Numerical simulation for the simple shear test in amorphous glassy polymers

In this paper, a driving stress finite element method of elastic-plastic large deformation based on implicit time integrating algorithm and an eight-chain molecular network model is used for the numerical simulation of the simple shear test of polycarbonate (PC) materials. The simulated results are compared with experimental ones. The strain localization propagation for the shear band deformation for simple shear deformation is investigated numerically. The effects of microstructure parameters in the model on strain softening and orientation hardening of the PC are discussed in detail. Supported by the National Natural Science Foundation of China.     

Nonproportional loading effects on elastic-plastic behavior based on stress resultants for thin plates of strain hardening materials

A stress resultant constitutive law in rate form is constructed for power-law hardening materials. The change of plate thickness is considered in the constitutive law. The elastic-plastic behavior of a plate element based on the stress resultant constitutive law under uniaxial combined tension and bending is determined under a limited number of nonproportional and unloading paths. The results based on the stress resultant constitutive law and the through-the-thickness integration method are compared within the context of both the small-strain and finite deformation approaches. The results indicate that the selection of the normalized equivalent stress resultant and the corresponding work-conjugate normalized equivalent generalized strain is appropriate for describing the hardening behavior in the stress resultant space. However, the hardening rule in a power law form must be modified for low hardening materials at large plastic deformation when finite deformation effects are considered.     

纤维增强韧性基体界面力学行为

分析了纤维增强韧性基体的界面力学行为及其失效机理,按剪滞理论和应变理化规律研究微复合材料的弹塑性变形和应力状态,讨论了幂硬化和线性硬化基体的弹塑性变形和界面应力分布,并给出纤维应力和位移的表达式。按最大剪应力强度理论建立了纤维／基体界面失效准则,推导出弹塑性界面失效的平均剪应力随纤维埋入长度的变化关系。     

Constitutive model for plastic deformation of nanocrystalline materials with shear band

A phase mixture model was used to study the plastic deformation behaviors in hardening stage of nanocrystalline materials. The material was considered as a composite of grain interior phase and grain boundary (GB) phase. The constitutive equations of the two phases were determined in term of their main deformation mechanisms. In softening stage, a shear band deformation mechanism was presented and the corresponding constitutive relation was established. Numerical simulations have shown that the predications fit well with experimental data. The investigation using the finite-element method (FEM) provided a direct insight into quantifying shear localization effect in nanocrystalline materials.     

三维轮轨法向接触力学行为弹塑性理论分析

基于Hertz接触理论和双线性强化模型,建立了轮轨法向接触弹塑性理论分析模型,分析了轮轨法向接触力学响应特征,讨论了轴重对接触压力和接触变形的影响规律。同时,基于三维轮轨接触有限元模型模拟了轮轨接触力学行为,并引入理论误差系数分析了弹性模型和双线性强化模型对轮轨接触力学响应预测结果的差异性。结果表明,轮轨最大接触压力和接触变形量均随轴重的增大而增大;双线性强化模型的理论误差系数较小,采用双线性强化分析模型能较准确地预测轮轨接触弹塑性力学行为。研究结果可为轮轨系统安全服役和损伤评估提供理论和技术支持。     

Incorporation of yield surface distortion in finite deformation constitutive modeling of rigid-plastic hardening materials based on the Hencky logarithmic strain

In this paper a constitutive model for rigid-plastic hardening materials based on the Hencky logarithmic strain tensor and its corotational rates is introduced. The distortional hardening is incorporated in the model using a distortional yield function. The flow rule of this model relates the corotational rate of the logarithmic strain to the difference of the Cauchy stress and the back stress tensors employing deformation-induced anisotropy tensor. Based on the Armstrong–Fredrick evolution equation the kinematic hardening constitutive equation of the proposed model expresses the corotational rate of the back stress tensor in terms of the same corotational rate of the logarithmic strain. Using logarithmic, Green–Naghdi and Jaumann corotational rates in the proposed constitutive model, the Cauchy and back stress tensors as well as subsequent yield surfaces are determined for rigid-plastic kinematic, isotropic and distortional hardening materials in the simple shear deformation. The ability of the model to properly represent the sign and magnitude of the normal stress in the simple shear deformation as well as the flattening of yield surface at the loading point and its orientation towards the loading direction are investigated. It is shown that among the different cases of using corotational rates and plastic deformation parameters in the constitutive equations, the results of the model based on the logarithmic rate and accumulated logarithmic strain are in good agreement with anticipated response of the simple shear deformation.     

