be unified.

  16. Thinning procedures and strains in the zones near crack tips of thin foils

    李红旗; 陈奇志; 褚武扬


    Thinning procedures were observed by TEM in 310 stainless steel and pure aluminum. Foils thinned through shearing of mode Ⅲ crack or through tearing of mode I crack. Using micro-beam electron diffraction, the strains in the areas right ahead of crack tips of pure aluminum and TiAI alloy were measured to be 0.05 or more.

  17. Factors influencing the Mode I interlaminar fracture toughness of a rubber toughened thermoplastic matrix composite

    Parker, D. S.; Yee, A. F.


    The use of a rubber modified thermoplastic resin has been investigated as a method to improve the Mode I interlaminar fracture toughness of a unidirectional continuous carbon fiber composite. Test results show that the improvement in the fracture toughness is less than expected due to rubber particle agglomeration, solvent and molding induced crystallization of the matrix and poor fiber/matrix adhesion. The plastic zone in composites utilizing tough matrices can extend well beyond a single interfibrillar spacing. However, the development of the plastic zone is limited due to the failure of the fiber/matrix interface. In order to fully evaluate the potential of tough composites using toughened matrices, any improvement made in the matrix toughness must be coupled with improvements in the fiber/matrix adhesion.

  18. Fracture Behavior Investigation of a Typical Sandstone Under Mixed-Mode I/II Loading Using the Notched Deep Beam Bending Method

    Luo, Y.; Ren, L.; Xie, L. Z.; Ai, T.; He, B.


    The brittle fracture behavior of rocks under mixed-mode loading is important in rock engineering. First, a new configuration called the notched deep beam (NDB) specimen was introduced for the fracture testing of rock materials under mixed-mode I/II loading, and a series of finite element analyses were performed to calibrate the dimensionless fracture parameters (i.e., Y I, Y II and T^{*}). The results showed that an NDB specimen subjected to three-point bending is able to generate pure mode I loading, pure mode II loading, and any mixed-mode loading in between. Then, several NDB specimens made of sandstone were used to investigate the brittle fracture behavior of rock under mixed-mode I/II loading. The fracture surfaces were theoretically described using a statistical method, and the results indicated that all the fracture surfaces generated under different mixed-mode loading were statistically identical; to some extent, these results experimentally showed that only tensile fracture occurs under mixed-mode I/II loading. The obtained fracture strengths were then analyzed using several brittle fracture criteria. The empirical criterion, maximum energy release rate criterion, generalized maximum tangential stress (GMTS) criterion, and improved R-criterion accurately predicted the fracture strength envelope of the sandstone. Finally, based on the concepts of point stress and mean stress, the micro-crack zones (MCZs) under different mixed-mode loading were theoretically estimated based on the MTS and GMTS criteria. The critical radius of MCZ in the crack propagation direction was not a constant for all mixed-mode loading conditions regardless of whether the T-stress was considered. This result suggests that the size of the core region used to predict the crack initiation direction and fracture strength based on the GMTS criterion should be chosen more carefully.

  19. Mode I Critical Stress Intensity Factor of Beech Wood (Fagus Sylvatica in a TL Configuration: A Comparison of Different Methods

    Miran Merhar, Dominika Gornik Bučar, Bojan Buča


    Full Text Available The paper presents a comparison between various methods of mode I critical stress intensity factor KIC calculations of beech wood in the TL configuration. The first method is the stress intensity factor extrapolation to the distance of 0 mm from the crack tip; the second method is the use of the J integral; and the third method is based on the differences in deformation energies from which the strain energy release rate per unit of crack propagation length was obtained. The fourth method is the calculation of material deformation around the crack or the displacement of the triangle element node; and the fifth method uses a generally known equation for the CT specimen for plane-strain conditions in isotropic material. Using the finite element method, it was found that the J integral was least sensitive to the size and shape of the elements. It was used to calculate the critical stress intensity factor KIC for beech wood in a TL configuration. The average value is 0.56 MPa√m with a standard deviation of 0.047 MPa√m.

  20. Effects of crack depth and specimen size on ductile crack growth of SENT and SENB specimens for fracture mechanics evaluation of pipeline steels

    Xu, J. [Department of Structural Engineering, Norwegian University of Science and Technology (NTNU), Richard Birkelands vei 1a, N-7491 Trondheim (Norway); School of Materials Science and Engineering, University of Science and Technology Beijing (USTB), 100083 Beijing (China); Zhang, Z.L., E-mail: zhiliang.zhang@ntnu.n [Department of Structural Engineering, Norwegian University of Science and Technology (NTNU), Richard Birkelands vei 1a, N-7491 Trondheim (Norway); Ostby, E.; Nyhus, B. [SINTEF, Materials and Chemistry, N-7465 Trondheim (Norway); Sun, D.B. [School of Materials Science and Engineering, University of Science and Technology Beijing (USTB), 100083 Beijing (China)


    A strong geometry dependence of ductile crack growth resistance emerges under large scale yielding. The geometry dependence is associated with different levels of crack tip constraint conditions. However, in a recent attempt to identify appropriate fracture mechanics specimens for pipeline steels, an 'independent' relationship between the crack growth resistance curves and crack depths for SENT specimens has been observed experimentally. In this paper, we use the complete Gurson model to study the effects of crack depth and specimen size on ductile crack growth behavior. Crack growth resistance curves for plane strain, mode I crack growth under large scale yielding conditions have been computed. SENB and SENT specimens with three different specimen sizes, each specimen size with three different crack depths, have been selected. It has been found that crack tip constraint (Q-parameter) has a weak dependence on the crack depth for specimens in the low constraint regime.

  1. Characterization of Mode I and mixed-mode delamination growth in T300/5208 graphite/epoxy

    Ramkumar, R. L.; Whitcomb, J. D.


    The roles played by Mode I and Mode II strain-energy release rates (G-I and G-II, respectively) in inducing delamination growth under static and fatigue loading were investigated, using T300/5208 graphite/epoxy specimens. Double cantilever beam (DCB) specimens and cracked lap shear (CLS) specimens were used for pure Mode I and mixed-mode tests, respectively. Fatigue-induced delamination growth was characterized by constant-amplitude fatigue tests at a minimum to maximum cyclic load ratio of 0.05 and a frequency of 10 Hz. During the tests, the maximum and minimum strain-energy release rates (Gmax, Gmin) and the delamination growth rate (da/dN) were monitored. Static tests on mixed-mode CLS specimens measured the total strain-energy release rate, which was broken into G-I and G-II components using finite-element analysis. A power-law relationship between da/dN and G-Imax, and da/dN and Gmax were obtained from fatigue test results on DCB and CLS specimens, respectively. The power law for a pure Mode II delamination was derived from CLS results by subtracting the contribution due to G-I.


    R. Daud


    Full Text Available Shielding interaction effects of two parallel edge cracks in finite thickness plates subjected to remote tension load is analyzed using a developed finite element analysis program. In the present study, the crack interaction limit is evaluated based on the fitness of service (FFS code, and focus is given to the weak crack interaction region as the crack interval exceeds the length of cracks (b > a. Crack interaction factors are evaluated based on stress intensity factors (SIFs for Mode I SIFs using a displacement extrapolation technique. Parametric studies involved a wide range of crack-to-width (0.05 ≤ a/W ≤ 0.5 and crack interval ratios (b/a > 1. For validation, crack interaction factors are compared with single edge crack SIFs as a state of zero interaction. Within the considered range of parameters, the proposed numerical evaluation used to predict the crack interaction factor reduces the error of existing analytical solution from 1.92% to 0.97% at higher a/W. In reference to FFS codes, the small discrepancy in the prediction of the crack interaction factor validates the reliability of the numerical model to predict crack interaction limits under shielding interaction effects. In conclusion, the numerical model gave a successful prediction in estimating the crack interaction limit, which can be used as a reference for the shielding orientation of other cracks.

  3. Characterization of mixed mode crack opening in concrete

    Jacobsen, Jonas Sejersbøl; Poulsen, Peter Noe; Olesen, John Forbes


    In real concrete structures cracks often open in mixed mode after their initiation. To capture the direct material behavior of a mixed mode crack opening a stiff biaxial testing machine, capable of imposing both normal and shear loads on a given crack area, has been applied. The opening and sliding...... components of the mixed mode displacement are measured using a custom made orthogonal gauge, and the measurements are used directly as the closed loop control signals. A double notch, concrete specimen is used for the crack investigation. The tests are divided into two steps, a pure Mode I opening step......, where a macro crack is initiated in the specimen followed by the mixed mode opening step. The high stiffness of the set-up together with the closed control loop ensures a stable crack initiation followed by a controllable mixed mode opening. The deep notches result in a plane crack, only influenced...

  4. 桥梁下部结构裂缝提取的改进C-V模型算法%Modified C-V model algorithm of crack extraction for bridge substructure

    李刚; 贺拴海; 杜凯; 刘伟; 杜秦文


    应用改进C-V模型,进行桥梁下部结构裂缝图像分割,通过裂缝截取、图像填充和旋转变换精确提取裂缝宽度。对不同光照条件下拍摄的在役混凝土桥梁结构裂缝图像,分别利用改进C-V模型算法、自适应阈值法、形态学算法、C-V模型以及Canny算法进行试验对比。分析结果表明:改进C-V模型算法误分率和运算时间最小,分别为3.02%与89ms;1 000幅桥梁结构裂缝图像试验对比显示裂缝检测准确率大于90.8%,裂缝宽度平均误差小于0.03mm。可见,改进算法可有效提高检测准确率,减少运算时间。%The crack image segmentation of bridge substructure was studied by utilizing a modified C-V model. Crack clip, image filling and rotation transformation were applied for the precise extraction of crack width. The crack images of existing concrete bridge structure were taken in different illuminations, and test results were compared by using modified C-V model algorithm, adaptive threshold algorithm, morphology algorithm, C-V model and Canny algorithm. Analysis result indicates that the miselassification rate of modified C-V model algorithm is 3.02%, the operation time is 89 ms, and the values are minimum compared with other methods. Based on the comparative test on 1 000 crack images of bridge structure, the accuracy rate of crack detection is greater than 90.8%, and the mean error of crack width is less than 0.03 mm. So the modified algorithm can effectively improve detection accuracy rate, and reduce operation time. 2 tabs, 6 figs, 16 refs.

  5. Fatigue crack growth simulations of 3-D linear elastic cracks under thermal load by XFEM

    Himanshu PATHAK[1; Akhilendra SINGH[2; I.V. SINGH[3; S. K. YADAV[3


    This paper deals with the fatigue crack growth simulations of three-dimensional linear elastic cracks by XFEM under cyclic thermal load. Both temperature and displacement approximations are extrinsically enriched by Heaviside and crack front enrichment functions. Crack growth is modelled by successive linear extensions, and the end points of these linear extensions are joined by cubic spline segments to obtain a modified crack front. Different crack geometries such as planer, non-planer and arbitrary spline shape cracks are simulated under thermal shock, adiabatic and isothermal loads to reveal the sturdiness and versatility of the XFEM approach.

  6. DBEM crack propagation for nonlinear fracture problems

    R. Citarella


    Full Text Available A three-dimensional crack propagation simulation is performed by the Dual Boundary Element Method (DBEM. The Stress Intensity Factors (SIFs along the front of a semi elliptical crack, initiated from the external surface of a hollow axle, are calculated for bending and press fit loading separately and for a combination of them. In correspondence of the latter loading condition, a crack propagation is also simulated, with the crack growth rates calculated using the NASGRO3 formula, calibrated for the material under analysis (steel ASTM A469. The J-integral and COD approaches are selected for SIFs calculation in DBEM environment, where the crack path is assessed by the minimum strain energy density criterion (MSED. In correspondence of the initial crack scenario, SIFs along the crack front are also calculated by the Finite Element (FE code ZENCRACK, using COD, in order to provide, by a cross comparison with DBEM, an assessment on the level of accuracy obtained. Due to the symmetry of the bending problem a pure mode I crack propagation is realised with no kinking of the propagating crack whereas for press fit loading the crack propagation becomes mixed mode. The crack growth analysis is nonlinear because of normal gap elements used to model the press fit condition with added friction, and is developed in an iterative-incremental procedure. From the analysis of the SIFs results related to the initial cracked configuration, it is possible to assess the impact of the press fit condition when superimposed to the bending load case.

  7. Representation of finite cracks by dislocation pileups: An application to atomic simulation of fracture

    Shastry, V.; Farkas, D. [Virginia Polytechnic Inst. and State Univ., Blacksburg, VA (United States). Dept. of Materials Science and Engineering


    The elastic displacement field solution of a semi-infinite crack in an anisotropic body, calculated using a complex variable approach due to Sih and Liebowitz, is usually used by atomistic simulations of fracture. The corresponding expression for the displacement field of a finite crack is numerically cumbersome since it involves multiple square roots of complex numbers. In this study, displacement field of the crack is calculated by superposing the displacements of dislocations in an equivalent double pileup, equilibrated under mode I conditions. An advantage of this method is its extensibility to atomistic studies of more complex systems containing multiple cracks or interfaces. The pileup representation of the finite crack is demonstrated as being equivalent to its corresponding continuum description using the example of a double ended crack in {alpha}-Fe, loaded in mode I. In these examples, the interatomic interaction in {alpha}-Fe is described by an empirical embedded atom (EAM) potential.

  8. Effect of fracture surface roughness on shear crack growth. Progress report, August 1, 1991--May 31, 1992

    Gross, T.S.; Watt, D.W. [New Hampshire Univ., Durham, NH (United States). Dept. of Mechanical Engineering; Mendelsohn, D.A. [Ohio State Univ., Columbus, OH (United States). Dept. of Engineering Mechanics


    A model of fracture surface interference for Mode I fatigue crack profiles was developed and evaluated. Force required to open the crack faces is estimated from point contact expressions for Mode I stress intensity factor. Force transfer across contacting asperities is estimated and used to calculate Mode II resistance stress intensity factor (applied factor is sum of effective and resistance factors). Electro-optic holographic interferometry was used to measure 3-D displacement field around a Mode I fatigue pre-crack in Al loaded in Mode II shear. Induced Mode I crack face displacements were greater than Mode II displacements. Plane stress shear lip caused displacement normal to surface as the crack faces are displaced. Algorithms are being developed to track the displacements associated with the original coordinate system in the camera. A 2-D boundary element method code for mixed mode I and II loading of a rough crack (sawtooth asperity model) has been completed. Addition of small-scale crack tip yielding and a wear model are completed and underway, respectively.

  9. Stress field near interface crack tip of double dissimilar orthotropic composite materials

    LI Jun-lin; ZHANG Shao-qin; YANG Wei-yang


    In this paper, double dissimilar orthotropic composite materials interracial crack is studied by constructing new stress functions and employing the method of com- posite material complex. When the characteristic equations' discriminants △1 >0 and △2 > 0, the theoretical formula of the stress field and the displacement field near the mode I interface crack tip are derived, indicating that there is no oscillation and inter- embedding between the interfaces of the crack.

  10. Knuckle Cracking

    ... Ask The Expert Ask a Question Physician Corner Rheumatology Conference Rheumatology Rounds Case Rounds Radiology Rounds Pathophysiology of the ... Appointment Information Contact Us Our Faculty Our Staff Rheumatology Specialty Centers Knuckle Cracking Q & A September 10, ...

  11. Fatigue reliability of cracked engineering structures

    Lanning, David Bruce, Jr.


    This study investigates the reliability of engineering structures containing fatigue cracks. Stress concentrations and welded joints are probable locations for the initiation and propagation of fatigue cracks. Due to the many unknowns of loading, materials properties, crack sizes and crack shapes present at these locations, a statistics-based reliability analysis is valuable in the careful consideration of these many different random factors involved in a fatigue life analysis, several of which are expanded upon in this study. The basic problem of a crack near a stress concentration is first considered. A formulation for the aspect ratio (a/c) of a propagating semi-elliptical fatigue crack located at the toe of a welded T-joint is developed using Newman and Raju's stress intensity factor for a cracked flat plate with a weld magnification factor and compared to that of a cracked flat plate, and the reliability in terms of fatigue lifetime is calculated with the aid of Paris' crack propagation equation for membrane and bending loadings. Crack closure effects are then introduced in the consideration of short crack effects, where crack growth rates typically may exceed those found using traditional linear elastic fracture mechanics solutions for long cracks. The probability of a very small, microstructurally influenced crack growing to a size influenced by local plastic conditions is calculated utilizing the probability of a crack continuing to grow past an obstacle, such as a grain boundary. The result is then combined with the probability for failure defined using the crack closure-modified Paris equation to find an overall reliability for the structure. Last, the probability of fracture is determined when a crack front encounters regions of non-uniform toughness, such as typical in the heat affected zone of a welded joint. An expression for the effective crack lengths of the dissimilar regions is derived, and used in a weakest-link fracture model in the evaluation

  12. Face/core debond fatigue crack growth characterization using the sandwich mixed mode bending specimen

    Manca, Marcello; Quispitupa, Amilcar; Berggreen, Christian;


    Face/core fatigue crack growth in foam-cored sandwich composites is examined using the mixed mode bending (MMB) test method. The mixed mode loading at the debond crack tip is controlled by changing the load application point in the MMB test fixture. Sandwich specimens were manufactured using H45...... critical load, at load ratios of R=0.1 and 0.2. The crack length was determined during fatigue testing using the analytical compliance expression and verified by visual measurements. Fatigue crack growth results revealed higher crack growth rates for mode I dominated loading. For specimens with H45 core...

  13. A thermo-mechanical study of mode I, small-scale yielding crack-tip fields in glassy polymers

    Basu, S.; van der Giessen, E.


    The objective of this work is to study the stress and temperature fields ahead of a blunted notch under mode 1, small-scale yielding situations. The investigation is motivated by the observation that certain polymers and polymer blends exhibit a marked increase in fracture toughness with increase in

  14. Effect of pure mode I, II or III loading or mode mixity on crack growth in a homogeneous solid

    Tvergaard, Viggo


    the maximum. The reason for this is discussed in terms of the local stress and strain fields around the tip. For pure mode II or mode Ill loading it is shown that there is no maximum before the steady-state. Also results for different mixed mode conditions are presented and discussed in relation...

  15. Dynamic initiation and propagation of cracks in unidirectional composite plates

    Coker, Demirkan

    Dynamic crack growth along weak planes is a significant mode of failure in composites and other layered/sandwiched structures and is also the principal mechanism of shallow crustal earthquakes. In order to shed light on this phenomenon dynamic crack initiation and propagation characteristics of a model fiber-reinforced unidirectional graphite/epoxy composite plate was investigated experimentally. Dynamic fracture experiments were conducted by subjecting the composite plates to in-plane, symmetric and asymmetric, impact loading. The lateral shearing interferometric technique of coherent gradient sensing (CGS) in conjunction with high-speed photography was used to visualize the failure process in real time. It was found that mode-I cracks propagated subsonically with crack speeds increasing to the neighborhood of the Rayleigh wave speed of the composite. Also in mode-I, the dependence of the dynamic initiation fracture toughness on the loading rate was determined and was found to be constant for low loading rates and to increase rapidly above K˙dI>10 5 . The dynamic crack propagation toughness, KID, was observed to decrease with crack tip speed up to the Rayleigh wave speed of the composite. For asymmetric, mode-II, types of loading the results revealed highly unstable and intersonic shear-dominated crack growth along the fibers. These cracks propagated with unprecedented speeds reaching 7400 m/s which is the dilatational wave speed of the composite along the fibers. For intersonic crack growth, the interferograms, featured a shock wave structure typical of disturbances traveling with speeds higher than one of the characteristic wave speeds in the solid. In addition high speed thermographic measurements are conducted that show concentrated hot spots behind the crack tip indicating non-uniform crack face frictional contact. In addition, shear dominated dynamic crack growth is investigated along composite/Homalite interfaces subjected to impact loading. The crack

  16. Constitutive Modeling of the Facesheet to Core Interface in Honeycomb Sandwich Panels Subject to Mode I Delamination

    Hoewer, Daniel; Lerch, Bradley A.; Bednarcyk, Brett A.; Pineda, Evan Jorge; Reese, Stefanie; Simon, Jaan-Willem


    A new cohesive zone traction-separation law, which includes the effects of fiber bridging, has been developed, implemented with a finite element (FE) model, and applied to simulate the delamination between the facesheet and core of a composite honeycomb sandwich panel. The proposed traction-separation law includes a standard initial cohesive component, which accounts for the initial interfacial stiffness and energy release rate, along with a new component to account for the fiber bridging contribution to the delamination process. Single cantilever beam tests on aluminum honeycomb sandwich panels with carbon fiber reinforced polymer facesheets were used to characterize and evaluate the new formulation and its finite element implementation. These tests, designed to evaluate the mode I toughness of the facesheet to core interface, exhibited significant fiber bridging and large crack process zones, giving rise to a concave downward concave upward pre-peak shape in the load-displacement curve. Unlike standard cohesive formulations, the proposed formulation captures this observed shape, and its results have been shown to be in excellent quantitative agreement with experimental load-displacement and apparent critical energy release rate results, representative of a payload fairing structure, as well as local strain fields measured with digital image correlation.

  17. The influence of modified water chemistries on metal oxide films, activity build-up and stress corrosion cracking of structural materials in nuclear power plants

    Maekelae, K.; Laitinen, T.; Bojinov, M. [VTT Manufacturing Technology, Espoo (Finland)


    The primary coolant oxidises the surfaces of construction materials in nuclear power plants. The properties of the oxide films influence significantly the extent of incorporation of actuated corrosion products into the primary circuit surfaces, which may cause additional occupational doses for the maintenance personnel. The physical and chemical properties of the oxide films play also an important role in different forms of corrosion observed in power plants. This report gives a short overview of the factors influencing activity build-up and corrosion phenomena in nuclear power plants. Furthermore, the most recent modifications in the water chemistry to decrease these risks are discussed. A special focus is put on zinc water chemistry, and a preliminary discussion on the mechanism via which zinc influences activity build-up is presented. Even though the exact mechanisms by which zinc acts are not yet known, it is assumed that Zn may block the diffusion paths within the oxide film. This reduces ion transport through the oxide films leading to a reduced rate of oxide growth. Simultaneously the number of available adsorption sites for {sup 60}Co is also reduced. The current models for stress corrosion cracking assume that the anodic and the respective cathodic reactions contributing to crack growth occur partly on or in the oxide films. The rates of these reactions may control the crack propagation rate and therefore, the properties of the oxide films play a crucial role in determining the susceptibility of the material to stress corrosion cracking. Finally, attention is paid also on the novel techniques which can be used to mitigate the susceptibility of construction materials to stress corrosion cracking. (orig.) 127 refs.

  18. Transition from Multiple Macro-Cracking to Multiple Micro-Cracking in Cementitious Composites

    ZHANG Jun; LENG Bing


    This paper presents an experimental study of the possibility of transition from multiple macro-cracking to multiple micro-cracking in cementitious composites.Conventional polyvinyl alcohol fiber reinforced cementitious composites normally exhibit macroscopic strain-hardening and multiple cracking after the first cracks appear.However,the individual crack width at the saturated stage is normally 60 to 80 μm.In the current study,the effect of fine aggregate size on the cracking performance,especially the individual crack width in the strain-hardening stage was studied by bending tests.The results show that the individual crack widths can be reduced from 60-80 μm to 10-30 μm by modifying the particle size of the fine aggregates used in the composites.

  19. Dynamics of crack penetration vs. branching at a weak interface: An experimental study

    Sundaram, Balamurugan M.; Tippur, Hareesh V.


    In this paper, the dynamic crack-interface interactions and the related mechanics of crack penetration vs. branching at a weak interface are studied experimentally. The interface is oriented perpendicular to the incoming mode-I crack in an otherwise homogeneous bilayer. The focus of this investigation is on the effect of interface location and the associated crack-tip parameters within the bilayer on the mechanics of the ensuing fracture behavior based on the optical methodologies laid down in Ref. Sundaram and Tippur (2016). Time-resolved optical measurement of crack-tip deformations, velocity and stress intensity factor histories in different bilayer configurations is performed using Digital Gradient Sensing (DGS) technique in conjunction with high-speed photography. The results show that the crack path selection at the interface and subsequently the second layer are greatly affected by the location of the interface within the geometry. Using optically measured fracture parameters, the mechanics of crack penetration and branching are explained. Counter to the intuition, a dynamically growing mode-I approaching a weak interface at a lower velocity and stress intensity factor penetrates the interface whereas a higher velocity and stress intensity factor counterpart gets trapped by the interface producing branched daughter cracks until they kink out into the next layer. An interesting empirical observation based on measured crack-tip parameters for crack penetration and branching is also made.

  20. Mechanism of fracture in macro- and micro-scales in hollow centre cracked disc specimen

    M. Eftekhari; A. Baghbanan; H. Hashemolhosseini; H. Amrollahi


    The hollow centre cracked disc (HCCD) specimen is one of the suggested alternative methods for determining the fracture toughness of rock. This work aims to investigate the fracture mechanism in HCCD in macro- and micro-scales using numerical methods, extended finite element method (X-FEM) and particle flow code (PFC) modeling, respectively. In the X-FEM, heaviside and near-tip enrichment functions are employed to consider the presence of the crack in the model. In PFC modeling the movement and interaction of stressed assemblies of rigid spherical particles are modeled using the distinct element method (DEM). A numerical code called MEX-FEM based on XFEM has been developed to simulate the problems involving crack. The models of pure modes I and II in macro-scale are simulated in micro-scale. The results show that dimensionless stress intensity factors (YI,YI) for pure modes I and II increase by increasing the crack length ratio. The angle at which the pure mode II occurs decreases by increasing the crack length ratio. In mixed mode I-II, The value ofYI decreases by increasing the crack angle, while the value ofYI increases to a given crack angle and then it decreases. Moreover, the fracture in micro-scale, unlike the macro-scale, includes a combination of different modes of fracturing.

  1. Mechanism of fracture in macro- and micro-scales in hollow centre cracked disc specimen

    M.Eftekhari; A.Baghbanan; H.Hashemolhosseini; H.Amrollahi


    The hollow centre cracked disc(HCCD) specimen is one of the suggested alternative methods for determining the fracture toughness of rock. This work aims to investigate the fracture mechanism in HCCD in macro- and micro-scales using numerical methods, extended finite element method(X-FEM) and particle flow code(PFC) modeling, respectively. In the X-FEM, heaviside and near-tip enrichment functions are employed to consider the presence of the crack in the model. In PFC modeling the movement and interaction of stressed assemblies of rigid spherical particles are modeled using the distinct element method(DEM). A numerical code called MEX-FEM based on XFEM has been developed to simulate the problems involving crack. The models of pure modes I and Ⅱ in macro-scale are simulated in micro-scale. The results show that dimensionless stress intensity factors(YI, YⅡ) for pure modes I and Ⅱ increase by increasing the crack length ratio. The angle at which the pure mode Ⅱ occurs decreases by increasing the crack length ratio. In mixed mode I-Ⅱ, The value of YI decreases by increasing the crack angle, while the value of YⅡ increases to a given crack angle and then it decreases. Moreover, the fracture in micro-scale, unlike the macro-scale, includes a combination of different modes of fracturing.

  2. Fatigue crack paths and properties in A356-T6 aluminum alloy microstructurally modified by friction stir processing under different conditions

    A. Tajiri


    Full Text Available A356-T6 cast aluminum alloy is a light weight structural material, but fatigue crack initiates and propagates from a casting defect leading to final fracture. Thus it is important to eliminate casting defects. In this study, friction stir processing (FSP was applied to A356-T6, in which rotating tool with probe and shoulder was plunged into the material and travels along the longitudinal direction to induce severe plastic deformation, resulting in the modification of microstructure. Two different processing conditions with low and high tool rotational speeds were tried and subsequently fully reversed fatigue tests were performed to investigate the effect of processing conditions on the crack initiation and propagation behavior. The fatigue strengths were successfully improved by both conditions due to the elimination of casting defects. But the lower tool rotational speed could further improve fatigue strength than the higher speed. EBSD analyses revealed that the higher tool rotational speed resulted in the severer texture having detrimental effects on fatigue crack initiation and propagation resistances.

  3. Propagation of Slepyan's crack in a non-uniform elastic lattice

    Nieves, Michael; Jones, Ian; Mishuris, Gennady


    We model and derive the solution for the problem of a Mode I semi-infinite crack propagating in a discrete triangular lattice with bonds having a contrast in stiffness in the principal lattice directions. The corresponding Green's kernel is found and from this wave dispersion dependencies are obtained in explicit form. An equation of the Wiener-Hopf type is also derived and solved along the crack face, in order to compute the stress intensity factor for the semi-infinite crack. The crack stability is analysed via the evaluation of the energy release rate for different contrasts in stiffness of the bonds.

  4. Numerical Computation of Stress Intensity Factors for Bolt-hole Corner Crack in Mechanical Joints

    Wang Liqing; Gai Bingzheng


    The three-dimensional finite element method is used to solve the problem of the quarter-elliptical comer crack of the bolt-hole in mechanical joints being subjected to remote tension. The square-root stress singularity around the corner crack front is simulated using the collapsed 20-node quarter point singular elements. The contact interaction between the bolt and the hole boundary is considered in the finite element analysis. The stress intensity factors (SIFs) along the crack front are evaluated by using the displacement correlation technique. The effects of the amount of clearance between the hole and the bolt on the SIFs are investigated. The numerical results indicate that the SIF for mode I decrease with the decreases in clearance, and in the cases of clearance being present, the corner crack is in a mix-mode, even if mode I loading is dominant.

  5. Kinetics of fracture in Fe-3Si steel under mode I loading

    Bessendorf, Michael H.


    This paper deals with experimental studies of fatigue crack propagation (FCP) in Fe-3Si steel. The FCP experiments were performed on single-edge crack specimens. Results show that an extensive damage zone consisting of slip bands surrounds and precedes the propagating crack. The system of the crack and the damage zone constitutes the crack layer (CL). The results demonstrate that fracture propagates by the translation, expansion, and distortion of the part of CL called the active zone. The contours of the damage distribution show that different loading stresses may cause significantly different shapes of damage. Application of the stability criteria is demonstrated. It was shown that the critical energy release rate depends on the history of loading.

  6. Effects of microstructure and crystallography on crack path and intrinsic resistance to shear-mode fatigue crack growth

    J. Pokluda


    Full Text Available The paper focuses on the effective resistance and the near-threshold growth mechanisms in the ferritic-pearlitic and the pure pearlitic steel. The influence of microstructure on the shear-mode fatigue crack growth is divided here into two factors: the crystal lattice type and the presence of different phases. Experiments were done on ferritic-pearlitic steel and pearlitic steel using three different specimens, for which the effective mode II and mode III threshold values were measured and fracture surfaces were reconstructed in three dimensions using stereophotogrammetry in scanning electron microscope. The ferritic-pearlitic and pearlitic steels showed a much different behaviour of modes II and III cracks than that of the ARMCO iron. Both the deflection angle and the mode II threshold were much higher and comparable to the austenitic steel. Mechanism of shear-mode crack behaviour in the ARMCO iron, titanium and nickel were described by the model of emission of dislocations from the crack tip under a dominant mode II loading. In other tested materials the cracks propagated under a dominance of the local mode I. In the ferritic-pearlitic and pearlitic steels, the reason for such behaviour was the presence of the secondary-phase particles (cementite lamellas, unlike in the previously austenitic steel, where the fcc structure and the low stacking fault energy were the main factors. A criterion for mode I deflection from the mode II crack-tip loading, which uses values of the effective mode I and mode II thresholds, was in agreement with fractographical observations.

  7. Constitutive Mixed Mode Behavior of Cracks in Concrete

    Jacobsen, Jonas Sejersbøl

    interpretation of the crack behavior. A stiff biaxial test set-up is applied to the mixed mode measurements. The relative opening and sliding of the crack is used as the control signals in a new enhanced closed control loop. The opening and the sliding of the crack are measured by clip gauges using a pair...... may open in mixed mode, i.e. a combination of opening and sliding. To get a thorough description of the structural consequences it is important to include the stress transferring effects related to the mixed mode opening. The existing constitutive mixed mode models either have a rather extensive model...... in a double notch specimen, the crack is exposed to mixed mode opening. The experiments may be used in a direct interpretation of the mixed mode behavior. The elliptic yield surface in the associated elasto-plastic material model is controlled by two hardening parameters, which represent the actual...

  8. La改性ZSM-5分子筛及其在催化裂解反应中的应用%Synthesis of La-modified ZSM-5 zeolite and performance for catalytic cracking reaction

    张络明; 许春芳; 马通; 巩雁军


    A series of La-modified ZSM-5 were prepared by hydrothermal treatment and incipient wetness impregnation. Compared with those of pristine ZSM-5, an increase in lattice constants and the amount of strong, weak and the total acid cites of La-modified ZSM-5 by the hydrothermal treatment occurs. The amount of acid cites of by La-modified ZSM-5 by incipient wetness impregnation increases, however, the lattice constants does not change. High yields of ethylene and propylene were obtained on both kinds of modified samples tested in the catalytic cracking of hexane. The yields of ethylene and propylene were achieved on the samples modified by hydrothermal treatment at WHSV=6 h−1 (23.39% of ethylene, 25.17% of propylene), which are 2% and 4% larger than those of the pristine ZSM-5 samples (21.19% of ethylene, 21.04% of propylene), and slightly better than those of the samples modified by incipient wetness impregnation. In the long-term experiment of hexane cracking with at WHSV=4 h−1, the samples modified by hydrothermal treatment (2000 min) and incipient wetness impregnation (1600 min), exhibited much longer durability than the pristine ZSM-5 sample (800 min). It suggested that the hydrothermal treatment is better modification method in the preparation of La-modified ZSM-5 catalyst to improve the performance of hexane catalytic cracking.%采用高温水热法和等体积浸渍法将La离子负载于ZSM-5分子筛上得到了改性ZSM-5分子筛材料。水热法La 改性样品改变了 ZSM-5的晶胞尺寸,提升了其强酸、弱酸及总酸量。浸渍法改性样品也提高了其酸量但是对晶胞参数没有影响。将改性样品应用于正己烷催化裂解反应中,两种方法均得到了较高的双烯收率,其中水热法改性样品在空速为6 h−1时乙烯收率和丙烯收率分别为23.39%和25.17%,这与原样相同空速下的乙烯丙烯收率(乙烯为21.19%,丙烯为21.04%)相比分别提升了约2%和4%,略高于浸渍法

  9. SIF-based fracture criterion for interface cracks

    Ji, Xing


    The complex stress intensity factor K governing the stress field of an interface crack tip may be split into two parts, i.e., hat{K} and s^{-iɛ}, so that K=hat{K}s^{-iɛ}, s is a characteristic length and ɛ is the oscillatory index. hat{K} has the same dimension as the classical stress intensity factor and characterizes the interface crack tip field. That means a criterion for interface cracks may be formulated directly with hat{K}, as Irwin (ASME J. Appl. Mech. 24:361-364, 1957) did in 1957 for the classical fracture mechanics. Then, for an interface crack, it is demonstrated that the quasi Mode I and Mode II tip fields can be defined and distinguished from the coupled mode tip fields. Built upon SIF-based fracture criteria for quasi Mode I and Mode II, the stress intensity factor (SIF)-based fracture criterion for mixed mode interface cracks is proposed and validated against existing experimental results.

  10. Effects of voids on delamination behavior under static and fatigue mode I and mode II

    Abdelal, Nisrin Rizek

    Composite materials have become materials of choice for wind turbine blade manufacturing due to their high specific stiffness, strength and fatigue life. Glass fiber composites are used extensively in light-weight structural components for wind turbines, aircrafts, marine craft and high performance automobile because glass fiber is inexpensive and usually provides high strength to weight ratio and good in-plane mechanical properties. The high cycle fatigue resistance of composite materials used in wind turbine blades has been recognized as a major uncertainty in predicting the reliability of wind turbines over their design lifetime. Blades are expected to experience 108 to 109 fatigue cycles over a 20 to 30 year lifetime. Delamination or interlaminar failure is a serious failure mode observed in composite structures. Even partial delamination will lead to a loss of local stiffness, which can preclude buckling failure. Manufacturing process defects such as voids and fiber waviness degrade the fatigue life and delamination resistance of the blade's composite. This research describes the effect of voids on static and fatigue interlaminar fracture behavior under mode I and mode II loading of wind turbine glass fiber composites. Samples with different void volume fractions in the 0.5%-7% range were successfully obtained by varying the vacuum in the hand layup vacuum bagging manufacturing process. Void content was characterized using four different methods; ultrasonic scanning, epoxy burn off, serial sectioning and X-Ray computed tomography. The effect of voids on both mode I and mode II interlaminar fracture toughness under static and fatigue loading was investigated. Finally, fractographic analysis (using optical and scanning electron microscopy) was conducted. The results showed that voids leads to slight reduction in static modes I and II interlaminar fracture toughness. In addition, voids lead to a decrease in modes I and II maximum cyclic strain energy release

  11. The geometry of soil crack networks

    Chertkov, V Y


    The subject of this work is the modification and specification of an approach to detail the estimation of soil crack network characteristics. The modification aims at accounting for the corrected soil crack volume based on the corrected shrinkage geometry factor compared to known estimates of crack volume and shrinkage geometry factor. The mode of the correction relies on recent results of the soil reference shrinkage curve. The main exposition follows the preliminary brief review of available approaches to dealing with the geometry of soil crack networks and gives a preliminary brief summary of the approach to be modified and specified. To validate and illustrate the modified approach the latter is used in the analysis of available data on soil cracking in a lysimeter.

  12. Optimization of Preventive Grinding of Backup Roll against Contact Fatigue Cracking

    DOU Peng; LI You-guo; LIANG Kai-ming; BAI Bing-zhe


    In order to optimize the current grinding procedure of the backup roll of 2050 continuously variable crown (CVC) mills, the behavior of rolling contact fatigue (RCF) cracking was investigated. Two RCF short cracks, including vertical short crack and ratcheting short crack initiated from ratcheting, were observed. The behavior of both RCF cracks was analyzed in detail. Then a modified grinding procedure was proposed according to the behavior of RCF cracks and the preventive grinding strategy.

  13. Interaction of a crack with crystal defects in solids

    Narita, N. [Kyushu Inst. of Tech., Kitakyushu (Japan). Dept. of Materials Science and Engineering; Higashida, K.


    The modifications of stress states near a crack tip by interstitial impurities and by dislocations are analyzed using 2-D and 3-D potential methods. In the case of interstitial impurities, the local stress intensity k{sub D} due to impurities is much affected by their location and is altered from crack tip shielding to anti-shielding as their location changes from behind a crack tip to the front. If impurities are mobile, their forward redistribution is induced by crack fields to increase k{sub D} values. The tetragonal strain of impurities also enhances the increase of the k{sub D} values. In dislocation-crack systems, two kinds of screw dislocation arrays are observed on each different slip plane ahead of a crack tip in MgO thin crystals and they mainly induce the mode I stress intensity of shielding type as a result of the mutual cancellation of the other modes. The effect of crack tip shielding/anti-shielding on crack extension is discussed in connection with the experimental observation of fracture toughness. (orig.). 7 refs.

  14. Steady-State Crack Growth in Rate-Sensitive Single Crystals

    Juul, Kristian Jørgensen; Nielsen, Kim Lau; Niordson, Christian Frithiof


    The characteristics of the active plastic zone surrounding a crack growingin a single crystal (FCC, BCC, and HCP) at constant velocity is investigated for ModeI loading under plane strain assumptions. The framework builds upon a steady-state relation bringing the desired solution out in a frame...




    Perturbation method for solving elastic three-dimensional (3D) problems for 3D icosahedral quasicrystals is pro posed. Considering an infinite 3D icosahedral quasicrystal weakened by a circular crack, we obtain the uniformly valid asymptotic solutions up to O(R2) for the mode I loading, where R is the elastic constant of phonon-phason coupling.

  16. The stress corrosion cracking behaviour of heat-treated Al-Zn-Mg-Cu alloy in modified salt spray fog testing

    Onoro, J. [Ingenieria y Ciencia de los Materiales, Universidad Politecnica de Madrid, ETS Ingenieros Industriales, Madrid (Spain)


    The stress corrosion cracking behaviour of 7075 (Al-Zn-Mg-Cu) alloy have been studied in a salt spray fog chamber with two vapourised aqueous solutions (0 and 5% NaCl). The paper analyses the stress corrosion resistance of 7075 aluminium alloy with several precipitation-ageing heat treatments. The results are compared with that obtained in 3.5% NaCl aqueous solution at 20 C. The salt spray fog testing has permitted a good evaluation of SCC susceptibility in 7075 alloy. All temper conditions studied were susceptible to SCC in the different environments tested. 7075-T6 temper was the most susceptible, while in all the cases studied 7075-T73 temper was the least susceptible. Compared to 7075-T6, 7075-RRA temper improved the resistance against the SCC process, but the mechanical properties obtained were lower. (Abstract Copyright [2010], Wiley Periodicals, Inc.)

  17. Study on stress intensity factors for crack on involute spur gear tooth

    Jian Cai


    Full Text Available Investigating the stress intensity factors has a great importance to predict the fatigue damage for the involute spur gears. The aim of this article is to reveal the variation laws of stress intensity factors for crack on the involute spur gear tooth. For this purpose, a three-dimensional finite element model for calculating the stress intensity factors of the involute spur gear containing a surface crack is established using the finite element code ABAQUS. Based on the established three-dimensional finite element model, the influences of several parameters, such as torque, friction coefficient, crack depth, crack initial location, and crack size, on mode I, mode II, and mode III stress intensity factors are investigated numerically. The results of the study provide valuable guidelines for enhanced understanding of stress intensity factors for the crack on the involute spur gear tooth.

  18. The Effect of Water on Crack Interaction

    Gaede, O.; Regenauer-Lieb, K.


    While the mechanical coupling between pore fluid and solid phase is relatively well understood, quantitative studies dealing with chemical-mechanical weakening in geological materials are rare. Many classical poroelastic problems can be addressed with the simple law of effective stress. Experimental studies show that the presence of a chemically active fluid can have effects that exceed the predictions of the law of effective stress. These chemical fluid-rock interactions alter the mechanical properties of the solid phase. Especially chemical-mechanical weakening has important ramifications for many areas of applied geosciences ranging from nuclear waste disposal over reservoir enhancement to fault stability. In this study, we model chemically induced changes of the size of the process zone around a crack tip. The knowledge of the process zone size is used to extend existing effective medium approximations of cracked solids. The stress distribution around a crack leads to a chemical potential gradient. This gradient will be a driver for mass diffusion through the solid phase. As an example, mass diffusion is towards the crack tip for a mode I crack. In this case a chemical reaction, that weakens the solid phase, will increase the size of the process zone around the crack tip. We apply our model to the prominent hydrolytic weakening effect observed in the quartz-water system (Griggs and Blacic, 1965). Hydrolytic weakening is generally attributed to water hydrolyzing the strong Si-O bonds of the quartz crystal. The hydrolysis replaces a Si-O-Si bridge with a relatively weak hydrogen bridge between two silanol groups. This enhances dislocation mobility and hence the yield stress is reduced. The plastic process zone around a crack tip is therefore larger in a wet crystal than in a dry crystal. We calculate the size of the process zone by solving this coupled mechanical-chemical problem with the Finite Element code ABAQUS. We consider single crack, collinear crack and

  19. A surface crack in shells under mixed-mode loading conditions

    Joseph, P. F.; Erdogan, F.


    The present consideration of a shallow shell's surface crack under general loading conditions notes that while the mode I state can be separated, modes II and III remain coupled. A line spring model is developed to formulate the part-through crack problem under mixed-mode conditions, and then to consider a shallow shell of arbitrary curvature having a part-through crack located on the outer or the inner surface of the shell; Reissner's transverse shear theory is used to formulate the problem under the assumption that the shell is subjected to all five moment and stress resultants.

  20. Characterization of cracking in Strain-Hardening Cementitious Composites using the compact tension test

    Pereira, Eduardo B.; Fischer, Gregor; Barros, Joaquim A. O.

    The characterization of the tensile behavior of strain hardening cementitious composites (SHCC) is of significant importance to the material design. In a previous work the tensile stress-crack opening response of different types of SHCC was characterized using notched specimens tested in direct...... plate specimens and the eccentrically applied tensile load create the local conditions necessary to the initiation of a single crack at the tip of the notch. Further propagation and opening of the crack in Mode I allow the assessment of the tensile load-displacement relationship. The experimental...

  1. Crack growth resistance for anisotropic plasticity with non-normality effects

    Tvergaard, Viggo; Legarth, Brian Nyvang


    For a plastically anisotropic solid a plasticity model using a plastic flow rule with non-normality is applied to predict crack growth. The fracture process is modelled in terms of a traction–separation law specified on the crack plane. A phenomenological elastic–viscoplastic material model...... is applied, using one of two different anisotropic yield criteria to account for the plastic anisotropy, and in each case the effect of the normality flow rule is compared with the effect of non-normality. Conditions of small scale yielding are assumed, with mode I loading conditions far from the crack...

  2. Gear Crack Propagation Investigation


    Reduced weight is a major design goal in aircraft power transmissions. Some gear designs incorporate thin rims to help meet this goal. Thin rims, however, may lead to bending fatigue cracks. These cracks may propagate through a gear tooth or into the gear rim. A crack that propagates through a tooth would probably not be catastrophic, and ample warning of a failure could be possible. On the other hand, a crack that propagates through the rim would be catastrophic. Such cracks could lead to disengagement of a rotor or propeller from an engine, loss of an aircraft, and fatalities. To help create and validate tools for the gear designer, the NASA Lewis Research Center performed in-house analytical and experimental studies to investigate the effect of rim thickness on gear-tooth crack propagation. Our goal was to determine whether cracks grew through gear teeth (benign failure mode) or through gear rims (catastrophic failure mode) for various rim thicknesses. In addition, we investigated the effect of rim thickness on crack propagation life. A finite-element-based computer program simulated gear-tooth crack propagation. The analysis used principles of linear elastic fracture mechanics, and quarter-point, triangular elements were used at the crack tip to represent the stress singularity. The program had an automated crack propagation option in which cracks were grown numerically via an automated remeshing scheme. Crack-tip stress-intensity factors were estimated to determine crack-propagation direction. Also, various fatigue crack growth models were used to estimate crack-propagation life. Experiments were performed in Lewis' Spur Gear Fatigue Rig to validate predicted crack propagation results. Gears with various backup ratios were tested to validate crack-path predictions. Also, test gears were installed with special crack-propagation gages in the tooth fillet region to measure bending-fatigue crack growth. From both predictions and tests, gears with backup ratios

  3. Determination of the size dependence of the energy release rate for mode I loaded DCB specimens

    Svenninggaard, Jon


    Large scale bridging in delamination of fiber reinforced composites is an important mechanism that is important to understand. In for example wind turbine blade design, this is of great importance as cracks may propagate from resin filled areas, wrinkles, air bubbles or manufacturing defects...

  4. Analyzing crack-tip dislocations and their shielding effect on fracture toughness

    Higashida, K. [Department of Materials Science and Engineering, Kyushu University, 744 Motooka, Fukuoka 819-0395 (Japan)], E-mail:; Tanaka, M. [Department of Materials Science and Engineering, Kyushu University, 744 Motooka, Fukuoka 819-0395 (Japan); Hartmaier, A. [Department of Materials Science and Engineering, University Erlangen-Nuernberg, Martensstrasse 5, 91058 Erlangen (Germany); Hoshino, Y. [Department of Materials Science and Engineering, Kyushu University, 744 Motooka, Fukuoka 819-0395 (Japan)


    With the aim of experimental clarification of the interaction between a crack and dislocations, crack-tip dislocations in two kinds of plastic zones in silicon crystals were directly observed by high-voltage electron microscopy to analyse by their detail characterisation. Three-dimensional analysis on crack-dislocation interaction revealed that they were shielding type dislocations in both 45 deg.-shear-type and hinge-type plastic zones, which accommodate mainly mode I stress intensity at the crack tip. The crack-tip shielding fields due to dislocations also have been visualised by photoelasticity. In specimens without pre-deformation, photoelastic images due to the mode I crack-tip field were observed when an external load was applied at room temperature. In specimens pre-deformed at high temperatures, photoelastic images corresponding to the dislocation shielding were observed. The shielding field has an effect of accommodating the tensile stress concentration due to the applied load, which increases the critical stress intensity factor for crack extension.

  5. Fatigue crack growth retardation in spot heated mild steel sheet

    B B Verma; P K Ray


    A fatigue crack can be effectively retarded by heating a spot near the crack tip under nil remote stress condition. The subcritical spot heating at a proper position modifies the crack growth behaviour in a way, more or less, similar to specimen subjected to overload spike. It is observed that the extent of crack growth retardation increases with increasing level of overload as well as with increasing spot temperature. It is also observed that modification in crack growth behaviour is a function of location of heating spot and maximum retardation is observed at + 5 position.

