Two-parameter characterization of the near-tip stress fields for a bi-material elastic-plastic interface crack

A particular case of interface cracks is considered. The materials at each side of the interface are assumed to have different yield strength and plastic strain hardening exponent, while elastic properties are identical. The problem is considered to be a relevant idealization of a crack at the fusion line in a weldment. A systematic investigation of the mismatch effect in this bi-material plane strain mode I dominating interface crack has been performed by finite strain finite element analyses. Results for loading causing small scale yielding at the crack tip are described. It is concluded that the near-tip stress field in the forward sector can be separated, at least approximately, into two parts. The first part is characterized by the homogeneous small scale yielding field controlled by J for one of the interface materials, the reference material. The second part which influences the absolute value of stresses at the crack tip and measures the deviation of the fields from the first part can be characterized by a mismatch constraint parameter M. Results have indicated that the second part is a very weak function of distance from the crack tip in the forward sector, and the angular distribution of the second part is only a function of the plastic hardening property of the reference material.     

Experimental strain-hardening behaviors and associated computational models with anisotropic sheet metals

Several anisotropic hardening models with simple loading conditions are proposed, including exponential hardening model, linear hardening model and multi-linear hardening model (which also suits for using the experimental data directly). Three special hardening curves, in the 0°, 45° and 90° angles, respectively, measured against the rolling direction, are the special cases of the proposed hardening models. These models make sense to be applied for simulating forming processes of the planar anisotropic hardening sheet metals, in particular for determining the springback and FLD of formed parts. In order to describe this view further, the constitutive relations of stress and strain, based on the plastic potential flow rule with isotropic hardening and kinematic hardening assumptions, have been discussed briefly. And then, the corresponding results of constitutive relations dependent on the proposed hardening models of materials will be represented, respectively.     

基于SMP破坏准则的土体弹塑性动力本构模型

利用土体的塑性流动理论,提出了用于描述饱和砂土动力反应性质的弹塑性本构模型。土体总的变形由三部分组成:即弹性应变、与体积屈服机制相关的塑性应变和与剪切屈服机制相关的塑性应变。土体在初始加载与卸载和重新加载阶段性质的差别通过采用不同的模型参数加以反映。该模型能够较为准确地描述饱和砂土在单调加载和循环加载条件下的反应性质。     

Plane-stress crack-tip fields for pressure-sensitive dilatant materials

In this paper we present plane-stress crack-tip stress and strain fields for pressure-sensitive dilatant materials. A hydrostatic stress-dependent yield criterion and the normality flow rule are used to account for pressure-sensitive yielding and plastic dilatancy. The material hardening response is specified by a power-law relation. The plane-stress mode I singular fields are found in a separable form similar to the HRR fields (Hutchinson, J. Mech. Phys. Solids 16, 13–31 and 337–347, 1968; Rice and Rosengren, J. Mech. Phys. Solids 16, 1–12, 1968). The angular variations of the fields depend on the material hardening exponent and the pressure sensitivity parameter. Our low-hardening solutions for different degrees of pressure sensitivity agree well with the corresponding perfectly plastic solutions. An important aspect of the effects of pressure-sensitive yielding and plastic dilatancy on crack-tip fields is the lowering of the opening stress and the hydrostatic stress directly ahead of the crack tip. This effect, similar to that under plane-strain conditions (Li and Pan, to appear in J. Appl. Mech. 1989), has implications in the material toughening observed in some ceramic and polymeric composites.     

