Assessment of stress-strain data suitable for finite-element elastic--plastic analysis of shipping containers

International Nuclear Information System (INIS)

Rack, H.J.; Knorovsky, G.A.

1978-09-01

Stress-strain data which describes the influence of strain rate and temperature on the mechanical response of materials presently being used for light water reactor fuel shipping containers have been assembled. Selection of data has been limited to that which is suitable for use in finite-element elastic--plastic analysis of shipping containers (e.g., they must include complete material history profiles). Based on this information, recommendations have been made for further work which is required to complete the necessary data base

Elastic-plastic behaviour of thick-walled containers considering plastic compressibility

International Nuclear Information System (INIS)

Betten, J.; Frosch, H.G.

1983-01-01

In this paper the elastic-plastic behaviour of thick-walled pressure vessels with internal and external pressure is studied. To describe the mechanical behaviour of isotropic, plastic compressible materials we use a plastic potential which is a single-valued function of the principle stresses. For cylinders and spheres an analytic expression for the computation of stresses and residual stresses is specified. Afterwards the strains are calculated by using the finite difference method. Some examples will high-light the influence of the plastic compressibility on the behaviour of pressure vessels. (orig.) [de

Change and anisotropy of elastic modulus in sheet metals due to plastic deformation

Science.gov (United States)

Ishitsuka, Yuki; Arikawa, Shuichi; Yoneyama, Satoru

2015-03-01

In this study, the effect of the plastic deformation on the microscopic structure and the anisotropy of the elastic modulus in the cold-rolled steel sheet (SPCC) is investigated. Various uniaxial plastic strains (0%, 2.5%, 5%, 7.5%, and 10%) are applied to the annealed SPCC plates, then, the specimens for the tensile tests are cut out from them. The elastic moduli in the longitudinal direction and the transverse direction to the direction that are pre-strained are measured by the tensile tests. Cyclic tests are performed to investigate the effects of the internal friction caused by the movable dislocations in the elastic deformation. Also, the movable dislocations are quantified by the boundary tracking for TEM micrographs. In addition, the behaviors of the change of the elastic modulus in the solutionized and thermal aged aluminum alloy (A5052) are measured to investigate the effect on the movable dislocations with the amount of the depositions. As a result in SPCC, the elastic moduli of the 0° and 90° directions decrease more than 10% as 10% prestrain applied. On the other hand, the elastic modulus shows the recovery behavior after the strain aging and the annealing. The movable dislocation and the internal friction show a tendency to increase as the plastic strain increases. The marked anisotropy is not observed in the elastic modulus and the internal friction. The elastic modulus in A5052 with many and few depositions decreases similarly by the plastic deformation. From the above, the movable dislocations affect the elastic modulus strongly without depending on the deposition amount. Moreover, the elastic modulus recovers after the plastic deformation by reducing the effects of them with the strain aging and the heat treatment.

Prediction of fretting fatigue behavior under elastic-plastic conditions

International Nuclear Information System (INIS)

Shin, Ki Su

2009-01-01

Fretting fatigue generally leads to the degradation of the fatigue strength of a material due to cyclic micro-slip between two contacting materials. Fretting fatigue is regarded as an important issue in designing aerospace structures. While many studies have evaluated fretting fatigue behavior under elastic deformation conditions, few have focused on fretting fatigue behavior under elastic-plastic deformation conditions, especially the crack orientation and fatigue life prediction for Ti-6Al-4V. The primary goal of this study was to characterize the fretting fatigue crack initiation behavior in the presence of plasticity. Experimental tests were performed using pad configurations involving elastic-plastic deformations. To calculate stress distributions under elastic-plastic fretting fatigue conditions, FEA was also performed. Several parametric approaches were used to predict fretting fatigue life along with stress distribution resulting from FEA. However, those parameters using surface stresses were unable to establish an equivalence between elastic fretting fatigue data and elastic-plastic fretting fatigue data. Based on this observation, the critical distance methods, which are commonly used in notch analysis, were applied to the fretting fatigue problem. In conclusion, the effective strain range method when used in conjunction with the SMSSR parameter showed a good correlation of data points between the pad configurations involving elastic and elastic plastic deformations

Simplified method for elastic plastic analysis of material presenting bilinear kinematic hardening

International Nuclear Information System (INIS)

Roche, R.

1983-12-01

A simplified method for elastic plastic analysis is presented. Material behavior is assumed to be elastic plastic with bilinear kinematic hardening. The proposed method give a strain-stress field fullfilling material constitutive equations, equations of equilibrium and continuity conditions. This strain-stress is obtained through two linear computations. The first one is the conventional elastic analysis of the body submitted to the applied load. The second one use tangent matrix (tangent Young's modulus and Poisson's ratio) for the determination of an additional stress due to imposed initial strain. Such a method suits finite elements computer codes, the most useful result being plastic strains resulting from the applied loading (load control or deformation control). Obviously, there is not unique solution, for stress-strain field is not depending only of the applied load, but of the load history. Therefore, less pessimistic solutions can be got by one or two additional linear computations [fr

Material Properties Test to Determine Ultimate Strain and True Stress-True Strain Curves for High Yield Steels

Energy Technology Data Exchange (ETDEWEB)

K.R. Arpin; T.F. Trimble

2003-04-01

This testing was undertaken to develop material true stress-true strain curves for elastic-plastic material behavior for use in performing transient analysis. Based on the conclusions of this test, the true stress-true strain curves derived herein are valid for use in elastic-plastic finite element analysis for structures fabricated from these materials. In addition, for the materials tested herein, the ultimate strain values are greater than those values cited as the limits for the elastic-plastic strain acceptance criteria for transient analysis.

A comparison of time-history elastic plastic piping analysis with measurement

International Nuclear Information System (INIS)

Scavuzzo, R.J.; Sansalone, K.H.

1992-01-01

The GE/ETEC Green piping system was subjected to high seismic inputs from hydraulic sleds at each pipe foundation. These inputs were high enough to force bending stresses into the plastic regime. Strain gages recorded the pipe response at various positions within the system. The ABAQUS finite element code was used to model this piping system and the dynamic input. Problems associated with the dynamic input are discussed. Various types of finite elements were evaluated for accurancy. Both an elastic time-history analysis and an elastic-plastic time-history analysis of the system were conducted. Results of these analyses are compared to each other and the experimental data. These comparisons indicated that elastic analysis of dynamic strains are conservative at all points of comparison and that there is good agreement between the nonlinear elastic-plastic analysis and experimental data. (orig.)

A calculational round robin in elastic-plastic fracture mechanics

International Nuclear Information System (INIS)

Larsson, L.H.

1983-01-01

Eighteen organisations participated in this elastic-plastic fracture mechanics (EPFM) numerical analysis round robin which treated the same three-point bend problem as a similar round robin conducted by ASTM four years earlier. The work involved the calculation of overall deformation, J, CTOD and crack profile using plane strain elastic-plastic finite element analysis for a monotonically increasing load up to a maximum deformation which was far beyond the elastic regime. It was found that all of the elastic solutions were accurate to within a few per cent. In the elastic-plastic regime, however, there was a large scatter of the results, increasing with increasing plastic deformation and roughly of the same order as in the ASTM round robin which contained ten solutions. No significant progress has taken place in the state of the art of numerical EPFM analysis over the four-year interval. The reasons for this scatter and tentative conclusions on the most suitable numerical analysis methods in EPFM are discussed. (author)

Comparison of theory and experiment for elastic-plastic plane-strain crack growth. [AISI 4140 steel

Energy Technology Data Exchange (ETDEWEB)

Hermann, L.; Rice, J.R.

1980-08-01

Recent theoretical results on elastic-plastic plane-strain crack growth are reviewed and experimental results for crack growth in a 4140 steel are discussed in terms of the theoretical concepts. The theory is based on a recent asymptotic analysis of crack surface opening and strain distributions at a quasistatically advancing crack tip in an ideally plastic solid. The analysis is incomplete in that some of the parameters which appear in it are known only approximately, especially at large-scale yielding. Nevertheless, it is sufficient for the derivation of a relation between the imposed loading and amount of crack growth prior to general yielding, based on the assumption that a geometrically similar near-tip crack profile is maintained during growth. The resulting predictions for the variation of J with crack growth are found to fit well to the experimental results obtained on deeply cracked compact specimens.

A calculational round robin in elastic-plastic fracture mechanics

International Nuclear Information System (INIS)

Larsson, L.H.

Eighteen organizations participated in this round robin which treated the same three-point bend problem as an ASTM round robin four years earlier. Overall deformation, J, CTOD and crack profile were the main results required using plane strain elastic-plastic finite element analysis for a monotonically increasing load up to a maximum deformation which was far beyond the elastic regime. All elastic solutions were accurate to within a few percent. In the elastic-plastic regime, however, there was a large scatter of the results, increasing with increasing plastic deformation and roughly of the same order as in the ASTM round robin which contained ten solutions. Apparently no significant progress has taken place in the state of the art of numerical EPFM analysis in four years time. The paper discusses the reasons for this scatter and draws tentative conclusions on the most suitable numerical analysis methods in EPFM. (Auth.)

ELASTIC-PLASTIC AND RESIDUAL STRESS ANALYSIS OF AN ALUMINUM DISC UNDER INTERNAL PRESSURES

Directory of Open Access Journals (Sweden)

Numan Behlül BEKTAŞ

2004-02-01

Full Text Available This paper deals with elastic-plastic stress analysis of a thin aluminum disc under internal pressures. An analytical solution is performed for satisfying elastic-plastic stress-strain relations and boundary conditions for small plastic deformations. The Von-Mises Criterion is used as a yield criterion, and elastic perfectly plastic material is assumed. Elastic-plastic and residual stress distributions are obtained from inner radius to outer radius, and they are presented in tables and figures. All radial stress components, ?r, are compressive, and they are highest at the inner radius. All tangential stress components, ??, are tensile, and they are highest where the plastic deformation begins. Magnitude of the tangential residual stresses is higher than those the radial residual stresses.

Three-dimensional elastic--plastic stress and strain analyses for fracture mechanics: complex geometries

International Nuclear Information System (INIS)

Bellucci, H.J.

1975-11-01

The report describes the continuation of research into capability for three-dimensional elastic-plastic stress and strain analysis for fracture mechanics. A computer program, MARC-3D, has been completed and was used to analyze a cylindrical pressure vessel with a nozzle insert. A method for generating crack tip elements was developed and a model was created for a cylindrical pressure vessel with a nozzle and an imbedded flaw at the inside nozzle corner. The MARC-3D program was again used to analyze this flawed model. Documentation for the use of the MARC-3D computer program has been included as an appendix

Elastic-plastic analysis of high speed rotors with no plane of symmetry

International Nuclear Information System (INIS)

Anantha Ramu, S.

1981-01-01

A general method of analysis of elastic plastic shells has been developed. The material of the shell is assumed to obey von Mises yield condition and a stress strain law on the basis of deformation theory of plasticity. The method permits an easy iterative solution of the complete set of coupled nonlinear differential equations. The iterative procedure is essentially the solution of the elastic problem several times with different sets of loads. The solution finally yields among other things, the location of the elastic-plastic boundary in the shell wall. The second approach suggested is a three-dimensional hexahedral isoparametric solid element. The computer program developed is capable of modelling perfectly plastic, bilinear as well as nonlinear strain hardening behaviour of materials. As an example, a radial impeller is analysed by both the approaches by idealizing it as a rotating conical shell. The complete history of plastification of the shell wall as the speed increases is determined. The results of both approaches are found to be in good agreement with each other. (orig./HP)

Quasi-static incremental behavior of granular materials: Elastic-plastic coupling and micro-scale dissipation

Science.gov (United States)

Kuhn, Matthew R.; Daouadji, Ali

2018-05-01

The paper addresses a common assumption of elastoplastic modeling: that the recoverable, elastic strain increment is unaffected by alterations of the elastic moduli that accompany loading. This assumption is found to be false for a granular material, and discrete element (DEM) simulations demonstrate that granular materials are coupled materials at both micro- and macro-scales. Elasto-plastic coupling at the macro-scale is placed in the context of thermomechanics framework of Tomasz Hueckel and Hans Ziegler, in which the elastic moduli are altered by irreversible processes during loading. This complex behavior is explored for multi-directional loading probes that follow an initial monotonic loading. An advanced DEM model is used in the study, with non-convex non-spherical particles and two different contact models: a conventional linear-frictional model and an exact implementation of the Hertz-like Cattaneo-Mindlin model. Orthotropic true-triaxial probes were used in the study (i.e., no direct shear strain), with tiny strain increments of 2 ×10-6 . At the micro-scale, contact movements were monitored during small increments of loading and load-reversal, and results show that these movements are not reversed by a reversal of strain direction, and some contacts that were sliding during a loading increment continue to slide during reversal. The probes show that the coupled part of a strain increment, the difference between the recoverable (elastic) increment and its reversible part, must be considered when partitioning strain increments into elastic and plastic parts. Small increments of irreversible (and plastic) strain and contact slipping and frictional dissipation occur for all directions of loading, and an elastic domain, if it exists at all, is smaller than the strain increment used in the simulations.

In-plane anisotropic strain of elastically and plastically deformed III-nitrides on lithium gallate

Energy Technology Data Exchange (ETDEWEB)

Namkoong, Gon, E-mail: gnamkoon@odu.ed [Old Dominion University, Electrical and Computer Engineering, Applied Research Center, 12050 Jefferson Avenue, Newport News, VA 23606 (United States); Huang, Sa; Moseley, Michael; Doolittle, W. Alan [Georgia Institute of Technology, School of Electrical and Computer Engineering, 777 Atlantic Dr., Atlanta, GA 30332 (United States)

2009-10-30

We have investigated both elastically and plastically deformed GaN films on lithium gallate, LiGaO{sub 2}, by molecular beam epitaxy. The in-plane lattice parameters were determined from high resolution X-ray diffraction and indicated two different groups of in-plane lattice parameters, influenced by the a- and b-axis of LiGaO{sub 2}. The measured in-plane lattice parameters indicate that there exist both compressive and tensile strains of in-plane GaN along the a- and b-axis of LiGaO{sub 2}, respectively. This anisotropic strain in GaN films forms a slight distortion of the basal-plane hexagonal structure of GaN films, leading to a different critical thickness of 4.0 {+-} 0.17 and 7.8 {+-} 0.7 nm along the a- and b-axis of LiGaO{sub 2}, respectively.

In-plane anisotropic strain of elastically and plastically deformed III-nitrides on lithium gallate

International Nuclear Information System (INIS)

Namkoong, Gon; Huang, Sa; Moseley, Michael; Doolittle, W. Alan

2009-01-01

We have investigated both elastically and plastically deformed GaN films on lithium gallate, LiGaO 2 , by molecular beam epitaxy. The in-plane lattice parameters were determined from high resolution X-ray diffraction and indicated two different groups of in-plane lattice parameters, influenced by the a- and b-axis of LiGaO 2 . The measured in-plane lattice parameters indicate that there exist both compressive and tensile strains of in-plane GaN along the a- and b-axis of LiGaO 2 , respectively. This anisotropic strain in GaN films forms a slight distortion of the basal-plane hexagonal structure of GaN films, leading to a different critical thickness of 4.0 ± 0.17 and 7.8 ± 0.7 nm along the a- and b-axis of LiGaO 2 , respectively.

A work-hardening rule for finite elastic-plastic deformation of metals at elevated temperatures

International Nuclear Information System (INIS)

Lee, L.H.N.; Horng, J.T.

1975-01-01

The paper is concerned with an extension of Prager-Ziegler's kinematic work-hardening rule for infinitesimal elastic-plastic deformation to a work-hardening rule for finite elastic-plastic deformation of a polycrystalline metal. It is shown that the finite work-hardening rule, which accounts for the Bauschinger and temperature effects within certain pressure and temperature ranges, satisfies certain invariant, continuity and thermodynamic requirements. A description of the kinematics of an elastic-plastic body is employed with reference to three separate configurations: initial, current and an intermediate configuration. The intermediate configuration is a conceptual, local configuration obtained by removing the stress and temperature changes in the neighborhood of an element. A rigid body rotation of the intermediate configuration is allowed. Piola-Kirchhoff stresses and Green deformation tensors referred to the initial and intermediate configurations are employed as stress and strain measures. The plastic deformation has been associated with the motion and production of dislocations. It has been observed that the motion of mobile dislocations usually occur in the narrow slip bands in each grain, leaving the basic lattice structure practically intact, so that the macroscopic elastic properties of the material are essentially independent of plastic deformation. Employing this fact and the thermodynamic laws, a simplified elastic stress-strain relationship of the plastically deformed material, which agrees with the results of Naghdi and Trapp, is obtained

A method of solution of the elastic-plastic thermal stress problem

International Nuclear Information System (INIS)

Rafalski, P.

1975-01-01

The purpose of the work is an improvement of the numerical technique for calculating the thermal stress distribution in an elastic-plastic structural element. The work consists of two parts. In the first a new method of solution of the thermal stress problem for the elastic-plastic body is presented. In the second a particular numerical technique, based on the above method, for calculating the stress and strain fields is proposed. A new mathematical approach consists in treating the stress and strain fields as mathematical objects defined in the space-time domain. The methods commonly applied use the stress and strain fields defined in the space domain and establish the relations between them at a given instant t. They reduce the problem to the system of ordinary differential equations with respect to time, which are usually solved with a step-by-step technique. The new method reduces the problem to the system of nonlinear algebraic equations. In the work the Hilbert space of admissible tensor fields is constructed. This space is the orthogonal sum of two subspaces: of statically admissible and kinematically admissible fields. Two alternative orthogonality conditions, which correspond to the equilibrium and compatibility equations with the appropriate boundary conditions, are derived. The results of the work are to be used for construction of the computer program for calculation the stress and strain fields in the elastic-plastic body with a prescribed temperature field in the interior and appropriate displacement and force conditions on the boundary

Strain concentration at structural discontinuities and its quantification by elastic follow-up parameter

International Nuclear Information System (INIS)

Kasahara, Naoto; Takasho, Hideki

1998-12-01

Elevated temperature structural design codes pay attention to strain concentration at structural discontinuities due to creep and plasticity, since it causes to enlarge creep-fatigue damage of material. One of the difficulties to predict strain concentration is its dependency on loading, constitutive equations, and relaxation time. This study investigated fundamental mechanism of strain concentration and its main factors. It was clarified that strain concentration was caused from strain redistribution between elastic and inelastic regions, which can be quantified by the elastic follow-up parameter. As a function of inelastic strain, the elastic follow-up parameter can describe variation of strain concentration during incremental loading and relaxation process, caused by transition of strain distribution from peak strain concentration to secondary stress redistribution. Structures have their own elastic follow-up characteristics as a function of inelastic strain, which is insensitive to constitutive equations. It means that application of inelastic analysis is not difficult to obtain elastic follow-up characteristics. (author)

Elastic and elastic-plastic behaviour of a piping system during blowdown - Comparison of measurement and calculation

International Nuclear Information System (INIS)

Petruschke, W.; Strunk, G.

1987-01-01

The investigations according to the system identification show that the piping model using beam theory and flexibility factors according to the Karman theory are adequate for evaluating natural frequencies, mode shapes, static displacements and stresses. The same accuracy can be seen by comparing the piping response due to blowdown within the elastic range. The simplified elastic-plastic analysis in general overestimates the maximum amplitudes while the frequency content is not simulated very well. For practical purposes, it can be an adequate tool in many cases. The elastic-plastic analysis is the most expensive procedure but gives also the best results. The use of beam elements with multilinear moment-curvature relationships results in a good approximation for the global behaviour (displacements). The strains according to this theory only include the beam deformation modes

Effect of tensile properties on time-dependent C(t) and J(t) integrals in elastic-plastic-creep FE analysis

International Nuclear Information System (INIS)

Lee, So-Dam; Lee, Han-Sang; Kim, Yun-Jae; Ainsworth, Robert A.; Dean, David W.

2016-01-01

This technical note presents the effect of elastic-plastic properties on calculated time-dependent C(t) and J(t) values. This is investigated via systematic elastic-plastic-creep finite element (FE) analysis. Three different stress-strain curves are used, having essentially the same plastic properties at large strains but different tensile data near the 0.2% proof (yield) strength. It is found that the plastic property in stress-strain curve affects the FE C(t) values only at short times (within approximately 20% of the redistribution time). The plastic property affects the initial J values at time t = 0 but not the rate of change of J(t) with time. - Highlights: • The effect of elastic-plastic properties on calculated time-dependent C(t) and J(t) values is presented via FE analysis. • The plastic property affects the FE C(t) values only at short times up to ∼20% of the redistribution time. • The plastic property affects the initial J values at time t = 0 but not the rate of change of J(t) with time.

Elastic-plastic analysis of the SS-3 tensile specimen

International Nuclear Information System (INIS)

Majumdar, S.

1998-01-01

Tensile tests of most irradiated specimens of vanadium alloys are conducted using the miniature SS-3 specimen which is not ASTM approved. Detailed elastic-plastic finite element analysis of the specimen was conducted to show that, as long as the ultimate to yield strength ratio is less than or equal to 1.25 (which is satisfied by many irradiated materials), the stress-plastic strain curve obtained by using such a specimen is representative of the true material behavior

Elastic-Plastic Behavior of U6Nb under Ramp Wave Loading

International Nuclear Information System (INIS)

Hayes, D. B.; Gray, G. T. III; Hixson, R. S.; Hall, C. A.

2006-01-01

When uranium-niobium (6 wt.%) alloy is shock loaded, the expected elastic precursor is absent. A prior model attributed this absence to shear-induced twinning and the concomitant shear stress reduction that prevented the shocked material from reaching the plastic yield point. In the present study, carefully prepared U6Nb was subjected to shock loading to verify the adequacy of the prior model. Other samples were loaded with a ramp pressure pulse with strain rate large enough so that significant twinning would not occur during the experiment. Backward integration analyses of these latter experiments' back surface motion give stress-strain loading paths in U6Nb that suggest ordinary elastic-plastic flow. Some of the U6Nb was pre-strained by cold rolling in an effort to further ensure that twinning did not affect wave propagation. Shock and ramp loadings yielded similar results to the baseline material except, as expected, they are consistent with a higher yield stress and twinning shear stress threshold

Wireless measurement of elastic and plastic deformation by a metamaterial-based sensor.

Science.gov (United States)

Ozbey, Burak; Demir, Hilmi Volkan; Kurc, Ozgur; Erturk, Vakur B; Altintas, Ayhan

2014-10-20

We report remote strain and displacement measurement during elastic and plastic deformation using a metamaterial-based wireless and passive sensor. The sensor is made of a comb-like nested split ring resonator (NSRR) probe operating in the near-field of an antenna, which functions as both the transmitter and the receiver. The NSRR probe is fixed on a standard steel reinforcing bar (rebar), and its frequency response is monitored telemetrically by a network analyzer connected to the antenna across the whole stress-strain curve. This wireless measurement includes both the elastic and plastic region deformation together for the first time, where wired technologies, like strain gauges, typically fail to capture. The experiments are further repeated in the presence of a concrete block between the antenna and the probe, and it is shown that the sensing system is capable of functioning through the concrete. The comparison of the wireless sensor measurement with those undertaken using strain gauges and extensometers reveals that the sensor is able to measure both the average strain and the relative displacement on the rebar as a result of the applied force in a considerably accurate way. The performance of the sensor is tested for different types of misalignments that can possibly occur due to the acting force. These results indicate that the metamaterial-based sensor holds great promise for its accurate, robust and wireless measurement of the elastic and plastic deformation of a rebar, providing beneficial information for remote structural health monitoring and post-earthquake damage assessment.

Linking strain anisotropy and plasticity in copper metallization

International Nuclear Information System (INIS)

Murray, Conal E.; Jordan-Sweet, Jean; Priyadarshini, Deepika; Nguyen, Son

2015-01-01

The elastic anisotropy of copper leads to significant variation in the x-ray elastic constants (XEC), which link diffraction-based strain measurements to stress. An accurate depiction of the mechanical response in copper thin films requires a determination of an appropriate grain interaction model that lies between Voigt and Reuss limits. It is shown that the associated XEC weighting fraction, x*, between these limits provides a metric by which strain anisotropy can be quantified. Experimental values of x*, as determined by a linear regression scheme of diffraction data collected from multiple reflections, reveal the degree of strain anisotropy and its dependence on plastic deformation induced during in-situ and ex-situ thermal treatments

Elastic-Plastic Endochronic Constitutive Model of 0Crl7Ni4Cu4Nb Stainless Steels

Directory of Open Access Journals (Sweden)

Jinquan Guo

2016-01-01

Full Text Available We presented an elastic-plastic endochronic constitutive model of 0Crl7Ni4Cu4Nb stainless steel based on the plastic endochronic theory (which does not need the yield surface and experimental stress-strain curves. The key feature of the model is that it can precisely describe the relation of stress and strain under various loading histories, including uniaxial tension, cyclic loading-unloading, cyclic asymmetric-stress axial tension and compression, and cyclic asymmetric-stress axial tension and compression. The effects of both mean stress and amplitude of stress on hysteresis loop based on the elastic-plastic endochronic constitutive model were investigated. Compared with the experimental and calculated results, it is demonstrated that there was a good agreement between the model and the experiments. Therefore, the elastic-plastic endochronic constitutive model provides a method for the accurate prediction of mechanical behaviors of 0Crl7Ni4Cu4Nb stainless steel subjected to various loadings.

Elastic-plastic collapse of super-elastic shock waves in face-centered-cubic solids

International Nuclear Information System (INIS)

Zhakhovsky, Vasily V; Demaske, Brian J; Oleynik, Ivan I; Inogamov, Nail A; White, Carter T

2014-01-01

Shock waves in the [110] and [111] directions of single-crystal Al samples were studied using molecular dynamics (MD) simulations. Piston-driven simulations were performed to investigate the split shock-wave regime. At low piston velocities, the material is compressed initially to a metastable over-compressed elastic state leading to a super-elastic single shock wave. This metastable elastic state later collapses to a plastic state resulting in the formation of a two-wave structure consisting of an elastic precursor followed by a slower plastic wave. The single two-zone elastic-plastic shock-wave regime appearing at higher piston velocities was studied using moving window MD. The plastic wave attains the same average speed as the elastic precursor to form a single two-zone shock wave. In this case, repeated collapse of the highly over-compressed elastic state near the plastic shock front produces ultrashort triangle pulses that provide the pressure support for the leading elastic precursor.

Elastic-plastic-creep analysis of brazed carbon-carbon/OFHC divertor tile concepts for TPX

International Nuclear Information System (INIS)

Chin, E.; Reis, E.E.

1995-01-01

The 7.5 MW/m 2 heat flux requirements for the TPX divertor necessitate the use of high conductivity carbon-carbon (C-C) tiles that are brazed to annealed copper (OFHC) coolant tubes. Significant residual stresses are developed in the C-C tiles during the braze process due to large differences in the thermal expansion coefficients between these materials. Analyses which account for only the elastic-plastic strains developed in the OFHC tube may not accurately characterize the behavior of the tube during brazing. The elevated temperature creep behavior of the copper coolant tubes intuitively should reduce the calculated residual stresses in the C-C tiles. Two divertor tile concepts, the monoblock and the archblock, were analyzed for residual stress using 2-D finite element analysis for elastic-plastic-creep behavior of the OFHC tube during an assumed braze cooldown cycle. The results show that the inclusion of elevated temperature creep effects decrease the calculated residual stresses by only about 10% when compared to those analyses in which only elastic-plastic behavior of the OFHC is accounted for. The primary reason that creep effects at higher temperatures are not more significant is due to the low yield stress and nearly flat-top stress-strain curve of annealed OFHC. Since high temperature creep plays less of a role in the residual stress levels than previously thought, future scoping studies can be done in an elastic-plastic analysis with confidence that the stresses will be within approximately 10% of an elastic-plastic-creep analysis

Elastic-plastic code in the static regime for two-dimensional structures

International Nuclear Information System (INIS)

Giuliani, S.

1976-07-01

The finite-element computer code STEP-2D, which was conceived as a numerical tool for basic research in fracture mechanics presently under way in the Materials Division of JRC Ispra is described. The code employs 8-node isoparametric elements for calculating elastic-plastic stress and strain distributions in 2-D geometries. The von Mises yield criterion is used. Material strain hardening is described by means of either the isotropic or the so-called 'overlay' model. An incremental solution is employed in the plastic range. The program has been written in Fortran IV and compiled on an IBM 370-165

Elastic plastic fracture mechanics

International Nuclear Information System (INIS)

Simpson, L.A.

1978-07-01

The application of linear elastic fracture mechanics (LEFM) to crack stability in brittle structures is now well understood and widely applied. However, in many structural materials, crack propagation is accompanied by considerable crack-tip plasticity which invalidates the use of LEFM. Thus, present day research in fracture mechanics is aimed at developing parameters for predicting crack propagation under elastic-plastic conditions. These include critical crack-opening-displacement methods, the J integral and R-curve techniques. This report provides an introduction to these concepts and gives some examples of their applications. (author)

Special Features of Strain Localization and Nanodipoles of Partial Disclinations in the Region of Elastic Distortions

Science.gov (United States)

Tyumentsev, A. N.; Ditenberg, I. A.; Sukhanov, I. I.

2018-02-01

In the zones of strain localization in the region of elastic distortions and nanodipoles of partial disclinations representing the defects of elastically deformed medium, a theoretical analysis of the elastically stressed state and the energy of these defects, including the cases of their transformation into more complex ensembles of interrelated disclinations, is performed. Using the analytical results, the mechanisms of strain localization are discussed in the stages of nucleation and propagation of the bands of elastic and plastic strain localization formed in these zones (including the cases of nanocrystalline structure formation).

Analysis of Elastic-Plastic J Integrals for 3-Dimensional Cracks Using Finite Element Alternating Method

International Nuclear Information System (INIS)

Park, Jai Hak

2009-01-01

SGBEM(Symmetric Galerkin Boundary Element Method)-FEM alternating method has been proposed by Nikishkov, Park and Atluri. In the proposed method, arbitrarily shaped three-dimensional crack problems can be solved by alternating between the crack solution in an infinite body and the finite element solution without a crack. In the previous study, the SGBEM-FEM alternating method was extended further in order to solve elastic-plastic crack problems and to obtain elastic-plastic stress fields. For the elastic-plastic analysis the algorithm developed by Nikishkov et al. is used after modification. In the algorithm, the initial stress method is used to obtain elastic-plastic stress and strain fields. In this paper, elastic-plastic J integrals for three-dimensional cracks are obtained using the method. For that purpose, accurate values of displacement gradients and stresses are necessary on an integration path. In order to improve the accuracy of stress near crack surfaces, coordinate transformation and partitioning of integration domain are used. The coordinate transformation produces a transformation Jacobian, which cancels the singularity of the integrand. Using the developed program, simple three-dimensional crack problems are solved and elastic and elastic-plastic J integrals are obtained. The obtained J integrals are compared with the values obtained using a handbook solution. It is noted that J integrals obtained from the alternating method are close to the values from the handbook

Strain-based plastic instability acceptance criteria for ferritic steel safety class 1 nuclear components under level D

International Nuclear Information System (INIS)

Kim, Ji Su; Lee, Han Sang; Kim, Yun Jae; Kim, Jong Sung; Kim, Jin Won

2015-01-01

This paper proposes strain-based acceptance criteria for assessing plastic instability of the safety class 1 nuclear components made of ferritic steel during level D service loads. The strain-based criteria were proposed with two approaches: (1) a section average approach and (2) a critical location approach. Both approaches were based on the damage initiation point corresponding to the maximum load-carrying capability point instead of the fracture point via tensile tests and finite element analysis (FEA) for the notched specimen under uni-axial tensile loading. The two proposed criteria were reviewed from the viewpoint of design practice and philosophy to select a more appropriate criterion. As a result of the review, it was found that the section average approach is more appropriate than the critical location approach from the viewpoint of design practice and philosophy. Finally, the criterion based on the section average approach was applied to a simplified reactor pressure vessel (RPV) outlet nozzle subject to SSE loads. The application shows that the strain-based acceptance criteria can consider cumulative damages caused by the sequential loads unlike the stress-based acceptance criteria and can reduce the over conservatism of the stress-based acceptance criteria, which often occurs for level D service loads.

Strain-based plastic instability acceptance criteria for ferritic steel safety class 1 nuclear components under level D

Energy Technology Data Exchange (ETDEWEB)

Kim, Ji Su; Lee, Han Sang; Kim, Yun Jae [Dept. of Mechanical Engineering, Korea University, Seoul (Korea, Republic of); Kim, Jong Sung [Dept. of Mechanical Engineering, Sunchon National University, Suncheon (Korea, Republic of); Kim, Jin Won [Dept. of Nuclear Engineering, Chosun University, Gwangju (Korea, Republic of)

2015-04-15

This paper proposes strain-based acceptance criteria for assessing plastic instability of the safety class 1 nuclear components made of ferritic steel during level D service loads. The strain-based criteria were proposed with two approaches: (1) a section average approach and (2) a critical location approach. Both approaches were based on the damage initiation point corresponding to the maximum load-carrying capability point instead of the fracture point via tensile tests and finite element analysis (FEA) for the notched specimen under uni-axial tensile loading. The two proposed criteria were reviewed from the viewpoint of design practice and philosophy to select a more appropriate criterion. As a result of the review, it was found that the section average approach is more appropriate than the critical location approach from the viewpoint of design practice and philosophy. Finally, the criterion based on the section average approach was applied to a simplified reactor pressure vessel (RPV) outlet nozzle subject to SSE loads. The application shows that the strain-based acceptance criteria can consider cumulative damages caused by the sequential loads unlike the stress-based acceptance criteria and can reduce the over conservatism of the stress-based acceptance criteria, which often occurs for level D service loads.

Mechanical behaviour of nanoparticles: Elasticity and plastic ...

Indian Academy of Sciences (India)

2015-06-03

Jun 3, 2015 ... Mechanical behaviour of nanoparticles: Elasticity and plastic deformation mechanisms ... The main results in terms of elasticity and plastic deformation mechanisms are then reported ... Pramana – Journal of Physics | News.

Mesoscopic approach to modeling elastic-plastic polycrystalline material behaviour

International Nuclear Information System (INIS)

Kovac, M.; Cizelj, L.

2001-01-01

Extreme loadings during severe accident conditions might cause failure or rupture of the pressure boundary of a reactor coolant system. Reliable estimation of the extreme deformations can be crucial to determine the consequences of such an accident. One of important drawbacks of classical continuum mechanics is idealization of inhomogenous microstructure of materials. This paper discusses the mesoscopic approach to modeling the elastic-plastic behavior of a polycrystalline material. The main idea is to divide the continuum (e.g., polycrystalline aggregate) into a set of sub-continua (grains). The overall properties of the polycrystalline aggregate are therefore determined by the number of grains in the aggregate and properties of randomly shaped and oriented grains. The random grain structure is modeled with Voronoi tessellation and random orientations of crystal lattices are assumed. The elastic behavior of monocrystal grains is assumed to be anisotropic. Crystal plasticity is used to describe plastic response of monocrystal grains. Finite element method is used to obtain numerical solutions of strain and stress fields. The analysis is limited to two-dimensional models.(author)

Elastic Plastic Fracture Analysis of an Aluminum COPV Liner

Science.gov (United States)

Forth, Scott; Gregg, Bradley; Bailey, Nathaniel

2012-01-01

Onboard any space-launch vehicle, composite over-wrapped pressure vessels (COPVs) may be utilized by propulsion or environmental control systems. The failure of a COPV has the potential to be catastrophic, resulting in the loss of vehicle, crew or mission. The latest COPV designs have reduced the wall-thickness of the metallic liner to the point where the material strains plastically during operation. At this time, the only method to determine the damage tolerance lifetime (safe-life) of a plastically responding metallic liner is through full-scale COPV testing. Conducting tests costs substantially more and can be far more time consuming than performing an analysis. As a result of this cost, there is a need to establish a qualifying process through the use of a crack growth analysis tool. This paper will discuss fracture analyses of plastically responding metallic liners in COPVs. Uni-axial strain tests have been completed on laboratory specimens to collect elastic-plastic crack growth data. This data has been modeled with the crack growth analysis tool, NASGRO 6.20 to predict the response of laboratory specimens and subsequently the complexity of a COPV.

A study of microindentation hardness tests by mechanism-based strain gradient plasticity

International Nuclear Information System (INIS)

Huang, Y.; Xue, Z.; Gao, H.; Nix, W. D.; Xia, Z. C.

2000-01-01

We recently proposed a theory of mechanism-based strain gradient (MSG) plasticity to account for the size dependence of plastic deformation at micron- and submicron-length scales. The MSG plasticity theory connects micron-scale plasticity to dislocation theories via a multiscale, hierarchical framework linking Taylor's dislocation hardening model to strain gradient plasticity. Here we show that the theory of MSG plasticity, when used to study micro-indentation, indeed reproduces the linear dependence observed in experiments, thus providing an important self-consistent check of the theory. The effects of pileup, sink-in, and the radius of indenter tip have been taken into account in the indentation model. In accomplishing this objective, we have generalized the MSG plasticity theory to include the elastic deformation in the hierarchical framework. (c) 2000 Materials Research Society

Finite element elastic-plastic analysis of LMFBR components

International Nuclear Information System (INIS)

Levy, A.; Pifko, A.; Armen, H. Jr.

1978-01-01

The present effort involves the development of computationally efficient finite element methods for accurately predicting the isothermal elastic-plastic three-dimensional response of thick and thin shell structures subjected to mechanical and thermal loads. This work will be used as the basis for further development of analytical tools to be used to verify the structural integrity of liquid metal fast breeder reactor (LMFBR) components. The methods presented here have been implemented into the three-dimensional solid element module (HEX) of the Grumman PLANS finite element program. These methods include the use of optimal stress points as well as a variable number of stress points within an element. This allows monitoring the stress history at many points within an element and hence provides an accurate representation of the elastic-plastic boundary using a minimum number of degrees of freedom. Also included is an improved thermal stress analysis capability in which the temperature variation and corresponding thermal strain variation are represented by the same functional form as the displacement variation. Various problems are used to demonstrate these improved capabilities. (Auth.)

Elastic-plastic analysis of an axi-symmetric problem by a finite element method

International Nuclear Information System (INIS)

Isozaki, Toshikuni

1984-06-01

Generally speaking, many structures are designed and fabricated on the basis of an axi-symmetric structure. Finite Element Method is the capable method to solve these axi-symmetric problems beyond the elastic limit. As the first step to solve these problems, the computer program for the elastic-plastic analysis of the axi-symmetric problem is composed. The basic program is based upon that described in Zienkiewicz's text book to solve the elastic plane stress problem, taking the plastic stress matrix by Yamada's method into consideration and it is converted to solve the axi-symmetric problem. For the verification of the program, the plane strain problem of a cylindrical tube under internal pressure was solved. The computed results were compared with those shown in ADINA's user's manual. They showed close agreement. (author)

On crack interaction effects of in-plane surface cracks using elastic and elastic-plastic finite element analyses

International Nuclear Information System (INIS)

Kim, Jong Min; Huh, Nam Su

2010-01-01

The crack-tip stress fields and fracture mechanics assessment parameters for a surface crack, such as the elastic stress intensity factor or the elastic-plastic J-integral, can be affected significantly by the adjacent cracks. Such a crack interaction effect due to multiple cracks can alter the fracture mechanics assessment parameters significantly. There are many factors to be considered, for instance the relative distance between adjacent cracks, the crack shape, and the loading condition, to quantify the crack interaction effect on the fracture mechanics assessment parameters. Thus, the current assessment codes on crack interaction effects (crack combination rules), including ASME Sec. XI, BS7910, British Energy R6 and API 579-1/ASME FFS-1, provide different rules for combining multiple surface cracks into a single surface crack. The present paper investigates crack interaction effects by evaluating the elastic stress intensity factor and the elastic-plastic J-integral of adjacent in-plane surface cracks in a plate through detailed 3-dimensional elastic and elastic-plastic finite element analyses. The effects on the fracture mechanics assessment parameters of the geometric parameters, the relative distance between two cracks, and the crack shape are investigated systematically. As for the loading condition, an axial tension is considered. Based on the finite element results, the acceptability of the crack combination rules provided in the existing guidance was investigated, and the relevant recommendations on a crack interaction for in-plane surface cracks are discussed. The present results can be used to develop more concrete guidance on crack interaction effects for crack shape characterization to evaluate the integrity of defective components

The effect of martensite plasticity on the cyclic deformation of super-elastic NiTi shape memory alloy

International Nuclear Information System (INIS)

Song, Di; Kang, Guozheng; Kan, Qianhua; Yu, Chao; Zhang, Chuanzeng

2014-01-01

Based on stress-controlled cyclic tension–unloading experiments with different peak stresses, the effect of martensite plasticity on the cyclic deformation of super-elastic NiTi shape memory alloy micro-tubes is investigated and discussed. The experimental results show that the reverse transformation from the induced martensite phase to the austenite phase is gradually restricted by the plastic deformation of the induced martensite phase caused by an applied peak stress that is sufficiently high (higher than 900 MPa), and the extent of such restriction increases with further increasing the peak stress. The residual and peak strains of super-elastic NiTi shape memory alloy accumulate progressively, i.e., transformation ratchetting occurs during the cyclic tension–unloading with peak stresses from 600 to 900 MPa, and the transformation ratchetting strain increases with the increase of the peak stress. When the peak stress is higher than 900 MPa, the peak strain becomes almost unchanged, but the residual strain accumulates and the dissipation energy per cycle decreases very quickly with the increasing number of cycles due to the restricted reverse transformation by the martensite plasticity. Furthermore, a quantitative relationship between the applied stress and the stabilized residual strain is obtained to reasonably predict the evolution of the peak strain and the residual strain. (paper)

Grain-resolved elastic strains in deformed copper measured by three-dimensional X-ray diffraction

DEFF Research Database (Denmark)

Oddershede, Jette; Schmidt, Søren; Poulsen, Henning Friis

2011-01-01

This X-ray diffraction study reports the grain-resolved elastic strains in about 1000 randomly oriented grains embedded in a polycrystalline copper sample. Diffraction data were collected in situ in the undeformed state and at a plastic strain of 1.5% while the sample was under tensile load...

Elastic-plastic failure analysis of pressure burst tests of thin toroidal shells

International Nuclear Information System (INIS)

Jones, D.P.; Holliday, J.E.; Larson, L.D.

1998-07-01

This paper provides a comparison between test and analysis results for bursting of thin toroidal shells. Testing was done by pressurizing two toroidal shells until failure by bursting. An analytical criterion for bursting is developed based on good agreement between structural instability predicted by large strain-large displacement elastic-plastic finite element analysis and observed burst pressure obtained from test. The failures were characterized by loss of local stability of the membrane section of the shells consistent with the predictions from the finite element analysis. Good agreement between measured and predicted burst pressure suggests that incipient structural instability as calculated by an elastic-plastic finite element analysis is a reasonable way to calculate the bursting pressure of thin membrane structures

Two-zone elastic-plastic single shock waves in solids.

Science.gov (United States)

Zhakhovsky, Vasily V; Budzevich, Mikalai M; Inogamov, Nail A; Oleynik, Ivan I; White, Carter T

2011-09-23

By decoupling time and length scales in moving window molecular dynamics shock-wave simulations, a new regime of shock-wave propagation is uncovered characterized by a two-zone elastic-plastic shock-wave structure consisting of a leading elastic front followed by a plastic front, both moving with the same average speed and having a fixed net thickness that can extend to microns. The material in the elastic zone is in a metastable state that supports a pressure that can substantially exceed the critical pressure characteristic of the onset of the well-known split-elastic-plastic, two-wave propagation. The two-zone elastic-plastic wave is a general phenomenon observed in simulations of a broad class of crystalline materials and is within the reach of current experimental techniques.

ACCEPT: a three-dimensional finite element program for large deformation elastic-plastic-creep analysis of pressurized tubes (LWBR/AWBA Development Program)

International Nuclear Information System (INIS)

Hutula, D.N.; Wiancko, B.E.

1980-03-01

ACCEPT is a three-dimensional finite element computer program for analysis of large-deformation elastic-plastic-creep response of Zircaloy tubes subjected to temperature, surface pressures, and axial force. A twenty-mode, tri-quadratic, isoparametric element is used along with a Zircaloy materials model. A linear time-incremental procedure with residual force correction is used to solve for the time-dependent response. The program features an algorithm which automatically chooses the time step sizes to control the accuracy and numerical stability of the solution. A contact-separation capability allows modeling of interaction of reactor fuel rod cladding with fuel pellets or external supports

In-situ measurement of texture and elastic strains with HIPPO-CRATES

International Nuclear Information System (INIS)

Hartig, Ch.; Vogel, S.C.; Mecking, H.

2006-01-01

In this paper, the micromechanical interaction between constituents of a metallic material during elastic and plastic deformation are analyzed by comparing experimental results with modeling predictions. This comparison aims at determining the locally acting internal stresses, the spatial distribution of strains and the rules allowing deriving the macroscopic behavior of the material from the behavior of its microscopic constituents. We report the application of a new deformation apparatus CRATES, which allows measuring texture and crystal lattice spacings, and from these crystal lattice strains, using neutron diffraction. From the in-situ measured elastic lattice strains ε hkl the corresponding local stresses can be derived. The deformation apparatus allows uni-axial tensile or compressive deformation up to 100 kN and is specifically designed for use in the HIPPO neutron time-of-flight diffractometer. In this paper, we report initial results on an iron-copper model system (Fe100, Fe33Cu67, Fe67Cu33, vol.%) and commercial magnesium alloys (Mg-AZ31 and Mg-AZ80). Finite element calculations using a crystal-plastic constitutive law, allowing for shear and hardening of crystallographic slip-systems, were used for the interpretation of the measurements

Elastic-plastic and creep analyses by assumed stress finite elements

International Nuclear Information System (INIS)

Pian, T.H.H.; Spilker, R.L.; Lee, S.W.

1975-01-01

A formulation is presented of incremental finite element solutions for both initial stress and initial strain problems based on modified complementary energy principle with relaxed inter-element continuity requirement. The corresponding finite element model is the assumed stress hybrid model which has stress parameters in the interior of each element and displacements at the individual nodes as unknowns. The formulation includes an important consideration that the states of stress and strain and the beginning of each increment may not satisfy the equilibrium and compatibility equations. These imbalance and mismatch conditions all lead to correction terms for the equivalent nodal forces of the matrix equations. The initial stress method is applied to elastic-plastic analysis of structures. In this case the stress parameters for the individual elements can be eliminated resulting to a system of equations with only nodal displacements as unknowns. Two different complementary energy principles can be formulated, in one of which the equilibrium of the final state of stress is maintained while in the other the equilibrium of the stress increments is maintained. Each of these two different formulations can be combined with different iterative schemes to be used at each incremental steps of the elastic-plastic analysis. It is also indicated clearly that for the initial stress method the state of stress at the beginning of each increments is in general, not in equilibrium and an imbalance correction is needed. Results of a comprehensive evaluation of various solution procedures by the initial stress method using the assumed stress hybrid elements are presented. The example used is the static response of a thick wall cylinder of elastic-perfectly plastic material under internal pressure. Solid of revolution elements with rectangular cross sections are used

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

DEFF Research Database (Denmark)

Goutianos, Stergios

2011-01-01

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...

The behavior of intermetallic compounds at large plastic strains

International Nuclear Information System (INIS)

Gray, G.T.; Embury, J.D.