Application of corotational rates of the logarithmic strain in constitutive modeling of hardening materials at finite deformations

In this paper a finite deformation constitutive model for rigid plastic hardening materials based on the logarithmic strain tensor is introduced. The flow rule of this constitutive model relates the corotational rate of the logarithmic strain tensor to the difference of the deviatoric Cauchy stress and the back stress tensors. The evolution equation for the kinematic hardening of this model relates the corotational rate of the back stress tensor to the corotational rate of the logarithmic strain tensor. Using Jaumann, Green–Naghdi, Eulerian and logarithmic corotational rates in the proposed constitutive model, stress–strain responses and subsequent yield surfaces are determined for rigid plastic kinematic and isotropic hardening materials in the simple shear problem at finite deformations.     

Effect of crack-tip shape on the near-tip field in glassy polymer

The physical nature of a crack tip is not absolutely sharp but blunt with finite curvature. In this paper, the effects of crack-tip shape on the stress and deformation fields ahead of blunted cracks in glassy polymers are numerically investigated under Mode I loading and small scale yielding conditions. An elastic–viscoplastic constitutive model accounting for the strain softening upon yield and then the subsequently strain hardening is adopted and two typical glassy polymers, one with strain hardening and the other with strain softening–rehardening are considered in analysis. It is shown that the profile of crack tip has obvious effect on the near-tip plastic field. The size of near-tip plastic zone reduces with the increase of curvature radius of crack tip, while the plastic strain rate and the stresses near crack tip enhance obviously for two typical polymers. Also, the plastic energy dissipation behavior near cracks with different curvatures is discussed for both materials.     

The time development of eulerian/lagrangian perturbations to simple shear and its applications to shear banding

T of two-dimensional linear disturbances to the simple shear deformation of viscoplastic hardening/softening solids and its consequences on the localization of the plastic flow into shear bands are investigated. Attention is focused on the orientation features of shear banding. A local analysis is carried out on the basis of a generalized Orr-Sommerfeld equation ; the classic time-independent characteristic lines theory is embedded in a time-dependent analysis. It is shown that the characteristic directions are not equivalent when the time evolution is considered, owing to the convective nature of the shear banding instability. The transition between a time-independent behavior for which a pair of shear bands occurs abruptly along the characteristic directions, and a time-dependent regime where a single shear band goes to completion in the shearing direction is discussed.     

QUASI－FLOW CORNER THEORY ON LARGE PLASTIC DEFORMATION OF DUCTILE METALS AND ITS APPLICATIONS

ＱＵＡＳＩ－ＦＬＯＷＣＯＲＮＥＲＴＨＥＯＲＹＯＮＬＡＲＧＥＰＬＡＳＴＩＣＤＥＦＯＲＭＡＴＩＯＮＯＦＤＵＣＴＩＬＥＭＥＴＡＬＳＡＮＤＩＴＳＡＰＰＬＩＣＡＴＩＯＮＳＨｕＰｉｎｇ（胡平）ＬｉｕＹｕｑｉ（柳玉启）ＧｕｏＷｅｉ（郭威）ＴａｉＦｅｎｇ（台风）（Ｒ...     

A research note on certain loading directions in rate independent plasticity

Starting with the strain space formulation of rate independent elastic-plastic materials, the notion of “work-instability”, i.e. the possibility of an elastic plastic material undergoing spontaneous plastic deformation in a workless manner, is discussed. Some simple criteria for a material to be work stable are presented. An example of a material that satisfies Prandtl-Reuss type equations with strain softening is presented and it is demonstrated that for plane homogeneous deformations, the material shows the possibility of spontaneous plastic flow even if the in-plane strains are held fixed, if it softens beyond a critical amount.     