A Cosserat point element (CPE) for the numerical solution of transient large planar motions of elastic–plastic and elastic–viscoplastic beams

The objective of this paper is to develop constitutive equations of a Cosserat point element (CPE) for the numerical solution of transient large planar motions of elastic–plastic and elastic–viscoplastic beams with rigid cross-sections. Specifically, attention is limited to response of a material with constant yield strength. A yield function is proposed which couples the inelastic responses of tension and shear. Another yield function is proposed for bending which depends on a hardening variable that models motion of the elastic–plastic boundary in the beam’s cross-section. Evolution equations are proposed for elastic strains and the hardening variable and an overstress-type formulation is used for elastic–viscoplastic response. In contrast, with standard finite element approaches the CPE model needs no integration through the element region. Also, an implicit scheme is developed to integrate the evolution equations without iteration. Examples of transient large motions of beams, which are impulsively loaded, indicate that the CPE produces reasonably accurate response relative results in the literature and full three-dimensional calculations using ABAQUS.     

Mechanical characterization and modeling of the deformation and failure of the highly crosslinked RTM6 epoxy resin

The nonlinear deformation and fracture of RTM6 epoxy resin is characterized as a function of strain rate and temperature under various loading conditions involving uniaxial tension, notched tension, uniaxial compression, torsion, and shear. The parameters of the hardening law depend on the strain-rate and temperature. The pressure-dependency and hardening law, as well as four different phenomenological failure criteria, are identified using a subset of the experimental results. Detailed fractography analysis provides insight into the competition between shear yielding and maximum principal stress driven brittle failure. The constitutive model and a stress-triaxiality dependent effective plastic strain based failure criterion are readily introduced in the standard version of Abaqus, without the need for coding user subroutines, and can thus be directly used as an input in multi-scale modeling of fibre-reinforced composite material. The model is successfully validated against data not used for the identification and through the full simulation of the crack propagation process in the V-notched beam shear test.     

Large inelastic deformation of glassy polymers. part I: rate dependent constitutive model

Glassy polymers constitute a large class of engineering solids. In order to successfully analyze the warm (near the glass transition temperature) mechanical processes by which many glassy polymeric products are manufactured, as well as to ascertain the response of the resulting part to service life loading conditions, a constitutive law that properly accounts for the large, inelastic deformation behavior of these materials is required. Such behavior is known to exhibit strain rate, temperature, and pressure dependent yield, as well as true strain softening and hardening after yield. This paper develops a three-dimensional constitutive model based on the macromolecular structure of these materials and the micromechanism of plastic flow which encompasses these above dependencies. The experiments necessary to determine the material properties used in the model are also identified. The model predictions for the true stress-strain behavior of PMMA are then compared with experimental data reported in the literature.     

Constitutive modelling of fibre-reinforced composites with unidirectional plies using a plasticity-based approach

This paper presents the development of a constitutive model able to accurately represent the full non-linear mechanical response of polymer-matrix fibre-reinforced composites with unidirectional (UD) plies under quasi-static loading. This is achieved by utilising an elasto-plastic modelling framework. The model captures key features that are often neglected in constitutive modelling of UD composites, such as the effect of hydrostatic pressure on both the elastic and non-elastic material response, the effect of multiaxial loading and dependence of the yield stress on the applied pressure.The constitutive model includes a novel yield function which accurately represents the yielding of the matrix within a unidirectional fibre-reinforced composite by removing the dependence on the stress in the fibre direction. A non-associative flow rule is used to capture the pressure sensitivity of the material. The experimentally observed translation of subsequent yield surfaces is modelled using a non-linear kinematic hardening rule. Furthermore, evolution laws are proposed for the non-linear hardening that relate to the applied hydrostatic pressure.Multiaxial test data is used to show that the model is able to predict the non-linear response under complex loading combinations, given only the experimental response from two uniaxial tests.     