  6. Uncertainty Quantification in Fatigue Crack Growth Prognosis

    Shankar Sankararaman


    Full Text Available This paper presents a methodology to quantify the uncertainty in fatigue crack growth prognosis, applied to structures with complicated geometry and subjected to variable amplitude multi-axial loading. Finite element analysis is used to address the complicated geometry and calculate the stress intensity factors. Multi-modal stress intensity factors due to multi-axial loading are combined to calculate an equivalent stress intensity factor using a characteristic plane approach. Crack growth under variable amplitude loading is modeled using a modified Paris law that includes retardation effects. During cycle-by-cycle integration of the crack growth law, a Gaussian process surrogate model is used to replace the expensive finite element analysis. The effect of different types of uncertainty – physical variability, data uncertainty and modeling errors – on crack growth prediction is investigated. The various sources of uncertainty include, but not limited to, variability in loading conditions, material parameters, experimental data, model uncertainty, etc. Three different types of modeling errors – crack growth model error, discretization error and surrogate model error – are included in analysis. The different types of uncertainty are incorporated into the crack growth prediction methodology to predict the probability distribution of crack size as a function of number of load cycles. The proposed method is illustrated using an application problem, surface cracking in a cylindrical structure.

  7. Analysis of SBS Modified Bitumen Waterproofing Membrane Cracking and Quality Control%浅析屋面 SBS 改性沥青防水卷材开裂及质量控制



    SBS modified bitumen waterproofing membrane cra-cking was widely used in the roof, toilet water proof. Because the product quality of their own and human operator improper proc-es, which make serious problem of leaks between the roof and th-e toilet with the bathroom. The article analysis it’s performance and the Construction points in the process, and puts forward so-me treatment methods%  SBS 改性沥青防水卷材在屋面、卫生间防水中被广泛采用,但由于产品的自身质量原因和在人为操作过程中的不当,使屋面及厕浴间渗漏等问题突出。本文通过对 SBS改性沥青防水卷材的性能、使用过程中施工的要点进行了分析,并提出了一些处理方法。


    Istadi Istadi


    Full Text Available The plastic waste utilization can be addressed toward different valuable products. A promising technology for the utilization is by converting it to fuels. Simultaneous modeling and optimization representing effect of reactor temperature, catalyst calcinations temperature, and plastic/catalyst weight ratio toward performance of liquid fuel production was studied over modified catalyst waste. The optimization was performed to find optimal operating conditions (reactor temperature, catalyst calcination temperature, and plastic/catalyst weight ratio that maximize the liquid fuel product. A Hybrid Artificial Neural Network-Genetic Algorithm (ANN-GA method was used for the modeling and optimization, respectively. The variable interaction between the reactor temperature, catalyst calcination temperature, as well as plastic/catalyst ratio is presented in surface plots. From the GC-MS characterization, the liquid fuels product was mainly composed of C4 to C13 hydrocarbons.KONVERSI LIMBAH PLASTIK MENJADI BAHAN BAKAR CAIR DENGAN METODE PERENGKAHAN KATALITIK MENGGUNAKAN KATALIS BEKAS YANG TERMODIFIKASI: PEMODELAN DAN OPTIMASI MENGGUNAKAN GABUNGAN METODE ARTIFICIAL NEURAL NETWORK DAN GENETIC ALGORITHM. Pemanfaatan limbah plastik dapat dilakukan untuk menghasilkan produk yang lebih bernilai tinggi. Salah satu teknologi yang menjanjikan adalah dengan mengkonversikannya menjadi bahan bakar. Permodelan, simulasi dan optimisasi simultan yang menggambarkan efek dari suhu reaktor, suhu kalsinasi katalis, dan rasio berat plastik/katalis terhadap kinerja produksi bahan bakar cair telah dipelajari menggunakan katalis bekas termodifikasi Optimisasi ini ditujukan untuk mencari kondisi operasi optimum (suhu reaktor, suhu kalsinasi katalis, dan rasio berat plastik/katalis yang memaksimalkan produk bahan bakar cair. Metode Hybrid Artificial Neural Network-Genetic Algorithm (ANN-GA telah digunakan untuk permodelan dan optimisasi simultan tersebut. Inetraksi antar variabel

  9. Photoelastic studies of crack propagation and crack arrest. [Homalite 100

    Irwin, G.R.; Dally, J.W.; Kobayashi, T.; Fourney, W.L.; Etheridge, J.M.


    This report describes the third year effort on research programs dealing with the characterization of dynamic aspects of fracture. The results included in this report are (1) verification of the BCL one-dimensional computer code; (2) determination of a-dot--K relationship from modified compact-tension specimen of Homalite 100; (3) verification of the MRL procedure for K/sub Ia/ measurement with machine-loaded C-DCB specimen of Homalite 100; (4) influence of adhesive toughness, adhesive thickness, and toughness of the arrest section on crack behavior in duplex specimens of both the M-CT and R-DCB types; (5) crack propagation in a thermally stressed ring specimen; and (6) development of a two-dimensional finite-difference code to predict fracture behavior in specimens of rectangular geometry under various a-dot vs K relationships. 118 figures, 53 tables.

  10. FEM simulation of a crack propagation in a round bar under combined tension and torsion fatigue loading



    Full Text Available An edge crack propagation in a steel bar of circular cross-section undergoing multiaxial fatigue loads is simulated by Finite Element Method (FEM. The variation of crack growth behaviour is studied under axial and combined in phase axial+torsional fatigue loading. Results show that the cyclic Mode III loading superimposed on the cyclic Mode I leads to a fatigue life reduction. Numerical calculations are performed using the FEM software ZENCRACK to determine the crack path and fatigue life. The FEM numerical predictions have been compared against corresponding experimental and numerical data, available from literature, getting satisfactory consistency.

  11. Stress corrosion-controlled rates of mode I fracture propagation in calcareous bedrock

    Voigtlaender, Anne; Leith, Kerry; Krautblatter, Michael


    Surface bedrock on natural rock slopes is subject to constant and cyclic environmental stresses (wind, water, wave, ice, seismic or gravitational). Studies indicate that these stresses range up to several hundred kPa, generally too low to cause macroscopic changes in intact rock, although clear evidence of fracture generation, crack propagation and weathering of bedrock illustrates the effect of environmental stresses at the Earth's surface. We suggest that material degradation and its extent, is likely to be controlled by the rate of stress corrosion cracking (SCC). Stress corrosion is a fluid-material reaction, where fluids preferentially react with strained atomic bonds at the tip of developing fractures. Stress corrosion in ferrous and siliceous materials is often accepted as the fracture propagation and degradation rate-controlling process where materials are subject to stresses and fluids. Although evidence for chemical weathering in propagating bedrock fractures is clear in natural environments, the physical system and quantification of stress corrosion in natural rocks is yet to be addressed. Here, we present preliminary data on the relationship between stresses at levels commonly present on natural rock slopes, and material damage resulting from stress corrosion under constant or cyclic tensile loading. We undertake single notch three-point bending tests (SNBT) on fresh calcareous bedrock specimens (1100x100x100mm) over a two-month period. Two beams containing an artificial notch are stressed to 75% of their ultimate strength, and a constant supply of weak acid is applied at the notch tip to enhance chemical reactions. A third, unloaded, beam is also exposed to weak acid in order to elucidate the contribution of stress corrosion cracking to the material degradation. Stresses at the tip of propagating cracks affect the kinetics of the chemical reaction in the specimen exposed to both loading and corrosion, leading to an increase in degradation, and greater

  12. Mode I Fracture Toughness of Rock - Intrinsic Property or Pressure-Dependent?

    Stoeckhert, F.; Brenne, S.; Molenda, M.; Alber, M.


    The mode I fracture toughness of rock is usually regarded as an intrinsic material parameter independent of pressure. However, most fracture toughness laboratory tests are conducted only at ambient pressure. To investigate fracture toughness of rock under elevated pressures, sleeve fracturing laboratory experiments were conducted with various rock types and a new numerical method was developed for the evaluation of these experiments. The sleeve fracturing experiments involve rock cores with central axial boreholes that are placed in a Hoek triaxial pressure cell to apply an isostatic confining pressure. A polymere tube is pressurized inside these hollow rock cylinders until they fail by tensile fracturing. Numerical simulations incorporating fracture mechanical models are used to obtain a relation between tensile fracture propagation and injection pressure. These simulations indicate that the magnitude of the injection pressure at specimen failure is only depending on the fracture toughness of the tested material, the specimen dimensions and the magnitude of external loading. The latter two are known parameters in the experiments. Thus, the fracture toughness can be calculated from the injection pressure recorded at specimen breakdown. All specimens had a borehole diameter to outer diameter ratio of about 1:10 with outer diameters of 40 and 62 mm. The length of the specimens was about two times the diameter. Maximum external loading was 7.5 MPa corresponding to maximum injection pressures at specimen breakdown of about 100 MPa. The sample set tested in this work includes Permian and Carboniferous sandstones, Jurassic limestones, Triassic marble, Permian volcanic rocks and Devonian slate from Central Europe. The fracture toughness values determined from the sleeve fracturing experiments without confinement using the new numerical method were found to be in good agreement with those from Chevron bend testing according to the ISRM suggested methods. At elevated

  13. Growth of inclined fatigue cracks using the biaxial CJP model

    G. Laboviciute


    Full Text Available The CJP model of crack tip stresses is a modified version of the Williams crack tip stress field which takes account of simplified stress distributions that arise from the presence of a zone of plastic deformation associated with the crack flanks and crack tip, and that act on the elastic field responsible for driving crack growth. The elastic stress field responsible for crack growth is therefore controlled by the applied loading and by the induced boundary stresses at the interface with the plastic zone. This meso-scale model of crack tip stresses leads to a modified set of crack tip stress intensity factors that include the resultant influence of plastic wake-induced crack tip shielding, and which therefore have the potential to help resolve some longstanding controversies associated with plasticity-induced closure. A full-field approach has now been developed for stress using photoelasticity and also for displacement using digital image correlation. This paper considers the characterisation of crack growth rate data with the biaxial CJP model, using compact tension specimens that contain inclined cracks at the notch tip with initial angles of 30°, 45° and 60° to the horizontal axis. Significant experimental difficulties are experienced in growing cracks in a biaxial field under uniaxial tensile loading, as the natural tendency of the crack is to turn so that it becomes perpendicular to the maximum principal stress direction. However, crack angle is not an issue in the CJP model which calculates the stress field parallel with, and perpendicular to, the crack plane. These stress components can be rotated into directions comparable with the usual KI and KII directions and used to calculate stress intensity parameters that should be directly comparable with the standard stress intensity formulations. Another difficulty arises, however, in finding published expressions for KI and KII for CT specimens with curved or kinked cracks. The CJP model

  14. Investigation of stress intensity factor for internal cracks in FG cylinders under static and dynamic loading

    Mahmoud Shariati


    Full Text Available his paper investigates the variations of mode I stress intensity factor (KI for inner penny-shaped and circumferential cracks in functionally graded solid and hollow thick walled cylinders, respectively with the changes of crack geometry, material gradation and loading conditions. The functionally graded material of cylinders consists of epoxy and glass. It is assumed that the mechanical properties vary with a power law in the radial direction of cylinders. Micromechanical models for conventional composites are used to estimate the material properties of functionally graded cylinders. The equations of motion obtained from the extended finite element discretization are solved by the Newmark method in the time domain. The interaction integral method is employed to calculate the mode I stress intensity factor (KI. The MATLAB programming environment was implemented to solve the problem.

  15. Composite interlaminar fracture toughness - Three-dimensional finite-element modeling for mixed mode I, II, and fracture

    Murthy, Pappu L. N.; Chamis, Christos C.


    A computational method/procedure is described which can be used to simulate individual and mixed mode interlaminar fracture progression in fiber composite laminates. Different combinations of Modes 1, 2, and 3 fracture are simulated by varying the crack location through the specimen thickness and by selecting appropriate unsymmetric laminate configurations. The contribution of each fracture mode to strain energy release rate is determined by the local crack closure methods while the mixed mode is determined by global variables. The strain energy release rates are plotted versus extending crack length, where slow crack growth, stable crack growth, and rapid crack growth regions are easily identified. Graphical results are presented to illustrate the effectiveness and versatility of the computational simulation for: (1) evaluating mixed-mode interlaminar fracture, (2) for identifying respective dominant parameters, and (3) for selecting possible simple test methods.

  16. Effect of Cyclic Loading on Cracking Behaviour of X-70 Pipeline Steel in Near-Neutral pH Solutions

    Hao GUO; Guangfu LI; Xun CAI; Ruipeng YANG; Wu YANG


    The cracking behaviour of X-70 pipeline steel in near-neutral pH solutions was studied under different modes of cyclic loading. The crack propagation process of X-70 pipeline steel under low frequency cyclic loading condition was controlled mainly by stress corrosion cracking (SCC) mechanism. Under mixed-mode cyclic loading, both higher tensile stress and shear stress made cracks easier to propagate. Applied cathodic potentials and high content of carbon dioxide in solutions also promoted the propagation of cracks. The propagation directions of cracks were different under different cyclic loading conditions. Under mode I (pure tensile stress) cyclic loading condition, cracks were straight and perpendicular to the tensile stress axis, while under mixed-mode Ⅰ/Ⅲ (tensile/shear stress) cyclic loading,cracks were sinuous and did not propagate in the direction perpendicular to the main tensile stress axis. Under the mixed-mode cyclic loading, cracks were much easier to propagate, suggesting that shear stress intensified the role of tensile stress. In addition, shear stress promoted the interaction between cracks, resulting in easier coalescence of cracks.

  17. Stress distribution and effective stress intensity factor of a blunt crack after dislocation emission


    The stress fields induced by a dislocation and its image dislocations around a narrow elliptic void are formulated. Based on the solution, the stress distribution and effective stress intensity factor of a blunt (elliptic) crack were calculated under mode I constant loading. The results show that a dislocation-free zone (DFZ) is formed after dislocation emission. There exists a second stress peak in the DFZ except a stress peak at the blunt crack tip. With an increase in the applied stress intensity factor KIa or the friction stress τf of the material, the DFZ size and the peak stress at the crack tip decrease, but the peak stress in the DFZ and the effective stress intensity factor KIf presiding at the crack tip increase. Because of dislocation shielding effects, shielding ratio KIa/KIf increases with increasing KIa}, but it decreases with increasing τf.

  18. Stress distribution and effective stress intensity factor of a blunt crack after dislocation emission

    钱才富; 乔利杰; 褚武扬


    The stress fields induced by a dislocation and its image dislocations around a narrow elliptic void are formulated. Based on the solution, the stress distribution and effective stress intensity factor of a blunt (elliptic) crack were calculated under mode I constant loading. The results show that a dislocation-free zone (DFZ) is formed after dislocation emission. There exists a second stress peak in the DFZ except a stress peak at the blunt crack tip. With an increase in the applied stress intensity factor Kla or the friction stress T, of the material, the DFZ size and the peak stress at the crack tip decrease, but the peak stress in the DFZ and the effective stress intensity factor Klf presiding at the crack tip increase. Because of dislocation shielding effects, shielding ratio Kla/Klf increases with increasing Kla, but it decreases with increasing Tf.

  19. Fatigue crack growth prediction in 2xxx AA with friction stir weld HAZ properties

    A. Tzamtzis


    Full Text Available An analytical model is developed to predict fatigue crack propagation rate under mode I loading in 2024 aluminum alloy with FSW HAZ material characteristics. Simulation of the HAZ local properties in parent 2024 AA was performed with overaging using specific heat treatment conditions. The model considers local cyclic hardening behavior in the HAZ to analyze crack growth. For the evaluation of the model, the analytical results have been compared with experimental fatigue crack growth on overaged 2024 alloy simulating material behavior at different positions within the HAZ. The analytical results showed that cyclic hardening at the crack tip can be used successfully with the model to predict FCG in a material at overaged condition associated with a location in the FSW HAZ.

  20. Effect of band-overload on fatigue crack growth rate of HSLA steel

    Abhinay, S. V.; Tenduwe, Om Prakash; Kumar, Ajit; Dutta, K.; Verma, B. B.; Ray, P. K.


    Fatigue crack growth behavior is important parameter of structural materials. This parameters can be used to predict their life, service reliability and operational safety in different conditions. The material used in this investigation is an HSLA steel. In this investigation effect of single overload and band-overload on fatigue crack growth of same steel are studied using compact tension (CT) specimens under mode-I condition and R=0.3. It is observed that overload and band-overload applications resulted retardation on the fatigue crack growth rate in most of the cases. It is also noticed that maximum retardation took place on application of seven successive overload cycles. Application of ten and more overload cycles caused no crack growth retardation.

  1. Comparison of optical and acoustical monitoring during a crack propagation, implication for slow earthquake dynamics

    Lengliné, Olivier; Schmittbuhl, Jean; Elkhoury, Jean; Toussaint, Renaud; Daniel, Guillaume; Maloy, Knut Jurgen


    Observations of aseismic transients in several tectonic context suggest that they might be linked to seismicity. However a clear observation and description of these phenomena and their interaction is lacking. This owes to the difficulty of characterizing with a sufficient resolution processes taking place at depth. Here we aim to study these interactions between aseismic and seismic slip taking advantage of an unique experimental setup. We conducted a series of mode I crack propagation experiments on transparent materials (PMMA). The crack advance is trapped in a weakness plane which is the interface between two previously sandblasted and annealed plexiglass plates. A fast video camera taking up to 500 frames per second ensures the tracking of the front rupture. The acoustic system is composed of a maximum of 44 channels continuously recording at 5 MHz for a few tens of seconds. Piezo-electric sensors are composed of a 32 elements linear array and individual sensors surrounding the crack front. An automatic detection and localization procedure allows us to obtain the position of acoustic emission (A.E.) that occurred during the crack advance. Crack front image processing reveals an intermittent opening which might be linked to the time and space clustering of the AE. An analogy between the mode I (opening) and the mode III (antiplane slip) allows us to interpret our results in term of slip on faults. Our experiment thus helps to reveal the interplay between seismic and aseismic slip on faults.


    XIA Song; WANG Tzuchiang; CHEN Shaoha


    The mode I plane strain crack tip field with strain gradient effects is presented in this paper based on a simplified strain gradient theory within the framework proposed by Acharya and Bassani. The theory retains the essential structure of the incremental version of the conventional J2 deformation theory. No higher-order stress is introduced and no extra boundary value conditions beyond the conventional ones are required. The strain gradient effects are considered in the constitutive relation only through the instantaneous tangent modulus. The strain gradient measures are included into the tangent modulus as internal parameters. Therefore the boundary value problem is the same as that in the conventional theory. Two typical crack problems are studied: (a) the crack tip field under the small scale yielding condition induced by a linear elastic mode-I K-field and (b) the complete field for a compact tension specimen. The calculated results clearly show that the stress level near the crack tip with strain gradient effects is considerable higher than that in the classical theory. The singularity of the strain field near the crack tip is nearly equal to the square-root singularity and the singularity of the stress field is slightly greater than it. Consequently, the J-integral is no longer path independent and increases monotonically as the radius of the calculated circular contour decreases.

  3. Cracking characteristics of dust-containing tar over modified dolomite catalyst%含尘焦油在改性白云石催化剂上的裂解特性


    A Ni-dolomite catalyst with promoter Lanthanum was prepared by kneading method. The catalyst was used for the cracking reaction of tar model compound containing N-dodecane, cyclohexane, toluene and methylnaphthalene in an atmospheric fixed reactor. The effects of temperature, space velocity and the ratio of water and ingredient on the yield of gas products were examined. The stability test and reaction-regeneration experiments were conducted. Moreover, cracking characteristics of dust-containing tar over the catalyst and dust deposition mechanism were investigated. The results show that the optimum operating condition for the catalyst is reaction temperature 800 ℃, space velocity 300 h-1 , the ratio of water to ingredient 5 :1 . The optimum regeneration condition is 700 ℃ and 1 h. XRD results show that MgO-NiO solid solution and La ( NiO3 ) crystalline phase are converted in the modified dolomite catalyst. Different dust species depositing on the catalyst surface have different influences on the catalytic activity. CaO can improve the catalytic activity. The deposition of Fe2 O3 can convert into a new crystalline phase NiFe2 O4 . SiO2 plays a promoting role in carbon deposition, which can significantly inhibit the catalytic activity.%采用混捏法制备了一种添加助剂La的Ni-白云石催化剂。在常压固定床反应器中,以正十二烷、环己烷、甲苯和甲基萘的混合物作为焦油模型化合物,进行焦油裂解特性研究。考察了温度、空速、水料比等条件对气相产物产率的影响,对该催化剂进行了稳定性和再生性评价,在此基础上探讨了粉尘在催化剂表面沉积对催化剂性能影响的作用及机理。结果表明,该催化剂的最佳操作条件为反应温度800℃、空速300 h-1、水料比5:1、再生温度700℃、再生时间1 h。 XRD表征结果表明,改性白云石催化剂中形成了MgO-NiO固溶体和La( NiO3)晶相。粉尘中的不同组分对催化剂性能的影响

  4. Crack layer theory

    Chudnovsky, A.


    A damage parameter is introduced in addition to conventional parameters of continuum mechanics and consider a crack surrounded by an array of microdefects within the continuum mechanics framework. A system consisting of the main crack and surrounding damage is called crack layer (CL). Crack layer propagation is an irreversible process. The general framework of the thermodynamics of irreversible processes are employed to identify the driving forces (causes) and to derive the constitutive equation of CL propagation, that is, the relationship between the rates of the crack growth and damage dissemination from one side and the conjugated thermodynamic forces from another. The proposed law of CL propagation is in good agreement with the experimental data on fatigue CL propagation in various materials. The theory also elaborates material toughness characterization.


    LouLullang; ZengPan


    A meshless method integrated with linear elastic fracture mechanics (LEFM) is presented for 2D mixed-mode crack propagation analysis. The domain is divided automatically into sub-domains based on Voronoi cells, which are used for quadrature for the potential energy. The continuous crack propagation is simulated with an incremental crack-extension method which assumes a piecewise linear discretization of the unknown crack path. For each increment of the crack extension, the meshless method is applied to carry out a stress analysis of the cracked structure. The J-integral, which can be decomposed into mode I and mode II for mixed-mode crack, is used for the evaluation of the stress intensity factors (SIFs). The crack-propagation direction, predicted on an incremental basis, is computed by a criterion defined in terms of the SIFs. The flowchart of the proposed procedure is presented and two numerical problems are analyzed with this method. The meshless results agree well with the experimental ones, which validates the accuracy and efficiency of the method.

  6. Standard test method for determination of resistance to stable crack extension under low-constraint conditions

    American Society for Testing and Materials. Philadelphia


    1.1 This standard covers the determination of the resistance to stable crack extension in metallic materials in terms of the critical crack-tip-opening angle (CTOAc), ψc and/or the crack-opening displacement (COD), δ5 resistance curve (1). This method applies specifically to fatigue pre-cracked specimens that exhibit low constraint (crack-length-to-thickness and un-cracked ligament-to-thickness ratios greater than or equal to 4) and that are tested under slowly increasing remote applied displacement. The recommended specimens are the compact-tension, C(T), and middle-crack-tension, M(T), specimens. The fracture resistance determined in accordance with this standard is measured as ψc (critical CTOA value) and/or δ5 (critical COD resistance curve) as a function of crack extension. Both fracture resistance parameters are characterized using either a single-specimen or multiple-specimen procedures. These fracture quantities are determined under the opening mode (Mode I) of loading. Influences of environment a...

  7. Quasi-static crack tip fields in rate-sensitive FCC single crystals

    P Biswas; R Narasimhan


    In this work, the effects of loading rate, material rate sensitivity and constraint level on quasi-static crack tip fields in a FCC single crystal are studied. Finite element simulations are performed within a mode I, plane strain modified boundary layer framework by prescribing the two term $(K −T)$ elastic crack tip field as remote boundary conditions. The material is assumed to obey a rate-dependent crystal plasticity theory. The orientation of the single crystal is chosen so that the crack surface coincides with the crystallographic (010) plane and the crack front lies along $[10\\bar{1}]$ direction. Solutions corresponding to different stress intensity rates $\\dot{K}$, -stress values and strain rate exponents are obtained. The results show that the stress levels ahead of the crack tip increase with $\\dot{K}$ which is accompanied by gradual shrinking of the plastic zone size. However, the nature of the shear band patterns around the crack tip is not affected by the loading rate. Further, it is found that while positive -stress enhances the opening and hydrostatic stress levels ahead of crack tip, they are considerably reduced with imposition of negative -stress. Also, negative -stress promotes formation of shear bands in the forward sector ahead of the crack tip and suppresses them behind the tip.

  8. Effect of crack propagation on crack tip fields

    F.V. Antunes


    Full Text Available Crack closure influences fatigue crack growth rate and must be included in the design of components. Plasticity induced crack closure is intimately linked with the crack tip plastic deformation, which becomes residual as the crack propagates. The objective here is to study numerically the effect of crack propagation on crack tip fields. The transient effect observed at the beginning of crack propagation is linked to the hardening behavior of material. The effect of mesh refinement is studied, and a singular behavior is evident, which is explained by the sharp crack associated with mesh topology, composed of a regular pattern of square elements. The plastic zone size measured perpendicularly to crack flank in the residual plastic wake is quantified and compared with literature models. Finally, the removal of material at the first node behind crack tip with load cycling was observed for plane strain state and some hardening models in plane stress state.

  9. Effects of gamma ray and sub-cracks on ethanol-assisted crack healing in poly(methyl methacrylate)

    Lin, P.Y.; Lin, Y.T. [Department of Materials Science and Engineering, National Tsing Hua University, Hsinchu 300, Taiwan (China); Yang, Fuqian [Department of Chemical and Materials Engineering, University of Kentucky, Lexington KY 40506 (United States); Lee, Sanboh, E-mail: [Department of Materials Science and Engineering, National Tsing Hua University, Hsinchu 300, Taiwan (China)


    The effects of gamma ray and sub-cracks on ethanol-assisted crack healing in poly(methyl methacrylate) (PMMA) were investigated. The transport of ethanol in the gamma-irradiated PMMA was analyzed, using the Harmon model. Both the cracked-gamma-irradiated PMMA and the cracked PMMA with sub-cracks were ethanol-treated at a temperature above the effective glass transition point of the corresponding bulk PMMA. The crack closure rate, which followed the modified Arrhenius equation, increased with increasing gamma ray dose at a given temperature. The fracture strength of the healed PMMA increased with increasing gamma ray dose for short healing time at a given healing temperature, while long healing time led to the decrease of the fracture strength of the healed PMMA with increasing gamma ray dose. The fracture strength of the healed PMMA increased with increasing number of sub-cracks. These results provide the potential to develop self-healing polymeric materials in which structural damage can activate an autonomous healing process without any external stimuli. - Highlights: • The process of sorption and desorption of ethanol in PMMA can heal crack. • Crack closure rate is controlled by Case I diffusion in gamma-irradiated PMMA. • Mechanical strength versus healing time follows the power law with exponent 1/4. • Gamma irradiation degrades solvent healing while sub-cracks enhance.

  10. Small-crack test methods

    Larsen, James M.; Allison, John E.

    This book contains chapters on fracture mechanics parameters for small fatigue cracks, monitoring small-crack growth by the replication method, measurement of small cracks by photomicroscopy (experiments and analysis), and experimental mechanics of microcracks. Other topics discussed are the real-time measurement of small-crack-opening behavior using an interferometric strain/displacement gage; direct current electrical potential measurement of the growth of small cracks; an ultrasonic method for the measurement of the size and opening behavior of small fatigue cracks; and the simulation of short crack and other low closure loading conditions, utilizing constant K(max) Delta-K-decreasing fatigue crack growth procedures.

  11. Effect of graded interlayer on the mode I edge delamination by residual stresses in multilayer coating-based systems

    Zhang, X. C.; Xu, B. S.; Wang, H. D.; Wu, Y. X.


    The mode I edge delamination could be initiated due to the presence of the interfacial peeling stresses near the edges of the multilayered systems due to the material mismatches between the adjacent layers. However, the exact peeling stress distributions could not be obtained by using the existing analytical and numerical models. It was proposed recently that the peeling moment resulting from the localized peeling stresses could be used to characterize mode I edge delamination. In this paper, the effect of the graded interlayer on the mode I edge delamination by thermal residual stresses in multilayer coating-based systems was investigated. Following the previous analysis approaches, the exact closed-form solutions for the peeling moments at individual interfaces and the curvatures for bilayer system, typical thermal barrier coating (TBC) system and TBC-based system with a graded interlayer inserted between the metallic layer and the ceramic layer were, respectively, derived. Case studies showed that the edge delamination by thermal stress could be impeded by properly selecting the coating materials and individual layer thicknesses. These studies may provide some important insights for developing fail-safe designing methodologies for multilayered systems.

  12. Effect of crack surface geometry on fatigue crack closure

    Drury, W.J. [P and L Technologies, Inc., Atlanta, GA (United States); Gokhale, A.M. [Georgia Inst. of Tech., Atlanta, GA (United States). School of Materials Science and Engineering; Antolovich, S.D. [Washington State Univ., Pullman, WA (United States). School of Mechanical and Materials Engineering


    The geometry of crack faces often plays a critical role in reducing crack extension forces when crack closure occurs during fatigue crack growth. Most previous studies of fatigue crack closure are concerned with mechanical measure of closure as related to the crack growth rate; very little attention has been given to the geometry of the crack surfaces. The objective is to identify those aspects of crack surface geometry that are important in the closure process, to develop quantitative fractographic techniques to estimate such attributes in a statistically significant and robust manner, and to correlate them to the physical process of crack closure. For this purpose, fatigue crack propagation experiments were performed on a Ni-base superalloy and crack growth rates and crack closure loads were measured. Digital image profilometry and software-based analysis techniques were used for statistically reliable and detailed quantitative characterization of fatigue crack profiles. It is shown that the dimensionless, scale-independent attributes, such a height-to-width ratio of asperities, fractal dimensions, dimensionless roughness parameters, etc., do not represent the aspects of crack geometry that are of primary importance in the crack closure phenomena. Furthermore, it is shown that the scale-dependent characteristics, such as average asperity height, do represent the aspects of crack geometry that play an interactive role in the closure process. These observations have implications concerning the validity of geometry-dependent, closure-based models for fatigue crack growth.

  13. Quantity effect of radial cracks on the cracking propagation behavior and the crack morphology.

    Jingjing Chen

    Full Text Available In this letter, the quantity effect of radial cracks on the cracking propagation behavior as well as the circular crack generation on the impacted glass plate within the sandwiched glass sheets are experimentally investigated via high-speed photography system. Results show that the radial crack velocity on the backing glass layer decreases with the crack number under the same impact conditions during large quantities of repeated experiments. Thus, the "energy conversion factor" is suggested to elucidate the physical relation between the cracking number and the crack propagation speed. Besides, the number of radial crack also takes the determinative effect in the crack morphology of the impacted glass plate. This study may shed lights on understanding the cracking and propagation mechanism in laminated glass structures and provide useful tool to explore the impact information on the cracking debris.

  14. Engineering the crack path by controlling the microstructure

    Srivastava, A.; Osovski, S.; Needleman, A.


    We explore the possibility of engineering the crack path by controlling a material's microstructure in order to increase its crack growth resistance. Attention is confined to a specific type of microstructure that is encountered in a variety of structural metals and alloys - second phase particles distributed in a ductile matrix. The type of controlled microstructure modeled is characterized by various sinusoidal distributions of particles with fixed mean particle spacing. Three dimensional, finite deformation small scale yielding calculations of mode I crack growth are carried out for such controlled microstructures using an elastic-viscoplastic constitutive relation for a progressively cavitating solid. The results show that appropriately engineered sinusoidal distributions of particles can give fracture toughness values 2 to 3 times greater than a random distribution of particles with the same mean particle spacing. Tearing modulus values can be increased by a factor of 1.5 to 2. The greatest crack growth resistance generally occurs when the amplitude and the wavelength of the sinusoidal distribution are increased together. When the amplitude and the wavelength of the sinusoidal distribution do not increase together the crack can jump from one crest (or trough) to the next crest (or trough) which tends to reduce the crack growth resistance. Fracture surface roughness statistics are also calculated. In contrast to the essentially universal value for random distributions of particles, the value of the computed Hurst exponent is found to depend on the amplitude and the wavelength of the sinusoidal profile. A correlation is found between the computed fracture toughness values and values of characteristic length scales of the fracture surface roughness.

  15. Catalytic Cracking of C4 Olefins over P-Modified HZSM-5 Zeolite%P改性HZSM-5分子筛上C4烯烃裂解性能研究

    赵国良; 藤加伟; 金文清; 杨为民; 谢在库; 陈庆龄


    @@ Propylene is one of the most important basic organic products. The traditional method for producing propylene cannot satisfy the faster-growing demand for it. The new methods to produce propylene include the catalytic cracking of olefin-rich hydrocarbon feedstocks[1~3], which has higher selectivity.

  16. Environmental stress cracking of PVC and PVC-CPE - Part III Crack growth

    Breen, J.


    The fracture toughness of Polyvinylchloride (PVC) and PVC modified with 10% chlorinated polyethylene (PVC-CPE) was studied in vapour and in liquid environments by crack growth measurements on single-edge notch specimens under three-point bending at 23°C. In addition, some results obtained in air at

  17. Modelling of Corrosion Cracks

    Thoft-Christensen, Palle

    Modelling of corrosion cracking of reinforced concrete structures is complicated as a great number of uncertain factors are involved. To get a reliable modelling a physical and mechanical understanding of the process behind corrosion in needed.......Modelling of corrosion cracking of reinforced concrete structures is complicated as a great number of uncertain factors are involved. To get a reliable modelling a physical and mechanical understanding of the process behind corrosion in needed....

  18. The crack problem in a specially orthotropic shell with double curvature

    Delale, F.; Erdogan, F.


    The crack problem of a shallow shell with two nonzero curvatures is considered. It is assumed that the crack lies in one of the principal planes of curvature and the shell is under Mode I loading condition. The material is assumed to be specially orthotropic. After giving the general formulation of the problem the asymptotic behavior of the stress state around the crack tip is examined. The analysis is based on Reissner's transverse shear theory. Thus, as in the bending of cracked plates, the asymptotic results are shown to be consistent with that obtained from the plane elasticity solution of crack problems. Rather extensive numerical results are obtained which show the effect of material orthotropy on the stress intensity factors in cylindrical and spherical shells and in shells with double curvature. Other results include the stress intensity factors in isotropic toroidal shells with positive or negative curvature ratio, the distribution of the membrane stress resultant outside the crack, and the influence of the material orthotropy on the angular distribution of the stresses around the crack tip.

  19. The concept of the average stress in the fracture process zone for the search of the crack path

    Yu.G. Matvienko


    Full Text Available The concept of the average stress has been employed to propose the maximum average tangential stress (MATS criterion for predicting the direction of fracture angle. This criterion states that a crack grows when the maximum average tangential stress in the fracture process zone ahead of the crack tip reaches its critical value and the crack growth direction coincides with the direction of the maximum average tangential stress along a constant radius around the crack tip. The tangential stress is described by the singular and nonsingular (T-stress terms in the Williams series solution. To demonstrate the validity of the proposed MATS criterion, this criterion is directly applied to experiments reported in the literature for the mixed mode I/II crack growth behavior of Guiting limestone. The predicted directions of fracture angle are consistent with the experimental data. The concept of the average stress has been also employed to predict the surface crack path under rolling-sliding contact loading. The proposed model considers the size and orientation of the initial crack, normal and tangential loading due to rolling–sliding contact as well as the influence of fluid trapped inside the crack by a hydraulic pressure mechanism. The MATS criterion is directly applied to equivalent contact model for surface crack growth on a gear tooth flank.

  20. Analysis of mixed-mode fracture in concrete using interface elements and a cohesive crack model

    Víctor O García-Álvarez; Ravindra Gettu; Ignacio Carol


    The paper presents a model, based on nonlinear fracture mechanics, for analysing crack propagation in quasi-brittle materials, such as concrete. The work is limited to two-dimensions, and therefore, the fracture modes of interest are mode I (pure tension) and mode II (pure shear). The constitutive model has been implemented in the context of the finite element method using interface elements. The fracture is simulated through a discrete crack represented by the interface with a cohesive crack stress-separation relation derived from the model, which is based on a fracture criterion, together with a flow rule and a softening law. The model is used for simulating results from an experimental study on beams with centric and eccentric notches of high and normal strength concretes, and explaining other test results available in the literature.

  1. Stress induced martensite at the crack tip in NiTi alloys during fatigue loading

    E. Sgambitterra


    Full Text Available Crack tip stress-induced phase transformation mechanisms in nickel-titanium alloys (NiTi were analyzed by Digital Image Correlation (DIC, under fatigue loads. In particular, Single Edge Crack (SEC specimens, obtained from a commercial pseudoelastic NiTi sheet, and an ad-hoc experimental setup were used, for direct measurements of the near crack tip displacement field by the DIC technique. Furthermore, a fitting procedure was developed to calculate the mode I Stress Intensity Factor (SIF, starting from the measured displacement field. Finally, cyclic tensile tests were performed at different operating temperature, in the range 298-338 K, and the evolution of the SIF was studied, which revealed a marked temperature dependence.

  2. Sensitivity Analysis of Material Microstructure Effects on Predicted Crack Paths Using Finite Element Simulations

    Jacob, Anaïs; Mehmanparast, Ali


    The effects of microstructure, grain and grain boundary (GB) properties on predicted damage paths and indicative crack propagation direction have been examined for a polycrystalline material using mesoscale finite element simulations. Numerical analyses were carried out on a compact tension specimen geometry containing granular mesh structures with random grain shapes and sizes of average diameter 100μm. Nanoindentation tests were performed to investigate the dependency of mesoscale hardness measurements on the indentation location with respect to grain and GB regions. Finite element results have shown that under tensile loading conditions, the predicted damage paths are very sensitive to the granular mesh structure, GB properties and individual grain properties. Furthermore, finite element results have revealed that the cracking mode (i.e., transgranular/intergranular) and maximum crack deviation angle are strongly dependent on the material microstructures employed in simulations.

  3. Effect of a Local Reinforcement on the Stress Intensity Factor of a Cracked Plate

    JIANGCui-xiang; ZHA0Yao; LIUTu-guang


    Stress intensity factors are calculated for a cracked plate reinforced locally subject to mode I loading.The stiffeners are considered to have both longitudinal and transverse stiffness.There is no relative displacement between the plate and the stiffener.It is considered that the shear stresses are lumped at a finite number of locations,the result is obtained by summation.The influence of the stiffener location and the stiffener relative stiffness on cracked plate is included.The stress intensity factor depends on all these factors.Case study shows that the shear stress acting parallel to the stiffener gives more effect on the stress intensity factor than the shear stress acting perpendicular to the stiffener.To increase the relative stiffness of stiffener avails to reduce the stress intensity factor of the cracked plate.

  4. Nonlocal Peridynamic Modeling and Simulation on Crack Propagation in Concrete Structures

    Dan Huang


    Full Text Available An extended peridynamic approach for crack propagation analysis in concrete structures was proposed. In the peridynamic constitutive model, concrete material was described as a series of interacting particles, and the short-range repulsive force and anisotropic behavior of concrete were taken into account in the expression of the interactive bonding force, which was given in terms of classical elastic constants and peridynamic horizon. The damage of material was defined locally at the level of pairwise bond, and the critical stretch of material bond was described as a function of fracture strength in the classical concrete failure theory. The efficiency and accuracy of the proposed model and algorithms were validated by simulating the propagation of mode I and I-II mixed mode cracks in concrete slabs. Furthermore, crack propagation in a double-edge notched concrete beam subjected to four-point load was simulated, in which the experimental observations are captured naturally as a consequence of the solution.

  5. Experimental approach for mixed-mode fatigue delamination crack growth with large-scale bridging in polymer composites

    Holmes, John W.; Liu, Liu; Sørensen, Bent F.


    of delaminations in a typical fibre-reinforced polymer composite was investigated under a constant cyclic loading amplitude. Pure mode I, mode II and mixed-mode crack growth conditions were examined. The results, analysed using a J-integral approach, show that the double cantilever beam loaded with uneven bending......An experimental apparatus utilizing double cantilever beam specimens loaded with uneven bending moments was developed to study the mixed-mode fatigue crack growth in composites. The approach is suitable when large-scale bridging of cracks is present. To illustrate the testing method, cyclic growth...... crack growth rate observed. In addition to details concerning the equipment, a general discussion of the development of cyclic bridging laws for delamination growth in the presence of large-scale bridging is provided....

  6. The significance of crack-resistance curves to the mixed-mode fracture toughness of human cortical bone

    Zimmermann, Elizabeth A.; Launey, Maximilien E.; Ritchie, Robert O.


    The majority of fracture mechanics studies on the toughness of bone have been performed under tensile loading. However, it has recently been shown that the toughness of human cortical bone in the transverse (breaking) orientation is actually much lower in shear (mode II) than in tension (mode I); a fact that is physiologically relevant as in vivo bone is invariably loaded multiaxially. Since bone is a material that derives its fracture resistance primarily during crack growth through extrinsic toughening mechanisms, such as crack deflection and bridging, evaluation of its toughness is best achieved through measurements of the crack-resistance or R-curve, which describes the fracture toughness as a function of crack extension. Accordingly, in this study, we attempt to measure for the first time the R-curve fracture toughness of human cortical bone under physiologically relevant mixed-mode loading conditions. We show that the resulting mixed-mode (mode I + II) toughness depends strongly on the crack trajectory and is the result of the competition between the paths of maximum mechanical driving force and 'weakest' microstructural resistance.

  7. Finite Element Analysis of the Crack Propagation for Solid Materials

    Miloud Souiyah


    Full Text Available Problem statement: The use of fracture mechanics techniques in the assessment of performance and reliability of structure is on increase and the prediction of crack propagation in structure play important part. The finite element method is widely used for the evaluation of SIF for various types of crack configurations. Source code program of two-dimensional finite element model had been developed, to demonstrate the capability and its limitations, in predicting the crack propagation trajectory and the SIF values under linear elastic fracture analysis. Approach: Two different geometries were used on this finite element model in order, to analyze the reliability of this program on the crack propagation in linear and nonlinear elastic fracture mechanics. These geometries were namely; a rectangular plate with crack emanating from square-hole and Double Edge Notched Plate (DENT. Where, both geometries are in tensile loading and under mode I conditions. In addition, the source code program of this model was written by FORTRAN language. Therefore, a Displacement Extrapolation Technique (DET was employed particularly, to predict the crack propagations directions and to, calculate the Stress Intensity Factors (SIFs. Furthermore, the mesh for the finite elements was the unstructured type; generated using the advancing front method. And, the global h-type adaptive mesh was adopted based on the norm stress error estimator. While, the quarter-point singular elements were uniformly generated around the crack tip in the form of a rosette. Moreover, make a comparison between this current study with other relevant and published research study. Results: The application of the source code program of 2-D finite element model showed a significant result on linear elastic fracture mechanics. Based on the findings of the two different geometries from the current study, the result showed a good agreement. And, it seems like very close compare to the other published

  8. Multilayered piezomagnetic/piezoelectric composites with periodic interfacial cracks subject to in-plane loading

    Tian, Wenxiang; Zhong, Zheng; Li, Yaochen


    A two-dimensional fracture problem of periodically distributed interfacial cracks in multilayered piezomagnetic/piezoelectric composites is studied under in-plane magnetic or electric loading. The magnetic permittivity of the piezoelectric material and the dielectric constant of the piezomagnetic material are considered. A system of singular integral equations of the second kind with a Cauchy kernel is obtained by means of Fourier transform and further solved by using Jacobi polynomials. The problem is solved in the real domain by constructing real fundamental solutions. The primary interfacial fracture mechanic parameters, such as the stress intensity factors (SIFs), the electric displacement intensity factors (EDIFs), the magnetic induction intensity factors (MIIFs) and the energy release rates (ERRs) are then obtained. It is found that a magnetic or electric loading normal to the crack surfaces can lead to a mixture of mode I and mode II type stress singularities at the crack tips. Numerical results show that increasing the thickness of the active layer will favor the crack initiation. Inversely, increasing the thickness of the passive layer will retard the crack initiation. Furthermore, the results indicate that the crack initiation can be inhibited by adjusting the direction of the applied magnetic or electric loading.

  9. Strip-coalesced interior zone model for two unequal collinear cracks weakening piezoelectric media



    In this paper, a mathematical strip-saturation model is proposed for a poled transversely isotropic piezoelectric plate weakened by two impermeable unequal-collinear hairline straight cracks. Remotely applied in-plane unidirectional electromechanical loads open the cracks in mode-I such that the saturation zone developed at the interior tips of cracks gets coalesced. The developed saturation zones are arrested by distributing over their rims in-plane normal cohesive electrical displacement. The problem is solved using the Stroh formalism and the complex variable technique. The expressions are derived for the stress intensity factors (SIFs), the lengths of the saturation zones developed, the crack opening displacement (COD), and the energy release rate. An illustrative numerical case study is presented for the poled PZT-5H ceramic to investigate the effect of prescribed electromechanical loads on parameters affecting crack arrest. Also, the effect of different lengths of cracks on the SIFs and the local energy release rate (LERR) has been studied. The results obtained are graphically presented and analyzed.

  10. Coulomb traction on a penny-shaped crack in a three dimensional piezoelectric body

    Li, Qun; Kuna, Meinhard [TU Bergakademie Freiberg, Institute of Mechanics and Fluid Dynamics, Freiberg (Germany); Ricoeur, Andreas [University of Kassel, Institute of Mechanics, Kassel (Germany)


    The axisymmetric problem of a penny-shaped crack embedded in an infinite three-dimensional (3D) piezoelectric body is considered. A general formulation of Coulomb traction on the crack surfaces can be obtained based on thermodynamical considerations of electromechanical systems. Three-dimensional electroelastic solutions are derived by the classical complex potential theory when Coulomb traction is taken into account and the poling direction of piezoelectric body is perpendicular to the crack surfaces. Numerical results show that the magnitude of Coulomb tractions can be large, especially when a large electric field in connection with a small mechanical load is applied. Unlike the traditional traction-free crack model, Coulomb tractions induced by an applied electric field influence the Mode I stress intensity factor for a penny-shaped crack in 3D piezoelectric body. Moreover, compared to the current model, the traditional traction-free crack model always overestimates the effect of the applied electric load on the field intensity factors and energy release rates, which has consequences for 3D piezoelectric fracture mechanics. (orig.)

  11. Lifetime prediction for the subsurface crack propagation using three-dimensional dynamic FEA model

    Yin, Yuan; Chen, Yun-Xia; Liu, Le


    The subsurface crack propagation is one of the major interests for gear system research. The subsurface crack propagation lifetime is the number of cycles remaining for a spall to appear, which can be obtained through either stress intensity factor or accumulated plastic strain analysis. In this paper, the heavy loads are applied to the gear system. When choosing stress intensity factor, the high compressive stress suppresses Mode I stress intensities and severely reduces Mode II stress intensities in the heavily loaded lubricated contacts. Such that, the accumulated plastic strain is selected to calculate the subsurface crack propagation lifetime from the three-dimensional FEA model through ANSYS Workbench transient analysis. The three-dimensional gear FEA dynamic model with the subsurface crack is built through dividing the gears into several small elements. The calculation of the total cycles of the elements is proposed based on the time-varying accumulated plastic strain, which then will be used to calculate the subsurface crack propagation lifetime. During this process, the demonstration from a subsurface crack to a spall can be uncovered. In addition, different sizes of the elements around the subsurface crack are compared in this paper. The influences of the frictional coefficient and external torque on the crack propagation lifetime are also discussed. The results show that the lifetime of crack propagation decreases significantly when the external load T increasing from 100 N m to 150 N m. Given from the distributions of the accumulated plastic strain, the lifetime shares no significant difference when the frictional coefficient f ranging in 0.04-0.06.

  12. Determination of the Mode I Interlaminar Fracture Toughness by Using a Nonlinear Double-Cantilever Beam Specimen

    Pavelko, V.; Lapsa, K.; Pavlovskis, P.


    The aim of this study is estimation of the effect of large deflections of a double-cantilever beam (DCB) on the accuracy of determination of the mode I interlaminar fracture toughness GIc of layered composites by using the nonlinear theory of bending of beams. The differential equation of the deflection curve of arm of the DCB specimen in the natural form was used to analyze the strain energy of the specimen and its strain energy release rate GI upon propagation of delamination under the action of cleavage forces at the ends of cantilevers. An algorithm for calculating the strain energy and its release rate in the DCB specimens is realized in the form of a MATLAB code. An experimental study was carried out on DCB specimens of a highly flexible carbon/epoxy laminate. The validity of the nonlinear model developed is demonstrated. The standard methods used to determine GIc are refined for the case of highly flexible specimens.

  13. Mode I fracture toughness behavior of hydro-thermally aged carbon fibre reinforced DGEBA-HHPA-PES systems

    Alessi, Sabina; Pitarresi, Giuseppe; Spadaro, Giuseppe; Tumino, Davide


    In this work the Mode I fracture toughness behavior of unidirectional CFRP laminates is investigated by means of Double Cantilever Beam (DCB) tests. The composite samples were manufactured by thermal curing after impregnation of a Carbon fabric with a DGEBA epoxy and anhydride HHPA curing agent. One resin batch was also mixed with a PES thermoplastic monomer to enhance the matrix toughness. Two lots of samples, toughened and untoughened, were then left to soak in hot water to achieve various degrees of aging. The influence of matrix toughening and hydrothermal aging on the delamination behavior of the composite have then been assessed and correlated with characterization data from Dynamic Mechanical Thermal Analysis (DMTA) and Scanning Electron Microscopy (SEM).