1993-01-01

This paper contains a summary of a broad study of intermetallics which includes the following materials, Ni 3 Al, Ti-48Al-1V, Ti-24Al-11Nb, Ti-48Al-2Cr-2Nb, and Ti-24.5 Al-10.5Nb-1.5Mo. Much effort has been devoted to the study of ordered materials at modes plastic strains and the problem of premature failure. However by utilizing stress states other than simple tension it is possible to study the deformation of intermetallic compounds up to large plastic strains and to consider the behavior of these materials in the regime where stresses approach the theoretical stress. The current work outlines studies of the work hardening rate of a number of titanium and nickel-based intermetallic compounds deformed in compression. Attention is given to the structural basis of the sustained work hardening. The large strain plasticity of these materials is summarized in a series of diagrams. Fracture in these materials in compression occurs via catastrophic shear at stresses of the order of E/80 (where E is the elastic modulus)

Finite element implementation of strain-hardening Drucker–Prager plasticity model with application to tunnel excavation

Directory of Open Access Journals (Sweden)

K. Liu

2017-09-01

Full Text Available This paper presents a finite element implementation of a strain-hardening Drucker–Prager model and its application to tunnel excavation. The computational model was constructed based on the return mapping scheme, in which an elastic trial step was first executed, followed by plastic correction involving the Newton–Raphson method to return the predicted state of stresses to the supposed yield surface. By combining the plastic shear hardening rule and stress correction equations, the loading index for the strain-hardening Drucker–Prager model was solved. It is therefore possible to update the stresses, elastic and plastic strains, and slope of the yield locus at the end of each incremental step. As an illustrative example, an integration algorithm was incorporated into ABAQUS through the user subroutine UMAT to solve the tunnel excavation problem in strain-hardening Drucker–Prager rock formations. The obtained numerical results were found to be in excellent agreement with the available analytical solutions, thus indicating the validity and accuracy of the proposed UMAT code, as well as the finite element model.

Semi-exact solution of non-uniform thickness and density rotating disks. Part II: Elastic strain hardening solution

International Nuclear Information System (INIS)

Hojjati, M.H.; Jafari, S.

2009-01-01

Analytical solutions for the elastic-plastic stress distribution in rotating annular disks with uniform and variable thicknesses and densities are obtained under plane stress assumption. The solution employs a technique called the homotopy perturbation method. A numerical solution of the governing differential equation is also presented based on the Runge-Kutta's method for both elastic and plastic regimes. The analysis is based on Tresca's yield criterion, its associated flow rule and linear strain hardening. The results of the two methods are compared and generally show good agreement. It is shown that, depending on the boundary conditions used, the plastic core may contain one, two or three different plastic regions governed by different mathematical forms of the yield criterion. Four different stages of elastic-plastic deformation occur. The expansion of these plastic regions with increasing angular velocity is obtained together with the distributions of stress and displacement

Basic Strain Gradient Plasticity Theories with Application to Constrained Film Deformation

DEFF Research Database (Denmark)

Niordson, Christian Frithiof; Hutchinson, John W.

2011-01-01

films: the compression or extension of a finite layer joining rigid platens. Full elastic-plastic solutions are obtained for the same problem based on a finite element method devised for the new class of flow theories. Potential difficulties and open issues associated with the new class of flow theories......A family of basic rate-independent strain gradient plasticity theories is considered that generalize conventional J(2) deformation and flow theories of plasticity to include a dependence on strain gradients in a simple way. The theory builds on three recent developments: the work of Gudmundson (J....... Mech. Phys. Solids 52 (2004), 1379-1406) and Gurtin and Anand (J. Mech. Phys. Solids 57 (2009), 405-421), proposing constitutive relations for flow theories consistent with requirements of positive plastic dissipation; the work of Fleck and Willis (J. Mech. Phys. Solids 57 (2009), 161-177 and 1045...

On lower order strain gradient plasticity theories

DEFF Research Database (Denmark)

Niordson, Christian Frithiof; Hutchinson, J. W.

2003-01-01

By way of numerical examples, this paper explores the nature of solutions to a class of strain gradient plasticity theories that employ conventional stresses, equilibrium equations and boundary conditions. Strain gradients come into play in these modified conventional theories only to alter...... the tangent moduli governing increments of stress and strain. It is shown that the modification is far from benign from a mathematical standpoint, changing the qualitative character of solutions and leading to a new type of localization that is at odds with what is expected from a strain gradient theory....... The findings raise questions about the physical acceptability of this class of strain gradient theories....

Shear banding in large strain plasticity - Influence of specimen dimensions

Science.gov (United States)

Mucha, Marzena; Wcisło, Balbina; Pamin, Jerzy

2018-01-01

The paper deals with numerical analysis of shear banding which occurs in an elongated rectangular plate for a large strain elastic-plastic material model. It is focused on the influence of plate size proportions and finite element mesh density on numerical results. The discussion is limited to isothermal conditions and ideal plasticity. First a plain strain case is computed for different lengths of the plate, then simulations are repeated for plane stress for which different thicknesses of the plate are considered. Most of the computations are performed for three finite element meshes to verify discretization sensitivity of the results. The simulations are performed using AceGen and AceFEM packages for Wolfram Mathematica.

Elastic-plastic response of a piping system due to simulated double-ended guillotine break events

International Nuclear Information System (INIS)

Kussmaul, K.; Diem, H.; Hunger, H.; Katzenmeier, G.

1987-01-01

From the blowdown experiments performed on the HDR feedwater line with feedwater check valve the conclusion can be drawn that high transient loads of up to plastic strains of 3%, acting on an initially integer piping system, can be sustained without loss of integrity for a low number of load cycles due to the plasticizing capacity of the pipework materials nowadays used in the reactor technology. In the experiments carried out with ferritic piping of ND 400 pressure peaks up to about 31,5 mPA were achieved which resulted in excessive strains of up to 3%. By nonlinear finite element computations (ABAQUS) it was possible to describe the elastic-plastic behaviour of the piping in a good approximation. On account of the safety margins proved in the experiments, potential inaccuracies in theoretical structure analyses are recommended so as to be on the safe side. On the other hand, it appears that designing pipework with reference to elastic stress categories does not adequately take into account the actual reserves of the pipework material

A study on plastic strain accumulation caused by traveling of temperature distribution synchronizing with temperature rise

International Nuclear Information System (INIS)

Okajima, Satoshi

2016-01-01

The prevention of excessive deformation by thermal ratcheting is important in the design of high-temperature components of fast breeder reactors (FBR). This includes evaluation methods for a new type of thermal ratcheting caused by an axial traveling of temperature distribution, which corresponds to moving-up of liquid sodium surface in startup phase. Long range traveling of the axial temperature distribution brings flat plastic deformation profile in wide range. Therefore, at the center of this range, residual stress that brings shakedown behavior does not accumulate. As a result, repeating of this temperature traveling brings continuous accumulation of the plastic strain, even if there is no primary stress. In contrast, in the case with short range traveling, residual stress is caused by constraint against elastic part, and finally it results in shakedown. Because of this mechanism, we supposed that limit for the shakedown behavior depends on distance from the elastic part (i.e. half length of region with plastic deformation). In this paper, we examined characteristics of the accumulation of the plastic strain caused by realistic heat transients, namely, traveling of temperature distribution synchronizing with temperature rise. This examination was based on finite element analyses using elastic-perfectly plastic material. As a result, we confirmed that the shakedown limit depends not on the traveling range of the temperature distribution but the plastic deformation range, which was predicted by the elastic analysis. In the actual application, we can control the plastic deformation range by changing rate of the moving-up of liquid sodium surface. (author)

Elastic-plastic response of a piping system due to simulated double-ended guillotine break events

International Nuclear Information System (INIS)

Kussmaul, K.; Diem, H.; Hunger, H.; Katzenmeier, G.

1987-01-01

From the blowdown experiments performed on the HDR feedwater line with feedwater check valve the conclusion can be drawn that high transient loads of up to plastic strains of 3%, acting on an initially integer piping system, can be sustained without loss of integrity for a low number of load cycles due to the plasticizing capacity of the pipework materials nowadays used in reactor technology. In the experiments carried out with ferritic piping of ND 400 pressure peaks up to about 31,5 MPa were achieved which resulted in excessive strains of up to 3%. By nonlinear finite element computations (ABAQUS) it was possible to describe the elastic-plastic behaviour of the piping in a good approximation. (orig./GL)

Electrical resistivity response due to elastic-plastic deformations

International Nuclear Information System (INIS)

Stout, R.B.

1987-01-01

The electrical resistivity of many materials is sensitive to changes in the electronic band configurations surrounding the atoms, changes in the electron-phonon interaction cross-sections, and changes in the density of intrinsic defect structures. These changes are most directly dependent on interatomic measures of relative deformation. For this reason, a model for resistivity response is developed in terms of interatomic measures of relative deformation. The relative deformation consists of two terms, a continuous function to describe the recoverable displacement between two atoms in the atomic lattice structure and a functional to describe the nonrecoverable displacement between two atoms as a result of interatomic discontinuities from dislocation kinetics. This model for resistivity extends the classical piezoresistance representation and relates electric resistance change directly to physical mechanisms. An analysis for the resistivity change of a thin foil ideally embedded in a material that undergoes elastic-plastic deformation is presented. For the case of elastic deformations, stress information in the material surrounding the thin foil is inferred for the cases of pure strain coupling boundary conditions, pure stress coupling boundary conditions, and a combination of stress-strain coupling boundary conditions. 42 refs., 4 figs

Dynamic elastic-plastic response of a 2-DOF mass-spring system.

Energy Technology Data Exchange (ETDEWEB)

Corona, Edmundo [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2018-02-01

The objective of the work presented here arose from abnormal, drop scenarios and specifically the question of how the accelerations and accumulation of plastic strains of internal components could be a ected by the material properties of the external structure. In some scenarios, the impact loads can induce cyclic motion of the internal components. Therefore, a second objective was to explore di erences that could be expected when simulations are conducted using isotropic hardening vs. kinematic hardening plasticity models. The simplest model that can be used to investigate the objectives above is a two-degree-offreedom mass/spring model where the springs exhibit elastic-plastic behavior. The purpose of this memo is to develop such model and present a few results that address the objectives.

Low temperature uniform plastic deformation of metallic glasses during elastic iteration

International Nuclear Information System (INIS)

Fujita, Takeshi; Wang Zheng; Liu Yanhui; Sheng, Howard; Wang Weihua; Chen Mingwei

2012-01-01

Molecular dynamics simulations and dynamic mechanical analysis experiments were employed to investigate the mechanical behavior of metallic glasses subjected to iteration deformation in a nominally elastic region. It was found that cyclic deformation leads to the formation of irreversible shear transformation zones (STZs) and a permanent uniform strain. The initiation of STZs is directly correlated with the atomic heterogeneity of the metallic glass and the accumulated permanent strain has a linear relation with the number of STZs. This study reveals a new deformation mode and offers insights into the atomic mechanisms of STZ formation and low temperature uniform plastic deformation of metallic glasses.

Microcracking and Healing in Semibrittle Salt-Rock: Elastic and Plastic Behavior

Science.gov (United States)

Ding, J.; Chester, F. M.; Chester, J. S.; Shen, X.; Arson, C. F.

2017-12-01

Microcracking and healing during semibrittle deformation are important processes that affect physical properties such as elastic moduli and permeability. We study these processes through triaxial compression tests involving cyclic differential loading and isostatic-holds on synthetic salt-rock at room temperature and low confining pressure (Pc, 1 to 4 MPa). The salt samples are produced by uniaxial pressing of granular (300 µm dia.) halite to 75 MPa at 150˚C for 10^3 s, to create low-porosity ( 5%) aggregates of nearly equant, work-hardened grains. Alternating large- and small-load cycles are performed to track the evolution of plastic and elastic properties, respecitively, with progressive strain to 8% axial shortening. 24-hour holds are carried out at about 4% axial shortening followed by renewed cyclic loading to investigate healing. During large load cycles samples yield and exhibit distributed flow with dilatancy and small work hardening. Young's Modulus (YM) decreases and then tends to stabilize, while Poisson's Ratio (PR) increases at a reducing rate, with progressive strain. Microstructures at sequential stages show that opening-mode grain-boundary cracking, grain-boundary sliding, and some intracrystalline plasticity are the dominant deformation processes. Opening and shear occur preferentially on boundaries that are parallel and inclined to the shortening axis, respectively, leading to progressive redistribution of porosity. Opening-mode grain-boundary cracks increase in number and aperature with strain, and are linked by sliding grain-boundaries to form en echelon arrays. After a 24-hour hold, samples show yielding and flow behavior consistent with that prior to the hold, whereas YM and PR are reset to the same values documented at zero strain and subsequently evolve with additional strain similar to that documented at smaller strains prior to the hold. Open grain-boundary cracks are not closed or healed during the hold. Observations suggest that

Structural evaluation method for class 1 vessels by using elastic-plastic finite element analysis in code case of JSME rules on design and construction

International Nuclear Information System (INIS)

Asada, Seiji; Hirano, Takashi; Nagata, Tetsuya; Kasahara, Naoto

2008-01-01

A structural evaluation method by using elastic-plastic finite element analysis has been developed and published as a code case of Rules on Design and Construction for Nuclear Power Plants (The First Part: Light Water Reactor Structural Design Standard) in the JSME Codes for Nuclear Power Generation Facilities. Its title is 'Alternative Structural Evaluation Criteria for Class 1 Vessels Based on Elastic-Plastic Finite Element Analysis' (NC-CC-005). This code case applies elastic-plastic analysis to evaluation of such failure modes as plastic collapse, thermal ratchet, fatigue and so on. Advantage of this evaluation method is free from stress classification, consistently use of Mises stress and applicability to complex 3-dimensional structures which are hard to be treated by the conventional stress classification method. The evaluation method for plastic collapse has such variation as the Lower Bound Approach Method, Twice-Elastic-Slope Method and Elastic Compensation Method. Cyclic Yield Area (CYA) based on elastic analysis is applied to screening evaluation of thermal ratchet instead of secondary stress evaluation, and elastic-plastic analysis is performed when the CYA screening criteria is not satisfied. Strain concentration factors can be directly calculated based on elastic-plastic analysis. (author)

Diverging strains near threshold: Breakdown of the elastic description of a charge density wave model

International Nuclear Information System (INIS)

Mungan, M.; Coppersmith, S.; Vinokur, V.M.

1999-01-01

We analyze the strains near threshold in 1-d charge density wave models at zero temperature and strong pinning. We show that in these models local strains diverge near the depinning threshold and characterize the scaling behavior of the phenomenon. This helps quantify when the underlying elastic description breaks down and plastic effects have to be included

Elastic-Plastic Calculation of a Dilatation Compensation Component

Science.gov (United States)

Atanasiu, Costică; Iliescu, Nicolae; Sorohan, Ștefan

2017-12-01

Compensators are elastic structures that have the role of taking over the axial displacements that occur in the junction areas of the technological equipment (pipelines or containers) through which the fluids circulate at pressures and high temperatures. These elastic structures, realized in a very wide range of shapes and sizes, are sujected by the inner pressure and an axial force produced by dilatation of structures in which they are mounted. The calculation of the expansion compensators raises many problems caused by the working regimes of the technological equipments they belong to. Following previous studies, undertaken by calculus and experimental, by the authors of this paper, it was found that in operation the state of stress in these elastic structures exceeds the flow limit of the material from which they are manufacturated. For this reason, in the present paper, the authors present the results of a calculus study, by FEM, on the stress and strain state, in the elasto-plastic regime of a leticular compensator. The calculation was made for two loading modes, separately applied and superimposed. The nonlinear mechanical behavior of this compensator is analyzed and discussed comparatively to the results of previous studies performed in elastic regime on the same type of compensator.

Plastic incompatibility stresses and stored elastic energy in plastically deformed copper

Energy Technology Data Exchange (ETDEWEB)

Baczmanski, A. [Faculty of Physics and Applied Computer Science, AGH-University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow (Poland)], E-mail: baczman@ftj.agh.edu.pl; Hfaiedh, N.; Francois, M. [LASMIS, Universite de Technologie de Troyes, 11 rue Marie Curie, B.P. 2060, 10010 Troyes (France); Wierzbanowski, K. [Faculty of Physics and Applied Computer Science, AGH-University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow (Poland)

2009-02-15

The X-ray diffraction method and theoretical model of elastoplastic deformation were used to examine the residual stresses in polycrystalline copper. To this end, the {l_brace}2 2 0{r_brace} strain pole figures were determined for samples subjected to different magnitudes of tensile deformation. Using diffraction data and the self-consistent model, the tensor of plastic incompatibility stress was found for each orientation of a polycrystalline grain. Crystallographic textures, macroscopic and second-order residual stresses were considered in the analysis. As a result, the distributions of elastic stored energy and von Mises equivalent stress were presented in Euler space and correlated with the preferred orientations of grains. Moreover, using the model prediction, the variation of the critical resolved shear stress with grain orientation was determined.

Adhesive friction for elastic-plastic contacting rough surfaces considering asperity interaction

International Nuclear Information System (INIS)

Sahoo, Prasanta

2006-01-01

The paper describes a theoretical study of adhesive friction at the contact between rough surfaces taking asperity interaction into consideration and using an elastic-plastic model of contact deformation that is based on an accurate finite element analysis of an elastic-plastic single asperity contact. The micro-contact model of asperity interactions, developed by Zhao and Chang, is integrated into the improved elastic-plastic rough surface adhesive contact analysis to consider the adhesive friction behaviour of rough surfaces. The model considers a large range of interference values from fully elastic through elastic-plastic to fully plastic regimes of contacting asperities. Two well-established adhesion indices are used to consider different conditions that arise as a result of varying load, surface and material parameters. Results are obtained for the coefficient of friction against applied load for various combinations of these parameters. The results show that the coefficient of friction depends strongly on the applied load for the no-interaction case while it becomes insensitive to the load for interaction consideration. Moreover, the inclusion of elastic-plastic asperities further reduces the friction coefficient

Analytical solution for stress, strain and plastic instability of pressurized pipes with volumetric flaws

International Nuclear Information System (INIS)

Cunha, Sérgio B.; Netto, Theodoro A.

2012-01-01

The mechanical behavior of internally pressurized pipes with volumetric flaws is analyzed. The two possible modes of circumferentially straining the pipe wall are identified and associated to hypothesized geometries. The radial deformation that takes place by bending the pipe wall is studied by means of axisymmetric flaws and the membrane strain developed by unequal hoop deformation is analyzed with the help of narrow axial flaws. Linear elastic shell solutions for stress and strain are developed, the plastic behavior is studied and the maximum hoop stress at the flaw is related to the undamaged pipe hoop stress by means of stress concentration factors. The stress concentration factors are employed to obtain equations predicting the pressure at which the pipe fails by plastic instability for both types of flaw. These analytical solutions are validated by comparison with burst tests on 3″ diameter pipes and finite element simulations. Forty-one burst tests were carried out and two materials with very dissimilar plastic behavior, carbon steel and austenitic stainless steel, were used in the experiments. Both the analytical and the numerical predictions showed good correlation with the experimentally observed burst pressures. - Highlights: ► An analytical model for the burst of a pipe with a volumetric flaw is developed. ► Deformation, strain and stress are modeled in the elastic and plastic domains. ► The model is comprehensively validated by experiments and numerical simulations. ► The burst pressure model’s accuracy is equivalent to finite element simulations.

Elastic-plastic-creep analysis of shells

International Nuclear Information System (INIS)

Pai, D.H.

1979-01-01

This paper presents the recent experience of a designer/fabricator of nuclear heat transport components in the area of elastic-plastic-creep analysis of shell-like structures. A brief historical perspective is first given to highlight the evolution leading to the present industry practice. The ASME elevated temperature design criteria will be discussed followed by examples of actual computations performed to support the design/analysis and fabrication of a breeder reactor component in which a substantial amount of elastic-plastic-creep analysis was performed. Mathematical challenges encountered by the design analyst in these problems will be highlighted. Developmental needs and future trends will then be given

Strain fluctuations and elastic constants

Energy Technology Data Exchange (ETDEWEB)

Parrinello, M.; Rahman, A.

1982-03-01

It is shown that the elastic strain fluctuations are a direct measure of elastic compliances in a general anisotropic medium; depending on the ensemble in which the fluctuation is measured either the isothermal or the adiabatic compliances are obtained. These fluctuations can now be calculated in a constant enthalpy and pressure, and hence, constant entropy, ensemble due to recent develpments in the molecular dynamics techniques. A calculation for a Ni single crystal under uniform uniaxial 100 tensile or compressive load is presented as an illustration of the relationships derived between various strain fluctuations and the elastic modulii. The Born stability criteria and the behavior of strain fluctuations are shown to be related.

Interaction of heat production, strain rate and stress power in a plastically deforming body under tensile test

Science.gov (United States)

Paglietti, A.

1982-01-01

At high strain rates the heat produced by plastic deformation can give rise to a rate dependent response even if the material has rate independent constitutive equations. This effect has to be evaluated when interpreting a material test, or else it could erroneously be ascribed to viscosity. A general thermodynamic theory of tensile testing of elastic-plastic materials is given in this paper; it is valid for large strain at finite strain rates. It enables discovery of the parameters governing the thermodynamic strain rate effect, provides a method for proper interpretation of the results of the tests of dynamic plasticity, and suggests a way of planning experiments in order to detect the real contribution of viscosity.

Continuum mechanics elasticity, plasticity, viscoelasticity

CERN Document Server

Dill, Ellis H

2006-01-01

FUNDAMENTALS OF CONTINUUM MECHANICSMaterial ModelsClassical Space-TimeMaterial BodiesStrainRate of StrainCurvilinear Coordinate SystemsConservation of MassBalance of MomentumBalance of EnergyConstitutive EquationsThermodynamic DissipationObjectivity: Invariance for Rigid MotionsColeman-Mizel ModelFluid MechanicsProblems for Chapter 1BibliographyNONLINEAR ELASTICITYThermoelasticityMaterial SymmetriesIsotropic MaterialsIncompressible MaterialsConjugate Measures of Stress and StrainSome Symmetry GroupsRate Formulations for Elastic MaterialsEnergy PrinciplesGeometry of Small DeformationsLinear ElasticitySpecial Constitutive Models for Isotropic MaterialsMechanical Restrictions on the Constitutive RelationsProblems for Chapter 2BibliographyLINEAR ELASTICITYBasic EquationsPlane StrainPlane StressProperties of SolutionsPotential EnergySpecial Matrix NotationThe Finite Element Method of SolutionGeneral Equations for an Assembly of ElementsFinite Element Analysis for Large DeformationsProblems for Chapter 3Bibliograph...

A new macroscopically anisotropic pressure dependent yield function for metal matrix composite based on strain gradient plasticity for the microstructure

DEFF Research Database (Denmark)

Azizi, Reza; Legarth, Brian Nyvang; Niordson, Christian Frithiof

2013-01-01

Metal matrix composites with long aligned elastic fibers are studied using an energetic rate independent strain gradient plasticity theory with an isotropic pressure independent yield function at the microscale. The material response is homogenized to obtain a conventional macroscopic model...... is investigated numerically using a unit cell model with periodic boundary conditions containing a single fiber deformed under generalized plane strain conditions. The homogenized response can be modeled by conventional plasticity with an anisotropic yield surface and a free energy depending on plastic strain...

Analytical solution for stress, strain and plastic instability of pressurized pipes with volumetric flaws

Energy Technology Data Exchange (ETDEWEB)

Cunha, Sergio B., E-mail: sbcunha@petrobras.com.br [PETROBRAS/TRANSPETRO, Av. Pres. Vargas 328 - 7th floor, Rio de Janeiro, RJ 20091-060 (Brazil); Netto, Theodoro A., E-mail: tanetto@lts.coppe.ufrj.br [COPPE, Federal University ot Rio de Janeiro, Ocean Engineering Department, PO BOX 68508, Rio de Janeiro - RJ (Brazil)

2012-01-15

The mechanical behavior of internally pressurized pipes with volumetric flaws is analyzed. The two possible modes of circumferentially straining the pipe wall are identified and associated to hypothesized geometries. The radial deformation that takes place by bending the pipe wall is studied by means of axisymmetric flaws and the membrane strain developed by unequal hoop deformation is analyzed with the help of narrow axial flaws. Linear elastic shell solutions for stress and strain are developed, the plastic behavior is studied and the maximum hoop stress at the flaw is related to the undamaged pipe hoop stress by means of stress concentration factors. The stress concentration factors are employed to obtain equations predicting the pressure at which the pipe fails by plastic instability for both types of flaw. These analytical solutions are validated by comparison with burst tests on 3 Double-Prime diameter pipes and finite element simulations. Forty-one burst tests were carried out and two materials with very dissimilar plastic behavior, carbon steel and austenitic stainless steel, were used in the experiments. Both the analytical and the numerical predictions showed good correlation with the experimentally observed burst pressures. - Highlights: Black-Right-Pointing-Pointer An analytical model for the burst of a pipe with a volumetric flaw is developed. Black-Right-Pointing-Pointer Deformation, strain and stress are modeled in the elastic and plastic domains. Black-Right-Pointing-Pointer The model is comprehensively validated by experiments and numerical simulations. Black-Right-Pointing-Pointer The burst pressure model's accuracy is equivalent to finite element simulations.

Computer implementation of an elastic-plastic concrete relationship

International Nuclear Information System (INIS)

Murray, D.W.; Chitnuyanondh, L.; Wong, C.

1979-01-01

The purpose of this paper is to describe the difficulties that arose, and the strategies that were developed to overcome these difficulties, during the incorporation of a relatively complex elastic-plastic concrete constitutive relationship into an existing computer code for the analysis of axisymmetric loading acting on thin shells of revolution. The program had the capability of elastic-plastic analysis using a von-Mises yield curve prior to any modification by the writers. (orig.)

Practical solution of plastic deformation problems in elastic-plastic range

Science.gov (United States)

Mendelson, A; Manson, S

1957-01-01

A practical method for solving plastic deformation problems in the elastic-plastic range is presented. The method is one of successive approximations and is illustrated by four examples which include a flat plate with temperature distribution across the width, a thin shell with axial temperature distribution, a solid cylinder with radial temperature distribution, and a rotating disk with radial temperature distribution.

Elastic-Plastic Nonlinear Response of a Space Shuttle External Tank Stringer. Part 2; Thermal and Mechanical Loadings

Science.gov (United States)

Knight, Norman F., Jr.; Warren, Jerry E.; Elliott, Kenny B.; Song, Kyongchan; Raju, Ivatury S.

2012-01-01

Elastic-plastic, large-deflection nonlinear thermo-mechanical stress analyses are performed for the Space Shuttle external tank s intertank stringers. Detailed threedimensional finite element models are developed and used to investigate the stringer s elastic-plastic response for different thermal and mechanical loading events from assembly through flight. Assembly strains caused by initial installation on an intertank panel are accounted for in the analyses. Thermal loading due to tanking was determined to be the bounding loading event. The cryogenic shrinkage caused by tanking resulted in a rotation of the intertank chord flange towards the center of the intertank, which in turn loaded the intertank stringer feet. The analyses suggest that the strain levels near the first three fasteners remain sufficiently high that a failure may occur. The analyses also confirmed that the installation of radius blocks on the stringer feet ends results in an increase in the stringer capability.

Method of determining elastic and plastic mechanical properties of ceramic materials using spherical indenters

Science.gov (United States)

Adler, Thomas A.

1996-01-01

The invention pertains a method of determining elastic and plastic mechanical properties of ceramics, intermetallics, metals, plastics and other hard, brittle materials which fracture prior to plastically deforming when loads are applied. Elastic and plastic mechanical properties of ceramic materials are determined using spherical indenters. The method is most useful for measuring and calculating the plastic and elastic deformation of hard, brittle materials with low values of elastic modulus to hardness.

Analysis of elastic-plastic problems using edge-based smoothed finite element method

International Nuclear Information System (INIS)

Cui, X.Y.; Liu, G.R.; Li, G.Y.; Zhang, G.Y.; Sun, G.Y.

2009-01-01

In this paper, an edge-based smoothed finite element method (ES-FEM) is formulated for stress field determination of elastic-plastic problems using triangular meshes, in which smoothing domains associated with the edges of the triangles are used for smoothing operations to improve the accuracy and the convergence rate of the method. The smoothed Galerkin weak form is adopted to obtain the discretized system equations, and the numerical integration becomes a simple summation over the edge-based smoothing domains. The pseudo-elastic method is employed for the determination of stress field and Hencky's total deformation theory is used to define effective elastic material parameters, which are treated as field variables and considered as functions of the final state of stress fields. The effective elastic material parameters are then obtained in an iterative manner based on the strain controlled projection method from the uniaxial material curve. Some numerical examples are investigated and excellent results have been obtained demonstrating the effectivity of the present method.

Elastic-plastic transition: A universal law

Directory of Open Access Journals (Sweden)

Chen Zhong

2016-01-01

Full Text Available Although the initial stress-strain behavior in a tensile test is often characterized as linear elastic up to a yield stress and nonlinear plastic thereafter, the pre-yield transition region is known to exhibit significant curvature and hysteresis. Hundreds of high-precision loading-unloading-loading tensile tests were performed using 26 commercial sheet alloys exhibiting a wide range of strength, ductility and crystal structure. Analysis of the results reveals the following: 1.There is no significant linear elastic region; the proportional limit is ~0 MPa when measured with sufficient sensitivity. 2.Each of the hundreds of measured transitional stress-strain curves can be characterized by a single parameter, here called the “modulus reduction rate.”The corresponding equation captures ~80% of the observed variation, a factor of 3 to 6 better than a one-parameter linear approximation. 3.Most interestingly, the transitional behavior for all alloys follows a “Universal Law” requiring no fit parameters. The law depends only upon the strength of the material and its Young’s modulus, both of which are can be measured by independent tests or adopted from handbooks. The Universal Law captures ~90% of the variation represented by the one-parameter representation and eliminates the need for mechanical testing to implement and apply. The practical and theoretical implications of these results are discussed. The results provide a simple path to significantly improving applied constitutive models in the transitional regime. The consistency of the effect for such a wide range of metals and suggests that the origin of the behavior lies in the pile-up and relaxation of dislocation arrays.

X-ray measurement of plastic strain by means of Eshelby/Mori-Tanaka model and its application

International Nuclear Information System (INIS)

Sasaki, Toshihiko; Lin, Zheng; Hirose, Yukio

1997-01-01

A new method is proposed in this paper for determining plastic strains in composite materials using the X-ray diffraction method. The present method was derived by using both Eshelby's approach and the Mori-Tanaka theory to express the stress state in composite materials instead of the elasticity in single-phase materials which is used in the conventional method of X-ray stress measurement. It was found that the plastic strain can be determined from the slope of the linear relation between lattice strains measured by the X-ray diffraction technique and sin 2 ψ using almost the same procedure as that for determining stresses by the conventional X-ray method. The results on ferritic and austenitic dual-phase stainless steel are shown. We discuss the effects of a uniaxial tensile load in a range of plastic deformation on the field of plastic strain as well as on residual macro-, micro- and phase stresses built up in the sample. (author)

Elastic-plastic fracture mechanics study of thermal shock cracking

International Nuclear Information System (INIS)

Hirano, K.; Kobayashi, H.; Nakazawa, H.

1980-01-01

This paper describes thermal shock experiments conducted on a nuclear pressure vessel steel (A533 Grade B Class 1), an AISI304 steel and a tool steel (JIS SKD62) using both a new thermal shock test facility and method. Analysis of their quasi-static thermal stress intensity factors is performed on the basis of linear-elastic fracture mechanics; and a thermal shock fracture toughness value, Ksub(tsc) is evaluated. Then elastic-plastic fracture toughness tests are carried out in the same high temperature range of the thermal shock experiment, and a relation between the stretched zone width, SZW, formed as a result of the fatigue precrack tip plastic blunting and the J-integral is clarified. An elastic-plastic thermal shock fracture toughness value, Jsub(tsc), is evaluated from a critical value of the stretched zone width, SZWsub(tsc), at the initiation of the thermal shock cracking by using the relation between SZW and J. The Jsub(tsc) value is compared with an elastic-plastic fracture toughness value, Jsub(Ic), and the difference between these Jsub(tsc) and Jsub(Ic) values is discussed on the basis of fractography. (author)

On generalization uniaxial stress-strain relation

International Nuclear Information System (INIS)

Sahay, C.; Dubey, R.N.

1980-01-01

Different forms of constitutive relations have been advanced for elastic, plastic and elastic-plastic behaviour of materials. It is shown that the various forms of the stress-strain relationship are specialized forms of generalization of a single stress-strain relation. For example, it is shown how the laws of elastic deformation, and the incremental and total deformation relationship for plastic behaviour are derivable from the Ramberg-Osgood relation. (orig.)

On the use of elastic-plastic material characteristics for linear-elastic component assessments

International Nuclear Information System (INIS)

Kussmaul, K.; Silcher, H.; Eisele, U.

1995-01-01

In this paper the procedure of safety assessment of components by fracture mechanics analysis as recommended in TECDOC 717 is applied to two standard specimens of ductile cast iron. It is shown that the use of a pseudo-elastic K IJ -value in linear elastic safety analysis may lead to non-conservative results, when elastic-plastic material behaviour can be expected. (author)

Mechanically equivalent elastic-plastic deformations and the problem of plastic spin

Directory of Open Access Journals (Sweden)

Steigmann David J.

2011-01-01

Full Text Available The problem of plastic spin is phrased in terms of a notion of mechanical equivalence among local intermediate configurations of an elastic/ plastic crystalline solid. This idea is used to show that, without further qualification, the plastic spin may be suppressed at the constitutive level. However, the spin is closely tied to an underlying undistorted crystal lattice which, once specified, eliminates the freedom afforded by mechanical equivalence. As a practical matter a constitutive specification of plastic spin is therefore required. Suppression of plastic spin thus emerges as merely one such specification among many. Restrictions on these are derived in the case of rate-independent response.

Study of Wood Plastic Composites elastic behaviour using full field measurements

Science.gov (United States)

Ben Mbarek, T.; Robert, L.; Hugot, F.; Orteu, J. J.; Sammouda, H.; Graciaa, A.; Charrier, B.

2010-06-01

In this study, the mechanical properties and microstructure of HDPE/wood fibre composites are investigated. The four-point bending and tensile behaviour of Wood Plastic Composite (WPC) with or without additive are studied by using full-field strain measurements by 3-D Digital Image Correlation (3-D DIC). A non-linear behaviour is shown. The modulus of elasticity (MOE) is calculated as the tangent at zero strain of a Maxwell-Bingham model fitted onto experimental data. Four-point bending tests are analyzed thanks to the spatial standard deviation of the longitudinal strain field to determine the degree of heterogeneity. Cyclic tensile tests have been performed in order to analyze the damage of the material. Moreover, Scanning Electron Microscope (SEM) is used to characterize the morphology of the wood fibre/HDPE matrix interface for specimens with maleic anhydride modified polyethylene additive (MAPE).

New constitutive equations to describe infinitesimal elastic-plastic deformations

International Nuclear Information System (INIS)

Boecke, B.; Link, F.; Schneider, G.; Bruhns, O.T.

1983-01-01

A set of constitutive equations is presented to describe infinitesimal elastic-plastic deformations of austenitic steel in the range up to 600 deg C. This model can describe the hardening behaviour in the case of mechanical loading and hardening, and softening behaviour in the case of thermal loading. The loading path can be either monotonic or cyclic. For this purpose, the well-known isotropic hardening model is continually transferred into the kinematic model according to Prager, whereby suitable internal variables are chosen. The occurring process-dependent material functions are to be determined by uniaxial experiments. The hardening function g and the translation function c are determined by means of a linearized stress-strain behaviour in the plastic range, whereby a coupling condition must be taken into account. As a linear hardening process is considered to be too unrealistic, nonlinearity is achieved by introducing a small function w, the determination procedure of which is given. (author)

Elasto-plastic bond mechanics of embedded fiber optic sensors in concrete under uniaxial tension with strain localization

Science.gov (United States)

Li, Qingbin; Li, Guang; Wang, Guanglun

2003-12-01

Brittleness of the glass core inside fiber optic sensors limits their practical usage, and therefore they are coated with low-modulus softer protective materials. Protective coatings absorb a portion of the strain, and hence part of the structural strain is sensed. The study reported here corrects for this error through development of a theoretical model to account for the loss of strain in the protective coating of optical fibers. The model considers the coating as an elasto-plastic material and formulates strain transfer coefficients for elastic, elasto-plastic and strain localization phases of coating deformations in strain localization in concrete. The theoretical findings were verified through laboratory experimentation. The experimental program involved fabrication of interferometric optical fiber sensors, embedding within mortar samples and tensile tests in a closed-loop servo-hydraulic testing machine. The elasto-plastic strain transfer coefficients were employed for correction of optical fiber sensor data and results were compared with those of conventional extensometers.

Plastic deformation and contact area of an elastic-plastic contact of ellipsoid bodies after unloading

NARCIS (Netherlands)

Jamari, Jamari; Schipper, Dirk J.

2007-01-01

This paper presents theoretical and experimental results of the residual or plastic deformation and the plastic contact area of an elastic–plastic contact of ellipsoid bodies after unloading. There are three regime responses of the deformation and contact area: elastic, elastic–plastic and fully

Elastic-plastic fracture assessment using a J-R curve by direct method

International Nuclear Information System (INIS)

Asta, E.P.

1996-01-01

In the elastic-plastic evaluation methods, based on J integral and tearing modulus procedures, an essential input is the material fracture resistance (J-R) curve. In order to simplify J-R determination direct, a method from load-load point displacement records of the single specimen tests may be employed. This procedure has advantages such as avoiding accuracy problems of the crack growth measuring devices and reducing testing time. This paper presents a structural integrity assessment approach, for ductile fracture, using the J-R obtained by a direct method from small single specimen fracture tests. The J-R direct method was carried out by means of a developed computational program based on theoretical elastic-plastic expressions. A comparative evaluation between the direct method J resistance curves and those obtained by the standard testing methodology on typical pressure vessel steels has been made. The J-R curves estimated from the direct method give an acceptable agreement with the approach proposed in this study which is reliable to use for engineering determinations. (orig.)

Elastic-plastic analysis of fracture mechanics test specimens. Part 2

International Nuclear Information System (INIS)

Talja, H.; Wallin, K.

1984-12-01

This is second part of the report of the research program 'Comparisons between computational and experimental elastic-plastic results' started at the Technical Research Centre of Finland in 1981. The first part of the research program was reported earlier and contained a two dimensional linear elastic finite element analysis of four specimen geometries (CT, RCT, ASTM-3P and Charpy-V) and testing and elastic-plastic analysis of the specimen (EGF71; 1TCT, material A 542). In this report the second part of the program containing the testing and 2-D elastic-plastic analyses of five specimens is described. The four specimen geometries mentioned above and two different materials (stainless steel AISI 304 and ferrite pressure vessel steel A533B) are considered. The following comparisons are presented in the report: load vs. load displacement curves, J-integral, crack opening displacement (COD), J vs. COD and the size of the plastic zone. The agreement between the computational and experimental results is quite good. Complete agreement can be achieved only with 3-dimensional calculation models. (author)

Indentation of elastically soft and plastically compressible solids

NARCIS (Netherlands)

Needleman, A.; Tvergaard, V.; Van der Giessen, E.

The effect of soft elasticity, i.e., a relatively small value of the ratio of Young's modulus to yield strength and plastic compressibility on the indentation of isotropically hardening elastic-viscoplastic solids is investigated. Calculations are carried out for indentation of a perfectly sticking

Asperity interaction in elastic-plastic contact of rough surfaces in presence of adhesion

International Nuclear Information System (INIS)

Sahoo, Prasanta; Banerjee, Atanu

2005-01-01

This paper presents an analysis of the effect of asperity interaction in elastic-plastic contact of rough surfaces in the presence of adhesion. The micro-contact model of asperity interactions, developed by Zhao and Chang (2001 Trans. ASME: J. Tribol. 123 857-64), is integrated into the elastic-plastic contact model developed by Roy Chowdhury and Ghosh (1994 Wear 174 9-19) to allow the asperity interaction and elastic-plastic deformation in the presence of surface forces to be considered simultaneously. The well-established elastic and plastic adhesion indices are used to consider the different conditions that arise as a result of varying load and material parameters. Results show that asperity interaction influences the loading-unloading behaviour in elastic-plastic adhesive contact of rough surfaces and in general asperity interactions reduce the effect of surface forces

Elastic-plastic analysis of part-through crack propagation in piping and pressure vessels

International Nuclear Information System (INIS)

Souza, L.A. de; Ebecken, N.F.F.

1986-01-01

The shell structures, often used in the construction of reservoirs, pipings, pressure vessels, nuclear power plants, etc, with part-through crack along its thickness, are analysed, using a computer system developed by the finite element method. The surface is discretized with three-dimensional quadratic elements, degenerated in its mid-surface, such the fracture is simulated by scalar elements (non linear springs). The results are analysed by the stress intensity factor K Sub(I) and the strain energy release rate, which is known as J-integral. The analysis is performed in the elastic and elastic-plastic regime. The basic hipothesis and the formulation adopted in the derivation of the scalar elements are also shown. (Author) [pt

Elastic-plastic analysis using an efficient formulation of the finite element method

International Nuclear Information System (INIS)

Aamodt, B.; Mo, O.

1975-01-01

Based on the flow theory of plasticity, the von Mises or the Tresca yield criterion and the isotropic hardening law, an incremental stiffness relationship can be established for a finite element model of the elasto-plastic structure. However, instead of including all degrees of freedom and all finite elements of the total model in a nonlinear solution process, a separation of elastic and plastic parts of the structure can be carried out. Such a separation can be obtained by identifying elastic parts of the structure as 'elastic' superelements and elasto-plastic parts of the structure as 'elasto-plastic' superelements. Also, it may be of advantage to use several levels of superelements in modelling the elastic parts of the structure. For the 'elasto-plastic' superelements the specific plastic computations such as updating of the incremental stiffness matrix and subsequent reduction (i.e. static condensation of all degrees of freedom being local to the superelements) have to be carried out repeatedly during the nonlinear solution process. The solution of the nonlinear equations is performed utilizing a combination of load incrementation and equilibrium interations. The present method of analysis is demonstrated for two larger examples of elasto-plastic analysis. (Auth.)

Numerical estimate of fracture parameters under elastic and elastic-plastic conditions

International Nuclear Information System (INIS)

Soba, Alejandro; Denis, Alicia C.

2003-01-01

The importance of the stress intensity factor K in the elastic fracture analysis is well known. In this work three methods are developed to estimate the parameter K I , corresponding to the normal loading mode, employing the finite elements method. The elastic-plastic condition is also analyzed, where the line integral J is the relevant parameter. Two cases of interest are studied: sample with a crack in its center and tubes with internal pressure. (author)

Study of Wood Plastic Composites elastic behaviour using full field measurements

Directory of Open Access Journals (Sweden)

Graciaa A.

2010-06-01

Full Text Available In this study, the mechanical properties and microstructure of HDPE/wood fibre composites are investigated. The four-point bending and tensile behaviour of Wood Plastic Composite (WPC with or without additive are studied by using full-field strain measurements by 3-D Digital Image Correlation (3-D DIC. A non-linear behaviour is shown. The modulus of elasticity (MOE is calculated as the tangent at zero strain of a Maxwell-Bingham model fitted onto experimental data. Four-point bending tests are analyzed thanks to the spatial standard deviation of the longitudinal strain field to determine the degree of heterogeneity. Cyclic tensile tests have been performed in order to analyze the damage of the material. Moreover, Scanning Electron Microscope (SEM is used to characterize the morphology of the wood fibre/HDPE matrix interface for specimens with maleic anhydride modified polyethylene additive (MAPE.

Texture, residual strain, and plastic deformation around scratches in alloy 600 using synchrotron X-ray Laue micro-diffraction

Energy Technology Data Exchange (ETDEWEB)

Suominen Fuller, M.L. [Surface Science Western, Room G-1, Western Science Centre, University of Western Ontario, London, Ontario, N6A 5B7 (Canada)], E-mail: mfuller@uwo.ca; Klassen, R.J. [Department of Mechanical and Materials Engineering, Room 3002 Spencer Engineering Building, University of Western Ontario, London, Ontario, N6A 5B9 (Canada); McIntyre, N.S. [Surface Science Western, Room G-1, Western Science Centre, University of Western Ontario, London, Ontario, N6A 5B7 (Canada); Gerson, A.R. [Applied Centre for Structural and Synchrotron Studies, Mawson Lakes Campus, University of South Australia, Adelaide, South Australia 5095 (Australia); Ramamurthy, S. [Surface Science Western, Room G-1, Western Science Centre, University of Western Ontario, London, Ontario, N6A 5B7 (Canada); King, P.J. [Babcock and Wilcox Canada, 581 Coronation Blvd., Cambridge, Ontario, N1R5V3 (Canada); Liu, W. [Advanced Photon Source, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439 (United States)

2008-03-15

Deformation around two scratches in Alloy 600 (A600) was studied nondestructively using synchrotron Laue differential aperture X-ray microscopy. The orientation of grains and elastic strain distribution around the scratches were measured. A complex residual deviatoric elastic strain state was found to exist around the scratches. Heavy plastic deformation was observed up to a distance of 20 {mu}m from the scratches. In the region 20-30 {mu}m from the scratches the diffraction spots were heavily streaked and split indicating misoriented dislocation cell structures.

Dynamics of shock waves in elastic-plastic solids

OpenAIRE

Favrie , Nicolas; Gavrilyuk , Sergey ,

2010-01-01

Submitted in ESAIM Procedings; The Maxwell type elastic-plastic solids are characterized by decaying the absolute values of the principal components of the deviatoric part of the stress tensor during the plastic relaxation step. We propose a mathematical formulation of such a model which is compatible with the von Mises criterion of plasticity. Numerical examples show the ability of the model to deal with complex physical phenomena.

Comparison of elastic-viscous-plastic and viscous-plastic dynamics models using a high resolution Arctic sea ice model

Energy Technology Data Exchange (ETDEWEB)

Hunke, E.C. [Los Alamos National Lab., NM (United States); Zhang, Y. [Naval Postgraduate School, Monterey, CA (United States)

1997-12-31

A nonlinear viscous-plastic (VP) rheology proposed by Hibler (1979) has been demonstrated to be the most suitable of the rheologies commonly used for modeling sea ice dynamics. However, the presence of a huge range of effective viscosities hinders numerical implementations of this model, particularly on high resolution grids or when the ice model is coupled to an ocean or atmosphere model. Hunke and Dukowicz (1997) have modified the VP model by including elastic waves as a numerical regularization in the case of zero strain rate. This modification (EVP) allows an efficient, fully explicit discretization that adapts well to parallel architectures. The authors present a comparison of EVP and VP dynamics model results from two 5-year simulations of Arctic sea ice, obtained with a high resolution sea ice model. The purpose of the comparison is to determine how differently the two dynamics models behave, and to decide whether the elastic-viscous-plastic model is preferable for high resolution climate simulations, considering its high efficiency in parallel computation. Results from the first year of this experiment (1990) are discussed in detail in Hunke and Zhang (1997).

Strain Limits within the Scope of the Integrity Assessment of Piping Systems

International Nuclear Information System (INIS)

Mutz, Alexander

2008-01-01

Allowable stresses in nuclear power plant piping resulting from loading conditions to be considered in Germany are determined on the basis of the German Safety Standards of the Nuclear Safety Standards Commission, KTA. The limitation of the different stress categories within the analysis of the mechanical behaviour is based on a linear elastic material behaviour. Because of the ductile material used in high energy nuclear piping, a more realistic assessment can be performed on the basis of allowable strains using elastic plastic material behaviour. In the present work comparison between the analysis of piping systems considering the elastic material model and the actual elastic plastic material behaviour is performed. The possibilities of allocating plastic strains to calculated elastic stresses is discussed. A parametric study on straight pipes with the actual elastic plastic material model under pure bending is the basis of deriving the elastic plastic strains for the calculated elastic stresses. Strain limits are suggested which correspond to the different stress categories. The aim is to utilize the deformation possibilities of ductile materials used in German nuclear piping and the allocation of maximum strains to different load categories. Keywords: strain limit, ductile material, stress category. (author)

Strain Limits within the Scope of the Integrity Assessment of Piping Systems

Energy Technology Data Exchange (ETDEWEB)

Mutz, Alexander [EnBW, Durlacher Allee 93, Karlsruhe 76131 (Germany)

2008-07-01

Allowable stresses in nuclear power plant piping resulting from loading conditions to be considered in Germany are determined on the basis of the German Safety Standards of the Nuclear Safety Standards Commission, KTA. The limitation of the different stress categories within the analysis of the mechanical behaviour is based on a linear elastic material behaviour. Because of the ductile material used in high energy nuclear piping, a more realistic assessment can be performed on the basis of allowable strains using elastic plastic material behaviour. In the present work comparison between the analysis of piping systems considering the elastic material model and the actual elastic plastic material behaviour is performed. The possibilities of allocating plastic strains to calculated elastic stresses is discussed. A parametric study on straight pipes with the actual elastic plastic material model under pure bending is the basis of deriving the elastic plastic strains for the calculated elastic stresses. Strain limits are suggested which correspond to the different stress categories. The aim is to utilize the deformation possibilities of ductile materials used in German nuclear piping and the allocation of maximum strains to different load categories. Keywords: strain limit, ductile material, stress category. (author)

Investigation on crack growth parameters in the elastic plastic region (interim report)

International Nuclear Information System (INIS)

Prij, J.