Springback investigation of anisotropic aluminum alloy sheet with a mixed hardening rule and Barlat yield criteria in sheet metal forming

A mixed hardening model has been implemented based on Lemaitre and Chaboche non-linear kinematic hardening theory to consider cyclic behavior and the Bauschinger effect. The Chaboche isotropic hardening theory is incorporated into the non-linear kinematic hardening model to introduce a surface of nonhardening in the plastic strain space. The bending and reverse bending case study has verified the effectiveness of the mixed hardening model by comparison with the proposed experiment results. Barlat’89 yielding criterion is adopted for it does not has any limitation while Hill’s non-quadratic yield criterion is for the case that the principal axes of anisotropy coincides with principal stress direction. The Backward–Euler return mapping algorithm was applied to calculate the stress and strain increment. The mixed hardening model is implemented using ABAQUS user subroutine (UMAT). The comparisons with linear kinematic hardening model and isotropic hardening model in NUMISHEET’93 benchmark show that the mixed hardening model coupled with Barlat’89 yield criteria can well reflect stress and strain distributions and give a more favorable springback angle prediction.     

Elastoplastic orthotropy at finite strains: multiplicative formulation and numerical implementation

A constitutive model for orthotropic elastoplasticity at finite plastic strains is discussed and basic concepts of its numerical implementation are presented. The essential features are the multiplicative decomposition of the deformation gradient in elastic and inelastic parts, the definition of a convex elastic domain in stress space and a representation of the constitutive equations related to the intermediate configuration. The elastic free energy function and the yield function are formulated in an invariant setting by means of the introduction of structural tensors reflecting the privileged directions of the material. The model accounts for kinematic and isotropic hardening. The associated flow rule is integrated using the so-called exponential map which preserves exactly the plastic incompressibility condition. The constitutive equations are implemented in a brick-type shell element. Representative numerical simulations demonstrate the suitability of the proposed formulations.     

On plastic potentials for anisotropic metals and their derivation from the texture function

Summary Plastic yielding of anisotropic metals can be either described by a macroscopic constitutive relation or assessed by means of a model which correlates single and polycrystal behaviors. The mathematical identification of the plastic work rate derived from the two approaches, for all strain rate tensors, leads to a fit of the polycrystal yield surface by an analytical function. When a quadratic from is assumed, the macroscopic anisotropy parameters become explicit functions of the texture coefficients. This identification method is applied to calculate yield surfaces andR-values of rolled and annealed steel sheets: theR-values and in general the flow rule, are more significantly modified by the fitting than the yield surface. Thus, it is worth extending the method to more general constitutive relations which may be given by the form of their work function: alternative forms of the work function for plastic materials are explored, especially in the bearing of convexity and homogeneity where quadratic forms have a distinct advantage. Finally, it is shown that the identification of the work function allows to express the phenomenological coefficients as analytical functions of the texture parameters for many forms of the work function; in the other cases, these coefficients may be obtained by linear or non-linear regression.     

Simulations of stress distributions in crankshaft sections under fillet rolling and bending fatigue tests

The residual stresses due to fillet rolling and the bending stresses near the fillets of crankshaft sections under bending fatigue tests are important driving forces to determine the bending fatigue limits of crankshafts. In this paper, the residual stresses and the bending stresses near the fillet of a crankshaft section under fillet rolling and subsequent bending fatigue tests are investigated by a two-dimensional plane strain finite element analysis based on the anisotropic hardening rule of Choi and Pan [Choi KS, Pan J. A generalized anisotropic hardening rule based on the Mroz multi-yield-surface model for pressure insensitive and sensitive materials (in preparation)]. The evolution equation for the active yield surface during the unloading/reloading process is first presented based on the anisotropic hardening rule of Choi and Pan (in preparation) and the Mises yield function. The tangent modulus procedure of Peirce et al. [Peirce D, Shih CF, Needleman A. A tangent modulus method for rate dependent solids. Comput Struct 1984;18:875–87] for rate-sensitive materials is adopted to derive the constitutive relation. A user material subroutine based on the anisotropic hardening rule and the constitutive relation was written and implemented into ABAQUS. Computations were first conducted for a simple plane strain finite element model under uniaxial monotonic and cyclic loading conditions based on the anisotropic hardening rule, the isotropic and nonlinear kinematic hardening rules of ABAQUS. The results indicate that the plastic response of the material follows the intended input stress–strain data for the anisotropic hardening rule whereas the plastic response depends upon the input strain ranges of the stress–strain data for the nonlinear kinematic hardening rule. Then, a two-dimensional plane-strain finite element analysis of a crankshaft section under fillet rolling and subsequent bending was conducted based on the anisotropic hardening rule of Choi and Pan (in preparation) and the nonlinear kinematic hardening rule of ABAQUS. In general, the trends of the stress distributions based on the two hardening rules are quite similar after the release of roller and under bending. However, the compressive hoop stress based on the anisotropic hardening rule is larger than that based on the nonlinear kinematic hardening rule within the depth of 2 mm from the fillet surface under bending with consideration of the residual stresses of fillet rolling. The critical locations for fatigue crack initiation according to the stress distributions based on the anisotropic hardening rule appear to agree with the experimental observations in bending fatigue tests of crankshaft sections.     