On shakedown theory for elastic-plastic materials and extensions

The idea that an elastic-plastic structure under given loading history may shake down to some purely elastic state (and hence to a safe state) after a finite amount of initial plastic deformation, can apply to many sophisticated material models with possible allowable changes of additional material characteristics, as has been done in the literature. Despite some claims to the contrary, it is shown; however, that the shakedown theorems in a Melan-Koiter path-independent sense have been extended successfully only for certain elastic-plastic hardening materials of practical significance. Shakedown of kinematic hardening material is determined by the ultimate and initial yield stresses, not the generally plastic deformation history-dependent hardening curve between. The initial yield stress is no longer the convenient one (corresponding to the plastic deformation at the level of 0.2%) as in usual elastic-plastic analysis but to be related to the shakedown safety requirement of the structure and should be as small as the fatigue limit for arbitrary high-cycle loading. Though the ultimate yield strength is well defined in the standard monotonic loading experiment, it also should be reduced to the so-called “high-cycle ratchetting” stress for the path-independent shakedown analysis. A reduced simple form of the shakedown kinematic theorem without time integrals is conjectured for general practical uses. Application of the theorem is illustrated by examples for a hollow cylinder, sphere, and a clamped disk, under variable (including quasiperiodic dynamic) pressure.     

Constitutive modeling of temperature and strain rate dependent elastoplastic hardening materials using a corotational rate associated with the plastic deformation

In this paper, a constitutive model with a temperature and strain rate dependent flow stress (Bergstrom hardening rule) and modified Armstrong-Frederick kinematic evolution equation for elastoplastic hardening materials is introduced. Based on the multiplicative decomposition of the deformation gradient,new kinematic relations for the elastic and plastic left stretch tensors as well as the plastic deformation-dependent spin tensor are proposed. Also, a closed-form solution has been obtained for the elastic and plastic left stretch tensors for the simple shear problem.To evaluate model validity, results are compared with known experimental data for SUS 304 stainless steel, which shows a good agreement with the results of the proposed theoretical model.Finally, the stress-deformation curve, as predicted by the model, is plotted for the simple shear problem at room and elevated temperatures using the same material properties for AA5754-O aluminium alloy.     

On the application of the additive decomposition of generalized strain measures in large strain plasticity

In the present paper two thermodynamically consistent large strain plasticity models are examined and compared in finite simple shear. The first model (A) is based on the multiplicative decomposition of the deformation gradient, while the second one (B) on the additive decomposition of generalized strain measures. Both models are applied to a rigid-plastic material described by the von Mises-type yield criterion. Since both models include neither hardening nor softening law, a constant shear stress response even for large amounts of shear is expected. Indeed, the model A exhibits the true constant shear stress behavior independent of the elastic material law. In contrast, the model B leads to a spurious shear stress increase or drop such that its applicability under finite shear deformations may be questioned.     

Large strain responses of elastic-perfect plasticity and kinematic hardening plasticity with the logarithmic rate: Swift effect in torsion

A new Eulerian rate type elastic-perfectly plastic model has recently been established by utilizing the newly discovered logarithmic rate. It has been proved that this model is unique among the objective elastic-perfectly plastic models with all objective corotational stress rates and other known objective stress rates by virtue of the self-consistency criterion: the hypoelastic formulation intended for elastic behaviour must be exactly integrable to deliver a hyperelastic relation. The finite simple shear response of this model has been studied and shown to be reasonable for both shear and normal stress components. On the other hand, a kinematic hardening plasticity model may be formulated by adopting the logarithmic rate. The objective of this work is to further study the large deformation responses of the foregoing two kinds of idealized models, in particular the well-known Swift effect, in torsion of thin-walled cylindrical tubes. A complete, rigorous analysis is made for the orders of magnitude of all stress components. A closed-form solution is obtained for the kinematic hardening plastic case, and an analytical perturbation solution is derived for the elastic-perfectly plastic case. It is shown that the simple idealized kinematic hardening model with the logarithmic rate, which uses only two classical material constants, i.e., the initial (tensile) yield stress and the hardening modulus, may arrive at satisfactory explanation for and reasonable accord with salient features of experimental observation.     