1982-03-01

Some theoretical as well as numerical results are presented with respect to the 2D and 3D application of linear elastic fracture mechanics. The application of the finite element method to calculate the stress and strain field in cracked bodies has been discussed with special attention to: singularity representation, parameter extraction and mesh refinement. Detailed 3D stress analyses of fracture mechanics test specimen are presented showing that: the stress intensity concept cannot be extended simply into a 3D concept, the energy release concept is more promising within this aspect and the plastic region along the crackfront will not have a dogbone shape. The 3D elastic fracture mechanics concept is applied to evaluate the consequences of the thermal stresses due to γ-heating in an in-pile crack growth experiment

Crack tip stress and strain

International Nuclear Information System (INIS)

Francois, D.

1975-01-01

The study of potential energy variations in a loaded elastic solid containing a crack leads to determination of the crack driving force G. Generalization of this concept to cases other than linear elasticity leads to definition of the integral J. In a linear solid, the crack tip stress field is characterized by a single parameter: the stress-intensity factor K. When the crack tip plastic zone size is confined to the elastic singularity J=G, it is possible to establish relationship between these parameters and plastic strain (and in particular the crack tip opening displacement delta). The stress increases because of the triaxiality effect. This overload rises with increasing strain hardening. When the plastic zone size expands, using certain hypotheses, delta can be calculated. The plastic strain intensity is exclusively dependent on parameter J [fr

Theory of reversal nonisothermal elastic-plastic deformation

International Nuclear Information System (INIS)

Shorr, B.F.

1979-01-01

Considered is approximated theory of nonisothermal elastic-plastic deformation at arbitrary laws of loading, permitting to describe nonisothermal isotropic and anisotropic strengthening of the material, Bauschinger effect and different tempo of plastic deformation development over different directions of loading depending on the deformation prehistory. The comparison of the theory with the experimental data showed good coincidence and sufficient simplicity permits to use it in technical calcualtions

Split-Ring Springback Simulations with the Non-associated Flow Rule and Evolutionary Elastic-Plasticity Models

Science.gov (United States)

Lee, K. J.; Choi, Y.; Choi, H. J.; Lee, J. Y.; Lee, M. G.

2018-06-01

Finite element simulations and experiments for the split-ring test were conducted to investigate the effect of anisotropic constitutive models on the predictive capability of sheet springback. As an alternative to the commonly employed associated flow rule, a non-associated flow rule for Hill1948 yield function was implemented in the simulations. Moreover, the evolution of anisotropy with plastic deformation was efficiently modeled by identifying equivalent plastic strain-dependent anisotropic coefficients. Comparative study with different yield surfaces and elasticity models showed that the split-ring springback could be best predicted when the anisotropy in both the R value and yield stress, their evolution and variable apparent elastic modulus were taken into account in the simulations. Detailed analyses based on deformation paths superimposed on the anisotropic yield functions predicted by different constitutive models were provided to understand the complex springback response in the split-ring test.

The effects of plastic waves on the numerical convergence of the viscous-plastic and elastic-viscous-plastic sea-ice models

Science.gov (United States)

Williams, James; Tremblay, L. Bruno; Lemieux, Jean-François

2017-07-01

The plastic wave speed is derived from the linearized 1-D version of the widely used viscous-plastic (VP) and elastic-viscous-plastic (EVP) sea-ice models. Courant-Friedrichs-Lewy (CFL) conditions are derived using the propagation speed of the wave. 1-D numerical experiments of the VP, EVP and EVP* models successfully recreate a reference solution when the CFL conditions are satisfied, in agreement with the theory presented. The IMplicit-EXplicit (IMEX) method is shown to effectively alleviate the plastic wave CFL constraint on the timestep in the implicitly solved VP model in both 1-D and 2-D. In 2-D, the EVP and EVP* models show first order error in the simulated velocity field when the plastic wave is not resolved. EVP simulations are performed with various advective timestep, number of subcycles, and elastic-wave damping timescales. It is found that increasing the number of subcycles beyond that needed to resolve the elastic wave does not improve the quality of the solution. It is found that reducing the elastic wave damping timescale reduces the spatial extent of first order errors cause by the unresolved plastic wave. Reducing the advective timestep so that the plastic wave is resolved also reduces the velocity error in terms of magnitude and spatial extent. However, the parameter set required for convergence to within the error bars of satellite (RGPS) deformation fields is impractical for use in climate model simulations. The behavior of the EVP* method is analogous to that of the EVP method except that it is not possible to reduce the damping timescale with α = β.

Elastic-Plastic Behavior of U6Nb Under Ramp Wave Loading

Science.gov (United States)

Hayes, D. B.; Hall, C.; Hixson, R. S.

2005-07-01

Prior shock experiments on the alloy uranium-niobium-6 wt.% (U6Nb) were absent an elastic precursor when one was expected (A. K. Zurek, et. al., Journal de Physique IV, 10 (#9) p677-682). This was later explained as a consequence of shear stress relaxation from time-dependent twinning that prevented sufficient shear stress for plastic yielding. (D. B. Hayes, et. al., Shock Compression of Condensed Matter-2003, p1177, American Institute of Physics 2004) Pressure was ramped to 13 GPa in 150-ns on eight U6Nb specimens with thicknesses from 0.5 -- 1.1-mm and the back surface velocities were measured with laser interferometry. This pressure load produces a stress wave with sufficiently fast rise time so that, according to the prior work, twins do not have time to form. Four of the U6Nb specimens had been cold-rolled which increased the yield stress. Each velocity history was analyzed with a backward integration analysis to give the stress-strain response of the U6Nb. Comparison of these results with prior Hugoniot measurements shows that the U6Nb in the present experiments responds as an elastic-plastic material and the deduced yield strength of the baseline and of the cold-rolled material agree with static results.

Computational strain gradient crystal plasticity

DEFF Research Database (Denmark)

Niordson, Christian Frithiof; Kysar, Jeffrey W.

2014-01-01

A numerical method for viscous strain gradient crystal plasticity theory is presented, which incorporates both energetic and dissipative gradient effects. The underlying minimum principles are discussed as well as convergence properties of the proposed finite element procedure. Three problems...... of plane crystal plasticity are studied: pure shear of a single crystal between rigid platens as well as plastic deformation around cylindrical voids in hexagonal close packed and face centered cubic crystals. Effective in-plane constitutive slip parameters for plane strain deformation of specifically...... oriented face centered cubic crystals are developed in terms of the crystallographic slip parameters. The effect on geometrically necessary dislocation structures introduced by plastic deformation is investigated as a function of the ratio of void radius to plasticity length scale....

Determination of dynamic fracture initiation toughness of elastic-plastic materials at intermediate strain rates

International Nuclear Information System (INIS)

Fernandez-Saez, J.; Luna de, S.; Rubio, L.; Perez-Castellanos, J. L.; Navarro, C.

2001-01-01

An earlier paper dealt with the experimental techniques used to determine the dynamic fracture properties of linear elastic materials. Here we describe those most commonly used as elastoplastic materials, limiting the study to the initiation fracture toughness at the intermediate strain rate (of around 10''2 s''-1). In this case the inertial forces are negligible and it is possible to apply the static solutions. With this stipulation, the analysis can be based on the methods of testing in static conditions. The dynamic case differs basically, from the static one, in the influence of the strain rate on the properties of the material. (Author) 57 refs

Correlating elastic and plastic deformation with magnetic permeability values

Science.gov (United States)

Papadopoulou, S.

2017-12-01

This paper investigates the utilization of magnetic permeability method in determining elastic and plastic deformation state of ferromagnetic steels. The results have shown a strong degradation of the magnetic values on plastically region due to the irreversible movements of the magnetic domain walls.

Self-consistent modelling of lattice strains during the in-situ tensile loading of twinning induced plasticity steel

International Nuclear Information System (INIS)

Saleh, Ahmed A.; Pereloma, Elena V.; Clausen, Bjørn; Brown, Donald W.; Tomé, Carlos N.; Gazder, Azdiar A.

2014-01-01

The evolution of lattice strains in a fully recrystallised Fe–24Mn–3Al–2Si–1Ni–0.06C TWinning Induced Plasticity (TWIP) steel subjected to uniaxial tensile loading up to a true strain of ∼35% was investigated via in-situ neutron diffraction. Typical of fcc elastic and plastic anisotropy, the {111} and {200} grain families record the lowest and highest lattice strains, respectively. Using modelling cases with and without latent hardening, the recently extended Elasto-Plastic Self-Consistent model successfully predicted the macroscopic stress–strain response, the evolution of lattice strains and the development of crystallographic texture. Compared to the isotropic hardening case, latent hardening did not have a significant effect on lattice strains and returned a relatively faster development of a stronger 〈111〉 and a weaker 〈100〉 double fibre parallel to the tensile axis. Close correspondence between the experimental lattice strains and those predicted using particular orientations embedded within a random aggregate was obtained. The result suggests that the exact orientations of the surrounding aggregate have a weak influence on the lattice strain evolution

Converging shocks in elastic-plastic solids.

Science.gov (United States)

Ortega, A López; Lombardini, M; Hill, D J

2011-11-01

We present an approximate description of the behavior of an elastic-plastic material processed by a cylindrically or spherically symmetric converging shock, following Whitham's shock dynamics theory. Originally applied with success to various gas dynamics problems, this theory is presently derived for solid media, in both elastic and plastic regimes. The exact solutions of the shock dynamics equations obtained reproduce well the results obtained by high-resolution numerical simulations. The examined constitutive laws share a compressible neo-Hookean structure for the internal energy e=e(s)(I(1))+e(h)(ρ,ς), where e(s) accounts for shear through the first invariant of the Cauchy-Green tensor, and e(h) represents the hydrostatic contribution as a function of the density ρ and entropy ς. In the strong-shock limit, reached as the shock approaches the axis or origin r=0, we show that compression effects are dominant over shear deformations. For an isothermal constitutive law, i.e., e(h)=e(h)(ρ), with a power-law dependence e(h) is proportional to ρ(α), shock dynamics predicts that for a converging shock located at r=R(t) at time t, the Mach number increases as M is proportional to [log(1/R)](α), independently of the space index s, where s=2 in cylindrical geometry and 3 in spherical geometry. An alternative isothermal constitutive law with p(ρ) of the arctanh type, which enforces a finite density in the strong-shock limit, leads to M is proportional to R(-(s-1)) for strong shocks. A nonisothermal constitutive law, whose hydrostatic part e(h) is that of an ideal gas, is also tested, recovering the strong-shock limit M is proportional to R(-(s-1)/n(γ)) originally derived by Whitham for perfect gases, where γ is inherently related to the maximum compression ratio that the material can reach, (γ+1)/(γ-1). From these strong-shock limits, we also estimate analytically the density, radial velocity, pressure, and sound speed immediately behind the shock. While the

Simplified theory of plastic zones based on Zarka's method

CERN Document Server

Hübel, Hartwig

2017-01-01

The present book provides a new method to estimate elastic-plastic strains via a series of linear elastic analyses. For a life prediction of structures subjected to variable loads, frequently encountered in mechanical and civil engineering, the cyclically accumulated deformation and the elastic plastic strain ranges are required. The Simplified Theory of Plastic Zones (STPZ) is a direct method which provides the estimates of these and all other mechanical quantities in the state of elastic and plastic shakedown. The STPZ is described in detail, with emphasis on the fact that not only scientists but engineers working in applied fields and advanced students are able to get an idea of the possibilities and limitations of the STPZ. Numerous illustrations and examples are provided to support the reader's understanding.

Progress in elastic-plastic fracture mechanics and its applications

International Nuclear Information System (INIS)

Paris, P.C.; Zahalak, G.I.

1980-01-01

This paper surveys recent developments in the application of J-Integral methods to problems of elastic-plastic fracture. The analytical and experimental development of the J-Integral concept over the last ten years is reviewed briefly. Tearing instability theory is presented in general terms, and specific applications of the theory are discussed. Principles of fracture-proof design are shown to follow naturally from the tearing instability theory. These principles are illustrated first for simple structures, and then generalized to more complex configurations and loading conditions. Examples include multiple member tension structures, beams, frames, nuclear reactor pressure vessel nozzles and piping, and beams on elastic foundations. It is concluded that J-integral based methods offer the best immediate opportunity for the development of sound analytical techniques for treating important practical problems of elastic-plastic fracture

Elastic-plastic transition on rotating spherical shells in dependence of compressibility

Directory of Open Access Journals (Sweden)

Thakur Pankaj

2017-01-01

Full Text Available The purpose of this paper is to establish the mathematical model on the elastic-plastic transitions occurring in the rotating spherical shells based on compressibility of materials. The paper investigates the elastic-plastic stresses and angular speed required to start yielding in rotating shells for compressible and incompressible materials. The paper is based on the non-linear transition theory of elastic-plastic shells given by B.R. Seth. The elastic-plastic transition obtained is treated as an asymptotic phenomenon at critical points & the solution obtained at these points generates stresses. The solution obtained does not require the use of semi-empirical yield condition like Tresca or Von Mises or other certain laws. Results are obtained numerically and depicted graphically. It has been observed that Rotating shells made of the incompressible material are on the safer side of the design as compared to rotating shells made of compressible material. The effect of density variation has been discussed numerically on the stresses. With the effect of density variation parameter, rotating spherical shells start yielding at the internal surface with the lower values of the angular speed for incompressible/compressible materials.

Elastic-plastic analysis of tube expansion in tubesheets

International Nuclear Information System (INIS)

Kasraie, B.; O'Donnell, W.J.; Porowski, J.S.; Selz, A.

1983-01-01

Conditions for expansion of tubes in tubesheets are often determined by the test. The tightness of the joint and pull out force are used as criteria for evaluation of the results. For closely spaced tubes, it is also necessary to control development of the plastic regions in the ligaments surrounding the tube being expanded. High local strains may occur and excessive distortion may result if the expansion of the tube is continued beyond the admissible limits. Elastic-plastic finite element analyses are performed herein in order to establish conditions for rolling of the tubes in tubesheets of low ligament efficiency. Such penetration patterns are often required in the design of tubular reactors for catalytic processes. The model considered includes individual tube expansion in tubesheets with triangular penetration patterns. The effect of prior expansion of the neighboring tubes is also evaluated. Gap elements are used to model the initial clearance of the tube in the hole. Development of the plastic zones and distortion of the ligaments is monitored during radial expansion of the tube diameter. The residual stresses between the tube and the hole surface and the history of gap closing after removal of the expansion tool are determined. The effect of axial extension of the tube on the tube thinning is determined. Tube thinning is often used as a measure of tube expansion in manufacturing processes. For the analyzed ligament efficiency, reliable joints are obtained for a thinning range within 2% to 3%

Elastic-Plastic Nonlinear Response of a Space Shuttle External Tank Stringer. Part 1; Stringer-Feet Imperfections and Assembly

Science.gov (United States)

Knight, Norman F., Jr.; Song, Kyongchan; Elliott, Kenny B.; Raju, Ivatury S.; Warren, Jerry E.

2012-01-01

Elastic-plastic, large-deflection nonlinear stress analyses are performed for the external hat-shaped stringers (or stiffeners) on the intertank portion of the Space Shuttle s external tank. These stringers are subjected to assembly strains when the stringers are initially installed on an intertank panel. Four different stringer-feet configurations including the baseline flat-feet, the heels-up, the diving-board, and the toes-up configurations are considered. The assembly procedure is analytically simulated for each of these stringer configurations. The location, size, and amplitude of the strain field associated with the stringer assembly are sensitive to the assumed geometry and assembly procedure. The von Mises stress distributions from these simulations indicate that localized plasticity will develop around the first eight fasteners for each stringer-feet configuration examined. However, only the toes-up configuration resulted in high assembly hoop strains.

Integrating a logarithmic-strain based hyper-elastic formulation into a three-field mixed finite element formulation to deal with incompressibility in finite-strain elasto-plasticity

International Nuclear Information System (INIS)

Dina Al Akhrass; Bruchon, Julien; Drapier, Sylvain; Fayolle, Sebastien

2014-01-01

This paper deals with the treatment of incompressibility in solid mechanics in finite-strain elasto-plasticity. A finite-strain model proposed by Miehe, Apel and Lambrecht, which is based on a logarithmic strain measure and its work-conjugate stress tensor is chosen. Its main interest is that it allows for the adoption of standard constitutive models established in a small-strain framework. This model is extended to take into account the plastic incompressibility constraint intrinsically. In that purpose, an extension of this model to a three-field mixed finite element formulation is proposed, involving displacements, a strain variable and pressure as nodal variables with respect to standard finite element. Numerical examples of finite-strain problems are presented to assess the performance of the formulation. To conclude, an industrial case for which the classical under-integrated elements fail is considered. (authors)

Asymptotic techniques in elastic-plastic analysis of structures

International Nuclear Information System (INIS)

Sayir, M.

1983-01-01

Elastic-plastic structures can nowadays be analyzed with the powerful numerical procedures of the finite element method. Nevertheless, in many engineering applications, analytical expressions capable of predicting with sufficient accuracy the stress distributions, the extent of the plastic zones and the load displacement behaviour could be of great practical value. For simple structures and loading stages not too far from the elastic limit, such analytical expressions may be obtained by using perturbation methods and asymptotic expansions. A small dimensionless parameter epsilon is defined as the ratio of a length characterizing the extent of the narrow plastic zone, to a conveniently chosen typical dimension of the structure. Stresses and displacements are formally expanded as asymptotic series in terms of powers of epsilon. For each order of magnitude, the exact basic relations lead to a separate set of simplified differential equations which can be integrated analytically or numerically by using standard procedures. The method is very general and can be applied to several classes of plastic behaviour and of structural problems. Three examples of very simple structures are chosen in particular to illustrate the applicability of the perturbation method to engineering problems. (orig./RW)

Elastic-plastic fracture analysis of carbon steel piping using the latest CEGB R6 approach

International Nuclear Information System (INIS)

Kanno, S.; Hasegawa, K.; Shimizu, T.; Kobayashi, H.

1991-01-01

The elastic-plastic fracture of carbon steel piping having various pipe diameters and circumferential crack angles and subjected to a bending moment is analyzed using the latest United Kingdom Central Electricity Generating Board R6 approach. The elastic-plastic fracture criterion must be applied instead of the plastic collapse criterion with increase of the pipe diameter and the crack angle. A simplified elastic-plastic fracture analysis procedure based on the R6 approach is proposed. (author)

Elastic plastic buckling of elliptical vessel heads

International Nuclear Information System (INIS)

Alix, M.; Roche, R.L.

1981-08-01

The risks of buckling of dished vessel head increase when the vessel is thin walled. This paper gives the last results on experimental tests of 3 elliptical heads and compares all the results with some empirical formula dealing with elastic and plastic buckling

Variation of the Young's modulus with plastic strain applying to elastoplastic software

International Nuclear Information System (INIS)

Morestin, F.; Boivin, M.

1993-01-01

Work hardening of steel involves modifications of the elastic properties of the material, for instance, an increase of its yield stress. It may be also the cause of an appreciable decrease of the Young's modulus. This property decreases as plastic strain increases. Experiments with a microcomputer controlled tensile test machine indicated that diminution could reach more than 10% of the initial value, after only 5% of plastic strain. In spite of this fact, lots of elastoplastic softwares don't combine the decrease of the Young's modulus with plastification though it may involve obvious differences among results. As an application we have developed a software which computes the deformation of steel sheet in press forming, after springback. This software takes into account the decrease of the Young's modulus and its results are very close to experimental values. Quite arbitrarily, we noticed a recovery of the Young's modulus of plastified specimens after few days but not for all steels tested. (author)

Elastic-plastic FEM-analysis of a nozzle corner crack and discussion of the results by some fracture mechanics concepts

International Nuclear Information System (INIS)

Aurich, D.; Brocks, W.; Noack, D.; Veith, H.

1981-01-01

From a three-dimensional elastic-plastic stress-distortion analysis according to the finite element method (FEM) for a straight inner edge crack at room temperature in a nozzle of the intermediate vessel ZB 2 made of 22 NiMoCr 37 steel, the results obtained for stresses and strains in the ligament before the crack front, the crack opening profile, and the propagation of the plastic zone as a function of internal pressure until through-plastifying of the ligament are shown and explained. (orig.) [de

Uzawa algorithm to solve elastic and elastic-plastic fretting wear problems within the bipotential framework

Science.gov (United States)

Ning, Po; Feng, Zhi-Qiang; Quintero, Juan Antonio Rojas; Zhou, Yang-Jing; Peng, Lei

2018-03-01

This paper deals with elastic and elastic-plastic fretting problems. The wear gap is taken into account along with the initial contact distance to obtain the Signorini conditions. Both the Signorini conditions and the Coulomb friction laws are written in a compact form. Within the bipotential framework, an augmented Lagrangian method is applied to calculate the contact forces. The Archard wear law is then used to calculate the wear gap at the contact surface. The local fretting problems are solved via the Uzawa algorithm. Numerical examples are performed to show the efficiency and accuracy of the proposed approach. The influence of plasticity has been discussed.

Elastic-plastic dynamic analysis of a reactor building

International Nuclear Information System (INIS)

Umemura, Hajime; Tanaka, Hiroshi.

1976-01-01

The basic characteristics of the dynamic response of a reactor building to severe earthquake ground motion are very important for the evaluation of the safety of nuclear plant systems. A computer program for elastic-plastic dynamic analysis of reactor buildings using lumped mass models is developed. The box and cylindrical walls of boiling water reactor buildings are treated as vertical beams. The nonlinear moment-rotation and shear force-shear deformation relationships of walls are based in part upon the experiments of prototype structures. The geometrical non-linearity of the soil rocking spring due to foundation separation is also considered. The nonlinear equation of motion is expressed in incremental form using tangent stiffness matrices, following the algorithm developed by E.L. Wilson et al. The damping matrix in the equation is formulated as the combination of the energy evaluation method and Penzien-Wilson's approach to accomodate the different characteristics of soil and building damping. The analysis examples and the comparison of elastic and elastic-plastic analysis results are presented. (auth.)

Elastic-plastic Fracture Mechanics Assessment of nozzle corners submitted to thermal shock loading

International Nuclear Information System (INIS)

Chapuliot, S.; Marie, S.

2016-01-01

This paper focuses on the development of a simplified analytical scheme for the elastic-plastic Fracture Mechanics Assessment of large nozzle corners. Within that frame, following the specific numerical effort performed for the definition of a Stress Intensity Factor compendium, complementary elastic-plastic developments are proposed here for the consideration of the thermal shock loading in the elastic-plastic domain: this type of loading is a major loading for massive structures such as nozzle corners of large components. Thus, an important numerical was performed in order to extend the applicability domain of existing analytical schemes to those complex geometries. The final formulation is a simple one, applicable to a large variety of materials and geometrical configurations as long as the structure is large and the defect remains small in comparison to the internal radius of the nozzle. - Highlights: • Fracture Mechanics Assessment of large nozzle corners. • Elastic-plastic Stress Intensity Factor determination under thermal shock loading. • Semi-analytical schemes for J calculation.

FRICTION ANALYSIS ON SCRATCH DEFORMATION MODES OF VISCO-ELASTIC-PLASTIC MATERIALS

Directory of Open Access Journals (Sweden)

Budi Setiyana

2013-11-01

Full Text Available Understanding of abrasion resistance and associated surfaces deformation mechanisms is of primary importance in materials engineering and design. Instrumented scratch testing has proven to be a useful tool for characterizing the abrasion resistance of materials. Using a conical indenter in a scratch test may result in different deformation modes, like as elastic deformation, ironing, ductile ploughing and cutting. This paper presents the friction analysis of some deformation modes of visco-elastic-plastic behaving polymer materials, especially PEEK (poly ether ether ketone.In general, it is accepted that the friction consist of an adhesion and a deformation component, which can be assumed to be independent to each others. During a scratch test, the friction coefficient is influenced by some parameters, such as the sharpness of indenter, the deformation modes and the degree of elastic recovery. Results show that the adhesion component strongly influences the friction in the elastic and ironing deformation mode (scratching with a blunt cone, friction for the cutting deformation mode (scratching with a sharp cone is dominantly influenced by the deformation component. From the analysis, it can be concluded that the adhesion friction model is suitable for ironing - elastic deformation mode and the deformation friction model with elastic recovery is good for cutting mode. Moreover, the ductile ploughing mode is combination of the adhesion and plastic deformation friction model. ANALISIS FRIKSI PADA BENTUK DEFORMASI AKIBAT GORESAN PADA MATERIAL VISKO-ELASTIK-PLASTIK. Pemahaman tentang ketahanan abrasi dan deformasi permukaan  yang  menyertainya merupakan hal yang penting dalam rekayasa dan disain material. Peralatan uji gores terbukti ampuh untuk menyatakan ketahanan abrasi dari material. Pemakaian indenter kerucut dalam uji gores akan menghasilkan beberapa bentuk deformasi seperti halnya deformasi elastik, penyetrikaan, plowing dan pemotongan

Richtmyer-Meshkov instability in elastic-plastic media

Science.gov (United States)

Piriz, Antonio R.; López Cela, Juan J.; Tahir, Naeem A.; Hoffmann, Dieter H. H.

2008-04-01

Hydrodynamic instabilities are of great importance in the LAPLAS (Laboratory of Planetary Sciences) experiment that is being designed for the study of high energy density states of matter in the framework of the FAIR projectDuring the implosion of the LAPLAS cylindrical target Richtmyer-Meshkov (RM) instability occurs when a shock is launched into a material pusher with elastic and plastic properties that determines the physics of the instability evolution. We have studied the evolution of the interface from which the shock is launched as a consequence of the RM instability. For this we have developed an analytical model and we have performed two-dimensional numerical simulations in order to validate the model. Model and simulations show the asymptotic stability state in which the interface oscillates elastically around a mean value higher than the initial perturbation amplitude. Such a mean value is determined by an initial plastic phase. Applications to the measurement of the yield strength of materials under extreme conditions are foreseen.

An elastic-plastic contact model for line contact structures

Science.gov (United States)

Zhu, Haibin; Zhao, Yingtao; He, Zhifeng; Zhang, Ruinan; Ma, Shaopeng

2018-06-01

Although numerical simulation tools are now very powerful, the development of analytical models is very important for the prediction of the mechanical behaviour of line contact structures for deeply understanding contact problems and engineering applications. For the line contact structures widely used in the engineering field, few analytical models are available for predicting the mechanical behaviour when the structures deform plastically, as the classic Hertz's theory would be invalid. Thus, the present study proposed an elastic-plastic model for line contact structures based on the understanding of the yield mechanism. A mathematical expression describing the global relationship between load history and contact width evolution of line contact structures was obtained. The proposed model was verified through an actual line contact test and a corresponding numerical simulation. The results confirmed that this model can be used to accurately predict the elastic-plastic mechanical behaviour of a line contact structure.

The correlation between the ultrasonic elastic strain ratio of thyroid cancer and the malignant biological characteristics of cancer cells in the lesions

Directory of Open Access Journals (Sweden)

Li Ma

2017-04-01

Full Text Available Objective: To study the correlation between the ultrasonic elastic strain ratio of thyroid cancer and the malignant biological characteristics of cancer cells in the lesions. Methods: A total of 90 patients with thyroid cancer who accepted surgical treatment in our hospital between March 2015 and September 2016 were selected as the observation group, and 50 patients who received surgery in our hospital during the same period and were with clear pathological diagnosis of thyroid adenoma were selected as the control group. According to the median of ultrasonic elastic strain ratio, the observing group were further divided into high elastic strain ratio group and low elastic strain ratio group (n=45. RT-PCR was used to determine the mRNA expression of proliferation genes, invasion genes and autophagy genes in lesions of all groups of patients. Results: The mean elastic strain ratio of observation group was significantly lower than that of control group. Proliferation gene FOXA1 mRNA expression in lesions of low elastic strain ratio group and high elastic strain ratio group were higher than those of control group while PP4R1 and Smac mRNA expression were lower than those of control group, and as the elastic strain ratio decreased, the FOXA1 mRNA expression increased while PP4R1 and Smac mRNA expression decreased; invasion genes BCORL1, SATB1, Twist1 and CXCR4 mRNA expression in lesions of low elastic strain ratio group and high elastic strain ratio group were higher than those of control group, and as the elastic strain ratio decreased, the BCORL1, SATB1, Twist1 and CXCR4 mRNA expression increased; autophagy genes ARHI, Beclin1, LC3 and PTEN mRNA expression in lesions of low elastic strain ratio group and high elastic strain ratio group were lower than those of control group, and as the elastic strain ratio decreased, the ARHI, Beclin1, LC3 and PTEN mRNA expression decreased. Conclusion: The ultrasonic elastic strain ratio of thyroid cancer is

Finite Difference Solution of Elastic-Plastic Thin Rotating Annular Disk with Exponentially Variable Thickness and Exponentially Variable Density

Directory of Open Access Journals (Sweden)

Sanjeev Sharma

2013-01-01

Full Text Available Elastic-plastic stresses, strains, and displacements have been obtained for a thin rotating annular disk with exponentially variable thickness and exponentially variable density with nonlinear strain hardening material by finite difference method using Von-Mises' yield criterion. Results have been computed numerically and depicted graphically. From the numerical results, it can be concluded that disk whose thickness decreases radially and density increases radially is on the safer side of design as compared to the disk with exponentially varying thickness and exponentially varying density as well as to flat disk.

comparison of elastic-plastic FE method and engineering method for RPV fracture mechanics analysis

International Nuclear Information System (INIS)

Sun Yingxue; Zheng Bin; Zhang Fenggang

2009-01-01

This paper described the FE analysis of elastic-plastic fracture mechanics for a crack in RPV belt line using ABAQUS code. It calculated and evaluated the stress intensity factor and J integral of crack under PTS transients. The result is also compared with that by engineering analysis method. It shows that the results using engineering analysis method is a little larger than the results using FE analysis of 3D elastic-plastic fracture mechanics, thus the engineering analysis method is conservative than the elastic-plastic fracture mechanics method. (authors)

Plastic strain caused by contraction of pores in polycrystalline graphites

International Nuclear Information System (INIS)

Ioka, Ikuo; Yoda, Shinichi; Konishi, Takashi.

1989-01-01

The effects of porosity on mechanical properties and deformation behavior of four isotropic polycrystalline graphites were studied. The pore size distributions of the graphites were measured using a conventional mercury penetration technique. The average pore radius of ISO-88 graphite was about one-tenth of that of ISEM-1, IG-11 or IG-15 graphites. Young's modulus of the graphites decreased with increasing porosity. The stress-strain curve of each graphite was measured in its lateral and axial directions. Young's modulus of graphite decreased with increasing load. The plastic strain at a given compressive load was calculated from the stress-strain curve and the initial gradient of the unloading curve at the load. The ratio of lateral plastic strain to axial plastic strain for the graphites was less than 0.5, indicating that the volume of the graphites decreased during compressive loading. By assuming that the volume change was caused by contraction of pores, plastic strain associated with contraction of pores was calculated from the axial plastic strain and lateral plastic strain by slips along the basal planes. The plastic strain increased with increasing axial plastic strain and porosity of graphite. (author)

Mechanisms of strain accommodation in plastically-deformed zircon under simple shear deformation conditions during amphibolite-facies metamorphism

Science.gov (United States)

Kovaleva, Elizaveta; Klötzli, Urs; Wheeler, John; Habler, Gerlinde

2018-02-01

This study documents the strain accommodation mechanisms in zircon under amphibolite-facies metamorphic conditions in simple shear. Microstructural data from undeformed, fractured and crystal-plastically deformed zircon crystals are described in the context of the host shear zone, and evaluated in the light of zircon elastic anisotropy. Our work challenges the existing model of zircon evolution and shows previously undescribed rheological characteristics for this important accessory mineral. Crystal-plastically deformed zircon grains have axis oriented parallel to the foliation plane, with the majority of deformed grains having axis parallel to the lineation. Zircon accommodates strain by a network of stepped low-angle boundaries, formed by switching between tilt dislocations with the slip systems {010} and {110} and rotation axis [001], twist dislocations with the rotation axis [001], and tilt dislocations with the slip system {001} and rotation axis [010]. The slip system {110} is newly described for zircon. Most misorientation axes in plastically-deformed zircon grains are parallel to the XY plane of the sample and have [001] crystallographic direction. Such behaviour of strained zircon lattice is caused by elastic anisotropy that has a direct geometric control on the rheology, deformation mechanisms and dominant slip systems in zircon. Young's modulus and P wave velocity have highest values parallel to zircon [001] axis, indicating that zircon is elastically strong along this direction. Poisson ratio and Shear modulus demonstrate that zircon is also most resistant to shearing along [001]. Thus, [001] axis is the most common rotation axis in zircon. The described zircon behaviour is important to take into account during structural and geochronological investigations of (poly)metamorphic terrains. Geometry of dislocations in zircon may help reconstructing the geometry of the host shear zone(s), large-scale stresses in the crust, and, possibly, the timing of

Elastic-plastic deformation of fiber composites with a tetragonal structure

Energy Technology Data Exchange (ETDEWEB)

Makarova, E.IU.; Svistkova, L.A. (Permskii Politekhnicheskii Institut, Perm (USSR))

1991-02-01

Results of numerical solutions are presented for elastic-plastic problems concerning arbitrary loading of unidirectional composites in the transverse plane. The nucleation and evolution of microplastic zones in the matrix and the effect of this process on the macroscopic characteristics of the composite are discussed. Attention is also given to the effect of the fiber shape on the elastic-plastic deformation of the matrix and to deformation paths realized in simple microdeformation processes. The discussion is illustrated by results obtained for a composite consisting of a VT1-0 titanium alloy matrix reinforced by Ti-Mo fibers.

Effect of plastic strain on fracture strength of cracked components

International Nuclear Information System (INIS)

Kamaya, Masayuki

2009-01-01

Nuclear power plant components are occasionally subjected to large load by earthquake and may suffer plastic strain. Although the plastic strain induced in materials increases the strength, it may reduce the fracture toughness due to a crack in the components. In this study, the effect of the plastic strain on strength of cracked components was investigated. Firstly, the change in the tensile properties and fracture toughness due to plastic strain were examined for Type 316 stainless steel and carbon steel (SM490). The degree of nominal plastic strain was 5%, 10%, 20% and 40% (only for stainless steel). Secondly, the J-integral values of surface crack on a pipe were evaluated by finite element analyses. Finally, the critical load for fracture of the cracked pipe was evaluated for various pipe and crack geometries using the J-integral values and the fracture toughness obtained. It was concluded that the plastic strain enhances the fracture strength of the cracked components when the induced plastic strain is less than 10%, although the extremely large plastic strain could reduce the strength. (author)

Effect of plastic strain on fracture strength of cracked components

International Nuclear Information System (INIS)

Kamaya, Masayuki

2010-01-01

Nuclear power plant components are occasionally subjected to excessive load by earthquake and may suffer plastic strain. Although the plastic strain introduced in materials increases the strength, it may reduce the fracture toughness. In this study, the effect of the plastic strain on strength of cracked components was investigated. Firstly, the change in the tensile properties and fracture toughness due to plastic strain were examined for Type 316 stainless steel and carbon steel (SM 490). The degree of nominal plastic strain was 5%, 10%, 20% and 40% (only for stainless steel). Secondly, the J-integral values of surface crack on a pipe were evaluated by finite element analyses. Finally, the critical load for fracture of the cracked pipe was evaluated for various pipe and crack geometries using the J-integral values and the fracture toughness obtained. It was concluded that the plastic strain enhances the fracture strength of the cracked components when the induced plastic strain is less than 10%, although the extremely large plastic strain could reduce the strength. (author)

Fracture toughness evaluation of elastic-plastic J-integral for high temperature components of gas turbine in power plants

International Nuclear Information System (INIS)

Chung, Nam Yong; Kim, Moon Young; Kim, Jong Woo

1999-01-01

In the study, the analysis of elastic-plastic J-integral was performed in high temperature components for gas turbine based on elastic-plastic fracture mechanics. It had been operated on the range of about 700 deg C and degraded by high temperature. It was tested for material properties of used component because of material properties changing at high temperature condition. The elastic-plastic fracture mechanics parameter, J is obtained with finite element method. A method is suggested which determines J Ic applying analysis of elastic-plastic finite element method and results of experimental load-displacements with CT specimen. It is also investigated that J-integral is applied for the elastic-plastic analysis in high temperature components. The elastic-plastic fracture toughness. J Ic determined by finite element was obtained with high accuracy using the experimental method.=20

Dynamic elastic-plastic behaviour of a frame including coupled bending and torsion

International Nuclear Information System (INIS)

Messmer, S.; Sayir, M.

1989-01-01

The full time response of a space frame under impact loading perpendicular to the frame plane is discussed. Theoretical solutions and experimental results are presented and compared. A space frame clamped at its two ends is loaded by a 0.22 lead bullet that hits a mass in the middle of the transversal beam of the frame. The loading time is about 40 to 60 μs and the resulting linear momentum of the impact in the experiment is 0.5 to 1 N s. The time response of this frame can be divided in four phases where different physical effects are dominant: (a) The loading phase where elastic wave motion dominates the time response. Because of the high impact forces, plastic deformation occurs in the vicinity of the mass and must be included in a theoretical model. The influence of reflections at the corners on the time response is shown in theory and experiment. (b) The evolution phase. Within this phase, a plastic collapse mechanism develops. Most of this phase is dominated by elastic deformation but local plastic deformations beside the mass are also present. Because many reflections at corners, clamps and the mass occur within this phase, a modal analysis method is used to predict time histories. (c) The plastic phase with plastic zones at the clamps. The phase sets in after the bending wave reaches the clamps. It is characterized by plastic deformation near the clamps and elastic deformation of the other parts of the frame. We used a modal analysis including plastic 'modes' to get accurate results. (d) The elastic vibration phase

Metamodel-based inverse method for parameter identification: elastic-plastic damage model

Science.gov (United States)

Huang, Changwu; El Hami, Abdelkhalak; Radi, Bouchaïb

2017-04-01

This article proposed a metamodel-based inverse method for material parameter identification and applies it to elastic-plastic damage model parameter identification. An elastic-plastic damage model is presented and implemented in numerical simulation. The metamodel-based inverse method is proposed in order to overcome the disadvantage in computational cost of the inverse method. In the metamodel-based inverse method, a Kriging metamodel is constructed based on the experimental design in order to model the relationship between material parameters and the objective function values in the inverse problem, and then the optimization procedure is executed by the use of a metamodel. The applications of the presented material model and proposed parameter identification method in the standard A 2017-T4 tensile test prove that the presented elastic-plastic damage model is adequate to describe the material's mechanical behaviour and that the proposed metamodel-based inverse method not only enhances the efficiency of parameter identification but also gives reliable results.

A three-dimensional cell-based smoothed finite element method for elasto-plasticity

International Nuclear Information System (INIS)

Lee, Kye Hyung; Im, Se Yong; Lim, Jae Hyuk; Sohn, Dong Woo

2015-01-01

This work is concerned with a three-dimensional cell-based smoothed finite element method for application to elastic-plastic analysis. The formulation of smoothed finite elements is extended to cover elastic-plastic deformations beyond the classical linear theory of elasticity, which has been the major application domain of smoothed finite elements. The finite strain deformations are treated with the aid of the formulation based on the hyperelastic constitutive equation. The volumetric locking originating from the nearly incompressible behavior of elastic-plastic deformations is remedied by relaxing the volumetric strain through the mean value. The comparison with the conventional finite elements demonstrates the effectiveness and accuracy of the present approach.

A three-dimensional cell-based smoothed finite element method for elasto-plasticity

Energy Technology Data Exchange (ETDEWEB)

Lee, Kye Hyung; Im, Se Yong [KAIST, Daejeon (Korea, Republic of); Lim, Jae Hyuk [KARI, Daejeon (Korea, Republic of); Sohn, Dong Woo [Korea Maritime and Ocean University, Busan (Korea, Republic of)

2015-02-15

This work is concerned with a three-dimensional cell-based smoothed finite element method for application to elastic-plastic analysis. The formulation of smoothed finite elements is extended to cover elastic-plastic deformations beyond the classical linear theory of elasticity, which has been the major application domain of smoothed finite elements. The finite strain deformations are treated with the aid of the formulation based on the hyperelastic constitutive equation. The volumetric locking originating from the nearly incompressible behavior of elastic-plastic deformations is remedied by relaxing the volumetric strain through the mean value. The comparison with the conventional finite elements demonstrates the effectiveness and accuracy of the present approach.

Elastic-Plastic Constitutive Equation of WC-Co Cemented Carbides with Anisotropic Damage

International Nuclear Information System (INIS)

Hayakawa, Kunio; Nakamura, Tamotsu; Tanaka, Shigekazu

2007-01-01

Elastic-plastic constitutive equation of WC-Co cemented carbides with anisotropic damage is proposed to predict a precise service life of cold forging tools. A 2nd rank symmetric tensor damage tensor is introduced in order to express the stress unilaterality; a salient difference in uniaxial behavior between tension and compression. The conventional framework of irreversible thermodynamics is used to derive the constitutive equation. The Gibbs potential is formulated as a function of stress, damage tensor, isotropic hardening variable and kinematic hardening variable. The elastic-damage constitutive equation, conjugate forces of damage, isotropic hardening and kinematic hardening variable is derived from the potential. For the kinematic hardening variable, the superposition of three kinematic hardening laws is employed in order to improve the cyclic behavior of the material. For the evolution equation of the damage tensor, the damage is assumed to progress by fracture of the Co matrix - WC particle interface and by the mechanism of fatigue, i.e. the accumulation of microscopic plastic strain in matrix and particles. By using the constitutive equations, calculation of uniaxial tensile and compressive test is performed and the results are compared with the experimental ones in the literature. Furthermore, finite element analysis on cold forward extrusion was carried out, in which the proposed constitutive equation was employed as die insert material

Strain gradient plasticity effects in whisker-reinforced metals

DEFF Research Database (Denmark)

Niordson, Christian Frithiof

2002-01-01

A metal reinforced by fibers in the micron range is studied using the strain gradient plasticity theory of Fleck and Hutchinson (2001). Cell-model analyzes are used to study the influence of the material length parameters numerically. Different higher order boundary conditions are considered...... at the fiber-matrix interface. The results are presented as overall stress-strain curves for the whisker-reinforced metal, and also contour plots of effective plastic strain are shown. The strain gradient plasticity theory predicts a significant stiffening effect when compared to conventional models...

Simplified Theory of Plastic Zones for cyclic loading and multilinear hardening

International Nuclear Information System (INIS)

Hübel, Hartwig

2015-01-01

The Simplified Theory of Plastic Zones (STPZ) is a direct method based on Zarka's method, primarily developed to estimate post-shakedown quantities of structures under cyclic loading, avoiding incremental analyses through a load histogram. In a different paper the STPZ has previously been shown to provide excellent estimates of the elastic–plastic strain ranges in the state of plastic shakedown as required for fatigue analyses. In the present paper, it is described how the STPZ can be used to predict the strains accumulated through a number of loading cycles due to a ratcheting mechanism, until either elastic or plastic shakedown is achieved, so that strain limits can be satisfied. Thus, a consistent means of estimating both, strain ranges and accumulated strains is provided for structural integrity assessment as required by pressure vessel codes. The computational costs involved typically consist of few linear elastic analyses and some local calculations. Multilinear kinematic hardening and temperature dependent yield stresses are accounted for. The quality of the results and the computational burden involved are demonstrated through four examples. - Highlights: • A method is provided to estimate accumulated elastic–plastic strains. • A consistent method is provided to estimate elastic–plastic strain ranges. • Effect of multilinear kinematic hardening is captured. • Temperature dependent material properties are accounted for. • Few linear elastic analyses required

Stress Wave Propagation in Viscoelastic-Plastic Rock-Like Materials

Directory of Open Access Journals (Sweden)

Liu Lang

2016-05-01

Full Text Available Rock-like materials are composites that can be regarded as a mixture composed of elastic, plastic, and viscous components. They exhibit viscoelastic-plastic behavior under a high-strain-rate loading according to element model theory. This paper presents an analytical solution for stress wave propagation in viscoelastic-plastic rock-like materials under a high-strain-rate loading and verifies the solution through an experimental test. A constitutive equation of viscoelastic-plastic rock-like materials was first established, and then kinematic and kinetic equations were then solved to derive the analytic solution for stress wave propagation in viscoelastic-plastic rock-like materials. An experimental test using the SHPB (Split Hopkinson Pressure Bar for a concrete specimen was conducted to obtain a stress-strain curve under a high-strain-rate loading. Inverse analysis based on differential evolution was conducted to estimate undetermined variables for constitutive equations. Finally, the relationship between the attenuation factor and the strain rate in viscoelastic-plastic rock-like materials was investigated. According to the results, the frequency of the stress wave, viscosity coefficient, modulus of elasticity, and density play dominant roles in the attenuation of the stress wave. The attenuation decreases with increasing strain rate, demonstrating strongly strain-dependent attenuation in viscoelastic-plastic rock-like materials.

Elastic-plastic analysis of the toroidal field coil inner leg of the compact ignition tokamak

International Nuclear Information System (INIS)

Horie, T.

1987-07-01

Elastic-plastic analyses were made for the inner leg of the Compact Ignition Tokamak toroidal field (TF) coil, which is made of copper-Inconel composite material. From the result of the elastic-plastic analysis, the effective Young's moduli of the inner leg were determined by the analytical equations. These Young's moduli are useful for the three-dimensional, elastic, overall TF coil analysis. Comparison among the results of the baseline design (R = 1.324 m), the bucked pressless design, the 1.527-m major radius design, and the 1.6-m major radius design was also made, based on the elastic-plastic TF coil inner leg analyses

Robust Return Algorithm for Anisotropic Plasticity Models

DEFF Research Database (Denmark)

Tidemann, L.; Krenk, Steen

2017-01-01

Plasticity models can be defined by an energy potential, a plastic flow potential and a yield surface. The energy potential defines the relation between the observable elastic strains ϒe and the energy conjugate stresses Τe and between the non-observable internal strains i and the energy conjugat...

Elastic constants from microscopic strain fluctuations

Science.gov (United States)

Sengupta; Nielaba; Rao; Binder

2000-02-01

Fluctuations of the instantaneous local Lagrangian strain epsilon(ij)(r,t), measured with respect to a static "reference" lattice, are used to obtain accurate estimates of the elastic constants of model solids from atomistic computer simulations. The measured strains are systematically coarse-grained by averaging them within subsystems (of size L(b)) of a system (of total size L) in the canonical ensemble. Using a simple finite size scaling theory we predict the behavior of the fluctuations as a function of L(b)/L and extract elastic constants of the system in the thermodynamic limit at nonzero temperature. Our method is simple to implement, efficient, and general enough to be able to handle a wide class of model systems, including those with singular potentials without any essential modification. We illustrate the technique by computing isothermal elastic constants of "hard" and "soft" disk triangular solids in two dimensions from Monte Carlo and molecular dynamics simulations. We compare our results with those from earlier simulations and theory.

A strain gradient plasticity theory with application to wire torsion

KAUST Repository

Liu, J. X.; El Sayed, Tamer S.

2014-01-01

Based on the framework of the existing strain gradient plasticity theories, we have examined three kinds of relations for the plastic strain dependence of the material intrinsic length scale, and thus developed updated strain gradient plasticity

Mathematical theory of elastic and elasto-plastic bodies an introduction

CERN Document Server

Necas, J

2013-01-01

The book acquaints the reader with the basic concepts and relations of elasticity and plasticity, and also with the contemporary state of the theory, covering such aspects as the nonlinear models of elasto-plastic bodies and of large deflections of plates, unilateral boundary value problems, variational principles, the finite element method, and so on.

