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The present study aims to thoroughly investigate the edge‐cracking phenomenon in high‐strength sheets. Hence, the edge crack sensitivity of three dual‐phase steels is studied in various combinations of edge manufacturing and forming processes. Finite element simulations are performed to elaborate the study. In this regard, the Yoshida–Uemori kinematic hardening model is employed to describe the plasticity behavior of the materials under multistep processes. A stress‐state fracture model is coupled with this plasticity model to illustrate the distinguished local fracture strains of each material. Moreover, the effects of strain rate and the consequent temperature rise on hardening and damage are taken into account, which play significant roles during shear‐cutting. The results show that although the shear‐cutting processes are applied at very low speed, the strain rate and induced temperature are still high at the cutting area. The hole expansion results show different fracture behaviors for different cases. In brief, cracking is initiated at a location, which shows the highest damage accumulation during edge manufacturing plus the subsequent forming process. Such a complicated situation can only be successfully predicted by using a computer‐aided approach along with proper material modeling, like the applied model in this study. [ABSTRACT FROM AUTHOR]

By blending the primal‐dual interior point method (PDIPM) and the return mapping algorithm, we propose a hybrid strategy of implicit stress update for a class of hypoelastic‐plastic models with the hardening rule whose evolution is restricted by the memory surface. The inequality constraint relevant to the memory surface is replaced by the equality constraint by the introduction of a slack variable, and the duality gap is gradually reduced by using path‐following method. First, we formulate an optimization problem corresponding to the principle of maximum plastic dissipation for the standard von‐Mises plasticity with isotropic and kinematic hardening rules and its variant for the model with the memory surface. Next, after function forms employed for the elastic‐plastic model are specified, the PDIPM to realize an implicit stress update is briefly reviewed and then applied to the model involving the memory surface to replace the relevant inequality constraint by the equality constraint by the introduction of a slack variable. Then, we present a hybrid scheme that combines the standard return mapping algorithm with the PDIPM. The numerical accuracy of the proposed stress update algorithm for the conventional elastic‐plastic model is verified in comparison with the standard return mapping algorithm using iso‐error map. Also, targeting a notched round steel bar under cyclic loading with three different amplitudes, we demonstrate the performance for the stress update using the elastic‐plastic model with the memory surface. Finally, the capability of the proposed algorithm is proven through a typical real‐life example such that a steel bridge is subjected to earthquake for which the residual load carrying capacity must be estimated. [ABSTRACT FROM AUTHOR]

In finite deformation inelasticity, one often has to deal with the incompressibility constraint. In the past, this was dealt with using, for example, an exponential mapping approach, which yields exact volume preservation in plastic deformations. In this article however, the special‐linear update approach by Hurtado et al. The special‐linear update: An application of differential manifold theory to the update of isochoric plasticity flow rules, Int J Numer Methods Eng. 2014;97(4):298‐312, which utilizes a projection method to fulfill the incompressibility constraint is used. The model is applied to isotropic plasticity by a novel approximation of the logarithm and treats kinematic hardening without losing the symmetry of the internal variables. The model results are compared to models utilizing an exponential mapping approach in numerical experiments. [ABSTRACT FROM AUTHOR]

For many materials, plastic deformations under cyclic loadings differ from monotonic loading. Cyclic plastic zone with considering the strain hardening effects becomes complicated during unloading step. In this research, the effects of nonlinear kinematic and isotropic hardening behaviours on the cyclic plastic reaction around the crack tip for different conditions are investigated. For study of various hardening characteristics, as‐received and annealed copper are tested under same symmetric cyclic loadings. The results indicate considerable isotropic hardening behaviour in annealed material. A Chaboche nonlinear hardening model was used to determine the hardening parameters. The cyclic plastic zone around the crack tip in C(T) specimen was measured by back stresses. The cyclic plastic zones are specified via variations of the back stresses in a cycle. The cyclic plastic zones predicted by Chaboche model are smaller than those for Irwin model because of the hardening effects. Also, Irwin model for prediction of the cyclic plastic zone size is modified with considering the cyclic plastic effects. According to the results, the cyclic plastic zone around the crack tip is almost constant in the same load range, and load ratio (R) has a slight effect on this zone. Whereas, for constant load range, cyclic J‐integral (∆J) is different for various R values. For studying of the fatigue crack growth, two parameters of ∆J and cyclic plastic zone area were evaluated. These parameters can apply in fracture mechanics especially in elastic–plastic conditions with considering the cyclic plastic responses. [ABSTRACT FROM AUTHOR]