Three-dimensional micromechanical modeling of voided polymeric materials

A three-dimensional micromechanical unit cell model for particle-filled materials is presented. The cell model is based on a Voronoi tessellation of particles arranged on a body-centered cubic (BCC) array. The three-dimensionality of the present cell model enables the study of several deformation modes, including uniaxial, plane strain and simple shear deformations, as well as arbitrary principal stress states.The unit cell model is applied to studies on the micromechanical and macromechanical behavior of rubber-toughened polycarbonate. Different load cases are examined, including plane strain deformation, simple shear deformation and principal stress states. For a constant macroscopic strain rate, the different load cases show that the macroscopic flow strength of the blend decreases with an increase in void volume fraction, as expected. The main mechanism for plastic deformation is broad shear banding across inter-particle ligaments. The distributed nature of plastic straining acts to reduce the amount of macroscopic strain softening in the blend as the initial void volume fraction is increased. In the case of plane strain deformation, the plastic flow is observed to initiate across inter-particle ligaments in the direction of constraint. This particular mode of deformation could not have been captured using a two-dimensional, plane strain idealization of cylindrical voids in a matrix.The potential for localized crazing and/or cavitation in the matrix is addressed. It is observed that the introduction of voids acts to relieve hydrostatic stress in the matrix material, compared to the homopolymer. It is also seen that the predicted peak hydrostatic stress in the matrix is higher under plane strain deformation than under triaxial tension (with equal lateral stresses), for the same macroscopic stress triaxiality.The effect of void volume fraction on the macroscopic uniaxial tension behavior of the different blends is examined using a Considère construction for dilatant materials. The natural draw ratio was predicted to decrease with an increase in void volume fraction.     

Ratcheting of cyclically hardening and softening materials: I. Uniaxial behavior

The phenomenon of ratcheting of materials cyclically loaded in the plastic range is studied through combined experimental and analytical efforts (ratcheting here describes the cyclic accumulation of deformation). In particular the work seeks to illustrate how cyclic hardening and softening influence ratcheting. To this end, systematic sets of experiments were performed on stainless steel 304 and carbon steel 1018 which, respectively, exhibit cyclic hardening and softening. Due to the wide variety of behavior observed, and to better illustrate the modelling challenges, the results are divided into uniaxial and multiaxial behavior, and are presented in Parts I and II, respectively. In Part I, the results from a series of uniaxial stress-controlled experiments are presented, which illustrate the parametric dependence of ratcheting in the two materials examined. Results from a set of auxiliary strain-controlled experiments required for quantifying the cyclic hardening and softening characteristics of the materials are also presented. In a preceding publication, the authors demonstrated that ratcheting in cyclically stable materials could be simulated with consistent accuracy by allowing the bounds of the two-surface model of Dafalias-Popov to translate in the direction of ratcheting at the rate of ratcheting. This modified model, coupled with previously developed schemes for simulating cyclic hardening in strain-controlled cycling, are used to simulate the experimental results developed. Strengths, weaknesses and plausible alternatives are critically presented. The results are quite promising.     

模型复合材料弹塑性界面应力分析

由纤维增强弹塑性基体所产生的界面具有弹塑性力学行为。考虑到一般材料的塑性变形都遵循幂硬化规律,对模型复合材料的界面进行弹性和应变硬化状态下的变形规律及其应力分析。以纤维拔出试验为研究模型,将界面分成弹性区和塑性区。利用界面应力剪滞理论,分别建立弹性区和塑性区的界面力学基本方程。选择适当的位移函数满足基本方程及埋入纤维的边界条件,再按位移函数求出弹性区和塑性区的界面剪应力。推导出平均界面剪应力与纤维