Effective X-ray elastic constant measurement for in situ stress measurement of biaxially strained AA5754-O

International Nuclear Information System (INIS)

Iadicola, Mark A.; Gnäupel-Herold, Thomas H.

2012-01-01

Accurate measurement of stresses by X-ray diffraction requires accurate X-ray elastic constants. Calibration experiments are one method to determine these for a specific material in a specific condition. In this paper, uniaxial tension experiments are used to investigate the variation of these constants after uniaxial and equal-biaxial plastic deformation for an aluminum alloy (AA5754-O) of interest to the automotive industry. These data are critical for accurate measurement of the biaxial mechanical properties of the material using a recent experimental method combining specialized sheet metal forming equipment with portable X-ray diffraction equipment. The measured effective X-ray elastic constants show some minor variation with increased plastic deformation, and this behavior was found to be consistent for both uniaxially and equal-biaxially strained samples. The use of two average values for effective X-ray elastic constants, one in the rolling direction and one transverse to the rolling direction of the sheet material, is shown to be of sufficient accuracy for the combined tests of interest. Comparison of uniaxial data measured using X-ray diffraction and standard methods show good agreement, and biaxial stress–strain results show good repeatability. Additionally, the calibration data show some non-linear behavior, which is analyzed in regards to crystallographic texture and intergranular stress effects. The non-linear behavior is found to be the result of intergranular stresses based on comparison with additional measurements using other X-ray diffraction equipment and neutron diffraction.

Elastic and plastic buckling of shells. The CEASEMT system. Available results. Comparison with tests

International Nuclear Information System (INIS)

Hoffmann, A.; Roche, R.; Jeanpierre, F.; Goldstein, S.

1977-01-01

Specific routines for the analysis of elastic and elastic-plastic buckling have been written in the CEASEMT system of analysis by the finite element method. The basis of formulation are reviewed with emphasis on important points like: the correct and comprehensive formulation of the second order terms, the nonconservative loads. Some computational results are given and a comparison is made with experimental results (Euler type buckling of a long tube, elastic-plastic buckling of torispherical ends) [fr

On fracture in finite strain gradient plasticity

DEFF Research Database (Denmark)

Martínez Pañeda, Emilio; Niordson, Christian Frithiof

2016-01-01

In this work a general framework for damage and fracture assessment including the effect of strain gradients is provided. Both mechanism-based and phenomenological strain gradient plasticity (SGP) theories are implemented numerically using finite deformation theory and crack tip fields are invest......In this work a general framework for damage and fracture assessment including the effect of strain gradients is provided. Both mechanism-based and phenomenological strain gradient plasticity (SGP) theories are implemented numerically using finite deformation theory and crack tip fields...... are investigated. Differences and similarities between the two approaches within continuum SGP modeling are highlighted and discussed. Local strain hardening promoted by geometrically necessary dislocations (GNDs) in the vicinity of the crack leads to much higher stresses, relative to classical plasticity...... in the multiple parameter version of the phenomenological SGP theory. Since this also dominates the mechanics of indentation testing, results suggest that length parameters characteristic of mode I fracture should be inferred from nanoindentation....

Burial stress and elastic strain of carbonate rocks

DEFF Research Database (Denmark)

Fabricius, Ida Lykke

2014-01-01

Burial stress on a sediment or sedimentary rock is relevant for predicting compaction or failure caused by changes in, e.g., pore pressure in the subsurface. For this purpose, the stress is conventionally expressed in terms of its effect: “the effective stress” defined as the consequent elastic...... strain multiplied by the rock frame modulus. We cannot measure the strain directly in the subsurface, but from the data on bulk density and P‐wave velocity, we can estimate the rock frame modulus and Biot's coefficient and then calculate the “effective vertical stress” as the total vertical stress minus...... the product of pore pressure and Biot's coefficient. We can now calculate the elastic strain by dividing “effective stress” with the rock frame modulus. By this procedure, the degree of elastic deformation at a given time and depth can be directly expressed. This facilitates the discussion of the deformation...

X-Ray Elastic Constants for Cubic Materials

Energy Technology Data Exchange (ETDEWEB)

Malen, K.

1974-10-15

The stress-strain relation to be used in X-ray stress measurements in anisotropic texture-free media is studied. The method for evaluation of appropriate elastic constants for a cubic medium is described. Some illustrative numerical examples have been worked out including line broadening due to elastic anisotropy. The elastic stress and strain compatibility at grain boundaries is taken into account using Kroner's method. These elastic constants obviously only apply when no internal stresses due to plastic deformation are present. The case of reorientation of free interstitials in the stress field can be taken into account

X-Ray Elastic Constants for Cubic Materials

International Nuclear Information System (INIS)

Malen, K.

1974-10-01

The stress-strain relation to be used in X-ray stress measurements in anisotropic texture-free media is studied. The method for evaluation of appropriate elastic constants for a cubic medium is described. Some illustrative numerical examples have been worked out including line broadening due to elastic anisotropy. The elastic stress and strain compatibility at grain boundaries is taken into account using Kroner's method. These elastic constants obviously only apply when no internal stresses due to plastic deformation are present. The case of reorientation of free interstitials in the stress field can be taken into account

X-Ray Elastic Constants for Cubic Materials

Energy Technology Data Exchange (ETDEWEB)

Malen, K

1974-10-15

The stress-strain relation to be used in X-ray stress measurements in anisotropic texture-free media is studied. The method for evaluation of appropriate elastic constants for a cubic medium is described. Some illustrative numerical examples have been worked out including line broadening due to elastic anisotropy. The elastic stress and strain compatibility at grain boundaries is taken into account using Kroner's method. These elastic constants obviously only apply when no internal stresses due to plastic deformation are present. The case of reorientation of free interstitials in the stress field can be taken into account

Strain gradient crystal plasticity effects on flow localization

DEFF Research Database (Denmark)

Borg, Ulrik

2007-01-01

for metals described by the reformulated Fleck-Hutchinson strain gradient plasticity theory. The theory is implemented numerically within a finite element framework using slip rate increments and displacement increments as state variables. The formulation reduces to the classical crystal plasticity theory...... in the absence of strain gradients. The model is used to study the effect of an internal material length scale on the localization of plastic flow in shear bands in a single crystal under plane strain tension. It is shown that the mesh sensitivity is removed when using the nonlocal material model considered...

Modeling Pseudo-elastic Behavior of Springback

International Nuclear Information System (INIS)

Xia, Z. Cedric

2005-01-01

constant. In the context of this investigation we refer psuedoelastic behavior in the most general sense as any deviation from linearity in the unloading curve. The non-linearity leads to a hysteresis loop upon reloading. The approach is based on the non-conventional theory with a vanishing elastic region as advanced by Dafalias and Popov. The treatment is purely phenomenological where we don't distinguish between macroscopic plasticity and micro-plasticity. The macroscopic uniaxial stress-strain curve is used to define effective plastic response in the same manner as classical plasticity theory except that the nonlinearity during unloading and reloading are incorporated into plasticity. It is shown that such models can be easily formulated within the context of elastoplasticity without violating any physical mechanisms of deformation. Springback for a plane strain bending model is used to demonstrate the potential effect if such a model is applied

Elastic-Plastic Behaviour of Ultrasonic Assisted Compression of Polyvinyl Chloride (PVC) Foam

Science.gov (United States)

Muhalim, N. A. D.; Hassan, M. Z.; Daud, Y.

2018-04-01

The present study aims to investigate the elastic-plastic behaviour of ultrasonic assisted compression of PVC closed-cell foam. A series of static and ultrasonic compression test of PVC closed-cell foam were conducted at a constant cross head speed of 30 mm/min on dry surface condition. For quasi-static test, specimen was compressed between two rigid platens using universal testing machine. In order to evaluate the specimen behavior under ultrasonic condition, specimen was placed between a specifically design double-slotted block horn and rigid platen. The horn was designed and fabricated prior to the test as a medium to transmit the ultrasonic vibration from the ultrasonic transducer to the working specimen. It was tuned to a frequency of 19.89 kHz in longitudinal mode and provided an average oscillation amplitude at 6 µm on the uppermost surface. Following, the characteristics of stress-strain curves for quasi-static and ultrasonic compression tests were analyzed. It was found that the compressive stress was significantly reduced at the onset of superimposed ultrasonic vibration during plastic deformation.

Some comment on the use of J criterion in elastic plastic fracture mechanics

International Nuclear Information System (INIS)

Roche, R.L.

1978-01-01

In Post Yield Fracture Mechanics, several criteria have been proposed for the onset of crack propagation, one of the most popular being the J 1 integral criterion. This is only well established for elastic materials, where it can be shown that J 1 is not path dependent, and that J 1 is equal to the variation of potential energy with crack length. Extension is easy for material exhibiting deformation type plasticity, but there is no proof of path independence for flow-type plastic material. Experimental results are often given as a proof of J 1 criterion validity, but a critical analysis shows that important assumptions are made in the use of the test results. The main assumption is that the received work, known as strain energy, is not dependent on the loading history and is only dependent on the mechanical state. The study of the J 1 path dependence is the main point of the J 1 criteria validation. A general method to assess path dependence can be founded on the 'defect vector' (or driving force) concept. The space-density of defect is given by j = grad W - σ grad (W = strain-energy, σ stress tensor, epsilon strain tensor). It is shown that the virtual translation delta a of the defect vectors inside a volume, lead to a virtual work variation given by J 1 delta a and that J 1 is the resultant of all the defect vectors included in the volume surrounded by the integration surface. Using these results the path independence conditions are examined. Some numerical results are given for incremental processes such as plasticity or creep, and where the loading path is radial (proportional) and monotonic, no appreciable path variations found. Finally the results of direct applications of J 1 criterion to real structures are examined. (author)

Micro-scale measurements of plastic strain field, and local contributions of slip and twinning in TWIP steels during in situ tensile tests

Energy Technology Data Exchange (ETDEWEB)

Yang, H.K. [Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, 72 Wenhua Road, Shenyang 110016 (China); Laboratoire de Mécanique des Solides, Ecole Polytechnique, CNRS UMR7649, Université Paris-Saclay, 91128 Palaiseau (France); Doquet, V., E-mail: doquet@lms.polytechnique.fr [Laboratoire de Mécanique des Solides, Ecole Polytechnique, CNRS UMR7649, Université Paris-Saclay, 91128 Palaiseau (France); Zhang, Z.F. [Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, 72 Wenhua Road, Shenyang 110016 (China)

2016-08-30

In-situ tensile tests were carried out on Fe22Mn0.6C and Fe22Mn0.6C3Al (wt%) twinning-induced plasticity (TWIP) steels specimens covered with gold micro-grids. High resolution atomic force microscopy (AFM) and scanning electron microscope (SEM) images were periodically captured. The latter were used for measurements of the plastic strain field, using digital image correlation (DIC). Although no meso-scale localization bands appeared, some areas were deformed three times more than average. Plastic deformation inside the grains was more heterogeneous in Fe22Mn0.6C, but at meso-scale, the degree of strain heterogeneity was not higher, at least up to 12% strain. Plastic deformation started from grain boundaries or annealing twin boundaries in both materials, due to a high elastic anisotropy of the grains. An original method based on DIC was developed to estimate the twin fraction in grains that exhibit a single set of slip/twin bands. Deformation twinning accommodated 60–80% of the plastic strain in some favorably oriented grains, from the onset of plastic flow in Fe22Mn0.6C, but was not observed in the Al-bearing steel until 12% strain. The back stress was important in both materials, but significantly higher in Fe22Mn0.6C.

Micro-scale measurements of plastic strain field, and local contributions of slip and twinning in TWIP steels during in situ tensile tests

International Nuclear Information System (INIS)

Yang, H.K.; Doquet, V.; Zhang, Z.F.

2016-01-01

In-situ tensile tests were carried out on Fe22Mn0.6C and Fe22Mn0.6C3Al (wt%) twinning-induced plasticity (TWIP) steels specimens covered with gold micro-grids. High resolution atomic force microscopy (AFM) and scanning electron microscope (SEM) images were periodically captured. The latter were used for measurements of the plastic strain field, using digital image correlation (DIC). Although no meso-scale localization bands appeared, some areas were deformed three times more than average. Plastic deformation inside the grains was more heterogeneous in Fe22Mn0.6C, but at meso-scale, the degree of strain heterogeneity was not higher, at least up to 12% strain. Plastic deformation started from grain boundaries or annealing twin boundaries in both materials, due to a high elastic anisotropy of the grains. An original method based on DIC was developed to estimate the twin fraction in grains that exhibit a single set of slip/twin bands. Deformation twinning accommodated 60–80% of the plastic strain in some favorably oriented grains, from the onset of plastic flow in Fe22Mn0.6C, but was not observed in the Al-bearing steel until 12% strain. The back stress was important in both materials, but significantly higher in Fe22Mn0.6C.

An incremental flow theory for crystal plasticity incorporating strain gradient effects

DEFF Research Database (Denmark)

Nellemann, Christopher; Niordson, Christian Frithiof; Nielsen, Kim Lau

2017-01-01

The present work investigates a new approach to formulating a rate-independent strain gradient theory for crystal plasticity. The approach takes as offset recent discussions published in the literature for isotropic plasticity, and a key ingredient of the present work is the manner in which...... a gradient enhanced effective slip measure governs hardening evolution. The effect of both plastic strains and plastic strain gradients are combined into this scalar effective slip quantity, the energy associated with plastic strain is dissipative (unrecoverable), while the energy from plastic strain...... gradients is recoverable (free). The framework developed forms the basis of a finite element implementation and is demonstrated on benchmark problems designed to bring out effects such as strengthening and hardening. Monotonic loading and plane strain deformation is assumed throughout, but despite this, non...

Comparison of linear-elastic-plastic, and fully plastic failure models in the assessment of piping integrity

International Nuclear Information System (INIS)

Streit, R.D.

1981-01-01

The failure evaluation of Pressurized Water Reactor (PWR) primary coolant loop pipe is often based on a plastic limit load criterion; i.e., failure occurs when the stress on the pipe section exceeds the material flow stress. However, in addition the piping system must be safe against crack propagation at stresses less than those leading to plastic instability. In this paper, elastic, elastic-plastic, and fully-plastic failure models are evaluated, and the requirements for piping integrity based on these models are compared. The model yielding the 'more' critical criteria for the given geometry and loading conditions defines the appropriate failure criterion. The pipe geometry and loading used in this study was choosen based on an evaluation of a guillotine break in a PWR primary coolant loop. It is assumed that the piping may contain cracks. Since a deep circumferential crack, can lead to a guillotine pipe break without prior leaking and thus without warning it is the focus of the failure model comparison study. The hot leg pipe, a 29 in. I.D. by 2.5 in. wall thickness stainless pipe, was modeled in this investigation. Cracks up to 90% through the wall were considered. The loads considered in this evaluation result from the internal pressure, dead weight, and seismic stresses. For the case considered, the internal pressure contributes the most to the failure loading. The maximum moment stress due to the dead weight and seismic moments are simply added to the pressure stress. Thus, with the circumferential crack geometry and uniform pressure stress, the problem is axisymmetric. It is analyzed using NIKE2D--an implicit, finite deformation, finite element code for analyzing two-dimensional elastic-plastic problems. (orig./GL)

Thermodynamic analysis of elastic-plastic deformation

International Nuclear Information System (INIS)

Lubarda, V.

1981-01-01

The complete set of constitutive equations which fully describes the behaviour of material in elastic-plastic deformation is derived on the basis of thermodynamic analysis of the deformation process. The analysis is done after the matrix decomposition of the deformation gradient is introduced into the structure of thermodynamics with internal state variables. The free energy function, is decomposed. Derive the expressions for the stress response, entropy and heat flux, and establish the evolution equation. Finally, we establish the thermodynamic restrictions of the deformation process. (Author) [pt

On the Effect of Unit-Cell Parameters in Predicting the Elastic Response of Wood-Plastic Composites

Directory of Open Access Journals (Sweden)

Fatemeh Alavi

2013-01-01

Full Text Available This paper presents a study on the effect of unit-cell geometrical parameters in predicting elastic properties of a typical wood plastic composite (WPC. The ultimate goal was obtaining the optimal values of representative volume element (RVE parameters to accurately predict the mechanical behavior of the WPC. For each unit cell, defined by a given combination of the above geometrical parameters, finite element simulation in ABAQUS was carried out, and the corresponding stress-strain curve was obtained. A uniaxial test according to ASTM D638-02a type V was performed on the composite specimen. Modulus of elasticity was determined using hyperbolic tangent function, and the results were compared to the sets of finite element analyses. Main effects of RVE parameters and their interactions were demonstrated and discussed, specially regarding the inclusion of two adjacent wood particles within one unit cell of the material. Regression analysis was performed to mathematically model the RVE parameter effects and their interactions over the modulus of elasticity response. The model was finally employed in an optimization analysis to arrive at an optimal set of RVE parameters that minimizes the difference between the predicted and experimental moduli of elasticity.

Quantifying the Mechanical Properties of Materials and the Process of Elastic-Plastic Deformation under External Stress on Material

Directory of Open Access Journals (Sweden)

Jan Valíček

2015-11-01

Full Text Available The paper solves the problem of the nonexistence of a new method for calculation of dynamics of stress-deformation states of deformation tool-material systems including the construction of stress-strain diagrams. The presented solution focuses on explaining the mechanical behavior of materials after cutting by abrasive waterjet technology (AWJ, especially from the point of view of generated surface topography. AWJ is a flexible tool accurately responding to the mechanical resistance of the material according to the accurately determined shape and roughness of machined surfaces. From the surface topography, it is possible to resolve the transition from ideally elastic to quasi-elastic and plastic stress-strain states. For detecting the surface structure, an optical profilometer was used. Based on the analysis of experimental measurements and the results of analytical studies, a mathematical-physical model was created and an exact method of acquiring the equivalents of mechanical parameters from the topography of surfaces generated by abrasive waterjet cutting and external stress in general was determined. The results of the new approach to the construction of stress-strain diagrams are presented. The calculated values agreed very well with those obtained by a certified laboratory VÚHŽ.

Quantifying the Mechanical Properties of Materials and the Process of Elastic-Plastic Deformation under External Stress on Material

Science.gov (United States)

Valíček, Jan; Harničárová, Marta; Öchsner, Andreas; Hutyrová, Zuzana; Kušnerová, Milena; Tozan, Hakan; Michenka, Vít; Šepelák, Vladimír; Mitaľ, Dušan; Zajac, Jozef

2015-01-01

The paper solves the problem of the nonexistence of a new method for calculation of dynamics of stress-deformation states of deformation tool-material systems including the construction of stress-strain diagrams. The presented solution focuses on explaining the mechanical behavior of materials after cutting by abrasive waterjet technology (AWJ), especially from the point of view of generated surface topography. AWJ is a flexible tool accurately responding to the mechanical resistance of the material according to the accurately determined shape and roughness of machined surfaces. From the surface topography, it is possible to resolve the transition from ideally elastic to quasi-elastic and plastic stress-strain states. For detecting the surface structure, an optical profilometer was used. Based on the analysis of experimental measurements and the results of analytical studies, a mathematical-physical model was created and an exact method of acquiring the equivalents of mechanical parameters from the topography of surfaces generated by abrasive waterjet cutting and external stress in general was determined. The results of the new approach to the construction of stress-strain diagrams are presented. The calculated values agreed very well with those obtained by a certified laboratory VÚHŽ. PMID:28793645

Analysis of elastic-plastic dynamic response of reinforced concrete frame structure

International Nuclear Information System (INIS)

Li Zhongcheng

2009-01-01

Based on a set of data from seismic response test on an R/C frame, a force-based R/C beam fibre model with non-linear material properties and bond-slip effects are presented firstly in this paper, and then the applications to the tested R/C frame are presented to illustrate the model characteristics and to show the accuracy of seismic analysis including consideration of non-linear factors. It can be concluded that the elastic-plastic analysis is a potential step toward the accurate modelling for the dynamic analyses of R/C structures. Especially for the seismic safety re-evaluation of the existing NPPs, the elastic-plastic methodology with consideration of different non-linearities should be involved. (author)

Influence of plastic strain on deformation-induced martensitic transformations

NARCIS (Netherlands)

Perdahcioglu, Emin Semih; Geijselaers, Hubertus J.M.; Groen, M.

2008-01-01

The effects of plastic strain on deformation-induced martensitic transformations have been investigated experimentally. Austenitic metastable stainless steel samples were heated to a temperature at which the transformation is suppressed and were plastically strained to different amounts. The

Interrelationship between flexoelectricity and strain gradient elasticity in ferroelectric nanofilms: A phase field study

Science.gov (United States)

Jiang, Limei; Xu, Xiaofei; Zhou, Yichun

2016-12-01

With the development of the integrated circuit technology and decreasing of the device size, ferroelectric films used in nano ferroelectric devices become thinner and thinner. Along with the downscaling of the ferroelectric film, there is an increasing influence of two strain gradient related terms. One is the strain gradient elasticity and the other one is flexoelectricity. To investigate the interrelationship between flexoelectricity and strain gradient elasticity and their combined effect on the domain structure in ferroelectric nanofilms, a phase field model of flexoelectricity and strain gradient elasticity on the ferroelectric domain evolution is developed based on Mindlin's theory of strain-gradient elasticity. Weak form is derived and implemented in finite element formulations for numerically solving the model equations. The simulation results show that upper bounds for flexoelectric coefficients can be enhanced by increasing strain gradient elasticity coefficients. While a large flexoelectricity that exceeds the upper bound can induce a transition from a ferroelectric state to a modulated/incommensurate state, a large enough strain gradient elasticity may lead to a conversion from an incommensurate state to a ferroelectric state. Strain gradient elasticity and the flexoelectricity have entirely opposite effects on polarization. The observed interrelationship between the strain gradient elasticity and flexoelectricity is rationalized by an analytical solution of the proposed theoretical model. The model proposed in this paper could help us understand the mechanism of phenomena observed in ferroelectric nanofilms under complex electromechanical loads and provide some guides on the practical application of ferroelectric nanofilms.

Attenuation of stress waves in single and multi-layered structures. [mitigation of elastic and plastic stress waves during spacecraft landing

Science.gov (United States)

Yang, J. C. S.; Tsui, C. Y.

1972-01-01

Analytical and experimental studies were made of the attenuation of the stress waves during passage through single and multilayer structures. The investigation included studies on elastic and plastic stress wave propagation in the composites and those on shock mitigating material characteristics such as dynamic stress-strain relations and energy absorbing properties. The results of the studies are applied to methods for reducing the stresses imposed on a spacecraft during planetary or ocean landings.

Birefringence and incipient plastic deformation in elastically overdriven [100] CaF2 under shock compression

Science.gov (United States)

Li, Y.; Zhou, X. M.; Cai, Y.; Liu, C. L.; Luo, S. N.

2018-04-01

[100] CaF2 single crystals are shock-compressed via symmetric planar impact, and the flyer plate-target interface velocity histories are measured with a laser displacement interferometry. The shock loading is slightly above the Hugoniot elastic limit to investigate incipient plasticity and its kinetics, and its effects on optical properties and deformation inhomogeneity. Fringe patterns demonstrate different features in modulation of fringe amplitude, including birefringence and complicated modulations. The birefringence is attributed to local lattice rotation accompanying incipient plasticity. Spatially resolved measurements show inhomogeneity in deformation, birefringence, and fringe pattern evolutions, most likely caused by the inhomogeneity associated with lattice rotation and dislocation slip. Transiently overdriven elastic states are observed, and the incubation time for incipient plasticity decreases inversely with increasing overdrive by the elastic shock.

The elastic strain energy of crystallographic shear planes in reduced tungsten trioxide

International Nuclear Information System (INIS)

Iguchi, E.; Tilley, R.J.D.

1977-01-01

Calculations of the elastic strain energy due to crystallographic shear (c.s.) planes lying upon 102, 103 and 001 planes in reduced tungsten trioxide crystals have been made. The cases analysed in detail are for both isolated c.s. planes and for pairs of c.s. planes. These results are used to determine the elastic strain energy per unit volume for crystals containing ordered arrays of c.s. planes. It was found that the magnitude of the elastic strain energy was in the sequence 001 < 102 < 103 and that at relatively small inter-c.s. spacings the curves of elastic strain energy against c.s. plane separation take the form of a series of peaks and valleys. These results are compared with experimental observations of c.s. plane spacings in substantially reduced crystals containing quasi-ordered arrays of c.s. planes and with observations of c.s. plane nucleation and growth in both slightly and more appreciably reduced crystals. It was found that the elastic strain energy plays a significant part in controlling the microstructure of c.s. plane arrays in such cases. (author)

Effect of plastic strain on the evolution of crystallographic texture in Zircaloy-2

Energy Technology Data Exchange (ETDEWEB)

Ballinger, R.G. (Massachusetts Inst. of Tech., Cambridge (USA)); Lucas, G.E. (California Univ., Santa Barbara (USA)); Pelloux, R.M. (Massachusetts Inst. of Tech., Cambridge (USA). Dept. of Materials Science and Engineering)

1984-09-01

The evolution of crystallographic texture during plastic deformation was investigated in Zircaloy-2 using X-ray and metallographic techniques. Inverse pole figures, the resolved fraction of basal poles, and the volume fraction of twinned material, were determined as a function of plastic strain for several strain paths and initial textures at 298 K and 623 K. Incremental transverse platic strain ratios (R) were measured as a function of plastic strain. Texture rotation occurs early in the deformation process, after as little as 1.5% plastic strain. For compressive plastic strains, the resolved fraction of basal poles increases in the direction parallel to the strain axis. For tensile plastic strains, the resolved fraction of basal poles decreases in the direction parallel to the strain axis. The rate of change of the resolved fraction of basal poles with plastic strain is a function of the initial resolved fraction of basal poles. The texture rotation can be explained by considering the operating of the principal tensile twinning systems, (10anti 12), .

Steady-state, elastic-plastic growth of slanted cracks in symmetrically loaded plates

DEFF Research Database (Denmark)

Nielsen, Kim Lau; Hutchinson, J. W.

2017-01-01

parameter through the plate in the plastic zone at the crack tip. The distribution of the mode I and mode III stress intensity factors along the crack front are obtained for the elastic problem. The out-of-plane bending constraint imposed on the plate significantly influences the mixed mode behavior along......Elastic and elastic-plastic results are obtained for a semi-infinite slanted through-crack propagating in a symmetrically loaded plate strip with the aim of providing theoretical background to commonly observed plate tearing behavior. Were it is not for the slant of the crack through the thickness...... of the plate, the problem would be mode I, but due to the slant the local conditions along the crack front are a combination of mode I and mode III. A three-dimensional formulation for steady-state crack propagation is employed to generate distributions of effective stress, stress triaxiality and Lode...

Elastic-plastic adhesive contact of rough surfaces using n-point asperity model

International Nuclear Information System (INIS)

Sahoo, Prasanta; Mitra, Anirban; Saha, Kashinath

2009-01-01

This study considers an analysis of the elastic-plastic contact of rough surfaces in the presence of adhesion using an n-point asperity model. The multiple-point asperity model, developed by Hariri et al (2006 Trans ASME: J. Tribol. 128 505-14) is integrated into the elastic-plastic adhesive contact model developed by Roy Chowdhury and Ghosh (1994 Wear 174 9-19). This n-point asperity model differs from the conventional Greenwood and Williamson model (1966 Proc. R. Soc. Lond. A 295 300-19) in considering the asperities not as fixed entities but as those that change through the contact process, and hence it represents the asperities in a more realistic manner. The newly defined adhesion index and plasticity index defined for the n-point asperity model are used to consider the different conditions that arise because of varying load, surface and material parameters. A comparison between the load-separation behaviour of the new model and the conventional one shows a significant difference between the two depending on combinations of mean separation, adhesion index and plasticity index.

A new strain gage method for measuring the contractile strain ratio of Zircaloy tubing

International Nuclear Information System (INIS)

Hwang, S.K.; Sabol, G.P.

1988-01-01

An improved strain gage method for determining the contractile strain ratio (CSR) of Zircaloy tubing was developed. The new method consists of a number of load-unload cyclings at approximately 0.2% plastic strain interval. With this method the CSR of Zircaloy-4 tubing could be determined accurately because it was possible to separate the plastic strains from the elastic strain involvement. The CSR values determined by use of the new method were in good agreement with those calculated from conventional post-test manual measurements. The CSR of the tubing was found to decrease with the amount of deformation during testing because of uneven plastic flow in the gage section. A new technique of inscribing gage marks by use of a YAG laser is discussed. (orig.)

Deformation mechanism study of a hot rolled Zr-2.5Nb alloy by transmission electron microscopy. I. Dislocation microstructures in as-received state and at different plastic strains

Energy Technology Data Exchange (ETDEWEB)

Long, Fei; Daymond, Mark R., E-mail: mark.daymond@queensu.ca; Yao, Zhongwen [Department of Mechanical and Materials Engineering, Queen' s University Kingston, Ontario K7L 3N6 (Canada)

2015-03-07

Thin foil dog bone samples prepared from a hot rolled Zr-2.5Nb alloy have been deformed by tensile deformation to different plastic strains. The development of slip traces during loading was observed in situ through SEM, revealing that deformation starts preferentially in certain sets of grains during the elastic-plastic transition region. TEM characterization showed that sub-grain boundaries formed during hot rolling consisted of screw 〈a〉 dislocations or screw 〈c〉 and 〈a〉 dislocations. Prismatic 〈a〉 dislocations with large screw or edge components have been identified from the sample with 0.5% plastic strain. Basal 〈a〉 and pyramidal 〈c + a〉 dislocations were found in the sample that had been deformed with 1.5% plastic strain, implying that these dislocations require larger stresses to be activated.

What is behind the plastic strain rate?

NARCIS (Netherlands)

Hütter, M.; Grmela, M.; Öttinger, H.C.

2009-01-01

The plastic strain rate plays a central role in macroscopic models on elasto-viscoplasticity. In order to discuss the concept behind this quantity, we propose, first, a kinetic toy model to describe the dynamics of sliding layers representative of plastic deformation of single crystalline metals.

Plastic strain and flux jumps in hard and composite superconductors

International Nuclear Information System (INIS)

Maksimov, I.L.; Mints, R.G.

1981-01-01

A study is made into the effect of the critical current density dependence upon the value of plastic strain on the critical state stability in hard and composite superconductors under conditions of plastic yield of the material. Criteria of the critical state stability relative to the jointly developing magnetic flux jumps and plastic strain jerks, are found. (author)

Comparison of elastic and inelastic analyses

International Nuclear Information System (INIS)

Ammerman, D.J.; Heinstein, M.W.; Wellman, G.W.

1992-01-01

The use of inelastic analysis methods instead of the traditional elastic analysis methods in the design of radioactive material (RAM) transport packagings leads to a better understanding of the response of the package to mechanical loadings. Thus, better assessment of the containment, thermal protection, and shielding integrity of the package after a structure accident event can be made. A more accurate prediction of the package response can lead to enhanced safety and also allow for a more efficient use of materials, possibly leading to a package with higher capacity or lower weight. This paper discusses the advantages and disadvantages of using inelastic analysis in the design of RAM shipping packages. The use of inelastic analysis presents several problems to the package designer. When using inelastic analysis the entire nonlinear response of the material must be known, including the effects of temperature changes and strain rate. Another problem is that there currently is not an acceptance criteria for this type of analysis that is approved by regulatory agencies. Inelastic analysis acceptance criteria based on failure stress, failure strain , or plastic energy density could be developed. For both elastic and inelastic analyses it is also important to include other sources of stress in the analyses, such as fabrication stresses, thermal stresses, stresses from bolt preloading, and contact stresses at material interfaces. Offsetting these added difficulties is the improved knowledge of the package behavior. This allows for incorporation of a more uniform margin of safety, which can result in weight savings and a higher level of confidence in the post-accident configuration of the package. In this paper, comparisons between elastic and inelastic analyses are made for a simple ring structure and for a package to transport a large quantity of RAM by rail (rail cask) with lead gamma shielding to illustrate the differences in the two analysis techniques

Elastic and plastic characteristics of a model Cu–Zr amorphous alloy

International Nuclear Information System (INIS)

Nakamura, Akiho; Kamimura, Yasushi; Edagawa, Keiichi; Takeuchi, Shin

2014-01-01

Athermal quasistatic simulation of shear deformation has been conducted for a realistic model Cu–Zr amorphous alloy to investigate characteristic features of elasticity and plasticity of the material. Significant reduction of the shear modulus by nonaffine atomic displacements and appreciable nonlinearity of elasticity have been observed. The fourth-order elastic constant in shear deformation and the ideal shear strength have been evaluated. Plastic deformation has been observed to start with isolated local shear transformations (LSTs) followed by collective LSTs leading to the formation of a shear band. Participation-ratio analysis (PRA) has demonstrated how the nonaffine displacement field converges as the system approaches the critical point of losing structural stability. PRA has also evaluated quantitatively the numbers of atoms participating in LSTs – the average number is about 30. Spatially anisotropic development of nascent shear band on a plane has been shown, attributable to anisotropic internal stress field induced by an LST. The evaluated stresses for the shear-band nucleation and for its propagation have indicated that the yielding in real materials is controlled by the shear-band propagation, as previously pointed out

Effect of cyclic plastic pre-strain on low cycle fatigue life

International Nuclear Information System (INIS)

Kanno, Satoshi; Nakane, Motoki; Yorikawa, Morio; Takagi, Yoshio

2010-01-01

In order to evaluate structural integrity of nuclear components subjected large seismic load which produce locally plastic strain, low cycle fatigue life was examined using cyclic plastic pre-strained materials of austenitic steel (SUS316, SUS316L, SUS304TP: JIS (Japanese Industrial Standards)) and ferritic steel (SFVQ1A, STS480, STPT410, SFVC2B, SS400: JIS). It was not found that cyclic plastic pre-strain up to range of 16%, 2.5 times affected on low cycle fatigue life. The validity of existing procedure of fatigue life estimation based on usage factor was confirmed when large seismic load brought nuclear materials cyclic plastic strain. (author)

Elastic-plastic stress analysis and ASME code evaluation of a bottomhead penetration in a reactor pressure vessel

International Nuclear Information System (INIS)

Ranganath, S.

1979-01-01

Nuclear pressure vessel components are designed to meet the requirements of Section III of the ASME Boiler and Pressure Vessel Code. Specifically, the design must satisfy the limits on stress range and fatigue usage prescribed in NB-3200, Section III ASME Code for the various design and operating conditions for the component. The Code requirements assure that the component does not experience gross yielding and that in general, elastic shakedown occurs following cyclic loading. When elastic stress analysis is performed this can be shown by meeting the limits in the Code on Primary and Primary plus Secondary (P+Q) stress intensities. However, when the P+Q limits cannot be met and elastic Shakedown cannot be demonstrated, plastic analysis may be performed to meet the requirements of the Code. This paper describes the elastic-plastic stress analysis of a Boiling Water Reactor Vessel bottom head in-core penetration and illustrates how plastic analysis can be used in ASME Code evaluations to show Code compliance. Details of the thermal analysis, elastic-plastic stress analysis and fatigue evaluation are presented and it is shown that the in-core penetration satisfies the code requirements. 6 refs

On the homogenization of metal matrix composites using strain gradient plasticity

DEFF Research Database (Denmark)

Azizi, Reza; Niordson, Christian Frithiof; Legarth, Brian Nyvang

2014-01-01

The homogenized response of metal matrix composites (MMC) is studied using strain gradient plasticity. The material model employed is a rate independent formulation of energetic strain gradient plasticity at the micro scale and conventional rate independent plasticity at the macro scale. Free...

Elasto-plastic model for transversely isotropic Tournemire shale based on microstructure approach

International Nuclear Information System (INIS)

Abdi, H.; Evgin, E.; Fall, M.; Nguyen, T.S.; Labrie, D.; Barnichon, J.D.; Su, G.; Simon, R.

2012-01-01

Document available in extended abstract form only. Argillaceous formations being considered as potential host rocks for the geological disposal of nuclear wastes are usually characterized by the presence of bedding planes, resulting in anisotropy of their strength and deformation properties. A laboratory program of uniaxial tests, triaxial tests, cyclic tests, and Brazilian tests with concurrent monitoring of acoustic emission was performed in order to determine the above properties. The experimental results and their interpretation are presented in detail in a companion paper (Abdi et al., 2012, in these proceedings). Typical results from triaxial tests indicate the following behaviour: 1. There is a strong dependence of the stress-strain behaviour with the loading orientation with respect to the bedding planes. 2. There are four distinct zones of the stress strain curve: a crack and/or bedding closure zone; an elastic zone, a plastic zone with strain hardening, and a collapse zone after the peak that leads abruptly to a residual strength value. 3. There is damage, especially after the peak, resulting in the degradation of the stiffness as shown by unloading-reloading cycles. In order to reproduce the above behaviour, we adopted a classical elasto-plastic framework. In the elastic range, the transversely isotropic nature of the material is taken into account by the adoption of an elastic stiffness matrix that requires five independent elastic constants. These elastic constants show degradation with the accumulated damage. Using the deviatoric plastic strain as a measure of damage, we expressed functional relationships for these constants, using the results of cyclic triaxial tests. For the plastic behaviour, we used a Mohr-Coulomb yield criterion which takes into account the relative orientation of the applied stress and the bedding planes, and also strain hardening and softening. In this work we used the deviatoric plastic strain as the hardening parameter in

Elastic-plastic creep response of structures under composite time history

Energy Technology Data Exchange (ETDEWEB)

Zudans, Z [Franklin Inst. Research Labs., Philadelphia, Pa. (USA)

1975-12-01

High temperature nuclear reactor components are subject to a complex history of thermal and mechanical loading cycles. To evaluate the adequacy of such components, detailed information on the accumulated inelastic strains and strain cycling is required. This paper presents the theory, describes efficient numerical techniques accounting for plasticity, creep and overall equilibrium, describes the overall structure of the resulting computer program, and demonstrates the capability of the analysis method on a real three-dimensional structure. The new results of this work are the efficient handling of an arbitrary load history, introduction of the 'plastic stress' concept for inelastic computation, novel implementation of classical plasticity with recognition of incrementation conditions for the kinematic hardening, use of the load incrementation algorithm based on the 'plastic stress' concept, and development of a computer code capable of solving practical three-dimensional problems.

Elastic-plastic creep response of structures under composite time history

International Nuclear Information System (INIS)

Zudans, Z.

1975-01-01

High temperature nuclear reactor components are subject to a complex history of thermal and mechanical loading cycles. To evaluate the adequacy of such components, detailed information on the accumulated inelastic strains and strain cycling is required. This paper presents the theory, describes efficient numerical techniques accounting for plasticity, creep and overall equilibrium, describes the overall structure of the resulting computer program, and demonstrates the capability of the analysis method on a real three-dimensional structure. The new results of this work are the efficient handling of an arbitrary load history, introduction of the 'plastic stress' concept for inelastic computation, novel implementation of classical plasticity with recognition of incrementation conditions for the kinematic hardening, use of the load incrementation algorithm based on the 'plastic stress' concept, and development of a computer code capable of solving practical three-dimensional problems. (Auth.)

Elastic-plastic fracture mechanics for nuclear pressure vessels: a preliminary appraisal

International Nuclear Information System (INIS)

Hahn, G.T.; Broek, D.; Marschall, C.W.; Rosenfield, A.R.; Rybicki, E.F.; Schmueser, D.W.; Stonesifer, R.B.; Kanninen, M.F.

1978-01-01

A research program directed at assessing the margin of safety of flawed nuclear pressure vessels near and beyond general yielding is described. The program has the general objective of developing an elastic-plastic fracture mechanics methodology. The approach is based on the use of finite element models together with experimental results to identify criteria appropriate for the onset of crack extension and for stable crack growth. A number of criteria beyond the conventional LEFM R curve are being evaluated. These include the critical values of the J-integral, its derivative, the crack tip opening angle, the average crack opening angle, a generalized energy release rate, its components and a crack tip force. The optimum fracture criterion for nuclear vessels is being determined by systematic measurements of load extension curves, strain distribution, crack opening displacement, stable crack growth and instability on 'toughness scaled' model materials. Computations have been performed for center cracked panels of a model material (2219-T87 aluminium) for full shear failure. (author)

A strain gradient plasticity theory with application to wire torsion

KAUST Repository

Liu, J. X.

2014-06-05

Based on the framework of the existing strain gradient plasticity theories, we have examined three kinds of relations for the plastic strain dependence of the material intrinsic length scale, and thus developed updated strain gradient plasticity versions with deformation-dependent characteristic length scales. Wire torsion test is taken as an example to assess existing and newly built constitutive equations. For torsion tests, with increasing plastic strain, a constant intrinsic length predicts too high a torque, while a decreasing intrinsic length scale can produce better predictions instead of the increasing one, different from some published observations. If the Taylor dislocation rule is written in the Nix-Gao form, the derived constitutive equations become singular when the hardening exponent gets close to zero, which seems questionable and calls for further experimental clarifications on the exact coupling of hardening due to statistically stored dislocations and geometrically necessary dislocations. Particularly, when comparing the present model with the mechanism-based strain gradient plasticity, the present model satisfies the reciprocity relation naturally and gives different predictions even under the same parameter setting. © The Author(s) 2014 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav.

On lower order strain gradient plasticity theories

DEFF Research Database (Denmark)

Niordson, Christian Frithiof; Hutchinson, J. W.

2002-01-01

By way of numerical examples, this paper explores the nature of solutions to a class of strain gradient plasticity theories that employ conventional stresses, equilibrium equations and boundary conditions. Strain gradients come into play in these modified conventional theories only to alter...

A model for plasticity kinetics and its role in simulating the dynamic behavior of Fe at high strain rates

Energy Technology Data Exchange (ETDEWEB)

Colvin, J D; Minich, R W; Kalantar, D H

2007-03-29

The recent diagnostic capability of the Omega laser to study solid-solid phase transitions at pressures greater than 10 GPa and at strain rates exceeding 10{sup 7} s{sup -1} has also provided valuable information on the dynamic elastic-plastic behavior of materials. We have found, for example, that plasticity kinetics modifies the effective loading and thermodynamic paths of the material. In this paper we derive a kinetics equation for the time-dependent plastic response of the material to dynamic loading, and describe the model's implementation in a radiation-hydrodynamics computer code. This model for plasticity kinetics incorporates the Gilman model for dislocation multiplication and saturation. We discuss the application of this model to the simulation of experimental velocity interferometry data for experiments on Omega in which Fe was shock compressed to pressures beyond the {alpha}-to-{var_epsilon} phase transition pressure. The kinetics model is shown to fit the data reasonably well in this high strain rate regime and further allows quantification of the relative contributions of dislocation multiplication and drag. The sensitivity of the observed signatures to the kinetics model parameters is presented.

The Finite Strain Johnson Cook Plasticity and Damage Constitutive Model in ALEGRA.

Energy Technology Data Exchange (ETDEWEB)

Sanchez, Jason James [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2018-02-01

A finite strain formulation of the Johnson Cook plasticity and damage model and it's numerical implementation into the ALEGRA code is presented. The goal of this work is to improve the predictive material failure capability of the Johnson Cook model. The new implementation consists of a coupling of damage and the stored elastic energy as well as the minimum failure strain criteria for spall included in the original model development. This effort establishes the necessary foundation for a thermodynamically consistent and complete continuum solid material model, for which all intensive properties derive from a common energy. The motivation for developing such a model is to improve upon ALEGRA's present combined model framework. Several applications of the new Johnson Cook implementation are presented. Deformation driven loading paths demonstrate the basic features of the new model formulation. Use of the model produces good comparisons with experimental Taylor impact data. Localized deformation leading to fragmentation is produced for expanding ring and exploding cylinder applications.

Elastic limit at macroscopic deformation of icosahedral Al-Pd-Mn single quasicrystals

International Nuclear Information System (INIS)

Ledig, L.; Bartsch, M.; Messerschmidt, U.

2006-01-01

Al 70.5 Pd 21 Mn 8.5 single quasicrystals were plastically deformed between 482 and 821 deg. C. The strain rate sensitivity of the flow stress was measured by stress relaxation tests. At several temperatures, the dislocation structures were imaged by diffraction contrast in a high-voltage electron microscope for determining the dislocation densities. At all temperatures, the plastic deformation starts with a range of very high work-hardening. The transition point between almost elastic and elastic-plastic deformation is called the elastic limit. At low temperatures, the deformation was stopped at about 1.5 GPa to prevent fracture. Above about 580 deg. C, the stress-strain curves bend down and show a yield point effect followed by a range of almost steady state deformation. At low temperatures, the elastic limit is much lower than the steady state flow stress or the maximum stresses reached without fracture. The activation parameters are different for the elastic limit, the range of high work-hardening and steady state deformation. The flow stresses are interpreted by the stress necessary to move individual dislocations and the athermal component due to the elastic interaction between dislocations. At low temperatures, a further component is necessary to explain the very high flow stresses reached by work-hardening

Taylor-plasticity-based analysis of length scale effects in void growth

KAUST Repository

Liu, Junxian

2014-09-25

We have studied the void growth problem by employing the Taylor-based strain gradient plasticity theories, from which we have chosen the following three, namely, the mechanism-based strain gradient (MSG) plasticity (Gao et al 1999 J. Mech. Phys. Solids 47 1239, Huang et al 2000 J. Mech. Phys. Solids 48 99-128), the Taylor-based nonlocal theory (TNT; 2001 Gao and Huang 2001 Int. J. Solids Struct. 38 2615) and the conventional theory of MSG (CMSG; Huang et al 2004 Int. J. Plast. 20 753). We have addressed the following three issues which occur when plastic deformation at the void surface is unconstrained. (1) Effects of elastic deformation. Elasticity is essential for cavitation instability. It is therefore important to guarantee that the gradient term entering the Taylor model is the effective plastic strain gradient instead of the total strain gradient. We propose a simple elastic-plastic decomposition method. When the void size approaches the minimum allowable initial void size related to the maximum allowable geometrically necessary dislocation density, overestimation of the flow stress due to the negligence of the elastic strain gradient is on the order of lεY/R0 near the void surface, where l, εY and R0 are, respectively, the intrinsic material length scale, the yield strain and the initial void radius. (2) MSG intrinsic inconsistency, which was initially mentioned in Gao et al (1999 J. Mech. Phys. Solids 47 1239) but has not been the topic of follow-up studies. We realize that MSG higher-order stress arises due to the linear-strain-field approximation within the mesoscale cell with a nonzero size, lε. Simple analysis shows that within an MSG mesoscale cell near the void surface, the difference between microscale and mesoscale strains is on the order of (lε/R0)2, indicating that when lε/R0 ∼ 1.0, the higher-order stress effect can make the MSG result considerably different from the TNT or CMSG results. (3) Critical condition for cavitation instability

Simplified computational methods for elastic and elastic-plastic fracture problems

Science.gov (United States)

Atluri, Satya N.

1992-01-01

An overview is given of some of the recent (1984-1991) developments in computational/analytical methods in the mechanics of fractures. Topics covered include analytical solutions for elliptical or circular cracks embedded in isotropic or transversely isotropic solids, with crack faces being subjected to arbitrary tractions; finite element or boundary element alternating methods for two or three dimensional crack problems; a 'direct stiffness' method for stiffened panels with flexible fasteners and with multiple cracks; multiple site damage near a row of fastener holes; an analysis of cracks with bonded repair patches; methods for the generation of weight functions for two and three dimensional crack problems; and domain-integral methods for elastic-plastic or inelastic crack mechanics.

Strain gradient elasticity within the symmetric BEM formulation

Directory of Open Access Journals (Sweden)

S. Terravecchia,

2014-07-01

Full Text Available The symmetric Galerkin Boundary Element Method is used to address a class of strain gradient elastic materials featured by a free energy function of the (classical strain and of its (first gradient. With respect to the classical elasticity, additional response variables intervene, such as the normal derivative of the displacements on the boundary, and the work-coniugate double tractions. The fundamental solutions - featuring a fourth order partial differential equations (PDEs system - exhibit singularities which in 2D may be of the order 1/ r 4 . New techniques are developed, which allow the elimination of most of the latter singularities. The present paper has to be intended as a research communication wherein some results, being elaborated within a more general paper [1], are reported.