In this paper, the mean stress relaxation behavior of simple Al‐alloy 2024‐T3 specimens and also the mean stress relaxation around the hole of cold expanded specimen are studied. The analyses are performed through the combination of the nonlinear isotropic hardening and Chaboche nonlinear kinematic hardening model accompanied by the results of experimental tests. The strain‐controlled axial tests are performed at two different strain amplitudes, while the stress‐controlled tests of cold expanded specimens are performed for three different imposed load amplitudes. The constitutive equations of the hardening model are coded as a UMAT subroutine in FORTRAN programming language and implemented in the commercial finite element code of ABAQUS. The accuracy of the hardening model has been proved in two steps: first by simulations of mean stress relaxation during the uniaxial strain‐controlled cyclic tests and second by simulation of strain ratcheting during the stress‐controlled cyclic loading. The stress and strain distributions after cold expansion process are examined as well as the mean stress relaxation due to cyclic loading. The results show the influences of imposed stress amplitude on increasing mean stress relaxation and also the effect of cold expansion level on reducing the mean stress relaxation. [ABSTRACT FROM AUTHOR]

Abstract: The objective of this article is the evaluation of the validity range of two objective rates, the nowadays most frequently used Jaumann rate and the recently introduced logarithmic rate, in material behaviour prediction due to large deformations. For that purpose the model subjected to large monotonic uniaxial elastoplastic deformation has been examined as well as the initially prestressed models which are afterwards exposed to the cyclic process of combined elastic lengthening and shearing. It is shown that whenever the participation of shear deformation to the total deformation stays in the small deformation range both rates are almost equal in constitutive relations implementation since the outputs for both rates are nearly congruent. Otherwise, if the influence of rotations is significant the Jaumann rate gives theoretically and experimentally unexpected results whereas the logarithmic rate results are stable and consistent with the notion of elasticity, i.e. without any residual stresses at the end of the elastic deformation cycles. [ABSTRACT FROM AUTHOR]

SUMMARY A new method to compute numerically efficient closed-form representation of matrix exponential and its derivative is developed for 3 × 3 matrices with real eigenvalues. The matrix exponential is obtained by automatic differentiation of an appropriate scalar generating function in a general case, and highly accurate asymptotic expansions are derived for special cases in which the general formulation exhibits ill-conditioning, for instance, for almost equal eigenvalues. Accuracy and numerical efficiency of the closed-form matrix exponential as compared with the truncated series approximation are studied. The application of the closed-form matrix exponential in the finite-strain elastoplasticity is also presented. To this end, several time-discrete evolution laws employing the exponential map are discussed for J2 plasticity with isotropic hardening and nonlinear kinematic hardening of Armstrong-Frederick type. The discussion is restricted to the case of elastic isotropy and implicit time integration schemes. In this part, the focus is on a general automatic differentiation-based formulation of finite-strain plasticity models. Numerical efficiency of the corresponding incremental schemes is studied in the context of the FEM. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The need to change the reference configuration can naturally appear during the numerical simulation of multi-stage metal forming processes. In the current work, a refined approach to the consideration of previously induced plastic anisotropy is discussed, which is based on such configuration change. The model of finite strain viscoplasticity proposed by Shutov and Kreißig is considered in this study as a practical tool, suitable to capture the evolution of mechanical properties of material during inelastic deformation. The initial plastic anisotropy can be considered within this model by a special choice of initial conditions imposed on the relevant internal variables. A simple transformation law which is based on the isochoric change of the reference configuration is obtained in the current study. This transformation allows to obtain relevant initial conditions with respect to a new reference configuration. Thus, the initial conditions are formulated using the simulation results from the foregoing loading. The advocated approach is exemplified by the numerical simulation of equal channel angular pressing of cylindrical billets. The plastic anisotropy accumulated during a single ECAP pass is estimated using a series of virtual tension tests. These tests were performed on samples cut from processed billet with their gage lengths in different directions. Finally, the impact of the plastic anisotropy on the rotation of the workpiece within the output channel during ECAP is numerically estimated. [ABSTRACT FROM AUTHOR]