  14. Tomato fruit continues growing while ripening, affecting cuticle properties and cracking.

    Domínguez, Eva; Fernández, María Dolores; Hernández, Juan Carlos López; Parra, Jerónimo Pérez; España, Laura; Heredia, Antonio; Cuartero, Jesús


    Fruit cuticle composition and their mechanical performance have a special role during ripening because internal pressure is no longer sustained by the degraded cell walls of the pericarp but is directly transmitted to epidermis and cuticle which could eventually crack. We have studied fruit growth, cuticle modifications and its biomechanics, and fruit cracking in tomato; tomato has been considered a model system for studying fleshy fruit growth and ripening. Tomato fruit cracking is a major disorder that causes severe economic losses and, in cherry tomato, crack appearance is limited to the ripening process. As environmental conditions play a crucial role in fruit growing, ripening and cracking, we grow two cherry tomato cultivars in four conditions of radiation and relative humidity (RH). High RH and low radiation decreased the amount of cuticle and cuticle components accumulated. No effect of RH in cuticle biomechanics was detected. However, cracked fruits had a significantly less deformable (lower maximum strain) cuticle than non-cracked fruits. A significant and continuous fruit growth from mature green to overripe has been detected with special displacement sensors. This growth rate varied among genotypes, with cracking-sensitive genotypes showing higher growth rates than cracking-resistant ones. Environmental conditions modified this growth rate during ripening, with higher growing rates under high RH and radiation. These conditions corresponded to those that favored fruit cracking. Fruit growth rate during ripening, probably sustained by an internal turgor pressure, is a key parameter in fruit cracking, because fruits that ripened detached from the vine did not crack.

  15. Combined effect of matrix cracking and stress-free edge on delamination

    Salpekar, S. A.; Obrien, T. K.


    The effect of the stress-free edge on the growth of local delaminations initiating from a matrix crack in (0 sub 2/90 sub 4) sub s and (+ or - 45.90 sub 4) sub s glass epoxy laminates is investigated using 3-D finite element analysis. The presence of high interlaminar normal stresses at the intersection (corner) of the matrix crack with the stress-free edge, suggests that a mode I delamination may initiate at the corners. The strain energy release rates (G) were calculated by modeling a uniform through-width delamination and two inclined delaminations at 10.6 deg and 45 deg to the matrix crack. All components of G have high values near the free edges. The mode I component of G is high at small delamination length and becomes zero for a delamination length of one-ply thickness. The total G values near the free edge agreed well with previously derived closed form solution. The quasi-3D solutions agreed well with the 3-D interior solutions.

  16. Crack elongation and its width of large depth reinforced concrete beams

    GUAN Jun-feng; ZHAO Shun-bo; HUANG Cheng-kui


    In order to meet the requirement of structural inspection,the crack spacing and crack width at various heights in the tensile zone of six large depth reinforced concrete beams were measured under several loading levels of serviceability state.The effects of the depth of normal section beams on the crack spacing and crack width were analyzed,and the modified model is proposed for calculating the average crack spacing by thinking about the depth of normal section,the reinforcement arrangement and the effective reinforcement ratio.The relationships of crack widths at any position in the tensile zone and at the reinforcement level on the side surface of beam were studied.By theoretical and statistical analysis,a method is proposed to calculate the ratios of crack widths between any position and the reinforcement level on the side surface of large depth reinforced concrete beams.

  17. Crack Growth Mechanisms under Anti-Plane Shear in Composite Laminates

    Horner, Allison Lynne

    The research conducted for this dissertation focuses on determining the mechanisms associated with crack growth in polymer matrix composite laminates subjected to anti-plane shear (mode III) loading. For mode III split-beam test methods were proposed, and initial evaluations were conducted. A single test method was selected for further evaluation. Using this test method, it was determined that the apparent mode III delamination toughness, GIIIc , depended on geometry, which indicated a true material property was not being measured. Transverse sectioning and optical microscopy revealed an array of transverse matrix cracks, or echelon cracks, oriented at approximately 45° and intersecting the plane of the delamination. Subsequent investigations found the echelon array formed prior to the onset of planar delamination advance and that growth of the planar delamination is always coupled to echelon array formation in these specimens. The evolution of the fracture surfaces formed by the echelon array and planar delamination were studied, and it was found that the development was similar to crack growth in homogenous materials subjected to mode III or mixed mode I-III loading, although the composite laminate architecture constrained the fracture surface development differently than homogenous materials. It was also found that, for split-beam specimens such as those used herein, applying an anti-plane shear load results in twisting of the specimen's uncracked region which gives rise to a mixed-mode I-III load condition. This twisting has been related to the apparent mode III toughness as well as the orientation of the transverse matrix cracks. A finite element model was then developed to study the mechanisms of initial echelon array formation. From this, it is shown that an echelon array will develop, but will become self-limiting prior to the onset of planar delamination growth.

  18. Fatigue Crack Topography.


    evaluating ciack initiation time and crack propagation, prgram I was used for performing the major fatigue test with the aircraft structure. In...advantage to begin with the end of the fracture, this is especially so in the case of the quantitative evaluation of striations. The overload fracture...Select the Measuring Line for Quantitative Evaluation Actually, the fatigue fracture should be inspected completely from the point of origin to the

  19. Cracking in desiccating soils

    Ledesma Alberto


    Soil shrinkage is produced typically under desiccating conditions. Eventually shrinkage may generate cracks in the soil mass, a phenomenon that is being studied by several researchers, because its prediction is far from being a routine in Soil Mechanics. Within this context, Unsaturated Soil Mechanics provides a promising framework to understand the mechanisms involved. In addition to that, physical modelling of desiccating soils constitutes a good tool to explore the nature of this problem. ...

  20. Utopia Cracks and Polygons


    MGS MOC Release No. MOC2-339, 23 April 2003This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows a pattern of polygonal cracks and aligned, elliptical pits in western Utopia Planitia. The picture covers an area about 3 km (about 1.9 mi) wide near 44.9oN, 274.7oW. Sunlight illuminates the scene from the left.

  1. STAC -- a new Swedish code for statistical analysis of cracks in SG-tubes

    Poern, K. [Poern Consulting, Nykoeping (Sweden)


    Steam generator (SG) tubes in pressurized water reactor plants are exposed to various types of degradation processes, among which stress corrosion cracking in particular has been observed. To be able to evaluate the safety importance of such cracking of SG-tubes one has to have a good and empirically founded knowledge about the scope and the size of the cracks as well as the rate of their continuous growth. The basis of experience is to a large extent constituted of the annually performed SG-inspections and crack sizing procedures. On the basis of this experience one can estimate the distribution of existing crack lengths, and modify this distribution with regard to maintenance (plugging) and the predicted rate of crack propagation. Finally, one can calculate the rupture probability of SG-tubes as a function of a given critical crack length. On account of the Swedish Nuclear Power Inspectorate an introductory study has been performed in order to get a survey of what has been done elsewhere in this field. The study resulted in a proposal of a computerizable model to be able to estimate the distribution of true cracks, to modify this distribution due to the crack growth and to compute the probability of tube rupture. The model has now been implemented in a compute code, called STAC (STatistical Analysis of Cracks). This paper is aimed to give a brief outline of the model to facilitate the understanding of the possibilities and limitations associated with the model.

  2. Crack Tip Parameters for Growing Cracks in Linear Viscoelastic Materials

    Brincker, Rune

    intensity factors. In the special case of a constant Poisson ratio only 2 deformation intensity factors are needed. Closed form solutions are given both for a slowly growing crack and for a crack that is suddenly arrested at a point at the crack extension path. Two examples are studied; a stress boundary...... value problem, and a displacement boundary value problem. The results show that the stress intensity factors and the displacement intensity factors do not depend explicitly upon the velocity of the crack tip....

  3. Self-healing of low-velocity impact and mode-I delamination damage in polymer composites via microchannels

    M. U. Saeed


    Full Text Available Microchannels embedded polymer composites were fabricated by resin infusion process using carbon fabric, epoxy resin and hollow glass tubes (HGTs. The effect of a range of low-velocity impact (LVI and mode-I delamination (M1D damage on the flexural strength of microchanneled carbon- epoxy composites was studied. A self-healing approach was also employed to recover their lost flexural strength due to these damages. Moreover, influence of LVI, M1D damage and healing on the failure behavior of microchanneled carbon- epoxy composites was also investigated. The results of flexural after impact (FAI and flexural after delamination (FAD showed that LVI has more deleterious effect on the flexural strength of carbon- epoxy composites than M1D damage. The loss in flexural strength increased linearly with increase in both impact (by higher impact energies and delamination damage (by longer delamination lengths. Scanning electron microscopic (SEM study revealed that self-healing agent (SHA, stored in HGTs placed within carbon- epoxy composites, effectively healed both LVI and M1D damage with excellent healing efficiencies.

  4. Finite deformation analysis of crack tip opening in elastic-plastic materials and implications for fracture initiation

    McMeeking, R M


    Analyses of the stress and strain fields around smoothly blunting crack tips in both non-hardening and hardening elastic-plastic materials, under contained plane strain yielding and subject to mode I opening loads, have been carried out by a finite element method suitably formulated to admit large geometry changes. The results include the crack tip shape and near-tip deformation field, and the crack tip opening displacement has been related to a parameter of the applied load, the J-integral. The hydrostatic stresses near the crack tip are limited due to the lack of constraint on the blunted tip, limiting achievable stress levels except in a very small region around the crack tip in power law hardening materials. The J-integral is found to be path independent except very close to the crack tip in the region affected by the blunted tip. Models for fracture are discussed in the light of these results including one based on the growth of voids. The rate of void growth near the tip in hardening materials seems to be little different from the rate in non-hardening materials when measured in terms of crack tip opening displacement, which leads to a prediction of higher toughness in hardening materials. It is suggested that improvement of this model would follow from better understanding of void-void and void-crack coalescence and void nucleation, and some criteria and models for these are discussed. The implications of the finite element results for fracture criteria based on critical stress, strain or both are discussed with respect to transition of fracture mode and the angle of initial crack growth. Localization of flow is discussed as a possible fracture model and as a model for void-crack coalescence.

  5. Cryptography cracking codes


    While cracking a code might seem like something few of us would encounter in our daily lives, it is actually far more prevalent than we may realize. Anyone who has had personal information taken because of a hacked email account can understand the need for cryptography and the importance of encryption-essentially the need to code information to keep it safe. This detailed volume examines the logic and science behind various ciphers, their real world uses, how codes can be broken, and the use of technology in this oft-overlooked field.

  6. Elastodynamic Stress Intensity Factor History for a Semi-infinite Crack Under Three-dimensional Transient Loading

    李湘平; 柳春图


    The dynamic stress intensity factor history for a semi-infinite crack in an otherwise unbounded elastic body is analyzed. The crack is subjected to a pair of suddenly-applied point loadings on its faces at a distance L away from the crack tip. The exact expression for the mode I stress intensity factor as a function of time is obtained. The method of solution is based on the direct application of integral transforms, the Wiener-Hopf technique and the Cagniard-de Hoop method. Due to the existence of the characteristic length in loading, this problem was long believed a knotty problem. Some features of the solutions are discussed and graphical result for numerical computation is presented.




    The plane elasticity theory of two-dimensional octagonal quasicrystals is developed in this paper. The plane elasticity problem of quasicrystals is reduced to a single higher-order partial differential equation by introducing a displacement function. As an example, the exact analytic solution of a Mode I Griffith crack in the material is obtained by using the Fourier transform and dual integral equations theory, then the displacement and stress fields, stress intensity factor and strain energy release rate can be calculated. The physical significance of the results relative to the phason and the difference between the mechanical behaviours of the crack problem in crystals and quasicrystals are figured out.These provide important information for studying the deformation and fracture of the new solid phase.

  8. Electroelastic Wave Scattering in a Cracked Dielectric Polymer under a Uniform Electric Field

    Shindo Yasuhide


    Full Text Available We investigate the scattering of plane harmonic compression and shear waves by a Griffith crack in an infinite isotropic dielectric polymer. The dielectric polymer is permeated by a uniform electric field normal to the crack face, and the incoming wave is applied in an arbitrary direction. By the use of Fourier transforms, we reduce the problem to that of solving two simultaneous dual integral equations. The solution of the dual integral equations is then expressed in terms of a pair of coupled Fredholm integral equations of the second kind having the kernel that is a finite integral. The dynamic stress intensity factor and energy release rate for mode I and mode II are computed for different wave frequencies and angles of incidence, and the influence of the electric field on the normalized values is displayed graphically.

  9. Strain gradient effects on steady state crack growth in rate-sensitive materials

    Nielsen, Kim Lau; Niordson, Christian Frithiof; Hutchinson, John W.


    Steady state crack propagation produce substantial plastic strain gradients near the tip, which are accompanied by a high density of geometrically necessary dislocations and additional local strain hardening. Here, the objective is to study these gradient effects on Mode I toughness...... of a homogeneous rate-sensitive metal, using a higher order plasticity theory. Throughout, emphasis is on the toughness rate-sensitivity, as a recent numerical study of a conventional material (no gradient effects) has indicated a significant influence of both strain rate hardening and crack tip velocity. Moreover......, a characteristic velocity, at which the toughness becomes independent of the rate-sensitivity, has been observed. It is the aim to bring forward a similar characteristic velocity for the current strain gradient visco-plastic model, as-well as to signify its use in future visco-plastic material modeling....

  10. Predictions of mixed mode interface crack growth using a cohesive zone model for ductile fracture

    Tvergaard, Viggo


    Special interface elements that account for ductile failure by the nucleation and growth of voids to coalescence are used to analyse crack growth. In these elements the stress component tangential to the interface is accounted for, as determined by the requirement of compatibility with the surrou......Special interface elements that account for ductile failure by the nucleation and growth of voids to coalescence are used to analyse crack growth. In these elements the stress component tangential to the interface is accounted for, as determined by the requirement of compatibility...... with the surrounding material in the tangential direction. Thus, the present interface description incorporates the important effect of stress triaxiality on damage evolution, which is not part of the usual cohesive zone models. The interface elements have been used previously for mode I loading conditions...... Elsevier Ltd. All rights reserved....

  11. Inclined crack problem in a rectangular slab of superconductor under an electromagnetic force

    Wang, Xin; Yong, Huadong; Xue, Cun; Zhou, Youhe


    In this paper, the critical state Bean model is employed to estimate the effect of the electromagnetic force on the fracture behavior of the superconductor slab. The superconductor slab with an inclined crack is subjected to an applied field. Based on the finite element method, the stress intensity factors are computed for two activation processes, zero field cooling and field cooling. Numerical results obtained show that the crack length and the inclined angle have significant effects on the fracture behavior. Generally, maximum of mode-I stress intensity factor is larger than that of mode-II stress intensity factor. The stress intensity factors analyzed in the paper are useful to learn fracture behavior and mechanical failure of superconductors.

  12. Fracture-Based Mesh Size Requirements for Matrix Cracks in Continuum Damage Mechanics Models

    Leone, Frank A.; Davila, Carlos G.; Mabson, Gerald E.; Ramnath, Madhavadas; Hyder, Imran


    This paper evaluates the ability of progressive damage analysis (PDA) finite element (FE) models to predict transverse matrix cracks in unidirectional composites. The results of the analyses are compared to closed-form linear elastic fracture mechanics (LEFM) solutions. Matrix cracks in fiber-reinforced composite materials subjected to mode I and mode II loading are studied using continuum damage mechanics and zero-thickness cohesive zone modeling approaches. The FE models used in this study are built parametrically so as to investigate several model input variables and the limits associated with matching the upper-bound LEFM solutions. Specifically, the sensitivity of the PDA FE model results to changes in strength and element size are investigated.

  13. Multiaxial mixed-mode cracking - small crack initiation and propagation

    Freitas, M. de; Reis, L.; Li Bin [Lisbon Univ. (Portugal). ICEMS - Inst. of Material and Surface Science and Engineering


    Both the fatigue crack path and fatigue life of CK45 steel and 42CrMo4 steel under various multiaxial loading paths are studied in this paper. The replica method was applied to monitor the crack initiation and small crack growth, the fractographic analyses were carried out on the fracture surface and the crack initiation angle was measured. The effects of non-proportional loading on both the crack path and fatigue life were studied, and the flattening of asperities on the crack surface due to compressive normal stress was also observed. An improved model is proposed based on correcting the strain range parameter of the ASME code approach, taking into account the additional hardening caused by the non-proportional loading path, which can improve the predictions of the fatigue lives for various non-proportional loading paths and provide an easy way to overcome the drawbacks of the current ASME code approach for non-proportional fatigue. Based on these corrected strain range parameters, a strain intensity factor range is used to correlate with the experimental results of small crack growth rates. It is concluded that the orientation of the early crack growth can be predicted well by the critical damage plane, but the fatigue life can not be predicted accurately using only the parameters on the critical plane, since the damage on all the planes contributes to fatigue damage as stated by the integral approaches. (orig.)

  14. Catalytic cracking of lignites

    Seitz, M.; Nowak, S.; Naegler, T.; Zimmermann, J. [Hochschule Merseburg (Germany); Welscher, J.; Schwieger, W. [Erlangen-Nuernberg Univ. (Germany); Hahn, T. [Halle-Wittenberg Univ., Halle (Germany)


    A most important factor for the chemical industry is the availability of cheap raw materials. As the oil price of crude oil is rising alternative feedstocks like coal are coming into focus. This work, the catalytic cracking of lignite is part of the alliance ibi (innovative Braunkohlenintegration) to use lignite as a raw material to produce chemicals. With this new one step process without an input of external hydrogen, mostly propylene, butenes and aromatics and char are formed. The product yield depends on manifold process parameters. The use of acid catalysts (zeolites like MFI) shows the highest amount of the desired products. Hydrogen rich lignites with a molar H/C ratio of > 1 are to be favoured. Due to primary cracking and secondary reactions the ratio between catalyst and lignite, temperature and residence time are the most important parameter to control the product distribution. Experiments at 500 C in a discontinuous rotary kiln reactor show yields up to 32 wt-% of hydrocarbons per lignite (maf - moisture and ash free) and 43 wt-% char, which can be gasified. Particularly, the yields of propylene and butenes as main products can be enhanced four times to about 8 wt-% by the use of catalysts while the tar yield decreases. In order to develop this innovative process catalyst systems fixed on beads were developed for an easy separation and regeneration of the used catalyst from the formed char. (orig.)

  15. Effect of Embedded Piezoelectric Sensors on Fracture Toughness and Fatigue Resistance of Composite Laminates Under Mode I Loading

    Murri, Gretchen B.


    Double-cantilevered beam (DCB) specimens of a glass/epoxy composite material with embedded piezoelectric sensors were tested both statically and under fatigue loading to determine the effect of the embedded material on the Mode I fracture toughness and fatigue resistance compared to baseline data without the embedded elements. A material known as LaRC-Macrofiber Composite (LaRC-MFC (TradeMark)), or MFC, was embedded at the midplane of the specimen during the layup. Specimens were manufactured with the embedded MFC material either at the loaded end of the specimen to simulate an initial delamination; or with the MFC material located at the delaminating interface, with a Teflon film at the loaded end to simulate an initial delamination. There were three types of specimens with the embedded material at the delaminating interface: co-cured with no added adhesive; cured with a paste adhesive applied to the embedded element; or cured with a film adhesive added to the embedded material. Tests were conducted with the sensors in both the passive and active states. Results were compared to baseline data for the same material without embedded elements. Interlaminar fracture toughness values (G(sub Ic)) for the passive condition showed little change when the MFC was at the insert end. Passive results varied when the MFC was at the delaminating interface. For the co-cured case and with the paste adhesive, G(sub Ic) decreased compared to the baseline toughness, whereas, for the film adhesive case, G(sub Ic) was significantly greater than the baseline toughness, but the failure was always catastrophic. When the MFC was in the active state, G(sub Ic) was generally lower compared to the passive results. Fatigue tests showed little effect of the embedded material whether it was active or passive compared to baseline values.

  16. Influence of Shear Stiffness Degradation on Crack Paths in Uni-Directional Composite Laminates

    Satyanarayana, Arunkumar; Bogert, Phil B.


    Influence of shear stiffness degradation in an element, due to damage, on crack paths in uni-directional laminates has been demonstrated. A new shear stiffness degradation approach to improve crack path prediction has been developed and implemented in an ABAQUS/Explicit frame work using VUMAT. Three progressive failure analysis models, built-in ABAQUS (TradeMark), original COmplete STress Reduction (COSTR) and the modified COSTR damage models have been utilized in this study to simulate crack paths in five unidirectional notched laminates, 15deg, 30deg, 45deg, 60deg and 75deg under uniaxial tension load. Results such as crack paths and load vs. edge displacement curves are documented in this report. Modified COSTR damage model shows better accuracy in predicting crack paths in all the uni-directional laminates compared to the ABAQUS (TradeMark) and the original COSTR damage models.

  17. Experiences on IGSCC crack manufacturing

    Veron, P. [Equipos Nucleares, S.A., Maliano (Spain)


    The author presents his experience in manufacturing IGSCC realistic defects, mainly in INCONEL 600 MA Steam Generator Tubes. From that experience he extracts some knowledge about this cracking (influence of chemistry in the environment, stress state, crack growth rate, and occurrence in laboratory condition of break before leak).



    Hydrogen transfer is an important secondary reaction of catalytic cracking reactions, which affects product yield distribution and product quality. It is an exothermic reaction with low activation energy around 43.3 kJ/mol. Catalyst properties and operation parameters in catalytic cracking greatly influence the hydrogen transfer reaction. Satisfactory results are expected through careful selection of proper catalysts and operation conditions.

  19. Three dimensional K-Tz stress fields around the embedded center elliptical crack front in elastic plates

    Junhua Zhao; Wanlin Guo; Chongmin She; Bo Meng


    Through detailed three-dimensional(3D)finite element(FE)calculations,the out-of-plane constraints Tz along embedded center-elliptical cracks in mode I elastic plates are studied.The distributions of Tz are obtained near the crack front with aspect ratios (a/c) of 0.2,0.4,0.5,0.6,0.8 and 1.0.Tz decreases from an approximate value of Poisson ratio ν at the crack tip to zero with increasing normalized radialdistances (r/a) in the normal plane of the crack front line,and increases gradually when the elliptical parameter angle φ changes from 0°to 90°at the sanle r/a.with a/c rising to 1.0,Tz is getting nearly independent of φ and is only related to r/a.Based on the present FE calculations for Tz,empirical formulas for Tz are obtained to describe the 3D distribution of Tz for embedded center-elliptical cracks using the least squares method in the range of 0.2 ≤ a/c ≤ 1.0.These Tz results together with the corresponding stress intensity factor K are well suitable for the analysis of the 3D embedded center-elliptical crack front field,and a two-parameter K-Tz principle is proposed.

  20. Cracking Tendency of Restrained Concrete at Early Ages

    BA Hengjing; SU Anshuang; GAO Xiaojian; TAO Qi


    A modified testing system characterized by full automation, steady operation and high accuracy of strain and stress measurements was developed to determine the cracking tendency of high strength concrete (HSC) in restrained condition at early ages. The shrinkage stress and the tensile creep behavior of HSC at early ages were investigated. The influence of W/C ratio and curing conditions on the early-age shrinkage stress and tensile creep was evaluated. It was found that the lower W/C ratio and drying curing condition resulted in higher shrinkage stress, stress induced tensile creep and greater cracking tendency.

  1. A consistent partly cracked XFEM element for cohesive crack growth

    Asferg, Jesper L.; Poulsen, Peter Noe; Nielsen, Leif Otto


    capable of modelling variations in the discontinuous displacement field on both sides of the crack and hence also capable of modelling the case where equal stresses are present on each side of the crack. The enrichment was implemented for the 3-node constant strain triangle (CST) and a standard algorithm...... was used to solve the non-linear equations. The performance of the element is illustrated by modelling fracture mechanical benchmark tests. Investigations were carried out on the performance of the element for different crack lengths within one element. The results are compared with previously obtained...

  2. Influence of Mixed Mode I-Mode II Loading on Fatigue Delamination Growth Characteristics of a Graphite Epoxy Tape Laminate

    Ratcliffe, James G.; Johnston, William M., Jr.


    Mixed mode I-mode II interlaminar tests were conducted on IM7/8552 tape laminates using the mixed-mode bending test. Three mixed mode ratios, G(sub II)/G(sub T) = 0.2, 0.5, and 0.8, were considered. Tests were performed at all three mixed-mode ratios under quasi-static and cyclic loading conditions, where the former static tests were used to determine initial loading levels for the latter fatigue tests. Fatigue tests at each mixed-mode ratio were performed at four loading levels, Gmax, equal to 0.5G(sub c), 0.4G(sub c), 0.3G(sub c), and 0.2G(sub c), where G(sub c) is the interlaminar fracture toughness of the corresponding mixed-mode ratio at which a test was performed. All fatigue tests were performed using constant-amplitude load control and delamination growth was automatically documented using compliance solutions obtained from the corresponding quasi-static tests. Static fracture toughness data yielded a mixed-mode delamination criterion that exhibited monotonic increase in Gc with mixed-mode ratio, G(sub II)/G(sub T). Fatigue delamination onset parameters varied monotonically with G(sub II)/G(sub T), which was expected based on the fracture toughness data. Analysis of non-normalized data yielded a monotonic change in Paris law exponent with mode ratio. This was not the case when normalized data were analyzed. Fatigue data normalized by the static R-curve were most affected in specimens tested at G(sub II)/G(sub T)=0.2 (this process has little influence on the other data). In this case, the normalized data yielded a higher delamination growth rate compared to the raw data for a given loading level. Overall, fiber bridging appeared to be the dominant mechanism, affecting delamination growth rates in specimens tested at different load levels and differing mixed-mode ratios.

  3. The asymptotic field of a dynamically growing crack in a viscoelastic materia


    A mechanical model of a fracturing viscoelastic material was developed to investigate viscous effects in a dynamically growing crack-tip field.It was shown that in the stable creep-growing phase, elastic deformation and viscous deformation are equally dominant in the near-tip field, and stress and strain have the same singularity, namely, (σ,ε)αγ-1/(n-1).The asymptotic solution of separating variables of stress, stain and displacement in the crack-tip field was obtained by asymptotic analysis, and the resulting numerical value of stress and strain in the crack-tip field was obtained by the shooting method and the boundary condition of a mode I crack.Through numerical calculation, it was shown that the near-tip fields are mainly governed by the creep exponent n and Mach number M.When n→∞, the asymptotic solution of a viscoelastic material can be degenerated into that of Freund's elastic-ideally plastic material by analyzing basic equations.

  4. Probabilistic Analysis of Crack Width

    J. Marková


    Full Text Available Probabilistic analysis of crack width of a reinforced concrete element is based on the formulas accepted in Eurocode 2 and European Model Code 90. Obtained values of reliability index b seem to be satisfactory for the reinforced concrete slab that fulfils requirements for the crack width specified in Eurocode 2. However, the reliability of the slab seems to be insufficient when the European Model Code 90 is considered; reliability index is less than recommended value 1.5 for serviceability limit states indicated in Eurocode 1. Analysis of sensitivity factors of basic variables enables to find out variables significantly affecting the total crack width.

  5. Analysis of Crack Arrest Toughness.


    vload(m) vp tn(m) Vertical Source Load (kN) on wedge HY80 Finite Element 0.0122 0.0099 3.81x10 -4 144 Steel Calculations Experiment 0.0122 --- 3.74x10-4...curve, are bona fide measures of the fracture arrest capability of tough ductile steels . The second is that the J-values represent the crack driving...fibrous mode of crack extension. (b) A new test method for studying fast fracture and arrest in tough steels . (c) Measurements of fast fracture and crack

  6. A computational algorithm for crack determination: The multiple crack case

    Bryan, Kurt; Vogelius, Michael


    An algorithm for recovering a collection of linear cracks in a homogeneous electrical conductor from boundary measurements of voltages induced by specified current fluxes is developed. The technique is a variation of Newton's method and is based on taking weighted averages of the boundary data. The method also adaptively changes the applied current flux at each iteration to maintain maximum sensitivity to the estimated locations of the cracks.

  7. Further Study of near Solidus Intergranular Cracking in Inconel 718

    Thompson, R. G.


    A series of tests, performed to determine the strain necessary to initiate intergranular cracking in Inconel 718 as a function of temperature, contained enough scatter near the melting temperature that questions remained as to the best curve of curves to fit to the data. Fracture surface analysis showed that the scatter was due to incipient melting in the grain boundary region. The melting contributed to low fracture strain but had only a small on the incipient cracking strain. Gleeble tests, which could be interrupted by water quenching, were used to study the incipient intergranular melting of Inconel 718. This modified weld simulation test provided a sufficiently rapid quench to preserve the intergranular microstructure created during incipient melting. This structure was studied both microscopically and with energy dispensive X-ray analysis. The implications of incipient melting and low-strain incipient cracking on the development of microfissuring envelopes are discussed.

  8. Development and Application of Benchmark Examples for Mixed-Mode I/II Quasi-Static Delamination Propagation Predictions

    Krueger, Ronald


    The development of benchmark examples for quasi-static delamination propagation prediction is presented. The example is based on a finite element model of the Mixed-Mode Bending (MMB) specimen for 50% mode II. The benchmarking is demonstrated for Abaqus/Standard, however, the example is independent of the analysis software used and allows the assessment of the automated delamination propagation prediction capability in commercial finite element codes based on the virtual crack closure technique (VCCT). First, a quasi-static benchmark example was created for the specimen. Second, starting from an initially straight front, the delamination was allowed to propagate under quasi-static loading. Third, the load-displacement as well as delamination length versus applied load/displacement relationships from a propagation analysis and the benchmark results were compared, and good agreement could be achieved by selecting the appropriate input parameters. The benchmarking procedure proved valuable by highlighting the issues associated with choosing the input parameters of the particular implementation. Overall, the results are encouraging, but further assessment for mixed-mode delamination fatigue onset and growth is required.

  9. Cracks in Utopia


    Many of the craters found on the northern plains of Mars have been partly filled or buried by some material (possibly sediment). The Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image presented here (MOC2-136b, above left) shows a high-resolution view of a tiny portion of the floor of one of these northern plains craters. The crater, located in Utopia Planitia at 44oN, 258oW, is shown on the right (MOC2-136a)with a small white box to indicate the location of the MOC image. The MOC image reveals that the material covering the floor of this crater is cracked and pitted. The origin and source of material that has been deposited in this crater is unknown.The MOC image was acquired in June 1999 and covers an area only 1.1 kilometers (0.7 miles) wide at a resolution of 1.8 meters (6 feet) per pixel. The context picture is a mosaic of Viking 2 orbiter images 010B53 and 010B55, taken in 1976. Both images are illuminated from the left. Malin Space Science Systems and the California Institute of Technology built the MOC using spare hardware from the Mars Observer mission. MSSS operates the camera from its facilities in San Diego, CA. The Jet Propulsion Laboratory's Mars Surveyor Operations Project operates the Mars Global Surveyor spacecraft with its industrial partner, Lockheed Martin Astronautics, from facilities in Pasadena, CA and Denver, CO.

  10. Peridynamic model for fatigue cracking.

    Silling, Stewart Andrew; Abe Askari (Boeing)


    The peridynamic theory is an extension of traditional solid mechanics in which the field equations can be applied on discontinuities, such as growing cracks. This paper proposes a bond damage model within peridynamics to treat the nucleation and growth of cracks due to cyclic loading. Bond damage occurs according to the evolution of a variable called the "remaining life" of each bond that changes over time according to the cyclic strain in the bond. It is shown that the model reproduces the main features of S-N data for typical materials and also reproduces the Paris law for fatigue crack growth. Extensions of the model account for the effects of loading spectrum, fatigue limit, and variable load ratio. A three-dimensional example illustrates the nucleation and growth of a helical fatigue crack in the torsion of an aluminum alloy rod.

  11. 21 CFR 137.190 - Cracked wheat.


    ... 21 Food and Drugs 2 2010-04-01 2010-04-01 false Cracked wheat. 137.190 Section 137.190 Food and... Related Products § 137.190 Cracked wheat. Cracked wheat is the food prepared by so cracking or cutting into angular fragments cleaned wheat other than durum wheat and red durum wheat that, when tested by...

  12. The crack growth mechanism in asphaltic mixes

    Jacobs, .M.M.J.; Hopman, P.C.; Molenaar, A.A.A.


    The crack growth mechanism in asphalt concrete (Ac) mixes is studied. In cyclic tests on several asphaltic mixes crack growth is measured, both with crack foils and with cOD-gauges. It is found that crack growth in asphaltic mixes is described by three processes which are parallel in time: cohesive

  13. Chemical and metallurgical aspects of environmentally assisted fatigue crack growth in 7075-T651 aluminum alloy

    Gao, Ming; Wei, R. P.; Pao, P. S.


    A comprehensive study has been carried out on a 7075-T651 alloy to examine the influence of water vapor on fatigue crack growth. The kinetics of fatigue crack growth were determined as a function of water vapor pressure at room temperature and at 353 K. Detailed fractographic analyses and surface chemistry studies were carried out to identify the micromechanisms and to quantify the chemical interactions for corrosion fatigue crack growth in this alloy. Experiments were also carried out in ultra-high vacuum and in oxygen to provide for comparisons. Two regions of fatigue crack growth response were identified. In the low pressure region (below 67 Pa at 5 Hz), crack growth is controlled by the rate of transport of water vapor to the crack tip, and the response can be described by a model for transport controlled crack growth. At pressures above 67 Pa, additional increases in crack growth rate occurred, which are attributed to the further reactions of water vapor with segregated magnesium in this alloy. Different micromechanisms for crack growth have been identified for vacuum, oxygen, and water vapor. These micromechanisms are considered in relation to the environmental parameters through a modified superposition model for corrosion fatigue.

  14. Salinity effects on the dynamics and patterns of desiccation cracks

    Shokri, N.; Zhou, P.


    Cracking arising from desiccation is a ubiquitous phenomenon encountered in various industrial and geo-environmental applications including drying of clayey soil, cement, ceramics, gels, and many more colloidal suspensions. Presence of cracks in muddy sediments modifies the characteristics of the medium such as pore structure, porosity, and permeability which in turn influence various flow and transport processes. Thus it remains a topic of great interest in many disciplines to describe the dynamics of desiccation cracking under various boundary conditions. To this end, we conducted a comprehensive study to investigate effects of NaCl concentrations on cracking dynamics and patterns during desiccation of Bentonite. Mixtures of Bentonite and NaCl solutions were prepared with NaCl concentration varying from 2 to 10 percent in 0.5 percent increment (totally 17 configurations). The slurry was placed in a Petri dish mounted on a digital balance to record the evaporation dynamics. The atmospheric conditions were kept constant using an environmental chamber. An automatic camera was used to record the dynamics of macro-cracks (mm scale) at the surface of desiccating clay each minute. The obtained results illustrate the significant effects of salt concentration on the initiation, propagation, morphology and general dynamics of macro-cracks. We found that higher salt concentrations results in larger macro cracks' lengths attributed to the effects of NaCl on compressing the electric double layer of particles at increasing electrolyte concentrations which reduce considerably the repulsive forces among the particles and causing instability of the slurry and flocculation of the colloidal particles. Rheological measurements by means of a stress controlled rheometer revealed that the yield stress of the slurry decreases as NaCl concentration increases which may indicate aggregation of larger units in the slurry as a result of flocculation causing larger cracks' lengths due to

  15. Avaliação da susceptibilidade à fragilização induzida por hidrogênio na soldagem de um aço microligado para blindagens por meio de um ensaio de implante com geometria modificada Evaluation of susceptibility of hydrogen induced cracking in microalloyed armor steel welds using a geometry modified implant test

    Jimy Unfried Silgado


    Full Text Available A susceptibilidade à fragilização induzida pelo Hidrogênio (FIH foi avaliada em soldas de aço para blindagem temperado e revenido (T&R de 4,5mm de espessura. As soldas foram desenvolvidas utilizando o processo SMAW com um baixo aporte de calor e consumível AWS E11018M de 2,4 mm. A susceptibilidade a FIH foi avaliada por médio de um ensaio de implante com geometria modificada em juntas soldadas com e sem aplicação de preaquecimento, utilizando consumíveis em condições de estocagem ideais e expostos à atmosfera. Encontrou-se que a condição de estocagem do consumível foi mais relevante que o preaquecimento na susceptibilidade ao FIH.The Hydrogen Induced Cracking (HIC susceptibility of 4,5mm thickness quenched and tempered (Q&T armor plate steel welding joints was evaluated. The joints were obtained using low heat input and SMAW process with 2,4 mm AWS E11018M electrode. The HIC susceptibility was evaluated using a geometry modified implant test for thin plates. The joints studied were produced with and without preheating and using welding electrodes with and without exposure to atmospheric conditions. The HIC resistance was severely impaired by improperly storage while preheating conditions did not preclude HIC.

  16. Fiber Sensing of Micro -Crack


    Optical fiber sensors are used for sensing micro-cracking in composite and metal materials in aerospace applications. The sensing mechanism is based on the detection of acoustic emission signals, which are known to emanate from micro-cracks when they grow under further loading. The sensor head consists of a fiber Bragg grating that is capable of detecting acoustic emission signals generated by pencil lead breaking, of frequencies up to 200 kHz.

  17. Elasto-plastic fatigue crack growth analysis of plane problems in the presence of flaws using XFEM



    ABSTRACT In this paper, elasto-plastic XFEM simulations have been perfonaaed to evaluate the fatigue life of plane crack problems in the presence of various defects. The stress-strain response of the material is modeled by Ramberg- Osgood equation. The von-Mises failure criterion has been used with isotropic hardening. The J-integral for two fracture modes (mode-I and mode-If) is obtained by decomposing the displacement and stress fields into their symmetric and antisymmetric parts, then individual stress intensity factors are extracted from J-integral. The fatigue life obtained by EPFM is found quite close to that obtained by LEFM.


    Z.X.Wu; X.C.Wu


    The progressive fatigue damage of a material is closely related to the whole populationof cracks on the surface of an un-notched specimen.In order to understand whichparameter is a more useful indicator of fatigue damage,rotatory bending fatigue testswere carried out using smooth specimens of medium-carbon steel.The behavior ofshort crack propagation during fatigue was examined and a new parameter "totalcrack area" was suggested.The aim of this paper is to extend the research on fatiguedamage in the already studied steel and to study how these damage parameters arecorrelated with the process of fatigue damage in order to evaluate the effectiveness ofdamage detection methods.


    邹剑; 陈进; 蒲亚鹏


    The dynamic equation of cracked rotor in rotational frame was modelled, the numerical simulation solutions of the cracked rotor and the uncracked rotor were obtained. By the wavelet transform, the time-frequency properties of the cracked rotor and the uncracked rotor were discussed, the difference of the time-frequency properties between the cracked rotor and the uncracked rotor was compared. A new detection algorithm using wavelet transform to identify crack was proposed. The experiments verify the availability and validity of the wavelet transform in identification of crack.

  20. Review of Environmentally Assisted Cracking

    Sadananda, K.; Vasudevan, A. K.


    Many efforts have been made in the past by several researchers to arrive at some unifying principles governing the embrittlement phenomena. An inescapable conclusion reached by all these efforts was that the behavior is very complex. Hence, recognizing the complexity of material/environment behavior, we focus our attention here only in extracting some similarities in the experimental trends to arrive at some generic principles of behavior. Crack nucleation and growth are examined under static load in the presence of internal and external environments. Stress concentration, either pre-existing or in-situ generated, appears to be a requirement for embrittlement. A chemical stress concentration factor is defined for a given material/environment system as the ratio of failure stress with and without the damaging chemical environment. All factors that affect the buildup of the required stress concentration, such as planarity of slip, stacking fault energy, etc., also affect the stress-corrosion behavior. The chemical stress concentration factor is coupled with the mechanical stress concentration factor. In addition, generic features for all systems appear to be (a) an existence of a threshold stress as a function of concentration of the damaging environment and flow properties of the material, and (b) an existence of a limiting threshold as a function of concentration, indicative of a damage saturation for that environment. Kinetics of crack growth also depends on concentration and the mode of crack growth. In general, environment appears to enhance crack tip ductility on one side by the reduction of energy for dislocation nucleation and glide, and to reduce cohesive energy for cleavage, on the other. These two opposing factors are coupled to provide environmentally induced crack nucleation and growth. The relative ratio of these two opposing factors depends on concentration and flow properties, thereby affecting limiting thresholds. The limiting concentration or

  1. Cracking and corrosion recovery boiler

    Suik, H. [Tallinn Technical University, Horizon Pulp and Paper, Tallinn (Estonia)


    The corrosion of heat surfaces and the cracking the drums are the main problems of the recovery boiler. These phenomena have been appeared during long-term operation of boiler `Mitsubishi - 315` erected at 1964. Depth of the crack is depending on the number of shutdowns and on operation time. Corrosion intensity of different heat surfaces is varying depend on the metal temperature and the conditions at place of positioning of tube. The lowest intensity of corrosion is on the bank tubes and the greatest is on the tubes of the second stage superheater and on the tubes at the openings of air ports. (orig.) 5 refs.




    Experimental results indicate that propagation paths of cracks in geomaterials are often irregular, producing rough fracture surfaces which are fractal. A formula is derived for the fractal kinematics of crack propagation in geomaterials. The formula correlates the dynamic and static fracture toughnesses with crack velocity, crack length and a microstructural parameter, and allows the fractal dimension to be obtained. From the equations for estimating crack velocity and fractal dimension it can be shown that the measured crack velocity, Vo , should be much smaller than the fractal crack velocity, V. It can also be shown that the fractal dimension of the crack propagation path can be calculated directly from Vo and from the fracture toughness.

  3. Interacting Cracks in an Environmentally Assisted Fracture

    Levandovsky, Artem; Balazs, Anna


    We perform the study of environmentally assisted fracture within the framework of a lattice model. Formation of an ensemble of environmentally assisted microcracks, their coalescence and formation of crack ``avalanches'' lead to a very rich dynamical picture. Under specific condition crack healing can occur due to cohesive forces, which hold material together and tend to pull atoms together even if they are separated by a crack over several lattice units. We investigate the dynamical interplay between crack formation, arrest, healing and re-cracking. The goal here is to provide an understanding of the conditions leading to the phenomena of crack healing that happens along with the crack formation. We study the morphology of crack patterns with the intentions to establish a way to enhance the healing property of a material sample.

  4. On multiple crack detection in beam structures

    Moradi, Shapour; Kargozarfard, Mohammad [Shahid Chamran University, Ahvaz (Iran, Islamic Republic of)


    This study presents an inverse procedure to identify multiple cracks in beams using an evolutionary algorithm. By considering the crack detection procedure as an optimization problem, an objective function can be constructed based on the change of the eigenfrequencies and some strain energy parameters. Each crack is modeled by a rotational spring. The changes in natural frequencies due to the presence of the cracks are related to a damage index vector. Then, the bees algorithm, a swarm-based evolutionary optimization technique, is used to optimize the objective function and find the damage index vector, whose positive components show the number and position of the cracks. A second objective function is also optimized to find the crack depths. Several experimental studies on cracked cantilever beams are conducted to ensure the integrity of the proposed method. The results show that the number of cracks as well as their sizes and locations can be predicted well through this method.

  5. Crack and flip phacoemulsification technique.

    Fine, I H; Maloney, W F; Dillman, D M


    The crack and flip phacoemulsification technique combines the advantages of circumferential division of the nucleus and nucleofactis techniques. As such, it adds safety and control to the procedure. We describe each of the surgical maneuvers, including machine settings, and explain the rationale for maneuvers and machine settings.

  6. China Cracks Down Internet Piracy


      National Copyright Administration of China carried out a special operation to crack down on behaviors involving network infringement and piracy from September to December in 2005 ,according to the speech of Yan Xiaohong,Deputy Commissioner of National Copyright Administration on the Press Conference of the State Council.Now the relevant conditions are as follows:……

  7. China Cracks Down Internet Piracy


    @@ National Copyright Administration of China carried out a special operation to crack down on behaviors involving network infringement and piracy from September to December in 2005 ,according to the speech of Yan Xiaohong,Deputy Commissioner of National Copyright Administration on the Press Conference of the State Council.Now the relevant conditions are as follows:



    The hydrothermal cracking of heavy oils, such as Canadian oil sand bitumen and Arabian heavy vacuum residue, as well as their model compound were performed over sulfided Ni/Al2O3 and NiMo/Al2O3 catalysts under 663~703 K and 6.0~8.0 MPa of hydrogen pressure in a batch autoclave reactor. According to the reaction mechanism of hydrothermal cracking, a small amount of free redical initiators, such as di-tert-peroxide, sulfur, etc., was added into the feed to generate free redicals at lower temperature, and obviously showed promotional effect on the conversion of hydrocarbons. The reaction mechanisms of hydrothermal cracking as well as the enhancing effect of initiators were studied by a probe reaction with 1-phenyldodecane as a model compound. The hydrothermal cracking of hydrocarbon proceeded via free redical mechanism and hydrogenating quench. The initiators might easily generate free redicals under reaction temperature, these redicals might abstract H from hydrocarbon molecule and reasonably initiate the chain reactions, therefore, promote the conversion of hydrocarbon even at lower reaction temperature.

  9. Confining crack propagation in defective graphene.

    López-Polín, Guillermo; Gómez-Herrero, Julio; Gómez-Navarro, Cristina


    Crack propagation in graphene is essential to understand mechanical failure in 2D materials. We report a systematic study of crack propagation in graphene as a function of defect content. Nanoindentations and subsequent images of graphene membranes with controlled induced defects show that while tears in pristine graphene span microns length, crack propagation is strongly reduced in the presence of defects. Accordingly, graphene oxide exhibits minor crack propagation. Our work suggests controlled defect creation as an approach to avoid catastrophic failure in graphene.

  10. Subcritical crack growth of selected aerospace pressure vessel materials

    Hall, L. R.; Bixler, W. D.


    This experimental program was undertaken to determine the effects of combined cyclic/sustained loads, stress level, and crack shape on the fatigue crack growth rate behavior of cracks subjected to plane strain conditions. Material/environment combinations tested included: 2219-T87 aluminum plate in gaseous helium, room air, and 3.5% NaCl solution at room temperature, liquid nitrogen, and liquid hydrogen; 5Al-2.5 Sn (ELI) titanium plate in liquid nitrogen and liquid hydrogen and 6AL-4V (ELI) STA titanium plate in gaseous helium and methanol at room temperature. Most testing was accomplished using surface flawed specimens instrumented with a clip gage to continuously monitor crack opening displacements at the specimen surface. Tapered double cantilever beam specimens were also tested. Static fracture and ten hour sustained load tests were conducted to determine fracture toughness and apparent threshold stress intensity values. Cyclic tests were performed using sinusoidal loading profiles at 333 MHz (20 cpm) and trapezoidal loading profiles at both 8.3 MHz (0.5 cpm) and 3.3 MHz (0.2 cpm). Data were evaluated using modified linear elastic fracture mechanics parameters.

  11. Correction to the crack extension direction in numerical modelling of mixed mode crack paths

    Lucht, Tore; Aliabadi, M.H.


    In order to avoid introduction of an error when a local crack-growth criterion is used in an incremental crack growth formulation, each straight crack extension would have to be infinitesimal or have its direction corrected. In this paper a new procedure to correct the crack extension direction i...

  12. Mesh sensitivity effects on fatigue crack growth by crack-tip blunting and re-sharpening

    Tvergaard, Viggo


    Crack-tip blunting under tensile loads and re-sharpening of the crack-tip during unloading is one of the basic mechanisms for fatigue crack growth in ductile metals. Based on an elastic–perfectly plastic material model, crack growth computations have been continued up to 700 full cycles by using...

  13. Fatigue crack growth from a cracked elastic particle into a ductile matrix

    Groh, S.; Olarnrithinun, S.; Curtin, W. A.; Needleman, A.; Deshpande, V. S.; Van der Giessen, E.