The effect of plastic strain on the evolution of crystallographic texture in Zircaloy-2

International Nuclear Information System (INIS)

Ballinger, R.G.; Lucas, G.E.; Pelloux, R.M.

1984-01-01

The evolution of crystallographic texture during plastic deformation was investigated in Zircaloy-2 using X-ray and metallographic techniques. Inverse pole figures, the resolved fraction of basal poles, and the volume fraction of twinned material, were determined as a function of plastic strain for several strain paths and initial textures at 298 K and 623 K. Incremental transverse platic strain ratios (R) were measured as a function of plastic strain. Texture rotation occurs early in the deformation process, after as little as 1.5% plastic strain. For compressive plastic strains, the resolved fraction of basal poles increases in the direction parallel to the strain axis. For tensile plastic strains, the resolved fraction of basal poles decreases in the direction parallel to the strain axis. The rate of change of the resolved fraction of basal poles with plastic strain is a function of the initial resolved fraction of basal poles. The texture rotation can be explained by considering the operating of the principal tensile twinning systems, [10anti 12], . (orig.)

The effect of plastic strain on the evolution of crystallographic texture in Zircaloy-2

Science.gov (United States)

Ballinger, R. G.; Lucas, G. E.; Pelloux, R. M.

1984-09-01

The evolution of crystallographic texture during plastic deformation was investigated in Zircaloy-2 using X-ray and metallographic techniques. Inverse pole figures, the resolved fraction of basal poles, and the volume fraction of twinned material, were determined as a function of plastic strain for several strain paths and initial textures at 298 K and 623 K. Incremental transverse platic strain ratios ( R) were mesured as a function of plastic strain. Texture rotation occurs early in the deformation process, after as little as 1.5% plastic strain. For compressive plastic strains, the resolved fraction of basal poles increases in the direction parallel to the strain axis. For tensile plastic strains, the resolved fraction of basal poles decreases in the direction parallel to the strain axis. The rate of change of the resolved fraction of basal poles with plastic strain is a function of the initial resolved fraction of basal poles. The texture rotation can be explained by considering the operation of the principal tensile twinning systems, {101¯2}.

Plasticity size effects in voided crystals

DEFF Research Database (Denmark)

Hussein, M. I.; Borg, Ulrik; Niordson, Christian Frithiof

singularities in an elastic material. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and annihilation are incorporated through a set of constitutive rules. Over the range of length scales investigated, both the discrete dislocation and strain......The shear and equi-biaxial straining responses of periodic voided single crystals are analysed using discrete dislocation plasticity and a continuum strain gradient crystal plasticity theory. In the discrete dislocation formulation the dislocations are all of edge character and are modelled as line...... predictions of the two formulations for all crystal types and void volume fractions considered when the material length scale in the non-local plasticity model chosen to be $0.325\\mu m$ (around ten times the slip plane spacing in the discrete dislocation models)....

Elastic-plastic finite element analyses for reducers with constant-depth internal circumferential surface cracks

International Nuclear Information System (INIS)

Wu, Szu-Ying; Tsai, Bor-Jiun; Chen, Jien-Jong

2015-01-01

In this study, a 3-D automatic elastic-plastic finite element mesh generator is established to accurately predict the J-integral value of an arbitrary reducer with a constant-depth internal circumferential surface crack under bending and axial force. The contact pairs are used on the crack surfaces to simulate the actual contact behaviors of the crack model under loadings. In order to verify the accuracy of the proposed elastic-plastic finite element model for a reducer with a surface crack, the cracked straight pipe models are generated according to a special modeling procedure for a flawed reducer. The J-integral values along the crack front of surface crack are calculated and compared with the straight pipe models which have been verified in the previous published studies. Based on the comparison of computed results, good agreements are obtained to show the accuracy of present numerical models. More confidence on using the 3-D elastic-plastic finite element analysis for reducers with internal circumferential surface cracks can be thus established in this work

Atomistic Calculation of Elastic Moduli in Strained Silicon

National Research Council Canada - National Science Library

Zhu, Richard; Pan, Ernian; Chung, Peter W; Cai, Xinli; Liew, Kim M; Buldum, Alper

2007-01-01

.... Using our approach, the bulk modulus, effective elastic stiffnesses C11, C12, and C44 of the strained silicon, including also the effective Young's modulus and Poisson's ratio, are all calculated...

Crack nucleation and elastic / plastic deformation of TiAl alloys investigated by in-situ loaded atomic force microscopy

Energy Technology Data Exchange (ETDEWEB)

Iqbal, F.; Pyczak, F.; Neumeier, S.; Göken, M.

2017-03-24

The crack propagation mechanisms of γ-titanium aluminides with fully lamellar microstructure have been studied using in-situ deformation in the Atomic Force Microscope (AFM). AFM demonstrated the unique capability to detect elastic as well as plastic deformation during in-situ tests from topography changes on the surface. It was found that the crack nucleation, which can occur at γ/γ and α{sub 2}/γ interfaces as well as inside the γ-phase, is always preceded by strong local elastic deformation. No cracking inside the α{sub 2}-phase was observed. The elastic and plastic deformation was confined inside the γ-phase and especially pronounced near interfaces which can be explained by the differences of the elastic and plastic deformation behavior of the γ- and α{sub 2}- phase.

Finite element analysis of a finite-strain plasticity problem

International Nuclear Information System (INIS)

Crose, J.G.; Fong, H.H.

1984-01-01

A finite-strain plasticity analysis was performed of an engraving process in a plastic rotating band during the firing of a gun projectile. The aim was to verify a nonlinear feature of the NIFDI/RB code: plastic large deformation analysis of nearly incompressible materials using a deformation theory of plasticity approach and a total Lagrangian scheme. (orig.)

Lattice strain evolution in IMI 834 under applied stress

International Nuclear Information System (INIS)

Daymond, Mark R.; Bonner, Neil W.

2003-01-01

The effect of elastic and plastic anisotropy on the evolution of lattice strains in the titanium alloy IMI834 has been examined during a uniaxial tensile test, by in situ monitoring on the Engin instrument at the ISIS pulsed neutron source. Measurements were made at load during an incremental loading test. The data is analysed in the light of the requirements for engineering residual stress scanning measurements performed at polychromatic neutron and synchrotron diffraction sources. Comparisons between the measured strains from different lattice families and the predictions from an elasto-plastic self-consistent model are made. Agreement is good in the elastic regime and for most diffraction planes in the plastic regime

Mechanical strength model for plastic bonded granular materials at high strain rates and large strains

International Nuclear Information System (INIS)

Browning, R.V.; Scammon, R.J.

1998-01-01

Modeling impact events on systems containing plastic bonded explosive materials requires accurate models for stress evolution at high strain rates out to large strains. For example, in the Steven test geometry reactions occur after strains of 0.5 or more are reached for PBX-9501. The morphology of this class of materials and properties of the constituents are briefly described. We then review the viscoelastic behavior observed at small strains for this class of material, and evaluate large strain models used for granular materials such as cap models. Dilatation under shearing deformations of the PBX is experimentally observed and is one of the key features modeled in cap style plasticity theories, together with bulk plastic flow at high pressures. We propose a model that combines viscoelastic behavior at small strains but adds intergranular stresses at larger strains. A procedure using numerical simulations and comparisons with results from flyer plate tests and low rate uniaxial stress tests is used to develop a rough set of constants for PBX-9501. Comparisons with the high rate flyer plate tests demonstrate that the observed characteristic behavior is captured by this viscoelastic based model. copyright 1998 American Institute of Physics

Elastic-Plastic J-Integral Solutions or Surface Cracks in Tension Using an Interpolation Methodology

Science.gov (United States)

Allen, P. A.; Wells, D. N.

2013-01-01

No closed form solutions exist for the elastic-plastic J-integral for surface cracks due to the nonlinear, three-dimensional nature of the problem. Traditionally, each surface crack must be analyzed with a unique and time-consuming nonlinear finite element analysis. To overcome this shortcoming, the authors have developed and analyzed an array of 600 3D nonlinear finite element models for surface cracks in flat plates under tension loading. The solution space covers a wide range of crack shapes and depths (shape: 0.2 less than or equal to a/c less than or equal to 1, depth: 0.2 less than or equal to a/B less than or equal to 0.8) and material flow properties (elastic modulus-to-yield ratio: 100 less than or equal to E/ys less than or equal to 1,000, and hardening: 3 less than or equal to n less than or equal to 20). The authors have developed a methodology for interpolating between the goemetric and material property variables that allows the user to reliably evaluate the full elastic-plastic J-integral and force versus crack mouth opening displacement solution; thus, a solution can be obtained very rapidly by users without elastic-plastic fracture mechanics modeling experience. Complete solutions for the 600 models and 25 additional benchmark models are provided in tabular format.

Performance study of Ke factors in simplified elastic plastic fatigue analyses with emphasis on thermal cyclic loading

International Nuclear Information System (INIS)

Lang, Hermann; Rudolph, Juergen; Ziegler, Rainer

2011-01-01

As code-based fully elastic plastic code conforming fatigue analyses are still time consuming, simplified elastic plastic analysis is often applied. This procedure is known to be overly conservative for some conditions due to the applied plastification (penalty) factor K e . As a consequence, less conservative fully elastic plastic fatigue analyses based on non-linear finite element analyses (FEA) or simplified elastic plastic analysis based on more realistic K e factors have to be used for fatigue design. The demand for more realistic K e factors is covered as a requirement of practical fatigue analysis. Different code-based K e procedures are reviewed in this paper with special regard to performance under thermal cyclic loading conditions. Other approximation formulae such as those by Neuber, Seeger/Beste or Kuehnapfel are not evaluated in this context because of their applicability to mechanical loading excluding thermal cyclic loading conditions typical for power plant operation. Besides the current code-based K e corrections, the ASME Code Case N-779 (e.g. Adam's proposal) and its modification in ASME Section VIII is considered. Comparison of elastic plastic results and results from the Rules for Nuclear Facility Components and Rules for Pressure Vessels reveals a considerable overestimation of usage factor in the case of ASME III and KTA 3201.2 for the examined examples. Usage factors according to RCC-M, Adams (ASME Code Case N-779), ASME VIII (alternative) and EN 13445-3 are essentially comparable and less conservative for these examples. The K v correction as well as the applied yield criterion (Tresca or von Mises) essentially influence the quality of the more advanced plasticity corrections (e.g. ASME Code Case N-779 and RCC-M). Hence, new proposals are based on a refined K v correction.

Analysis of elastic strain and crystallographic texture in poled rhombohedral PZT ceramics

International Nuclear Information System (INIS)

Hall, D.A.; Steuwer, A.; Cherdhirunkorn, B.; Mori, T.; Withers, P.J.

2006-01-01

The elastic strain and crystallographic texture of a rhombohedral lead zirconate titanate ceramic have been characterised in the remanent state, after poling, using high-energy synchrotron X-ray diffraction as a function of the grain orientation ψ relative to the poling direction. It is observed that the (2 0 0) diffraction peak exhibits pronounced shifts as a function of ψ, indicating an elastic lattice strain, while others ({1 1 1}, {1 1 2} and {2 2 0}) show marked changes in intensity as a result of preferred ferroelectric domain orientation. It is shown that the (2 0 0) peak is not affected by the domain switching itself but rather acts like an elastic macrostrain sensor. A simple Eshelby analysis is used to demonstrate that both the elastic strain and texture vary systematically with ψ according to the factor (3cos 2 ψ - 1). This angular dependence is evaluated through micromechanics modelling. The physical meaning of the texture variations with ψ is also discussed

Thermo-elastic-plastic analysis for elastic component under high temperature fatigue crack growth rate

Science.gov (United States)

Ali, Mohammed Ali Nasser

The research project presents a fundamental understanding of the fatigue crack growth mechanisms of AISI 420 martensitic stainless steel, based on the comparison analysis between the theoretical and numerical modelling, incorporating research findings under isothermal fatigue loading for solid cylindrical specimen and the theoretical modelling with the numerical simulation for tubular specimen when subjected to cyclic mechanical loading superimposed by cyclic thermal shock.The experimental part of this research programme studied the fatigue stress-life data for three types of surface conditions specimen and the isothermal stress-controlled fatigue testing at 300 °C - 600 °C temperature range. It is observed that the highest strength is obtained for the polished specimen, while the machined specimen shows lower strength, and the lowest strength is the notched specimen due to the high effect of the stress concentration. The material behaviour at room and high temperatures shows an initial hardening, followed by slow extension until fully plastic saturation then followed by crack initiation and growth eventually reaching the failure of the specimen, resulting from the dynamic strain ageing occurred from the transformation of austenitic microstructure to martensite and also, the nucleation of precipitation at grain boundaries and the incremental temperature increase the fatigue crack growth rate with stress intensity factor however, the crack growth rate at 600 °C test temperature is less than 500 °C because of the creep-fatigue taking place.The theoretical modelling presents the crack growth analysis and stress and strain intensity factor approaches analysed in two case studies based on the addition of thermo-elastic-plastic stresses to the experimental fatigue applied loading. Case study one estimates the thermal stresses superimposed sinusoidal cyclic mechanical stress results in solid cylinder under isothermal fatigue simulation. Case study two estimates the

Representative Stress-Strain Curve by Spherical Indentation on Elastic-Plastic Materials

Directory of Open Access Journals (Sweden)

Chao Chang

2018-01-01

Full Text Available Tensile stress-strain curve of metallic materials can be determined by the representative stress-strain curve from the spherical indentation. Tabor empirically determined the stress constraint factor (stress CF, ψ, and strain constraint factor (strain CF, β, but the choice of value for ψ and β is still under discussion. In this study, a new insight into the relationship between constraint factors of stress and strain is analytically described based on the formation of Tabor’s equation. Experiment tests were performed to evaluate these constraint factors. From the results, representative stress-strain curves using a proposed strain constraint factor can fit better with nominal stress-strain curve than those using Tabor’s constraint factors.

Constitutive relations in plasticity, damage and fracture mechanics based on a work property

International Nuclear Information System (INIS)

Marigo, J.J.

1989-01-01

This paper is devoted to restrictions imposed by a work property of Drucker-Iliushin's type on the general class of mechanical systems with an elastic range which contains plastic, damaged and cracked media. The analysis is purely mechanical and quasi-static. Starting from very weak assumptions relative to this constitutive class, we obtain a fundamental inequality which generalizes Hill's maximal work principle. So we can justify, for instance: the convexity of the elastic domain and the normality rule of the plastic strain rate in stress space for the infinitesimal and some finite plasticity theories, Griffith's criterion in brittle fracture mechanics, and we obtain some original results for elastic and elastic plastic damaged materials. It must be noted that the procedure is purely deductive, the assumptions are explicit and the results are implications

A structural strain method for low-cycle fatigue evaluation of welded components

International Nuclear Information System (INIS)

Dong, P.; Pei, X.; Xing, S.; Kim, M.H.

2014-01-01

In this paper, a new structural strain method is presented to extend the early structural stress based master S–N curve method to low cycle fatigue regime in which plastic deformation can be significant while an elastic core is still present. The method is formulated by taking advantage of elastically calculated mesh-insensitive structural stresses based on nodal forces available from finite element solutions. The structural strain definition is consistent with classical plate and shell theory in which a linear through-thickness deformation field is assumed a priori in both elastic or elastic–plastic regimes. With considerations of both yield and equilibrium conditions, the resulting structural strains are analytically solved if assuming elastic and perfectly plastic material behavior. The formulation can be readily extended to strain-hardening materials for which structural strains can be numerically calculated with ease. The method is shown effective in correlating low-cycle fatigue test data of various sources documented in the literature into a single narrow scatter band which is remarkable consistent with the scatter band of the existing master S–N curve adopted ASME B and PV Code since 2007. With this new method, some of the inconsistencies of the pseudo-elastic structural stress procedure in 2007 ASME Div 2 Code can now be eliminated, such as its use of Neuber's rule in approximating structural strain beyond yield. More importantly, both low cycle and high cycle fatigue behaviors can now be treated in a unified manner. The earlier mesh-insensitive structural stress based master S–N curve method can now be viewed as an application of the structural strain method in high cycle regime, in which structural strains are linearly related to traction-based structural stresses according to Hooke's law. In low-cycle regime, the structural strain method characterizes fatigue damage directly in terms of structural strains that satisfy linear through

On the concept of elasticity used in some fast reactor accident analysis codes

International Nuclear Information System (INIS)

Malmberg, T.

1975-01-01

The analysis presented restricts attention to the elastic part of the elastic-plastic equation used in several Fast Reactor Accident Analysis Codes and originally applied by M.L. Wilkins: Calculation of Elastic-Plastic Flow, UCRL-7322, Rev. 1, Jan 1969. It is shown that the used elasticity concept is within the frame of hypo-elasticity. On the basis of a test found by Bernstein it is proven that the state of stress is generally depending on the path of deformation. Therefore this concept of elasticity is not compatible with finite elasticity. For several deformation processes this special hypo-elastic constitutive equation is integrated to give a stress-strain relation. The path-dependence of this relation is demonstrated. Further the phenomenon of hypo-elastic yield under shear deformation is pointed out. The relevance to modelling material behaviour in primary containment analysis is discussed. (Auth.)

Evolution of elastic precursor and plastic shock wave in copper via molecular dynamics simulations

International Nuclear Information System (INIS)

Perriot, Romain; Zhakhovsky, Vasily V; Oleynik, Ivan I; Inogamov, Nail A

2014-01-01

Large-scale molecular dynamics (MD) simulations are performed to investigate shock propagation in single crystal copper. It is shown that the P-V plastic Hugoniot is unique regardless of the sample's orientation, its microstructure, or its length. However, the P-V pathway to the final state is not, and depends on many factors. Specifically, it is shown that the pressure in the elastic precursor (the Hugoniot elastic limit (HEL)) decreases as the shock wave propagates in a micron-sized sample. The attenuation of the HEL in sufficiently-long samples is the main source of disagreement between previous MD simulations and experiment: while single crystal experiments showed that the plastic shock speed is orientation-independent, the simulated plastic shock speed was observed to be orientation-dependent in relatively short single-crystal samples. Such orientation dependence gradually disappears for relatively long, micrometer-sized, samples for all three low-index crystallographic directions (100), (110), and (111), and the plastic shock velocities for all three directions approach the one measured in experiment. The MD simulations also demonstrate the existence of subsonic plastic shock waves generated by relatively weak supporting pressures.

AC loss characteristics of Bi2223/Ag sheathed tape wires subjected to mechanical strains and stresses

International Nuclear Information System (INIS)

Tsukamoto, Osami; Li, Z

2007-01-01

The influence of uniaxial tensile stress-strain on the AC loss characteristics of multifilamentary Bi2223/Ag sheathed tape wires was investigated. The uniaxial tensile stress-strain was applied to the sample wire in liquid nitrogen at atmospheric pressure, and the AC losses (transport, magnetization and total losses) were measured by an electric method. Two kinds of wire, oxide-dispersion strengthened Ag-alloy sheathed and Ag-alloy sheathed wires, were tested. The stress-strain curves of the tested wires were divided in three regions, i.e. elastic deformation, continuous plastic deformation and serrated-like plastic deformation regions, though the ranges of those regions were different for different kinds of wire. In the elastic and continuous plastic regions, the stress-strain curve was smooth and continuous, and in the serrated-like plastic region, the curve was rough. In the serrated-like plastic region, the wires kept elongating, while increase of the tensile stress was suspended. Dependences of the critical currents on the stress-strain were generally as follows. While decreases of the wire critical currents were in the range of less than 4% of the original values of the no-stress condition, the critical currents of the wires were reversible, that is, the critical currents recovered the original values at zero stress when the stress were released, regardless of whether the wires were in the elastic or continuous plastic region. In the continuous plastic region, the critical currents decreased up to 10%-15% of the original values and the critical currents were irreversible when the degradations of the critical currents exceeded about 4%. In the serrated-like plastic regions, the critical currents were more severely degraded. The AC loss characteristics of the wires are different in those regions. In the elastic and continuous plastic regions, the absolute values of AC losses were dependent on the stress-strain. However, the dependences of those normalized

Relationship between side necking and plastic zone size at fracture

International Nuclear Information System (INIS)

Kim, Do Hyung; Kang, Ki Ju; Kim, Dong Hak

2004-01-01

Generally, fracture of a material is influenced by plastic zone size developed near the crack tip. Hence, according to the relative size of plastic zone in the material, the mechanics as a tool for analyzing the fracture process are classified into three kinds, that is, Linear Elastic Fracture Mechanics, Elastic Plastic Fracture Mechanics, Large Deformation Fracture Mechanics. Even though the plastic zone size is such an important parameter, the practical measurement techniques are very limited and the one for in-situ measurement is not virtually available. Therefore, elastic-plastic FEA has been performed to estimate the plastic zone size. In this study, it is noticed that side necking at the surface is a consequence of plastic deformation and lateral contraction and the relation between the plastic zone and side necking is investigated. FEA for modified boundary layer models with finite thickness, various mode mixes 0 .deg., 30 deg., 60 deg., 90 .deg. and strain hardening exponent n=3, 10 are performed. The results are presented and the implication regarding to application to experiment is discussed

An alternative treatment of phenomenological higher-order strain-gradient plasticity theory

DEFF Research Database (Denmark)

Kuroda, Mitsutoshi; Tvergaard, Viggo

2010-01-01

strain is discussed, applying a dislocation theory-based consideration. Then, a differential equation for the equivalent plastic strain-gradient is introduced as an additional governing equation. Its weak form makes it possible to deduce and impose extra boundary conditions for the equivalent plastic...... strain. A connection between the present treatment and strain-gradient theories based on an extended virtual work principle is discussed. Furthermore, a numerical implementation and analysis of constrained simple shear of a thin strip are presented....

Elastic, plastic, fracture analysis of masonry arches: A multi-span bridge case study

Science.gov (United States)

Lacidogna, Giuseppe; Accornero, Federico

2018-01-01

In this work a comparison is presented between elastic, plastic, and fracture analysis of the monumental arch bridge of Porta Napoli, Taranto (Italy). By means of a FEM model and applying the Mery's Method, the behavior of the curved structure under service loads is verified, while considering the Safe Theorem approach byHeyman, the ultimate carrying capacity of the structure is investigated. Moreover, by using Fracture Mechanics concepts, the damage process which takes place when the conditions assessed through linear elastic analysis are no longer valid, and before the set-in of the conditions established by means of the plastic limit analysis, is numerically analyzed. The study of these transitions returns an accurate and effective whole service life assessment of the Porta Napoli masonry arch bridge.

Effects of the Strain Rate Sensitivity and Strain Hardening on the Saturated Impulse of Plates

Directory of Open Access Journals (Sweden)

Ling Zhu

Full Text Available Abstract This paper studies the stiffening effects of the material strain rate sensitivity and strain hardening on the saturated impulse of elastic, perfectly plastic plates. Finite element (FE code ABAQUS is employed to simulate the elastoplastic response of square plates under rectangular pressure pulse. Rigid-plastic analyses for saturated impulse, which consider strain rate sensitivity and strain hardening, are conducted. Satisfactory agreement between the finite element models (FEM and predictions of the rigid-plastic analysis is obtained, which verifies that the proposed rigid-plastic methods are effective to solve the problem including strain rate sensitivity and strain hardening. The quantitative results for the scale effect of the strain rate sensitivity are given. The results for the stiffening effects suggest that two general stiffening factors n 1 and n 2, which characterizes the strain rate sensitivity and strain hardening effect, respectively can be defined. The saturated displacement is inversely proportional to the stiffening factors (i.e. n 1 and n 2 and saturated impulse is inversely proportional to the square roots of the stiffening factors (i.e. n 1 and n 2. Formulae for displacement and saturated impulse are proposed based on the empirical analysis.

Nonlinear analysis of AS4/PEEK thermoplastic composite laminate using a one parameter plasticity model

Science.gov (United States)

Sun, C. T.; Yoon, K. J.

1990-01-01

A one-parameter plasticity model was shown to adequately describe the orthotropic plastic deformation of AS4/PEEK (APC-2) unidirectional thermoplastic composite. This model was verified further for unidirectional and laminated composite panels with and without a hole. The nonlinear stress-strain relations were measured and compared with those predicted by the finite element analysis using the one-parameter elastic-plastic constitutive model. The results show that the one-parameter orthotropic plasticity model is suitable for the analysis of elastic-plastic deformation of AS4/PEEK composite laminates.

Plastic flow in weak shock waves in uranium

International Nuclear Information System (INIS)

Tonks, D.L.

1992-01-01

Measurements of the particle velocity in weak shock waves in metals are available for a number of materials. These measurements use the laser interferometer or VISAR technique in conjunction with a plate impact experiment. These measurements are important for determining the elastic -- plastic behavior of materials at high strain rates. Strain rates up to 10 7 /s are measurable with this technique, while more conventional mechanical testing machines, such as the Hopkinson bar, achieve rates only up to about 10 4 /s. In this paper, the VISAR measurements of Grady on uranium are analyzed using the weak shock analysis of Wallace to extract the plastic and total strains, the deviatoric and total stresses, and the plastic strain rates. A brief error analysis of the results will be given. 7 refs

Stressed-deformed state of mountain rocks in elastic stage and between elasticity

Directory of Open Access Journals (Sweden)

Samedov A.M.

2017-12-01

destroy as a plastic material. In the elastic stage, the link between stress and strain is linear.

Elasto-plastic strain analysis by a semi-analytical method

Indian Academy of Sciences (India)

Non-uniform taper bar; rotating disk; elasto-plastic strain analysis; loaded natural frequency. ... The location of initiation of elasto-plastic front and its growth are found to be functions of geometry of the bar and loading ... Sadhana | News.

Steady State Crack Propagation in Layered Material Systems Displaying Visco-plastic Behaviour

DEFF Research Database (Denmark)

Nielsen, Kim Lau

2012-01-01

The steady state fracture toughness of elastic visco-plastic materials is studied numerically, using both a conventional and a higher order model. Focus is on the combined effect of strain hardening, strain gradient hardening and strain rate hardening on cracking in layered material systems...

Development of a formalism of movable cellular automaton method for numerical modeling of fracture of heterogeneous elastic-plastic materials

Directory of Open Access Journals (Sweden)

S. Psakhie

2013-04-01

Full Text Available A general approach to realization of models of elasticity, plasticity and fracture of heterogeneous materials within the framework of particle-based numerical methods is proposed in the paper. It is based on building many-body forces of particle interaction, which provide response of particle ensemble correctly conforming to the response (including elastic-plastic behavior and fracture of simulated solids. Implementation of proposed approach within particle-based methods is demonstrated by the example of the movable cellular automaton (MCA method, which integrates the possibilities of particle-based discrete element method (DEM and cellular automaton methods. Emergent advantages of the developed approach to formulation of many-body interaction are discussed. Main of them are its applicability to various realizations of the concept of discrete elements and a possibility to realize various rheological models (including elastic-plastic or visco-elastic-plastic and models of fracture to study deformation and fracture of solid-phase materials and media. Capabilities of particle-based modeling of heterogeneous solids are demonstrated by the problem of simulation of deformation and fracture of particle-reinforced metal-ceramic composites.

Stress and strain fluctuations in plastic deformation of crystals with disordered microstructure

International Nuclear Information System (INIS)

Kapetanou, O; Zaiser, M; Weygand, D

2015-01-01

We investigate the spatial structure of stress and strain patterns in crystal plasticity. To this end, we combine theoretical arguments with plasticity simulations using three different models: (i) a generic model of bulk crystal plasticity with stochastic evolution of the local microstructure, (ii) a 2D discrete dislocation simulation assuming single-slip deformation in a bulk crystal, and (iii) a 3D discrete dislocation model for deformation of micropillars in multiple slip. For all three models we investigate the scale-dependent magnitude of local fluctuations of internal stress and plastic strain, and we determine the spatial structure of the respective auto- and cross-correlation functions. The investigations show that, in the course of deformation, nontrivial long range correlations emerge in the stress and strain patterns. We investigate the influence of boundary conditions on the observed spatial patterns of stress and strain, and discuss implications of our findings for larger-scale plasticity models. (paper)

A general shakedown theorem for elastic/plastic bodies with work hardening

International Nuclear Information System (INIS)

Ponter, A.R.S.

1975-01-01

In recent years the design of metallic structures under variable loading has been assisted by the application of Melan's lower bound theorem for the shakedown on an elastic/perfectly plastic structure. The design codes for both portal frames and pressure vessels have taken account of such calculations. The theory of shakedown suffers from two defects, geometry changes are ignored and the material behaviour is described by a perfectly plastic constitutive relationship which includes neither work hardening nor the Bauschinger effect. This paper is concerned with the latter problem. A very general lower bound shakedown theorem is derived for an arbitrary time-independent material in terms of functional properties of the constitutive relationship. The theorem is then applied to perfect, isotropic and kinematic hardening plasticity. (Auth.)

Plastic strain accumulation during asymmetric cyclic loading of Zircaloy-2 at room temperature

International Nuclear Information System (INIS)

Rajpurohit, R.S.; Santhi Srinivas, N.C.; Singh, Vakil

2016-01-01

Asymmetric cyclic loading leads to accumulation of cyclic plastic strain and reduces the fatigue life of components. This phenomenon is known as ratcheting fatigue. Zircaloy-2 is a important structural material in nuclear reactors and used as pressure tubes and fuel cladding in pressurized light and heavy water nuclear reactors. Due to power fluctuations, these components experience plastic strain cycles in the reactor and their life is reduced due to strain cycles. Power fluctuations also cause asymmetric straining of the material and leads to accumulation of plastic strain. The present investigation deals with the effect of the magnitude of mean stress, stress amplitude and stress rate on hardening/softening behavior of Zircaloy-2 under asymmetric cyclic loading, at room temperature. It was observed that plastic strain accumulation increased with mean stress and stress amplitude; however, it decreased with stress rate. (author)

On the concept of elasticity used in some fast reactor accident analysis codes

International Nuclear Information System (INIS)

Malmberg, T.

1975-01-01

The analysis to be presented will restrict attention to the elastic part of the elastic-plastic constitutive equation used in several Fast Reactor Accident Analysis Codes and originally applied by M.L. Wilkins: Calculation of Elastic-Plastic Flow, UCRL-7322, Rev. 1, Jan. 1969. It is shown that the used elasticity concept is within the frame of hypo-elasticity. On the basis of a test found by Bernstein it is proven that the state of stress is generally depending on the path of deformation. Therefore this concept of elasticity is not compatible with finite elasticity. For several simple deformation processes this special hypo-elastic constitutive equation is integrated to give a stress-strain relation. The path-dependence of this relation is demonstrated. Further the phenomenon of hypo-elastic yield under shear deformation is pointed out. The relevance to modelling material behaviour in primary containment analysis is discussed

Plasticity dependent damage evolution in composites with strain-gradient effects

DEFF Research Database (Denmark)

Legarth, Brian Nyvang

2015-01-01

. (2013). In this study the reinforcement is assumed perfectly stiff and consequently only one new cohesive material parameter is introduced. Results are shown for both conventional isotropy as well as plastic anisotropy with higher-order material behavior. Due to fiber-matrix decohesion a sudden stress......A unit cell approach is adopted to numerically analyze the effect of reinforcement size on fracture evolution in metal matrix composites. The matrix material shows plastic size-effects and is modeled by an anisotropic version of the single parameter strain-gradient (higher-order) plasticity model...... by Fleck and Hutchinson (2001). The fracture process along the fiber-matrix interface is modeled using a recently proposed cohesive law extension, where plasticity affects the fracture process as both the average as well as the jump in plastic strain across the interface are accounted for Tvergaard et al...

The elastic-plastic failure assessment diagram of surface cracked structure

International Nuclear Information System (INIS)

Ning, J.; Gao, Q.

1987-01-01

The simplified NLSM is able to calculate the EPFM parameters and failure assessment curve for the surface cracked structure correctly and conveniently. The elastic-plastic failure assessment curve of surface crack is relevant to crack geometry, loading form and material deformation behaviour. It is necessary to construct the EPFM failure assessment curve of the surface crack for the failure assessment of surface cracked structure. (orig./HP)

Hardening and strengthening behavior in rate-independent strain gradient crystal plasticity

DEFF Research Database (Denmark)

Nellemann, C.; Niordson, C. F.; Nielsen, K.L.

2018-01-01

Two rate-independent strain gradient crystal plasticity models, one new and one previously published, are compared and a numerical framework that encompasses both is developed. The model previously published is briefly outlined, while an in-depth description is given for the new, yet somewhat...... related,model. The difference between the two models is found in the definitions of the plastic work expended in the material and their relation to spatial gradients of plastic strains. The model predictions are highly relevant to the ongoing discussion in the literature, concerning 1) what governs...... the increase in the apparent yield stress due to strain gradients (also referred to as strengthening)? And 2), what is the implication of such strengthening in relation to crystalline material behavior at the micron scale? The present work characterizes material behavior, and the corresponding plastic slip...

Comprehensive Report For Proposed Elevated Temperature Elastic Perfectly Plastic (EPP) Code Cases Representative Example Problems

Energy Technology Data Exchange (ETDEWEB)

Hollinger, Greg L. [Idaho National Lab. (INL), Idaho Falls, ID (United States)

2014-06-01

Background: The current rules in the nuclear section of the ASME Boiler and Pressure Vessel (B&PV) Code , Section III, Subsection NH for the evaluation of strain limits and creep-fatigue damage using simplified methods based on elastic analysis have been deemed inappropriate for Alloy 617 at temperatures above 1200F (650C)1. To address this issue, proposed code rules have been developed which are based on the use of elastic-perfectly plastic (E-PP) analysis methods and which are expected to be applicable to very high temperatures. The proposed rules for strain limits and creep-fatigue evaluation were initially documented in the technical literature 2, 3, and have been recently revised to incorporate comments and simplify their application. The revised code cases have been developed. Task Objectives: The goal of the Sample Problem task is to exercise these code cases through example problems to demonstrate their feasibility and, also, to identify potential corrections and improvements should problems be encountered. This will provide input to the development of technical background documents for consideration by the applicable B&PV committees considering these code cases for approval. This task has been performed by Hollinger and Pease of Becht Engineering Co., Inc., Nuclear Services Division and a report detailing the results of the E-PP analyses conducted on example problems per the procedures of the E-PP strain limits and creep-fatigue draft code cases is enclosed as Enclosure 1. Conclusions: The feasibility of the application of the E-PP code cases has been demonstrated through example problems that consist of realistic geometry (a nozzle attached to a semi-hemispheric shell with a circumferential weld) and load (pressure; pipe reaction load applied at the end of the nozzle, including axial and shear forces, bending and torsional moments; through-wall transient temperature gradient) and design and operating conditions (Levels A, B and C).

Multiaxial probabilistic elastic-plastic constitutive simulations of soils

Science.gov (United States)

Sadrinezhad, Arezoo

Fokker-Planck-Kolmogorov (FPK) equation approach has recently been developed to simulate elastic-plastic constitutive behaviors of materials with uncertain material properties. The FPK equation approach transforms the stochastic constitutive rate equation, which is a stochastic, nonlinear, ordinary differential equation (ODE) in the stress-pseudo time space into a second-order accurate, deterministic, linear FPK partial differential equation (PDE) in the probability density of stress-pseudo time space. This approach does not suffer from the drawbacks of the traditional approaches such as the Monte Carlo approach and the perturbation approach for solving nonlinear ODEs with random coefficients. In this study, the existing one dimensional FPK framework for probabilistic constitutive modeling of soils is extended to multi--dimension. However, the multivariate FPK PDEs cannot be solved using the traditional mathematical techniques such as finite difference techniques due to their high computational cost. Therefore, computationally efficient algorithms based on the Fourier spectral approach are developed for solving a class of FPK PDEs that arises in probabilistic elasto-plasticity. This class includes linear FPK PDEs in (stress) space and (pseudo) time - having space-independent but time-dependent, and both space- and time-dependent coefficients - with impulse initial conditions and reflecting boundary conditions. The solution algorithms, rely on first mapping the stress space of the governing PDE between 0 and 2pi using the change of coordinates rule, followed by approximating the solution of the PDE in the 2pi-periodic domain by a finite Fourier series in the stress space and unknown time-dependent solution coefficients. Finally, the time-dependent solution coefficients are obtained from the initial condition. The accuracy and efficiency of the developed algorithms are tested. The developed algorithms are used to simulate uniaxial and multiaxial, monotonic and cyclic

Plasticity size effects in voided crystals

DEFF Research Database (Denmark)

Hussein, M.I.; Borg, Ulrik; Niordson, Christian Frithiof

2008-01-01

as line singularities in an elastic material. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and annihilation are incorporated through a set of constitutive rules. Over the range of length scales investigated, both the discrete dislocation......The shear and equi-biaxial straining responses of periodic voided single crystals are analysed using discrete dislocation plasticity and a continuum strain gradient crystal plasticity theory. In the discrete dislocation formulation, the dislocations are all of edge character and are modelled...... between predictions of the two formulations for all crystal types and void volume fractions considered when the material length scale in the non-local plasticity model is chosen to be 0.325 mu m (about 10 times the slip plane spacing in the discrete dislocation models)....

Plastic Strain Induced Damage Evolution and Martensitic Transformation in Ductile Materials at Cryogenic Temperatures

CERN Document Server

Garion, C

2002-01-01

The Fe-Cr-Ni stainless steels are well known for their ductile behaviour at cryogenic temperatures. This implies development and evolution of plastic strain fields in the stainless steel components subjected to thermo-mechanical loads at low temperatures. The evolution of plastic strain fields is usually associated with two phenomena: ductile damage and strain induced martensitic transformation. Ductile damage is described by the kinetic law of damage evolution. Here, the assumption of isotropic distribution of damage (microcracks and microvoids) in the Representative Volume Element (RVE) is made. Formation of the plastic strain induced martensite (irreversible process) leads to the presence of quasi-rigid inclusions of martensite in the austenitic matrix. The amount of martensite platelets in the RVE depends on the intensity of the plastic strain fields and on the temperature. The evolution of the volume fraction of martensite is governed by a kinetic law based on the accumulated plastic strain. Both of thes...

Fracture of anisotropic materials with plastic strain-gradient effects

DEFF Research Database (Denmark)

Legarth, Brian Nyvang

2013-01-01

A unit cell is adopted to numerically analyze the effect of plastic anisotropy on frac-ture evolution in a micro-reinforced fiber-composite. The matrix material exhibit size-effects and an anisotropic strain-gradient plasticity model accounting for such size-effects through a mate-rial length scale...

Simplified inelastic (plastic and creep) analysis of pipe elbows subjected to inplane and out-of-plane bending

International Nuclear Information System (INIS)

Mello, R.M.; Scheller, J.D.

1975-01-01

The inelastic analysis of elbows typical of use in Liquid Metal Fast Reactor piping systems is described. Detailed information on stresses, plastic and creep strains, and deformations throughout the elbow bodies resulting from elastic/plastic, elastic/plastic/creep, and elastic/plastic-creep/relaxation material behavior was obtained for the cases of applied inplane and out-of-plane moment loading on the elbows. Some conclusions are made concerning the nature of the resulting stresses in the elbows. The simplified pipe-bend element in the MARC nonlinear finite element program is used as the analytical tool. This element permits nonlinear analysis of piping elbows and pipeline systems at realistic cost. 16 refs

A comparative study on the elastic modulus of polyvinyl alcohol sponge using different stress-strain definitions.

Science.gov (United States)

Karimi, Alireza; Navidbakhsh, Mahdi; Alizadeh, Mansour; Razaghi, Reza

2014-10-01

There have been different stress-strain definitions to measure the elastic modulus of spongy materials, especially polyvinyl alcohol (PVA) sponge. However, there is no agreement as to which stress-strain definition should be implemented. This study was aimed to show how different results are given by the various definitions of stress-strain used, and to recommend a specific definition when testing spongy materials. A fabricated PVA sponge was subjected to a series of tensile tests in order to measure its mechanical properties. Three stress definitions (second Piola-Kichhoff stress, engineering stress, and true stress) and four strain definitions (Almansi-Hamel strain, Green-St. Venant strain, engineering strain, and true strain) were used to determine the elastic modulus. The results revealed that the Almansi-Hamel strain definition exhibited the highest non-linear stress-strain relation and, as a result, may overestimate the elastic modulus at different stress definitions (second Piola-Kichhoff stress, engineering stress, and true stress). The Green-St. Venant strain definition failed to address the non-linear stress-strain relation using different definitions of stress and invoked an underestimation of the elastic modulus values. Engineering stress and strain definitions were only valid for small strains and displacements, which make them impractical when analyzing spongy materials. The results showed that the effect of varying the stress definition on the maximum stress measurements was significant but not when calculating the elastic modulus. It is important to consider which stress-strain definition is employed when characterizing the mechanical properties of spongy materials. Although the true stress-true strain definition exhibits a non-linear relation, we favor it in spongy materials mechanics as it gives more accurate measurements of the material's response using the instantaneous values.

Energetic dislocation interactions and thermodynamical aspects of strain gradient crystal plasticity theories

NARCIS (Netherlands)

Ertürk, I.; Dommelen, van J.A.W.; Geers, M.G.D.

2009-01-01

This paper focuses on the unification of two frequently used and apparently different strain gradient crystal plasticity frameworks: (i) the physicallymotivated strain gradient crystal plasticity models proposed by Evers et al. (2004a,b) and Bayley et al. (2006, 2007) (here referred to as

Internal strain estimation for quantification of human heel pad elastic modulus: A phantom study.

Science.gov (United States)

Holst, Karen; Liebgott, Hervé; Wilhjelm, Jens E; Nikolov, Svetoslav; Torp-Pedersen, Søren T; Delachartre, Philippe; Jensen, Jørgen A

2013-02-01

Shock absorption is the most important function of the human heel pad. However, changes in heel pad elasticity, as seen in e.g. long-distance runners, diabetes patients, and victims of Falanga torture are affecting this function, often in a painful manner. Assessment of heel pad elasticity is usually based on one or a few strain measurements obtained by an external load-deformation system. The aim of this study was to develop a technique for quantitative measurements of heel pad elastic modulus based on several internal strain measures from within the heel pad by use of ultrasound images. Nine heel phantoms were manufactured featuring a combination of three heel pad stiffnesses and three heel pad thicknesses to model the normal human variation. Each phantom was tested in an indentation system comprising a 7MHz linear array ultrasound transducer, working as the indentor, and a connected load cell. Load-compression data and ultrasound B-mode images were simultaneously acquired in 19 compression steps of 0.1mm each. The internal tissue displacement was for each step calculated by a phase-based cross-correlation technique and internal strain maps were derived from these displacement maps. Elastic moduli were found from the resulting stress-strain curves. The elastic moduli made it possible to distinguish eight of nine phantoms from each other according to the manufactured stiffness and showed very little dependence of the thickness. Mean elastic moduli for the three soft, the three medium, and the three hard phantoms were 89kPa, 153kPa, and 168kPa, respectively. The combination of ultrasound images and force measurements provided an effective way of assessing the elastic properties of the heel pad due to the internal strain estimation. Copyright © 2012 Elsevier B.V. All rights reserved.

Bulk nonlinear elastic strain waves in a bar with nanosize inclusions

DEFF Research Database (Denmark)

Gula, Igor A.; Samsonov (†), Alexander M.

2018-01-01

We propose a mathematical model for propagation of the long nonlinearly elastic longitudinal strain waves in a bar, which contains nanoscale structural inclusions. The model is governed by a nonlinear doubly dispersive equation (DDE) with respect to the one unknown longitudinal strain function. We...

Elastic unloading of a disk after plastic deformation by a circular heat source

International Nuclear Information System (INIS)

Gamer, U.; Mack, W.

1987-01-01

Subject of the investigation is the transient stress distribution in an elastic-plastic disk acted upon by a circular heat source. The disk serves as a mechanical model of the rotating anode of an X-ray-tube. The calculation is based on Tresca's yield criterion and the flow rule associatd to it. During heating, a plastic region spreads around the source, which is absorbed by an unloaded zone after the removal of the source. (orig.) [de

Performance study of K{sub e} factors in simplified elastic plastic fatigue analyses with emphasis on thermal cyclic loading

Energy Technology Data Exchange (ETDEWEB)

Lang, Hermann, E-mail: hermann.lang@areva.com [AREVA NP GmbH, PEEA-G, Henri-Dunant-Strasse 50, 91058 Erlangen (Germany); Rudolph, Juergen; Ziegler, Rainer [AREVA NP GmbH, PEEA-G, Henri-Dunant-Strasse 50, 91058 Erlangen (Germany)

2011-08-15

As code-based fully elastic plastic code conforming fatigue analyses are still time consuming, simplified elastic plastic analysis is often applied. This procedure is known to be overly conservative for some conditions due to the applied plastification (penalty) factor K{sub e}. As a consequence, less conservative fully elastic plastic fatigue analyses based on non-linear finite element analyses (FEA) or simplified elastic plastic analysis based on more realistic K{sub e} factors have to be used for fatigue design. The demand for more realistic K{sub e} factors is covered as a requirement of practical fatigue analysis. Different code-based K{sub e} procedures are reviewed in this paper with special regard to performance under thermal cyclic loading conditions. Other approximation formulae such as those by Neuber, Seeger/Beste or Kuehnapfel are not evaluated in this context because of their applicability to mechanical loading excluding thermal cyclic loading conditions typical for power plant operation. Besides the current code-based K{sub e} corrections, the ASME Code Case N-779 (e.g. Adam's proposal) and its modification in ASME Section VIII is considered. Comparison of elastic plastic results and results from the Rules for Nuclear Facility Components and Rules for Pressure Vessels reveals a considerable overestimation of usage factor in the case of ASME III and KTA 3201.2 for the examined examples. Usage factors according to RCC-M, Adams (ASME Code Case N-779), ASME VIII (alternative) and EN 13445-3 are essentially comparable and less conservative for these examples. The K{sub v} correction as well as the applied yield criterion (Tresca or von Mises) essentially influence the quality of the more advanced plasticity corrections (e.g. ASME Code Case N-779 and RCC-M). Hence, new proposals are based on a refined K{sub v} correction.

Scalable parallel elastic-plastic finite element analysis using a quasi-Newton method with a balancing domain decomposition preconditioner

Science.gov (United States)

Yusa, Yasunori; Okada, Hiroshi; Yamada, Tomonori; Yoshimura, Shinobu

2018-04-01

A domain decomposition method for large-scale elastic-plastic problems is proposed. The proposed method is based on a quasi-Newton method in conjunction with a balancing domain decomposition preconditioner. The use of a quasi-Newton method overcomes two problems associated with the conventional domain decomposition method based on the Newton-Raphson method: (1) avoidance of a double-loop iteration algorithm, which generally has large computational complexity, and (2) consideration of the local concentration of nonlinear deformation, which is observed in elastic-plastic problems with stress concentration. Moreover, the application of a balancing domain decomposition preconditioner ensures scalability. Using the conventional and proposed domain decomposition methods, several numerical tests, including weak scaling tests, were performed. The convergence performance of the proposed method is comparable to that of the conventional method. In particular, in elastic-plastic analysis, the proposed method exhibits better convergence performance than the conventional method.

Computational Strain Gradient Crystal Plasticity

DEFF Research Database (Denmark)

Niordson, Christian Frithiof; Kysar, Jeffrey W.

2011-01-01

A model for strain gradient crystal visco-plasticity is formulated along the lines proposed by Fleck andWillis (2009) for isotropic plasticity. Size-effects are included in the model due to the addition of gradient terms in both the free energy as well as through a dissipation potential. A finite...... element solution method is presented, which delivers the slip-rate field and the velocity-field based on two minimum principles. Some plane deformation problems relevant for certain specific orientations of a face centered cubic crystal under plane loading conditions are studied, and effective in......-plane parameters are developed based on the crystallographic properties of the material. The problem of cyclic shear of a single crystal between rigid platens is studied as well as void growth of a cylindrical void....

Stress-strain response of plastic waste mixed soil.