Numerical simulation of the plastic flow properties of iron single crystals

Summary The present paper deals with the numerical simulation of the plastic flow properties of iron single crystals as well as their influence on the macroscopic elastic-plastic deformation and localization behavior affected by superimposed hydrostatic pressure. Based on experimental observations the onset of plastic yielding on the microscale is described by an extended microscopic yield condition taking into account various microscopic stress components acting on the respective slip systems. In addition, to be able to compute inelastic deformations from a plastic potential, the latter is expressed in terms of workconjugate microscopic stress and strain measures which leads to a non-associated flow rule for the macroscopic plastic strain rate. On the numerical side, generalized functions for constitutive parameters will be used to be able to simulate the single crystal's microscopic deformation behavior observed in experiments. Estimates of the current microscopic stresses and strains are obtained via an efficient and remarkably stable plastic predictor-elastic corrector technique which is incorporated into a nonlinear finite element program. Numerical simulations of uniaxial tests show quantitatively the influence of hydrostatic pressure on current material data. Further numerical studies on the additional constitutive non-Schmid terms elucidate their effect on iron single crystal's macroscopic deformation and localization behavior.     

Constitutive modeling of the mechanical behavior of high strength ferritic steels for static and dynamic applications

A constitutive relation is presented in this paper to describe the plastic behavior of ferritic steel over a broad range of temperatures and strain rates. The thermo-mechanical behavior of high strength low alloy (HSLA-65) and DH-63 naval structural steels is considered in this study at strains over 40%. The temperatures and strain rates are considered in the range where dynamic strain aging is not effective. The concept of thermal activation analysis as well as the dislocation interaction mechanism is used in developing the flow model for both the isothermal and adiabatic viscoplastic deformation. The flow stresses of the two steels are very sensitive to temperature and strain rate, the yield stresses increase with decreasing temperatures and increasing strain rates. That is, the thermal flow stress is mainly captured by the yield stresses while the hardening stresses are totally pertained to the athermal component of the flow stress. The proposed constitutive model predicts results that compare very well with the measured ones at initial temperature range of 77 K to 1000 K and strain rates between 0.001 s⁻¹ and 8500 s⁻¹ for both steels.     

Implementation of a constitutive model in finite element method for intense deformation

Since the constitutive information is one of the most important aspects of material deformation analysis, here a new constitutive model is proposed that can investigate the behavior of material during intense deformation better than existent models. The model that is completely based on physical mechanisms can predict all stages of flow stress evolution and also can elucidate the effects of strain and strain rate on flow stress evolution of material during intense plastic deformation. Here as an application, implementation of the constitutive model in finite element method (FEM) is used to compare two methods of sever plastic deformation (SPD) processes of copper sheet; repetitive corrugation and straightening (RCS) and constrained groove pressing (CGP). The modeling results are in good agreement with the experimental data and show that the hardness uniformity and its magnitude for RCSed sheet are higher than that for CGPed sheet. However, the prominence of these processes in strain uniformity depends on pass number.