    The monotonic and cyclic crack growth rate of cracks is strongly influenced by the microstructure. Here, the growth of cracks emanating from pre-cracked micron-scale elastic particles and growing into single crystals is investigated, with a focus on the effects of (i) plastic confinement due to the

  14. Twisting cracks in Bouligand structures.

    Suksangpanya, Nobphadon; Yaraghi, Nicholas A; Kisailus, David; Zavattieri, Pablo


    The Bouligand structure, which is found in many biological materials, is a hierarchical architecture that features uniaxial fiber layers assembled periodically into a helicoidal pattern. Many studies have highlighted the high damage-resistant performance of natural and biomimetic Bouligand structures. One particular species that utilizes the Bouligand structure to achieve outstanding mechanical performance is the smashing Mantis Shrimp, Odontodactylus Scyllarus (or stomatopod). The mantis shrimp generates high speed, high acceleration blows using its raptorial appendage to defeat highly armored preys. The load-bearing part of this appendage, the dactyl club, contains an interior region [16] that consists of a Bouligand structure. This region is capable of developing a significant amount of nested twisting microcracks without exhibiting catastrophic failure. The development and propagation of these microcracks are a source of energy dissipation and stress relaxation that ultimately contributes to the remarkable damage tolerance properties of the dactyl club. We develop a theoretical model to provide additional insights into the local stress intensity factors at the crack front of twisting cracks formed within the Bouligand structure. Our results reveal that changes in the local fracture mode at the crack front leads to a reduction of the local strain energy release rate, hence, increasing the necessary applied energy release rate to propagate the crack, which is quantified by the local toughening factor. Ancillary 3D simulations of the asymptotic crack front field were carried out using a J-integral to validate the theoretical values of the energy release rate and the local stress intensity factors. Copyright © 2017 Elsevier Ltd. All rights reserved.

  15. Fatigue Crack Growth Rate of Ti-6Al-4V Considering the Effects of Fracture Toughness and Crack Closure

    ZHANG Junhong; YANG Shuo; LIN Jiewei


    Fatigue fracture is one of the main failure modes of Ti-6Al-4V alloy, fracture toughness and crack closure have strong effects on the fatigue crack growth(FCG) rate of Ti-6Al-4V alloy. The FCG rate of Ti-6Al-4V is investigated by using experimental and analytical methods. The effects of stress ratio, crack closure and fracture toughness on the FCG rate are studied and discussed. A modified prediction model of the FCG rate is proposed, and the relationship between the fracture toughness and the stress intensity factor(SIF) range is redefined by introducing a correcting coefficient. Notched plate fatigue tests (including the fracture toughness test and the FCG rate test) are conducted to investigate the influence of affecting factors on the FCG rate. Comparisons between the predicted results of the proposed model, the Paris model, the Walker model, the Sadananda model, and the experimental data show that the proposed model gives the best agreement with the test data particularly in the near–threshold region and the Paris region, and the corresponding calculated fatigue life is also accurate in the same regions. By considering the effects of fracture toughness and crack closure, the novel FCG rate prediction model not only improves the estimating accuracy, but also extends the adaptability of the FCG rate prediction model in engineering.

  16. Fatigue crack growth rate of Ti-6Al-4V considering the effects of fracture toughness and crack closure

    Zhang, Junhong; Yang, Shuo; Lin, Jiewei


    Fatigue fracture is one of the main failure modes of Ti-6Al-4V alloy, fracture toughness and crack closure have strong effects on the fatigue crack growth(FCG) rate of Ti-6Al-4V alloy. The FCG rate of Ti-6Al-4V is investigated by using experimental and analytical methods. The effects of stress ratio, crack closure and fracture toughness on the FCG rate are studied and discussed. A modified prediction model of the FCG rate is proposed, and the relationship between the fracture toughness and the stress intensity factor(SIF) range is redefined by introducing a correcting coefficient. Notched plate fatigue tests (including the fracture toughness test and the FCG rate test) are conducted to investigate the influence of affecting factors on the FCG rate. Comparisons between the predicted results of the proposed model, the Paris model, the Walker model, the Sadananda model, and the experimental data show that the proposed model gives the best agreement with the test data particularly in the near-threshold region and the Paris region, and the corresponding calculated fatigue life is also accurate in the same regions. By considering the effects of fracture toughness and crack closure, the novel FCG rate prediction model not only improves the estimating accuracy, but also extends the adaptability of the FCG rate prediction model in engineering.

  17. Stress analysis of the cracked-lap-shear specimen - An ASTM round-robin

    Johnson, W. S.


    This ASTM Round Robin was conducted to evaluate the state of the art in stress analysis of adhesively bonded joint specimens. Specifically, the participants were asked to calculate the strain-energy-release rate for two different geometry cracked lap shear (CLS) specimens at four different debond lengths. The various analytical techniques consisted of 2- and 3-dimensional finite element analysis, beam theory, plate theory, and a combination of beam theory and finite element analysis. The results were examined in terms of the total strain-energy-release rate and the mode I to mode II ratio as a function of debond length for each specimen geometry. These results basically clustered into two groups: geometric linear or geometric nonlinear analysis. The geometric nonlinear analysis is required to properly analyze the CLS specimens. The 3-D finite element analysis gave indications of edge closure plus some mode III loading. Each participant described his analytical technique and results. Nine laboratories participated.

  18. Stress analysis of the cracked lap shear specimens: An ASTM round robin

    Johnson, W. S.


    This ASTM Round Robin was conducted to evaluate the state of the art in stress analysis of adhesively bonded joint specimens. Specifically, the participants were asked to calculate the strain-energy-release rate for two different geometry cracked lap shear (CLS) specimens at four different debond lengths. The various analytical techniques consisted of 2- and 3-dimensional finite element analysis, beam theory, plate theory, and a combination of beam theory and finite element analysis. The results were examined in terms of the total strain-energy-release rate and the mode I to mode II ratio as a function of debond length for each specimen geometry. These results basically clustered into two groups: geometric linear or geometric nonlinear analysis. The geometric nonlinear analysis is required to properly analyze the CLS specimens. The 3-D finite element analysis gave indications of edge closure plus some mode III loading. Each participant described his analytical technique and results. Nine laboratories participated.

  19. Inhibiting Corrosion Cracking: Crack Tip Chemistry and Physics.


    5 5. Swuzary 113 Rferences 114 wl NO 4L iv . List of Figuring 1. Microipette pulling machine . 29 2. Anodic polarization of 7075-T6 Al alloy in dilute...environment has a strong effect on microplastic behavior at the tip of a fatigue crack. Stolz and Pelloux suggest that nitrate ion competes with chloride...Crystalline Na2 N 20 29H20 precipitates when the filtrate is placed in a vacunm desiccator over sulfuric acid. The filtered precipitate is washed

  20. Crack branching in carbon steel. Fracture mechanisms

    Syromyatnikova, A. S.; Alekseev, A. A.; Levin, A. I.; Lyglaev, A. V.


    The fracture surfaces of pressure vessels made of carbon steel that form during crack branching propagation are examined by fractography. Crack branching is found to occur at a crack velocity higher than a certain critical value V > V c . In this case, the material volume that is involved in fracture and depends on the elastoplastic properties of the material and the sample width has no time to dissipate the energy released upon crack motion via the damage mechanisms intrinsic in the material under given deformation conditions (in our case, via cracking according to intragranular cleavage).

  1. Strength of Cracked Reinforced Concrete Disks

    Hoang, Cao Linh; Nielsen, Mogens Peter


    The paper deals with models, based on the theory of plasticity, to be used in strength assessments of reinforced concrete disks suffering from different kinds of cracking. Based on the assumption that the sliding strength of concrete is reduced in sections where cracks are located, solutions...... for the shear strength of disks with initial cracks and disks suffering from isotropic cracking are presented. Furthermore, in the case of isotropicly cracked disks subjected to arbitrary in-plane loading, a general yield condition is derived....


    Karin Kocúrová


    Full Text Available The article deals with the analysis of a damaged part, which was designed for use in a mechanical clutch of a car. The crack in the part was found during the production inspection. The aim of metallographic and fractography analyses of the fracture surfaces was to discover the reasons for the crack. The reason for creating the crack was the formation of smaller cracks in the production during pressing process of the semiproduct. These cracks even grew after the following thermochemical treatment. The fracture was initiated during the straightening process of quenched part.

  3. Crack detection in plastic pipe using piezoelectric transducers based on nonlinear ultrasonic modulation

    Hong, Xiaobin; Lin, Xiaohui; Yang, Bo; Li, Maodong


    As a common kind of failure, crack damages account for major losses in plastic pipeline systems, which are now increasingly being used. In this study, a crack detection method for plastic pipes using piezoelectric transducers based on nonlinear ultrasonic modulation is developed. First, the low frequency and the high frequency (HF) inputs generated by two lead zirconate titanate (PZT) transducers that are bonded to the outer surface of a plastic pipe are used to induce stress waves along the pipe. For the response signal detected by another PZT, the first spectral sideband is extracted using filtering and synchronous demodulation and then modified by a proposed mean equalization method. Subsequently, by applying wavelet packet analysis, the wavelet energy of the signal can be obtained and is used as an index to determine the damaged state. Finally, a series of experiments on plastic pipes of different crack damaged states were conducted using several ways to verify their effectiveness. Experimental results show that wavelet energy of the response signal decreases as the crack grows and it is mainly determined by the HF component of the response signal, while the wavelet energy of the modified first spectral sideband tends to become larger when the crack grows. Among the investigated approaches, it is found that the first spectral sideband can detect the crack damage state effectively.

  4. Alternating grain orientation and weld solidification cracking

    Kou, S.; Le, Y.


    A new mechanism for reducing weld solidification cracking was proposed, based on the concept of the crack path and resistance to crack propagation, and its effectiveness was verified in magnetically oscillated GTA welds of a rather crack susceptible material 2014 aluminum alloy. This mechanism, i.e., alternating grain orientation, was most pronounced in welds made with transverse arc oscillation of low frequency and high amplitude, and solidification cracking was dramatically reduced in these welds. The effect of the arc oscillation pattern, amplitude, and frequency on the formation of alternating columnar grains and the reduction of solidification cracking in GTA welds of 2014 aluminum alloy was examined and explained. The present study demonstrated for the first time that columnar grains can, in fact, be very effective in reducing solidification cracking, provided that they are oriented favorably.

  5. Open crack depth sizing by multi-speed continuous laser stimulated lock-in thermography

    Boué, C.; Holé, S.


    A crack located in the thermal diffusion zone of a heat source behaves like a thermal barrier modifying the heat diffusion. For a moving continuous source, the sample surface is heated on a little area near the crack for a duration which depends on the speed of the thermal source. A lock-in process synchronized by the displacement of the continuous heat source along the crack is studied. The thermal signature of the crack is extracted via a space operator applied to the amplitude and the phase of surface temperature images for various speeds of the thermal source. With the technical solution presented in this article, the thermal signature images are analysed according to a length representative of the thermal diffusion length to give a local evaluation of the crack depth (around 3 mm at the maximum) for crack lengths of about few centimetres long. The multi-speed lock-in thermography approach is initially studied with finite element method simulations. Experimental tests using an infra-red camera validate the method in a second part. The results do not depend on the heating source if its power is sufficient to produce a temperature rise detectable by an infra-red camera. The depth estimations are obtained independently of the crack width and heat source trajectory. The multi-speed lock-in thermography is a method without contact, without sample preparation, non-polluting, non-destructive and with simple optical adjustments.

  6. Fatigue and fracture assessment of cracks in steel elements using acoustic emission

    Nemati, Navid; Metrovich, Brian; Nanni, Antonio


    Single edge notches provide a very well defined load and fatigue crack size and shape environment for estimation of the stress intensity factor K, which is not found in welded elements. ASTM SE(T) specimens do not appear to provide ideal boundary conditions for proper recording of acoustic wave propagation and crack growth behavior observed in steel bridges, but do provide standard fatigue crack growth rate data. A modified versions of the SE(T) specimen has been examined to provide small scale specimens with improved acoustic emission(AE) characteristics while still maintaining accuracy of fatigue crack growth rate (da/dN) versus stress intensity factor (ΔK). The specimens intend to represent a steel beam flange subjected to pure tension, with a surface crack growing transverse to a uniform stress field. Fatigue test is conducted at low R ratio. Analytical and numerical studies of stress intensity factor are developed for single edge notch test specimens consistent with the experimental program. ABAQUS finite element software is utilized for stress analysis of crack tips. Analytical, experimental and numerical analysis were compared to assess the abilities of AE to capture a growing crack.

  7. Crack detection in pipelines using multiple electromechanical impedance sensors

    Zuo, Chunyuan; Feng, Xin; Zhang, Yu; Lu, Lu; Zhou, Jing


    An extensive network of pipeline systems is used to transport and distribute national energy resources that heavily influence a nation’s economy. Therefore, the structural integrity of these pipeline systems must be monitored and maintained. However, structural damage detection remains a challenge in pipeline engineering. To this end, this study developed a modified electromechanical impedance (EMI) technique for crack detection that involves fusing information from multiple sensors. We derived a new damage-sensitive feature factor based on a pipeline EMI model that considers the influence of the bonding layer between the EMI sensors and pipeline. We experimentally validated the effectiveness of the proposed method. Finally, we used a damage index—root mean square deviation—to examine the degree and position of crack damage in a pipeline.

  8. 7-lump kinetic model for residual oil catalytic cracking

    XU Ou-guan; SU Hong-ye; MU Sheng-jing; CHU Jian


    In this paper a novel 7-lump kinetic model is proposed to describe residual oil catalytic cracking, in which coke is lumped separately for accurate prediction. The reactor block is modeled as a combination of an ideal pipe flow reactor (PFR)and a continuously stirred tank reactor (CSTR). Unit factors are designed to correct the deviation between model predictions and practical plant data and tuned by modified Levenberg-Marquardt algorithm. The parameters estimated are reliable and good agreement between the model predictions and plant observations is observed. The model helps us get good insight into the performance of an industrial riser reactor that would be useful for optimization of residual oil catalytic cracking.

  9. Modifying Resonance Modes of Dissipative Structures using Magnitude and Phase Information

    Peters, H.J.; Tiso, P.; Goosen, J.F.L.; Van Keulen, A.


    Several Flapping Wing Micro Air Vehicle (FWMAV) designs exploit structural resonance to decrease power consumption. Practical use of most resonating structures requires temporary modifications to the resonance mode (i.e., the eigensolution). This paper presents a systematic design approach to modify

  10. Biaxial Fatigue Cracking from Notch


    Leevers (reference 11) noticed that the variation in  from 0 to 2 has little effect on the da/dN in PVC ( polyvinyl - chloride ), but reduces the da/dN...under biaxial rotating and bending. Ahmad (reference 2) formulated a model for the biaxial fatigue crack growth in aggressive environment, outlined by...1962, Vol. 90, pp. 238-239. 20. ASM Handbook , Vol. 12 Fractography: 1992, p. 430, 438. 21. Metals Handbook , Vol. 9 Fractography and Atlas of

  11. The use of COD and plastic instability in crack propagation and arrest in shells

    Erdogan, F.; Ratwani, M.


    The initiation, growth, and possible arrest of fracture in cylindrical shells containing initial defects are dealt with. For those defects which may be approximated by a part-through semi-elliptic surface crack which is sufficiently shallow so that part of the net ligament in the plane of the crack is still elastic, the existing flat plate solution is modified to take into account the shell curvature effect as well as the effect of the thickness and the small scale plastic deformations. The problem of large defects is then considered under the assumptions that the defect may be approximated by a relatively deep meridional part-through surface crack and the net ligament through the shell wall is fully yielded. The results given are based on an 8th order bending theory of shallow shells using a conventional plastic strip model to account for the plastic deformations around the crack border.

  12. Mechanics of finite cracks in dissimilar anisotropic elastic media considering interfacial elasticity

    Juan, Pierre-Alexandre; Dingreville, Rémi


    Interfacial crack fields and singularities in bimaterial interfaces (i.e., grain boundaries or dissimilar materials interfaces) are considered through a general formulation for two-dimensional (2-D) anisotropic elasticity while accounting for the interfacial structure by means of an interfacial elasticity paradigm. The interfacial elasticity formulation introduces boundary conditions that are effectively equivalent to those for a weakly bounded interface. This formalism considers the 2-D crack-tip elastic fields using complex variable techniques. While the consideration of the interfacial elasticity does not affect the order of the singularity, it modifies the oscillatory effects associated with problems involving interface cracks. Constructive or destructive "interferences" are directly affected by the interface structure and its elastic response. This general formulation provides an insight on the physical significance and the obvious coupling between the interface structure and the associated mechanical fields in the vicinity of the crack tip.

  13. The Growth of Small Corrosion Fatigue Cracks in Alloy 7075

    Piascik, Robert S.


    The corrosion fatigue crack growth characteristics of small (greater than 35 micrometers) surface and corner cracks in aluminum alloy 7075 is established. The early stage of crack growth is studied by performing in situ long focal length microscope (500×) crack length measurements in laboratory air and 1% sodium chloride (NaCl) environments. To quantify the "small crack effect" in the corrosive environment, the corrosion fatigue crack propagation behavior of small cracks is compared to long through-the-thickness cracks grown under identical experimental conditions. In salt water, long crack constant K(sub max) growth rates are similar to small crack da/dN.

  14. Fatigue cracks in Eurofer 97 steel: Part II. Comparison of small and long fatigue crack growth

    Kruml, T.; Hutař, P.; Náhlík, L.; Seitl, S.; Polák, J.


    The fatigue crack growth rate in the Eurofer 97 steel at room temperature was measured by two different methodologies. Small crack growth data were obtained using cylindrical specimens with a shallow notch and no artificial crack starters. The growth of semicircular cracks of length between 10-2000 μm was followed in symmetrical cycling with constant strain amplitude ( R ɛ = -1). Long crack data were measured using standard CT specimen and ASTM methodology, i.e. R = 0.1. The growth of cracks having the length in the range of 10-30 mm was measured. It is shown that the crack growth rates of both types of cracks are in a very good agreement if J-integral representation is used and usual assumptions of the crack closure effects are taken into account.

  15. Fatigue cracks in Eurofer 97 steel: Part II. Comparison of small and long fatigue crack growth

    Kruml, T., E-mail: [Institute of Physics of Materials, Academy of Sciences of the Czech Republic, Zizkova 22, CZ 61662 Brno (Czech Republic); Hutar, P.; Nahlik, L.; Seitl, S.; Polak, J. [Institute of Physics of Materials, Academy of Sciences of the Czech Republic, Zizkova 22, CZ 61662 Brno (Czech Republic)


    The fatigue crack growth rate in the Eurofer 97 steel at room temperature was measured by two different methodologies. Small crack growth data were obtained using cylindrical specimens with a shallow notch and no artificial crack starters. The growth of semicircular cracks of length between 10-2000 {mu}m was followed in symmetrical cycling with constant strain amplitude (R{sub {epsilon}} = -1). Long crack data were measured using standard CT specimen and ASTM methodology, i.e. R = 0.1. The growth of cracks having the length in the range of 10-30 mm was measured. It is shown that the crack growth rates of both types of cracks are in a very good agreement if J-integral representation is used and usual assumptions of the crack closure effects are taken into account.

  16. Stress Corrosion Cracking and Fatigue Crack Growth Studies Pertinent to Spacecraft and Booster Pressure Vessels

    Hall, L. R.; Finger, R. W.


    This experimental program was divided into two parts. The first part evaluated stress corrosion cracking in 2219-T87 aluminum and 5Al-2.5Sn (ELI) titanium alloy plate and weld metal. Both uniform height double cantilever beam and surface flawed specimens were tested in environments normally encountered during the fabrication and operation of pressure vessels in spacecraft and booster systems. The second part studied compatibility of material-environment combinations suitable for high energy upper stage propulsion systems. Surface flawed specimens having thicknesses representative of minimum gage fuel and oxidizer tanks were tested. Titanium alloys 5Al-2.5Sn (ELI), 6Al-4V annealed, and 6Al-4V STA were tested in both liquid and gaseous methane. Aluminum alloy 2219 in the T87 and T6E46 condition was tested in fluorine, a fluorine-oxygen mixture, and methane. Results were evaluated using modified linear elastic fracture mechanics parameters.

  17. Effects of leachate infiltration and desiccation cracks on hydraulic conductivity of compacted clay

    Jun HE


    Full Text Available Both cracks in clay liner and the complex composition of landfill leachate might have effects on the hydraulic conductivity of a compacted clay liner. In this study, the hydraulic conductivities of natural clay and bentonite-modified clay with and without desiccation cracks were measured, respectively, using three types of liquids as permeating liquid: 2 500 mg/L acetic acid solution, 0.5 mol/L CaCl2 solution, and tap water. When tap water was adopted as the permeating liquid, desiccation cracks resulted in increases in the average value of hydraulic conductivity: a 25-fold increase for the natural clay and a 5.7-fold increase for the bentonite-modified clay. It was also found out that the strong self-healing capability of bentonite helped to reduce the adverse impact of cracks on hydraulic performance. In contrast to tap water, simulated leachates (acetic acid and CaCl2 solutions show no adverse effect on the hydraulic conductivities of natural and bentonite-modified clays. It is concluded that desiccation cracks and bentonite have more significant effects on hydraulic performance than simulated leachates.

  18. Subsidence crack closure: rate, magnitude and sequence

    De Graff, J.V.; Romesburg, H.C.


    Tension cracks are a major surface disturbance resulting from subsidence and differential settlement above underground coal mines. Recent engineering studies of subsidence indicate that cracks may close where tensile stresses causing the cracks are reduced or relaxed. This stress reduction occurs as mining in the area is completed. Crack closure was confirmed by a study in the Wasatch Plateau coal field of central Utah. Cracks occurred in both exposed bedrock and regolith in an area with maximum subsidence of 3 m. Mean closure rate was 0.3 cm per week with individual crack closure rates between 0.2 cm and 1.0 cm per week. The mean crack closure magnitude was 80% with closure magnitudes varying between 31% and 100%. Actual magnitude values ranged from 0.6 cm to 6.5 cm with a mean value of 3.8 cm. Statistical analysis compared width change status among cracks over time. It was found that: 1) a 41% probability existed that a crack would exhibit decreasing width per weekly measurement, 2) closure state sequences seem random over time, and 3) real differences in closure state sequence existed among different cracks. (6 refs.) (In English)


    W.C. Cui; X.P. Huang


    Crack growth rate curves are the fundamental material property for metal structures under fatigue loading. Although there are many crack growth rate curves available in the literature, few of them showed the capability to explain various special phenomena observed in tests. A modified constitutive relation recently proposed by McEvily and his co-workers showed very promising capability. This modified constitutive relation is further generalized by (1) introducing an unstable fracture condition; (2) defining a virtual strength to replace the yield stress; and (3) defining an overload and underload parameter. The performances of this general constitutive relation for fatigue crack growth is extensively studied and it is found that this general constitutive relation is able to explain various phenomena observed with particular strong capability on load sequence effect.

  20. Controlling fatigue crack paths for crack surface marking and growth investigations

    S. Barter


    Full Text Available While it is well known that fatigue crack growth in metals that display confined slip, such as high strength aluminium alloys, develop crack paths that are responsive to the loading direction and the local microstructural orientation, it is less well known that such paths are also responsive to the loading history. In these materials, certain loading sequences can produce highly directional slip bands ahead of the crack tip and by adjusting the sequence of loads, distinct fracture surface features or progression marks, even at very small crack depths can result. Investigating the path a crack selects in fatigue testing when particular combinations of constant and variable amplitude load sequences are applied is providing insight into crack growth. Further, it is possible to design load sequences that allow very small amounts of crack growth to be measured, at very small crack sizes, well below the conventional crack growth threshold in the aluminium alloy discussed here. This paper reports on observations of the crack path phenomenon and a novel test loading method for measuring crack growth rates for very small crack depths in aluminium alloy 7050-T7451 (an important aircraft primary structural material. The aim of this work was to firstly generate short- crack constant amplitude growth data and secondly, through the careful manipulation of the applied loading, to achieve a greater understanding of the mechanisms of fatigue crack growth in the material being investigated. A particular focus of this work is the identification of the possible sources of crack growth retardation and closure in these small cracks. Interpreting these results suggests a possible mechanism for why small fatigue crack growth through this material under variable amplitude loading is faster than predicted from models based on constant amplitude data alone.

  1. Online Bridge Crack Monitoring with Smart Film

    Benniu Zhang


    Full Text Available Smart film crack monitoring method, which can be used for detecting initiation, length, width, shape, location, and propagation of cracks on real bridges, is proposed. Firstly, the fabrication of the smart film is developed. Then the feasibility of the method is analyzed and verified by the mechanical sensing character of the smart film under the two conditions of normal strain and crack initiation. Meanwhile, the coupling interference between parallel enameled wires of the smart film is discussed, and then low-frequency detecting signal and the custom communication protocol are used to decrease interference. On this basis, crack monitoring system with smart film is designed, where the collected crack data is sent to the remote monitoring center and the cracks are simulated and recurred. Finally, the monitoring system is applied to six bridges, and the effects are discussed.

  2. Crack Propagation in Bamboo's Hierarchical Cellular Structure

    Habibi, Meisam K.; Lu, Yang


    Bamboo, as a natural hierarchical cellular material, exhibits remarkable mechanical properties including excellent flexibility and fracture toughness. As far as bamboo as a functionally graded bio-composite is concerned, the interactions of different constituents (bamboo fibers; parenchyma cells; and vessels.) alongside their corresponding interfacial areas with a developed crack should be of high significance. Here, by using multi-scale mechanical characterizations coupled with advanced environmental electron microscopy (ESEM), we unambiguously show that fibers' interfacial areas along with parenchyma cells' boundaries were preferred routes for crack growth in both radial and longitudinal directions. Irrespective of the honeycomb structure of fibers along with cellular configuration of parenchyma ground, the hollow vessels within bamboo culm affected the crack propagation too, by crack deflection or crack-tip energy dissipation. It is expected that the tortuous crack propagation mode exhibited in the present study could be applicable to other cellular natural materials as well.

  3. Air flow through smooth and rough cracks

    Kula, H.-G.; Sharples, S. [Sheffield Univ. (United Kingdom). Dept. of Building Science


    A series of laboratory experiments are described which investigated the effect of surface roughness on the air flow characteristics of simple, straight-through, no-bend cracks with smooth and rough internal surfaces. The crack thicknesses used in the study were 1.0, 1.5 and 2.0mm. The crack lengths, in the direction of flow, were 50.8mm and 76.2mm. For the rough cracks the roughness was simulated with two different grades of commercially available energy-cloth (grade 60 and 100). The experimental results were satisfactorily fitted to a quadratic relationship between {Delta}p and Q of the form {Delta}p = AQ + BQ{sup 2} for both the smooth and rough crack data. The effect of roughness on the reduction of air flowing through a crack is also discussed. (author)

  4. Crack problem in a long cylindrical superconductor

    Yong, Hua-Dong; Zhou, You-He; Zeng, Jun


    In this work, the general problem of a center crack in a long cylindrical superconductor is studied. The dependence of the stress intensity factor on the parameters, including the crack length and the applied field, is investigated. We presented a simple model in which the effect of the crack on the critical current is taken into account. It is assumed that the crack forms a perfect barrier to the flow of current. The Bean model and the Kim model are considered for the critical state. Based on the complex potential and boundary collocation methods, the stress intensity factor under the magnetic field is obtained for a long cylindrical superconductor containing a central crack. The results show that the crack length and the applied field have significant effects on the fracture behavior of the superconductor.

  5. Numerical Study of Corrosion Crack Opening

    Thoft-Christensen, Palle; Frandsen, Henrik Lund; Svensson, Staffan


    for the corrosion crack opening. Experiments and theoretical analysis by a numerical method, FEM, support that the relation between the reduction of the reinforcement bar diameter due to corrosion and the corresponding increase in crack width for a given time interval, measured on the surface of a concrete specimen...... is proportional. More recently, the constant of proportionality, the so-called crack-corrosion index, has been studied further with respect to its dependence on the diameter of the reinforcement and the concrete cover. In the present paper the above-mentioned work is presented and extended with more realistic 3D......-models of the cracked concrete beam. The crack-corrosion index is evaluated for a variation of different parameters, i.e. bar diameter, concrete cover, crack length and type of corrosion product. This paper is an extended version of a paper by Thoft-Christensen et al. (2005) presented at the IFIP WG 7.5 Conference...

  6. Fatigue Crack Closure Analysis Using Digital Image Correlation

    Leser, William P.; Newman, John A.; Johnston, William M.


    Fatigue crack closure during crack growth testing is analyzed in order to evaluate the critieria of ASTM Standard E647 for measurement of fatigue crack growth rates. Of specific concern is remote closure, which occurs away from the crack tip and is a product of the load history during crack-driving-force-reduction fatigue crack growth testing. Crack closure behavior is characterized using relative displacements determined from a series of high-magnification digital images acquired as the crack is loaded. Changes in the relative displacements of features on opposite sides of the crack are used to generate crack closure data as a function of crack wake position. For the results presented in this paper, remote closure did not affect fatigue crack growth rate measurements when ASTM Standard E647 was strictly followed and only became a problem when testing parameters (e.g., load shed rate, initial crack driving force, etc.) greatly exceeded the guidelines of the accepted standard.

  7. Crack

    ... rate, breathing rate, blood pressure , and body temperature decreased appetite and less need for sleep feelings of restlessness, ... effects include: gangrene in the bowels resulting from decreased blood ... chest pain reduced appetite, plus health problems associated with not eating a ...



    En este trabajo de tesis presentamos dos experimentos en que trayectorias de fracturas sumamente reproducibles son obtenidas en láminas delgadas frágiles. En ambos casos, a partir de configuraciones iniciales sumamente simples y pequeñas, las trayectorias obtenidas son espirales logarítmicas de gran tamao. Nuestro primer experimento consiste en un crack que se inicia desde un corte recto hecho en una lámina delgada y que es forzado a propagarse por medio de empujar con un objeto sólido....

  9. Fatigue Crack Closure - A Review


    gauge along the crack line. They used CCT speci- mens of high tensile strength steel ( HY80 ). The measured value of U was found to be a minimum at the...ultrasonic surface wave technique on 12.5mm thick specimens of 2024-T851, 2024-T351, Al 2219, Ti-6AI-4V and 17-4 PH steel . Most of the results were...medium and high strength steels . Exami- nation of the fracture surfaces suggested that raising the mean stress in low fracture toughness steels could

  10. Expansive Soil Crack Depth under Cumulative Damage

    Bei-xiao Shi


    Full Text Available The crack developing depth is a key problem to slope stability of the expansive soil and its project governance and the crack appears under the roles of dry-wet cycle and gradually develops. It is believed from the analysis that, because of its own cohesion, the expansive soil will have a certain amount of deformation under pulling stress but without cracks. The soil body will crack only when the deformation exceeds the ultimate tensile strain that causes cracks. And it is also believed that, due to the combined effect of various environmental factors, particularly changes of the internal water content, the inherent basic physical properties of expansive soil are weakened, and irreversible cumulative damages are eventually formed, resulting in the development of expansive soil cracks in depth. Starting from the perspective of volumetric strain that is caused by water loss, considering the influences of water loss rate and dry-wet cycle on crack developing depth, the crack developing depth calculation model which considers the water loss rate and the cumulative damages is established. Both the proposal of water loss rate and the application of cumulative damage theory to the expansive soil crack development problems try to avoid difficulties in matrix suction measurement, which will surely play a good role in promoting and improving the research of unsaturated expansive soil.

  11. Nonlinear modal method of crack localization

    Ostrovsky, Lev; Sutin, Alexander; Lebedev, Andrey


    A simple scheme for crack localization is discussed that is relevant to nonlinear modal tomography based on the cross-modulation of two signals at different frequencies. The scheme is illustrated by a theoretical model, in which a thin plate or bar with a single crack is excited by a strong low-frequency wave and a high-frequency probing wave (ultrasound). The crack is assumed to be small relative to all wavelengths. Nonlinear scattering from the crack is studied using a general matrix approach as well as simplified models allowing one to find the nonlinear part of crack volume variations under the given stress and then the combinational wave components in the tested material. The nonlinear response strongly depends on the crack position with respect to the peaks or nodes of the corresponding interacting signals which can be used for determination of the crack position. Juxtaposing various resonant modes interacting at the crack it is possible to retrieve both crack location and orientation. Some aspects of inverse problem solutions are also discussed, and preliminary experimental results are presented.

  12. Wettability Induced Crack Dynamics and Morphology

    Ghosh, Udita Uday; Bhandari, Aditya Bikram; Chakraborty, Suman; DasGupta, Sunando


    Substrate wettability alteration induced control over crack formation process in thin colloidal films has been addressed in the present study. Colloidal nanosuspension (53nm, mean particle diameter) droplets have been subjected to natural drying to outline the effects of substrate surface energies over the dry-out characteristics with emphasis on crack dynamics, crack morphology and underlying particle arrangements. Experimental findings indicate that number of cracks formed decreases with increase in substrate hydrophobicity. These physical phenomena have been explained based on the magnitude of stress dissipation incurred by the substrate. DLVO predictions are also found to be in tune with the reported experimental investigations.

  13. Crack depth determination with inductive thermography

    Oswald-Tranta, B.; Schmidt, R.


    Castings, forgings and other steel products are nowadays usually tested with magnetic particle inspection, in order to detect surface cracks. An alternative method is active thermography with inductive heating, which is quicker, it can be well automated and as in this paper presented, even the depth of a crack can be estimated. The induced eddy current, due to its very small penetration depth in ferro-magnetic materials, flows around a surface crack, heating this selectively. The surface temperature is recorded during and after the short inductive heating pulse with an infrared camera. Using Fourier transformation the whole IR image sequence is evaluated and the phase image is processed to detect surface cracks. The level and the local distribution of the phase around a crack correspond to its depth. Analytical calculations were used to model the signal distribution around cracks with different depth and a relationship has been derived between the depth of a crack and its phase value. Additionally, also the influence of the heating pulse duration has been investigated. Samples with artificial and with natural cracks have been tested. Results are presented comparing the calculated and measured phase values depending on the crack depth. Keywords: inductive heating, eddy current, infrared

  14. Fatigue crack growth detect, assess, avoid

    Richard, Hans Albert


    This book offers a concise introduction to fatigue crack growth, based on practical examples. It discusses the essential concepts of fracture mechanics, fatigue crack growth under constant and variable amplitude loading and the determination of the fracture-mechanical material parameters. The book also introduces the analytical and numerical simulation of fatigue crack growth as well as crack initiation. It concludes with a detailed description of several practical case studies and some exercises. The target group includes graduate students, researchers at universities and practicing engineers.

  15. Investigations of Low Temperature Time Dependent Cracking

    Van der Sluys, W A; Robitz, E S; Young, B A; Bloom, J


    The objective of this project was to investigate metallurgical and mechanical phenomena associated with time dependent cracking of cold bent carbon steel piping at temperatures between 327 C and 360 C. Boiler piping failures have demonstrated that understanding the fundamental metallurgical and mechanical parameters controlling these failures is insufficient to eliminate it from the field. The results of the project consisted of the development of a testing methodology to reproduce low temperature time dependent cracking in laboratory specimens. This methodology was used to evaluate the cracking resistance of candidate heats in order to identify the factors that enhance cracking sensitivity. The resultant data was integrated into current available life prediction tools.

  16. Cracking of open traffic rigid pavement

    Niken Chatarina


    Full Text Available The research is done by observing the growth of real structure cracking in Natar, Lampung, Indonesia compared to C. Niken’s et al research and literature study. The rigid pavement was done with open traffic system. There are two main crack types on Natar rigid pavement: cracks cross the road, and cracks spreads on rigid pavement surface. The observation of cracks was analyzed by analyzing material, casting, curing, loading and shrinkage mechanism. The relationship between these analysis and shrinkage mechanism was studied in concrete micro structure. Open traffic make hydration process occur under vibration; therefore, fresh concrete was compressed and tensioned alternately since beginning. High temperature together with compression, cement dissociation, the growth of Ca2+ at very early age leads abnormal swelling. No prevention from outside water movement leads hydration process occur with limited water which caused spreads fine cracks. Limited water improves shrinkage and plastic phase becomes shorter; therefore, rigid pavement can’t accommodate the abnormal swelling and shrinking alternately and creates the spread of cracks. Discontinuing casting the concrete makes both mix under different condition, the first is shrink and the second is swell and creates weak line on the border; so, the cracks appear as cracks across the road.

  17. Crack spacing of unsaturated soils in the critical state

    SUN JiChao; WANG GuangQian; SUN QiCheng


    The cracking mechanism of unsaturated soils due to evaporation is poorly understood, and the magnitude of crack spacing is usually hard to estimate. In this work, cracks were postulated to occur suc-cedently rather than simultaneously, that is, secondary cracks appear after primary cracks as evaporation continues. Formulae of the secondary crack spacing and secondary trend crack spacing were then derived after stress analysis. The calculated spacing values were consistent with the published experimental data. Meanwhile, the effect of the Poisson ratio on the crack spacing was analyzed, which showed that the magnitude of crack spacing was proportional to the Poisson ratio in the range of [0.30,0.35].

  18. On the application of cohesive crack modeling in cementitious materials

    Stang, Henrik; Olesen, John Forbes; Poulsen, Peter Noe;


    Cohesive crack models-in particular the Fictitious Crack Model - are applied routinely in the analysis of crack propagation in concrete and mortar. Bridged crack models-where cohesive stresses are assumed to exist together with a stress singularity at the crack tip-on the other hand, are used....... Further, a quantitative condition is established indicating when a bridged crack model can be approximated with a cohesive crack model with smooth crack closure in terms of the ratio between the energy dissipation associated with the crack tip and the process zone....

  19. Thermodynamic analysis of a process for producing high-octane gasoline components from catalytic cracking gas

    Ismailova, Z. R.; Pirieva, Kh. B.; Kasimov, A. A.; Dzhamalova, S. A.; Gadzhizade, S. M.; Nuriev, Sh. A.; Zeinalova, S. Kh.; Dzhafarov, R. P.


    The results from a thermodynamic analysis of high-octane gasoline component production from catalytic cracking gases using zeolite catalyst OMNIKAT-210P modified with Ni, Co, Cr are presented. The equilibrium constants of the reactions assumed to occur in this process are calculated, along with the equilibrium yield of the reactions.

  20. Challenges and limitations in studying the shrink-swell and crack dynamics of vertisol soils

    The need to study the shrink-swell and crack properties of vertic soils has long been recognized given their dynamics in time and space, which modifies the physical properties that impact water and air movement in the soil, flow of water into the subsoil and ground water, and generally alter the hyd...

  1. Effect of Crack Closure on Ultrasonic Detection of Fatigue Cracks at Fastener Holes

    Bowles, S. J.; Harding, C. A.; Hugo, G. R.


    The ultrasonic response from closed fatigue cracks grown in aluminium alloy specimens using a representative aircraft spectrum loading has been characterised as a function of tensile applied load using pulse-echo 45° shear-wave ultrasonic C-scans with focused immersion transducers. Observed trends with crack size and applied load are described and compared to results for artificial machined defects. The results demonstrate that crack closure significantly reduces the ultrasonic response compared to open cracks or machined defects.

  2. Fractografia de compósito estrutural aeronáutico submetido à caracterização de tenacidade à fratura interlaminar em modo I Fractography of aeronautical composite structures submitted to mode I interlaminar fracture toughness characterization

    Geraldo Maurício Cândido


    used method to determine the Mode I fracture toughness of structural composites. In this work samples prepared from a plain weave fabric laminate were submitted to Mode I delamination under static load at room temperature. The analysis of the delaminated surfaces was performed with scanning electron microscopy (SEM. The results show that the fracture process initiates at the resin pockets after a Teflon® insert and propagates along the resin rich areas at the crossing of weft and warp tows. The main fractographical aspects revealed are identified, reported and discussed.

  3. Extended propagation model for interfacial crack in composite material structure

    闫相桥; 冯希金


    An interfacial crack is a common damage in a composite material structure . An extended propaga-tion model has been established for an interfacial crack to study the dependence of crack growth on the relativesizes of energy release rates at left and right crack tips and the properties of interfacial material characterize thegrowth of interfacial crack better.

  4. Mode-Ⅰ crack in a two-dimensional fibre-reinforced generalized thermoelastic problem

    Kh. Lotfy


    A general model of the equations of the Lord-?ulman theory including one relaxation time and the Green-Lindsay theory with two relaxation times,as well as the classical dynamical coupled theory,are applied to the study of the influence of reinforcement on the total deformation for an infinite space weakened by a finite linear opening modeI crack.We study the influence of reinforcement on the total deformation of rotating thermoelastic half-space and their interaction with each other.The material is homogeneous isotropic elastic half space.The crack is subjected to prescribed temperature and stress distributions.The normal mode analysis is used to obtain the exact expressions for displacement components,force stresses,and temperature.The variations of the considered variables with the horizontal distance are illustrated graphically.Comparisons are made with the results obtained in the three theories with and without rotation.A comparison is also made between the two theories for different depths.

  5. Chloride Penetration through Cracks in High-Performance Concrete and Surface Treatment System for Crack Healing

    In-Seok Yoon


    Full Text Available For enhancing the service life of concrete structures, it is very important to minimize crack at surface. Even if these cracks are very small, the problem is to which extend these cracks may jeopardize the durability of these decks. It was proposed that crack depth corresponding with critical crack width from the surface is a crucial factor in view of durability design of concrete structures. It was necessary to deal with chloride penetration through microcracks characterized with the mixing features of concrete. This study is devoted to examine the effect of high strength concrete and reinforcement of steel fiber on chloride penetration through cracks. High strength concrete is regarded as an excellent barrier to resist chloride penetration. However, durability performance of cracked high strength concrete was reduced seriously up to that of ordinary cracked concrete. Steel fiber reinforcement is effective to reduce chloride penetration through cracks because steel fiber reinforcement can lead to reduce crack depth significantly. Meanwhile, surface treatment systems are put on the surface of the concrete in order to seal the concrete. The key-issue is to which extend a sealing is able to ensure that chloride-induced corrosion can be prevented. As a result, penetrant cannot cure cracks, however, coating and combined treatment can prevent chloride from flowing in concrete with maximum crack width of 0.06 mm and 0.08 mm, respectively.

  6. On fatigue crack growth in ductile materials by crack-tip blunting

    Tvergaard, Viggo


    One of the basic mechanisms for fatigue crack growth in ductile metals is that depending on crack-tip blunting under tensile loads and re-sharpening of the crack-tip during unloading. In a standard numerical analysis accounting for finite strains it is not possible to follow this process during...

  7. A Creaking and Cracking Comet

    Faurschou Hviid, Stubbe; Hüttig, Christian; Groussin, Olivier; Mottola, Stefano; Keller, Horst Uwe; OSIRIS Team


    Since the middle of 2014 the OSIRIS cameras on the ESA Rosetta mission have been monitoring the evolution of the comet 67P/Churyumov-Gerasimenko as it passed through perihelion. During the perihelion passage several change events have been observed on the nucleus surface. For example existing large scale cracks have expanded and new large scale cracks have been created. Also several large scale "wave pattern" like change events have been observed in the Imhotep and Hapi regions. These are events not directly correlated with any normal visible cometary activity. One interpretation is that these are events likely caused by "seismic" activity. The seismic activity is created by the self-gravity stress of the non-spherical comet nucleus and stress created by the non-gravitational forces acting on the comet. The non-gravitational forces are changing the rotation period of the comet (~20min/perihelion passage) which induces a changing mechanical stress pattern through the perihelion passage. Also the diurnal cycle with its changing activity pattern is causing a periodic wobble in the stress pattern that can act as a trigger for a comet quake. The stress pattern has been modeled using a finite element model that includes self-gravity, the comet spin and the non-gravitational forces based on a cometary activity model. This paper will discuss what can be learned about the comet nucleus structure and about the cometary material properties from these events and from the FEM model.

  8. What can cracked polymer do

    Jiao, Kexin; Zhou, Chuanhong; Kohli, Punit; Poudel, Anish; Chu, Tsuchin


    Buckling, delamination, and cracking are very well known phenomenon observed in most thin films. They were theoretically explained by the existence of mechanical instability due to the residue stress generated when a thin film is deposited on substrates or undergoing environmental stimulus. Buckled structures at micro- or nano-scale have been of great interests and have been used extensively in many applications including particles self-assembling, surface wettability modification, and micro-electronic device fabrication. However, peeling of a layer from a substrate due to delamination or fractures on a thin film due to cracking is mostly taken as an undesirable result. Therefore, strategies are inspired for preventing or removing these often undesired structures. We found that after being heated above its decomposition temperature and then cooled to room temperature, a PDMS thin film showed micro-fibers of 100 μm width and up to 1.5 cm in length. By studying the formation mechanism, control of the dimensions and of the growth pattern on a substrate for PDMS micro-fibers were realized. Giving credit to their high flexibility and optical transparency, a PDMS micro-fiber were utilized in high resolution near field imaging achieved by attaching a micro-lens on the fiber. Interestingly, a surface covered by PDMS micro-fibers will turn from superhydrophobic into superhydrophilic by further heating providing potential applications in surface wettability modification. In future, we will investigate and simulate the growth of PDMS micro-fiber and look for more possible applications.

  9. On the detectability of transverse cracks in laminated composites using electrical potential change measurements

    Selvakumaran, Lakshmi


    Real-time health monitoring of structures made of laminated composites is necessary as significant damage may occur without any visible signs on the surface. Inspection by electrical tomography (ET) seems a viable approach that relies on voltage measurements from a network of electrodes across the inspected domain to infer conductivity change within the bulk material. If conductivity decreases significantly with increasing damage, the obtained conductivity map can be correlated to the degradation state of the material. We focus here on detection of transverse cracks. As transverse cracks modify the in-plane transverse conductivity of a single ply, we expect them to be detectable by electrical measurements. Yet, the quality of detection is directly related to the sensitivity of the measurements to the presence of cracks. We use numerical experiments to demonstrate that the sensitivity depends on several material and geometrical parameters. Based on the results, the applicability of ET to detect transverse cracks is discussed. One conclusion from the study is that detecting transverse cracks using ET is more reliable in some laminate configurations than in others. Recommendations about the properties of either the pristine material or the inspected structures are provided to establish if ET is reliable in detecting transverse cracks.

  10. Integrity analysis of cracked welded components; Analyse de l`integrite des composants soudes fissures

    Hornet, P.; Eripret, C.; Gilles, P.; Franco, C.; Ignaccolo, S. [Service Reacteurs Nucleaire et Echangeurs, Departement Mecanique et Technologies des Composants, Direction des Etudes et Recherches, Electricite de France (EDF), 92 - Clamart (France)


    In the frame of the integrity analysis of pressure vessel and piping, welded joints can be very sensitive regions since the neighbouring zones of welded joints can be subjected to crack problems. Moreover, the mechanical analysis of a cracked welded component can be difficult because of the presence around the crack of at least three regions (base metal, weld metal and heat affected zone) having very different mechanical properties and metallurgical structures. In fact, common defect assessment procedures have been developed for homogeneous structures and there have to be modified to take into account the heterogeneity. In order to solve this problem a large research program has been conducted since 1992 in the frame of a collaboration between CEA, Framatome and EDF as well as other laboratories in France or around the world. This paper puts forward the work done during the last years and presents the important advantage for the integrity analysis of cracked welded structures. It is a kind of synthesis of the knowledge acquired during this project. Four aspects are pointed out: 1. the important parameters which govern the mechanical behaviour of welded component and more precisely the plasticity development in such structures; 2. some recommendations for the experimental determination of fracture hardness of weld; 3. a defect assessment procedure for cracked welded components, developed in collaboration with Framatome; 4. the ability of finite element codes of modelling the mechanical behaviour of cracked welded structures 15 refs., 9 figs.

  11. An experimental investigation of the effect of shear-induced diffuse damage on transverse cracking in carbon-fiber reinforced laminates

    Nouri, Hedi


    When subjected to in-plane loading, carbon-fiber laminates experience diffuse damage and transverse cracking, two major mechanisms of degradation. Here, we investigate the effect of pre-existing diffuse damage on the evolution of transverse cracking. We shear-loaded carbon fiber-epoxy pre-preg samples at various load levels to generate controlled configurations of diffuse damage. We then transversely loaded these samples while monitoring the multiplication of cracking by X-ray radiography. We found that diffuse damage has a great effect on the transverse cracking process. We derived a modified effective transverse cracking toughness measure, which enabled a better definition of coupled transverse cracking/diffuse damage in advanced computational models for damage prediction. © 2013 Elsevier Ltd.

  12. Development of crack shape: LBB methodology for cracked pipes

    Moulin, D.; Chapuliot, S.; Drubay, B. [Commissariat a l Energie Atomique, Gif sur Yvette (France)


    For structures like vessels or pipes containing a fluid, the Leak-Before-Break (LBB) assessment requires to demonstrate that it is possible, during the lifetime of the component, to detect a rate of leakage due to a possible defect, the growth of which would result in a leak before-break of the component. This LBB assessment could be an important contribution to the overall structural integrity argument for many components. The aim of this paper is to review some practices used for LBB assessment and to describe how some new R & D results have been used to provide a simplified approach of fracture mechanics analysis and especially the evaluation of crack shape and size during the lifetime of the component.

  13. Characterization of crack growth under combined loading

    Feldman, A.; Smith, F. W.; Holston, A., Jr.


    Room-temperature static and cyclic tests were made on 21 aluminum plates in the shape of a 91.4x91.4-cm Maltese cross with 45 deg flaws to develop crack growth and fracture toughness data under mixed-mode conditions. During cyclic testing, it was impossible to maintain a high proportion of shear-mode deformation on the crack tips. Cracks either branched or turned. Under static loading, cracks remained straight if shear stress intensity exceeded normal stress intensity. Mixed-mode crack growth rate data compared reasonably well with published single-mode data, and measured crack displacements agreed with the straight and branched crack analyses. Values of critical strain energy release rate at fracture for pure shear were approximately 50% higher than for pure normal opening, and there was a large reduction in normal stress intensity at fracture in the presence of high shear stress intensity. Net section stresses were well into the inelastic range when fracture occurred under high shear on the cracks.