Science.gov (United States)

Babu, G L Sivakumar; Chouksey, Sandeep Kumar

2011-03-01

Recycling plastic waste from water bottles has become one of the major challenges worldwide. The present study provides an approach for the use plastic waste as reinforcement material in soil. The experimental results in the form of stress-strain-pore water pressure response are presented. Based on experimental test results, it is observed that the strength of soil is improved and compressibility reduced significantly with addition of a small percentage of plastic waste to the soil. The use of the improvement in strength and compressibility response due to inclusion of plastic waste can be advantageously used in bearing capacity improvement and settlement reduction in the design of shallow foundations. Copyright © 2010 Elsevier Ltd. All rights reserved.

Elastic-Plastic Fracture Mechanics Analyses for Circumferential Part-Through Surface Cracks at the Interface Between elbows and Pipes

International Nuclear Information System (INIS)

Song, Tae Kwang; Oh, Chang Kyun; Kim, Yun Jae; Kim, Jong Sung; Jin, Tae Eun

2007-01-01

This paper presents plastic limit loads and approximate J-integral estimates for circumferential part-through surface crack at the interface between elbows and pipes. Based on finite element limit analyses using elastic-perfectly plastic materials, plastic limit moments under in-plane bending are obtained and it is found that they are similar those for circumferential part-through surface cracks in the center of elbow. Based on present FE results, closed-form limit load solutions are proposed. Welds are not explicitly considered and all materials are assumed to be homogeneous. And the method to estimate the elastic-plastic J-integral for circumferential part-through surface cracks at the interface between elbows and straight pipes is proposed based on the reference stress approach, which was compared with corresponding solutions for straight pipes

Elastic-Plastic Fracture Mechanics Analyses For circumferential Part-through Surface Cracks At The Interface Between Elbows and Pipes

International Nuclear Information System (INIS)

Song, Tae Kwang; Kim, Yun Jae; Oh, Chang Kyun; Kim, Jong Sung; Jin, Tae Eun

2007-01-01

This paper presents plastic limit loads and approximate J-integral estimates for circumferential part-through surface crack at the interface between elbows and pipes. Based on finite element limit analyses using elastic-perfectly plastic materials, plastic limit moments under in-plane bending are obtained and it is found that they are similar those for circumferential part-through surface cracks in the center of elbow. Based on present FE results, closed-form limit load solutions are proposed. Welds are not explicitly considered and all materials are assumed to be homogeneous. And the method to estimate the elastic-plastic J-integral for circumferential part-through surface cracks at the interface between elbows and straight pipes is proposed based on the reference stress approach, which was compared with corresponding solutions for straight pipes

Effect of plastic strain on shape memory characteristics in sputter-deposited Ti-Ni thin films

International Nuclear Information System (INIS)

Nomura, K.

1995-01-01

The plastic strain which is introduced during cooling and heating under a constant stress has an influence upon the transformation and deformation characteristics of sputter-deposited Ti-Ni shape memory alloy thin films. With increasing the accumulated plastic strain, Ms rises and recovery strain increases. The changes in such characteristics are due to the internal stress field that is formed by plastic deformation. However, the change in Ms in Ti-50.5at%Ni is larger than that in Ti-48.9at%Ni, although the plastic strain in the former is lower than that in the latter. In order to understand this point, the effective internal stresses were estimated in both alloys; the internal stress in the former is more effectively created by the introduction of plastic strain than in the latter. (orig.)

Task force activity to take the effect of elastic-plastic behaviour into account on the seismic safety evaluation of nuclear piping systems

International Nuclear Information System (INIS)

Nakamura, Izumi; Shiratori, Masaki; Morishita, Masaki; Otani, Akihito; Shibutani, Tadahito

2015-01-01

According to investigations of several nuclear power plants (NPPs) hit by actual seismic events and a number of experimental researches on the failure behavior of piping systems under seismic loads, it is recognized that piping systems used in NPPs include a large seismic safety margin until boundary failure. Since the stress assessment based on the elastic analysis does not reflect actual seismic capability of piping systems including plastic region, it is necessary to develop a rational procedures to estimate the elastic-plastic behavior of piping systems under a large seismic load. With the aim of establishing a procedure that takes into account the elastic-plastic behavior effect in the seismic safety estimation of nuclear piping systems, a task force activity has been planned. Through the activity, the authors intend to establish guidelines to estimate the elastic-plastic behavior of piping systems rationally and conservatively, and to provide new rational seismic safety criteria taking the effect of elastic-plastic behavior into account. As the first step of making out the analysis guideline, benchmark analyses are conducted for a pipe element test and a piping system test. In this paper, the outline of the research activity and the preliminary results of benchmark analyses are described. (author)

Plastic strain induced damage evolution and martensitic transformation in ductile materials at cryogenic temperatures

International Nuclear Information System (INIS)

Garion, C.; Skoczen, B.T.

2002-01-01

The Fe-Cr-Ni stainless steels are well known for their ductile behavior at cryogenic temperatures. This implies development and evolution of plastic strain fields in the stainless steel components subjected to thermo-mechanical loads at low temperatures. The evolution of plastic strain fields is usually associated with two phenomena: ductile damage and strain induced martensitic transformation. Ductile damage is described by the kinetic law of damage evolution. Here, the assumption of isotropic distribution of damage (microcracks and microvoids) in the Representative Volume Element (RVE) is made. Formation of the plastic strain induced martensite (irreversible process) leads to the presence of quasi-rigid inclusions of martensite in the austenitic matrix. The amount of martensite platelets in the RVE depends on the intensity of the plastic strain fields and on the temperature. The evolution of the volume fraction of martensite is governed by a kinetic law based on the accumulated plastic strain. Both of these irreversible phenomena, associated with the dissipation of plastic power, are included into the constitutive model of stainless steels at cryogenic temperatures. The model is tested on the thin-walled corrugated shells (known as bellows expansion joints) used in the interconnections of the Large Hadron Collider, the new proton storage ring being constructed at present at CERN

Geometrical foundations of continuum mechanics an application to first- and second-order elasticity and elasto-plasticity

CERN Document Server

Steinmann, Paul

2015-01-01

This book illustrates the deep roots of the geometrically nonlinear kinematics of generalized continuum mechanics in differential geometry. Besides applications to first- order elasticity and elasto-plasticity an appreciation thereof is particularly illuminating for generalized models of continuum mechanics such as second-order (gradient-type) elasticity and elasto-plasticity.   After a motivation that arises from considering geometrically linear first- and second- order crystal plasticity in Part I several concepts from differential geometry, relevant for what follows, such as connection, parallel transport, torsion, curvature, and metric for holonomic and anholonomic coordinate transformations are reiterated in Part II. Then, in Part III, the kinematics of geometrically nonlinear continuum mechanics are considered. There various concepts of differential geometry, in particular aspects related to compatibility, are generically applied to the kinematics of first- and second- order geometrically nonlinear con...

Deformation patterning driven by rate dependent non-convex strain gradient plasticity

NARCIS (Netherlands)

Yalcinkaya, T.; Brekelmans, W.A.M.; Geers, M.G.D.

2011-01-01

A rate dependent strain gradient plasticity framework for the description of plastic slip patterning in a system with non-convex energetic hardening is presented. Both the displacement and the plastic slip fields are considered as primary variables. These fields are determined on a global level by

Modeling Shock Induced Plasticity in Copper Single Crystal: Numerical and Strain Localization Issues

International Nuclear Information System (INIS)

Shehadeh, M

2011-01-01

Multiscale dislocation dynamics plasticity (MDDP) simulations are carried out to address the following issues in modeling shock-induced plasticity: 1- the effect of finite element (FE) boundary conditions on shock wave characteristics and wave-dislocation interaction, 2- the effect of the evolution of the dislocation microstructure on lattice rotation and strain localization. While uniaxial strain is achieved with high accuracy using confined boundary condition, periodic boundary condition yields a disturbed wave profile due the edge effect. Including lattice rotation in the analysis leads to higher dislocation density and more localized plastic strain. (author)

Closed-form critical earthquake response of elastic-plastic structures on compliant ground under near-fault ground motions

Directory of Open Access Journals (Sweden)

Kotaro eKojima

2016-01-01

Full Text Available The double impulse is introduced as a substitute of the fling-step near-fault ground motion. A closed-form solution of the elastic-plastic response of a structure on compliant (flexible ground by the ‘critical double impulse’ is derived for the first time based on the solution for the corresponding structure with fixed base. As in the case of fixed-base model, only the free-vibration appears under such double impulse and the energy approach plays an important role in the derivation of the closed-form solution of a complicated elastic-plastic response on compliant ground. It is remarkable that no iteration is needed in the derivation of the critical elastic-plastic response. It is shown via the closed-form expression that, in the case of a smaller input level of double impulse to the structural strength, as the ground stiffness becomes larger, the maximum plastic deformation becomes larger. On the other hand, in the case of a larger input level of double impulse to the structural strength, as the ground stiffness becomes smaller, the maximum plastic deformation becomes larger. The criticality and validity of the proposed theory are investigated through the comparison with the response analysis to the corresponding one-cycle sinusoidal input as a representative of the fling-step near-fault ground motion. The applicability of the proposed theory to actual recorded pulse-type ground motions is also discussed.

Internal strain and texture evolution during deformation twinning in magnesium

Energy Technology Data Exchange (ETDEWEB)

Brown, D.W. [MS-H805, BLDG 622, TA-53, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States)]. E-mail: dbrown@lanl.gov; Agnew, S.R. [Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA 22904 (United States); Bourke, M.A.M. [MS-H805, BLDG 622, TA-53, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Holden, T.M. [Northern Stress Technologies, Deep River, Ont., K0J 1P0 (Canada); Vogel, S.C. [MS-H805, BLDG 622, TA-53, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Tome, C.N. [MS-H805, BLDG 622, TA-53, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States)

2005-06-15

The development of a twinned microstructure in hexagonal close-packed rolled magnesium compressed in the in-plane direction has been monitored in situ with neutron diffraction. The continuous conversion of the parent to daughter microstructure is tracked through the variation of diffraction peak intensities corresponding to each. Approximately 80% of the parent microstructure twins by 8% compression. Elastic lattice strain measurements indicate that the stress in the newly formed twins (daughters) is relaxed relative to the stress field in the surrounding matrix. However, since the daughters are in a plastically 'hard' deformation orientation, they quickly accumulate elastic strain as surrounding grains deform plastically. Polycrystal modeling of the deformation process provides insight about the crystallographic deformation mechanism involved.

A new approach for elasto-plastic finite strain analysis of cantilever ...

Indian Academy of Sciences (India)

A new approach for elasto-plastic finite strain analysis of cantilever beams subjected to uniform bending moment ... Curvature; deflection curve; cantilever beam; elasto-plastic analysis; tapered beam subjected to tipmoment; ... Sadhana | News.

Cyclic steady states in diffusion-induced plasticity with applications to lithium-ion batteries

Science.gov (United States)

Peigney, Michaël

2018-02-01

Electrode materials in lithium-ion batteries offer an example of medium in which stress and plastic flow are generated by the diffusion of guest atoms. In such a medium, deformation and diffusion are strongly coupled processes. For designing electrodes with improved lifetime and electro-mechanical efficiency, it is crucial to understand how plasticity and diffusion evolve over consecutive charging-recharging cycles. With such questions in mind, this paper provides general results for the large-time behavior of media coupling plasticity with diffusion when submitted to cyclic chemo-mechanical loadings. Under suitable assumptions, we show that the stress, the plastic strain rate, the chemical potential and the flux of guest atoms converge to a cyclic steady state which is largely independent of the initial state. A special emphasis is laid on the special case of elastic shakedown, which corresponds to the situation where the plastic strain stops evolving after a sufficiently large number of cycles. Elastic shakedown is expected to be beneficial for the fatigue behavior and - in the case of lithium-ion batteries - for the electro-chemical efficiency. We provide a characterization of the chemo-mechanical loadings for which elastic shakedown occurs. Building on that characterization, we suggest a general method for designing structures in such fashion that they operate in the elastic shakedown regime, whatever the initial state is. An attractive feature of the proposed method is that incremental analysis of the fully coupled plasticity-diffusion problem is avoided. The results obtained are applied to the model problem of a battery electrode cylinder particle under cyclic charging. Closed-form expressions are obtained for the set of charging rates and charging amplitudes for which elastic shakedown occurs, as well as for the corresponding cyclic steady states of stress, lithium concentration and chemical potential. Some results for a spherical particle are also presented.

A modified Gurson-type plasticity model at finite strains: formulation, numerical analysis and phase-field coupling

Science.gov (United States)

Aldakheel, Fadi; Wriggers, Peter; Miehe, Christian

2017-12-01

The modeling of failure in ductile materials must account for complex phenomena at the micro-scale, such as nucleation, growth and coalescence of micro-voids, as well as the final rupture at the macro-scale, as rooted in the work of Gurson (J Eng Mater Technol 99:2-15, 1977). Within a top-down viewpoint, this can be achieved by the combination of a micro-structure-informed elastic-plastic model for a porous medium with a concept for the modeling of macroscopic crack discontinuities. The modeling of macroscopic cracks can be achieved in a convenient way by recently developed continuum phase field approaches to fracture, which are based on the regularization of sharp crack discontinuities, see Miehe et al. (Comput Methods Appl Mech Eng 294:486-522, 2015). This avoids the use of complex discretization methods for crack discontinuities, and can account for complex crack patterns. In this work, we develop a new theoretical and computational framework for the phase field modeling of ductile fracture in conventional elastic-plastic solids under finite strain deformation. It combines modified structures of Gurson-Tvergaard-Needelman GTN-type plasticity model outlined in Tvergaard and Needleman (Acta Metall 32:157-169, 1984) and Nahshon and Hutchinson (Eur J Mech A Solids 27:1-17, 2008) with a new evolution equation for the crack phase field. An important aspect of this work is the development of a robust Explicit-Implicit numerical integration scheme for the highly nonlinear rate equations of the enhanced GTN model, resulting with a low computational cost strategy. The performance of the formulation is underlined by means of some representative examples, including the development of the experimentally observed cup-cone failure mechanism.

Three-dimensional microstructural effects on plane strain ductile crack growth

DEFF Research Database (Denmark)

Tvergaard, Viggo; Needleman, Alan

2006-01-01

Ductile crack growth under mode 1, plane strain, small scale yielding conditions is analyzed. Overall plane strain loading is prescribed, but a full 3D analysis is carried out to model three dimensional microstructural effects. An elastic-viscoplastic constitutive relation for a porous plastic...

Influence of elastic strain on the thermodynamics and kinetics of lithium vacancy in bulk LiCoO2

Science.gov (United States)

Moradabadi, Ashkan; Kaghazchi, Payam; Rohrer, Jochen; Albe, Karsten

2018-01-01

The influence of elastic strain on the lithium vacancy formation and migration in bulk LiCoO2 is evaluated by means of first-principles calculations within density functional theory (DFT). Strain dependent energies are determined directly from defective cells and also within linear elasticity theory from the elastic dipole tensor (Gi j) for ground state and saddle point configurations. We analyze finite size effects in the calculation of Gi j, compare the predictions of the linear elastic model with those obtained from direct calculations of defective cells under strain, and discuss the differences. Based on our data, we calculate the variations in vacancy concentration and mobility due to the presence of external strain in bulk LiCoO2 cathodes. Our results reveal that elastic in-plane and out-of-plane strains can significantly change the ionic conductivity of bulk LiCoO2 by up to several orders of magnitude and thus strongly affect the performance of Li-secondary batteries.

Correlation between relaxations and plastic deformation, and elastic model of flow in metallic glasses and glass-forming liquids

International Nuclear Information System (INIS)

Wang Weihua

2011-01-01

We study the similarity and correlations between relaxations and plastic deformation in metallic glasses (MGs) and MG-forming liquids. It is shown that the microscope plastic events, the initiation and formation of shear bands, and the mechanical yield in MGs where the atomic sites are topologically unstable induced by applied stress, can be treated as the glass to supercooled liquid state transition induced by external shear stress. On the other hand, the glass transition, the primary and secondary relaxations, plastic deformation and yield can be attributed to the free volume increase induced flow, and the flow can be modeled as the activated hopping between the inherent states in the potential energy landscape. We then propose an extended elastic model to describe the flow based on the energy landscape theory. That is, the flow activation energy density is linear proportional to the instantaneous elastic moduli, and the activation energy density ρ E is determined to be a simple expression of ρ E =(10/11)G+(1/11)K. The model indicates that both shear and bulk moduli are critical parameters accounting for both the homogeneous and inhomogeneous flows in MGs and MG-forming liquids. The elastic model is experimentally certified. We show that the elastic perspectives offers a simple scenario for the flow in MGs and MG-forming liquids and are suggestive for understanding the glass transition, plastic deformation, and nature and characteristics of MGs

Fatigue analysis - computation of the actual strain range using elastic calculation

International Nuclear Information System (INIS)

Roche, R.L.

1987-04-01

The design codes used in nuclear industry do not contain all the same rules allowing to deduce from an elastic calculation the actual deformation variation. Knowledge of strain range is needed for fatigue analysis. Elastic calculation does not give the actual range. The aim of this paper is discussing ways to correct elastic results and proposing a practical method to do it. Two corrections are required. The first one is related to elastic follow up effect when shakedown is not obtained (correction on secondary stress). The second one is related to stress raisers effect (correction on peak stress). It is shown that NEUBER's rule is not convenient for the second correction when shakedown is not fulfilled [fr

Simplified elastic-plastic analysis of reinforced concrete structures - design method for self-restraining stress

International Nuclear Information System (INIS)

Aihara, S.; Atsumi, K.; Ujiie, K.; Satoh, S.

1981-01-01

Self-restraining stresses generate not only moments but also axial forces. Therefore the moment and force equilibriums of cross section are considered simultaneously, in combination with other external forces. Thus, under this theory, two computer programs are prepared for. Using these programs, the design procedures which considered the reduction of self-restraining stress, become easy if the elastic design stresses, which are separated normal stresses and self-restraining stresses, are given. Numerical examples are given to illustrate the application of the simplified elastic-plastic analysis and to study its effectiveness. First this method is applied to analyze an upper shielding wall in MARK-2 type's Reactor building. The results are compared with those obtained by the elastic-plastic analysis of Finite Element Method. From this comparison it was confirmed that the method described, had adequate accuracy for re-bar design. As a second example, Mat slab of Reactor building is analyzed. The quantity of re-bars calculated by this method, comes to about two third of re-bars less than those required when self-restraining stress is considered as normal stress. Also, the self-restraining stress reduction factor is about 0.5. (orig./HP)

The variation in elastic modulus throughout the compression of foam materials

International Nuclear Information System (INIS)

Sun, Yongle; Amirrasouli, B.; Razavi, S.B.; Li, Q.M.; Lowe, T.; Withers, P.J.

2016-01-01

We present a comprehensive experimental study of the variation in apparent unloading elastic modulus of polymer (largely elastic), aluminium (largely plastic) and fibre-reinforced cement (quasi-brittle) closed-cell foams throughout uniaxial compression. The results show a characteristic “zero-yield-stress” response and thereafter a rapid increase in unloading modulus during the supposedly “elastic” regime of the compressive stress–strain curve. The unloading modulus then falls with strain due to the localised cell-wall yielding or failure in the pre-collapse stage and the progressive cell crushing in the plateau stage, before rising sharply during the densification stage which is associated with global cell crushing and foam compaction. A finite element model based on the actual 3D cell structure of the aluminium foam imaged by X-ray computed tomography (CT) predicts an approximately linear fall of elastic modulus from zero strain until a band of collapsed cells forms. It shows that the subsequent gradual decrease in modulus is caused by the progressive collapse of cells. The elastic modulus rises sharply after the densification initiation strain has been reached. However, the elastic modulus is still well below that of the constituent material even when the “fully” dense state is approached. This work highlights the fact that the unloading elastic modulus varies throughout compression and challenges the idea that a constant elastic modulus can be applied in a homogenised foam model. It is suggested that the most representative value of elastic modulus may be obtained by extrapolating the measured unloading modulus to zero strain.

Micro-Structural Evolution and Size-Effects in Plastically Deformed Single Crystals: Strain Gradient Continuum Modeling

DEFF Research Database (Denmark)

El-Naaman, Salim Abdallah

the macroscopic effects related to strain gradients, most predict smooth micro-structures. The evolution of dislocation micro-structures, during plastic straining of ductile crystalline materials, is highly complex and nonuniform. Published experimental measurements on deformed metal crystals show distinct......An extensive amount of research has been devoted to the development of micro-mechanics based gradient plasticity continuum theories, which are necessary for modeling micron-scale plasticity when large spatial gradients of plastic strain appear. While many models have proven successful in capturing...... strain. It is clear that many challenges are associated with modeling dislocation structures, within a framework based on continuum fields, however, since the strain gradient effects are attributed to the dislocation micro-structure, it is a natural step, in the further development of gradient theories...

Performance study of the simplified theory of plastic zones and the Twice-Yield method for the fatigue check

International Nuclear Information System (INIS)

Hübel, Hartwig; Willuweit, Adrian; Rudolph, Jürgen; Ziegler, Rainer; Lang, Hermann; Rother, Klemens; Deller, Simon

2014-01-01

As elastic–plastic fatigue analyses are still time consuming the simplified elastic–plastic analysis (e.g. ASME Section III, NB 3228.5, the French RCC-M code, paragraphs B 3234.3, B 3234.5 and B3234.6 and the German KTA rule 3201.2, paragraph 7.8.4) is often applied. Besides linearly elastic analyses and factorial plasticity correction (K e factors) direct methods are an option. In fact, calculation effort and accuracy of results are growing in the following graded scheme: a) linearly elastic analysis along with K e correction, b) direct methods for the determination of stabilized elastic–plastic strain ranges and c) incremental elastic–plastic methods for the determination of stabilized elastic–plastic strain ranges. The paper concentrates on option b) by substantiating the practical applicability of the simplified theory of plastic zones STPZ (based on Zarka's method) and – for comparison – the established Twice-Yield method. The Twice-Yield method is explicitly addressed in ASME Code, Section VIII, Div. 2. Application relevant aspects are particularly addressed. Furthermore, the applicability of the STPZ for arbitrary load time histories in connection with an appropriate cycle counting method is discussed. Note, that the STPZ is applicable both for the determination of (fatigue relevant) elastic–plastic strain ranges and (ratcheting relevant) locally accumulated strains. This paper concentrates on the performance of the method in terms of the determination of elastic–plastic strain ranges and fatigue usage factors. The additional performance in terms of locally accumulated strains and ratcheting will be discussed in a future publication. - Highlights: • Simplified elastic–plastic fatigue analyses. • Simplified theory of plastic zones. • Thermal cyclic loading. • Twice-Yield method. • Practical application examples

First-principles studies on the pressure dependences of the stress-strain relationship and elastic stability of semiconductors

International Nuclear Information System (INIS)

Wang, S Q; Ye, H Q; Yip, S

2006-01-01

We investigate the stress-strain relationship and elastic stability of zinc-blende GaP, GaN, InP and BN lattices under hydrostatic pressure by first-principles calculation. A simple and direct ab initio implementation for studying the mechanical properties of cubic crystals is developed. The four phases' full-set stress-strain coefficients in wide pressure ranges are theoretically calculated. The fundamental mechanism of elastic stability and the origin of phase transformation under hydrostatic pressure are explored. We found that the abilities for most of these lattices are enhanced to sustain axial strain but weaken to shear strain under higher pressure. The conditions of lattice stability are analysed using both the thermodynamic work-energy criterion and the elastic-stiffness criteria. We show that the lattice collapse of the perfect crystals is caused by the disappearance of their bulk moduli under volume dilation. Lattice defects are considered to be the main reason causing phase transformation under pressure. The correlation between the phonon softening and the variation of elastic coefficients is studied. The pressure dependence of the Kleinman internal strain parameter and its relationship to elastic stability is also explored

Global Existence Results for Viscoplasticity at Finite Strain

Science.gov (United States)

Mielke, Alexander; Rossi, Riccarda; Savaré, Giuseppe

2018-01-01

We study a model for rate-dependent gradient plasticity at finite strain based on the multiplicative decomposition of the strain tensor, and investigate the existence of global-in-time solutions to the related PDE system. We reveal its underlying structure as a generalized gradient system, where the driving energy functional is highly nonconvex and features the geometric nonlinearities related to finite-strain elasticity as well as the multiplicative decomposition of finite-strain plasticity. Moreover, the dissipation potential depends on the left-invariant plastic rate, and thus depends on the plastic state variable. The existence theory is developed for a class of abstract, nonsmooth, and nonconvex gradient systems, for which we introduce suitable notions of solutions, namely energy-dissipation-balance and energy-dissipation-inequality solutions. Hence, we resort to the toolbox of the direct method of the calculus of variations to check that the specific energy and dissipation functionals for our viscoplastic models comply with the conditions of the general theory.

Neutron-diffraction measurement of the evolution of strain for non-uniform plastic deformation

CERN Document Server

Rogge, R B; Boyce, D

2002-01-01

Neutrons are particularly adept for the validation of modeling predictions of stress and strain. In recent years, there has been a significant effort to model the evolution of both the macroscopic stresses and the intergranular stress during plastic deformation. These have had broad implications with regard to understanding the evolution of residual stress and to diffraction-based measurements of strain. Generally the modeling and associated measurements have been performed for simple uniaxial tension, leaving questions with regard to plastic deformation under multi-axial stress and non-uniform stress. Extensive measurements of the strain profile across a plastic hinge for each of a series of loading and unloading cycles to progressively higher degrees of plastic deformation are presented. These measurements are used to assess multiple-length-scale finite-element modeling (FEM) of the plastic hinge, in which the elements will range in size from single crystallites (as used in successful simulations of uniaxia...

Neutron-diffraction measurement of the evolution of strain for non-uniform plastic deformation

International Nuclear Information System (INIS)

Rogge, R.B.; Dawson, P.R.; Boyce, D.

2002-01-01

Neutrons are particularly adept for the validation of modeling predictions of stress and strain. In recent years, there has been a significant effort to model the evolution of both the macroscopic stresses and the intergranular stress during plastic deformation. These have had broad implications with regard to understanding the evolution of residual stress and to diffraction-based measurements of strain. Generally the modeling and associated measurements have been performed for simple uniaxial tension, leaving questions with regard to plastic deformation under multi-axial stress and non-uniform stress. Extensive measurements of the strain profile across a plastic hinge for each of a series of loading and unloading cycles to progressively higher degrees of plastic deformation are presented. These measurements are used to assess multiple-length-scale finite-element modeling (FEM) of the plastic hinge, in which the elements will range in size from single crystallites (as used in successful simulations of uniaxial tension) to macroscopic elements (as typically used in FEM simulations). (orig.)

Plastic limit analysis with non linear kinematic strain hardening for metalworking processes applications

International Nuclear Information System (INIS)

Chaaba, Ali; Aboussaleh, Mohamed; Bousshine, Lahbib; Boudaia, El Hassan

2011-01-01

Limit analysis approaches are widely used to deal with metalworking processes analysis; however, they are applied only for perfectly plastic materials and recently for isotropic hardening ones excluding any kind of kinematic hardening. In the present work, using Implicit Standard Materials concept, sequential limit analysis approach and the finite element method, our objective consists in extending the limit analysis application for including linear and non linear kinematic strain hardenings. Because this plastic flow rule is non associative, the Implicit Standard Materials concept is adopted as a framework of non standard plasticity modeling. The sequential limit analysis procedure which considers the plastic behavior with non linear kinematic strain hardening as a succession of perfectly plastic behavior with yielding surfaces updated after each sequence of limit analysis and geometry updating is applied. Standard kinematic finite element method together with a regularization approach is used for performing two large compression cases (cold forging) in plane strain and axisymmetric conditions

Probabilistic analysis of structures involving random stress-strain behavior

Science.gov (United States)

Millwater, H. R.; Thacker, B. H.; Harren, S. V.

1991-01-01

The present methodology for analysis of structures with random stress strain behavior characterizes the uniaxial stress-strain curve in terms of (1) elastic modulus, (2) engineering stress at initial yield, (3) initial plastic-hardening slope, (4) engineering stress at point of ultimate load, and (5) engineering strain at point of ultimate load. The methodology is incorporated into the Numerical Evaluation of Stochastic Structures Under Stress code for probabilistic structural analysis. The illustrative problem of a thick cylinder under internal pressure, where both the internal pressure and the stress-strain curve are random, is addressed by means of the code. The response value is the cumulative distribution function of the equivalent plastic strain at the inner radius.

CYCLIC PLASTIC BEHAVIOUR OF UFG COPPER UNDER CONTROLLED STRESS AND STRAIN LOADING

Directory of Open Access Journals (Sweden)

Lucie Navrátilová

2012-01-01

Full Text Available The influence of stress- and strain-controlled loading on microstructure and cyclic plastic behaviour of ultrafine-grained copper prepared by equal channel angular pressing was examined. The stability of microstructure is a characteristic feature for stress-controlled test whereas grain coarsening and development of bimodal structure was observed after plastic strain-controlled tests. An attempt to explain the observed behaviour was made.

Strain induced tunable wavelength filters based on flexible polymer waveguide Bragg reflector.

Science.gov (United States)

Kim, Kyung-Jo; Seo, Jun-Kyu; Oh, Min-Cheol

2008-02-04

A tunable wavelength filter is demonstrated by imposing a strain on a polymeric Bragg reflection waveguide fabricated on a flexible substrate. The highly elastic property of flexible polymer device enables much wider tuning than the silica fiber. To produce a uniform grating pattern on a flexible plastic substrate, a post lift-off process along with an absorbing layer is incorporated. The flexible Bragg reflector shows narrow bandwidth, which is convincing the uniformity of the grating structure fabricated on plastic film. By stretching the flexible polymer device, the Bragg reflection wavelength is tuned continuously up to 45 nm for the maximum strain of 31,690 muepsilon, which is determined by the elastic expansion limit of waveguide polymer. From the linear wavelength shift proportional to the strain, the photoelastic coefficient of the ZPU polymer is found.

Probing the Effect of Hydrogen on Elastic Properties and Plastic Deformation in Nickel Using Nanoindentation and Ultrasonic Methods

Science.gov (United States)

Lawrence, S. K.; Somerday, B. P.; Ingraham, M. D.; Bahr, D. F.

2018-04-01

Hydrogen effects on small-volume plasticity and elastic stiffness constants are investigated with nanoindentation of Ni-201 and sonic velocity measurements of bulk Ni single crystals. Elastic modulus of Ni-201, calculated from indentation data, decreases 22% after hydrogen charging. This substantial decrease is independently confirmed by sonic velocity measurements of Ni single crystals; c 44 decreases 20% after hydrogen exposure. Furthermore, clear hydrogen-deformation interactions are observed. The maximum shear stress required to nucleate dislocations in hydrogen-charged Ni-201 is markedly lower than in as-annealed material, driven by hydrogen-reduced shear modulus. Additionally, a larger number of depth excursions are detected prior to general yielding in hydrogen-charged material, suggesting cross-slip restriction. Together, these data reveal a direct correlation between hydrogen-affected elastic properties and plastic deformation in Ni alloys.

Strain hardening and plastic instability properties of austenitic stainless steels after proton and neutron irradiation

International Nuclear Information System (INIS)

Byun, T.S.; Farrell, K.; Lee, E.H.; Hunn, J.D.; Mansur, L.K.

2001-01-01

Strain hardening and plastic instability properties were analyzed for EC316LN, HTUPS316, and AL6XN austenitic stainless steels after combined 800 MeV proton and spallation neutron irradiation to doses up to 10.7 dpa. The steels retained good strain-hardening rates after irradiation, which resulted in significant uniform strains. It was found that the instability stress, the stress at the onset of necking, had little dependence on the irradiation dose. Tensile fracture stress and strain were calculated from the stress-strain curve data and were used to estimate fracture toughness using an existing model. The doses to plastic instability and fracture, the accumulated doses at which the yield stress reaches instability stress or fracture stress, were predicted by extrapolation of the yield stress, instability stress, and fracture stress to higher dose. The EC316LN alloy required the highest doses for plastic instability and fracture. Plastic deformation mechanisms are discussed in relation to the strain-hardening properties of the austenitic stainless steels

A numerical basis for strain-gradient plasticity theory: Rate-independent and rate-dependent formulations

DEFF Research Database (Denmark)

Nielsen, Kim Lau; Niordson, Christian Frithiof

2014-01-01

of a single plastic zone is analyzed to illustrate the agreement with earlier published results, whereafter examples of (ii) multiple plastic zone interaction, and (iii) elastic–plastic loading/unloading are presented. Here, the simple shear problem of an infinite slab constrained between rigid plates......A numerical model formulation of the higher order flow theory (rate-independent) by Fleck and Willis [2009. A mathematical basis for strain-gradient plasticity theory – part II: tensorial plastic multiplier. Journal of the Mechanics and Physics of Solids 57, 1045-1057.], that allows for elastic–plastic...... loading/unloading and the interaction of multiple plastic zones, is proposed. The predicted model response is compared to the corresponding rate-dependent version of visco-plastic origin, and coinciding results are obtained in the limit of small strain-rate sensitivity. First, (i) the evolution...

The correlation between the ultrasonic elastic strain ratio of thyroid cancer and the malignant biological characteristics of cancer cells in the lesions

OpenAIRE

Li Ma; Rong Zhou; Yun-Zhu Li

2017-01-01

Objective: To study the correlation between the ultrasonic elastic strain ratio of thyroid cancer and the malignant biological characteristics of cancer cells in the lesions. Methods: A total of 90 patients with thyroid cancer who accepted surgical treatment in our hospital between March 2015 and September 2016 were selected as the observation group, and 50 patients who received surgery in our hospital during the same period and were with clear pathological diagnosis of thyroid...

Elasto/visco-plastic analysis of orthotropic moderately thick shells of revolution

International Nuclear Information System (INIS)

Takezono, S.; Tao, K.

1985-01-01

This paper describes an analytical formulation and a numerical analysis on the elasto/visco-plastic problems of orthotropic moderately thick shells of revolution under axi-symmetrical loads with applications to a cylindrical shell, and with comparison to experimental results. The analytical formulation is developed by extension of the Reissner-Naghdi theory in elastic shells where a consideration on the effect of shear deformation is given. As the constitutive equation, Hooke's law for orthotropic materials is used in the elastic range, and equations based on the orthotropic visco-plastic theory derived from the orthotropic plastic theory by Hill are employed in the plastic range. The visco-plastic strain rates are related to the stresses by Perzyna's equation. In order to check up the adequacy of the numerical analysis, experiments on elasto/visco-plastic deformation of a titanium cylindrical shell subject to internal axi-symmetrical loads are performed. Good agreement is obtained between experimental results and analytical solution. (orig.)

Boundary value problems of the circular cylinders in the strain-gradient theory of linear elasticity

International Nuclear Information System (INIS)

Kao, B.G.

1979-11-01

Three boundary value problems in the strain-gradient theory of linear elasticity are solved for circular cylinders. They are the twisting of circular cylinder, uniformly pressuring of concentric circular cylinder, and pure-bending of simply connected cylinder. The comparisons of these solutions with the solutions in classical elasticity and in couple-stress theory reveal the differences in the stress fields as well as the apparent stress fields due to the influences of the strain-gradient. These aspects of the strain-gradient theory could be important in modeling the failure behavior of structural materials

The J-integral concept for elastic-plastic material behavior

International Nuclear Information System (INIS)

Schmitt, W.; Kienzler, R.

1987-03-01

A simple analytical extension of the J integral has been presented which extends the J concept to apply for materials described by an incremental theory of plasticity. The stress work density replacing the strain energy density is load-history dependent. The J integral may be made path independent by virtue of an additional volume integral and may be understood as work dissipation rate. The discussion of the consequences for the applicability of the J concept to describe fracture processes showed that validity criteria proposed in the standards are not sufficient to yield configuration-independent J-resistance curves. However, a possibility is sketched to assess those structure-dependent resistance curves based on plastic-collapse considerations. With 6 figs., 33 refs

Computational Modelling of Fracture Propagation in Rocks Using a Coupled Elastic-Plasticity-Damage Model

Directory of Open Access Journals (Sweden)

Isa Kolo

2016-01-01

Full Text Available A coupled elastic-plasticity-damage constitutive model, AK Model, is applied to predict fracture propagation in rocks. The quasi-brittle material model captures anisotropic effects and the distinct behavior of rocks in tension and compression. Calibration of the constitutive model is realized using experimental data for Carrara marble. Through the Weibull distribution function, heterogeneity effect is captured by spatially varying the elastic properties of the rock. Favorable comparison between model predictions and experiments for single-flawed specimens reveal that the AK Model is reliable and accurate for modelling fracture propagation in rocks.

Strain gradient effects on cyclic plasticity

DEFF Research Database (Denmark)

Niordson, Christian Frithiof; Legarth, Brian Nyvang

2010-01-01

Size effects on the cyclic shear response are studied numerically using a recent higher order strain gradient visco-plasticity theory accounting for both dissipative and energetic gradient hardening. Numerical investigations of the response under cyclic pure shear and shear of a finite slab between...... rigid platens have been carried out, using the finite element method. It is shown for elastic–perfectly plastic solids how dissipative gradient effects lead to increased yield strength, whereas energetic gradient contributions lead to increased hardening as well as a Bauschinger effect. For linearly...... hardening materials it is quantified how dissipative and energetic gradient effects promote hardening above that of conventional predictions. Usually, increased hardening is attributed to energetic gradient effects, but here it is found that also dissipative gradient effects lead to additional hardening...

Effect of transient change in strain rate on plastic flow behaviour of ...

Indian Academy of Sciences (India)

Steels; stress–strain measurement; plastic flow; mechanical properties; metallurgy. Abstract. Plastic flow behaviour of low carbon steel has been studied at room temperature during tensile deformation by ... Bulletin of Materials Science | News.

Reduce, reuse, recycle: Acceptance of CO_2-utilization for plastic products

International Nuclear Information System (INIS)

Heek, Julia van; Arning, Katrin; Ziefle, Martina

2017-01-01

Global warming is a central threat for today's society caused by greenhouse gas emissions, mostly carbon dioxide emissions. Carbon dioxide capture and utilization (CCU) is a promising approach to reduce emissions and the use of expensive and limited fossil resources. Applying CCU, carbon dioxide (CO_2) can be incorporated as raw material during the manufacture of plastic products. While most of the studies address technical feasibilities, hardly any systematic research on public perception and acceptance of those specific products exists so far. This study empirically investigates the acceptance of CCU plastic products (mattress as example). First, interviews with experts and lay people revealed critical acceptance factors (CO_2 proportion, saving of fossil resources, disposal conditions, perceived health complaints). Their relative importance was detailed in two consecutive conjoint studies. Study 1 revealed disposal conditions and saving of fossil resources as essential for product selection, while the products’ CO_2 proportion was less important. In study 2, potential health complaints were integrated as well as individual levels of domain knowledge and risk perception, which significantly affected acceptance of CCU products. Recommendations concerning communication strategies for policy and industry were derived. - Highlights: • Study provides insights into the acceptance of specific CCU products. • Disposal conditions and savings of fossil resource are main drivers of acceptance. • Concerns about potential health effects act as major barrier especially for laypeople. • Perceived knowledge and risk perception affect CCU product acceptance. • Communication strategy recommendations for policy and industry are derived.

Metallic nanomaterials formed by exerting large plastic strains

International Nuclear Information System (INIS)

Richert, M; Richert, J.; Zasadzinski, J.; Hawrylkiewicz, S.

2002-01-01

The investigations included pure Al and Cu single crystals, AlMg5 alloy and AlCuZr alloy have been presented. The materials were deformed by the cyclic extrusion compression method (CEC) within the range of true strains φ = 0.4-59.8 (1 to 67 deformation cycles by the CEC method). In all examined materials a strong tendency to form banded was observed. Within the range of very large plastic strains there was observed intensive rebuilding of the banded microstructure into subgrains, at first of rhombic shape, and next into equiaxial subgrains. A characteristic feature of the newly formed subgrains, not encountered in the range of conventional deformations, was the occurrence of large misorientation angles between the newly formed subgrains. The proportion of large misorientation angles in the microstructure varied, and it increased with increasing deformation. Reduction of the recovery process in AlMg5 and AlCuZr alloys preserved the growth of the newly formed nanograins, favoring the retaining of the nanomeric dimensions. This results show that there is the effective possibility of production of metallic nanomaterials by exerting of very large nonconventional plastic strains. (author)

High Strain Rate and Shock-Induced Deformation in Metals

Science.gov (United States)

Ravelo, Ramon

2012-02-01

Large-scale non-equilibrium molecular Dynamics (MD) simulations are now commonly used to study material deformation at high strain rates (10^9-10^12 s-1). They can provide detailed information-- such as defect morphology, dislocation densities, and temperature and stress profiles, unavailable or hard to measure experimentally. Computational studies of shock-induced plasticity and melting in fcc and bcc single, mono-crystal metals, exhibit generic characteristics: high elastic limits, large directional anisotropies in the yield stress and pre-melting much below the equilibrium melt temperature for shock wave propagation along specific crystallographic directions. These generic features in the response of single crystals subjected to high strain rates of deformation can be explained from the changes in the energy landscape of the uniaxially compressed crystal lattice. For time scales relevant to dynamic shock loading, the directional-dependence of the yield strength in single crystals is shown to be due to the onset of instabilities in elastic-wave propagation velocities. The elastic-plastic transition threshold can accurately be predicted by a wave-propagation stability analysis. These strain-induced instabilities create incipient defect structures, which can be quite different from the ones, which characterize the long-time, asymptotic state of the compressed solid. With increase compression and strain rate, plastic deformation via extended defects gives way to amorphization associated with the loss in shear rigidity along specific deformation paths. The hot amorphous or (super-cooled liquid) metal re-crystallizes at rates, which depend on the temperature difference between the amorphous solid and the equilibrium melt line. This plastic-amorphous transition threshold can be computed from shear-waves stability analyses. Examples from selected fcc and bcc metals will be presented employing semi-empirical potentials of the embedded atom method (EAM) type as well as

Determining Recoverable and Irrecoverable Contributions to Accumulated Strain in a NiTiPd High-Temperature Shape Memory Alloy During Thermomechanical Cycling

Science.gov (United States)

Monroe, J. A.; Karaman, I.; Lagoudas, D. C.; Bigelow, G.; Noebe, R. D.; Padula, S., II

2011-01-01

When Ni(29.5)Ti(50.5)Pd30 shape memory alloy is thermally cycled under stress, significant strain can accumulate due to elasticity, remnant oriented martensite and plasticity. The strain due to remnant martensite can be recovered by further thermal cycling under 0 MPa until the original transformation-induced volume change and martensite coefficient of thermal expansion are obtained. Using this technique, it was determined that the 8.15% total accumulated strain after cycling under 200 MPa consisted of 0.38%, 3.97% and 3.87% for elasticity, remnant oriented martensite and creep/plasticity, respectively.

A plastic stress intensity factor approach to turbine disk structural integrity assessment

Directory of Open Access Journals (Sweden)

V. Shlyannikov

2016-07-01

Full Text Available This study based on a new fracture mechanics parameter is concerned with assessing the integrity of cracked steam turbine disk which operate under startup-shutdown cyclic loading conditions. Damage accumulation and growth in service have occurred on the inner surface of slot fillet of key. In order to determine elastic-plastic fracture mechanics parameters full-size stress-strain state analysis of turbine disk was performed for a quote-elliptical part-through cracks under considering loading conditions. As a result distributions of elastic and plastic stress intensity factors along crack front in slot fillet of key of turbine disk depending on surface crack form are defined. An engineering approach to the prediction of carrying capacity of cracked turbine disk which is sensitive to the loading history at maintenance is proposed. The predictions of the rate of crack growth and residual lifetime of steam turbine disk are compared for elastic and elastic-plastic solutions. It is shown that the previously proposed elastic crack growth models provide overestimate the lifetime with respect to the present one. An advantage to use the plastic stress intensity factor to characterize the fracture resistance as the self-dependent unified parameter for a variety of turbine disk configurations rather than the magnitude of the elastic stress intensity factors alone is discussed.

Mode I crack analysis in single crystals with anisotropic discrete dislocation plasticity : I. Formulation and crack growth

NARCIS (Netherlands)

Shishvan, Siamak Soleymani; Van der Giessen, Erik

Analyses of monotonic loading of a plane-strain mode I crack in an fcc single crystal under small-scale yielding are carried out using discrete dislocation plasticity (DDP) incorporating anisotropic elasticity. Two crystallographically symmetric crack orientations are considered where plane-strain

Room temperature elastic--plastic response of thin-walled tubes subjected to nonradial combinations of axial and torsional loadings

International Nuclear Information System (INIS)

Liu, K.C.

1975-01-01

Two tubular specimens of type 304 stainless steel with uniform thin walls were subjected to a program of segmental combined tension/compression and torsion loadings at room temperature. A proportional, or radial, loading into the plastic range was initially applied to each specimen. Two nonproportional (nonradial) loadings along straight line segments for which neither the loading paths nor their linear extrapolations passed through the origin of the stress space were then applied. The axial and torsional stress-strain curves for these segmental prestress loadings were plotted. Hence, the stress-strain response characteristics for nonproportional loadings as well as for proportional loading can be studied. In addition, the axial and torsional plastic strain components were calculated, and the total plastic strain trajectories were plotted in a plastic strain space. Finally, using results from a detailed study of yield surfaces, which was performed for the first specimen, a spectrum of initial and subsequent yield curves corresponding to the segmental prestress loadings is presented. (U.S.)

Phase diagrams of ferroelectric nanocrystals strained by an elastic matrix

Science.gov (United States)

Nikitchenko, A. I.; Azovtsev, A. V.; Pertsev, N. A.

2018-01-01

Ferroelectric crystallites embedded into a dielectric matrix experience temperature-dependent elastic strains caused by differences in the thermal expansion of the crystallites and the matrix. Owing to the electrostriction, these lattice strains may affect polarization states of ferroelectric inclusions significantly, making them different from those of a stress-free bulk crystal. Here, using a nonlinear thermodynamic theory, we study the mechanical effect of elastic matrix on the phase states of embedded single-domain ferroelectric nanocrystals. Their equilibrium polarization states are determined by minimizing a special thermodynamic potential that describes the energetics of an ellipsoidal ferroelectric inclusion surrounded by a linear elastic medium. To demonstrate the stability ranges of such states for a given material combination, we construct a phase diagram, where the inclusion’s shape anisotropy and temperature are used as two parameters. The ‘shape-temperature’ phase diagrams are calculated numerically for PbTiO3 and BaTiO3 nanocrystals embedded into representative dielectric matrices generating tensile (silica glass) or compressive (potassium silicate glass) thermal stresses inside ferroelectric inclusions. The developed phase maps demonstrate that the joint effect of thermal stresses and matrix-induced elastic clamping of ferroelectric inclusions gives rise to several important features in the polarization behavior of PbTiO3 and BaTiO3 nanocrystals. In particular, the Curie temperature displays a nonmonotonic variation with the ellipsoid’s aspect ratio, being minimal for spherical inclusions. Furthermore, the diagrams show that the polarization orientation with respect to the ellipsoid’s symmetry axis is controlled by the shape anisotropy and the sign of thermal stresses. Under certain conditions, the mechanical inclusion-matrix interaction qualitatively alters the evolution of ferroelectric states on cooling, inducing a structural transition

Elastic limit and microplastic response of hardened steels

Energy Technology Data Exchange (ETDEWEB)

Zaccone, M.A. (McDonnell Douglas Aerospace Co., St. Louis, MO (United States)); Krauss, G. (Colorado School of Mines, Golden, CO (United States). Dept. of Metallurgical and Materials Engineering)

1993-10-01

Tempered martensite-retained austenite microstructures were produced by direct quenching a series of 41XX medium carbon steels, direct quenching and reheating a series of five 0.8C-Cr-Ni-Mo steels and intercritically austenitizing at various temperatures, and quenching a SAE 52100 steel. All specimens were tempered either at 150 C or at 200 C. Specimens were subjected to compression and tension testing in the microstrain regime to determine the elastic limits and microplastic response of the microstructures. The retained austenite and matrix carbon content of the intercritically austenized specimens were measured by X-ray diffraction and Mossbauer spectroscopy. The elastic limit of the microstructures decreases with increasing amounts of retained austenite. Refining of the austenite distribution increases the elastic limit. Low elastic limits are mainly due to low flow stresses in the austenite and not internal stresses. The elastic limit correlates with the largest austenite free-mean path by a Hall-Petch type equation. The elastic limit increases with decreasing intercritical austenitizing temperature in the SAE 52100 due to a lower carbon content in the matrix reducing the retained austenite levels and retained carbides that refine grain size and, therefore, the austenite distribution in quenched specimens. In the microplastic region, the strain is accommodated by successively smaller austenite regions until the flow strength matches that of the martensite. Reheating and quenching refines the microstructure and renders the austenite unstable in the microplastic regime, causing transformation of the austenite to martensite by a strain-induced mechanism. The transformation of austenite to martensite occurs by a stress-assisted mechanism in medium carbon steels. The low elastic limits in medium carbon steels were due to the inability of the strain from the stress-assisted transformation to balance the plastic strain accumulated in the austenite.