In this paper we suggest a thermodynamically consistent approach to the simulation of a rate dependent material response at finite strains. The nonlinear mechanical phenomena which are covered by the proposed material model include distortional, kinematic, and isotropic hardening. Firstly, we present a new two-dimensional rheological model of distortional hardening, which predicts the yield curve in the stress space to be a limac¸on of Pascal. Such effects like the distortion of the yield surface in the stress space andits orientation depending on the loading path are captured by the rheological model in a vivid way. Next, the rheological model serves as a guideline for the construction of the constitutive equations. In particular, the kinematic assumptions, the ansatz for the free energy, and the form of the yield function are motivated by the rheological model. Further, two types of flow rules are considered in this study: a normality rule and a radial rule, both thermodynamically consistent. Moreover, we formulate explicitly the constraints on the material parameters, which guarantee the convexity of the yield surface. Furthermore, implicit time-stepping methods are considered which exactly preserve the incompressibility of the inelastic flow. Finally, the basic features of the predicted material response are illustrated by a series of numerical simulations. In particular, the simulation results are compared to the real experimental data. [ABSTRACT FROM AUTHOR]

A constitutive materials model, which includes Ohno-Wang's kinematic hardening rule, is employed to simulate the isothermal monotonic and cyclic behaviours of high-pressure die cast magnesium AM60B alloy under uniaxial loading condition. An implicit constitutive stress integration scheme developed by Kobayashi and Ohno is used to code the model into an ABAQUS user materials subroutine (UMAT). After the material parameters used in the current model were obtained from the experimental results, the predictive capability of the model was verified. [ABSTRACT FROM AUTHOR]

A formulation combining kinematic translation and isotropic expansion for a yield surface based on Gurson–Tvergaard function is used to describe void growth. By adopting a criterion of internal necking of the ligaments between voids, fracture strains for tensile bars made of conventional alloys and powder metal compacts—with micromechanical parameters mostly identified from experiments—are predicted according to kinematic, isotropic and mixed hardening models. Fracture strains predicted by the kinematic-hardening model are in closer agreement with experiments whereas those estimated according to isotropic-hardening model are overestimated. The consideration of either step-like or continuous void nucleation models indicates its great influence on fracture strains and emphasizes a further need to quantify the statistical parameters involved in these models. [ABSTRACT FROM AUTHOR]

An elasto-plastic formulation at finite strains was considered with isotropic and kinematic hardening and anisotropic yield functions. In order to find a simple but thermomechanically consistent continuum mechanical basis for stress integration algorithms of shell problems, evolution equations of the plastic strain rate and internal variables were derived. This was performed in the stress-free intermediate configuration with the Mandel stress and corresponding back stress tensors. The resulting relations were then transformed into the current configuration and restricted to small elastic strains. For an algorithmic treatment of this material formulation for shell problems, the kinematic hardening was reformulated in stress-related terms to obtain a set of equations for planar anisotropic elasto-plastic materials. Finally, an updated iterative treatment for the elasto-plastic shell at finite strains was derived utilizing the cutting plane algorithm. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Because creep–fatigue is mainly studied in uniaxial tension, it is shown here how to proceed to perform both experiments and calculations under multiaxial loading and when the temperature varies both in time and space. The constitutive equations used are those of elasto-visco-plasticity coupled or not, to damage, with isotropic and kinematic hardening. It is shown that the unified damage law first proposed for ductile failure and then for fatigue may also be applied to multiaxial creep–fatigue interactions with a new expression for the damage threshold. The procedure for the identification of material parameters is described in detail. Finally, it is shown that the uncoupled calculation procedure, where damage is calculated as a post-processing of an elasto-visco-plastic computation, gives satisfactory results in comparison to the fully coupled analysis; the latter being more accurate but very expensive in computer time. [ABSTRACT FROM AUTHOR]

The effect of overloads, underloads and stress ratio on plasticity-induced crack opening level is examined for different ‘model’ materials. This study is focused on the consequences of the Bauschinger effect on the crack opening level. Various finite element analyses were conducted using ABAQUS to test these effects, involving the Chaboche constitutive equations that take into account both the Bauschinger effect of the material and its cyclic hardening or softening. The cyclic plastic behaviour of the material is found to strongly affect the crack behaviour after an overload or an underload. The experimental data obtained on a 0.4% carbon mild steel confirm the numerical results. [ABSTRACT FROM AUTHOR]