  14. Locating a leaking crack by safe stimulation

    Coleman, C.E.; Sagat, S. (Atomic Energy of Canada Ltd., Chalk River, ON (Canada). Chalk River Nuclear Labs.); Shek, G.K.; Graham, D.B.; Durand, M.A. (Ontario Hydro, Toronto, ON (Canada))


    A few Zr-2.5 Nb alloy pressure tubes in CANDU nuclear reactors have leaked through cracks that have grown by delayed hydride cracking (DHC). In some instances, tubes contained confirmed leaks that were leaking at a rate too low for precise identification of the leaking channel. Controlled stimulation of DHC can be used to help locate these leaks by extending the crack and increasing the leak rate without approaching crack instability. In the event of a leak being detected, a plant operator can gain time for leak location by a heating and unloading manoeuvre that will arrest crack growth and increase the critical crack length. This manoeuvre increases the safety margin against tube rupture. If required, the operator can then stimulate cracking in a controlled manner to aid in leak identification. Sequences of temperature and load manoeuvres for safe crack stimulation have been found by laboratory tests on dry specimens and the efficacy of the process has been demonstrated, partly in a power reactor, and partly in a full-scale simulation of a leaking pressure tube. (author).

  15. Entering a Crack: An Encounter with Gossip

    Henderson, Linda


    In this paper, I enter a crack to think otherwise about the concept "gossip". Drawing on previous scholarship engaging with Deleuzian concepts to inform research methodologies, this paper builds on this body of work. Following Deleuze and Guattari, the paper undertakes a mapping of gossip, subsequent to an encounter with a crack.…

  16. Crack propagation directions in unfilled resins.

    Baran, G; Sadeghipour, K; Jayaraman, S; Silage, D; Paul, D; Boberick, K


    Posterior composite restorative materials undergo accelerated wear in the occlusal contact area, primarily through a fatigue mechanism. To facilitate the timely development of new and improved materials, a predictive wear model is desirable. The objective of this study was to develop a finite element model enabling investigators to predict crack propagation directions in resins used as the matrix material in composites, and to verify these predictions by observing cracks formed during the pin-on-disc wear of a 60:40 BISGMA:TEGDMA resin and an EBPADMA resin. Laser confocal scanning microscopy was used to measure crack locations. Finite element studies were done by means of ABAQUS software, modeling a cylinder sliding on a material with pre-existing surface-breaking cracks. Variables included modulus, cylinder/material friction coefficient, crack face friction, and yield behavior. Experimental results were surprising, since most crack directions were opposite previously published observations. The majority of surface cracks, though initially orthogonal to the surface, changed direction to run 20 to 30 degrees from the horizontal in the direction of indenter movement. Finite element modeling established the importance of subsurface shear stresses, since calculations provided evidence that cracks propagate in the direction of maximum K(II)(theta), in the same direction as the motion of the indenter, and at an angle of approximately 20 degrees. These findings provide the foundation for a predictive model of sliding wear in unfilled glassy resins.

  17. Entering a Crack: An Encounter with Gossip

    Henderson, Linda


    In this paper, I enter a crack to think otherwise about the concept "gossip". Drawing on previous scholarship engaging with Deleuzian concepts to inform research methodologies, this paper builds on this body of work. Following Deleuze and Guattari, the paper undertakes a mapping of gossip, subsequent to an encounter with a crack.…

  18. Investigation of Cracked Lithium Hydride Reactor Vessels

    bird, e.l.; mustaleski, t.m.


    Visual examination of lithium hydride reactor vessels revealed cracks that were adjacent to welds, most of which were circumferentially located in the bottom portion of the vessels. Sections were cut from the vessels containing these cracks and examined by use of the metallograph, scanning electron microscope, and microprobe to determine the cause of cracking. Most of the cracks originated on the outer surface just outside the weld fusion line in the base material and propagated along grain boundaries. Crack depths of those examined sections ranged from {approximately}300 to 500 {micro}m. Other cracks were reported to have reached a maximum depth of 1/8 in. The primary cause of cracking was the creation of high tensile stresses associated with the differences in the coefficients of thermal expansion between the filler metal and the base metal during operation of the vessel in a thermally cyclic environment. This failure mechanism could be described as creep-type fatigue, whereby crack propagation may have been aided by the presence of brittle chromium carbides along the grain boundaries, which indicates a slightly sensitized microstructure.

  19. Fracture Mechanical Markov Chain Crack Growth Model

    Gansted, L.; Brincker, Rune; Hansen, Lars Pilegaard


    On the basis of the B-model developed in [J. L. Bogdanoff and F. Kozin, Probabilistic Models of Cumulative Damage. John Wiley, New York (1985)] a new numerical model incorporating the physical knowledge of fatigue crack propagation is developed. The model is based on the assumption that the crack...

  20. Solute transport in cracking clay soils

    Bronswijk, J.J.B.; Ritsema, C.J.; Oostindie, K.; Hamminga, P.


    A bromide tracer applied to a cracked clay soil was adsorbed in the soil matrix close to the soil surface. Upon subsequent precipitation, a small part of the bromide dissolved and flowed rapidly through cracks to the subsoil and the groundwater. As a result, the groundwater and the drain discharge

  1. Strength of Cracked Reinforced Concrete Disks

    Hoang, Cao Linh; Nielsen, Mogens Peter


    The paper deals with models, based on the theory of plasticity, to be used in strength assessments of reinforced concrete disks suffering from different kinds of cracking. Based on the assumption that the sliding strength of concrete is reduced in sections where cracks are located, solutions...

  2. Corrosion and Cracking of Reinforced Concrete

    Thoft-Christensen, Palle

    Modelling of the deterioration of reinforced concrete has in recent years changed from being a deterministic modelling based on experience to be stochastic modelling based on sound and consistent physical, chemical and mechanical principles. In this paper is presented a brief review of modern mod...... for time to initial corrosion, time to initial cracking, and time to a given crack width may be obtained....

  3. An Experimental Study of Fatigue Crack Growth in Different Orientation of Extruded AZ31B Mg Alloy Bar%挤压AZ31B镁合金圆棒不同取向的疲劳裂纹扩展

    郑三龙; 陈冰冰; 张玮; 高增梁


    Fatigue crack growth (FCG) experiments were carried out using extruded AZ31B magnesium alloy bar.The pre-crack compact tension (CT) specimens were oriented in three different directions with respect to the extrusion direction.The experimental results reveal that the specimen orientation has a significant influence on the FCG rate and crack path.The FGC rate of the T-L specimen is the highest while the L-T specimen shows the lowest value.Typical macroscopic Mode I crack is developed in the T-L and T-R specimens whereas a deviation from the Mode I crack path and branching occur in the L-T specimens.For the L-T specimens,a plateau of constant crack growth rate occurs at low stress intensity factor range (△K) Transgranular cracking is the major cracking mode.Slip induced cleavage dominates the transgranular cracking in the T-L and L-T specimens whereas both twin boundary cracking and slip inducad cleavage exist in the T-R specimens.The FCG rate decreases with the increasing load frequency at △K > 3 MPa √m.%使用紧凑拉伸(CT)试样,研究了挤压AZ31B镁合金圆棒三个方向的组织及疲劳裂纹扩展性能.结果表明,疲劳裂纹以穿晶为主的混合方式沿滑移带扩展.T-L方向裂纹呈直线扩展,扩展速率最高,T-R方向孪生和滑移协同塑性变形,裂纹局部偏转,呈波浪形沿径向扩展,扩展速率较低,强织构和不均匀组织引起L-T方向裂纹分叉和偏离,降低了裂纹尖端有效驱动应力强度因子幅,裂纹扩展速率最低,在疲劳裂纹扩展速率(da/dN)与应力强度因子幅(△K)的关系曲线上出现水平段.在△K较小时加载频率对裂纹扩展速率的影响不大,AK>3 MPa√m时裂纹扩展速率随着加载频率的提高而减小.

  4. 基于 VIC 3D 技术的重组竹I 型断裂参数确定方法%Determination of mode-I fracture parameters of parallel strand bamboo based on VIC-3D technology

    杨蕾; 周爱萍; 黄东升; 何晨


    Fabricated via industrial process using raw bamboo,Parallel strand bamboo (PSB)is a high strength composite which has been used in building constructions in recent years.Microvoids are inevitably left in PSB composite owing to the dimensional inconsistence of bamboo fibers;hence fracture due to mocrovids coalescence and expanding maybe a major failure mode of PSB components.This paper amid at studying on the Mode I fracture properties based on LEFM theory and Iwrin’s energy theory. Wedge splitting test was employed as test method.The length of crack expending was determined by three dimensional virtual image correlation (VIC-3D)global-field deformation acquisition system.Fracture toughness of PSB and R-curves were obtained.The results showed that the VIC-3D global-field acquisition system can precisely determine the crack tip and the complicated calculation for crack length determination may be avoided.Good agreement may be achieved between the result of this method and compliance approach,which indicated that the proposed method in this study is efficient.%重组竹是原竹经工业化制造而成的一种高强复合材料,近年来被用于建筑结构。由于重组竹内部存在许多微裂纹,断裂破坏是重组竹构件的主要失效模式。本文基于线弹性断裂理论和 Irwin 能量原理,采用 VIC 3D 全场变形测量技术确定裂纹扩展长度,通过重组竹楔形试件断裂试验,研究重组竹 I 型裂纹的断裂性能,给出重组竹的断裂韧度和 R 曲线。试验表明:VIC 3D 全场变形测量技术可准确确定裂纹尖端,避免了等效柔度法的复杂运算。该方法的结构与等效柔度法高度一致,是研究重组竹断裂性能的一种有效测量手段。

  5. Crack spacing threshold of double cracks propagation for large-module rack

    赵铁柱; 石端伟; 姚哲皓; 毛宏勇; 程术潇; 彭惠


    Large-module rack of the Three Gorges shiplift is manufactured by casting and machining, which is unable to avoid slag inclusions and surface cracks. To ensure its safety in the future service, studying on crack propagation rule and the residual life estimation method of large-module rack is of great significance. The possible crack distribution forms of the rack in the Three Gorges shiplift were studied. By applying moving load on the model in FRANC3D and ANSYS, quantitative analyses of interference effects on double cracks in both collinear and offset conditions were conducted. The variation rule of the stress intensity factor (SIF) influence factor,RK, of double collinear cracks changing with crack spacing ratio,RS, was researched. The horizontal and vertical crack spacing threshold of double cracks within the design life of the shiplift were obtained, which are 24 and 4 times as large as half of initial crack length,c0, respectively. The crack growth rates along the length and depth directions in the process of coalescence on double collinear cracks were also studied.

  6. Unsaturated Seepage Analysis of Cracked Soil including Development Process of Cracks

    Ling Cao


    Full Text Available Cracks in soil provide preferential pathways for water flow and their morphological parameters significantly affect the hydraulic conductivity of the soil. To study the hydraulic properties of cracks, the dynamic development of cracks in the expansive soil during drying and wetting has been measured in the laboratory. The test results enable the development of the relationships between the cracks morphological parameters and the water content. In this study, the fractal model has been used to predict the soil-water characteristic curve (SWCC of the cracked soil, including the developmental process of the cracks. The cracked expansive soil has been considered as a crack-pore medium. A dual media flow model has been developed to simulate the seepage characteristics of the cracked expansive soil. The variations in pore water pressure at different part of the model are quite different due to the impact of the cracks. This study proves that seepage characteristics can be better predicted if the impact of cracks is taken into account.

  7. Probabilistic analysis of linear elastic cracked structures


    This paper presents a probabilistic methodology for linear fracture mechanics analysis of cracked structures. The main focus is on probabilistic aspect related to the nature of crack in material. The methodology involves finite element analysis; statistical models for uncertainty in material properties, crack size, fracture toughness and loads; and standard reliability methods for evaluating probabilistic characteristics of linear elastic fracture parameter. The uncertainty in the crack size can have a significant effect on the probability of failure, particularly when the crack size has a large coefficient of variation. Numerical example is presented to show that probabilistic methodology based on Monte Carlo simulation provides accurate estimates of failure probability for use in linear elastic fracture mechanics.

  8. Strain rate effects in stress corrosion cracking

    Parkins, R.N. (Newcastle upon Tyne Univ. (UK). Dept. of Metallurgy and Engineering Materials)


    Slow strain rate testing (SSRT) was initially developed as a rapid, ad hoc laboratory method for assessing the propensity for metals an environments to promote stress corrosion cracking. It is now clear, however, that there are good theoretical reasons why strain rate, as opposed to stress per se, will often be the controlling parameter in determining whether or not cracks are nucleated and, if so, are propagated. The synergistic effects of the time dependence of corrosion-related reactions and microplastic strain provide the basis for mechanistic understanding of stress corrosion cracking in high-pressure pipelines and other structures. However, while this may be readily comprehended in the context of laboratory slow strain tests, its extension to service situations may be less apparent. Laboratory work involving realistic stressing conditions, including low-frequency cyclic loading, shows that strain or creep rates give good correlation with thresholds for cracking and with crack growth kinetics.

  9. Crack front propagation by kink formation

    Roesch, Frohmut; Trebin, Hans-Rainer [Universitaet Stuttgart, Institut fuer Theoretische und Angewandte Physik, 70550 Stuttgart (Germany)


    In a brittle material a travelling crack generates an upper and a lower fracture surface, which meet at a one-dimensional crack front. From a macroscopic point of view there is no reason why this curve should deviate from a straight line, contrary to the atomistic point of view, where a crack propagates by successive rupture of cohesive bonds. We investigate fracture of the C15 NbCr{sub 2} Friauf-laves phase on an atomic level by means of molecular dynamics simulations. The numerical experiments highlight that crack fronts in general do not form a straight line and propagate by kink-pair formation at low loads (EPL 87 (2009) 66004). This mechanism should be relevant for crack propagation in any ordered brittle solid.

  10. XFEM for Thermal Crack of Massive Concrete

    Guowei Liu


    Full Text Available Thermal cracking of massive concrete structures occurs as a result of stresses caused by hydration in real environment conditions. The extended finite element method that combines thermal fields and creep is used in this study to analyze the thermal cracking of massive concrete structures. The temperature field is accurately simulated through an equivalent equation of heat conduction that considers the effect of a cooling pipe system. The time-dependent creep behavior of massive concrete is determined by the viscoelastic constitutive model with Prony series. Based on the degree of hydration, we consider the main properties related to cracking evolving with time. Numerical simulations of a real massive concrete structure are conducted. Results show that the developed method is efficient for numerical calculations of thermal cracks on massive concrete. Further analyses indicate that a cooling system and appropriate heat preservation measures can efficiently prevent the occurrence of thermal cracks.

  11. Field cracking performance of airfield rigid pavements

    Yusuf Mehta


    Full Text Available This paper discusses cracking in airport pavements as studied in Construction Cycle 6 of testing carried out at the National Airport Pavement Testing Facility by the Federal Aviation Administration. Pavements of three different flexural strengths as well as two different subgrades, a soft bituminous layer and a more rigid layer known as econocrete, were tested. In addition to this, cracking near two types of isolated transition joints, a reinforced edge joint and a thickened edge joint, was considered. The pavement sections were tested using a moving load simulating that of an aircraft. It has been determined that the degree of cracking was reduced as the flexural strength of the pavement was increased and that fewer cracks formed over the econocrete base than over the bituminous base. In addition, the thickened edge transition joint was more effective in preventing cracking at the edges compared to the reinforced edge joint.

  12. Crack Growth in Concrete Gravity Dams Based on Discrete Crack Method

    A. R. Lohrasbi


    Full Text Available Seepage is the most parameter in water management safety and in stable agricultural. This seepage is passed through the cracks that are present to some degree in hydraulic structures. They may exist as basic defects in the constituent materials or may be induced in construction or during service life. To avoid such failure in concrete dams, safety would be an important factor. Over-design carries heavy penalty in terms of excess weight. So the fracture mechanics theory is a principal necessity of evaluating the stability of such crack propagation. For the process of crack propagation analysis in concrete structures, there are two general models: discrete crack and smeared crack. This study surveys the crack propagation in concrete gravity dams based on discrete crack methods. Moreover, we use a program provided specifically for this purpose.

  13. Crack shape developments and leak rates for circumferential complex-cracked pipes

    Brickstad, B.; Bergman, M. [SAQ Inspection Ltd., Stockholm (Sweden)


    A computerized procedure has been developed that predicts the growth of an initial circumferential surface crack through a pipe and further on to failure. The crack growth mechanism can either be fatigue or stress corrosion. Consideration is taken to complex crack shapes and for the through-wall cracks, crack opening areas and leak rates are also calculated. The procedure is based on a large number of three-dimensional finite element calculations of cracked pipes. The results from these calculations are stored in a database from which the PC-program, denoted LBBPIPE, reads all necessary information. In this paper, a sensitivity analysis is presented for cracked pipes subjected to both stress corrosion and vibration fatigue.

  14. Fully plastic crack opening analyses of complex-cracked pipes for Ramberg-Osgood materials

    Jeong, Jae Uk; Choi, Jae Boong [Sungkyunkwan University, Suwon (Korea, Republic of); Huh, Nam Su [Seoul National University, Seoul (Korea, Republic of); Kim, Yun Jae [Korea University, Seoul (Korea, Republic of)


    The plastic influence functions for calculating fully plastic Crack opening displacement (COD) of complex-cracked pipes were newly proposed based on systematic 3-dimensional (3-D) elastic-plastic Finite element (FE) analyses using Ramberg-Osgood (R-O) relation, where global bending moment, axial tension and internal pressure are considered separately as a loading condition. Then, crack opening analyses were performed based on GE/EPRI concept by using the new plastic influence functions for complex-cracked pipes made of SA376 TP304 stainless steel, and the predicted CODs were compared with FE results based on deformation plasticity theory of tensile material behavior. From the comparison, the confidence of the proposed fully plastic crack opening solutions for complex-cracked pipes was gained. Therefore, the proposed engineering scheme for COD estimation using the new plastic influence functions can be utilized to estimate leak rate of a complex-cracked pipe for R-O material.

  15. General forms of elastic-plastic matching equations for mode-Ⅲ cracks near crack line

    Zhi-jian YI; Chao-hua ZHAO; Qing-guo YANG; Kai PENG; Zong-ming HUANG


    Crack line analysis is an effective way to solve elastic-plastic crack problems.Application of the method does not need the traditional small-scale yielding conditions and can obtain sufficiently accurate solutions near the crack line. To address mode-Ⅲ crack problems under the perfect elastic-plastic condition,matching procedures of the crack line analysis method are summarized and refined to give general forms and formulation steps of plastic field,elastic-plastic boundary,and elastic-plastic matching equations near the crack line. The research unifies mode-Ⅲ crack problems under different conditions into a problem of determining four integral constants with four matching equations.An example is given to verify correctness,conciseness,and generality of the procedure.

  16. Analysis Of Ductile Crack Growth In Pipe Test In STYLE Project

    Yin, Shengjun [ORNL; Williams, Paul T [ORNL; Klasky, Hilda B [ORNL; Bass, Bennett Richard [ORNL


    The Oak Ridge National Laboratory (ORNL) is conducting structural analyses, both deterministic and probabilistic, to simulate a large scale mock-up experiment planned within the European Network for Structural Integrity for Lifetime Management non-RPV Components (STYLE). The paper summarizes current ORNL analyses of STYLE s Mock-up3 experiment to simulate/evaluate ductile crack growth in a cladded ferritic pipe. Deterministic analyses of the large-scale bending test of ferritic surge pipe, with an internal circumferential crack, are simulated with a number of local micromechanical approaches, such as Gurson-Tvergaard-Needleman (GTN) model and cohesive-zone model. Both WARP 3D and ABAQUS general purpose finite element programs are being used to predict the failure load and the failure mode, i.e. ductile tearing or net-section collapse, as part of the pre-test phase of the project. Companion probabilistic analyses of the experiment are utilizing the ORNL developed open-source Structural Integrity Assessment Modular - Probabilistic Fracture Mechanics (SIAM-PFM) framework. SIAM-PFM contains engineering assessment methodology such as the tearing instability (J-T analysis) module developed for inner surface cracks under bending load. The driving force J-integral estimations are based on the SC.ENG1 or SC.ENG2 models. The J-A2 methodology is used to transfer (constraint-adjust) J-R curve material data from standard test specimens to the Mock-up3 experiment configuration. The probabilistic results of the Mock-Up3 experiment obtained from SIAM-PFM will be compared to those generated using the deterministic finite element modeling approach. The objective of the probabilistic analysis is to provide uncertainty bounds that will assist in assessing the more detailed 3D finite-element solutions and to also assess the level of confidence that can be placed in the best-estimate finite-element solutions.

  17. Investigating Reaction-Driven Cracking

    Kelemen, P. B.; Hirth, G.; Savage, H. M.


    Many metamorphic reactions lead to large volume changes, and potentially to reaction-driven cracking [1,2]. Large-scale hydration of mantle peridotite to produce serpentine or talc is invoked to explain the rheology of plate boundaries, the nature of earthquakes, and the seismic properties of slow-spread ocean crust and the 'mantle wedge' above subduction zones. Carbonation of peridotite may be an important sink in the global carbon cycle. Zones of 100% magnesite + quartz replacing peridotite, up to 200 m thick, formed where oceanic mantle was thrust over carbonate-bearing metasediments in Oman. Talc + carbonate is an important component of the matrix in subduction mélanges at Santa Catalina Island , California, and the Sanbagawa metamorphic belt, Japan. Engineered systems to emulate natural mineral carbonation could provide relatively inexpensive CO2 capture and storage [3]. More generally, engineered reaction-driven cracking could supplement or replace hydraulic fracture in geothermal systems, solution mining, and extraction of tight oil and gas. The controls on reaction-driven cracking are poorly understood. Hydration and carbonation reactions can be self-limiting, since they potentially reduce permeability and armor reactive surfaces [4]. Also, in some cases, hydration or carbonation may take place at constant volume. Small changes in volume due to precipitation of solid products increases stress, destabilizing solid reactants, until precipitation and dissolution rates become equal at a steady state stress [5]. In a third case, volume change due to precipitation of solid products causes brittle failure. This has been invoked on qualitative grounds to explain, e.g., complete serpentinization of mantle peridotite [6]. Below ~ 300°C, the available potential energy for hydration and carbonation of olivine could produce stresses of 100's of MPa [2], sufficient to fracture rocks to 10 km depth or more, causing brittle failure below the steady state stress required

  18. Cracks assessment using ultrasonic technology

    Martinez, Maria Pia; Tomasella, Marcelo [OLDELVAL S.A. Oleoductos del Valle, Rio Negro (Argentina). Pipeline Integrity Dept.


    The goal of Oldelval Integrity Program is to prevent ruptures and leaks, developing strategies for a better handling of the integrity of our pipelines. In order to achieve it we have studied and modeled each process that involved in the integrity pipeline. Those processes are mainly based on defects reported by an internal inspection tool and supplied with field inspection and monitoring data. Years of evaluation, study and the continuous effort overturned towards a phenomenon that worries to the industry, as it is the SCC. Since 1998 up to 2004 SCC was included in the integrity program with some preventive maintenance programs. The accomplishment of the inspection based on ultrasound tools, is the culmination of years of evaluation and investigations supported by field digs and materials susceptibility. This paper describes Oldelval's results with ultrasonic crack detection tool, and how it can be reliably to detect SCC. (author)

  19. Three-Dimensional Gear Crack Propagation Studied

    Lewicki, David G.


    Gears used in current helicopters and turboprops are designed for light weight, high margins of safety, and high reliability. However, unexpected gear failures may occur even with adequate tooth design. To design an extremely safe system, the designer must ask and address the question, "What happens when a failure occurs?" With gear-tooth bending fatigue, tooth or rim fractures may occur. A crack that propagates through a rim will be catastrophic, leading to disengagement of the rotor or propeller, loss of an aircraft, and possible fatalities. This failure mode should be avoided. A crack that propagates through a tooth may or may not be catastrophic, depending on the design and operating conditions. Also, early warning of this failure mode may be possible because of advances in modern diagnostic systems. One concept proposed to address bending fatigue fracture from a safety aspect is a splittooth gear design. The prime objective of this design would be to control crack propagation in a desired direction such that at least half of the tooth would remain operational should a bending failure occur. A study at the NASA Lewis Research Center analytically validated the crack-propagation failsafe characteristics of a split-tooth gear. It used a specially developed three-dimensional crack analysis program that was based on boundary element modeling and principles of linear elastic fracture mechanics. Crack shapes as well as the crack-propagation life were predicted on the basis of the calculated stress intensity factors, mixed-mode crack-propagation trajectory theories, and fatigue crack-growth theories. The preceding figures show the effect of the location of initial cracks on crack propagation. Initial cracks in the fillet of the teeth produced stress intensity factors of greater magnitude (and thus, greater crack growth rates) than those in the root or groove areas of the teeth. Crack growth was simulated in a case study to evaluate crack-propagation paths. Tooth

  20. Modified cyanobacteria

    Vermaas, Willem F J.


    Disclosed is a modified photoautotrophic bacterium comprising genes of interest that are modified in terms of their expression and/or coding region sequence, wherein modification of the genes of interest increases production of a desired product in the bacterium relative to the amount of the desired product production in a photoautotrophic bacterium that is not modified with respect to the genes of interest.

  1. Preliminary studies of three dimensional effects on artificial cracks at simulated rocket moter liners by the frozen stress method

    Smith, C.W.; Finlayson, E.F. [Virginia Polytechnic Institute and State Univ., Blacksburg, VA (United States); Liu, C.T. [OL/AC/PL/RKS, Edwards Air Force Base, CA (United States)


    In a preliminary study limited to stress freezing materials, two types of bimaterial specimens, one consisting of two photoelastic materials with different critical temperatures (Type A) and one consisting of a photoelastic material with and without aluminum powder (the powder added to alter the modulus of elasticity without changing the critical temperature (Type B)) are constructed by bonding two halves of the dissimilar materials together. Each type of specimen contains an artificial edge crack along the bond line and loaded normal to the bond line. After evaluating the two specimen types by measuring the variation of the Mode I stress intensity distribution through the specimen thickness, Type B was selected as a superior model and its features studied in detail.

  2. Crack detection in a beam with an arbitrary number of transverse cracks using genetic algorithms

    Khaji, N. [Tarbiat Modares University, Tehran (Iran, Islamic Republic of); Mehrjoo, M. [Islamic Azad University, Tehran (Iran, Islamic Republic of)


    In this paper, a crack detection approach is presented for detecting depth and location of cracks in beam-like structures. For this purpose, a new beam element with an arbitrary number of embedded transverse edge cracks, in arbitrary positions of beam element with any depth, is derived. The components of the stiffness matrix for the cracked element are computed using the conjugate beam concept and Betti's theorem, and finally represented in closed-form expressions. The proposed beam element is efficiently employed for solving forward problem (i.e., to gain precise natural frequencies and mode shapes of the beam knowing the cracks' characteristics). To validate the proposed element, results obtained by new element are compared with two-dimensional (2D) finite element results and available experimental measurements. Moreover, by knowing the natural frequencies and mode shapes, an inverse problem is established in which the location and depth of cracks are determined. In the inverse approach, an optimization problem based on the new finite element and genetic algorithms (GAs) is solved to search the solution. It is shown that the present algorithm is able to identify various crack configurations in a cracked beam. The proposed approach is verified through a cracked beam containing various cracks with different depths.

  3. Identification of cracks in thick beams with a cracked beam element model

    Hou, Chuanchuan; Lu, Yong


    The effect of a crack on the vibration of a beam is a classical problem, and various models have been proposed, ranging from the basic stiffness reduction method to the more sophisticated model involving formulation based on the additional flexibility due to a crack. However, in the damage identification or finite element model updating applications, it is still common practice to employ a simple stiffness reduction factor to represent a crack in the identification process, whereas the use of a more realistic crack model is rather limited. In this paper, the issues with the simple stiffness reduction method, particularly concerning thick beams, are highlighted along with a review of several other crack models. A robust finite element model updating procedure is then presented for the detection of cracks in beams. The description of the crack parameters is based on the cracked beam flexibility formulated by means of the fracture mechanics, and it takes into consideration of shear deformation and coupling between translational and longitudinal vibrations, and thus is particularly suitable for thick beams. The identification procedure employs a global searching technique using Genetic Algorithms, and there is no restriction on the location, severity and the number of cracks to be identified. The procedure is verified to yield satisfactory identification for practically any configurations of cracks in a beam.

  4. Subcritical crack growth in two titanium alloys.

    Williams, D. N.


    Measurement of subcritical crack growth during static loading of precracked titanium alloys in salt water using samples too thin for plane strain loading to predominate was examined as a method for determining the critical stress intensity for crack propagation in salt water. Significant internal crack growth followed by arrest was found at quite low stress intensities, but crack growth rates were relatively low. Assuming these techniques provided a reliable measurement of the critical stress intensity, the value for annealed Ti-4Al-1.5Mo-0.5V alloy was apparently about 35 ksi-in. to the 1/2 power, while that for annealed Ti-4Al-3Mo-1V was below 45 ksi-in. to the 1/2 power. Crack growth was also observed in tests conducted in both alloys in an air environment. At 65 ksi-in. to the 1/2 power, the extent of crack growth was greater in air than in salt water. Ti-4Al-3Mo-1V showed arrested crack growth in air at a stress intensity of 45 ksi-in. to the 1/2 power.

  5. Crack growth monitoring at CFRP bond lines

    Rahammer, M.; Adebahr, W.; Sachse, R.; Gröninger, S.; Kreutzbruck, M.


    With the growing need for lightweight technologies in aerospace and automotive industries, fibre-reinforced plastics, especially carbon-fibre (CFRP), are used with a continuously increasing annual growth rate. A promising joining technique for composites is adhesive bonding. While rivet holes destroy the fibres and cause stress concentration, adhesive bond lines distribute the load evenly. Today bonding is only used in secondary structures due to a lack of knowledge with regard to long-term predictability. In all industries, numerical simulation plays a critical part in the development process of new materials and structures, while it plays a vital role when it comes to CFRP adhesive bondings conducing the predictability of life time and damage tolerance. The critical issue with adhesive bondings is crack growth. In a dynamic tensile stress testing machine we dynamically load bonded CFRP coupon specimen and measure the growth rate of an artificially started crack in order to feed the models with the results. We also investigate the effect of mechanical crack stopping features. For observation of the bond line, we apply two non-contact NDT techniques: Air-coupled ultrasound in slanted transmission mode and active lockin-thermography evaluated at load frequencies. Both methods give promising results for detecting the current crack front location. While the ultrasonic technique provides a slightly higher accuracy, thermography has the advantage of true online monitoring, because the measurements are made while the cyclic load is being applied. The NDT methods are compared to visual inspection of the crack front at the specimen flanks and show high congruence. Furthermore, the effect of crack stopping features within the specimen on the crack growth is investigated. The results show, that not all crack fronts are perfectly horizontal, but all of them eventually come to a halt in the crack stopping feature vicinity.

  6. Slow crack growth in spinel in water

    Schwantes, S.; Elber, W.


    Magnesium aluminate spinel was tested in a water environment at room temperature to establish its slow crack-growth behavior. Ring specimens with artificial flaws on the outside surface were loaded hydraulically on the inside surface. The time to failure was measured. Various precracking techniques were evaluated and multiple precracks were used to minimize the scatter in the static fatigue tests. Statistical analysis techniques were developed to determine the strength and crack velocities for a single flaw. Slow crack-growth rupture was observed at stress intensities as low as 70 percent of K sub c. A strengthening effect was observed in specimens that had survived long-time static fatigue tests.

  7. Mitigation strategies for autogenous shrinkage cracking

    Bentz, Dale P.; Jensen, Ole Mejlhede


    , the fundamental parameters contributing to the autogenous shrinkage and resultant early-age cracking of concrete are presented. Basic characteristics of the cement paste that contribute to or control the autogenous shrinkage response include the surface tension of the pore solution, the geometry of the pore...... of early-age cracking due to autogenous shrinkage. Mitigation strategies discussed in this paper include: the addition of shrinkage-reducing admixtures more commonly used to control drying shrinkage, control of the cement particle size distribution, modification of the mineralogical composition......, it should be possible to minimize cracking due to autogenous shrinkage via some combination of the presented approaches....

  8. Prediction of Crack Growth in Aqueous Environments.


    Impedance for the Propagation of a Crack Through HY80 Steel in 3.5Z NaCl Solution at 25*C Under Sinusoidal Loading Condi t ions...THE PROPAGATION OF A CRACK THROUGH HY80 STEEL IN 3.5% NaCI SOLUTION AT 25°C UNDER SINUSOIDAL LOADING CONDITIONS 49 and the properties of greatest...VELOCITY AS A FUNCTION OF TIME FOR A CRACK GROWN AT CONSTANT CURRENT IN HY80 STEEL Initial conditions CI in Table 5. 66 400 UJ x v> l/> L. 0

  9. Aluminum alloy weldability. Identification of weld solidification cracking mechanisms through novel experimental technique and model development

    Coniglio, Nicolas


    et al. (2000) revealed that crack growth is controlled by local strain rate conditions. Finally, a simplified strain partition model provides a link between critical strain rates measured across the weld and predicted at grain boundaries within the mushy zone. Although based on simplified assumptions, predicted and measured critical strain rate values are of the same order of magnitude. However, because of a longer mushy zone experienced at higher 4043 filler dilution related to a reduction in cooling rate, these models predict a lower weldability with increasing filler dilution, in contradiction with experimental observations. Combining the crack initiation and growth models suggests that hydrogen and strain rate, respectively, determine crack formation. An hypothetical hydrogen - strain rate map defines conceptually the conditions for cracking, suggesting better weldability at low weld metal hydrogen content. With the aid of the modified varestraint test (MVT) and a controlled hydrogen contamination system, results, presented in the form of ram speed - hydrogen map, revealed that hydrogen has little effect on crack growth, providing support to the proposed cracking models. However, a drop in weldability corresponding to the peak in weld metal hydrogen supersaturation suggests a different solidification cracking mechanism, where cavitation supports crack growth. (orig.)

  10. Catalytic ramifications of steam deactivation of Y zeolites: An analysis using 2-methylhexane cracking

    Yaluris, G.; Dumesic, J.A. [Univ. of Wisconsin, Madison, WI (United States); Madon, R.J. [Engelhard Corp., Iselin, NJ (United States)


    Kinetic analysis of experimental data for 2-methylhexane cracking demonstrates that trends in activity and selectivity are well simulated by adjusting a single parameter that represents the acid strength of a Y-based FCC catalyst. This acid strength may be modified via steam deactivation, and the authors have experimentally corroborated acidity changes using ammonia microcalorimetry and infrared spectroscopy. Increased severity of steam treatment reduces the number and strength of catalyst acid sites, and it leads to a reduction in the turnover frequency of all surface processes and a decrease in overall site time yield. Streaming of the catalyst does not change the fundamental chemistry involved in catalytic cracking. However, change in acidity caused by steaming alters product selectivity by changing relative rates of various catalytic cycles in the cracking process. For example, steam treatment increases olefin selectivity by favoring catalytic cycles that produce olefins.

  11. Study on Deactivation and Cracking Performance of Catalysts Containing Y and MFI Zeolites

    Chen Zhenyu; Li Caiying; Tian Huiping; Huang Zhiqing


    This article investigated the deactivation caused by hydrothermal treatment and metal contamination of two cracking catalysts containing the Y and ZRP- 1 zeolites aimed at maximization of light olefin yield.Test results had shown that the hydrothermal stability and resistance to metal contamination of the ZRP-1zeolite were apparently better than those of the Y zeolite. Hydrothermal treatment and metal contamination had not only changed the catalytic cracking performance of respective zeolites, but at the same time had also modified to a definite degree of the relative proportions of effective components in these two zeolites and affected the synergistic effects between them, resulting in a relative enhancement of secondary cracking ability of the catalyst and increased olefin selectivity in the FCC products. In the course of application of catalyst for maximization of light olefins yield appropriate adjustment of the relative proportion of two active components can help to alleviate the products distribution and selectivity changes caused by deactivationof FCC catalysts.

  12. 3D Finite Element Analysis of HMA Overlay Mix Design to Control Reflective Cracking

    Ghauch, Ziad G


    One of the most common rehabilitation techniques of deteriorated pavements is the placement of an HMA overlay on top of the existing Asphalt Concrete (AC) or Portland Cement Concrete (PCC) pavement. However, shortly after pavement resurfacing, HMA overlays exhibit a cracking pattern similar to that of the underlying pavement. This phenomenon is known as reflective cracking. This study examines the effectiveness of several HMA overlay mix design strategies for the purpose of controlling the development of reflective cracking. A parametric study was conducted using a 3D Finite Element (FE) model of a rigid pavement section including a Linear Viscoelastic (LVE) model for Hot Mix Asphalt (HMA) materials and non-uniform tire-pavement contact stresses. Results obtained show that for the intermediate and surface courses, using a Dense Graded (DG) or Polymer Modified (PM) asphalt mixture instead of a Standard Binder (SB) mixture results in reduced tensile stresses at the bottom of the HMA overlay but higher levels of...

  13. Interfacial Crack Arrest in Sandwich Panels with Embedded Crack Stoppers Subjected to Fatigue Loading

    Martakos, G.; Andreasen, J. H.; Berggreen, C.; Thomsen, O. T.


    A novel crack arresting device has been implemented in sandwich panels and tested using a special rig to apply out-of-plane loading on the sandwich panel face-sheets. Fatigue crack propagation was induced in the face-core interface of the sandwich panels which met the crack arrester. The effect of the embedded crack arresters was evaluated in terms of the achieved enhancement of the damage tolerance of the tested sandwich panels. A finite element (FE) model of the experimental setup was used for predicting propagation rates and direction of the crack growth. The FE simulation was based on the adoption of linear fracture mechanics and a fatigue propagation law (i.e. Paris law) to predict the residual fatigue life-time and behaviour of the test specimens. Finally, a comparison between the experimental results and the numerical simulations was made to validate the numerical predictions as well as the overall performance of the crack arresters.

  14. Interfacial Crack Arrest in Sandwich Panels with Embedded Crack Stoppers Subjected to Fatigue Loading

    Martakos, G.; Andreasen, J. H.; Berggreen, C.; Thomsen, O. T.


    A novel crack arresting device has been implemented in sandwich panels and tested using a special rig to apply out-of-plane loading on the sandwich panel face-sheets. Fatigue crack propagation was induced in the face-core interface of the sandwich panels which met the crack arrester. The effect of the embedded crack arresters was evaluated in terms of the achieved enhancement of the damage tolerance of the tested sandwich panels. A finite element (FE) model of the experimental setup was used for predicting propagation rates and direction of the crack growth. The FE simulation was based on the adoption of linear fracture mechanics and a fatigue propagation law (i.e. Paris law) to predict the residual fatigue life-time and behaviour of the test specimens. Finally, a comparison between the experimental results and the numerical simulations was made to validate the numerical predictions as well as the overall performance of the crack arresters.

  15. On Cracking of Charged Anisotropic Polytropes

    Azam, M


    Recently in \\cite{34}, the role of electromagnetic field on the cracking of spherical polytropes has been investigated without perturbing charge parameter explicitly. In this study, we have examined the occurrence of cracking of anisotropic spherical polytropes through perturbing parameters like anisotropic pressure, energy density and charge. We consider two different types of polytropes in this study. We discuss the occurrence of cracking in two different ways $(i)$ by perturbing polytropic constant, anisotropy and charge parameter $(ii)$ by perturbing polytropic index, anisotropy and charge parameter for each case. We conclude that cracking appears for a wide range of parameters in both cases. Also, our results are reduced to \\cite{33} in the absence of charge.

  16. Struggling with Fitzgerald's "Crack-Up" Essays.

    Fulcher, James


    Ponders F. Scott Fitzgerald's essays about his "crack-up" and relates them to the many complex aspects of the struggles of a teacher using post-structural literary theory and teaching two-year college students. (SR)

  17. Inner Crack Detection Method for Cantilever Beams

    Li, Zheng; Zhang, Wei; Li, Yixuan; Su, Xianyue


    In this paper, continuous wavelet transform has been performed to extract the inner crack information from the guided waves in cantilever beams, and the location and size of crack can be detected exactly. Considering its best time-frequency property, Gabor continuous wavelet transform is employed to analyze the complicated flexible wave signals in cantilever beam, which is inspirited by an impact on the free end. Otherwise, in order to enhance the sensitivity of detection for some small cracks, an improved method is discussed. Here, both computational and experimental methods are carried out for comparing the influence of different crack location in beam. Therefore, the method proposed can be expected to expand to a powerful damage detection method in a broad engineering application.

  18. Initiating, growing and cracking of hydrogen blisters

    REN Xuechong; SHAN Guangbin; CHU Wuyang; SU Yanjing; GAO Kewei; QIAO Lijie; JIANG Bo; CHEN Gang; CUI Yinhui


    The growing process of a hydrogen blister in a wheel steel was observed in situ with an optical microscope, and the fracture surfaces formed from broken blisters on a wheel steel and bulk metallic glass were investigated. The initiating, growing, cracking and breaking of hydrogen blisters are as follows. Supersaturated vacancies can increase greatly during charging and gather together into a vacancy cluster (small cavity). Hydrogen atoms become hydrogen molecules in the vacancy cluster and hydrogen molecules can stabilize the vacancy cluster. The small cavity becomes the nucleus of hydrogen blister. The blister will grow with entering of vacancies and hydrogen atoms. With increasing hydrogen pressure, plastic deformation occurs first, the hydrogen blister near the surface extrudes, and then cracks initiate along the wall of the blister with further increasing hydrogen pressure. A cracked blister can grow further through propagating of cracks until it breaks.

  19. Dynamic Strain and Crack Monitoring Sensor Project

    National Aeronautics and Space Administration — Los Gatos Research proposes to develop a new automated vehicle health monitoring sensor system capable of measuring loads and detecting crack, corrosion, and...

  20. A novel two-stage discrete crack method based on the screened Poisson equation and local mesh refinement

    Areias, P.; Rabczuk, T.; de Sá, J. César


    We propose an alternative crack propagation algorithm which effectively circumvents the variable transfer procedure adopted with classical mesh adaptation algorithms. The present alternative consists of two stages: a mesh-creation stage where a local damage model is employed with the objective of defining a crack-conforming mesh and a subsequent analysis stage with a localization limiter in the form of a modified screened Poisson equation which is exempt of crack path calculations. In the second stage, the crack naturally occurs within the refined region. A staggered scheme for standard equilibrium and screened Poisson equations is used in this second stage. Element subdivision is based on edge split operations using a constitutive quantity (damage). To assess the robustness and accuracy of this algorithm, we use five quasi-brittle benchmarks, all successfully solved.

  1. Assessment of The Cracking Properties of Stainless Steel Alloys and their Usability for Laser Welding in Production

    Juhl, Thomas Winther


    Methods to assess stainless steel alloys’ cracking properties and usability for laser welding has been studied. Also tests to assess alloys’ susceptibility to hot cracking has been conducted. Among these is the so-called Weeter test which assesses the alloy by executing a number of spot welds...... to provoke cracking in the alloy. In this work the Weeter test has been modified and changed in order to develop a faster and easier test also applicable to small specimens. The new test, called a Groove test differs from the Weeter test by its procedure in which linear seam welds are conducted instead...... of spot welds. The Groove test has the advantage of an easier microscopy and analysis in the welds. Results from crack tests was partly confirmed by predictions made on the basis of the alloy’s constituents and solidification growth rate....

  2. Finite element analysis of surface cracks in the Wilkins Ice Shelf using fracture mechanics

    Plate, Carolin; Müller, Ralf; Gross, Dietmar; Humbert, Angelika; Braun, Matthias


    Ice shelves, located between the warming atmosphere and the ocean, are sensitive elements of the climate system. The Wilkins Ice Shelf is situated in the south-western part of the Antarctic Peninsula, a well known hot spot of global warming. Recent break-up events exemplified the potential of disintegration of the ice shelf. A multi interdisciplinary project consisting of remote sensing, modeling of the ice dynamics and fracture mechanics intends to improve the understanding of the impacts of temperature increase on ice shelf stability. As a part of this project the aim of this presentation is to demonstrate the fracture mechanical approach using finite elements and configurational forces. For fracture mechanical purposes the material behavior of ice is treated as a brittle solid, and linear fracture mechanics is used. Crucial to all methods in linear fracture mechanics is the evaluation of the stress intensity factor K which is a measure for the load concentration at the crack tip and which depends on the geometry of the body and on the applied loading. The computed value of K can be compared to the critical stress intensity factor Kc, a material property obtained from experimental examinations, to judge whether a crack will propagate. One very effective procedure to obtain the stress intensity factor takes advantage of configurational forces, which can be easily obtained in the finite element analysis. An initial investigation is based on a 2-dimensional analysis of a single crack with a mode-I load type using a static plane strain model in the finite element analysis software COMSOL and additional routines to compute and evaluate the configurational forces. Analytical solutions of simple geometry and load cases are called on in comparison. The application to the Wilkins Ice Shelf follows by using material parameters, geometries and loading situations, which are obtained from literature values, remote sensing data analysis and modeling of the ice dynamics

  3. Finite Element Analysis of the Effect of Crack Depth and Crack Opening On the Girder

    Md. Kamrul Hassan


    Full Text Available In order to identify the effect of crack depth and opening on the girder, finite element method (FEM has been used in this paper. In FE analysis, six nodded two dimensional plane elements (PLANE-2 are considered. Each node has two degree of freedom such as UX and UY. For the plane elements, a plane stress width/thickness option is chosen. For analytical model of crack of the concrete bridge girder, crack opening was increased from 0.2 mm to 1mm at an interval 0.2 mm and crack depth also increased from 30 mm to 150 mm at an interval 30 mm. The models were discreatized by a triangular mesh and convergence test was executed to obtain satisfactory results from the Plane-2 element. From the numerical result, it is seen that the principal stress become a higher with increased the crack depth and also crack opening with respect to load increasing. But the crack depth at 90 mm and crack opening at 0.6 mm, it has more effect on the girder because the stress concentration is higher than other crack depth and opening.

  4. Calculation of the crack tip opening displacement of a crack lying in a subsurface layer

    Higashida, Y.; Kamada, K.


    Crack tip opening displacement of a crack lying parallel to a free surface is calculated by counting the number of dislocations emitted into the plastic zone from a crack tip. A discrete dislocation model was used to simulate the crack, while varying the strength of dislocations so as to satisfy the boundary condition. The result coincides numerically with the predictions made in a previous paper, in which the stress intensity factor appearing in a theory of bulk materials was replaced with the one which includes the surface correction.

  5. Crack Closure Effects on Fatigue Crack Propagation Rates: Application of a Proposed Theoretical Model

    José A. F. O. Correia


    Full Text Available Structural design taking into account fatigue damage requires a thorough knowledge of the behaviour of materials. In addition to the monotonic behaviour of the materials, it is also important to assess their cyclic response and fatigue crack propagation behaviour under constant and variable amplitude loading. Materials whenever subjected to fatigue cracking may exhibit mean stress effects as well as crack closure effects. In this paper, a theoretical model based on the same initial assumptions of the analytical models proposed by Hudak and Davidson and Ellyin is proposed to estimate the influence of the crack closure effects. This proposal based further on Walker’s propagation law was applied to the P355NL1 steel using an inverse analysis (back-extrapolation of experimental fatigue crack propagation results. Based on this proposed model it is possible to estimate the crack opening stress intensity factor, Kop, the relationship between U=ΔKeff/ΔK quantity and the stress intensity factor, the crack length, and the stress ratio. This allows the evaluation of the influence of the crack closure effects for different stress ratio levels, in the fatigue crack propagation rates. Finally, a good agreement is found between the proposed theoretical model and the analytical models presented in the literature.

  6. Hydration Process and Crack Tendency of Concrete Based on Resistivity and Restrained Shrinkage Crack

    MUAZU Bawa Samaila; WEI Xiaosheng; WANG Lei


    Hydration process, crack potential and setting time of concrete grade C30, C40 and C50 were monitored by using a non-contact electrical resistivity apparatus, a novel plastic ring mould and penetration resistance methods, respectively. The results show the highest resistivity of C30 at the early stage until a point when C50 accelerated and overtook the others. It has been experimentally conifrmed that the crossing point of C30 and C50 corresponds to the ifnal setting time of C50. From resistivity derivative curve, four different stages were observed upon which the hydration process is classiifed; these are dissolution, induction, acceleration and deceleration periods. Consequently, restrained shrinkage crack and setting time results demonstrated that C50 set and cracked the earliest. The cracking time of all the samples occurred within a reasonable experimental period thus the novel plastic ring is a convenient method for predicting concrete’s crack potential. The highest inlfection time (ti) obtained from resistivity curve and the ifnal setting time (tf) were used with crack time (tc) in coming up with mathematical models for the prediction of concrete’s cracking age for the range of concrete grade considered. Finally, an ANSYS numerical simulation supports the experimental ifndings in terms of the earliest crack age of C50 and the crack location.