Strain solitons in solids and how to construct them

CERN Document Server

Samsonov, Alexander M

2001-01-01

Although the theory behind solitary waves of strain shows that they hold significant promise in nondestructive testing and a variety of other applications, an enigma has long persisted-the absence of observable elastic solitary waves in practice. Inspired by this apparent contradiction, Strain Solitons in Solids and How to Construct Them refines the existing theory, explores how to construct a powerful deformation pulse in a waveguide without plastic flow or fracture, and proposes a direct method of strain soliton generation, detection, and observation.The author focuses on the theory, simulation, generation, and propagation of strain solitary waves in a nonlinearly elastic, straight cylindrical rod under finite deformations. He introduces the general theory of wave propagation in nonlinearly elastic solids and shows, from first principles, how its main ideas can lead to successful experiments. In doing so, he develops a new approach to solving the corresponding doubly dispersive equation (DDE) with dissipati...

An analysis of heat field of metal sheet during elastic-plastic deformation

International Nuclear Information System (INIS)

Li, S.X.; Huang, Y.; Shih, C.H.

1985-08-01

This paper describes the application of the finite element analysis to calculate the temperature distribution generated during the process of elastic-plastic deformation. A better agreement is found between the results of heat field computed by use of the finite element analysis and that measured by use of an infrared camera. The results indicate that the method of finite element analysis used for heat field evaluation is reliable. (author)

Testing plastic deformations of materials in the introductory undergraduate mechanics laboratory

International Nuclear Information System (INIS)

Romo-Kröger, C M

2012-01-01

Normally, a mechanics laboratory at the undergraduate level includes an experiment to verify compliance with Hooke's law in materials, such as a steel spring and an elastic rubber band. Stress-strain curves are found for these elements. Compression in elastic bands is practically impossible to achieve due to flaccidity. A typical experiment for the complete loading-unloading cycle is to subject a tubular object to torsion. This paper suggests simple experiments for studying properties concerning elasticity and plasticity in elements of common use, subjected to stretching or compression, and also torsion reinforcing. The experiments use plastic binders, rubber bands and metal springs under a moderate load. This paper discusses an experiment with an original device to measure torsion deformations as a function of applied torques, which permitted construction of the hysteresis cycle for a rubber hose and various tubes. Another experiment was designed to define the temporal recovery of a plastic spring with initial stretching. A simple mathematical model was developed to explain this phenomenon. (paper)

Elastoplastic phase-field modeling of ζ-hydride precipitation in zirconium alloy: dynamics evolution in inhomogeneous elasticity

International Nuclear Information System (INIS)

Oum, G.; Thuinet, L.; Legris, A.

2015-07-01

A phase-field (PF) model was developed within the framework of homogeneous and heterogeneous elasticity theory to study the precipitation of ζ-hydride in zirconium. By coupling crystal plasticity to PF we show that plastic strain participates in lowering the transformation stresses, and therefore induces changes in nucleation, growth and morphology evolution of the precipitates. (authors)

Use of abrupt strain path change for determining subsequent yield surface

DEFF Research Database (Denmark)

Kuroda, Mitsutoshi; Tvergaard, Viggo

1999-01-01

is prescribed, which makes the stress point move quickly along the yield surface. It is assumed that a closed-loop testing machine is used for the experiment, so that the strain path can be prescribed according to strain gauge measurements. Relative to the standard method of determining yield surface shapes...... by probing in many different stress directions from the elastic region, using some chosen plastic strain offset, the main advantage of the proposed method is that elastic unloading is not needed prior to tracing the yield surface. The method is illustrated here by a few analyses, first for the simplest how...

Comparison of elastic and inelastic seismic response of high temperature piping systems

International Nuclear Information System (INIS)

Thomas, F.M.; McCabe, S.L.; Liu, Y.

1994-01-01

A study of high temperature power piping systems is presented. The response of the piping systems is determined when subjected to seismic disturbances. Two piping systems are presented, a main steam line, and a cold reheat line. Each of the piping systems are modeled using the ANSYS computer program and two analyses are performed on each piping system. First, each piping system is subjected to a seismic disturbance and the pipe material is assumed to remain linear and elastic. Next the analysis is repeated for each piping system when the pipe material is modeled as having elastic-plastic behavior. The results of the linear elastic analysis and elastic-plastic analysis are compared for each of the two pipe models. The pipe stresses, strains, and displacements, are compared. These comparisons are made so that the effect of the material yielding can be determined and to access what error is made when a linear analysis is performed on a system that yields

Mathematical and numerical analysis of hyper-elastic systems and introduction of plasticity

International Nuclear Information System (INIS)

Kluth, G.

2008-12-01

The goal is to model mathematically and numerically the dynamic phenomenons for solids in finite plasticity. We suggest a model that we call hyper-elasto-plastic based on hyper-elastic systems of conservation laws and on the use of an equation of state that we have constructed so as to achieve the plastic yield criterion of Von Mises. This model gives exact (analytic) solutions with shock split to flyer-plate experiments. The mathematical analysis of this model is done (hyperbolicity, characteristic fields, involutions and entropy). In the numerical part, we give 1D and 2D Lagrangian schemes which satisfy an entropy criterion. Moreover, thanks to a special discretization of the equations on deformation gradient, we satisfy some discrete involutions. In this work, the degeneracy of the solid model into hydrodynamic models is studied at the continuous level, and achieved at the numerical one. On different problems, we show the validity of our model and our numerical schemes. (author)

Microstructure-property relationships and constitutive response of plastically graded case hardened steels

Science.gov (United States)

Klecka, Michael A.

Case hardened materials, popularly used in many demanding engineering applications such as bearings, gears, and wear/impact surfaces, have high surface hardness and a gradient in material properties (hardness, yield strength, etc.) as a function of depth; therefore, they behave as plastically graded materials. In the current study, two different commercially available case carburized steels along with two through hardened steels are characterized to obtain relationships among the volume fraction of subsurface carbides, indentation hardness, elastic modulus, and yield strength as a function of depth. A variety of methods including microindentation, nanoindentation, ultrasonic measurements, compression testing, rule of mixtures, and upper and lower bound models are used to determine the relationships for elastic modulus and compare the experimental results with model predictions. In addition, the morphology, composition, and properties of the carbide particles are also determined. The gradient in hardness with depth in graded materials is commonly determined using microindentation on the cross-section of the material which contains the gradation in microstructure or composition. In the current study, a novel method is proposed to predict the hardness gradient profile using solely surface indentations at a range of loads. The method does not require the graded material to be sectioned, and has practical utility in the surface heat-treatment industry. For a material with a decreasing gradient in hardness, higher indent loads result in a lower measured hardness due to the influence of the softer subsurface layers. A power-law model is presented which relates the measured surface indentation hardness under increasing load to the subsurface gradient in hardness. A coordinated experimental and numerical study is presented to extract the constitutive response of graded materials, utilizing relationships between hardness, plastic deformation, and strain hardening response

Finite strain logarithmic hyperelasto-plasticity with softening: a strongly non-local implicit gradient framework

NARCIS (Netherlands)

Geers, M.G.D.

2004-01-01

This paper addresses the extension of a Eulerian logarithmic finite strain hyperelasto-plasticity model in order to incorporate an isotropic plastic damage variable that leads to softening and failure of the plastic material. It is shown that a logarithmic elasto-plastic model with a strongly

Elasto/visco-plastic analysis of moderately thick shells of revolution under asymmetrical loading

International Nuclear Information System (INIS)

Tao, K.; Takezono, S.

1987-01-01

In the present paper the analytical formulation for the elasto/visco-plastic problems of general, moderately thick shells of revolution subjected to asymmetrical loads is developed in consideration of the effect of shear deformation. The equations of equilibrium and the relations between the strains and displacements are derived by extending the Reissner-Naghdi theory (1941, 1957) for elastic shells with given consideration to the effect of shear deformation. As the constitutive relation, Hooke's law is used in the liner elastic range, and the elasto/visco-plastic equations by Perzyna (1966) are employed in the plastic range. The fundamental equations on the elasto/visco-plastic problems derived for incremental values are numerically solved by a finite difference method and the solutions are obtained by summation of the incremental values. (orig./GL)

Influence of time-dependent elastic-plastic material behaviour on the load-carrying capacity of shells of revolution

International Nuclear Information System (INIS)

Schnabel, F.

1987-01-01

The present report deals with the influence of time-dependent material behavior on the load-carrying capacity of thin-walled shells of revolution. In the first part various creep-hardening hypotheses as well as the spatial and temporal discretization procedures employed are described. The adaptation of a well-tested finite element method based on ring elements to the treatment of creep problems and several time-integration procedures, in particular the iterative treatment of the coupling between creep and elastic-plastic strains as well as the important aspect of time-step-control are discussed in detail. In the second part several typical shell configurations are analyzed and a comparison with available theoretical and experimental results is made. Finally, the time-dependent load-carrying behavior of torispherical pressure vessel ends subjected to internal and external pressure is investigated and design aids for the determination of creep collapse times are proposed. (orig.) [de

Strain gradient plasticity effects in whisker-reinforced metals

DEFF Research Database (Denmark)

Niordson, Christian Frithiof

2003-01-01

A metal reinforced by fibers in the micron range is studied using the strain gradient plasticity theory of Fleck and Hutchinson (J. Mech. Phys. Solids 49 (2001) 2245). Cell-model analyses are used to study the influence of the material length parameters numerically, for both a single parameter...

Plastic deformation of 2D crumpled wires

International Nuclear Information System (INIS)

Gomes, M A F; Donato, C C; Brito, V P; Coelho, A S O

2008-01-01

When a single long piece of elastic wire is injected through channels into a confining two-dimensional cavity, a complex structure of hierarchical loops is formed. In the limit of maximum packing density, these structures are described by several scaling laws. In this paper this packing process is investigated but using plastic wires which give rise to completely irreversible structures of different morphology. In particular, the plastic deformation from circular to oblate configurations of crumpled wires is experimentally studied, obtained by the application of an axial strain. Among other things, it is shown that in spite of plasticity, irreversibility and very large deformations, scaling is still observed.

Study on elastic-plastic fracture toughness test in high temperature water

International Nuclear Information System (INIS)

Miura, Yasufumi

2016-01-01

Structural integrity of internal components in light water reactors is important for the safety of operation and service lifetime. Fracture toughness is important parameter for structural integrity assessment of nuclear power plant. In general, fracture toughness of materials which compose the components in light water reactor is obtained with fracture toughness tests in air although some components are subjected to high temperature water because of the difficulty of fracture toughness test in high temperature water. However, the effects of high temperature water and hydrogen on fracture behavior of the structural materials in nuclear power plant such as low alloy steel, cast austenitic stainless steel, and Ni base alloy are concerned recently. In this study, elastic-plastic fracture toughness test of low alloy steel in simulated BWR water environment was studied. Fracture toughness test in high temperature water with original clip gage and normalization data reduction technique was established. The difference of fracture toughness J_Q tested in air between using elastic unload compliance method and normalization data reduction technique was also discussed. As a result, obtained value with normalization data reduction technique tended to be higher than the value with elastic unload compliance. (author)

Influence of the Martensitic Transformation on the Microscale Plastic Strain Heterogeneities in a Duplex Stainless Steel

Science.gov (United States)

Lechartier, Audrey; Martin, Guilhem; Comby, Solène; Roussel-Dherbey, Francine; Deschamps, Alexis; Mantel, Marc; Meyer, Nicolas; Verdier, Marc; Veron, Muriel

2017-01-01

The influence of the martensitic transformation on microscale plastic strain heterogeneity of a duplex stainless steel has been investigated. Microscale strain heterogeneities were measured by digital image correlation during an in situ tensile test within the SEM. The martensitic transformation was monitored in situ during tensile testing by high-energy synchrotron X-ray diffraction. A clear correlation is shown between the plasticity-induced transformation of austenite to martensite and the development of plastic strain heterogeneities at the phase level.

Characterization of residual stresses generated during inhomogeneous plastic deformation

DEFF Research Database (Denmark)

Lorentzen, T.; Faurholdt, T.; Clausen, B.

1998-01-01

Residual stresses generated by macroscopic inhomogeneous plastic deformation are predicted by an explicit finite element (FE) technique. The numerical predictions are evaluated by characterizing the residual elastic strains by neutron diffraction using two different (hkl) reflections. Intergranular...... compare well and verify the capability of the numerical technique as well as the possibilities of experimental validation using neutron diffraction. The presented experimental and numerical approach will subsequently be utilized for the evaluation of more complicated plastic deformation processes...

Improved incorporation of strain gradient elasticity in the flexoelectricity based energy harvesting from nanobeams

Science.gov (United States)

Zhou, Yarong; Yang, Xu; Pan, Dongmei; Wang, Binglei

2018-04-01

Flexoelectricity, the coupling of strain gradient and polarization, exists in all the dielectric materials and numerous models have been proposed to study this mechanism. However, the contribution of strain gradient elasticity has typically been underestimated. In this work, inspired by the one-length scale parameter model developed by Deng et al. [19], we incorporate three length-scale parameters to carefully capture the contribution of the purely mechanical strain gradients on flexoelectricity. This three-parameter model is more flexible and could be applied to investigate the flexoelectricity in a wide range of complicated deformations. Accordingly, we carry out our analysis by studying a dielectric nanobeam under different boundary conditions. We show that the strain gradient elasticity and flexoelectricity have apparent size effects and significant influence on the electromechanical response. In particular, the strain gradient effects could significantly reduce the energy efficiency, indicating their importance and necessity. This work may be helpful in understanding the mechanism of flexoelectricity at the nanoscale and sheds light on the flexoelectricity energy harvesting.

δ-hydride habit plane determination in α-zirconium by strain energy minimization technique at 25 and 300 deg C

International Nuclear Information System (INIS)

Singh, R.N.; Stahle, P.; Sairam, K.; Ristmana, Matti; Banerjee, S.

2008-01-01

The objective of the present investigation is to predict the habit plane of δ-hydride precipitating in α-Zr at 25 and 300 deg C using strain energy minimization technique. The δ-hydride phase is modeled to undergo isotropic elastic and plastic deformation. The α-Zr phase was modeled to undergo transverse isotropic elastic deformation. Both isotropic plastic and transverse isotropic plastic deformations of α-Zr were considered. Further, both perfect and linear work-hardening plastic behaviors of zirconium and its hydride were considered. Accommodation strain energy of δ-hydrides forming in α-Zr crystal was computed using initial strain method as a function of hydride nuclei orientation. Hydride was modeled as disk with circular edge. The simulation was carried out using materials properties reported at 25 and 300 deg C. Contrary to several habit planes reported in literature for δ-hydrides precipitating in α-Zr crystal the total accommodation energy minima suggests only basal plane i.e. (0001) as the habit plane. (author)

Elastic-plastic fracture mechanics of compact bone

Science.gov (United States)

Yan, Jiahau

Bone is a composite composed mainly of organics, minerals and water. Most studies on the fracture toughness of bone have been conducted at room temperature. Considering that the body temperature of animals is higher than room temperature, and that bone has a high volumetric percentage of organics (generally, 35--50%), the effect of temperature on fracture toughness of bone should be studied. Single-edged V-shaped notched (SEVN) specimens were prepared to measure the fracture toughness of bovine femur and manatee rib in water at 0, 10, 23, 37 and 50°C. The fracture toughness of bovine femur and manatee rib were found to decrease from 7.0 to 4.3 MPa·m1/2 and from 5.5 to 4.1 MPa·m1/2, respectively, over a temperature range of 50°C. The decreases were attributed to inability of the organics to sustain greater stresses at higher temperatures. We studied the effects of water and organics on fracture toughness of bone using water-free and organics-free SEVN specimens at 23°C. Water-free and organics-free specimens were obtained by placing fresh bone specimen in a furnace at different temperatures. Water and organics significantly affected the fracture toughness of bone. Fracture toughness of the water-free specimens was 44.7% (bovine femur) and 32.4% (manatee rib) less than that of fresh-bone specimens. Fracture toughness of the organics-free specimens was 92.7% (bovine femur) and 91.5% (manatee rib) less than that of fresh bone specimens. Linear Elastic Fracture Mechanics (LEFM) is widely used to study bone. However, bone often has small to moderate scale yielding during testing. We used J integral, an elastic-plastic fracture-mechanics parameter, to study the fracture process of bone. The J integral of bovine femur increased from 6.3 KJ/mm2 at 23°C to 6.7 KJ/mm2 at 37°C. Although the fracture toughness of bovine bone decreases as the temperature increases, the J integral results show a contrary trend. The energy spent in advancing the crack beyond the linear-elastic

Interpreting the stress–strain response of Al micropillars through gradient plasticity

International Nuclear Information System (INIS)

Zhang, Xu; Aifantis, Katerina E.; Ngan, Alfonso H.W.

2014-01-01

Micropillar compression has fascinated the materials and mechanics communities for over a decade, due to the unique stochastic effects and slip zones that dictate their stress–strain curves and microstructure. Although plethora studies exist that capture experimentally the mechanical response of various types of micropillars, limited theoretical models can interpret the observed behavior. Particularly, single crystal micropillars exhibit multiple serrations in their stress–strain response, indicating the activation of slip zones, while bi-crystal pillars, in which the grain boundary lies parallel to the pillar axis, do not display such serrations, but rather a distinct “knee”, which indicates dislocation pileups at the grain boundary. In-situ synchrotron microdiffraction experiments have illustrated that not only dislocations, but also significant plastic strain gradients develop during micropillar compression. In the present study, therefore, appropriate gradient plasticity models that can account for the pillar microstructure, are successfully used to capture the stress–strain response of single- and bi-crystal Al pillars

Evaluation of elastic-plastic fracture of toughness and fracture resistance of carbon steel STS42

International Nuclear Information System (INIS)

Kobayashi, Hideo; Nakamura, Haruo; Kashiwagi, Kohmei

1987-01-01

The elastic-plastic fracture toughness (J Ic ) and fracture resistance (J-R curve) of a carbon steel, STS42, used for piping in a nuclear reactor were evaluated according to the several evaluating methods recommended or proposed so far, to discuss their applicability and utility. The results obtained are as follows: (1) In evaluating J Ic , the multiple specimen method recommended by the Japan Society for Mechanical Engineers (JSME standard S001) gives the most reliable results by using smaller sized specimens. (2) The single-specimen methods by using the compliance technique, adopted in the ASTM standards (E813, E813 modified, Tentative test procedure for determining the plain strain J-R curve), do not give an accurate J-R curve or J Ic , due to an error in the calculated crack length. (3) In evaluating the J-R curve, it is necessary to account for crack extension in calculating the J-integral. (4) According to the above results, a new standard method for determining the J-R curve including the J Ic test method should be poprosed. (author)

X-ray microbeam measurements of individual dislocation cell elastic strains in deformed single-crystal copper

Energy Technology Data Exchange (ETDEWEB)

Levine, Lyle E. [National Institute of Standards and Technology (NIST); Larson, Ben C [ORNL; Yang, Wenge [Carnegie Institution of Washington; Kassner, Michael E. [University of Southern California; Tischler, Jonathan Zachary [ORNL; Delos-Reyes, Michael A. [University of Southern California; Fields, Richard J. [National Institute of Standards and Technology (NIST); Liu, Wenjun [Argonne National Laboratory (ANL)

2006-01-01

The distribution of elastic strains (and thus stresses) at the sub-micrometer length scale within deformed metal single crystals has surprisingly broad implications for our understanding of important physical phenomena. These include the evolution of the complex dislocation structures that govern mechanical behavior within individual grains [1-4], the transport of dislocations through such structures [5-7], changes in mechanical properties that occur during reverse loading [8-10] (e.g. sheet metal forming), and the analyses of diffraction line profiles for microstructural studies of these phenomena [11-17]. We present the first direct, spatially-resolved measurements of the elastic strains within individual dislocation cells in copper single crystals deformed in tension and compression along <100> axes. Broad distributions of elastic strains are found, with profound implications for theories of dislocation structure evolution [4,18], dislocation transport [5-7], and the extraction of dislocation parameters from X-ray line profiles [11-17,19].

High strain rate deformation and fracture of the magnesium alloy Ma2-1 under shock wave loading

Science.gov (United States)

Garkushin, G. V.; Kanel', G. I.; Razorenov, S. V.

2012-05-01

This paper presents the results of measurements of the dynamic elastic limit and spall strength under shock wave loading of specimens of the magnesium alloy Ma2-1 with a thickness ranging from 0.25 to 10 mm at normal and elevated (to 550°C) temperatures. From the results of measurements of the decay of the elastic precursor of a shock compression wave, it has been found that the plastic strain rate behind the front of the elastic precursor decreases from 2 × 105 s-1 at a distance of 0.25 mm to 103 s-1 at a distance of 10 mm. The plastic strain rate in a shock wave is one order of magnitude higher than that in the elastic precursor at the same value of the shear stress. The spall strength of the alloy decreases as the solidus temperature is approached.

Strain-rate dependent plasticity in thermo-mechanical transient analysis

International Nuclear Information System (INIS)

Rashid, Y.R.; Sharabi, M.N.

1980-01-01

The thermo-mechanical transient behavior of fuel element cladding and other reactor components is generally governed by the strain-rate properties of the material. Relevant constitutive modeling requires extensive material data in the form of strain-rate response as function of true-stress, temperature, time and environmental conditions, which can then be fitted within a theoretical framework of an inelastic constitutive model. In this paper, we present a constitutive formulation that deals continuously with the entire strain-rate range and has the desirable advantage of utilizing existing material data. The derivation makes use of strain-rate sensitive stress-strain curve and strain-rate dependent yield surface. By postulating a strain-rate dependent on Mises yield function and a strain-rate dependent kinematic hardening rule, we are able to derive incremental stress-strain relations that describe the strain-rate behavior in the entire deformation range spanning high strain-rate plasticity and creep. The model is sufficiently general as to apply to any materials and loading histories for which data is available. (orig.)

Comparative study of sea ice dynamics simulations with a Maxwell elasto-brittle rheology and the elastic-viscous-plastic rheology in NEMO-LIM3

Science.gov (United States)

Raulier, Jonathan; Dansereau, Véronique; Fichefet, Thierry; Legat, Vincent; Weiss, Jérôme

2017-04-01

Sea ice is a highly dynamical environment characterized by a dense mesh of fractures or leads, constantly opening and closing over short time scales. This characteristic geomorphology is linked to the existence of linear kinematic features, which consist of quasi-linear patterns emerging from the observed strain rate field of sea ice. Standard rheologies used in most state-of-the-art sea ice models, like the well-known elastic-viscous-plastic rheology, are thought to misrepresent those linear kinematic features and the observed statistical distribution of deformation rates. Dedicated rheologies built to catch the processes known to be at the origin of the formation of leads are developed but still need evaluations on the global scale. One of them, based on a Maxwell elasto-brittle formulation, is being integrated in the NEMO-LIM3 global ocean-sea ice model (www.nemo-ocean.eu; www.elic.ucl.ac.be/lim). In the present study, we compare the results of the sea ice model LIM3 obtained with two different rheologies: the elastic-viscous-plastic rheology commonly used in LIM3 and a Maxwell elasto-brittle rheology. This comparison is focused on the statistical characteristics of the simulated deformation rate and on the ability of the model to reproduce the existence of leads within the ice pack. The impact of the lead representation on fluxes between ice, atmosphere and ocean is also assessed.

Strain evolution after fiber failure in a single-fiber metal matrix composite under cyclic loading

Energy Technology Data Exchange (ETDEWEB)

Hanan, Jay C. [Department of Materials Science, California Institute of Technology, Pasadena, CA 91125 (United States)]. E-mail: jay.hanan@okstate.edu; Mahesh, Sivasambu [Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Uestuendag, Ersan [Department of Materials Science, California Institute of Technology, Pasadena, CA 91125 (United States)]. E-mail: ersan@caltech.edu; Beyerlein, Irene J. [Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Swift, Geoffrey A. [Department of Materials Science, California Institute of Technology, Pasadena, CA 91125 (United States); Clausen, Bjorn [Department of Materials Science, California Institute of Technology, Pasadena, CA 91125 (United States); Brown, Donald W. [Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Bourke, Mark A.M. [Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States)

2005-06-15

The evolution of in situ elastic strain with cyclic tensile loading in each phase of a single Al{sub 2}O{sub 3}-fiber/aluminum-matrix composite was studied using neutron diffraction (ND). An analytical model appropriate for metal matrix composites (MMCs) was developed to connect the measured axial strain evolution in each phase with the possible micromechanical events that could occur during loading at room temperature: fiber fracture, interfacial slipping, and matrix plastic deformation. Model interpretation showed that the elastic strain evolution in the fiber and matrix was governed by fiber fracture and interface slipping and not by plastic deformation of the matrix, whereas the macroscopic stress-strain response of the composite was influenced by all three. The combined single-fiber composite model and ND experiment introduces a new and quick engineering approach for qualifying the micromechanical response in MMCs due to cyclic loading and fiber fracture.

Strain evolution after fiber failure in a single-fiber metal matrix composite under cyclic loading

International Nuclear Information System (INIS)

Hanan, Jay C.; Mahesh, Sivasambu; Uestuendag, Ersan; Beyerlein, Irene J.; Swift, Geoffrey A.; Clausen, Bjorn; Brown, Donald W.; Bourke, Mark A.M.

2005-01-01

The evolution of in situ elastic strain with cyclic tensile loading in each phase of a single Al 2 O 3 -fiber/aluminum-matrix composite was studied using neutron diffraction (ND). An analytical model appropriate for metal matrix composites (MMCs) was developed to connect the measured axial strain evolution in each phase with the possible micromechanical events that could occur during loading at room temperature: fiber fracture, interfacial slipping, and matrix plastic deformation. Model interpretation showed that the elastic strain evolution in the fiber and matrix was governed by fiber fracture and interface slipping and not by plastic deformation of the matrix, whereas the macroscopic stress-strain response of the composite was influenced by all three. The combined single-fiber composite model and ND experiment introduces a new and quick engineering approach for qualifying the micromechanical response in MMCs due to cyclic loading and fiber fracture

Pb nanoprecipitates in Al: Magic-shape effects due to elastic strain

DEFF Research Database (Denmark)

Hamilton, J.C.; Leoard, F.; Johnson, Erik

2007-01-01

We present a theory for size-dependent shapes of Pb nanoprecipitates in Al, introducing the concept of "magic shapes," i.e., shapes having near-zero homogeneous elastic strains. Our quantitative atomistic calculations of edge energies show their effect on precipitate shape to be negligible, thus...

Fatique of Copper Polycrystals at Low Plastic Strain Amplitudes

DEFF Research Database (Denmark)

Rasmussen, K. V.; Pedersen, Ole Bøcker

1980-01-01

Single crystals and polycrystals of pure copper were fatigued in tension-compression at constant low amplitudes of plastic strain and low cycling frequencies at room temperature in air. Surface patterns of persistent slip bands were quantitatively examined by optical microscopy. Bulk dislocation...

Elastic-plastic-creep response of structures under composite time history of loadings

International Nuclear Information System (INIS)

Zudans, Z.

1975-01-01

The purpose of this work is to derive the theory, to develop efficient numerical techniques accounting for plasticity, creep and overall equilibrium, to describe the overall structure of the resulting computer program, and to demonstrate the capability of this analysis on a real structure. Classical plasticity theory is used to develop a novel method based on the concept of 'plastic stress' for consideration of inelastic behavior. It is shown that materials stres-strain curves can be followed to any desired degree of accuracy both for isotropic and kinematic hardening. It is further shown that for kinematic hardening it is necessary to base the incremental change on the state corresponding to the mean of the initial and the final states in order to satisfy the yield condition at the final state. The equation of state and strain hardening is used to describe the creep behavior. A novel numerical technique to describe a complex load history is developed by using time as a parameter, history breakpoint determination by scanning of various load vectors and by linear interpolation between any two breakpoints in the load history. The 'plastic stress' load vector concept is utilized with iteration and extrapolation to converge to the equilibrium states with simultaneous satisfaction of the stress-strain relations for each of the iterated states. The essential features of the computer program DYPLAS-FSH, based on the theory and techniques described above, and a postprocessor program POR-FSH, based on RDT F9-5T for ratcheting and fatigue evaluation, are identified and discussed. These computer programs are used to analyse the ellipsoidal pressure vessel head of the intermediate heat exchanger of EBR-II, penetrated by two closely spaced non-radial nozzles, subjected to four consecutive composite cycles of complex mechanical and thermal loads

Numerical studies of cavitation erosion on an elastic-plastic material caused by shock-induced bubble collapse

Science.gov (United States)

Turangan, C. K.; Ball, G. J.; Jamaluddin, A. R.; Leighton, T. G.

2017-09-01

We present a study of shock-induced collapse of single bubbles near/attached to an elastic-plastic solid using the free-Lagrange method, which forms the latest part of our shock-induced collapse studies. We simulated the collapse of 40 μm radius single bubbles near/attached to rigid and aluminium walls by a 60 MPa lithotripter shock for various scenarios based on bubble-wall separations, and the collapse of a 255 μm radius bubble attached to aluminium foil with a 65 MPa lithotripter shock. The coupling of the multi-phases, compressibility, axisymmetric geometry and elastic-plastic material model within a single solver has enabled us to examine the impingement of high-speed liquid jets from the shock-induced collapsing bubbles, which imposes an extreme compression in the aluminium that leads to pitting and plastic deformation. For certain scenarios, instead of the high-speed jet, a radially inwards flow along the aluminium surface contracts the bubble to produce a `mushroom shape'. This work provides methods for quantifying which parameters (e.g. bubble sizes and separations from the solid) might promote or inhibit erosion on solid surfaces.

Phase-field modelling of ductile fracture: a variational gradient-extended plasticity-damage theory and its micromorphic regularization.

Science.gov (United States)

Miehe, C; Teichtmeister, S; Aldakheel, F

2016-04-28

This work outlines a novel variational-based theory for the phase-field modelling of ductile fracture in elastic-plastic solids undergoing large strains. The phase-field approach regularizes sharp crack surfaces within a pure continuum setting by a specific gradient damage modelling. It is linked to a formulation of gradient plasticity at finite strains. The framework includes two independent length scales which regularize both the plastic response as well as the crack discontinuities. This ensures that the damage zones of ductile fracture are inside of plastic zones, and guarantees on the computational side a mesh objectivity in post-critical ranges. © 2016 The Author(s).

Elastic-plastic-creep response of structures under composite time history of loadings

International Nuclear Information System (INIS)

Zudans, Z.

1975-01-01

High temperature nuclear reactor components are subject to a complex history of thermal and mechanical loading cycles. To evaluate the adequacy of such components, detailed information on the accumulated inelastic strains and strain cycling is required. This work derives the theory, develops efficient numerical techniques accounting for plasticity, creep and overall equilibrium, describes the overall structure of the resulting computer program, and demonstrates the capability of this analysis on a real structure. (Auth.)

Elastic-plastic stress distributions near the endcap of a fuel element

International Nuclear Information System (INIS)

Tayal, M.; Hallgrimson, K.D.; Sejnoha, R.; Singh, P.N.

1993-06-01

This paper discusses the stress patterns in and near the endcap of a CANDU fuel element from the perspective of stress corrosion cracking. Simulations of out-reactor burst tests suggest that local plastic strains stay comparatively low for internal pressures below 26-30 MPa. Photoelastic measurements as well as analytical assessments show that the reentrant corner at the sheath/endcap junction results in high concentration of stresses and strains. Analytical assessments show that the in-reactor stresses and strains at the reentrant corner are highly multiaxial, and well into the plastic range. The maximum principal stress correlates well with the location and the direction of circumferential endcap cracks observed in fuel that failed in the Bruce reactor. Thus the maximum principal stress appears promising in ranking various geometries of the sheath/endcap junction with respect to their relative susceptibility to stress corrosion cracking. Design studies suggest that the most effective practical ways of lowering the stresses near the weld, in order of decreasing importance, are to provide a larger interference-free length between the ridge and the endcaps; to increase the pellet/sheath radial gap; to increase the pellet/endcap axial gap; and to keep the gas pressure low. (author). 16 refs., 16 figs

Modeling fracture in the context of a strain-limiting theory of elasticity: a single anti-plane shear crack

KAUST Repository

Rajagopal, K. R.

2011-01-06

This paper is the first part of an extended program to develop a theory of fracture in the context of strain-limiting theories of elasticity. This program exploits a novel approach to modeling the mechanical response of elastic, that is non-dissipative, materials through implicit constitutive relations. The particular class of models studied here can also be viewed as arising from an explicit theory in which the displacement gradient is specified to be a nonlinear function of stress. This modeling construct generalizes the classical Cauchy and Green theories of elasticity which are included as special cases. It was conjectured that special forms of these implicit theories that limit strains to physically realistic maximum levels even for arbitrarily large stresses would be ideal for modeling fracture by offering a modeling paradigm that avoids the crack-tip strain singularities characteristic of classical fracture theories. The simplest fracture setting in which to explore this conjecture is anti-plane shear. It is demonstrated herein that for a specific choice of strain-limiting elasticity theory, crack-tip strains do indeed remain bounded. Moreover, the theory predicts a bounded stress field in the neighborhood of a crack-tip and a cusp-shaped opening displacement. The results confirm the conjecture that use of a strain limiting explicit theory in which the displacement gradient is given as a function of stress for modeling the bulk constitutive behavior obviates the necessity of introducing ad hoc modeling constructs such as crack-tip cohesive or process zones in order to correct the unphysical stress and strain singularities predicted by classical linear elastic fracture mechanics. © 2011 Springer Science+Business Media B.V.

Modeling and Analysis of Size-Dependent Structural Problems by Using Low- Order Finite Elements with Strain Gradient Plasticity

International Nuclear Information System (INIS)

Park, Moon Shik; Suh, Yeong Sung; Song, Seung

2011-01-01

An elasto-plastic finite element method using the theory of strain gradient plasticity is proposed to evaluate the size dependency of structural plasticity that occurs when the configuration size decreases to micron scale. For this method, we suggest a low-order plane and three-dimensional displacement-based elements, eliminating the need for a high order, many degrees of freedom, a mixed element, or super elements, which have been considered necessary in previous researches. The proposed method can be performed in the framework of nonlinear incremental analysis in which plastic strains are calculated and averaged at nodes. These strains are then interpolated and differentiated for gradient calculation. We adopted a strain-gradient-hardening constitutive equation from the Taylor dislocation model, which requires the plastic strain gradient. The developed finite elements are tested numerically on the basis of typical size-effect problems such as micro-bending, micro-torsion, and micro-voids. With respect to the strain gradient plasticity, i.e., the size effects, the results obtained by using the proposed method, which are simple in their calculation, are in good agreement with the experimental results cited in previously published papers

Elasto/visco-plastic analysis of orthotropic moderately thick shells of revolution under asymmetrical loading

International Nuclear Information System (INIS)

Tao, K.; Takezono, S.

1989-01-01

An analytical method for the elasto/visco-plastic problems of general, orthotropic moderately thick shells of revolution subjected to asymmetrical loads is developed in consideration of the effect of shear deformations. The Reissner-Naghdi theory for elastic moderately thick shells is extended in this analysis. As the constitutive equation, Hooke's law for orthotropic materials is used in the elastic region, and equations based on the orthotropic visco-plastic theory derived from the orthotropic plastic theory by Hill are employed in the plastic range. The visco-plastic strain rates are related to the stresses by Perzyna's equation. The fundamental equations for the increment are numerically solved by a finite difference method and the solutions are obtained by summation of the incremental values. In order to check the adequacy of the numerical analysis, experiments are performed on the elasto/visco-plastic deformation of a titanium cylindrical shell subjected to locally distributed loads. Good agreement is obtained between the experimental results and analytical solutions

Introduction of damage in an elasto-plastic model for unsaturated geo-materials

International Nuclear Information System (INIS)

Le Pense, S.; Pouya, A.; Gatmiri, B.

2012-01-01

Document available in extended abstract form only. During the excavation of nuclear waste repository galleries, the surrounding soil is suspected to undergo structural changes as well as modification of its stress state. The desaturation due to ventilation of galleries during this stage makes it necessary to consider the unsaturated state of the host geo-material. The decompression occurring after the excavation leads to a modification of the stress state. The purpose of our work is to develop a mechanical model to simulate the non-linear stress-strain behaviour of geo-materials which will have to contain radioactivity of nuclear waste for a very long time. Two irreversible phenomena can explain the non-linear behaviour of geo-materials. Plasticity leads to irrecoverable strains. Damage, linked to the appearance and extension of microcracks, results in a deterioration of elastic and hydraulic properties. We will present here the bases of a new model coupling damage and plasticity for the stress-strain behaviour of unsaturated geo-materials. This model should be thermodynamically consistent and use only a reasonable number of parameters. Based on the work of Houlsby, (Houlsby 1997), we choose to use as constitutive variables for unsaturated soils Bishop's stress and suction. This choice as the advantage to allow for continuity at the transition between saturated and unsaturated states. Damage is taken into account by defining a damaged constitutive stress, which is similar to the effective stress principle defined by Kachanov (Kachanov 1958). A simple damage criterion is proposed and an associative flow rule is assumed. We choose to follow the principle of strain equivalence defined by Lemaitre (Lemaitre 1996). This leads to the following elasticity law giving the damaged constitutive stress as a function of elastic strain. If non-linear elasticity is considered, a pressure-dependent bulk modulus and a constant shear modulus can be chosen in order to fit

Internal strain estimation for quantification of human heel pad elastic modulus: A phantom study

DEFF Research Database (Denmark)

Holst, Karen; Liebgott, Hervé; Wilhjelm, Jens E.

2013-01-01

Shock absorption is the most important function of the human heel pad. However, changes in heel pad elasticity, as seen in e.g. long-distance runners, diabetes patients, and victims of Falanga torture are affecting this function, often in a painful manner. Assessment of heel pad elasticity...... is usually based on one or a few strain measurements obtained by an external load-deformation system. The aim of this study was to develop a technique for quantitative measurements of heel pad elastic modulus based on several internal strain measures from within the heel pad by use of ultrasound images. Nine...... heel phantoms were manufactured featuring a combination of three heel pad stiffnesses and three heel pad thicknesses to model the normal human variation. Each phantom was tested in an indentation system comprising a 7MHz linear array ultrasound transducer, working as the indentor, and a connected load...

Measurement of Plastic Stress and Strain for Analytical Method Verification (MSFC Center Director's Discretionary Fund Project No. 93-08)

Science.gov (United States)

Price, J. M.; Steeve, B. E.; Swanson, G. R.

1999-01-01

The analytical prediction of stress, strain, and fatigue life at locations experiencing local plasticity is full of uncertainties. Much of this uncertainty arises from the material models and their use in the numerical techniques used to solve plasticity problems. Experimental measurements of actual plastic strains would allow the validity of these models and solutions to be tested. This memorandum describes how experimental plastic residual strain measurements were used to verify the results of a thermally induced plastic fatigue failure analysis of a space shuttle main engine fuel pump component.

The effects of perturbations on the strain distribution in numerical simulations - elasto-viscoplastic modeling of boudinage as a case study

Science.gov (United States)

Peters, Max; Karrech, Ali; Poulet, Thomas; Herwegh, Marco; Regenauer-Lieb, Klaus

2014-05-01

During necking of a mechanically stiffer layer embedded in a weaker matrix, relatively large amounts of strain localize in small areas. As this deformation style appears under distinct geological conditions, necking phenomena, e.g. boudinaged veins, are associated with a variety of deformation modes. So far, there exists rather limited knowledge about the origin of instabilities and their role as precursory structures, i.e. strong localization of elastic energy affecting further plastic deformation (e.g. Regenauer-Lieb & Yuen, 1998; 2004; Karrech et al., 2011a). We applied the finite element solver ABAQUS in order to investigate the 2-D strain distribution in layers including different mechanical material properties during plane strain co-axial deformation. First, linear perturbation analyses were performed in order to evaluate the imperfection sensitivity in the elastic and viscous regimes. We perform a classical modal analysis to determine the natural mode shapes and frequencies of our geological structure during arbitrary vibrations. This analysis aims at detecting the eigenmodes of the geological structure, which are sinusoidal vibrations with geometry specific natural modal shapes and frequencies. The eigenvalues represent the nodal points where the onset of (visco)-elasto-plastic localization can initiate in the structure (Rice, 1977). The eigenmodes, eigenvalues and eigenvectors are highly sensitive to the layer-box' aspect ratio and differences in Young's moduli, or effective viscosity, respectively. Boundary effect-free strain propagation occurs for layer-box aspect ratios smaller than 1:10. Second, these preloading structures were used as seeds for imperfections in elasto-viscoplastic numerical modeling of continuous necking of a coarse-grained mineral layer embedded in a finer-grained matrix (pinch-and-swell type of boudinage), following the thermo-mechanical coupling of grain size evolutions by Herwegh et al. (in press). The evolution of symmetric necks

Detection of thermal aging degradation and plastic strain damage for duplex stainless steel using SQUID sensor

International Nuclear Information System (INIS)

Otaka, M.; Evanson, S.; Hesegawa, K.; Takaku, K.

1991-01-01

An apparatus using a SQUID sensor is developed for nondestructive inspection. The measurements are obtained with the SQUID sensor located approximately 150 mm from the specimen. The degradation of thermal aging and plastic strain for duplex stainless steel is successfully detected independently from the magnetic characterization measurements. The magnetic flux density under high polarizing field is found to be independent of thermal aging. Coercive force increases with thermal aging time. On the other hand, the magnetic flux density under high field increases with the plastic strain. Coercive force is found to be independent of the plastic strain. (author)

Substructure based modeling of nickel single crystals cycled at low plastic strain amplitudes

Science.gov (United States)

Zhou, Dong

In this dissertation a meso-scale, substructure-based, composite single crystal model is fully developed from the simple uniaxial model to the 3-D finite element method (FEM) model with explicit substructures and further with substructure evolution parameters, to simulate the completely reversed, strain controlled, low plastic strain amplitude cyclic deformation of nickel single crystals. Rate-dependent viscoplasticity and Armstrong-Frederick type kinematic hardening rules are applied to substructures on slip systems in the model to describe the kinematic hardening behavior of crystals. Three explicit substructure components are assumed in the composite single crystal model, namely "loop patches" and "channels" which are aligned in parallel in a "vein matrix," and persistent slip bands (PSBs) connected in series with the vein matrix. A magnetic domain rotation model is presented to describe the reverse magnetostriction of single crystal nickel. Kinematic hardening parameters are obtained by fitting responses to experimental data in the uniaxial model, and the validity of uniaxial assumption is verified in the 3-D FEM model with explicit substructures. With information gathered from experiments, all control parameters in the model including hardening parameters, volume fraction of loop patches and PSBs, and variation of Young's modulus etc. are correlated to cumulative plastic strain and/or plastic strain amplitude; and the whole cyclic deformation history of single crystal nickel at low plastic strain amplitudes is simulated in the uniaxial model. Then these parameters are implanted in the 3-D FEM model to simulate the formation of PSB bands. A resolved shear stress criterion is set to trigger the formation of PSBs, and stress perturbation in the specimen is obtained by several elements assigned with PSB material properties a priori. Displacement increment, plastic strain amplitude control and overall stress-strain monitor and output are carried out in the user

Crack formation mechanisms during micro and macro indentation of diamond-like carbon coatings on elastic-plastic substrates

DEFF Research Database (Denmark)

Thomsen, N.B.; Fischer-Cripps, A.C.; Swain, M.V.

1998-01-01

of cracking and the fracture mechanisms taking place. In the study various diamond-like carbon (DLC) coatings deposited onto stainless steel and tool steel were investigated. Results primarily for one DLC system will be presented here. (C) 1998 Published by Elsevier Science S.A. All rights reserved.......In the present study crack formation is investigated on both micro and macro scale using spherical indenter tips. in particular, systems consisting of elastic coatings that are well adhered to elastic-plastic substrates are studied. Depth sensing indentation is used on the micro scale and Rockwell...... indentation on the macro scale. The predominant driving force for coating failure and crack formation during indentation is plastic deformation of the underlying substrate. The aim is to relate the mechanisms creating both delamination and cohesive cracking on both scales with fracture mechanical models...

Structure, interface abruptness and strain relaxation in self-assisted grown InAs/GaAs nanowires

Energy Technology Data Exchange (ETDEWEB)

Frigeri, Cesare, E-mail: frigeri@imem.cnr.it [CNR-IMEM Institute, Parma (Italy); Scarpellini, David [L–NESS and Dept. Materials Science, University of Milano Bicocca, Milano (Italy); Department of Industrial Engineering University of Rome Tor Vergata, Rome (Italy); Fedorov, Alexey [LNESS and CNR-IFN, Como (Italy); Bietti, Sergio; Somaschini, Claudio [L–NESS and Dept. Materials Science, University of Milano Bicocca, Milano (Italy); Grillo, Vincenzo [CNR-IMEM Institute, Parma (Italy); CNR-S3-NANO Center, Modena (Italy); Esposito, Luca; Salvalaglio, Marco; Marzegalli, Anna; Montalenti, Francesco [L–NESS and Dept. Materials Science, University of Milano Bicocca, Milano (Italy); Sanguinetti, Stefano [L–NESS and Dept. Materials Science, University of Milano Bicocca, Milano (Italy); LNESS and CNR-IFN, Como (Italy)

2017-02-15

Highlights: • We study 2 critical issues (interface abruptness and strain release) in InAs/GaAs NWs. • Structural and chemical interface sharpness ≤1.5 nm, better than in previous reports. • Simultaneous elastic and plastic relaxation is shown that agrees with FEM simulations. • Structural, chemical and strain release investigations were performed by STEM. • New MBE self-seeded method whereby InAs is grown by splitting In and As depositions. - Abstract: The structure, interface abruptness and strain relaxation in InAs/GaAs nanowires grown by molecular beam epitaxy in the Ga self-catalysed mode on (111) Si have been investigated by transmission electron microscopy. The nanowires had the zincblende phase. The InAs/GaAs interface was atomically and chemically sharp with a width around 1.5 nm, i.e. significantly smaller than previously reported values. This was achieved by the consumption of the Ga droplet and formation of a flat top facet of the GaAs followed by the growth of InAs by splitting the depositions of In and As. Both elastic and plastic strain relaxation took place simultaneously. Experimental TEM results about strain relaxation very well agree with linear elasticity theory calculations by the finite element methods.

Structure, interface abruptness and strain relaxation in self-assisted grown InAs/GaAs nanowires

International Nuclear Information System (INIS)

Frigeri, Cesare; Scarpellini, David; Fedorov, Alexey; Bietti, Sergio; Somaschini, Claudio; Grillo, Vincenzo; Esposito, Luca; Salvalaglio, Marco; Marzegalli, Anna; Montalenti, Francesco; Sanguinetti, Stefano

2017-01-01

Highlights: • We study 2 critical issues (interface abruptness and strain release) in InAs/GaAs NWs. • Structural and chemical interface sharpness ≤1.5 nm, better than in previous reports. • Simultaneous elastic and plastic relaxation is shown that agrees with FEM simulations. • Structural, chemical and strain release investigations were performed by STEM. • New MBE self-seeded method whereby InAs is grown by splitting In and As depositions. - Abstract: The structure, interface abruptness and strain relaxation in InAs/GaAs nanowires grown by molecular beam epitaxy in the Ga self-catalysed mode on (111) Si have been investigated by transmission electron microscopy. The nanowires had the zincblende phase. The InAs/GaAs interface was atomically and chemically sharp with a width around 1.5 nm, i.e. significantly smaller than previously reported values. This was achieved by the consumption of the Ga droplet and formation of a flat top facet of the GaAs followed by the growth of InAs by splitting the depositions of In and As. Both elastic and plastic strain relaxation took place simultaneously. Experimental TEM results about strain relaxation very well agree with linear elasticity theory calculations by the finite element methods.