  7. Molecular dynamics simulation of propagating cracks

    Mullins, M.


    Steady state crack propagation is investigated numerically using a model consisting of 236 free atoms in two (010) planes of bcc alpha iron. The continuum region is modeled using the finite element method with 175 nodes and 288 elements. The model shows clear (010) plane fracture to the edge of the discrete region at moderate loads. Analysis of the results obtained indicates that models of this type can provide realistic simulation of steady state crack propagation.

  8. Fatigue Crack Initiation Analysis in 1060 Steel

    L. Gyansah


    Full Text Available This study investigates initiation of small cracks on dumble-shaped plate type specimens of 1060steel at the load ratio of R = 0 under varied cyclic stress amplitudes between 0.6 and 1.0 of yield stress usingthe Instron machine (model: 8501. Sinusoidal wave of a frequency of 10 Hz was used in the experiment. Theexperiment was conducted at a room temperature of 23ºC. Each test for different applied stress ranges wascarried out for 2×104 cycles. Microstructure and fractography of the fractured specimen were also analyzed.Nucleations of cracks were observed at Ferrite-Ferrite G rain Boundary (FFGB as well as inside Ferrite GrainBody (FGB, but the FFGB location was preferred. Results show that the average length of FFGB cracks isfound larger than that of the average length of cracks initiated inside FGB at the same cyclic loading conditions.The formation of slip band inside grain body, slip band impingement at grain boundary and elastic-plasticincompatibility synergistically have significant influence on fatigue crack initiation in 1060 steel. Additionally,the formation of irregular voids inside slip bands, initiation and growth of small voids at grain boundary andthe subsequent joining of these with other voids were seen as specific characteristics of 1060 steel. It was alsoestablished that cracks nucleate both at grain boundary and inside grain body in 1060 steel in the investigateddomain of 0.6 to 1.0Fy.It was further established that the orientation of the grain body cracks at low stress levelis greater than 45º and the average angle of orientation of these cracks increases like that of grain boundarycracks with increased magnitude of stress range.

  9. Molecular dynamics simulation of propagating cracks

    Mullins, M.


    Steady state crack propagation is investigated numerically using a model consisting of 236 free atoms in two (010) planes of bcc alpha iron. The continuum region is modeled using the finite element method with 175 nodes and 288 elements. The model shows clear (010) plane fracture to the edge of the discrete region at moderate loads. Analysis of the results obtained indicates that models of this type can provide realistic simulation of steady state crack propagation.

  10. Estimation of leak rate through circumferential cracks in pipes in nuclear power plants

    Jai Hak Park


    Full Text Available The leak before break (LBB concept is widely used in designing pipe lines in nuclear power plants. According to the concept, the amount of leaking liquid from a pipe should be more than the minimum detectable leak rate of a leak detection system before catastrophic failure occurs. Therefore, accurate estimation of the leak rate is important to evaluate the validity of the LBB concept in pipe line design. In this paper, a program was developed to estimate the leak rate through circumferential cracks in pipes in nuclear power plants using the Henry–Fauske flow model and modified Henry–Fauske flow model. By using the developed program, the leak rate was calculated for a circumferential crack in a sample pipe, and the effect of the flow model on the leak rate was examined. Treating the crack morphology parameters as random variables, the statistical behavior of the leak rate was also examined. As a result, it was found that the crack morphology parameters have a strong effect on the leak rate and the statistical behavior of the leak rate can be simulated using normally distributed crack morphology parameters.

  11. Atomistic observation of a crack tip approaching coherent twin boundaries.

    Liu, L; Wang, J; Gong, S K; Mao, S X


    Coherent twin boundaries (CTBs) in nano-twinned materials could improve crack resistance. However, the role of the CTBs during crack penetration has never been explored at atomic scale. Our in situ observation on nano-twinned Ag under a high resolution transmission electron microscope (HRTEM) reveals the dynamic processes of a crack penetration across the CTBs, which involve alternated crack tip blunting, crack deflection, twinning/detwinning and slip transmission across the CTBs. The alternated blunting processes are related to the emission of different types of dislocations at the crack tip and vary with the distance of the crack tip from the CTBs.

  12. Crack shape analysis of PWSCC in S/G tubings

    Park, I. K. [Sunmon Univ., Chonan (Korea, Republic of)


    Crack shape of PWSCC was analyzed, based on the fractured pulled-out S/G tubings of Ulchin-1 steam generator. The shape of the cracks in kiss roll transitions was elliptical shape for short cracks, and car shape for long cracks with flat crack front. The bulging was observed under the inner wall after shot-peening. Crack shape change after shot-peening was resulted from the crack growth restraint in axial direction due to compressive residual stresses on the primary side surface.

  13. Thermally activated processes of fatigue crack growth in steels

    Tanaka, Masaki; Fujii, Atsushi; Noguchi, Hiroshi; Higashida, Kenji


    Fatigue crack growth rates in steels at high and low temperatures have been investigated using Paris curves. The fatigue crack growth rates at high temperatures are quite different from those at low temperatures. Arrhenius plots between fatigue crack growth rate (da/dN) and test temperatures at constant stress intensity factor range (ΔKI) indicate a difference of the rate-controlling process for fatigue crack growth with temperature. Slip deformation at the crack tip governs fatigue crack growth at high temperatures, while hydrogen diffusion is associated with crack growth at low temperatures.

  14. An analytical formula for the longitudinal resonance frequencies of a fluid-filled crack

    Maeda, Y.; Kumagai, H.


    The fluid-filled crack model (Chouet, 1986, JGR) simulates the resonances of a rectangular crack filled with an inviscid fluid embedded in a homogeneous isotropic elastic medium. The model demonstrates the existence of a slow wave, known as the crack wave, that propagates along the solid-fluid interfaces. The wave velocity depends on the crack stiffness. The model has been used to interpret the peak frequencies of long-period (LP) and very long period (VLP) seismic events at various volcanoes (Chouet and Matoza, 2013, JVGR). Up to now, crack model simulations have been performed using the finite difference (Chouet, 1986) and boundary integral (Yamamoto and Kawakatsu, 2008, GJI) methods. These methods require computationally extensive procedures to estimate the complex frequencies of crack resonance modes. Establishing an easier way to calculate the frequencies of crack resonances would help understanding of the observed frequencies. In this presentation, we propose a simple analytical formula for the longitudinal resonance frequencies of a fluid-filled crack. We first evaluated the analytical expression proposed by Kumagai (2009, Encyc. Complex. Sys. Sci.) through a comparison of the expression with the peak frequencies computed by a 2D version of the FDM code of Chouet (1986). Our comparison revealed that the equation of Kumagai (2009) shows discrepancies with the resonant frequencies computed by the FDM. We then modified the formula as fmL = (m-1)a/[2L(1+2ɛmLC)1/2], (1) where L is the crack length, a is the velocity of sound in the fluid, C is the crack stiffness, m is a positive integer defined such that the wavelength of the normal displacement on the crack surface is 2L/m, and ɛmL is a constant that depends on the longitudinal resonance modes. Excellent fits were obtained between the peak frequencies calculated by the FDM and by Eq. (1), suggesting that this equation is suitable for the resonant frequencies. We also performed 3D FDM computations of the

  15. Hierarchical Formation of Intrasplat Cracks in Thermal Spray Ceramic Coatings

    Chen, Lin; Yang, Guan-Jun; Li, Cheng-Xin; Li, Chang-Jiu


    Intrasplat cracks, an essential feature of thermally sprayed ceramic coatings, play important roles in determining coating properties. However, final intrasplat crack patterns are always considered to be disordered and irregular, resulting from random cracking during splat cooling, since the detailed formation process of intrasplat cracks has scarcely been considered. In the present study, the primary formation mechanism for intrasplat cracking was explored based on both experimental observations and mechanical analysis. The results show that the intrasplat crack pattern in thermally sprayed ceramic splats presents a hierarchical structure with four sides and six neighbors, indicating that intrasplat crack patterns arise from successive domain divisions due to sequential cracking during splat cooling. The driving forces for intrasplat cracking are discussed, and the experimental data quantitatively agree well with theoretical results. This will provide insight for further coating structure designs and tailoring by tuning of intrasplat cracks.

  16. Electromagnetic pulsed thermography for natural cracks inspection

    Gao, Yunlai; Tian, Gui Yun; Wang, Ping; Wang, Haitao; Gao, Bin; Woo, Wai Lok; Li, Kongjing


    Emerging integrated sensing and monitoring of material degradation and cracks are increasingly required for characterizing the structural integrity and safety of infrastructure. However, most conventional nondestructive evaluation (NDE) methods are based on single modality sensing which is not adequate to evaluate structural integrity and natural cracks. This paper proposed electromagnetic pulsed thermography for fast and comprehensive defect characterization. It hybrids multiple physical phenomena i.e. magnetic flux leakage, induced eddy current and induction heating linking to physics as well as signal processing algorithms to provide abundant information of material properties and defects. New features are proposed using 1st derivation that reflects multiphysics spatial and temporal behaviors to enhance the detection of cracks with different orientations. Promising results that robust to lift-off changes and invariant features for artificial and natural cracks detection have been demonstrated that the proposed method significantly improves defect detectability. It opens up multiphysics sensing and integrated NDE with potential impact for natural understanding and better quantitative evaluation of natural cracks including stress corrosion crack (SCC) and rolling contact fatigue (RCF).

  17. Nonlinear modal methods for crack localization

    Sutin, Alexander; Ostrovsky, Lev; Lebedev, Andrey


    A nonlinear method for locating defects in solid materials is discussed that is relevant to nonlinear modal tomography based on the signal cross-modulation. The scheme is illustrated by a theoretical model in which a thin plate or bar with a single crack is excited by a strong low-frequency wave and a high-frequency probing wave (ultrasound). A crack is considered as a small contact-type defect which does not perturb the modal structure of sound in linear approximation but creates combinational-frequency components whose amplitudes depend on their closeness to a resonance and crack position. Using different crack models, including the hysteretic ones, the nonlinear part of its volume variations under the given stress and then the combinational wave components in the bar can be determined. Evidently, their amplitude depends strongly on the crack position with respect to the peaks or nodes of the corresponding linear signals which can be used for localization of the crack position. Exciting the sample by sweeping ultrasound frequencies through several resonances (modes) reduces the ambiguity in the localization. Some aspects of inverse problem solution are also discussed, and preliminary experimental results are presented.

  18. Electromagnetic pulsed thermography for natural cracks inspection

    Gao, Yunlai; Tian, Gui Yun; Wang, Ping; Wang, Haitao; Gao, Bin; Woo, Wai Lok; Li, Kongjing


    Emerging integrated sensing and monitoring of material degradation and cracks are increasingly required for characterizing the structural integrity and safety of infrastructure. However, most conventional nondestructive evaluation (NDE) methods are based on single modality sensing which is not adequate to evaluate structural integrity and natural cracks. This paper proposed electromagnetic pulsed thermography for fast and comprehensive defect characterization. It hybrids multiple physical phenomena i.e. magnetic flux leakage, induced eddy current and induction heating linking to physics as well as signal processing algorithms to provide abundant information of material properties and defects. New features are proposed using 1st derivation that reflects multiphysics spatial and temporal behaviors to enhance the detection of cracks with different orientations. Promising results that robust to lift-off changes and invariant features for artificial and natural cracks detection have been demonstrated that the proposed method significantly improves defect detectability. It opens up multiphysics sensing and integrated NDE with potential impact for natural understanding and better quantitative evaluation of natural cracks including stress corrosion crack (SCC) and rolling contact fatigue (RCF). PMID:28169361

  19. Dynamic behaviour of a rotating cracked beam

    Yashar, Ahmed; Ghandchi-Tehrani, Maryam; Ferguson, Neil


    This paper presents a new approach to investigate and analyse the vibrational behaviour of cracked rotating cantilever beams, which can for example represent helicopter or wind turbine blades. The analytical Hamiltonian method is used in modelling the rotating beam and two numerical methods, the Rayleigh-Ritz and FEM, are used to study the natural frequencies and the mode shapes of the intact rotating beams. Subsequently, a crack is introduced into the FE model and simulations are performed to identify the modal characteristics for an open cracked rotating beam. The effect of various parameters such as non-dimensional rotating speed, hub ratio and slenderness ratio are investigated for both the intact and the cracked rotating beam, and in both directions of chordwise and flapwise motion. The veering phenomena in the natural frequencies as a function of the rotational speed and the buckling speed are considered with respect to the slenderness ratio. In addition, the mode shapes obtained for the flapwise vibration are compared using the modal assurance criterion (MAC). Finally, a new three dimensional design chart is produced, showing the effect of crack location and depth on the natural frequencies of the rotating beam. This chart will be subsequently important in identifying crack defects in rotating blades.

  20. Protection of brittle film against cracking

    Musil, J.; Sklenka, J.; Čerstvý, R.


    This article reports on the protection of the brittle Zrsbnd Sisbnd O film against cracking in bending by the highly elastic top film (over-layer). In experiments the Zrsbnd Sisbnd O films with different elemental composition and structure were used. Both the brittle and highly elastic films were prepared by magnetron sputtering using a dual magnetron. The brittle film easily cracks in bending. On the other hand, the highly elastic film exhibits enhanced resistance to cracking in bending. Main characteristic parameters of both the brittle and highly elastic films are given. Special attention is devoted to the effect of the structure (crystalline, amorphous) of both the brittle and highly elastic top film on the resistance of cracking of the brittle film. It was found that (1) both the X-ray amorphous and crystalline brittle films easily crack in bending, (2) the highly elastic film can have either X-ray amorphous or crystalline structure and (3) both the X-ray amorphous and crystalline, highly elastic top films perfectly protect the brittle films against cracking in bending. The structure, mechanical properties and optical transparency of the brittle and highly elastic sputtered Zrsbnd Sisbnd O films are described in detail. At the end of this article, the principle of the low-temperature formation of the highly elastic films is also explained.

  1. Fatigue crack propagation analysis of plaque rupture.

    Pei, Xuan; Wu, Baijian; Li, Zhi-Yong


    Rupture of atheromatous plaque is the major cause of stroke or heart attack. Considering that the cardiovascular system is a classic fatigue environment, plaque rupture was treated as a chronic fatigue crack growth process in this study. Fracture mechanics theory was introduced to describe the stress status at the crack tip and Paris' law was used to calculate the crack growth rate. The effect of anatomical variation of an idealized plaque cross-section model was investigated. The crack initiation was considered to be either at the maximum circumferential stress location or at any other possible locations around the lumen. Although the crack automatically initialized at the maximum circumferential stress location usually propagated faster than others, it was not necessarily the most critical location where the fatigue life reached its minimum. We found that the fatigue life was minimum for cracks initialized in the following three regions: the midcap zone, the shoulder zone, and the backside zone. The anatomical variation has a significant influence on the fatigue life. Either a decrease in cap thickness or an increase in lipid pool size resulted in a significant decrease in fatigue life. Comparing to the previously used stress analysis, this fatigue model provides some possible explanations of plaque rupture at a low stress level in a pulsatile cardiovascular environment, and the method proposed here may be useful for further investigation of the mechanism of plaque rupture based on in vivo patient data.

  2. Stress corrosion cracking of copper canisters

    King, Fraser (Integrity Corrosion Consulting Limited (Canada)); Newman, Roger (Univ. of Toronto (Canada))


    A critical review is presented of the possibility of stress corrosion cracking (SCC) of copper canisters in a deep geological repository in the Fennoscandian Shield. Each of the four main mechanisms proposed for the SCC of pure copper are reviewed and the required conditions for cracking compared with the expected environmental and mechanical loading conditions within the repository. Other possible mechanisms are also considered, as are recent studies specifically directed towards the SCC of copper canisters. The aim of the review is to determine if and when during the evolution of the repository environment copper canisters might be susceptible to SCC. Mechanisms that require a degree of oxidation or dissolution are only possible whilst oxidant is present in the repository and then only if other environmental and mechanical loading conditions are satisfied. These constraints are found to limit the period during which the canisters could be susceptible to cracking via film rupture (slip dissolution) or tarnish rupture mechanisms to the first few years after deposition of the canisters, at which time there will be insufficient SCC agent (ammonia, acetate, or nitrite) to support cracking. During the anaerobic phase, the supply of sulphide ions to the free surface will be transport limited by diffusion through the highly compacted bentonite. Therefore, no HS. will enter the crack and cracking by either of these mechanisms during the long term anaerobic phase is not feasible. Cracking via the film-induced cleavage mechanism requires a surface film of specific properties, most often associated with a nano porous structure. Slow rates of dissolution characteristic of processes in the repository will tend to coarsen any nano porous layer. Under some circumstances, a cuprous oxide film could support film-induced cleavage, but there is no evidence that this mechanism would operate in the presence of sulphide during the long-term anaerobic period because copper sulphide

  3. Biogenic Cracks in Porous Rock

    Hemmerle, A.; Hartung, J.; Hallatschek, O.; Goehring, L.; Herminghaus, S.


    Microorganisms growing on and inside porous rock may fracture it by various processes. Some of the mechanisms of biofouling and bioweathering are today identified and partially understood but most emphasis is on chemical weathering, while mechanical contributions have been neglected. However, as demonstrated by the perseverance of a seed germinating and cracking up a concrete block, the turgor pressure of living organisms can be very significant. Here, we present results of a systematic study of the effects of the mechanical forces of growing microbial populations on the weathering of porous media. We designed a model porous medium made of glass beads held together by polydimethylsiloxane (PDMS), a curable polymer. The rheological properties of the porous medium, whose shape and size are tunable, can be controlled by the ratio of crosslinker to base used in the PDMS (see Fig. 1). Glass and PDMS being inert to most chemicals, we are able to focus on the mechanical processes of biodeterioration, excluding any chemical weathering. Inspired by recent measurements of the high pressure (~0.5 Mpa) exerted by a growing population of yeasts trapped in a microfluidic device, we show that yeast cells can be cultured homogeneously within porous medium until saturation of the porous space. We investigate then the effects of such an inner pressure on the mechanical properties of the sample. Using the same model system, we study also the complex interplay between biofilms and porous media. We focus in particular on the effects of pore size on the penetration of the biofilm within the porous sample, and on the resulting deformations of the matrix, opening new perspectives into the understanding of life in complex geometry. Figure 1. Left : cell culture growing in a model porous medium. The white spheres represent the grains, bonds are displayed in grey, and microbes in green. Right: microscopy picture of glass beads linked by PDMS bridges, scale bar: 100 μm.

  4. Environmentally assisted cracking in light water reactors.

    Chopra, O. K.; Chung, H. M.; Clark, R. W.; Gruber, E. E.; Shack, W. J.; Soppet, W. K.; Strain, R. V.


    This report summarizes work performed by Argonne National Laboratory on fatigue and environmentally assisted cracking (EAC) in light water reactors (LWRs) from January to December 2002. Topics that have been investigated include: (a) environmental effects on fatigue crack initiation in carbon and low-alloy steels and austenitic stainless steels (SSs), (b) irradiation-assisted stress corrosion cracking (IASCC) of austenitic SSs in BWRs, (c) evaluation of causes and mechanisms of irradiation-assisted cracking of austenitic SS in PWRs, and (d) cracking in Ni-alloys and welds. A critical review of the ASME Code fatigue design margins and an assessment of the conservation in the current choice of design margins are presented. The existing fatigue {var_epsilon}-N data have been evaluated to define the effects of key material, loading, and environmental parameters on the fatigue lives of carbon and low-alloy steels and austenitic SSs. Experimental data are presented on the effects of surface roughness on fatigue crack initiation in these materials in air and LWR environments. Crack growth tests were performed in BWR environments on SSs irradiated to 0.9 and 2.0 x 10{sup 21} n x cm{sup -2}. The crack growth rates (CGRs) of the irradiated steels are a factor of {approx}5 higher than the disposition curve proposed in NUREG-0313 for thermally sensitized materials. The CGRs decreased by an order of magnitude in low-dissolved oxygen (DO) environments. Slow-strain-rate tensile (SSRT) tests were conducted in high-purity 289 C water on steels irradiated to {approx}3 dpa. The bulk S content correlated well with the susceptibility to intergranular SCC in 289 C water. The IASCC susceptibility of SSs that contain >0.003 wt. % S increased drastically. bend tests in inert environments at 23 C were conducted on broken pieces of SSRT specimens and on unirradiated specimens of the same materials after hydrogen charging. The results of the tests and a review of other data in the literature

  5. Evaluation method of cracking resistance of lightweight aggregate concrete

    季韬; 张彬彬; 陈永波; 庄一舟


    The cracking behavior of lightweight aggregate concrete (LWAC) was investigated by mechanical analysis, SEM and cracking-resistant test where a shrinkage-restrained ring with a clapboard was used. The relationship between the ceramsite type and the cracking resistance of LWAC was built up and compared with that of normal-weight coarse aggregate concrete (NWAC). A new method was proposed to evaluate the cracking resistance of concrete, where the concepts of cracking coefficient ζt(t) and the evaluation index Acr(t) were proposed, and the development of micro-cracks and damage accumulation were recognized. For the concrete with an ascending cracking coefficient curve, the larger Acr(t) is, the lower cracking resistance of concrete is. For the concrete with a descending cracking coefficient curve, the larger Acr(t) is, the stronger the cracking resistance of concrete is. The evaluation results show that in the case of that all the three types of coarse aggregates in concrete are pre-soaked for 24 h, NWAC has the lowest cracking resistance, followed by the LWAC with lower water absorption capacity ceramsite and the LWAC with higher water absorption capacity ceramsite has the strongest cracking resistance. The proposed method has obvious advantages over the cracking age method, because it can evaluate the cracking behavior of concrete even if the concrete has not an observable crack.

  6. Firebox modeling of SRT cracking heaters

    Sundaram, K.M.; Albano, J.V. [ABB Lummus Crest Inc., Bloomfield, NJ (United States)


    Thermal cracking of hydrocarbons remains the most economically attractive route for the production of ethylene. The heat for the endothermic cracking reaction is supplied in high capacity fired heaters which are designed specifically to have high selectivity to olefins. In the cracking process, coke is deposited within the tubes of the radiant coil. The rate of coke deposition in a cracking furnace is a function not only of process conditions but of other factors as well. High tube metal temperatures in certain areas of the coil or hot spots can cause locally high coking rate leading to partial blockage of the tubes and consequently, short runs. The small diameter tubes used in modern high selectivity heaters are more sensitive than older large tube designs. The occurrence of these hot zones is a strong function of fireside conditions. For satisfactory performance, the heat flux profile in a cracking heater must be maintained as uniform as possible. In addition, it is important to minimize the variation of process temperatures entering the various cracking coils. These fireside variables are not only a function of the type of burners, excess air, type of fuel(s) and distribution of air and fuel but depend significantly on the air and flue gas flow patterns associated with the firebox, i.e., the firebox aerodynamics. Poor aerodynamics can adversely affect firing patterns and hence heat flux profiles in commercial furnaces. A variety of modeling techniques have been used to evaluate the firebox aerodynamics of Lummus, Short Residence Time, cracking heaters. These include flow visualization, physical cold flow modeling, and computational techniques. These approaches are discussed in this paper.

  7. Crack propagation modeling using Peridynamic theory

    Hafezi, M. H.; Alebrahim, R.; Kundu, T.


    Crack propagation and branching are modeled using nonlocal peridynamic theory. One major advantage of this nonlocal theory based analysis tool is the unifying approach towards material behavior modeling - irrespective of whether the crack is formed in the material or not. No separate damage law is needed for crack initiation and propagation. This theory overcomes the weaknesses of existing continuum mechanics based numerical tools (e.g. FEM, XFEM etc.) for identifying fracture modes and does not require any simplifying assumptions. Cracks grow autonomously and not necessarily along a prescribed path. However, in some special situations such as in case of ductile fracture, the damage evolution and failure depend on parameters characterizing the local stress state instead of peridynamic damage modeling technique developed for brittle fracture. For brittle fracture modeling the bond is simply broken when the failure criterion is satisfied. This simulation helps us to design more reliable modeling tool for crack propagation and branching in both brittle and ductile materials. Peridynamic analysis has been found to be very demanding computationally, particularly for real-world structures (e.g. vehicles, aircrafts, etc.). It also requires a very expensive visualization process. The goal of this paper is to bring awareness to researchers the impact of this cutting-edge simulation tool for a better understanding of the cracked material response. A computer code has been developed to implement the peridynamic theory based modeling tool for two-dimensional analysis. A good agreement between our predictions and previously published results is observed. Some interesting new results that have not been reported earlier by others are also obtained and presented in this paper. The final objective of this investigation is to increase the mechanics knowledge of self-similar and self-affine cracks.


    C.F.Lee; L.T.Hsiao


    In this paper, the FEM with the incremental endochronic cyclic plasticity (EndoFEM) and the rc controlled node-released strategy are employed to study the fatigue crack opened/closed load (Pop) of A1 2024-T3 CCT specimens provided by Mageed and Pandey under several crack lengths and the constant amplitude with various load ratio (R). After statisfactory results are achieved by comparisons of computed Pop values and cited experimental data, the simulations will be extended to the crack lengths with significant bending effect due to short ligaments or high peak (Pmax) or high positive or very low negative R cyclic loads. Through these simulations, the complete map of Pop/Pmax vs. Kmax and R can be constructed and thereafter its correspondant empirical formulae can be proposed. Using these formulae and selecting the traditional fatigue crack growth parameter ΔKeff, the A1 2024-T3 fatigue crack growth rate da/dN vs. ΔK and R data, provided by Hiroshi and Schijve, can be employed to proposed empirical formulae of da/dN vs. ΔKeff and R. After integration, fatigue-crack-growth length a vs. N curves computed by EndoFEM can be obtained. The results are agreed very well with the existing experimental curves. According to the above procedures of simulation and steps of comparions with experiment, this paper may provides an integrate methodology of numerical simulation in the studies of fatigue crack growth for academic and industrial researches and design analysis.


    Langton, C.


    Concrete containment structures and cement-based fills and waste forms are used at the Savannah River Site to enhance the performance of shallow land disposal systems designed for containment of low-level radioactive waste. Understanding and measuring transport through cracked concrete is important for describing the initial condition of radioactive waste containment structures at the Savannah River Site (SRS) and for predicting performance of these structures over time. This report transmits the results of a literature review on transport through cracked concrete which was performed by Professor Jason Weiss, Purdue University per SRR0000678 (RFP-RQ00001029-WY). This review complements the NRC-sponsored literature review and assessment of factors relevant to performance of grouted systems for radioactive waste disposal. This review was performed by The Center for Nuclear Waste Regulatory Analyses, San Antonio, TX, and The University of Aberdeen, Aberdeen Scotland and was focused on tank closure. The objective of the literature review on transport through cracked concrete was to identify information in the open literature which can be applied to SRS transport models for cementitious containment structures, fills, and waste forms. In addition, the literature review was intended to: (1) Provide a framework for describing and classifying cracks in containment structures and cementitious materials used in radioactive waste disposal, (2) Document the state of knowledge and research related to transport through cracks in concrete for various exposure conditions, (3) Provide information or methodology for answering several specific questions related to cracking and transport in concrete, and (4) Provide information that can be used to design experiments on transport through cracked samples and actual structures.

  10. Recent evaluations of crack-opening-area in circumferentially cracked pipes

    Rahman, S.; Brust, F.; Ghadiali, N.; Wilkowski, G.; Miura, N.


    Leak-before-break (LBB) analyses for circumferentially cracked pipes are currently being conducted in the nuclear industry to justify elimination of pipe whip restraints and jet shields which are present because of the expected dynamic effects from pipe rupture. The application of the LBB methodology frequently requires calculation of leak rates. The leak rates depend on the crack-opening area of the through-wall crack in the pipe. In addition to LBB analyses which assume a hypothetical flaw size, there is also interest in the integrity of actual leaking cracks corresponding to current leakage detection requirements in NRC Regulatory Guide 1.45, or for assessing temporary repair of Class 2 and 3 pipes that have leaks as are being evaluated in ASME Section XI. The objectives of this study were to review, evaluate, and refine current predictive models for performing crack-opening-area analyses of circumferentially cracked pipes. The results from twenty-five full-scale pipe fracture experiments, conducted in the Degraded Piping Program, the International Piping Integrity Research Group Program, and the Short Cracks in Piping and Piping Welds Program, were used to verify the analytical models. Standard statistical analyses were performed to assess used to verify the analytical models. Standard statistical analyses were performed to assess quantitatively the accuracy of the predictive models. The evaluation also involved finite element analyses for determining the crack-opening profile often needed to perform leak-rate calculations.

  11. Crack Growth Monitoring by Embedded Optical Fibre Bragg Grating Sensors: Fibre Reinforced Plastic Crack Growing Detection

    Pereira, Gilmar Ferreira; Mikkelsen, Lars Pilgaard; McGugan, Malcolm


    This article presents a novel method to asses a crack growing/damage event in fibre reinforced plastic, or adhesive using Fibre Bragg Grating (FBG) sensors embedded in a host material. Different features of the crack mechanism that induce a change in the FBG response were identified. Double Canti...

  12. Hydrocarbon cracking selectivities with a dual zeolite fluid cracking catalyst containing REY and ZSM-5

    Rajagopalan, K.; Young, G.W. (W.R. Grace and Company, Columbia, MD (USA))


    Synthetic Y faujasite zeolites have been used commercially as cracking catalysts for the past two decades, and more recently dual zeolite fluid cracking catalysts, containing faujasite and ZSM-5 were discovered to increase the octane number of the gasoline during catalytic cracking of gas oil. This concept, where ZSM-5 constitutes only a small fraction (about 1 wt %) of the cracking catalyst, has been tested commercially in Europe and in the United States. Cracking of paraffinic and olefinic hydrocarbons by ZSM-5 catalysts has been studied by several investigators over a range of temperatures (350 to 540{degree}C) and using nearly pure ZSM-5 as the catalyst. The mechanism of octane number enhancement with the dual zeolite catalyst was investigated by examining the effect on product selectivity of addition of 1 wt % ZSM-5 to a cracking catalyst composition during catalytic cracking of a commercial gas oil at 500{degree}C. Changes in composition of the product gasoline (paraffins, olefins, naphthenes and aromatics) caused by ZSM-5 were measured. Since commercial cracking catalysts undergo continuous high temperature regeneration in the presence of steam, the effect of hydrothermal treatment of ZSM-5 was also investigated.

  13. Evolving fracture patterns: columnar joints, mud cracks, and polygonal terrain

    Goehring, L.


    Contraction cracks can form captivating patterns, such as the artistic craquelure sometimes found in pottery glazes, to the cracks in dried mud, or the polygonal networks covering the polar regions of Earth and Mars. Two types are frequently encountered: those with irregular rectilinear patterns, such as that formed by an homogeneous slurry when dried (or cooled) uniformly, and more regular hexagonal patterns, such as those typified by columnar joints. Once cracks start to form in a thin contracting layer, they will sequentially break the layer into smaller and smaller pieces. A rectilinear crack pattern encodes information about the order of cracks, as later cracks tend to intersect with earlier cracks at right angles. In this manner they relieve the stresses perpendicular to the pre-existing crack. In a hexagonal pattern, in contrast, the angles between all cracks at a vertex are near 120°. In this presentation it will be shown how both types of pattern can arise from identical forces, and that a rectilinear, T-junction dominated pattern will develop into to a hexagonal pattern, with Y-junctions, if allowed to. Such an evolution can be explained as the result of three conditions: (1) if cracks advance through space, or heal and recur, that the previous positions of a crack tip acts as a line of weakness, guiding the next iteration of cracking; (2) that the order of opening of cracks can change in each iteration; and (3) that crack tips curve to maximise the local strain energy release rate. The ordering of crack patterns are seen in a number of systems: columnar joints in starch and lava; desiccation cracks in clays that are repeatedly wetted and dried; cracks in eroding gypsum-cemented sand layers; and the cracks in permafrost known as polygonal terrain. These patterns will each be briefly explored, in turn, and shown to obey the above principles of crack pattern evolution.

  14. Evaluation of Stress Intensity Factors for Multiple Cracked Circular Disks Under Crack Surface Tractions with SBFEM

    LIU Jun-yu; LIN Gao; LI Xiao-chuan; XU Feng-lin


    Stress intensity factors (SIFs) for the cracked circular disks under different distributing surface tractions are evaluated with the scaled boundary finite element method (SBFEM).In the SBFEM,the analytical advantage of the solution in the radial direction allows SIFs to be directly determined from its definition,therefore no special crack-tip treatment is necessary.Furthermore anisotropic material behavior can be treated easily.Different distributions of surface tractions are considered for the center and double-edge-cracked disks.The benchmark examples are modeled and an excellent agreement between the results in the present study and those in published literature is found.It shows that SBFEM is effective and possesses high accuracy.The SIFs of the cracked orthotropic material circular disks subjected to different surface tractions are also evaluated.The technique of substructure is applied to handle the multiple cracks problem.

  15. Failure analysis of corrosion cracking and simulated testing for a fluid catalytic cracking unit

    Hua Chen; Xiaogang Li; Chaofang Dong; Ming Li; Jinwen Yang


    The failure of a fluid catalysis and cracking unit (FCCU) in a Chinese refinery was investigated by using nondestructive detection methods, fracture surface examination, hardness measurement, chemical composition and corrosion products analysis. The results showed that the failure was caused by the dew point nitrate stress corrosion cracking. For a long operation period, the wall temperature of the regenerator in the FCCU was below the fume dew point. As a result, an acid fume NOx-SOx-H2O medium presented on the surface, resulting in stress corrosion cracking of the component with high residual stress. In order to confirm the relative conclusion, simulated testing was conducted in laboratory, and the results showed similar cracking characteristics. Finally, some suggestions have been made to prevent the stress corrosion cracking of an FCCU from re-occurring in the future.

  16. Shaft Crack Identification Based on Vibration and AE Signals

    Wenxiu Lu


    Full Text Available The shaft crack is one of the main serious malfunctions that often occur in rotating machinery. However, it is difficult to locate the crack and determine the depth of the crack. In this paper, the acoustic emission (AE signal and vibration response are used to diagnose the crack. The wavelet transform is applied to AE signal to decompose into a series of time-domain signals, each of which covers a specific octave frequency band. Then an improved union method based on threshold and cross-correlation method is applied to detect the location of the shaft crack. The finite element method is used to build the model of the cracked rotor, and the crack depth is identified by comparing the vibration response of experiment and simulation. The experimental results show that the AE signal is effective and convenient to locate the shaft crack, and the vibration signal is feasible to determine the depth of shaft crack.

  17. Virtual restoration of cracks in digitized image of paintings

    Spagnolo, G Schirripa; Somma, F


    An integrated methodology for the detection and removal of cracks on digitized image is presented in this paper. Crack-like pattern detection have been a matter of high concern among researchers mostly for its useful contribution to a variety of applications. The results presented here regard the craquelure of old paintings, however, the same methodology can be used for a much wider set of application. Many images contain similar patterns: crack in protective coating for polymers and other surfaces; fatigue crack in MEMS/NEMS; crack in epoxies used for underfill and encapsulation microelectronics components; etc. In this paper the cracks are detected by thresholding the output of the morphological top-hat transform. Afterwards, the thin dark brush strokes which have been misidentified as cracks are removed using automatic procedure. Finally, crack filling using texture synthesis algorithms. The methodology has been shown to perform very well on digitized images suffering from cracks.

  18. Fracture mechanics of piezoelectric solids with interface cracks

    Govorukha, Volodymyr; Loboda, Volodymyr; Lapusta, Yuri


    This book provides a comprehensive study of cracks situated at the interface of two piezoelectric materials. It discusses different electric boundary conditions along the crack faces, in particular the cases of electrically permeable, impermeable, partially permeable, and conducting cracks. The book also elaborates on a new technique for the determination of electromechanical fields at the tips of interface cracks in finite sized piezoceramic bodies of arbitrary shape under different load types. It solves scientific problems of solid mechanics in connection with the investigation of electromechanical fields in piezoceramic bodies with interface cracks, and develops calculation models and solution methods for plane fracture mechanical problems for piecewise homogeneous piezoceramic bodies with cracks at the interfaces. It discusses the “open” crack model, which leads to a physically unrealistic oscillating singularity at the crack tips, and the contact zone model for in-plane straight interface cracks betw...

  19. Frequency-dependent environmental fatigue crack propagation in the 7XXX alloy/aqueous chloride system

    Gasem, Zuhair Mattoug

    The need to predict the fatigue performance of aging aerospace structures has focused interest on environmentally assisted cracking in thick-section damage-tolerant aluminum alloys (AA). The objective of this research is to characterize and understand the time-dependent processes that govern environmental fatigue crack propagation (EFCP) in 7XXX series aluminum alloys exposed to an aggressive environment. Results are utilized to identify the rate-controlling step in growth enhancement in order to develop a mechanistic model describing the time dependency of EFCP. Aluminum alloy 7075, tested in the sensitive (SL) orientation and exposed to aqueous chloride solution, is studied. Da/dNcrit for different D K levels depends on 1/√fcrit, as predicted by process zone hydrogen-diffusion-limited crack growth modeling. A model based on hydrogen diffusion controlled growth is modified to include a stress-dependent critical hydrogen concentration normalized with the crack tip hydrogen concentration (Ccrit/CS). It is proposed that da/dNcrit for a given D K and R corresponds to the distance ahead of the crack tip where the local tensile stress associated with Kmax is maximum. The reversed plasticity estimate of this location equals da/dNcrit for two aging conditions of 7075 (SL)/NaCl at R = 0.1. The EFCP dependencies on alloy microstructure (T6 vs. T7), crack orientation (SL vs. LT), and stress ratio are measured and interpreted based on their effect on da/dN crit and fcrit as well as environmental closure. Chromate addition to the chloride solution eliminates the environmental acceleration of crack growth and reduces corrosion-product induced closure. In chromate-inhibited solution, the frequency dependence of EFCP in 7075 (SL) is unique. Da/dN is reduced at moderate and low frequencies to a value similar to crack growth rate in moist air, probably due to formation of a passive film which inhibits hydrogen uptake. Inhibition is mitigated by increasing frequency or increasing

  20. Bayesian Identification of a Cracked Plate using a Population-Based Markov Chain Monte Carlo Method


    serendipity elements, with nodes at each corner and at the middle of each side. Adjacent to the crack tip the eight-noded quads are modified as...noise variance) have been Fig. 4. (a) Nodal configuration of the Mindlin serendipity element, (b) resulting interpolation functions, (c) schematic of...repeated iterations of the forward model, great care was taken in developing an efficient model. This was accomplished by using tailored ‘‘ serendipity

  1. Automatic quantification of crack patterns by image processing

    Liu, Chun; Tang, Chao-Sheng; Shi, Bin; Suo, Wen-Bin


    Image processing technologies are proposed to quantify crack patterns. On the basis of the technologies, a software "Crack Image Analysis System" (CIAS) has been developed. An image of soil crack network is used as an example to illustrate the image processing technologies and the operations of the CIAS. The quantification of the crack image involves the following three steps: image segmentation, crack identification and measurement. First, the image is converted to a binary image using a cluster analysis method; noise in the binary image is removed; and crack spaces are fused. Then, the medial axis of the crack network is extracted from the binary image, with which nodes and crack segments can be identified. Finally, various geometric parameters of the crack network can be calculated automatically, such as node number, crack number, clod area, clod perimeter, crack area, width, length, and direction. The thresholds used in the operations are specified by cluster analysis and other innovative methods. As a result, the objects (nodes, cracks and clods) in the crack network can be quantified automatically. The software may be used to study the generation and development of soil crack patterns and rock fractures.

  2. Crack Detection with Lamb Wave Wavenumber Analysis

    Tian, Zhenhua; Leckey, Cara; Rogge, Matt; Yu, Lingyu


    In this work, we present our study of Lamb wave crack detection using wavenumber analysis. The aim is to demonstrate the application of wavenumber analysis to 3D Lamb wave data to enable damage detection. The 3D wavefields (including vx, vy and vz components) in time-space domain contain a wealth of information regarding the propagating waves in a damaged plate. For crack detection, three wavenumber analysis techniques are used: (i) two dimensional Fourier transform (2D-FT) which can transform the time-space wavefield into frequency-wavenumber representation while losing the spatial information; (ii) short space 2D-FT which can obtain the frequency-wavenumber spectra at various spatial locations, resulting in a space-frequency-wavenumber representation; (iii) local wavenumber analysis which can provide the distribution of the effective wavenumbers at different locations. All of these concepts are demonstrated through a numerical simulation example of an aluminum plate with a crack. The 3D elastodynamic finite integration technique (EFIT) was used to obtain the 3D wavefields, of which the vz (out-of-plane) wave component is compared with the experimental measurement obtained from a scanning laser Doppler vibrometer (SLDV) for verification purposes. The experimental and simulated results are found to be in close agreement. The application of wavenumber analysis on 3D EFIT simulation data shows the effectiveness of the analysis for crack detection. Keywords: : Lamb wave, crack detection, wavenumber analysis, EFIT modeling

  3. Applied Stress Affecting the Environmentally Assisted Cracking

    Vasudevan, A. K.


    Stress corrosion cracking (SCC) is affected by the mode of applied stress, i.e., tension, compression, or torsion. The cracking is measured in terms of initiation time to nucleate a crack or time to failure. In a simple uniaxial loading under tension or compression, it is observed that the initiation time can vary in orders of magnitude depending on the alloy and the environment. Fracture can be intergranular or transgranular or mixed mode. Factors that affect SCC are solubility of the metal into surrounding chemical solution, and diffusion rate (like hydrogen into a tensile region) of an aggressive element into the metal and liquid metallic elements in the grain boundaries. Strain hardening exponent that affects the local internal stresses and their gradients can affect the diffusion kinetics. We examine two environments (Ga and 3.5 pct NaCl) for the same alloy 7075-T651, under constant uniaxial tension and compression load. These two cases provide us application to two different governing mechanisms namely liquid metal embrittlement (7075-Ga) and hydrogen-assisted cracking (7075-NaCl). We note that, in spite of the differences in their mechanisms, both systems show similar behavior in the applied K vs crack initiation time plots. One common theme among them is the transport mechanism of a solute element to a tensile-stress region to initiate fracture.

  4. Crack buckling in soft gels under compression

    Rong Long; Chung-Yuen Hui


    Recent interest in designing soft gels with high fracture toughness has called for simple and robust methods to test fracture behavior.The conventional method of applying tension to a gel sample suffers from a difficulty of sample gripping.In this paper,we study a possible fracture mechanism of soft gels under uni-axial compression.We show that the surfaces of a pre-existing crack,oriented parallel to the loading axis,can buckle at a critical compressive stress.This buckling instability can open the crack surfaces and create highly concentrated stress fields near the crack tip,which can lead to crack growth.We show that the onset of crack buckling can be deduced by a dimensional argument combined with an analysis to determine the critical compression needed to induce surface instabilities of an elastic half space.The critical compression for buckling was verified for a neoHookean material model using finite element simulations.

  5. Imaging Cracks by Laser Excited Thermography

    Schlichting, J.; Kervalishvili, G. N.; Maierhofer, Ch.; Kreutzbruck, M.


    During the last years active thermography is increasingly used in a number of NDT problems in production and maintenance. In this work we focus on the detection of vertical cracks starting at the surface, which is an important indication of structural failure. By using local thermal excitation it is possible to image anisotropies in the lateral diffusivity by recording the temporal temperature data with an infrared camera. The regional transient behaviour of temperature distribution then can provide quantitative information of the crack parameter. In doing so, we present an advanced technique for the determination of the crack depth. The experimental set-up is based on an Nd:YAG laser. The beam is focused on the test sample by using an optical scanner to create the required lateral heat flow. The time resolved temperature distribution is recorded with an infrared camera (InSb FPA, 3 to 5 μm) providing a frame rate of up to 500 Hz. In addition we report on numerical simulation to investigate the concept of local heat excitation for a quantitative estimation of crack parameters. The modeling also includes the influence of surface to surface radiation inside the crack. We obtained a good consistency between experimental and theoretical data.

  6. Influence of nano-inclusions' grain boundaries on crack propagation modes in materials

    Karakasidis, T.E., E-mail: [Department of Civil Engineering, University of Thessaly, Pedion Areos, 38834 Volos (Greece); Charitidis, C.A. [National Technical University of Athens, School of Chemical Engineering, 9 Heroon Polytechniou st., Zografos, 157 80 Athens (Greece)


    The effect of nano-inclusions on materials' strength and toughness has attracted great interest in recent years. It has been shown that tuning the morphological and microstructural features of materials can tailor their fracture modes. The existence of a characteristic size of inclusions that favours the fracture mode (i.e. transgranular or intergranular) has been experimentally observed but also predicted by a 2D model based on energetic arguments which relates the crack propagation mode to the ratio of the interface area between the crystalline inclusion and the matrix with the area of the crystallite inclusion in a previous work. In the present work, a 3D model is proposed in order to extend the 2D model and take into account the influence of the size of grain boundary zone on the toughening/hardening behavior of the material as it was observed experimentally in the literature. The model relates crack propagation mode to the ratio of the volume of the grain boundary zone between the crystalline inclusion and the matrix with the volume of the nano-inclusion. For a ratio below a critical value, transgranular propagation is favoured while for larger values, intergranular propagation is favoured. We also demonstrate that the extent of the grain boundary region also can significantly affect this critical value. The results of the model are in agreement with the literature experimental observations related to the toughening/hardening behavior as a function of the size of crystalline inclusions as well as the width of the grain boundary regions.

  7. Propagation of stress corrosion cracks in alpha-brasses

    Beggs, Dennis Vinton [Univ. of Illinois, Urbana-Champaign, IL (United States)


    Transgranular and intergranular stress corrosion cracks were investigated in alpha-brasses in a tarnishing ammoniacal solution. Surface observation indicated that the transgranular cracks propagated discontinuously by the sudden appearance of a fine crack extending several microns ahead of the previous crack tip, often associated with the detection of a discrete acoustic emission (AE). By periodically increasing the deflection, crack front markings were produced on the resulting fracture surfaces, showing that the discontinuous propagation of the crack trace was representative of the subsurface cracking. The intergranular crack trace appeared to propagate continuously at a relatively blunt crack tip and was not associated with discrete AE. Under load pulsing tests with a time between pulses, Δt greater than or equal to 3 s, the transgranular fracture surfaces always exhibited crack front markings which corresponded with the applied pulses. The spacing between crack front markings, Δx, decreased linearly with Δt. With Δt less than or equal to 1.5 s, the crack front markings were in a one-to-one correspondence with applied pulses only at relatively long crack lengths. In this case, Δx = Δx* which approached a limiting value of 1 μm. No crack front markings were observed on intergranular fracture surfaces produced during these tests. It is concluded that transgranular cracking occurs by discontinuous mechanical fracture of an embrittled region around the crack tip, while intergranular cracking results from a different mechanism with cracking occurring via the film-rupture mechanism.

  8. Use of ultrasonic back-reflection intensity for predicting the onset of crack growth due to low-cycle fatigue in stainless steel under block loading.

    Islam, Md Nurul; Arai, Yoshio; Araki, Wakako


    The present study proposes the use of ultrasonic back-reflected waves for evaluating low cycle fatigue crack growth from persistent slip bands (PSBs) of stainless steel under block loading. Fatigue under high-low block loading changes the back-reflected intensity of the ultrasonic wave that emanates from the surface. Measuring the change in ultrasonic intensity can predict the start of crack growth with reasonable accuracy. The present study also proposes a modified constant cumulative plastic strain method and a PSB damage evolution model to predict the onset of crack growth under block loads.

  9. Crack tip shielding and anti-shielding effects of parallel cracks for a superconductor slab under an electromagnetic force

    Gao, Zhi Wen; Zhou, You He [Ministry of Education, Singapore (China); Lee, Kang Yong [Yonsei University, Seoul (Korea, Republic of)


    In this letter, the shielding or anti-shielding effect is firstly applied to obtain the behavior of two parallel cracks in a two-dimensional type-II superconducting under electromagnetic force. Fracture analysis is performed by the finite element method and the magnetic behavior of superconductor is described by the critical state Bean model. The stress intensity factors at the crack tips can be obtained and discussed for decreasing field after zero-field cooling. The shielding or anti-shielding effect at the crack tips depend on the distance between two parallel cracks and the crack length. The results indicate that the shielding effects of the two parallel cracks increase when the distance between the two parallel cracks decreases. It can be also obtained that the superconductors with shorter cracks has more remarkable shielding effect than those with longer cracks.

  10. Effects of plastic anisotropy on crack-tip behaviour

    Legarth, Brian Nyvang; Tvergaard, Viggo; Kuroda, Mitsutoshi


    loading remote from the crack-tip. In cases where the principal axes of the anisotropy are inclined to the plane of the crack it is found that the plastic zones as well as the stress and strain fields just around the blunted tip of the crack become non-symmetric. In these cases the peak strain...... on the blunted tip occurs off the center line of the crack, thus indicating that the crack may want to grow in a different direction. When the anisotropic axes are parallel to the crack symmetry is retained, but the plastic zones and the near-tip fields still differ from those predicted by standard isotropic...

  11. Evaluation of a Small-Crack Monitoring System

    Newman, John A.; Johnston, William M.


    A new system has been developed to obtain fatigue crack growth rate data from a series of images acquired during fatigue testing of specimens containing small surface cracks that initiate at highly-polished notches. The primary benefit associated with replica-based crack growth rate data methods is preserving a record of the crack configuration during the life of the specimen. Additionally, this system has the benefits of both reducing time and labor, and not requiring introduction of surface replica media into the crack. Fatigue crack growth rate data obtained using this new system are found to be in good agreement with similar results obtained from surface replicas.

  12. Sizing stress corrosion cracks using laser ultrasonics

    Rehman, Hamood; McNealy, Rick; Fingerhut, Martin [Applus-RTD. Houston, TX (United States); Klein, Marvin; Ansari, Homayoon [Intelligent Optical Systems, Inc. Los Angeles, CA (United States); Kania Richard [TransCanada. Calgary, AB (Canada); Rapp, Steve [Spectra Energy, Houston, TX (United States)


    Despite various efforts, no reliable tools and techniques are available to enable an operator to quantify the impact of an SCC (Stress Corrosion Cracking) colony on the safety and integrity of a pipeline. Reliable non-destructive detection and measurement tools are not available either. There is therefore a large gap between current technology and the needs of the pipeline industry. Recent developments promise that with a concentrated effort, a comprehensive solution can be devised. This paper describes technical work performed to develop and validate both the inspection tool and the time of flight diffraction (TOFD) technique for sizing the depth of SCC. It also presents preliminary results of work on a closely related project that provides, on the basis of this technology, an integrated approach and tool for mapping, sizing, and evaluating SCC, through which significant cracks are filtered from more benign cracks within an SCC colony.

  13. Environmentally assisted cracking in LWR materials

    Chopra, O.K.; Chung, H.M.; Kassner, T.F.; Park, J.H.; Shack, W.J. [Argonne National Lab., IL (United States); Zhang, J.; Brust, F.W.; Dong, P. [Battelle Columbus Labs., Columbus, OH (United States)


    The effect of dissolved oxygen level on fatigue life of austenitic stainless steels is discussed and the results of a detailed study of the effect of the environment on the growth of cracks during fatigue initiation are presented. Initial test results are given for specimens irradiated in the Halden reactor. Impurities introduced by shielded metal arc welding that may affect susceptibility to stress corrosion cracking are described. Results of calculations of residual stresses in core shroud weldments are summarized. Crack growth rates of high-nickel alloys under cyclic loading with R ratios from 0.2--0.95 in water that contains a wide range of dissolved oxygen and hydrogen concentrations at 289 and 320 C are summarized.

  14. Fatigue, Wear and Cracking of Dental Materials

    Traian Eugen Bolfa


    Full Text Available Evaluation of the method of failure and crack propagation in dental metals, ceramics and polymer composite materials associated with occlusal activity are associated with contact, twisting and sliding modes. Such loads can result in various combinations of damage due to fatigue and wear. In order to increase sustainability and longevity the dental materials must demonstrate sufficient strength to dynamic stresses. In the case of masticatory forces associated with high contact tensions, the contact area of the superficial layer is under a state of specialcomplex voltage. Variations in the material or the structure, impurities, scratches and voids can directly influence the structural integrity of the material and result in microscopic cracks. These cracks propagate under repeated cyclic loading leading to dental restoration failure.

  15. Inverse Crack Problems in Piezoelectric Solids

    Sladek, Jan; Sladek, Vladimir; Zhang, Chuanzeng


    In the present paper, the meshless local Petrov-Galerkin (MLPG) method is applied to cracked piezoelectric solids under a stationary or transient dynamic load and unspecified electrical conditions on the crack surfaces. On the outer surface of the cracked solid the electrical boundary conditions are over-specified. The coupled governing partial differential equations are satisfied in a weak-form on small fictitious sub-domains. Nodal points are introduced and spread on the analyzed domain and each node is surrounded by a small circle for simplicity, but without loss of generality. The spatial variations of the displacements and the electric potential are approximated by the Moving Least-Squares (MLS) scheme. After performing the spatial integrations, a system of linear algebraic equations for unknown nodal values is obtained. Singular value decomposition (SVD) is applied to solve the ill-conditioned linear system of algebraic equations obtained from the local integral equations (LIEs) after the MLS approximation.

  16. Computer Simulations of the Fatigue Crack Propagation

    A. Materna


    Full Text Available The following hypothesis for design of structures based on the damage tolerance philosophy is laid down: the perpendicular fatigue crack growth rate v in a certain point of a curved crack front is given by the local value of stress intensity factor per unit of nominal stress K' and the local triaxiality T which describes the constraint. The relationship v = f (K', T is supposed to be typical for a given loading spectrum and material. Such relationship for a 2024 Al alloy and the flight-simulation spectrum was derived from the fatigue test of the rectangular panel with the central hole and used for three-dimensional simulation of the corner fatigue crack propagation in the model of the wing spar flangeplate. Finite element and boundary element methods were used for these computations. The results of the simulation are in good agreement with the experiment.

  17. Dynamical observations on the crack tip zone and stress corrosion of two-dimensional MoS2

    Ly, Thuc Hue; Zhao, Jiong; Cichocka, Magdalena Ola; Li, Lain-Jong; Lee, Young Hee


    Whether and how fracture mechanics needs to be modified for small length scales and in systems of reduced dimensionality remains an open debate. Here, employing in situ transmission electron microscopy, atomic structures and dislocation dynamics in the crack tip zone of a propagating crack in two-dimensional (2D) monolayer MoS2 membrane are observed, and atom-to-atom displacement mapping is obtained. The electron beam is used to initiate the crack; during in situ observation of crack propagation the electron beam effect is minimized. The observed high-frequency emission of dislocations is beyond previous understanding of the fracture of brittle MoS2. Strain analysis reveals dislocation emission to be closely associated with the crack propagation path in nanoscale. The critical crack tip plastic zone size of nearly perfect 2D MoS2 is between 2 and 5 nm, although it can grow to 10 nm under corrosive conditions such as ultraviolet light exposure, showing enhanced dislocation activity via defect generation.

  18. Dynamical observations on the crack tip zone and stress corrosion of two-dimensional MoS2

    Ly, Thuc Hue


    Whether and how fracture mechanics needs to be modified for small length scales and in systems of reduced dimensionality remains an open debate. Here, employing in situ transmission electron microscopy, atomic structures and dislocation dynamics in the crack tip zone of a propagating crack in two-dimensional (2D) monolayer MoS2 membrane are observed, and atom-to-atom displacement mapping is obtained. The electron beam is used to initiate the crack; during in situ observation of crack propagation the electron beam effect is minimized. The observed high-frequency emission of dislocations is beyond previous understanding of the fracture of brittle MoS2. Strain analysis reveals dislocation emission to be closely associated with the crack propagation path in nanoscale. The critical crack tip plastic zone size of nearly perfect 2D MoS2 is between 2 and 5 nm, although it can grow to 10 nm under corrosive conditions such as ultraviolet light exposure, showing enhanced dislocation activity via defect generation.

  19. In Search of a Time Efficient Approach to Crack and Delamination Growth Predictions in Composites

    Krueger, Ronald; Carvalho, Nelson


    Analysis benchmarking was used to assess the accuracy and time efficiency of algorithms suitable for automated delamination growth analysis. First, the Floating Node Method (FNM) was introduced and its combination with a simple exponential growth law (Paris Law) and Virtual Crack Closure technique (VCCT) was discussed. Implementation of the method into a user element (UEL) in Abaqus/Standard(Registered TradeMark) was also presented. For the assessment of growth prediction capabilities, an existing benchmark case based on the Double Cantilever Beam (DCB) specimen was briefly summarized. Additionally, the development of new benchmark cases based on the Mixed-Mode Bending (MMB) specimen to assess the growth prediction capabilities under mixed-mode I/II conditions was discussed in detail. A comparison was presented, in which the benchmark cases were used to assess the existing low-cycle fatigue analysis tool in Abaqus/Standard(Registered TradeMark) in comparison to the FNM-VCCT fatigue growth analysis implementation. The low-cycle fatigue analysis tool in Abaqus/Standard(Registered TradeMark) was able to yield results that were in good agreement with the DCB benchmark example. Results for the MMB benchmark cases, however, only captured the trend correctly. The user element (FNM-VCCT) always yielded results that were in excellent agreement with all benchmark cases, at a fraction of the analysis time. The ability to assess the implementation of two methods in one finite element code illustrated the value of establishing benchmark solutions.

  20. Cohesive Laws for Analyzing Through-Crack Propagation in Cross Ply Laminates

    Bergan, Andrew C.; Davila, Carlos G.


    The laminate cohesive approach (LCA) is a methodology for the experimental characterization of cohesive through-the-thickness damage propagation in fiber-reinforced polymer matrix composites. LCA has several advantages over other existing approaches for cohesive law characterization, including: visual measurements of crack length are not required, structural effects are accounted for, and LCA can be applied when the specimen is too small to achieve steady-state fracture. In this work, the applicability of this method is investigated for two material systems: IM7/8552, a conventional prepreg, and AS4/VRM34, a non-crimp fabric cured using an out-of-autoclave process. The compact tension specimen configuration is used to propagate stable Mode I damage. Trilinear cohesive laws are characterized using the fracture toughness and the notch tip opening displacement. Test results are compared for the IM7/8552 specimens with notches machined by waterjet and by wire slurry saw. It is shown that the test results are nearly identical for both notch tip preparations methods, indicating that significant specimen preparation time and cost savings can be realized by using the waterjet to notch the specimen instead of the wire slurry saw. The accuracy of the cohesive laws characterized herein are assessed by reproducing the structural response of the test specimens using computational methods. The applicability of the characterization procedure for inferring lamina fracture toughness is also discussed.

  1. Crack initiation and crack growth behavior of carbon and low-alloy steels

    Gavenda, D.J.; Luebbers, P.R.; Chopra, O.K. [Argonne National Lab., IL (United States). Energy Technology Div.


    Section III of the ASME Boiler and Pressure Vessel Code specifies fatigue design curves for structural materials. These curves were based on tests of smooth polished specimens at room temperature in air. The effects of reactor coolant environments are not explicitly addressed by the Code design curves, but recent test data illustrate potentially significant effects of LWR coolant environments on the fatigue resistance of carbon and low-alloy steels. Under certain loading and environmental conditions, fatigue lives of test specimens may be a factor of {approx}70 shorter than in air. Results of fatigue tests that examine the influence of reactor environment on crack imitation and crack growth of carbon and low-alloy steels are presented. Crack lengths as a function of fatigue cycles were determined in air by a surface replication technique, and in water by block loading that leaves marks on the fracture surface. Decreases in fatigue life of low-alloy steels in high-dissolved-oxygen (DO) water are primarily caused by the effects of environment during early stages of fatigue damage, i.e., growth of short cracks <100 {micro}m in depth. For crack sizes of >100 {micro}m, crack growth rates in high-DO water are higher than in air by one order of magnitude. The effects of LWR environments on growth of short cracks are discussed.

  2. Production of steam cracking feedstocks by mild cracking of plastic wastes

    Angyal, Andras; Miskolczi, Norbert; Bartha, Laszlo; Tungler, Antal; Nagy, Lajos; Vida, Laszlo; Nagy, Gabor


    In this work the utility of new possible petrochemical feedstocks obtained by plastic waste cracking has been studied. The cracking process of polyethylene (PE), polyethylene-polypropylene (PEPP) and polyethylene-polystyrene (PEPS) has been carried out in a pilot scale tubular reactor. In this process mild reaction parameters has been applied, with the temperature of 530 C and the residence time of 15 min. The produced hydrocarbon fractions as light- and middle distillates were tested by using a laboratory steam cracking unit. It was concluded that the products of the mild cracking of plastic wastes could be applied as petrochemical feedstocks. Based on the analytical data it was determined that these liquid products contained in significant concentration (25-50 wt.%) of olefin hydrocarbons. Moreover the cracking of polystyrene containing raw material resulted in liquid products with significant amounts of aromatic hydrocarbons too. The steam cracking experiments proved that the products obtained by PE and PEPP cracking resulted in similar or better ethylene and propylene yields than the reference samples, however the aromatic content of PEPS products reduced the ethylene and propylene yields. (author)

  3. Thermographic characterization of stress during crack growth

    Cramer, K. E.; Dawicke, David S.; Welch, Christopher S.


    A full-field-thermographic technique for imaging stress patterns in dynamically loaded structures using general purpose IR imaging and image processing hardware is described. The inspection technique is based on the thermoelastic effect. A simple geometry is examined, and the experimentally determined values for the stress invariant are shown to be consistent with theoretical and numerical calculations. The application of full-field-thermographic measurement would ensure that the observed stress field has a common sampling period, thus allowing the observation of rapidly occurring stress anomalies such as the propagation of a fatigue crack. Fatigue crack propagation in two consecutive thermoelastic stress images from an aluminum sample is shown.

  4. Fast electromigration crack in nanoscale aluminum film

    Emelyanov, O. A.; Ivanov, I. O.


    The current-induced breakage of 20 nm thin aluminum layers deposited onto capacitor grade polypropylene (PP) films is experimentally studied. Biexponential current pulses of different amplitude (10-15 A) and duration (0.1-1 μs) were applied to the samples. Breakage occurred after fast development of electromigrating ˜200 nm-wide cracks with initial propagation velocity of ˜1 m/s under a high current density of ˜1012 A/m2. The cracks stopped when their lengths reached 250-450 μm. This behavior is explained by the balance of electromigration and stress-induced atomic fluxes.

  5. Crack Sensing Scheme in Rail Tracking System

    Ch. Muneendra Rao,


    Full Text Available A major share to the Indian economy is contributed by the commercial transport railway network. So, any problems of crack detection in railway network when encountered, may be dealt with a robust and cost effective solution, else, there may be a proportionate decrease in the nations economy. This paper attempts to provide a viable solution by discussing the technical details and design aspects. The discussion continues with the explanation of different criteria involved in choosing simple components like GPS module,PC,IR-photo diode based crack detector module, modeled for effective implementation in India.

  6. Fatigue crack growth under variable amplitude loading

    Sidawi, Jihad A.


    Fatigue crack growth tests were conducted on an Fe 510 E C-Mn steel and a submerged arc welded joint from the same material under constant, variable, and random loading amplitudes. Paris-Erdogan's crack growth rate law was tested for the evaluation of m and C using the stress intensity factor K, the J-integral, the effective stress intensity factor K(sub eff), and the root mean square stress intensity factor K(sub rms) fracture mechanics concepts. The effect of retardation and residual stresses resulting from welding was also considered. It was found that all concepts gave good life predictions in all cases.

  7. Multiple Gastrointestinal Complications of Crack Cocaine Abuse

    Neal Carlin


    Full Text Available Cocaine and its alkaloid free base “crack-cocaine” have long since been substances of abuse. Drug abuse of cocaine via oral, inhalation, intravenous, and intranasal intake has famously been associated with a number of medical complications. Intestinal ischemia and perforation remain the most common manifestations of cocaine associated gastrointestinal disease and have historically been associated with oral intake of cocaine. Here we find a rare case of two relatively uncommon gastrointestinal complications of hemorrhage and pancreatitis presenting within a single admission in a chronic crack cocaine abuser.

  8. Matrix cracking of fiber-reinforced ceramic composites in shear

    Rajan, Varun P.; Zok, Frank W.


    The mechanics of cracking in fiber-reinforced ceramic matrix composites (CMCs) under general loadings remains incomplete. The present paper addresses one outstanding aspect of this problem: the development of matrix cracks in unidirectional plies under shear loading. To this end, we develop a model based on potential energy differences upstream and downstream of a fully bridged steady-state matrix crack. Through a combination of analytical solutions and finite element simulations of the constituent stresses before and after cracking, we identify the dominant stress components that drive crack growth. We show that, when the axial slip lengths are much larger than the fiber diameter and when interfacial slip precedes cracking, the shear stresses in the constituents are largely unaffected by the presence of the crack; the changes that do occur are confined to a 'core' region within a distance of about one fiber diameter from the crack plane. Instead, the driving force for crack growth derives mainly from the axial stresses-tensile in the fibers and compressive in the matrix-that arise upon cracking. These stresses are well-approximated by solutions based on shear-lag analysis. Combining these solutions with the governing equation for crack growth yields an analytical estimate of the critical shear stress for matrix cracking. An analogous approach is used in deriving the critical stresses needed for matrix cracking under arbitrary in-plane loadings. The applicability of these results to cross-ply CMC laminates is briefly discussed.


    Yuezhong Feng; Zhihe Jin


    This work examines the fracture behavior of a functionally graded material (FGM) plate containing parallel surface cracks with alternating lengths subjected to a thermal shock. The thermal stress intensity factors (TSIFs) at the tips of long and short cracks are calculated using a singular integral equation technique. The critical thermal shock △T_c that causes crack initiation is calculated using a stress intensity factor criterion. Numerical examples of TSIFs and △T_c for an Al_2O_3/Si_3N_4 FGM plate are presented to illustrate the effects of thermal property gradation, crack spacing and crack length ratio on the TSIFs and △T_c. It is found that for a given crack length ratio, the TSIFs at the tips of both long and short cracks can be reduced significantly and △T_c can be enhanced by introducing appropriate material gradation. The TSIFs also decrease dramatically with a decrease in crack spacing. The TSIF at the tips of short cracks may be higher than that for the long cracks under certain crack geometry conditions. Hence, the short cracks instead of long cracks may first start to grow under the thermal shock loading.

  10. The effect of an East Pacific Rise offset on the formation of secondary cracks ahead of the Cocos-Nazca Rift at the Galapagos Triple Junction

    Smith, D. K.; Montesi, L. G.; Schouten, H.; Zhu, W.


    A succession of short-lived, E-W trending cracks at the Galapagos Triple Junction north and south of the Cocos-Nazca (C-N) Rift, has been explained by a simple crack interaction model. The locations of where the cracks initiate are controlled by tensile stresses generated at the East Pacific Rise (EPR) by two interacting cracks: One representing the north-south trending EPR, and the other the large, westward propagating C-N Rift, whose tip is separated from the EPR by a distance D. The model predicts symmetric cracking at the EPR north and south of the C-N Rift tip. Symmetry in the distribution of cracks north and south of the C-N Rift is observed and especially remarkable between 2.5 and 1.5 Ma when the rapid jumping of cracks toward the C-N Rift appears synchronous. The rapid jumping can be explained by decreasing D, which means that the tip of the C-N Rift was moving closer to the EPR. Symmetry of cracking breaks down at 1.5 Ma, however, with the establishment of the Dietz Deep Rift, the southern boundary of the Galapagos microplate. Symmetry of cracking also breaks down on older crust to the east between about 100 35'W and 100 45'W (about 2.6 Ma) where a rapid jumping of cracks toward the C-N Rift is observed in the south cracking region. There is no evidence of similar rapid jumping in the north cracking region. It could be simply that the response to changing the value of D is not always as predicted. It could also be that the shape of the EPR has not always been symmetric about the C-N Rift, as assumed in the model. Currently, an overlapping spreading center with a 15 km east-west offset between the limbs of the EPR has formed at 1 50'N. We assess the importance of the geometry of the EPR on the crack interaction model. The model has been modified to include a ridge offset similar to what is observed today. We find that the region of stress enhancement at the EPR (where cracks initiate) is subdued south of the C-N Rift tip because of the EPR offset. It is

  11. Crack Growth along Interfaces in Porous Ceramic Layers

    Sørensen, Bent F.; Horsewell, Andy


    Crack growth along porous ceramic layers was studied experimentally. Double cantilever beam sandwich specimens were loaded with pure bending moments to obtain stable crack growth. The experiments were conducted in an environmental scanning electron microscope enabling in situ observations...


    Wang Baolin; Han Jiecai


    This paper considers an anti-plane moving crack in a nonhomogencous material strip of finite thickness. The shear modulus and the mass density of the strip are considered for a class of functional forms for which the equilibrium equation has analytical solutions. The problem is solved by means of the singular integral equation technique. The stress field near the crack tip is obtained. The results are plotted to show the effect of the material non-homogeneity and crack moving velocity on the crack tip field. Crack bifurcation behaviour is also discussed. The paper points out that use of an appropriate fracture criterion is essential for studying the stability of a moving crack in nonhomogeneous materials. The prediction whether the unstable crack growth will be enhanced or retarded is strongly dependent on the type of the fracture criterion used. is a suitable failure criterion for moving cracks in nonhomogeneous materials.

  13. Partial discharge-induced crack growth in dielectric materials


    Partial discharge(PD) of an air-filled semi-permeable crack in a dielectric material is studied based on the streamer-type discharge mechanism to explore the effects of applied mechanical-electric fields on crack growth.Within the frame of two-dimensional deformation,the electric field inside the crack is first derived by taking the crack deformation into account.Then,the effects of electric field before PD are discussed through considering the contribution of the induced electric field inside the deformed crack space to the total energy release rate.Finally,PD and its effects on crack growth are investigated.It is found that:(1) before PD,the applied electric field always retards crack growth;(2) during PD,the applied electric field can induce crack growth in dielectric materials.

  14. Cracking the Genetic Code | NIH MedlinePlus the Magazine

    ... this page please turn Javascript on. Cracking the Genetic Code, From NIH Director Dr. Francis S. Collins Past Issues / ... moment in science in 2000: Cracking of the genetic code raised the prospect of pinpointing the root causes ...

  15. Acoustic emission assessment of interface cracking in thermal barrier coatings

    Yang, Li; Zhong, Zhi-Chun; Zhou, Yi-Chun; Zhu, Wang; Zhang, Zhi-Biao; Cai, Can-Ying; Lu, Chun-Sheng


    In this paper, acoustic emission (AE) and digital image correlation methods were applied to monitor interface cracking in thermal barrier coatings under compression. The interface failure process can be identified via its AE features, including buckling, delamination incubation and spallation. According to the Fourier transformation of AE signals, there are four different failure modes: surface vertical cracks, opening and sliding interface cracks, and substrate deformation. The characteristic frequency of AE signals from surface vertical cracks is 0.21 MHz, whilst that of the two types of interface cracks are 0.43 and 0.29 MHz, respectively. The energy released of the two types of interface cracks are 0.43 and 0.29 MHz, respectively. Based on the energy released from cracking and the AE signals, a relationship is established between the interface crack length and AE parameters, which is in good agreement with experimental results.

  16. A Parametric Study of Crack Propagation During Sonic IR Inspection

    Chen, J. C.; Kephart, J.; Riddell, W. T.


    We have developed an experiment to study the propagation of synthetic cracks under various controlled conditions during sonic IR inspection. The experiment provides for good repeatability in testing. The parameters of interest include the initial crack length, load history (stress intensity and load ratio) during crack generation, geometry of the crack, material, and also the various conditions involving the ultrasonic source. In general, we find that under typical sonic IR inspection conditions, the initial crack will propagate when subjected to sonic IR testing. The crack growth after each inspection event varies and exhibits a distribution in length of propagation. The results show that the average crack propagation decreases with increasing initial crack length and increasing stress intensity.

  17. Fatigue crack shape prediction based on vertex singularity

    Hutař P.


    Full Text Available Due to the existence of vertex singularity at the point where the crack intersects the free surface, stress distribution around the crack tip and the type of the singularity is changed. In the interior of the specimen the classical singular behaviour of the crack is dominant and can be described using analytic equations. Contrary to this, at the free surface or in the boundary layer close to free surface the vertex singularity is significant. The influence of vertex singularity on crack behaviour and a crack shape for a three-dimensional structure is described in this paper. The results presented make it possible to estimate fatigue crack growth rate and crack shape using the concept of the generalized stress intensity factor. The estimated fatigue crack shape can help to provide a more reliable estimation of the fatigue life of the structures considered.

  18. Crack Detection for Aerospace Quality Spur Gears

    Decker, Harry J.


    Health and Usage Monitoring System research and development involves analysis of the vibration signals produced by a gearbox throughout its life. There are two major advantages of knowing the actual lifetime of a gearbox component: safety and cost. In this report, a technique is proposed to help extract the critical data and present it in a manner that can be easy to understand. The key feature of the technique is to make it independent of speed, torque and prior history for localized, single tooth damage such as gear cracks. This extraction technique is demonstrated on two sets of digitized vibration data from cracked spur gears. Standard vibration diagnostic parameters are calculated and presented for comparison. Several new detection algorithms are also presented. The results of this study indicate that crack detection methods examined are not robust or repeatable. The proposed techniques provide a limited improvement to existing diagnostic parameters. Current techniques show that the cracks progressed at a much faster rate than anticipated which reduced available time for detection.

  19. Fatigue crack growth in Aluminium Alloys

    Van Kranenburg, C.


    Fatigue is a gradual process of local strength reduction. It is a phenomenon of damage accumulation at stress concentrations caused by fluctuating stresses and/or strains. In metals this results in microscopic cracks. These will start to grow under continued cyclic loading until final failure occurs

  20. Crack Propagation in Compressor Rotor Blade


    by local Public Affairs Office) 13. SUPPLEMENTARY NOTES 14. ABSTRACT Turbomachine blading crack propagation and initiations are one of...the most important problems. Design, operation and modernization of the contemporary turbomachines are impossible without a detailed numerical and...Rao, J. S., Turbine Blade Life Estimation, Narosa Publishing House, (2000). Rao, J. S., Narayan, R. and Ranjith, M. C., Lifing of Turbomachine

  1. Environmentally assisted cracking in light water reactors

    Chopra, O.K.; Chung, H.M.; Gruber, E.E. [and others


    This report summarizes work performed by Argonne National Laboratory on fatigue and environmentally assisted cracking (EAC) in light water reactors (LWRs) from April 1995 to December 1995. Topics that have been investigated include fatigue of carbon and low-alloy steel used in reactor piping and pressure vessels, EAC of Alloy 600 and 690, and irradiation-assisted stress corrosion cracking (IASCC) of Type 304 SS. Fatigue tests were conducted on ferritic steels in water that contained various concentrations of dissolved oxygen (DO) to determine whether a slow strain rate applied during different portions of a tensile-loading cycle are equally effective in decreasing fatigue life. Crack-growth-rate tests were conducted on compact-tension specimens from several heats of Alloys 600 and 690 in simulated LWR environments. Effects of fluoride-ion contamination on susceptibility to intergranular cracking of high- and commercial- purity Type 304 SS specimens from control-tensile tests at 288 degrees Centigrade. Microchemical changes in the specimens were studied by Auger electron spectroscopy and scanning electron microscopy to determine whether trace impurity elements may contribute to IASCC of these materials.

  2. Stress Corrosion Cracking of Pipeline Steels


    This paper provides a review of the differences between high pH and near-neutral pH stress corrosion cracking ofpipeline steels, influencing factors, and mechanisms. The characteristics and historical information on both forms ofSCC are discussed. The prospect for research in the future is also presented.

  3. Pregnant crack addicts in a psychiatric unit

    Gabriela de Moraes Costa


    Full Text Available OBJECTIVE: In this study we aim to characterize a sample of 85 pregnant crack addicts admitted for detoxification in a psychiatric inpatient unit. METHOD: Cross-sectional study. Sociodemographic, clinical, obstetric and lifestyle information were evaluated. RESULTS: Age of onset for crack use varied from 11 to 35 years (median = 21. Approximately 25% of the patients smoked more than 20 crack rocks in a typical day of use (median = 10; min-max = 1-100. Tobacco (89.4%, alcohol (63.5% and marijuana (51.8% were the drugs other than crack most currently used. Robbery was reported by 32 patients (41.2%, imprisonment experience by 21 (24.7%, trade of sex for money/drugs by 38 (44.7%, home desertion by 33 (38.8%; 15.3% were positive for HIV, 5.9% for HCV, 1.2% for HBV and 8.2% for syphilis. After discharge from the psychiatric unit, only 25% of the sample followed the proposed treatment in the chemical dependency outpatient service. CONCLUSION: Greater risky behaviors for STD, as well as high rates of maternal HIV and Syphilis were found. Moreover, the high rates of concurrent use of other drugs and involvement in illegal activities contribute to show their chaotic lifestyles. Prevention and intervention programs need to be developed to address the multifactorial nature of this problem.


    Yang Shanglei; Lu Xueqin; Lou Songnian; Zou Zengda


    A new surfacing electrode is developed with cracking resistance and wearability based on high microhardness of TiC and VC, carbides of Ti and V are formed in deposited metal by means of high temperature arc metallurgic reaction. The results show the hardness of surfacing metal increases with the increase of ferrotitanium (Fe-Ti), ferrovanadium (Fe-V) and graphite in the coat. However,when graphite reaches the volume fraction of 11%, the hardness reaches its peak value, and when beyond 11%, the hardness falls off. As Fe-Ti, Fe-V and graphite increase, the cracking resistance of deposited metal and usability of electrode declines. Carbides are dispersedly distributed in the matrix structure. The matrix microstructure of deposited metal is lath martensite. Carbides present irregular block. When using the researched surfacing electrode to continue weld with non-preheated, no seeable crack or only a few micro-cracks can be observed in the surface of deposited metal. The hardness is above 60 HRC. The wear resistance is better than that of EDZCr-C-15.

  5. The Lead Crack Fatigue Lifting Framework


    fracture properties of high strength aluminium and titanium alloys. ____________________ ________________________________________________ Russel...and the fatigue crack growth properties of high strength aluminium and titanium alloys. Russell and Simon have also collaborated on a chapter on...forms of machining damage (scratches, grooves, burrs, small tears and nicks); etch pits from surface treatments ( pickling , anodising); porosity

  6. 3D characterisation of RCF crack networks

    Ahlström Johan


    Full Text Available Rolling contact fatigue (RCF damage is becoming more frequent with increased traffic and loading conditions in the railway industry. Defects which are characterized by a two-lobe darkened surface and a V-shaped surface-breaking crack are often so-called squats. The origination and propagation of squats in railway rails is the topic of many recent studies; the associated crack networks develop with complicated geometry near the surface of rails that is difficult to characterise using most non-destructive methods. The cracks can be examined with repeated metallographic sectioning, but the process is time-consuming and destructive. In order to reduce time, as well as information and material loss, high-resolution and high-energy X-ray imaging of railway rails was done in the current study. Combining the exposures from a range of angles using image analysis, a 3D representation of the complex crack network is achieved. The latter was complemented with metallographic sectioning to determine the accuracy of prediction of the geometrical reconstruction.

  7. Repairing Hidden Cracks in Coolant Tubes

    Mills, R. C., Sr.; Duesberg, J.


    Repair technique closes leaks in tubes or conduits where access limited to wall opposite crack. Technique applicable to any tubular assembly where tubes bundled together or bonded to supporting shell, such as in heat exchangers. Procedure provides structural support to area failed and uninterrupted flow without significantly altering heat-transfer profile.

  8. Instantaneous crack detection using dual PZT transducers

    Kim, Seung Bum; Sohn, Hoon


    A new guided wave based nondestructive testing (NDT) technique is developed to detect crack damage in metallic plates commonly used in aircraft without using prior baseline data or a predetermined decision boundary. In conventional guided wave based techniques, damage is often identified by comparing the "current" data obtained from a potentially damaged condition of a structure with the "past" baseline data collected at the pristine condition of the structure. However, it has been reported that this type of pattern comparison with the baseline data can lead to increased false alarms due to its susceptibility to varying operational and environmental conditions of the structure. In order to tackle this issue, a reference-free damage detection technique is previously developed using two pairs of collocated lead zirconate titanate transducers (PZTs) placed on both sides of a plate. In this study, this reference-free technique is further advanced so that the PZT transducers can be placed only on one side of the specimen. Crack formation creates Lamb wave mode conversion due to a sudden change in the thickness of the structure. Then, the proposed technique instantly detects the appearance of the crack by extracting this mode conversion from the measured Lamb waves. This study suggests a reference-free statistical approach that enables damage classification using only the current data set. Numerical and experimental results are presented to demonstrate the applicability of the proposed technique to instantaneous crack detection.

  9. Durability of cracked fibre reinforced concrete structures

    Hansen, Ernst Jan De Place; Nielsen, Laila


    (capillary water uptake) is used, involving an in-situ method and a laboratory method. Three different concrete qualities as well as steel fibres (ZP) and polypropylene fibres (PP) are used. Results of the durability tests on cracked FRC-beams are compared to results for uncracked FRC-beams and beams without...

  10. 46 CFR 59.10-5 - Cracks.


    ... does not exceed 12 inches in length and after completion the weld is stress-relieved. Cracks in... the root of the weld shall be chipped or ground out to insure a clean surface of the originally... CFR 59.01-2). For thicknesses exceeding three-fourths inch, suitable U grooves should be employed....

  11. Fluid catalytic cracking : feedstocks and reaction mechanism

    Dupain, X.


    The Fluid Catalytic Cracking (FCC) process is one of the key units in a modern refinery. Traditionally, its design is primarily aimed for the production of gasoline from heavy oil fractions, but as co-products also diesel blends and valuable gasses (e.g. propene and butenes) are formed in

  12. Arc termination cracks in Inconel 718 and Incoloy 903

    Bayless, E.; Mccaig, J.; Poorman, R.


    The welding of the nickel base, heat resistant alloys that are used extensively for welded Shuttle engine components revealed solidification cracking characteristics at weld termination points. If not detected and removed, these crater cracks may cause costly component failure. To better understand this characteristic, welding termination techniques were studied and methods developed to eliminate crater cracks. It was determined that weld termination solidification cracking can be eliminated by controlled decrease of welding current, welding voltage, wire feed, and travel speed.

  13. Analysis of Multiple Cracks in an Infinite Functionally Graded Plate

    Shbeeb, N. I.; Binienda, W. K.; Kreider, K. L.


    A general methodology was constructed to develop the fundamental solution for a crack embedded in an infinite non-homogeneous material in which the shear modulus varies exponentially with the y coordinate. The fundamental solution was used to generate a solution to fully interactive multiple crack problems for stress intensity factors and strain energy release rates. Parametric studies were conducted for two crack configurations. The model displayed sensitivity to crack distance, relative angular orientation, and to the coefficient of nonhomogeneity.

  14. Onset of Propagation of Planar Cracks in Heterogeneous Media

    Ramanathan, Sharad; Fisher, Daniel S.


    The dynamics of planar crack fronts in hetergeneous media near the critical load for onset of crack motion are investigated both analytically and by numerical simulations. Elasticity of the solid leads to long range stress transfer along the crack front which is non-monotonic in time due to the elastic waves in the medium. In the quasistatic limit with instantaneous stress transfer, the crack front exhibits dynamic critical phenomenon, with a second order like transition from a pinned to a mo...

  15. Effect of segregations on mechanical properties and crack propagation in spring steel

    B. Žužek


    Full Text Available Considerable efforts have been made over the last decades to improve performance of spring steels, which would increase the service time of springs and also allow vehicles weight reduction. There are different possibilities of improving properties of spring steels, from modifying the chemical composition of steels to optimizing the deformation process and changing the heat treatment parameters. Another way of improving steel properties is through refining the microstructure and reducing amount of inclusions. Therefore, the focus of the current investigation was to determine the effect of more uniform and cleaner microstructure obtained through electro-slag remelting (ESR of steel on the mechanical and dynamic properties of spring steel, with special focus on the resistance to fatigue crack propagation. Effect of the microstructure refinement was evaluated in terms of tensile strength, elongation, fracture and impact toughness, and fatigue resistance under bending and tensile loading. After the mechanical tests the fracture surfaces of samples were analyzed using scanning electron microscope (SEM and the influence of microstructure properties on the crack propagation and crack propagation resistance was studied. Investigation was performed on hot rolled, soft annealed and vacuum heat treated 51CrV4 spring steel produced by conventional continuous casting and compared with steel additional refined through ESR. Results shows that elimination of segregations and microstructure refinement using additional ESR process gives some improvement in terms of better repeatability and reduced scattering, but on the other hand it has negative effect on crack propagation resistance and fatigue properties of the spring steel.

  16. Fatigue crack detection on structural steel members by using ultrasound excited thermography

    Plum, Robin Marc


    In the field of non-destructive testing (NDT), ultrasound excited thermography has been recognised as a promising technique that was successfully applied to metals, fibre composites and many more engineering materials in order to detect cracks, delaminations and other types of internal flaws. Dating back to the late 1970s, the idea of high-frequency vibration excitation of structural members combined with monitoring the surface temperature by means of infrared thermography aims at the localised energy dissipation at defect regions and its thermal detection. The purpose of this thesis is to investigate the potential use of ultrasound excited thermography for detecting surface breaking fatigue cracks in thick-walled components relevant to steel construction. The presented research is motivated by a lack of fast and imaging crack detection methods in the field and the growing acceptance and technological progress of active thermography techniques. After introducing the concept of ultrasound excited thermography or vibrothermography, its current state of the art is described by means of a comprehensive literature review focusing on research activities towards crack detection on metals. Owing to the interdisciplinarity of the test method, all relevant technical subdisciplines from the excitation of plate vibrations via potential heat generation mechanisms and heat transfer to infrared thermography are outlined. The experimental work starts with the manufacture and fatigue loading of suitable plate specimens made from low-carbon steel S355, mostly in the high cycle fatigue regime, to generate throughthickness cracks with specified depths. Using a modified high-power ultrasonic welding generator, basic dependencies of the defect heating on frequency, coupling location and excitation duration are clarified at first. Besides of an estimation of realistic detection limits depending on the plate thickness, main issues such as the relation between vibration intensity and

  17. The Mechanism of kIH in Delayed Hydride Cracking of Zr-2.5wt% Nb at 150 ℃



    This work studies the KIH mechanism of delayed hydride cracking (DHC) in Zr-2.5wt% Nb alloys. A modified experimental method was developed, in which specimens are fatigued between consecutive experiments, and a constant load instead of a decreasing load is used in each experiment. The hydride clusters formed and fractured at the crack tip during different experiments are thus separated and studied individually. A new R-curve phenomenon that characterizes the resistance to DHC was observed. KIH is thus more rigorously defined. Based on the measurement of the critical hydride cluster length at different K1, the threshold phenomenon of KIH is explained.

  18. CRACK2. Modelling calcium carbonate deposition from bicarbonate solutions in cracks in concrete

    Brodersen, Knud Erik


    The numerical CRACK2 model simulates precipitation of calcite from calcium bicarbonate solution (e.g. groundwater) passing through cracks in concrete or other cementitious materials. A summary of experimental work is followed by a detailed description ofthe model. Hydroxyl ions are transported...... by diffusion in pore systems in columns of cementitious materials. The hydroxyl is precipitating calcite from a flow of bicarbonate solution in a crack connecting the ends of a row of such columns. Thecementitious material is simulated as calcium hydroxide mixed with inert material but with sodium hydroxide...... dissolved in the pore solution. Diffusive migration of cesium as radioactive isotope is also considered. Electrical interaction of the migratingions is taken into account. Example calculations demonstrate effects of parameter variations on distribution of precipitated calcite in the crack...

  19. Seismic stability analysis of concrete gravity dams with penetrated cracks

    Shou-yan JIANG


    Full Text Available The seismic stability of a cracked dam was examined in this study. Geometric nonlinearity and large deformations, as well as the contact condition at the crack site, were taken into consideration. The location of penetrated cracks was first identified using the concrete plastic-damage model based on the nonlinear finite element method (FEM. Then, the hard contact algorithm was used to simulate the crack interaction in the normal direction, and the Coloumb friction model was used to simulate the crack interaction in the tangential direction. After verification of numerical models through a case study, the seismic stability of the Koyna Dam with two types of penetrated cracks is discussed in detail with different seismic peak accelerations, and the collapse processes of the cracked dam are also presented. The results show that the stability of the dam with two types of penetrated cracks can be ensured in an earthquake with a magnitude of the original Koyna earthquake, and the cracked dam has a large earthquake-resistant margin. The failure processes of the cracked dam in strong earthquakes can be divided into two stages: the sliding stage and the overturning stage. The sliding stage ends near the peak acceleration, and the top block slides a long distance along the crack before the collapse occurs. The maximum sliding displacement of the top block will decrease with an increasing friction coefficient at the crack site.

  20. Optimisation of the Crack Pattern in Continuously Reinforced Concrete Pavements

    Ren, D.


    Recent field investigations on several new Continuously Reinforced Concrete Pavements (CRCP) in Belgium indicate that its crack pattern is characterized by low mean crack spacing along with a high percentage of clusters of closely spaced cracks. Field surveys also indicate that it is difficult to si

  1. Optimisation of the Crack Pattern in Continuously Reinforced Concrete Pavements

    Ren, D.


    Recent field investigations on several new Continuously Reinforced Concrete Pavements (CRCP) in Belgium indicate that its crack pattern is characterized by low mean crack spacing along with a high percentage of clusters of closely spaced cracks. Field surveys also indicate that it is difficult to si

  2. Burst pressure predictions of pipelines with longitudinal cracks

    Dotta, Fernando; Riggieri, Claudio [Sao Paulo Univ., SP (Brazil). Dept. de Engenharia Naval e Oceanica


    This study extends a micro mechanics approach based upon the computational cell methodology to model ductile crack extension of longitudinal crack-like defects in a high strength pipeline steel. Laboratory testing of an API 5L X60 steel at room temperature using standard, deep crack C(T) specimens provides the data needed to measure the crack growth resistance curve for the material. In the computational cell model, ductile crack extension occurs through void growth and coalescence (by cell extinction) within a thin layer of material ahead of crack tip. A simple scheme to calibrate material-specific parameters for the cells is also described. A central focus of the paper is the application of the cell methodology to predict experimentally measured burst pressures for pre-cracked pipe specimens with different crack sizes. The experimental program includes longitudinally pre cracked 20'' (508 mm) O.D. pipe specimens with 15.8 mm thickness and varying crack geometries. Plane-strain computations are conducted on detailed finite element models for the pipe specimens to describe crack extension with increased pressure. The numerical simulations demonstrate the effectiveness of the cell approach to describe crack growth response and to predict the burst pressure for the tested pipes. (author)

  3. A cohesive segments method for the simulation of crack growth

    Remmers, J.J.C.; De Borst, R.; Needleman, A.


    A numerical method for crack growth is described in which the crack is not regarded as a single discontinuity that propagates continuously. Instead, the crack is represented by a set of overlapping cohesive segments. These cohesive segments are inserted into finite elements as discontinuities in the

  4. Finite elements simulation of reflective cracking in asphaltic overlays

    Scarpas, A.; De Bondt, A.H.


    Overlaying is one of the most popular and cost effective techniques of rehabilitation of cracked pavements. The placing of reinforcement between the overlay and the top layer of the cracked pavement is currently being utilised as a possible technique for delaying the development of cracks into the o

  5. Evolving fracture patterns: columnar joints, mud cracks, and polygonal terrain

    Goehring, Lucas


    When cracks form in a thin contracting layer, they sequentially break the layer into smaller and smaller pieces. A rectilinear crack pattern encodes information about the order of crack formation, as later cracks tend to intersect with earlier cracks at right angles. In a hexagonal pattern, in contrast, the angles between all cracks at a vertex are near 120$^\\circ$. However, hexagonal crack patterns are typically only seen when a crack network opens and heals repeatedly, in a thin layer, or advances by many intermittent steps into a thick layer. Here it is shown how both types of pattern can arise from identical forces, and how a rectilinear crack pattern evolves towards a hexagonal one. Such an evolution is expected when cracks undergo many opening cycles, where the cracks in any cycle are guided by the positions of cracks in the previous cycle, but when they can slightly vary their position, and order of opening. The general features of this evolution are outlined, and compared to a review of the specific p...

  6. Fretting fatigue crack propagation rate under variable loading conditions

    C. Gandiolle


    Full Text Available Fretting fatigue experiments aim to represent industrial problems and most of them endure variable loading. Being able to assess lifetime of assemblies, especially for low propagation rate conditions, is essential as experimental validation is often too expensive. Both experimental and numerical approaches are proposed to follow the crack propagation rate of steel on steel cylinder/plane fretting fatigue contact submitted to variable loading conditions. An original experimental monitoring has been implemented on the fretting-fatigue test device to observe crack propagation using a potential drop technique. A calibration curve relating crack length and electrical potential was established for the studied contact. It allows direct knowledge of the crack length and crack propagation rate. It was applied to mixed load test showing crack arrest for the last loading condition. To explain this behavior, a 2-dimensional FE modeling was implemented to simulate the complexes multi-axial contact stressing. The crack propagation rate was formalized using an effective stress intensity factor amplitude ΔKeff coupled with Paris law of the material. The crack arrest condition for a given loading was related to ΔKeff along the expected crack path crossing the material crack arrest threshold ΔK0. The failure was related to ΔKeff reaching the critical stress intensity factor KIC. A good correlation with experiments was observed allowing to predict the crack arrest condition although the model tends to overestimate the final crack length extension.

  7. Crack path in aeronautical titanium alloy under ultrasonic torsion loading

    A. Nikitin


    Full Text Available This paper discusses features of fatigue crack initiation and growth in aeronautical VT3-1 titanium alloy under pure torsion loading in gigacycle regime. Two materials: extruded and forged VT3-1 titanium alloys were studied. Torsion fatigue tests were performed up to fatigue life of 109 cycles. The results of the torsion tests were compared with previously obtained results under fully reversed axial loading on the same alloys. It has been shown that independently on production process as surface as well subsurface crack initiation may appear under ultrasonic torsion loading despite the maximum stress amplitude located at the specimen surface. In the case of surface crack initiation, a scenario of crack initiation and growth is similar to HCF regime except an additional possibility for internal crack branching. In the case of subsurface crack, the initiation site is located below the specimen surface (about 200 μm and is not clearly related to any material flaw. Internal crack initiation is produced by shear stress in maximum shear plane and early crack growth is in Mode II. Crack branching is limited in the case of internal crack initiation compared to surface one. A typical ‘fish-eye’ crack can be observed at the torsion fracture surface, but mechanism of crack initiation seems not to be the same than under axial fatigue loading.

  8. Research on pavement crack recognition methods based on image processing

    Cai, Yingchun; Zhang, Yamin


    In order to overview and analysis briefly pavement crack recognition methods , then find the current existing problems in pavement crack image processing, the popular methods of crack image processing such as neural network method, morphology method, fuzzy logic method and traditional image processing .etc. are discussed, and some effective solutions to those problems are presented.

  9. Optimisation of the Crack Pattern in Continuously Reinforced Concrete Pavements

    Ren, D.


    Recent field investigations on several new Continuously Reinforced Concrete Pavements (CRCP) in Belgium indicate that its crack pattern is characterized by low mean crack spacing along with a high percentage of clusters of closely spaced cracks. Field surveys also indicate that it is difficult to

  10. Characterisation of Fatigue Crack Growth in Silicone for Deap Technology

    Thorup, Thor


    In this paper, the fatigue crack growth characteristics of Elastosil R RT 625 are determined by performing fatigue crack experiments based on ISO 27727. Elastosil R RT 625 is a silicone rubber used by Danfoss PolyPower A/S as the dielectric material in their DEAP elements. Cracks were characteris...

  11. Catalytic oxidative cracking of hexane as a route to olefins

    Boyadjian, C.A.; Lefferts, Leonardus; Seshan, Kulathuiyer


    Catalytic oxidative cracking of naphtha is conceptually an alternative process to steam cracking. The performance of sol–gel synthesized Li/MgO in oxidative cracking of hexane as a model compound of naphtha, has been studied and compared to that of conventionally prepared catalyst. At a temperature

  12. The effect of fatigue cracks on fastener flexibility, load distribution, and fatigue crack growth

    Whitman, Zachary Layne

    Fatigue cracks typically occur at stress risers such as geometry changes and holes. This type of failure has serious safety and economic repercussions affecting structures such as aircraft. The need to prevent catastrophic failure due to fatigue cracks and other discontinuities has led to durability and damage tolerant methodologies influencing the design of aircraft structures. Holes in a plate or sheet filled with a fastener are common fatigue critical locations in aircraft structure requiring damage tolerance analysis (DTA). Often, the fastener is transferring load which leads to a loading condition involving both far-field stresses such as tension and bending, and localized bearing at the hole. The difference between the bearing stress and the tensile field at the hole is known as load transfer. The ratio of load transfer as well as the magnitude of the stresses plays a significant part in how quickly a crack will progress to failure. Unfortunately, the determination of load transfer in a complex joint is far from trivial. Many methods exist in the open literature regarding the analysis of splices, doublers and attachment joints to determine individual fastener loads. These methods work well for static analyses but greater refinement is needed for crack growth analysis. The first fastener in a splice or joint is typically the most critical but different fastener flexibility equations will all give different results. The constraint of the fastener head and shop end, along with the type of fastener, affects the stiffness or flexibility of the fastener. This in turn will determine the load that the fastener will transfer within a given fastener pattern. However, current methods do not account for the change in flexibility at a fastener as the crack develops. It is put forth that a crack does indeed reduce the stiffness of a fastener by changing its constraint, thus lessening the load transfer. A crack growth analysis utilizing reduced load transfer will result in

  13. Application of the cracked pipe element to creep crack growth prediction

    Brochard, J.; Charras, T.