Plastic and Elastic Responses of a Jacket Platform Subjected to Ship Impacts

Directory of Open Access Journals (Sweden)

Liang Li

2013-01-01

Full Text Available This paper deals with ship-jacket platform collisions. An examination on NORSOK N-004 rule is carried out. Furthermore, elastic and plastic response of jacket platform is studied. This paper also conducts a sensitivity analysis, focusing on collision points. Simulation models of a ductile and a rigid supply vessel were developed, as well as models of two typical jacket platforms. Data such as collision force, kinetic energy, and deformation energy have been obtained. Several conclusions have been drawn: NORSOK rule underestimates the resistance for certain indention, due to inaccurate description of column deformation mode. Elastic response is extremely important in dynamic analysis of ship-platform impacts, by contributing to reducing impact loads and local energy dissipation. Struck members are therefore subjected to impacts to a low extent, which can be regarded as result of a buffering effect. Before a buffering effect works, a time delay exists. This is caused because the topside has to take up adequate kinetic energy. Striking position has an effect on dynamic behavior of platform. High local strength is in favor of buffering an effect. Elastic response is more significant in a flexible platform than in a sticky one.

The creep low application for numerical modeling of elastic-plastic flows

Science.gov (United States)

Tyapin, Anatoly; Rudenko, Vladimir; Chekhunov, Evgeny; Shaburov, Michail

1999-06-01

The present paper demonstrates the applicability of Lomnitz logarithm creep law [1] in some approximated version for calculating the elastic-plastic flows. The model has been developed resulting from the intention to have appropriate calculation approximation for particle-velocity -vs-time histories observed in plate 6061-T6 Al samples of various thickness under shock loading and subsequent release and additional compression. The approximation is unique in the whole loading range, from very low to such that elastic precursor is swallowed up by plastic wave . The model is based on Lipkin and Asay [2] remark on scale similarity of the above mentioned particle velocity -vs-time histories for equal shock loading and on approximate equality of velocities that initial portions of release and recompression waves travel at. A Lomnitz creep law presents an ideal phenomenological tool providing both of the requirements be fulfilled at the same time. Its application to high rate processes of loading and release has required some law modification and a nontrivial review of the dislocation mechanism for stress relaxation. The agreement achieved with the experiment is illustrated in figures. The model is worked out and realized in the 1D user software MAG. 1. Lomnitz C. Joun. of Geology, 1956, vol. 64, p. 473-479. 2. Lipkin J., Asay J.R. J. Appl. Phys. ,1977, vol. 48, 1, p.182-189. 3. Johnson J., Barker L. J. Appl. Phys., 1969, vol. 40, 11, p. 4321-4334. 4. Asay J.R., Chhabildas L. M.: Metallurgia., 1984, p. 110-120.

Anisotropic chemical strain in cubic ceria due to oxygen-vacancy-induced elastic dipoles.

Science.gov (United States)

Das, Tridip; Nicholas, Jason D; Sheldon, Brian W; Qi, Yue

2018-06-06

Accurate characterization of chemical strain is required to study a broad range of chemical-mechanical coupling phenomena. One of the most studied mechano-chemically active oxides, nonstoichiometric ceria (CeO2-δ), has only been described by a scalar chemical strain assuming isotropic deformation. However, combined density functional theory (DFT) calculations and elastic dipole tensor theory reveal that both the short-range bond distortions surrounding an oxygen-vacancy and the long-range chemical strain are anisotropic in cubic CeO2-δ. The origin of this anisotropy is the charge disproportionation between the four cerium atoms around each oxygen-vacancy (two become Ce3+ and two become Ce4+) when a neutral oxygen-vacancy is formed. Around the oxygen-vacancy, six of the Ce3+-O bonds elongate, one of the Ce3+-O bond shorten, and all seven of the Ce4+-O bonds shorten. Further, the average and maximum chemical strain values obtained through tensor analysis successfully bound the various experimental data. Lastly, the anisotropic, oxygen-vacancy-elastic-dipole induced chemical strain is polarizable, which provides a physical model for the giant electrostriction recently discovered in doped and non-doped CeO2-δ. Together, this work highlights the need to consider anisotropic tensors when calculating the chemical strain induced by dilute point defects in all materials, regardless of their symmetry.

Analysis of stress and strain in a rotating disk mounted on a rigid shaft

Directory of Open Access Journals (Sweden)

Alexandrova Nelli N.

2006-01-01

Full Text Available The plane state of stress in an elastic-perfectly plastic isotropic rotating annular disk mounted on a rigid shaft is studied. The analysis of stresses, strains and displacements within the disk of constant thickness and density is based on the Mises yield criterion and its associated flow rule. It is observed that the plastic deformation is localized in the vicinity of the inner radius of the disk, and the disk of a sufficiently large outer radius never becomes fully plastic. The semi-analytical method of stress-strain analysis developed is illustrated by some numerical examples. .

Hydrogen-plasticity interactions in nickel and nickel base alloys

International Nuclear Information System (INIS)

Girardin, G.

2004-03-01

We evaluate the different contributions of the hydrogen-dislocation interactions to the plasticity of fcc materials in order to feed predictive models of stress corrosion cracking. Static strain ageing experiments are used to quantify the hardening contribution of solute drag by dislocations to the flow stress. We demonstrate the role of hydrogen transport by dislocations on the fracture mechanism. We model the influence of the screening of the elastic field of dislocations by hydrogen on elementary plasticity mechanisms and we conclude that the decrease of the cross slip ability arises from the combined action of elastic and core effects. The testing of single crystals shows that the major effect is on the cross slip mechanism. Tensile tests on polycrystals enlighten the diversity of macroscopic responses observed in alloys. (author)

Local, atomic-level elastic strain measurements of metallic glass thin films by electron diffraction

Energy Technology Data Exchange (ETDEWEB)

Ebner, C. [Physics of Nanostructured Materials, Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna (Austria); Sarkar, R. [Department of Materials Science and Engineering, School for Engineering of Matter Transport and Energy, Arizona State University, Tempe 85287 (United States); Rajagopalan, J. [Department of Materials Science and Engineering, School for Engineering of Matter Transport and Energy, Arizona State University, Tempe 85287 (United States); Department of Mechanical and Aerospace Engineering, School for Engineering of Matter Transport and Energy, Arizona State University, Tempe 85287 (United States); Rentenberger, C., E-mail: christian.rentenberger@univie.ac.at [Physics of Nanostructured Materials, Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna (Austria)

2016-06-15

A novel technique is used to measure the atomic-level elastic strain tensor of amorphous materials by tracking geometric changes of the first diffuse ring of selected area electron diffraction patterns (SAD). An automatic procedure, which includes locating the centre and fitting an ellipse to the diffuse ring with sub-pixel precision is developed for extracting the 2-dimensional strain tensor from the SAD patterns. Using this technique, atomic-level principal strains from micrometre-sized regions of freestanding amorphous Ti{sub 0.45}Al{sub 0.55} thin films were measured during in-situ TEM tensile deformation. The thin films were deformed using MEMS based testing stages that allow simultaneous measurement of the macroscopic stress and strain. The calculated atomic-level principal strains show a linear dependence on the applied stress, and good correspondence with the measured macroscopic strains. The calculated Poisson’s ratio of 0.23 is reasonable for brittle metallic glasses. The technique yields a strain accuracy of about 1×10{sup −4} and shows the potential to obtain localized strain profiles/maps of amorphous thin film samples. - Highlights: • A TEM method to measure elastic strain in metallic glass films is proposed. • Method is based on tracking geometric changes in TEM diffraction patterns. • An automatic procedure is developed for extracting the local strain tensor. • Atomic-level strain in amorphous TiAl film was analysed during in-situ deformation. • Capability of the method to obtain micrometer scale strain profiles/maps is shown.

Synchrotron X-ray microbeam diffraction measurements of full elastic long range internal strain and stress tensors in commercial-purity aluminum processed by multiple passes of equal-channel angular pressing

International Nuclear Information System (INIS)

Phan, Thien Q.; Levine, Lyle E.; Lee, I-Fang; Xu, Ruqing; Tischler, Jonathan Z.; Huang, Yi; Langdon, Terence G.; Kassner, Michael E.

2016-01-01

Synchrotron X-ray microbeam diffraction was used to measure the full elastic long range internal strain and stress tensors of low dislocation density regions within the submicrometer grain/subgrain structure of equal-channel angular pressed (ECAP) aluminum alloy AA1050 after 1, 2, and 8 passes using route B C . This is the first time that full tensors were measured in plastically deformed metals at this length scale. The maximum (most tensile or least compressive) principal elastic strain directions for the unloaded 1 pass sample for the grain/subgrain interiors align well with the pressing direction, and are more random for the 2 and 8 pass samples. The measurements reported here indicate that the local stresses and strains become increasingly isotropic (homogenized) with increasing ECAP passes using route B C . The average maximum (in magnitude) LRISs are −0.43 σ a for 1 pass, −0.44 σ a for 2 pass, and 0.14 σ a for the 8 pass sample. These LRISs are larger than those reported previously because those earlier measurements were unable to measure the full stress tensor. Significantly, the measured stresses are inconsistent with the two-component composite model.

Nonlinear elastic longitudinal strain-wave propagation in a plate with nonequilibrium laser-generated point defects

International Nuclear Information System (INIS)

Mirzade, Fikret Kh.

2005-01-01

The propagation of longitudinal strain wave in a plate with quadratic nonlinearity of elastic continuum was studied in the context of a model that takes into account the joint dynamics of elastic displacements in the medium and the concentration of the nonequilibrium laser-induced point defects. The input equations of the problem are reformulated in terms of only the total displacements of the medium points. In this case, the presence of structural defects manifests itself in the emergence of a delayed response of the system to the propagation of the strain-related perturbations, which is characteristic of media with relaxation or memory. The model equations describing the nonlinear displacement wave were derived with allowance made for the values of the relaxation parameter. The influence of the generation and relaxation of lattice defects on the propagation of this wave was analyzed. It is shown that, for short relaxation times of defects, the strain can propagate in the form of shock fronts. In the case of longer relaxation times, shock waves do not form and the strain wave propagates only in the form of solitary waves or a train of solitons. The contributions of the finiteness of the defect-recombination rate to linear and nonlinear elastic modulus, and spatial dispersion are determined

Hydraulic pressure pulses with elastic and plastic structural flexibility: test and analysis (LWBR Development Program)

International Nuclear Information System (INIS)

Schwirian, R.E.

1978-03-01

Pressure pulse tests were conducted with a flexible test section in a test vessel filled with room temperature water. The pressure pulses were generated with a drop hammer and piston pulse generator and were of a sufficient magnitude to cause plastic deformation of the test section. Because of the strong pressure relief effect of the deforming test section, pressure pulse magnitudes were below 265 psig in magnitude and had durations of 50 to 55 msecs. Calculations performed with the FLASH-35 bi-linear hysteresis model of structural deformation show good agreement with experiment. In particular, FLASH 35 adequately predicts the decrease in peak pressure and the increase in pulse duration due to elastic and plastic deformation of the test section. Predictions of flexible member motion are good, but are less satisfactory than the pressure pulse results due to uncertainties in the values of yield point and beyond yield stiffness used to model the various flexible members. Coupled with this is a strong sensitivity of the FLASH 35 predictions to the values of yield point and beyond yield stiffness chosen for the various flexible members. The test data versus calculation comparisons presented here provide preliminary qualification for FLASH 35 calculations of transient hydraulic pressures and pressure differentials in the presence of flexible structural members which deform both elastically and plastically

Application of elastic and elastic-plastic fracture mechanics methods to surface flaws

Science.gov (United States)

McCabe, Donald E.; Ernst, Hugo A.; Newman, James C., Jr.

Fuel tanks that are a part of the External Tank assembly for the Space Shuttle are made of relatively thin 2219-T87 aluminum plate. These tanks contain about 917 m of fusion weld seam, all of which is nondestructively inspected for flaws and all those found are repaired. The tanks are subsequently proof-tested to a pressure that is sufficiently severe to cause weld metal yielding in a few local regions of the weld seam. The work undertaken in the present project was to develop a capability to predict flaw growth from undetected surface flaws that are assumed to be located in the highly stressed regions. The technical challenge was to develop R-curve prediction capability for surface cracks in specimens that contain the flaws of unusual sizes and shapes deemed to be of interest. The test techniques developed and the elastic-plastic analysis concepts adopted are presented. The flaws of interest were quite small surface cracks that were narrow-deep ellipses that served to exacerbate the technical difficulties involved.

Plastic strain characterization in austenitic stainless steels and nickel alloys by electron backscatter diffraction

Energy Technology Data Exchange (ETDEWEB)

Saez-Maderuelo, A., E-mail: alberto.saez@ciemat.es [CIEMAT, Av. Complutense, 22-28040 Madrid (Spain); Castro, L.; Diego, G. de [CIEMAT, Av. Complutense, 22-28040 Madrid (Spain)

2011-09-01

Stress corrosion cracking (SCC) is enhanced by cold work and causes many problems in components of the nuclear power plants. Besides, during manufacturing, installation, welding and service of the material, residual strains can be produced increasing the susceptibility to SCC. For this reason, it is important to characterize the degree of plastic strain due to dislocation accumulation in each crystal. Electron backscatter diffraction (EBSD), in conjunction with scanning electron microscope (SEM), has been a great advance in this field because it enables to estimate the plastic strain in a quick and easy way. Nevertheless, over the last few years, a lot of different mathematical expressions to estimate the plastic strain have appeared in the literature. This situation hinders the election of one of them by a novel scientist in this field. Therefore, in this paper some of the more common expressions used in the calculation of the angular misorientation have been presented and discussed in order to clarify their more important aspects. Then, using one of these expressions (average local misorientation), curves relating misorientation density with known levels of strain will be obtained for an austenitic stainless steel 304L and nickel base alloy 690, which have shown a linear behaviour that is in good agreement with results found in the literature. Finally, using curves obtained in previous steps, levels of plastic strain in a plate of nickel base alloy 600 welded with weld metal 182 were estimated between 8 and 10% for a high temperature mill annealing sample.

Plastic strain characterization in austenitic stainless steels and nickel alloys by electron backscatter diffraction

International Nuclear Information System (INIS)

Saez-Maderuelo, A.; Castro, L.; Diego, G. de

2011-01-01

Stress corrosion cracking (SCC) is enhanced by cold work and causes many problems in components of the nuclear power plants. Besides, during manufacturing, installation, welding and service of the material, residual strains can be produced increasing the susceptibility to SCC. For this reason, it is important to characterize the degree of plastic strain due to dislocation accumulation in each crystal. Electron backscatter diffraction (EBSD), in conjunction with scanning electron microscope (SEM), has been a great advance in this field because it enables to estimate the plastic strain in a quick and easy way. Nevertheless, over the last few years, a lot of different mathematical expressions to estimate the plastic strain have appeared in the literature. This situation hinders the election of one of them by a novel scientist in this field. Therefore, in this paper some of the more common expressions used in the calculation of the angular misorientation have been presented and discussed in order to clarify their more important aspects. Then, using one of these expressions (average local misorientation), curves relating misorientation density with known levels of strain will be obtained for an austenitic stainless steel 304L and nickel base alloy 690, which have shown a linear behaviour that is in good agreement with results found in the literature. Finally, using curves obtained in previous steps, levels of plastic strain in a plate of nickel base alloy 600 welded with weld metal 182 were estimated between 8 and 10% for a high temperature mill annealing sample.

Numerical simulation of elasto-plastic deformation of composites: evolution of stress microfields and implications for homogenization models

Science.gov (United States)

González, C.; Segurado, J.; LLorca, J.

2004-07-01

The deformation of a composite made up of a random and homogeneous dispersion of elastic spheres in an elasto-plastic matrix was simulated by the finite element analysis of three-dimensional multiparticle cubic cells with periodic boundary conditions. "Exact" results (to a few percent) in tension and shear were determined by averaging 12 stress-strain curves obtained from cells containing 30 spheres, and they were compared with the predictions of secant homogenization models. In addition, the numerical simulations supplied detailed information of the stress microfields, which was used to ascertain the accuracy and the limitations of the homogenization models to include the nonlinear deformation of the matrix. It was found that secant approximations based on the volume-averaged second-order moment of the matrix stress tensor, combined with a highly accurate linear homogenization model, provided excellent predictions of the composite response when the matrix strain hardening rate was high. This was not the case, however, in composites which exhibited marked plastic strain localization in the matrix. The analysis of the evolution of the matrix stresses revealed that better predictions of the composite behavior can be obtained with new homogenization models which capture the essential differences in the stress carried by the elastic and plastic regions in the matrix at the onset of plastic deformation.

The Effect of Tensile Hysteresis and Contact Resistance on the Performance of Strain-Resistant Elastic-Conductive Webbing

Directory of Open Access Journals (Sweden)

Tien-Wei Shyr

2011-01-01

Full Text Available To use e-textiles as a strain-resistance sensor they need to be both elastic and conductive. Three kinds of elastic-conductive webbings, including flat, tubular, and belt webbings, made of Lycra fiber and carbon coated polyamide fiber, were used in this study. The strain-resistance properties of the webbings were evaluated in stretch-recovery tests and measured within 30% strain. It was found that tensile hysteresis and contact resistance significantly influence the tensile elasticity and the resistance sensitivity of the webbings. The results showed that the webbing structure definitely contributes to the tensile hysteresis and contact resistance. The smaller the friction is among the yarns in the belt webbing, the smaller the tensile hysteresis loss. However the close proximity of the conductive yarns in flat and tubular webbings results in a lower contact resistance.

Study on elastic-plastic behaviour of inclusions in cold drawn wire by using reverse analysis and nanoindentation test

Directory of Open Access Journals (Sweden)

Lee Kyung-Hun

2015-01-01

Full Text Available The purpose of this study is to investigate the elastic-plastic behavior of inclusions, i.e. SiO2 particles, in cold drawn wire using reverse analysis and nanoindentation test. First, the nanoindentation tests were performed to obtain indentation load P – penetration depth h curves. Second, the reverse analysis which is consisted of various dimensionless functions including change in E∗/σr, Wp/Wt and n was used to extract the elastic-plastic properties of the indented inclusions and metals from indentation responses. To verify the accuracy of calculated properties, uniaxial tensile tests were performed for different materials which are AISI 1045 and AISI 1080. Results (E, σy, n of tensile tests for each material were also compared with those of nanoindentation tests.

Interpretation of experiments and modeling of internal strains in Beryllium using a polycrystal model

International Nuclear Information System (INIS)

Tome, C.; Bourke, M.A.M.; Daymond, M.R.

2000-01-01

The elastic and plastic anisotropy of Be have been examined during a uniaxial compression test, by in-situ monitoring in a pulsed neutron beam. Comparisons between the measured hkil strains and the predictions from an elasto-plastic self-consistent (EPSC) model are made. Agreement is qualitatively correct for most planes in the elasto-plastic regime. Possible mechanisms responsible for the quantitative discrepancies between model and experiment are discussed

Cyclic plastic hinges with degradation effects for frame structures

DEFF Research Database (Denmark)

Tidemann, Lasse; Krenk, Steen

2017-01-01

A model of cyclic plastic hinges in frame structures including degradation effects for stiffness and strength is developed. The model is formulated via potentials in terms of section forces. It consists of a yield surface, described in a generic format permitting representation of general convex...... shapes including corners, and a set of evolution equations based on an internal energy potential and a plastic flow potential. The form of these potentials is specified by five parameters for each generalized stress-strain component describing yield level, ultimate stress capacity, elastic...... and stiffness parameters. The cyclic plastic hinges are introduced into a six-component equilibrium-based beam element, using additive element and hinge flexibilities. When converted to stiffness format the plastic hinges are incorporated into the element stiffness matrix. The cyclic plastic hinge model...

Finite element implementation and numerical issues of strain gradient plasticity with application to metal matrix composites

DEFF Research Database (Denmark)

Frederiksson, Per; Gudmundson, Peter; Mikkelsen, Lars Pilgaard

2009-01-01

A framework of finite element equations for strain gradient plasticity is presented. The theoretical framework requires plastic strain degrees of freedom in addition to displacements and a plane strain version is implemented into a commercial finite element code. A couple of different elements...... of quadrilateral type are examined and a few numerical issues are addressed related to these elements as well as to strain gradient plasticity theories in general. Numerical results are presented for an idealized cell model of a metal matrix composite under shear loading. It is shown that strengthening due...... to fiber size is captured but strengthening due to fiber shape is not. A few modelling aspects of this problem are discussed as well. An analytic solution is also presented which illustrates similarities to other theories....

Elastic and plastic strains and the stress corrosion cracking of austenitic stainless steels. Progress report, April 30, 1975--December 30, 1975

International Nuclear Information System (INIS)

Troiano, A.R.

1975-12-01

Homogeneous deformation of type 310 austenitic stainless steel only slightly influenced the corrosion potential in a boiling 3 percent NaCl aqueous environment. The difference in a deaerated solution was of the order of 25 mV and somewhat more for an aerated solution. Elastic strains appeared to have little or no influence on the corrosion potential for fully annealed as well as 10 percent and 25 percent homogeneously deformed 310 steel. Oxygen in the environment shifted the corrosion potential several hundred millivolts in the less active direction. The critical cracking potential in a deaerated 3 percent NaCl solution was approximately the same for the annealed and homogeneously deformed specimens at approximately -125 mV SCE

Theory of a new elastic-plastic-viscous model and its application to the nuclear fuel mechanical analysis

International Nuclear Information System (INIS)

Moreno, A.

1977-01-01

A new elastic-plastic-viscous model is described. The model is one of the multiple integral type, and has been included in a numerical code to predict the behaviour of a nuclear fuel of cylindrical form. Some features of this code are also described. (author)

Determination of post-shakedown quantities of a pipe bend via the simplified theory of plastic zones compared with load history dependent incremental analysis

Science.gov (United States)

Vollrath, Bastian; Hübel, Hartwig

2018-01-01

The Simplified Theory of Plastic Zones (STPZ) may be used to determine post-shakedown quantities such as strain ranges and accumulated strains at plastic or elastic shakedown. The principles of the method are summarized. Its practical applicability is shown by the example of a pipe bend subjected to constant internal pressure along with cyclic in-plane bending or/and cyclic radial temperature gradient. The results are compared with incremental analyses performed step-by-step throughout the entire load history until the state of plastic shakedown is achieved.

The role of plastic slip anisotropy in the modelling of strain path change effects

NARCIS (Netherlands)

Viatkina, E.M.; Brekelmans, W.A.M.; Geers, M.G.D.

2009-01-01

Most industrial metal forming processes are characterised by a complex strain path history. A change in strain path may have a significant effect on the mechanical response of metals. This paper concentrates on the role of the plastic slip anisotropy in the strain path dependency of materials

Time between plastic displacements of elasto-plastic oscillators subject to Gaussian white noise

DEFF Research Database (Denmark)

Tarp-Johansen, Niels Jacob; Ditlevsen, Ove Dalager

2001-01-01

A one degree of freedom elasto-plastic oscillator subject to stationary Gaussian white noise has a plastic displacement response process of intermittent character. During shorter or longer time intervals the oscillator vibrates within the elastic domain without undergoing any plastic displacements...... between the clumps of plastic displacements. This is needed for a complete description of the plastic displacement process. A quite accurate fast simulation procedure is presented based on an amplitude model to determine the short waiting times in the transient regime of the elastic vibrations existing...

A general shakedown theorem for elastic/plastic bodies with work hardening

International Nuclear Information System (INIS)

Ponter, A.R.S.

1975-01-01

In recent years the design of metallic structures under variable loading has been assisted by the application of Melan's lower bound theorem for the shakedown of an elastic/perfectly plastic structure. The design codes for both portal frames and pressure vessels have taken account of such calculations. The theory of shakedown suffers from two defects, geometry changes are ignored and the material behavior is described by a perfectly plastic constitutive relationship which includes neither work hardening nor the Bauschinger effect. This paper is concerned with the latter problem. A very general lower bound shakedown theorem for an arbitrary time-independent material in terms of functional properties of the constitutive relationship is derived. The theorem is then applied to perfect, isotropic and kinematic hardening plasticity. It is shown that the result for all three constitutive relationships may be related to each other through certain extremal stress histories. As well as providing a sufficient condition for shakedown, the theory also provides bounds of the deflection of the structure in the process of reaching the shakedown state. The bounds are discussed and derived for two simple beam problems. Both static and dynamic problems are considered. The theory derived in this paper demonstrates that shakedown analysis may be extended to a wide range of material behavior without increasing the complexity of the resulting calculation

Elasto/visco-plastic dynamic response of multi-layered shells of revolution

International Nuclear Information System (INIS)

Takezono, S.; Tao, K.; Taguchi, T.

1989-01-01

Many investigations of the elasto/visco-plastic dynamic response of shells have been conducted. These investigations, however, have been mostly concerned with the case of single-layered shells, and few studies on multi-layered shells have been reported in spite of their importance in engineering. In this paper, the authors study the elasto/visco-plastic dynamic response of the multi-layered shells of revolution subjected to impulsive loads. The equations of motion and the relations between the strains and displacements are derived by extending Sanders' theory for elastic thin shells. As the constitutive relation, Hooke's law is used in the linear elastic range, and the elasto/visco-plastic equations are employed in the plastic range. The criterion for yielding used in the analysis is the von Mises yield theory. In the numerical analysis of the fundamental equations for incremental values an usual finite difference form is employed for the spatial derivatives and the inertia terms are treated with the backward difference formula. The solutions are obtained by summation of the incremental values

Relationship between strain and central deflection in small punch creep specimens

International Nuclear Information System (INIS)

Yang Zhen; Wang Zhiwen

2003-01-01

Acquiring information about creep strain directly from small punch creep tests is difficult because the deformation behaviour of the small punch specimen is complicated. A routine is suggested in the present paper to treat this problem indirectly. Based on a finite element analysis, it is proposed that the relationship of central deflection δ to central creep strain ε c of a specimen subjected to creep can be represented approximately by the relationship of central deflection δ to central (elastic-plastic) strain ε of a specimen not subjected to creep. With this hypothesis, the δ∼ε c relation of the small punch creep specimen is obtained by resorting to a rigid-plastic membrane stretch forming model. Finally, small punch creep test results are used to evaluate creep strain and creep strain rate by taking advantage of this δ∼ε c relation

The strain path dependence of plastic deformation response of AA5754: Experiment and modeling

International Nuclear Information System (INIS)

Pham, Minh-Son; Hu, Lin; Iadicola, Mark; Creuziger, Adam; Rollett, Anthony D.

2013-01-01

This work presents modeling of experiments on a balanced biaxial (BB) pre-strained AA5754 alloy, subsequently reloaded uniaxially along the rolling direction and transverse direction. The material exhibits a complex plastic deformation response during the change in strain path due to 1) crystallographic texture, 2) aging (interactions between dislocations and Mg atoms) and 3) recovery (annihilation and re-arrangement of dislocations). With a BB prestrain of about 5 %, the aging process is dominant, and the yield strength for uniaxially deformed samples is observed to be higher than the flow stress during BB straining. The strain hardening rate after changing path is, however, lower than that for pre-straining. Higher degrees of pre-straining make the dynamic recovery more active. The dynamic recovery at higher strain levels compensates for the aging effect, and results in: 1) a reduction of the yield strength, and 2) an increase in the hardening rate of re-strained specimens along other directions. The yield strength of deformed samples is further reduced if these samples are left at room temperature to let static recovery occur. The synergistic influences of texture condition, aging and recovery processes on the material response make the modeling of strain path dependence of mechanical behavior of AA5754 challenging. In this study, the influence of crystallographic texture is taken into account by incorporating the latent hardening into a visco-plastic self-consistent model. Different strengths of dislocation glide interaction models in 24 slip systems are used to represent the latent hardening. Moreover, the aging and recovery effects are also included into the latent hardening model by considering strong interactions between dislocations and dissolved atom Mg and the microstructural evolution. These microstructural considerations provide a powerful capability to successfully describe the strain path dependence of plastic deformation behavior of AA5754

J-integral elastic plastic fracture mechanics evaluation of the stability of cracks in nuclear reactor pressure vessels

International Nuclear Information System (INIS)

Gomez, M.P.; McMeeking, R.M.; Parks, D.M.

1980-06-01

Contributions were made toward developing a new methodology to assess the stability of cracks in pressure vessels made from materials that exhibit a significant increase in toughness during the early increments of crack growth. It has a wide range of validity from linear elastic to fully plastic behavior

Strain gradient crystal plasticity analysis of a single crystal containing a cylindrical void

DEFF Research Database (Denmark)

Borg, Ulrik; Kysar, J.W.

2007-01-01

to one another. Finite element simulations are performed using a strain gradient crystal plasticity formulation with an intrinsic length scale parameter in a non-local strain gradient constitutive framework. For a vanishing length scale parameter the non-local formulation reduces to a local crystal...... plasticity formulation. The stress and deformation fields obtained with a local non-hardening constitutive formulation are compared to those obtained from a local hardening formulation and to those from a non-local formulation. Compared to the case of the non-hardening local constitutive formulation......, it is shown that a local theory with hardening has only minor effects on the deformation field around the void, whereas a significant difference is obtained with the non-local constitutive relation. Finally, it is shown that the applied stress state required to activate plastic deformation at the void is up...

Studies of elastic-plastic instabilities

DEFF Research Database (Denmark)

Tvergaard, Viggo

1999-01-01

Analyses of plastic instabilities are reviewed, with focus on results in structural mechanics as well as continuum mechanics. First the basic theories for bifurcation and post-bifurcation behavior are briefly presented. Then, localization of plastic flow is discussed, including shear band formati...

Non-Contact Acousto-Thermal Signatures of Plastic Deformation in TI-6AL-4V

Science.gov (United States)

Welter, J. T.; Malott, G.; Schehl, N.; Sathish, S.; Jata, K. V.; Blodgett, M. P.

2010-02-01

Plastic deformation introduces changes in a material which include increases in: dislocations, strains, residual stress, and yield stress. However, these changes have a very small impact on the material properties such as elastic modulus, conductivity and ultrasonic wave speed. This is due to the fact that interatomic forces govern these properties, and they are not affected by plastic deformation to any large degree. This is evident from the fact that the changes in electrical resistance and ultrasonic velocity in plastically deformed and virgin samples are very small and can only be determined by highly controlled experiments. Except for X-ray diffraction, there are no direct nondestructive methods for measuring strain and the residual stress. This paper presents an application of the non-contact acousto-thermal signature (NCATS) NDE methodology to detect plastic deformation in flat dog bone Ti-6Al-4V samples. Results of the NCATS measurements on samples subjected to incremental amounts of plastic deformation are presented. The maximum temperature attained by the sample due to acoustic excitation is found to be sensitive to the amount of plastic strain. It is observed that the temperature induced by acoustic excitation increases to a peak followed by a decrease to failure. The maximum temperature peak occurs at plastic strains of 12-14%. It is observed that there is a correlation between the peak in maximum temperature rise and the strain at the experimentally determined ultimate tensile strength. A microstructural based explanation for this will be presented. The results are discussed in reference to utilizing this technique for detection and evaluation of plastic deformation.

Strain gradient plasticity modeling of hydrogen diffusion to the crack tip

DEFF Research Database (Denmark)

Martínez Pañeda, Emilio; del Busto, S.; Niordson, Christian Frithiof

2016-01-01

to characterize the gradient-enhanced stress elevation and subsequent diffusion of hydrogen towards the crack tip. Results reveal that GNDs, absent in conventional plasticity predictions, play a fundamental role on hydrogen transport ahead of a crack. SGP estimations provide a good agreement with experimental......In this work hydrogen diffusion towards the fracture process zone is examined accounting for local hardening due to geometrically necessary dislocations (GNDs) by means of strain gradient plasticity (SGP). Finite element computations are performed within the finite deformation theory...

Fatigue assessment by the RCC-MR design rules: remarks on the elastic analysis

International Nuclear Information System (INIS)

Taleb, L.; Sidoroff, F.

1999-01-01

According to RCC--MR (French rules for mechanical engineering design of FBR), fatigue life assessment is based on the evaluation of the equivalent elastoplastic strain range resulting from a given cyclic loading. Two methods can be used according to whether an elastoplastic or an elastic structure analysis is performed. The elastic analysis is of course more attractive for it avoids a heavy iterative elastoplastic analysis and an expensive identification of the material behavior from mechanical tests. On the other hand it relies on some empirical extrapolation rules from the elastic to the real case. The purpose of the present paper is to draw attention to some limitations of this procedure. In particular attention will be focused on two points: 1, the classification of the applied stress into primary and secondary parts is essential and it is shown that the thermal stresses which are often considered as secondary may in some cases play a primary role; 2. the Neuber's rule which is used to evaluate the plastic strain from the elastic stress will be shown to be significantly wrong for some special configurations. This is in fact essentially related to situations where the elastic follow up effect is important. (authors)

Notch root strain measurement of WE43-T6 magnesium alloy using electronic speckle pattern interferometry

International Nuclear Information System (INIS)

Liew, H.L.; Ahmad, A.; Ramesh, S.; Purbolaksono, J.

2013-01-01

Highlights: • The use of ESPI for measuring total strains at the notch root of specimens. • Fine meshing in micron scale at the notch root regions. • The maximum elastic strain is shifted to be further away from the notch root tip. - Abstract: The notch root elasto-plastic strains of circumferentially grooved round specimen of cast magnesium WE43-T6 were experimentally measured using the electronic speckle pattern interferometry (ESPI) and numerically evaluated using the finite element analysis (FEA). The specimens have notch radii of 1.6 mm and 0.8 mm and an opening angle of 60°. The technique of ESPI showed its accuracy in measuring three-dimensional surface deformations on large negatively curved manifolds. The measured nominal stress for rupture is well beyond the ultimate strength, suggesting the existence of significant biaxial stress at the notch root region. The ESPI-based strains on the notch tips were shown to be in agreement with those evaluated by the FEA. The FEA also showed that the maximum elastic strain is shifted away from the notch root surface as the plastic strain is predominant

Fatigue analysis - computation of the actual strain range using elastic calculations (factor Ke)

International Nuclear Information System (INIS)

Roche, R.L.

1987-01-01

Pressure vessels are not eternal, their life is not endless, but must be long enough for profitable use. Fatigue is the most important damage limiting life time. It is due to variable loading and especially to deformation-controlled loading like thermal dilatation (thermal stress). Hence, it is of prime importance to perform an fatigue analysis in the design phase in order to be sure the pressure vessel life meet requirement of the design specification. It is also useful to perform such an analysis for assessing the remaining life. To compute the fatigue damage, knowledge of the strain range is needed. As calculation taking into account non linear behavior of the material are very expensive and not always reliable, the current practice is using elastic computation. The aim of this paper is to discuss the methods for correcting the elastically calculated strain range and to propose a sound and practical method

Modeling plasticity by non-continuous deformation

Science.gov (United States)

Ben-Shmuel, Yaron; Altus, Eli

2017-10-01

Plasticity and failure theories are still subjects of intense research. Engineering constitutive models on the macroscale which are based on micro characteristics are very much in need. This study is motivated by the observation that continuum assumptions in plasticity in which neighbour material elements are inseparable at all-time are physically impossible, since local detachments, slips and neighbour switching must operate, i.e. non-continuous deformation. Material microstructure is modelled herein by a set of point elements (particles) interacting with their neighbours. Each particle can detach from and/or attach with its neighbours during deformation. Simulations on two- dimensional configurations subjected to uniaxial compression cycle are conducted. Stochastic heterogeneity is controlled by a single "disorder" parameter. It was found that (a) macro response resembles typical elasto-plastic behaviour; (b) plastic energy is proportional to the number of detachments; (c) residual plastic strain is proportional to the number of attachments, and (d) volume is preserved, which is consistent with macro plastic deformation. Rigid body displacements of local groups of elements are also observed. Higher disorder decreases the macro elastic moduli and increases plastic energy. Evolution of anisotropic effects is obtained with no additional parameters.

Theory of a new elastic-plastic-viscous model and its application to the nuclear fuel mechanical analysis

International Nuclear Information System (INIS)

Moreno, A.

1977-01-01

In this work a new elastic-plastic-viscous model is described. The model is one of the multiple integral type, and has been included in a numerical code to predict the behaviour of a nuclear fuel of cylindrical form. Some features of this code are also described. (Author) 91 refs

Compatible-strain mixed finite element methods for incompressible nonlinear elasticity

Science.gov (United States)

Faghih Shojaei, Mostafa; Yavari, Arash

2018-05-01

We introduce a new family of mixed finite elements for incompressible nonlinear elasticity - compatible-strain mixed finite element methods (CSFEMs). Based on a Hu-Washizu-type functional, we write a four-field mixed formulation with the displacement, the displacement gradient, the first Piola-Kirchhoff stress, and a pressure-like field as the four independent unknowns. Using the Hilbert complexes of nonlinear elasticity, which describe the kinematics and the kinetics of motion, we identify the solution spaces of the independent unknown fields. In particular, we define the displacement in H1, the displacement gradient in H (curl), the stress in H (div), and the pressure field in L2. The test spaces of the mixed formulations are chosen to be the same as the corresponding solution spaces. Next, in a conforming setting, we approximate the solution and the test spaces with some piecewise polynomial subspaces of them. Among these approximation spaces are the tensorial analogues of the Nédélec and Raviart-Thomas finite element spaces of vector fields. This approach results in compatible-strain mixed finite element methods that satisfy both the Hadamard compatibility condition and the continuity of traction at the discrete level independently of the refinement level of the mesh. By considering several numerical examples, we demonstrate that CSFEMs have a good performance for bending problems and for bodies with complex geometries. CSFEMs are capable of capturing very large strains and accurately approximating stress and pressure fields. Using CSFEMs, we do not observe any numerical artifacts, e.g., checkerboarding of pressure, hourglass instability, or locking in our numerical examples. Moreover, CSFEMs provide an efficient framework for modeling heterogeneous solids.

Effect of strain path change on limits to ductility of anisotropic metal sheets

DEFF Research Database (Denmark)

Kuroda, M.; Tvergaard, Viggo

2000-01-01

of the anisotropic plasticity models, and it is shown that elastic straining plays a large role, as the stresses quickly move from one point of the yield surface to another. When the load is removed between steps, the stress point moves in a different manner, which results in quite different flow localization......Localized necking in thin metal sheets is analyzed by using the M-K-model approach, and the effect of a number of different non-proportional strain paths prior to the occurrence flow localization are considered. The analyses account for plastic anisotropy, using four different anisotropic...

The role of strain localization in the fracture of irradiated pressure tube material

International Nuclear Information System (INIS)

Dutton, R.

1989-04-01

This report reviews those phenomena that lead to strain localization in zirconium alloys, with particular reference to the role played by the formation of shear bands in fracture processes. The important influence of plastic deformation, in general, on fracture mechanisms is emphasized. This is to be expected when elastic-plastic fracture mechanics is the chosen analytical technique. Intensely inhomogeneous characteristics of strain localization cause an abrupt bifurcation in the evolution of deformation strain and lead to plastic instability linked with intrinsic material behaviour (e.g., work softening) or of geometric origin (e.g., localized necking). Both of these effects are discussed in relation to measurable deformation parameters, such as the work hardening rate and strain rate sensitivity, which determine the degree of resistance to plastic instability. The modifying effect of irradiation on these quantities is given specific attention, the appropriate literature pertaining to Zircaloy and Zr-2.5% Nb being reviewed. Recommendations are made for a combined experimental and theoretical program to characterize strain localization and reduced ductility in irradiated cold-worked Zr-2.5% Nb pressure tube material. The relationship between the deformation properties and the fracture behaviour is discussed

A finite difference method for off-fault plasticity throughout the earthquake cycle

Science.gov (United States)

Erickson, Brittany A.; Dunham, Eric M.; Khosravifar, Arash

2017-12-01

We have developed an efficient computational framework for simulating multiple earthquake cycles with off-fault plasticity. The method is developed for the classical antiplane problem of a vertical strike-slip fault governed by rate-and-state friction, with inertial effects captured through the radiation-damping approximation. Both rate-independent plasticity and viscoplasticity are considered, where stresses are constrained by a Drucker-Prager yield condition. The off-fault volume is discretized using finite differences and tectonic loading is imposed by displacing the remote side boundaries at a constant rate. Time-stepping combines an adaptive Runge-Kutta method with an incremental solution process which makes use of an elastoplastic tangent stiffness tensor and the return-mapping algorithm. Solutions are verified by convergence tests and comparison to a finite element solution. We quantify how viscosity, isotropic hardening, and cohesion affect the magnitude and off-fault extent of plastic strain that develops over many ruptures. If hardening is included, plastic strain saturates after the first event and the response during subsequent ruptures is effectively elastic. For viscoplasticity without hardening, however, successive ruptures continue to generate additional plastic strain. In all cases, coseismic slip in the shallow sub-surface is diminished compared to slip accumulated at depth during interseismic loading. The evolution of this slip deficit with each subsequent event, however, is dictated by the plasticity model. Integration of the off-fault plastic strain from the viscoplastic model reveals that a significant amount of tectonic offset is accommodated by inelastic deformation ( ∼ 0.1 m per rupture, or ∼ 10% of the tectonic deformation budget).

Dislocation-mediated strain hardening in tungsten: Thermo-mechanical plasticity theory and experimental validation

Science.gov (United States)

Terentyev, Dmitry; Xiao, Xiazi; Dubinko, A.; Bakaeva, A.; Duan, Huiling

2015-12-01

A self-consistent thermo-mechanical model to study the strain-hardening behavior of polycrystalline tungsten was developed and validated by a dedicated experimental route. Dislocation-dislocation multiplication and storage, as well dislocation-grain boundary (GB) pinning were the major mechanisms underlying the evolution of plastic deformation, thus providing a link between the strain hardening behavior and material's microstructure. The microstructure of the polycrystalline tungsten samples has been thoroughly investigated by scanning and electron microscopy. The model was applied to compute stress-strain loading curves of commercial tungsten grades, in the as-received and as-annealed states, in the temperature range of 500-1000 °C. Fitting the model to the independent experimental results obtained using a single crystal and as-received polycrystalline tungsten, the model demonstrated its capability to predict the deformation behavior of as-annealed samples in a wide temperature range and applied strain. The relevance of the dislocation-mediated plasticity mechanisms used in the model have been validated using transmission electron microscopy examination of the samples deformed up to different amounts of strain. On the basis of the experimental validation, the limitations of the model are determined and discussed.

Mechanical Behavior of UO2 at Sub-grain Length Scales: Quantification of Elastic, Plastic and Creep Properties via Microscale Testing

Energy Technology Data Exchange (ETDEWEB)

Peralta, Pedro

2018-04-16

Techniques were developed to measure properties at sub-grain scales using depleted Uranium Oxide (d-UO2) samples heat-treated to obtain different grain sizes and oxygen stoichiometries, through three main tasks: 1) sample processing and characterization, 2) microscale and conventional testing and 3) modeling. Grain size and crystallography were characterized using Scanning Electron Microscopy (SEM), in conjunction with Electron Backscattering Diffraction (EBSD) and Electron Channeling Contrast Imaging (ECCI). Grains were then carefully selected based on their crystallographic orientations to perform ex-situ micromechanical tests with samples machined via Focused Ion Beam (FIB), with emphasis on micro-cantilever bending. These experiments were performed under controlled atmospheres, to insure stoichiometry control, at temperatures up to 700 °C and allowed measurements involving elastic (effective Young’s modulus), plastic (critical resolved shear stresses) and creep (creep strain rates) behavior. Conventional compression experiments were performed simultaneously to compare with the ex-situ measurements and study potential size effects. Modeling was implemented using anisotropic elasticity and inelastic constitutive relations for plasticity and creep based on kinematics and kinetics of dislocation glide that account for the effects of crystal orientation, and stress. The models will be calibrated and validated using the experimental data. This project provided insight on correlations among stoichiometry, crystallography and mechanical behavior in advanced oxide fuels, provided valuable experimental data to validate and calibrate mesoscale fuel performance codes and also a framework to measure sub-grain scale mechanical properties that should be suitable for use with irradiated samples due to small volumes required. The goals and metrics of the ongoing study of thermo-mechanical behavior in depleted uranium dioxide (d-UO2) outlined in this project have been

Stability of surface plastic flow in large strain deformation of metals

Science.gov (United States)

Viswanathan, Koushik; Udapa, Anirduh; Sagapuram, Dinakar; Mann, James; Chandrasekar, Srinivasan

We examine large-strain unconstrained simple shear deformation in metals using a model two-dimensional cutting system and high-speed in situ imaging. The nature of the deformation mode is shown to be a function of the initial microstructure state of the metal and the deformation geometry. For annealed metals, which exhibit large ductility and strain hardening capacity, the commonly assumed laminar flow mode is inherently unstable. Instead, the imposed shear is accommodated by a highly rotational flow-sinuous flow-with vortex-like components and large-amplitude folding on the mesoscale. Sinuous flow is triggered by a plastic instability on the material surface ahead of the primary region of shear. On the other hand, when the material is extensively strain-hardened prior to shear, laminar flow again becomes unstable giving way to shear banding. The existence of these flow modes is established by stability analysis of laminar flow. The role of the initial microstructure state in determining the change in stability from laminar to sinuous / shear-banded flows in metals is elucidated. The implications for cutting, forming and wear processes for metals, and to surface plasticity phenomena such as mechanochemical Rehbinder effects are discussed.

Elastic strain relaxation in interfacial dislocation patterns: II. From long- and short-range interactions to local reactions

Science.gov (United States)

Vattré, A.

2017-08-01

The long- and short-range interactions as well as planar reactions between two infinitely periodic sets of crossing dislocations are investigated using anisotropic elasticity theory in face- (fcc) and body- (bcc) centered cubic materials. Two preliminary cases are proposed to examine the substantial changes in the elastic stress states and the corresponding strain energies due to a slight rearrangement in the internal dislocation geometries and characters. In general, significant differences and discrepancies resulting from the considered cubic crystal structure and the approximation of isotropic elasticity are exhibited. In a third scenario, special attention is paid to connecting specific internal dislocation structures from the previous cases with non-equilibrium configurations predicted by the quantized Frank-Bilby equation for the (111) fcc and (110) bcc twist grain boundaries. The present solutions lead to the formation of energetically favorable dislocation junctions with non-randomly strain-relaxed configurations of lower energy. In particular, the local dislocation interactions and reactions form equilibrium hexagonal-shaped patterns with planar three-fold dislocation nodes without producing spurious far-field stresses.Numerical application results are presented from a selection of cubic metals including aluminum, copper, tantalum, and niobium. In contrast to the fcc materials, asymmetric dislocation nodes occur in the anisotropic bcc cases, within which the minimum-energy paths for predicting the fully strain-relaxed dislocation patterns depend on the Zener anisotropic factor with respect to unity. The associated changes in the dislocation structures as well as the removal of the elastic strain energy upon relaxations are quantified and also discussed.

Monitoring elastic strain and damage by neutron and synchrotron beams

International Nuclear Information System (INIS)

Withers, P.J.

2001-01-01

Large-scale neutron and synchrotron X-ray facilities have been providing important information for physicists and chemists for many decades. Increasingly, materials engineers are finding that they can also provide them with important information non-destructively. Highly penetrating neutron and X-ray synchrotron beams provide the materials engineer with a means of obtaining information about the state of stress and damage deep within materials. In this paper the principles underlying the elastic strain measurement and damage characterization techniques are introduced. (orig.)

From plastic to elastic stress relaxation in highly mismatched SiGe/Si heterostructures