    The modification of a computer code for leak before break analysis is very briefly described. The CASTEM2000 code was developed for ductile fracture assessment of piping systems with postulated circumferential through-wall cracks under static or dynamic loading. The modification extends the capabilities of the cracked pipe element to the determination of fracture parameters under creep conditions (C*, {phi}c and {Delta}c). The model has the advantage of evaluating significant secondary effects, such as those from thermal loading.

  14. Fatigue Crack Growth on Double Butt Weld with Toe Crack of Pipelines Steel

    HADJOUI, Féthi; Benachour, Mustapha; Benguediab,Mohamed


    The welded structures have a broad applicability (car industry, aeronautical, marine, pipelines, etc.). The welding being an assembled process, presents both advantages and disadvantages. A simple existing defect after welding can generate a catastrophic fracture. This work studies the fatigue crack growth of double butt weld with toe crack. Two types of pipeline material are studied with knowing API 5L grades X60 and X70 where tension form of loading is applied. In order to p...

  15. Comportamiento violento entre consumidores de crack

    Nadja Cristiane Lappann Botti


    Full Text Available Considerando a relevância do uso abusivo de crack na atualidade brasileira e sua relação com a violência, este estudo propõe-se a analisar a associação entre comportamento violento -delitivo, auto e hetero agressivo- entre os usuários de crack e variáveis sociodemográficas e de uso de drogas. Realizado estudo quantitativo, transversal, com amostra de conveniência, com 72 homens usuários de crack em tratamento nas Comunidades Terapêuticas de seis cidades da região Oeste do Estado de Minas Gerais (Brasil. Os dados foram analisados estatisticamente no Statistical Package for the Social Sciences Versão 17.0, utilizando-se teste qui-quadrado para verificação de diferenças estatisticamente significantes. Os resultados apontam associação do tráfico com número de pedras consumidas e de tratamentos realizados; de prisão ou detenção com baixa escolaridade, ser solteiro e idade de início do uso de droga ilícita; de tentativa de suicídio com o tempo máximo de abstinência e de heteroagressão com idade de início do uso de droga ilícita e frequência diária do uso de crack. O uso de crack pode contribuir para o desenvolvimento de comportamento violento -delitivo, auto e heteroagressivo.

  16. Differential potential noise measurement during crack initiation

    Hettiarachchi, S. [GE-Hitachi Nuclear Energy, Vallecitos Nuclear Center, Sunol, California (United States)]. E-mail:


    Electrochemical potential and current noise have been used over the past two decades as methods of detecting general corrosion, pitting corrosion, crevice corrosion, stress corrosion, corrosion in concrete and corrosion under coatings. The methods involved the use of self-generated potential noise/current noise or both, of the material of choice in a given environment. In a variety of these studies, data processing involved techniques such as fast fourier transforms (FFT) to generate the power spectrum that provided the unique signature associated with the type of the corrosion process. This paper deals with a more simplistic method of monitoring differential potential noise measured between two identical slow strain rate test (SSRT) specimens placed close to each other, in a high temperature aqueous environment, while one is being subjected to dynamic strain and the other maintained under static conditions. The differential potential noise (DPN) was monitored as the applied load increased on the slow strain rate test specimen. Unlike self-generated noise, differential potential noise is less affected by electrical noise in the surroundings, and is able to signal the point of oxide film cracking or crack initiation more conveniently without extensive data processing. This method also allows the in-situ detection of crack initiation without interruption of the SSRT test. The DPN signal at the crack initiation stage is different from the signals acquired as cracking progressed due to continuing dynamic strain. Furthermore, the nature of the DPN signal response depends on the type of material used in this study, Type 304 stainless steel or Inconel 182. (author)

  17. Estimating crack growth in temperature damaged concrete

    Recalde, Juan Jose


    Evaluation of the structural condition of deteriorated concrete infrastructure and evaluation of new sustainable cementitious materials require an understanding of how the material will respond to applied loads and environmental exposures. A fundamental understanding of how microstructural changes in these materials relate to changes in mechanical properties and changes in fluid penetrability is needed. The ability to provide rapid, inexpensive assessment of material characteristics and relevant engineering properties is valuable for decision making and asset management purposes. In this investigation, the effects of changes in dynamic elastic properties with water content and fluid penetrability properties before and after a 300°C exposure were investigated based on estimates of the crack density parameter from dry and saturated cracked media. The experimental and analytical techniques described in this dissertation allow calculation of a value for the crack density parameter using nondestructive determination of wet and dry dynamic shear modulus of relatively thin disks. The techniques were used to compare a conventional concrete mixture to several mixtures with enhanced sustainability characteristics. The three enhanced sustainable materials investigated were a very high fly ash mixture, a magnesium phosphate cement based mortar, and a magnesium phosphate cement based concrete, and were compared to a conventional concrete mixture. The analysis provided both quantitative assessment of changes with high temperature damage and autogenous healing, and estimates of changes in mean crack trace lengths. The results showed that water interaction, deterioration due to damage, and autogenous healing recovery were different for the magnesium phosphate cement based mixtures than the portland cement based concrete mixtures. A strong correlation was found between log-transformed Air Permeability Index, dynamic shear modulus, and crack density parameter. The findings imply

  18. Microstructural mechanisms of cyclic deformation, fatigue crack initiation and early crack growth.

    Mughrabi, Haël


    In this survey, the origin of fatigue crack initiation and damage evolution in different metallic materials is discussed with emphasis on the responsible microstructural mechanisms. After a historical introduction, the stages of cyclic deformation which precede the onset of fatigue damage are reviewed. Different types of cyclic slip irreversibilities in the bulk that eventually lead to the initiation of fatigue cracks are discussed. Examples of trans- and intercrystalline fatigue damage evolution in the low cycle, high cycle and ultrahigh cycle fatigue regimes in mono- and polycrystalline face-centred cubic and body-centred cubic metals and alloys and in different engineering materials are presented, and some microstructural models of fatigue crack initiation and early crack growth are discussed. The basic difficulties in defining the transition from the initiation to the growth of fatigue cracks are emphasized. In ultrahigh cycle fatigue at very low loading amplitudes, the initiation of fatigue cracks generally occupies a major fraction of fatigue life and is hence life controlling.

  19. CRACK2 - Modelling calcium carbonate deposition from bicarbonate solution in cracks in concrete

    Brodersen, K


    The numerical CRACK2 model simulates precipitation of calcite from calcium bicarbonate solution (e.g. groundwater) passing through cracks in concrete or other cementitious materials. A summary of experimental work is followed by a detailed description of the model. Hydroxyl ions are transported by diffusion in pore systems in columns of cementitious materials. The hydroxyl is precipitating calcite from a flow of bicarbonate solution in a crack connecting the ends of a row of such columns. The cementitious material is simulated as calcium hydroxide mixed with inert material but with sodium hydroxide dissolved in the pore solution. Diffusive migration of cesium as radioactive isotope is also considered. Electrical interaction of the migrating ions is taken into account. Example calculations demonstrate effects of parameter variations on distribution of precipitated calcite in the crack and on the composition of the outflowing solution, which can be compared directly with experimental results. Leaching behavior of sodium can be used to tune the model to experimental observations. The calcite is mostly precipitated on top of the original crack surface and may under certain circumstances fill the crack. The produced thin layers of low porosity calcite act as a diffusion barrier limiting contact between cement and solution. Pore closure mechanisms in such layers are discussed. Implications for safety assessment of radioactive waste disposal are shortly mentioned. The model is also relevant for conventional uses of concrete. (au)

  20. 呼吸性椭圆裂纹转子弯曲刚度模型%Bending stiffness model of a breathing elliptical cracked rotor

    刘政; 王建军


    Usually a fatigue crack on a rotor shaft has an elliptical tip,while the current literatures at home and abroad mostly focus on straight-tip crack rotors,very few articles built models to study elliptical-tip crack breathing behavior.Here,a new breathing model of an elliptical crack on a cylindrical shaft was proposed to modify the neutral axis's position and determine crack open area.Based on the crack strain energy,the elliptical crack's additional flexibility coefficient was calculated,and the bending stiffness model of the elliptical cracked rotor was also established.It was shown that the proposed crack's breathing laws agree well with those of literatures and the finite element results,the crack's additional flexibility and rotor's dimensionless deflection both meet the requirements of computing,the effectiveness and feasibility of the model are validated.%通常转子轴上的疲劳裂纹为椭圆形尖端,而国内外现有文献大多关注直裂纹转子,很少对椭圆裂纹呼吸行为建立模型。提出了新的圆柱轴椭圆裂纹呼吸模型,修正中性轴位置确定裂纹张开面积,并基于裂纹应变能计算出椭圆裂纹附加柔性系数,建立了该类裂纹转子弯曲刚度模型。进一步,与文献和有限元结果进行对比,裂纹呼吸规律完全符合,裂纹附加柔度、转子无量纲挠度满足计算要求,验证了该模型有效可行。

  1. Modeling Delamination of Interfacial Corner Cracks in Multilayered Structures

    Veluri, Badrinath (Badri); Jensen, Henrik Myhre


    for steady-state propagation has been developed. The crack propagation is investigated by estimating the fracture mechanics parameters that include the strain energy release rate, crack front profiles and the three-dimensional mode-mixity along the crack front. The developed numerical approach...... for the calculation of fracture mechanical properties has been validated with threedimensional models for varying crack front shapes. A custom quantitative approach was formulated based on the finite element method with iterative adjustment of the crack front to estimate the critical delaminatio stress as a function...

  2. Cracking phenomena in lithium-di-silicate glass ceramics

    Rajat Banerjee


    Lithium-di-silicate glass ceramic (Li2O, SiO2) with uniformly oriented crystals was placed on a Vickers indentation with extrusion axis horizontally parallel to the base axis. The material was rotated through 0°– 90° and at each angle a 20 N load was applied to ascertain the crack path. It was observed that the crack length decreases and the crack deviates from its original path with increasing angle. The deviation of the crack was correlated with the component of the crack driving force and the theoretical strength of the aligned crystals at different angles.

  3. Modified Ureterosigmoidostomy


    Objective To introduce an operation procedure and evaluate the coutinence diversion results of the modified ureterosigmoidostomy after radical cystectomy. Methods Fourteen cases of bladder cancer or prostate carcinoma were operated on with modified Sigma pouch from Feb, 1998 to Dec, 1999. A longitudinal incision about 25 cm on the sigmoid uall was done to form a low pressure pouch. The vertex of the new pouch was fixed to sacrum. Both ends of ureters were anastomosed side to side and to form a big nipple and inserted into the top of pouch for 2 to 3 centimeters. Results It took about sixty five minutes to create a new low pressure pouch after radical cystectomy. Early complication of was found in two cases postoperatively, and cured with temporary colonostomy. Hydronephrosis and hypokalemia in one patient were cured by percutaneous anterograde ureter dilatation with balloon and oral replacement of potassium salt. All patients displayed urinary continence. No symptomatic renal infection or hypercholoraemic acidosis occurred. Conclusion Modified ureterosigmoidostomy is a safe procedure of urinary diversion and provides a big volume, low intravesical pressure pouch. The patients are free from the troublesome urine-bag, intermittert catheterization , and upper urinary tracts are protected effectively. The quality of life is satisfied.

  4. Simulation model of fatigue crack opening/closing phenomena for predicting RPG load under arbitrary stress distribution field

    Toyosada, M.; Niwa, T. [Kyushu Univ., Fukuoka (Japan)


    In this paper, Newman`s calculation model is modified to solve his neglected effect of the change of stress distribution ahead of a crack, and to leave elastic plastic materials along the crack surface because of the compatibility of Dugdale model. In addition to above treatment, the authors introduce plastic shrinkage at an immediate generation of new crack surfaces due to emancipation of internal force with the magnitude of yield stress level during unloading process in the model. Moreover, the model is expanded to arbitrary stress distribution field. By using the model, RPG load is simulated for a center notched specimen under constant amplitude loading with various stress ratios and decreased maximum load while keeping minimum load.

  5. Declining rates of health problems associated with crack smoking during the expansion of crack pipe distribution in Vancouver, Canada.

    Prangnell, Amy; Dong, Huiru; Daly, Patricia; Milloy, M J; Kerr, Thomas; Hayashi, Kanna


    Crack cocaine smoking is associated with an array of negative health consequences, including cuts and burns from unsafe pipes, and infectious diseases such as HIV. Despite the well-established and researched harm reduction programs for injection drug users, little is known regarding the potential for harm reduction programs targeting crack smoking to reduce health problems from crack smoking. In the wake of recent crack pipe distribution services expansion, we utilized data from long running cohort studies to estimate the impact of crack pipe distribution services on the rates of health problems associated with crack smoking in Vancouver, Canada. Data were derived from two prospective cohort studies of community-recruited people who inject drugs in Vancouver between December 2005 and November 2014. We employed multivariable generalized estimating equations to examine the relationship between crack pipe acquisition sources and self-reported health problems associated with crack smoking (e.g., cut fingers/sores, coughing blood) among people reported smoking crack. Among 1718 eligible participants, proportions of those obtaining crack pipes only through health service points have significantly increased from 7.2% in 2005 to 62.3% in 2014 (p pipes only through other sources (e.g., on the street, self-made), those acquiring pipes through health service points only were significantly less likely to report health problems from smoking crack (adjusted odds ratio: 0.82; 95% confidence interval: 0.73-0.93). These findings suggest that the expansion of crack pipe distribution services has likely served to reduce health problems from smoking crack in this setting. They provide evidence supporting crack pipe distribution programs as a harm reduction service for crack smokers.

  6. A dynamic model of a cantilever beam with a closed, embedded horizontal crack including local flexibilities at crack tips

    Liu, J.; Zhu, W. D.; Charalambides, P. G.; Shao, Y. M.; Xu, Y. F.; Fang, X. M.


    As one of major failure modes of mechanical structures subjected to periodic loads, embedded cracks due to fatigue can cause catastrophic failure of machineries. Understanding the dynamic characteristics of a structure with an embedded crack is helpful for early crack detection and diagnosis. In this work, a new three-segment beam model with local flexibilities at crack tips is developed to investigate the vibration of a cantilever beam with a closed, fully embedded horizontal crack, which is assumed to be not located at its clamped or free end or distributed near its top or bottom side. The three-segment beam model is assumed to be a linear elastic system, and it does not account for the nonlinear crack closure effect; the top and bottom segments always stay in contact at their interface during the beam vibration. It can model the effects of local deformations in the vicinity of the crack tips, which cannot be captured by previous methods in the literature. The middle segment of the beam containing the crack is modeled by a mechanically consistent, reduced bending moment. Each beam segment is assumed to be an Euler-Bernoulli beam, and the compliances at the crack tips are analytically determined using a J-integral approach and verified using commercial finite element software. Using compatibility conditions at the crack tips and the transfer matrix method, the nature frequencies and mode shapes of the cracked cantilever beam are obtained. The three-segment beam model is used to investigate the effects of local flexibilities at crack tips on the first three natural frequencies and mode shapes of the cracked cantilever beam. A stationary wavelet transform (SWT) method is used to process the mode shapes of the cracked cantilever beam; jumps in single-level SWT decomposition detail coefficients can be used to identify the length and location of an embedded horizontal crack.


    ZhongWeffang; WuYongdong; WuGuorong; LiangYide


    The acoustical scattering by a cracked elastic structure is studied. The mixed method of boundary element and fractal finite element is adopted to solve the cracked structure-acoustic coupling problem. The fractal two-level finite element method is employed for the cracked structure, which can reduce the degree of freedoms (DOFs) greatly, and the boundary element method is used for the exterior acoustic field which can automatically satisfy Sommerfeld's radiation condition. Numerical examples show that the resonance frequency is lower with the crack's depth increase, and that the effect on the acoustical field by the crack is particularly pronounced in the vicinity of the crack tip. This mixed method of boundary element and finite element is effective in solving the scattering problem by a cracked structure.

  8. Cracks Detection Using Active Modal Damping and Piezoelectric Components

    B. Chomette


    Full Text Available The dynamics of a system and its safety can be considerably affected by the presence of cracks. Health monitoring strategies attract so a great deal of interest from industry. Cracks detection methods based on modal parameters variation are particularly efficient in the case of large cracks but are difficult to implement in the case of small cracks due to measurement difficulties in the case of small parameters variation. Therefore the present study proposes a new method to detect small cracks based on active modal damping and piezoelectric components. This method uses the active damping variation identificated with the Rational Fraction Polynomial algorithm as an indicator of cracks detection. The efficiency of the proposed method is demonstrated through numerical simulations corresponding to different crack depth and locations in the case of a finite element model of a clamped-clamped beam including four piezoelectric transducers.

  9. Elasticity-Driven Backflow of Fluid-Driven Cracks

    Lai, Ching-Yao; Zheng, Zhong; Dressaire, Emilie; Ramon, Guy; Huppert, Herbert E.; Stone, Howard A.


    Fluid-driven cracks are generated by the injection of pressurized fluid into an elastic medium. Once the injection pressure is released, the crack closes up due to elasticity and the fluid in the crack drains out of the crack through an outlet, which we refer to as backflow. We experimentally study the effects of crack size, elasticity of the matrix, and fluid viscosity on the backflow dynamics. During backflow, the volume of liquid remaining in the crack as a function of time exhibits a transition from a fast decay at early times to a power law behavior at late times. Our results at late times can be explained by scaling arguments balancing elastic and viscous stresses in the crack. This work may relate to the environmental issue of flowback in hydraulic fracturing. This work is supported by National Science Foundation via Grant CBET-1509347 and partially supported by Andlinger Center for Energy and the Environment at Princeton University.

  10. Theoretical and numerical studies on morphological transitions in crack growth

    Mühle, V


    This paper investigates the formation of crack patterns in stationary and transient temperature fields analytically with linear elastic fracture mechanics and numerically with the finite elements method (FEM). In particular, we consider the experimental situation of a narrow thin strip of hot glass slowly lowered into cold water, with temperature difference and velocity as variable parameters. The parameter regions of no crack, one straight crack and one oscillating crack are determined. The type of phase transition related to the borderline between straight and oscillating crack is characterized. The theoretical results are compared with those of other Similar investigations and comparisons are done for the propagation of multiple cracks. Quenching of a wide thin strip leads to a hierarchy of cracks whose scaling properties are analyzed. Without any fitting, theory and experiment agree surprisingly well.

  11. Near tip strain evolution of a growing fatigue crack

    M.-L. Zhu


    Full Text Available Near tip full-field strains in a growing fatigue crack have been studied in situ using the Digital Image Correlation (DIC technique in a compact tension specimen of stainless steel 316L under tension-tension cyclic loading. An error analysis of displacements and strains has been carried out, and the results show that the precision of displacements and strains in the wake of the crack is worse than that in front of the crack. A method for the determination of crack tip location is proposed for the DIC analysis. Strain ratchetting is observed ahead of the growing fatigue crack tip and found to be dependent on the distance to the crack tip; whilst normal strains appear to stabilise behind the crack tip.

  12. Development of a Distributed Crack Sensor Using Coaxial Cable.

    Zhou, Zhi; Jiao, Tong; Zhao, Peng; Liu, Jia; Xiao, Hai


    Cracks, the important factor of structure failure, reflect structural damage directly. Thus, it is significant to realize distributed, real-time crack monitoring. To overcome the shortages of traditional crack detectors, such as the inconvenience of installation, vulnerability, and low measurement range, etc., an improved topology-based cable sensor with a shallow helical groove on the outside surface of a coaxial cable is proposed in this paper. The sensing mechanism, fabrication method, and performances are investigated both numerically and experimentally. Crack monitoring experiments of the reinforced beams are also presented in this paper, illustrating the utility of this sensor in practical applications. These studies show that the sensor can identify a minimum crack width of 0.02 mm and can measure multiple cracks with a spatial resolution of 3 mm. In addition, it is also proved that the sensor performs well to detect the initiation and development of cracks until structure failure.

  13. Experimental and theoretical strain distributions for stationary and growing cracks

    Gerberich, W. W.; Davidson, D. L.; Kaczorowski, M.

    E XPERIMENTAL strain distributions are determined very near the crack tip in Fe-3wt.%Si single crystals. Both in situ stereoimaging and electron channeling techniques give reasonably reproducible distributions. By growing fatigue cracks on a {100} cleavage plane, the singularity strengths have been determined for both growing and stationary cracks under relatively plane stress and plane strain conditions. This has allowed a comparison to existing theoretical models. It is shown that the HRR singularity (Hutchinson, Rice and Rosengren, 1968) for stationary cracks is very good to within I μm of the crack tip and a hardening model for the growing crack (gao and hwang, Advances in Fracture Research, edited by D. Francois. 5th Int. Conf. on Fracture, Cannes, France, 2, 669, 1981) is surprisingly good. Other issues such as fracture criteria are discussed since strains greater than unity were measured at the crack tip in this relatively brittle material.

  14. Soil cracking modelling using the mesh-free SPH method

    Bui, H H; Kodikara, J; Sanchez, M


    The presence of desiccation cracks in soils can significantly alter their mechanical and hydrological properties. In many circumstances, desiccation cracking in soils can cause significant damage to earthen or soil supported structures. For example, desiccation cracks can act as the preference path way for water flow, which can facilitate seepage flow causing internal erosion inside earth structures. Desiccation cracks can also trigger slope failures and landslides. Therefore, developing a computational procedure to predict desiccation cracking behaviour in soils is vital for dealing with key issues relevant to a range of applications in geotechnical and geo-environment engineering. In this paper, the smoothed particle hydrodynamics (SPH) method will be extended for the first time to simulate shrinkage-induced soil cracking. The main objective of this work is to examine the performance of the proposed numerical approach in simulating the strong discontinuity in material behaviour and to learn about the crack ...

  15. FEM Modeling of Crack Propagation in a Model Multiphase Alloy

    Lihe QIAN; Seishi NISHIDO; Hiroyuki TODA; Tosliro KOBAYASHI


    In this paper, several widely applied fracture criteria were first numerically examined and the crack-tip-region Jintegral criterion was confirmed to be more applicable to predict fracture angle in an elastic-plastic multiphase material. Then, the crack propagation in an idealized dendritic two-phase Al-7%Si alloy was modeled using an elastic-plastic finite element method. The variation of crack growth driving force with crack extension was also demonstrated. It is found that the crack path is significantly influenced by the presence of α-phase near the crack tip, and the crack growth driving force varies drastically from place to place. Lastly, the simulated fracture path in the two-phase model alloy was compared with the experimentally observed fracture path.

  16. Formation mechanism of internal cracks in continuously cast slab

    Guosen Zhu; Xinhua Wang; Huixiang Yu; Jiongming Zhang; Wanjun Wang


    In order to make clear the formation mechanism of centerline cracks in continuously cast slabs, the form, distribution and other characteristics of the cracks were analyzed. The final solidification point, surface temperature of the slabs and strain in solidifying shell were investigated. The results were that: (1) Five relatively low temperature zones exist on slab surface below the three water spraying nozzles and near the two edges, respectively, which corresponds to the places of centerline cracks and triangle-zone cracks. (2) Centerline cracks and triangle-zone cracks occur because of weak secondary cooling, uneven cooling along slab width,and large variation of roll gap. (3) After minimizing the variation of roll gap and applying the new secondary cooling pattern, the occurring frequency of centerline and triangle-zone cracks minimizes to zero.

  17. Detection of subcritical crack propagation for concrete dams

    BAO TengFei; YU Hong


    Subcritical propagation of cracks is a warning sign of fracture.If such propagation is detected at an early stage,timely maintenance measures can be taken to prevent the failure of structures.To detect the subcritical propagation of a crack,the crack needs to be monitored continuously in a long term,which is not realistic under certain conditions.However,cracks in concrete dams can be monitored continuously by dam monitoring to offer possible detection for subcritical propagation.In this paper,with measured crack openings from dam monitoring,a state equation for characterizing crack development is established based on the grey system theory.The relation between the stability of the equation and the subcritical crack propagation is investigated,then a criterion is proposed for detecting subcritical propagation.An example demonstrates the validity of the criterion and its potential for practical application.

  18. Crack control technology for the X80 large OD 1422 mm line pipes

    Chunyong Huo


    Full Text Available High-grade (API 5L X80 and large-diameter (OD 1422 mm line pipes are used in the Sino–Russian eastern route gas pipeline project for high pressure (12 MPa transmission, and this can significantly increase the transmission capacity and meet China's energy strategic demand. With the increase of steel grade, transmission pressure, pipe diameter and design coefficient, however, ductile crack of line pipes becomes the dominant crack mode, so it is necessary to focus on crack arrest and control study. In this paper, therefore, an intensive study was performed on the Battelle Two-Curve (BTC method which is the major solution to the calculation of arrest toughness, as well as the crack resistance curve and decompression curve. Based on the study, the principle and application range of the BTC method were confirmed. In addition, a series of analysis were conducted on the issues which occurred when the BTC method was applied to high-strength, high-toughness line pipe steel, and the commonly used modified approaches to BTC calculation results were also provided. After the crack control scheme of the X80 large OD 1422 mm line pipes for the Russian Bovanenkovo–Ukhta was reviewed, the BTC calculation results were corrected on the basis of the design parameters of the Sino–Russian eastern routine gas pipeline project, the Charpy V-notched (CVN impact energy which meets the project requirement was finally worked out to be 245 J.

  19. Cracking and hydrocracking of triglycerides for renewable liquid fuels: alternative processes to transesterification

    Frety, Roger; Rocha, Maria da Graca C. da; Brandao, Soraia T., E-mail: frety@unifacs.b [Universidade Federal da Bahia (IQ/UFBA), Salvador, BA (Brazil). Inst. de Quimica; Pontes, Luiz A.M; Padilha, Jose F. [Universidade de Salvador (UNIFACS), BA (Brazil); Borges, Luiz E.P.; Gonzalez, Wilma A. [Instituto Militar de Engenharia (IME), Rio de Janeiro, RJ (Brazil). Secao de Quimica


    The most used industrial processes for the production of liquid fuels like diesel type are based on the methanolysis and ethanolysis of various oil reactants, such as palm, soybean and rapeseed oils, in the presence of homogeneous base catalysts. However, thermal and catalytic transformations of vegetable oils using available reactors and industrial processes are possible alternatives and deserve attention. In fact, three industrial processes are operating and new projects are announced. The present work analyses the experimental studies performed up to now by Brazilian researchers in the field of cracking, catalytic cracking and hydrocracking of pure or modified vegetable oils. From the published results, some research areas for the near future are suggested. (author)

  20. The Mathematical Basis of the Inverse Scattering Problem for Cracks from Near-Field Data

    Yao Mao


    Full Text Available We consider the acoustic scattering problem from a crack which has Dirichlet boundary condition on one side and impedance boundary condition on the other side. The inverse scattering problem in this paper tries to determine the shape of the crack and the surface impedance coefficient from the near-field measurements of the scattered waves, while the source point is placed on a closed curve. We firstly establish a near-field operator and focus on the operator’s mathematical analysis. Secondly, we obtain a uniqueness theorem for the shape and surface impedance. Finally, by using the operator’s properties and modified linear sampling method, we reconstruct the shape and surface impedance.

  1. Strategy of changing cracking furnace feedstock based on improved group search optimization

    Xiaoyu Nian; Zhenlei Wang; Feng Qian


    The scheduling process of cracking furnace feedstock is important in an ethylene plant. In this paper it is described as a constraint optimization problem. The constraints consist of the cycle of operation, maximum tube metal temperature, process time of each feedstock, and flow rate. A modified group search optimizer is pro-posed to deal with the optimization problem. Double fitness values are defined for every group. First, the factor of penalty function should be changed adaptively by the ratio of feasible and general solutions. Second, the“excel-lent”infeasible solution should be retained to guide the search. Some benchmark functions are used to evaluate the new algorithm. Final y, the proposed algorithm is used to optimize the scheduling process of cracking furnace feedstock. And the optimizing result is obtained.

  2. Effect of Layers Position on Fracture Toughness of Functionally Graded Steels in Crack Divider Configuration

    Ali Nazari; Jamshid Aghazadeh Mohandesi; Shadi Riahi


    In the present study, fracture toughness of functionally graded steels in crack divider configuration has been modeled. By utilizing plain carbon and austenitic stainless steels slices with various thicknesses and arrangements as electroslag remelting electrodes, functionally graded steels were produced. The fracture toughness of the functionally graded steels in crack divider configuration has been found to depend on the composites' type together with the volume fraction and the position of the containing phases. According to the area under stress-strain curve of each layer in the functionally graded steels, a mathematical model has been presented for predicting fracture toughness of composites by using the rule of mixtures. The fracture toughness of each layer has been modified according to the position of that layer where for the edge layers, net plane stress condition was supposed and for the central layers, net plane strain condition was presumed. There is a good agreement between experimental results and those acquired from the analytical model.

  3. Numerical and experimental analysis of the directional stability on crack propagation under biaxial stresses

    RodrIguez-MartInez, R; Urriolagoitia-Calderon, G; Urriolagoitia-Sosa, G; Hernandez-Gomez, L H [Instituto Politecnico Nacional Seccion de Estudios de Posgrado e Investigacion (SEPI), Escuela Superior de IngenierIa Mecanica y Electrica (ESIME), Edificio 5. 2do Piso, Unidad Profesional Adolfo Lopez Mateos ' Zacatenco' Col. Lindavista, C.P. 07738, Mexico, D.F. (Mexico); Merchan-Cruz, E A; RodrIguez-Canizo, R G; Sandoval-Pineda, J M, E-mail: rrodriguezm@ipn.m, E-mail:, E-mail:, E-mail:, E-mail:, E-mail:, E-mail: jsandovalp@ipn.m [Instituto Politecnico Nacional Seccion de Estudios de Posgrado e Investigacion (SEPI), Escuela Superior de IngenierIa Mecanica y Electrica (ESIME). Unidad profesional, AZCAPOTZALCO, Av. de las Granjas No. 682, Col. Sta. Catarina Azcapotzalco, C.P. 02550, Mexico D.F. (Mexico)


    In this paper, the case of Single Edge Notch (SEN) specimens subject to opening/compressive loading was analyzed; The loads are applied in several ratios to evaluate the influence of the specimen geometry, and the Stress Intensity Factor (SIF) K{sub 1} values on the directional stability of crack propagation. The main purpose of this work is to evaluate the behaviour of the fracture propagation, when modifying the geometry of the SEN specimen and different relationships of load tension/compression are applied. Additionally, the precision of the numerical and experimental analysis is evaluated to determine its reliability when solving this type of problems. The specimens are subjected to biaxial opening/compression loading; both results (numerical and experimental) are compared in order to evaluate the condition of directional stability on crack propagation. Finally, an apparent transition point related to the length of specimens was identified, in which the behaviour of values of SIF changes for different loading ratios.

  4. Characterization of Cracking and Crack Growth Properties of the C5A Aircraft Tie-Box Forging

    Piascik, Robert S.; Smith, Stephen W.; Newman, John A.; Willard, Scott A.


    Detailed destructive examinations were conducted to characterize the integrity and material properties of two aluminum alloy (7075-T6) horizontal stabilizer tie box forgings removed.from US. Air Force C5A and C5B transport aircraft. The C5B tie box forging was,found to contain no evidence of cracking. Thirteen cracks were found in the CSA,forging. All but one of the cracks observed in the C5A component were located along the top cap region (one crack was located in the bottom cap region). The cracks in the C5A component initiated at fastener holes and propagated along a highly tunneled intergranular crack path. The tunneled crack growth configuration is a likelv result of surface compressive stress produced during peening of the .forging suijace. The tie box forging ,fatigue crack growth, fracture and stress corrosion cracking (SCC) properties were characterized. Reported herein are the results of laboratory air ,fatigue crack growth tests and 95% relative humidity SCC tests conducted using specimens machined from the C5A ,forging. SCC test results revealed that the C5A ,forging material was susceptible to intergranular environmental assisted cracking: the C5A forging material exhibited a SCC crack-tip stress-intensity factor threshold of less than 6 MPadn. Fracture toughness tests revealed that the C5A forging material exhibited a fracture toughness that was 25% less than the C5B forging. The C5A forging exhibited rapid laboratory air fatigue crack growth rates having a threshold crack-tip stress-intensity factor range of less than 0.8 MPa sup m. Detailed fractographic examinations revealed that the ,fatigue crack intergranular growth crack path was similar to the cracking observed in the C5A tie box forging. Because both fatigue crack propagation and SCC exhibit similar intergranular crack path behavior, the damage mechanism resulting in multi-site cracking of tie box forgings cannot be determined unless local cyclic stresses can be quantified.

  5. Experimental characterization of fatigue crack tip processes

    Lankford, J.; Leverant, G. R.


    Many analytical models have been proposed to describe the physical processes attendant to a fatigue crack tip, as well as the rate at which fatigue cracks grow. By applying advanced experimental methods (such as electron channeling, stereoimaging, and in-situ cyclic loading in an SEM) to a broad range of structural materials, it has been shown that it is possible to critically assess the physical assumptions incorporated into the models. Refinements in existing models and the development of new ones have resulted. New insights into materials' behavior are providing guidelines for improving the fatigue resistance of structural alloys. In the near future, even more advanced experimental methods, such as high temperature SEM stages and small angle neutron scattering, will be available to study creep/fatigue interactions in metals and ceramics.

  6. Stress-corrosion cracking of titanium alloys.

    Blackburn, M. J.; Feeney, J. A.; Beck, T. R.


    In the light of research material published up to May 1970, the current understanding of the experimental variables involved in the stress-corrosion cracking (SCC) behavior of titanium and its alloys is reviewed. Following a brief summary of the metallurgy and electrochemistry of titanium alloys, the mechanical, electrochemical, and metallurgical parameters influencing SCC behavior are explored with emphasis on crack growth kinetics. Macro- and microfeatures of fractures are examined, and it is shown that many transgranular SCC failures exhibit morphological and crystallographic features similar to mechanical cleavage failures. Current SCC models are reviewed with respect to their ability to explain the observed SCC behavior of titanium and its alloys. Possible methods for eliminating or minimizing stress corrosion hazards in titanium or titanium alloy components are described.

  7. On non-singular GRADELA crack fields

    Elias C. Aifantis


    Full Text Available A brief account is provided on crack-tip solutions that have recently been published in the literature by employing the so-called GRADELA model and its variants. The GRADELA model is a simple gradient elasticity theory involving one internal length in addition to the two Lame' constants, in an effort to eliminate elastic singularities and discontinuities and to interpret elastic size effects. The non-singular strains and non-singular (but sometimes singular or even hypersingular stresses derived this way under different boundary conditions differ from each other and their physical meaning in not clear. This is discussed which focus on the form and physical meaning of non-singular solutions for crack-tip stresses and strains that are possible to obtain within the GRADELA model and its extensions.

  8. Subcritical crack growth in fibrous materials

    Santucci, Stéphane; Deschanel, Stéphanie; Vanel, Loic; Ciliberto, Sergio


    We present experiments on the slow growth of a single crack in a fax paper sheet submitted to a constant force $F$. We find that statistically averaged crack growth curves can be described by only two parameters : the mean rupture time $\\tau$ and a characteristic growth length $\\zeta$. We propose a model based on a thermally activated rupture process that takes into account the microstructure of cellulose fibers. The model is able to reproduce the shape of the growth curve, the dependence of $\\zeta$ on $F$ as well as the effect of temperature on the rupture time $\\tau$. We find that the length scale at which rupture occurs in this model is consistently close to the diameter of cellulose microfibrils.

  9. Adolescentes e crack: pelo caminho das pedras

    Eduardo Tomm


    Full Text Available Nos últimos anos, a sociedade tem observado uma rápida expansão no uso de crack, especialmente por adolescentes e jovens. É evidente a necessidade de ouvir esses sujeitos de para melhor compreender sua situação. Para atender a essa necessidade, desenvolvemos uma pesquisa qualitativa descritivo-exploratória cujo foco foi um grupo terapêutico para adolescentes usuários de crack que ocorreu no Centro de Atenção Psicossocial Infanto-Juvenil (CAPSi em uma cidade do interior do Rio Grande do Sul, Brasil. Amparados na modalidade expost-facto, analisamos documentos produzidos nessa instituição. O resultado foi uma cartografia que acompanhou discursivamente os adolescentes pelo "caminho das pedras": os lugares, tratamentos, pessoas, ideias e momentos dos quais falam.

  10. Augmented Reality to Access Dam Cracks Information

    Fabiana Frata Furlan Peres


    Full Text Available Augmented reality technology is a tool with great potential for application in several areas, including engineering. During the early phases of the enterprise life cycle, as design and construction, augmented reality has been widely used. Concrete dams, during operation and maintenance phase, require regular inspections as part of the necessary activities to keep their structural safety. Cracks are common pathology in these structures that must be detected, mapped and measured as their evolution may evidence structure compromising, need for maintenance or intervention. In this context this paper aims to present a prototype to access in situ the dam cracks information through the use of augmented reality, thus giving a contribution to the effectiveness and efficiency of inspections

  11. Analysis of WWER 1000 collector cracking mechanisms

    Matocha, K.; Wozniak, J. [Vitkovice J.S.C., Ostrava (Switzerland)


    The presentation reviews the large experimental program, started in 1993 in Vitkovice, where the main aim was: (1) a detailed study of strain and thermal ageing, dissolved oxygen content and temperature on subcritical crack growth in 10NiMo8.5 (10GN2MFA) steel, (2) a detailed study of the effect of high temperature water and tube expansion technology on fracture behaviour of ligaments between holes for heat exchange tubes, and (3) a detailed study of the effect of drilling, tube expansion technology and heat treatment on residual stresses on the surface of holes for heat exchange tubes. The aim of all these investigations was to find a dominant damage mechanism responsible for collector cracking to be able to judge the efficiency of implemented modifications and suggested countermeasures and to answer a very important question whether proper operation conditions (mainly water chemistry) make the operation of steam generators made in Vitcovice safe throughout the planned lifetime. 10 refs.

  12. International Conference on Dynamic Crack Propagation


    The planning meeting for a conference on Dynamic Crack Propagation was held at M.LT. in February 1971 and attended by research workers from several industrial, governmental and academic organizations. It was felt that a more specialized meeting would provide a better opportunity for both U.S. and foreign researchers to exchange their ideas and views on dynamic fracture, a subject which is seldom emphasized in national or international fracture conferences. Dynamic crack propagation has been a concern to specialists in many fields: continuum mechanics, metallurgy, geology, polymer chemistry, orthopedics, applied mathematics, as well as structural design and testing. It impinges on a wide variety of problems such as rock breaking and earthquakes, pressure vessels and line pipes, comminution and the per­ formance of armament and ordnance, etc. Advances have been numerous, covering theories and experiments from both the microscopic and macro­ scopic points of view. Hence, the need for comparing the theoretical ...


    Klein, J; Jeffrey Holder, J


    Bench scale (1 to 6 gram) methane cracking tests have been performed on a variety of pure elements, some alloys, and SAES{reg_sign} commercial getters St 101, St 198, St 707, St 737, and St 909 to determine methane cracking performance (MCP) of 5% methane in a helium carrier at 700 C, 101.3 kPa (760 torr) with a 10 sccm feed. The MCP was almost absent from some materials tested while others showed varying degrees of MCP. Re, Cr, V, Gd, and Mo powders had good MCP, but limited capacities. Nickel supported on kieselguhr (Ni/k), a Zr-Ni alloy, and the SAES{reg_sign} getters had good MCP in a helium carrier. The MCP of these same materials was suppressed in a hydrogen carrier stream and the MCP of the Zr-based materials was reduced by nitride formation when tested with a nitrogen carrier gas.

  14. Sharp contact corners, fretting and cracks

    D. A. Hills


    Full Text Available Contacts with sharp edges subject to oscillatory loading are likely to nucleate cracks from the corners, if the loading is sufficiently severe. To a first approximation, the corners behave like notches, where the local elastic behaviour is relieved by plasticity, and which in turn causes irreversibilities that give rise to crack nucleation, but also by frictional slip. One question we aim to answer here is; when is the frictional slip enveloped by plastic slip, so that the corner is effectively a notch in a monolithic material? We do this by employing the classical Williams asymptotic solution to model the contact corner, and, in doing so, we render the solution completely general in the sense that it is independent of the overall geometry of the components. We then re-define the independent parameters describing the properties of the Williams solution by using the inherent length scale, a procedure that was described at the first IJFatigue and FFEMS joint workshop [1]. By proceeding in this way, we can provide a self-contained solution that can be ‘pasted in’ to any complete contact problem, and hence the likelihood of crack nucleation, and the circumstances under which it might occur, can be classified. Further, this reformulation of Williams' solution provides a clear means of obtaining the strength (defined by crack nucleation conditions of a material pair with a particular contact angle. This means that the results from a test carried out using a laboratory specimen may easily be carried over to any complicated contact problem found in engineering practice, and a mechanical test of the prototypical geometry, which may often be quite difficult, is avoided.

  15. Analysis of nonlinear frequency mixing in 1D waveguides with a breathing crack using the spectral finite element method

    Joglekar, D. M.; Mitra, M.


    A breathing crack, due to its bilinear stiffness characteristics, modifies the frequency spectrum of a propagating dual-frequency elastic wave, and gives rise to sidebands around the probing frequency. This paper presents an analytical-numerical method to investigate such nonlinear frequency mixing resulting from the modulation effects induced by a breathing crack in 1D waveguides, such as axial rods and the Euler-Bernoulli beams. A transverse edge-crack is assumed to be present in both the waveguides, and the local flexibility caused by the crack is modeled using an equivalent spring approach. A simultaneous treatment of both the waveguides, in the framework of the Fourier transform based spectral finite element method, is presented for analyzing their response to a dual frequency excitation applied in the form of a tone-burst signal. The intermittent contact between the crack surfaces is accounted for by introducing bilinear contact forces acting at the nodes of the damage spectral element. Subsequently, an iterative approach is outlined for solving the resulting system of nonlinear simultaneous equations. Applicability of the proposed method is demonstrated by considering several test cases. The existence of sidebands and the higher order harmonics is confirmed in the frequency domain response of both the waveguides under investigation. A qualitative comparison with the previous experimental observations accentuates the utility of the proposed solution method. Additionally, the influence of the two constituent frequencies in the dual frequency excitation is assessed by varying the relative strengths of their amplitudes. A brief parametric study is performed for bringing out the effects of the relative crack depth and crack location on the degree of modulation, which is quantified in terms of the modulation parameter. Results of the present investigation can find their potential use in providing an analytical-numerical support to the studies geared towards the

  16. Numerical simulations of material mismatch and ductile crack growth

    Oestby, Erling


    Both the global geometry and inhomogeneities in material properties will influence the fracture behaviour of structures in presence of cracks. In this thesis numerical simulations have been used to investigate how some aspects of both these issues affect the conditions at the crack-tip. The thesis is organised in an introduction chapter, summarising the major findings and conclusions, a review chapter, presenting the main aspects of the developments in the field of fracture mechanics, and three research papers. Paper I considers the effect of mismatch in hardening exponent on the local near-tip stress field for stationary interface cracks in bi-materials under small scale yielding conditions. It is demonstrated that the stress level in the weaker material increases compared to what is found in the homogeneous material for the same globally applied load level, with the effect being of increasing importance as the crack-tip is approached. Although a coupling between the radial and angular dependence of the stress fields exists, the evolving stress field can still be normalised with the applied J. The effect on the increase in stress level can closely be characterised by the difference in hardening exponent, {delta}n, termed the hardening mismatch, and is more or less independent of the absolute level of hardening in the two materials. Paper II and Ill deal with the effects of geometry, specimen size, hardening level and yield stress mismatch in relation to ductile crack growth. The ductile crack growth is simulated through use of the Gurson model. In Paper H the effect of specimen size on the crack growth resistance is investigated for deep cracked bend and shallow cracked tensile specimens. At small amounts of crack growth the effect of specimen size on the crack growth resistance is small, but a more significant effect is found for larger amounts of crack growth. The crack growth resistance decreases in smaller specimens loaded in tension, whereas the opposite is

  17. A viscoelastic Unitary Crack-Opening strain tensor for crack width assessment in fractured concrete structures

    Sciumè, Giuseppe; Benboudjema, Farid


    A post-processing technique which allows computing crack width in concrete is proposed for a viscoelastic damage model. Concrete creep is modeled by means of a Kelvin-Voight cell while the damage model is that of Mazars in its local form. Due to the local damage approach, the constitutive model is regularized with respect to finite element mesh to avoid mesh dependency in the computed solution (regularization is based on fracture energy). The presented method is an extension to viscoelasticity of the approach proposed by Matallah et al. (Int. J. Numer. Anal. Methods Geomech. 34(15):1615-1633, 2010) for a purely elastic damage model. The viscoelastic Unitary Crack-Opening (UCO) strain tensor is computed accounting for evolution with time of surplus of stress related to damage; this stress is obtained from decomposition of the effective stress tensor. From UCO the normal crack width is then derived accounting for finite element characteristic length in the direction orthogonal to crack. This extension is quite natural and allows for accounting of creep impact on opening/closing of cracks in time dependent problems. A graphical interpretation of the viscoelastic UCO using Mohr's circles is proposed and application cases together with a theoretical validation are presented to show physical consistency of computed viscoelastic UCO.

  18. Vibration analysis of a rectangular thin isotropic plate with a part-through surface crack of arbitrary orientation and position

    Bose, Tanmoy; Mohanty, A. R.


    In this paper, vibration analysis of a rectangular thin isotropic plate with a part-through surface crack of arbitrary orientation and position is performed by using the Kirchhoff plate theory. Simply supported (SSSS), clamped (CCCC) and simply supported-clamped (SCSC) boundary conditions are considered for the analysis. First, the governing differential equation of a cracked plate is formulated. A modified line spring model is then used to formulate the crack terms in the governing equation. Next, by the application of Burger's formulation, the differential equation is transformed into the well-known Duffing equation with cubic and quadratic nonlinearities. The Duffing equation is then solved by the method of multiple scales (MMS) to extract the frequency response curve. Natural frequencies are evaluated for different values of length, angle and position of a part-through surface crack. Some results are compared with the published literature. Amplitude variation with different values of length, angle and position of a part-through surface crack are presented, for all three types of the plate boundary conditions.

  19. Fracture behavior of block copolymer and graphene nanoplatelet modified epoxy and fiber reinforced/epoxy polymer composites

    Kamar, Nicholas T.

    Glass and carbon fiber reinforced/epoxy polymer composites (GFRPs and CFRPs) have high strength-to-weight and stiffness-to-weight ratios. Thus, GFRPs and CFRPs are used to lightweight aircraft, marine and ground vehicles to reduce transportation energy utilization and cost. However, GFRP and CFRP matrices have a low resistance to crack initiation and propagation; i.e. they have low fracture toughness. Current methods to increase fracture toughness of epoxy and corresponding GFRP and CFRPs often reduce composite mechanical and thermomechanical properties. With the advent of nanotechnology, new methods to improve the fracture toughness and impact properties of composites are now available. The goal of this research is to identify the fracture behavior and toughening mechanisms of nanoparticle modified epoxy, GFRPs and CFRPs utilizing the triblock copolymer poly(styrene)-block-poly(butadiene)-block-poly(methylmethacrylate) (SBM) and graphene nanoplatelets (GnPs) as toughening agents. The triblock copolymer SBM was used to toughen the diglycidyl ether of bisphenol-A (DGEBA) resin cured with m-phenylenediamine (mPDA) and corresponding AS4-12k CFRPs. SBM self assembled in epoxy to form nanostructured domains leading to larger increases in fracture toughness, KQ (MPa*m 1/2) than the traditional, phase separating carboxyl-terminated butadiene-acrylonitrile (CTBN) rubber. Additionally, SBM increased the mode-I fracture toughness, GIc (J/m2) of CFRPs without corresponding reductions in composite three-point flexural properties and glass transition temperature (Tg). Fractography of SBM modified epoxy and CFRPs via scanning electron microscopy (SEM) showed that sub 100 nm spherical micelles cavitated to induce void growth and matrix shear yielding toughening mechanisms. Furthermore, SBM did not suppress epoxy Tg, while CTBN decreased Tg with both increasing concentration and acrylonitrile content. Graphene nanoplatelets (GnPs) consist of a few layers of graphene sheets, which

  20. Effects of Crack on Vibration Characteristics of Mistuned Rotated Blades

    Hailong Xu


    Full Text Available Rotated blades are key mechanical components in turbine and high cycle fatigues often induce blade cracks. Meanwhile, mistuning is inevitable in rotated blades, which often makes it much difficult to detect cracks. In order to solve this problem, it is important and necessary to study effects of crack on vibration characteristics of mistuned rotated blades (MRBs. Firstly, a lumped-parameter model is established based on coupled multiple blades, where mistuned stiffness with normal distribution is introduced. Next, a breathing crack model is adopted and eigenvalue analysis is used in coupled lumped-parameter model. Then, numerical analysis is done and effects of depths and positions of a crack on natural frequency, vibration amplitude, and vibration localization parameters are studied. The results show that a crack causes natural frequency decease and vibration amplitude increase of cracked blade. Bifurcations will occur due to a breathing crack. Furthermore, based on natural frequencies and vibration amplitudes, variational factors are defined to detect a crack in MRBs, which are validated by numerical simulations. Thus, the proposed method provides theoretical guidance for crack detection in MRBs.