大变形扭转塑性硬化的实验和仿真研究

通过拉伸和扭转实验以及理论分析发现:在扭转实验中,当等效名义伸长率达到 286％时发生扭断,在此之前无明显局部化现象出现;相比较而言,单轴拉伸实验中的试件在颈缩失稳断裂时标距的最大伸长率仅为 29％.因此,用实心圆柱的扭转实验作为研究低碳钢这类弹塑性材料在大变形特征下的更为有效的基本实验,而以单轴拉伸实验作为补充是十分必要的.并通过数值模拟对在扭转过程中弹性核演变的历史进行了分析.     

A finite deformation nonlinear thermo-elastic model that mimics plasticity during monotonic loading

We present and study a nonlinear thermo-elastic constitutive model that under monotonic loading closely reproduces the response seen in plasticity, showing the initial stiff elastic response, kneeing as if yielding, and then showing response resembling post-yield hardening. The proposed large deformation thermo-elastic response model is constructed based on four physically identifiable mechanical parameters, that are closely related to the parameters used to construct plasticity models, thermal expansion parameters and two thermodynamic parameters. The four mechanical parameters are the initial elastic shear and bulk moduli, the yield point in shear, the hardening slope in shear. The thermodynamic parameters are the heat capacity at a reference temperature and its rate of change with changes of temperature. The model can be considered an alternate to deformation plasticity models currently used and, as such, can be used as a lightweight substitute for plasticity modeling in certain analysis. Since the proposed model is thermodynamically based, not only thermal effects are integrated into the model, but also the stress is calculated in terms of the applied deformation, allowing the model to be integrated with other models when conducting numerical analysis. We study the response of the proposed model under simple shear, uniaxial extension, confined compression, partially-confined compression, and biaxial extension. We incorporate the elastic model into ABAQUS using its UMAT subroutine for solid elements and using UHYPER for shell elements. We compare the large deformation response from the proposed elastic model with J2-plasticity, and with plasticity and deformation plasticity models implemented in ABAQUS. The model in most cases compares very favorably to all such models. This comparison is done for both homogeneous and non-homogeneous problems including the case of a cantilever beam under tip loading. We show that for the problems that it applies to, the models run in approximately one tenth the computational time and with one tenth the number of iterations needed to conduct the analysis using the plasticity model in ABAQUS.     

Effects of initial anisotropy on the finite strain deformation behavior of glassy polymers

Solid phase deformation processing of glassy polymers produces highly anisotropic polymer components as a result of the massive reorientation of molecular chains during the large strain forming operation. Indeed, the polymer preform used as the starting materials is usually anisotropic owing to its prior deformation history. The process end product has often been fashioned for a particular application, i.e. to possess an increased flow strength along a particular axis, thereby exploiting the orientation induced anisotropy effects. The fully three-dimensional issues involved in the use of glassy polymer components include anisotropic flow strenghts, limiting extensibilities, and deformation patterns. These characteristics have been altered by the initial forming operation but are obviously not expected to be enhanced in all directions. The presence of anisotropy in structural components may also lead to premature failure or unexpected shear localization. In this report the effects of initial deformation and the associated anisotropies are investigated through uniaxial compression tests on preoriented polycarbonate (PC) and polymethylmethacrylate (PMMA) specimens. The evolving anisotropy is monitored by testing materials preoriented by various amounts of strain and under different states of deformation. The tensorial nature of the anisotropic material is characterized by examining the preoriented material response in three orthogonal directions. A model for the large strain deformation response of glassy polymers has been shown by Arruda and Boyce [in press] to be well predictive of the evolution of anisotropy during deformation in initially isotropic materials. Here the authors evaluate the ability of the model developed in Arruda and Boyce [in press] to predict several aspects of the anisotropic response of preoriented materials. Using material properties determined from the characterization of the isotropic material response and a knowledge of the anisotropic state of the preoriented material, model simulations are shown to accurately capture all aspects of the large strain anisotropic response including flow strengths, strain hardening characteristics, cross-sectional deformation patterns, and limiting extensibilities. Although anisotropy has been shown to evolve with temperature and strain rate in Boyce, Arruda and Jayachandran [in press] and also state of deformation in Arruda and Boyce [in press], we submit an experimental observation that the subsequent deformation response of preoriented polymers may be predicted using only a measure of optical anisotropy, and not the prior strain or thermal history. Optical anisotropy, as measured for example by birefringence, therefore represents a true internal variable indicative of the evolution of anisotropy with inelastic strain, state of strain, and temperature.     

On quasi-non-destructive strength and toughness testing of elastic–plastic materials

Non-destructive evaluation of mechanical material properties, like strength and fracture toughness, is impossible for principal reasons. However, there are possibilities of quasi-non-destructive estimation methods, which can be quite useful in practice. Instrumented indentation tests are often suitable to get information about the elastic–plastic behaviour, where the indentation depth is measured as a function of indentation force. By approximate analytical methods, key parameters like ultimate tensile strength, work-hardening exponent or even yield stress can be derived from these measurements. A mobile indenter is presented here and its use in ambulant testing is described. To obtain the uniaxial stress–strain curve more directly and more exactly, the same instrument can be used for a miniature compression test, where a small pin is machined out from the surface of the material. Furthermore, to get information about the toughness of materials, a carving instrument has been developed, which allows the energy required to introduce a defined furrow to be measured and correlated with toughness parameters.     

金属材料平面应变拉伸变形局部化有限元分析

本文对于涉及韧性金属大变形中颈缩与剪切带断裂一类高度非线性变形局部化问题进行了弹塑性有限元数值模拟。采用改进的Ｊ２形变理论微分形式公式与交叉三角形四边形单元有限元网格，详细研究了应变硬化指数及初始表面不均匀特性的平面应变拉伸颈缩和剪切带形成的综合影响，给出此类问题的断裂机制图。     

Finite deformation of a polymer: experiments and modeling

The response of a polymer (polytetrafluoroethylene) to quasi-static and dynamic loading is determined and modeled. The polytetrafluoroethylene is extremely ductile and highly nonlinear in elastic as well as plastic behaviors including elastic unloading. Constitutive model developed earlier by Khan, Huang and Liang (KHL) is extended to include the responses of polymeric materials. The strain rate hardening, creep, and relaxation behaviors of polytetrafluoroethylene were determined through extensive experimental study. Based on the observation that both viscoelastic and viscoplastic deformation of polytetrafluoroethylene are time dependent and nonlinear, a phenomenalogical viscoelasto–plastic constitutive model is presented by a series connection of a viscoelastic deformation module (represented by three elements standard solid spring dashpot model), and a viscoplastic deformation module represented by KHL model. The KHL module is affected only when the stress exceeds the initial yield stress. The comparison between the predictions from the extended model and experimental data for uniaxial static and dynamic compression, creep and relaxation demonstrate that the proposed constitutive model is able to represent the observed time dependent mechanical behavior of polytetrafluoroethylene polytetrafluoroethylene qualitatively and quantitatively.     

A Study of Large Plastic Deformations in Dual Phase Steel Using Digital Image Correlation and FE Analysis

Large plastic deformation in sheets made of dual phase steel DP800 is studied experimentally and numerically. Shear testing is applied to obtain large plastic strains in sheet metals without strain localisation. In the experiments, full-field displacement measurements are carried out by means of digital image correlation, and based on these measurements the strain field of the deformed specimen is calculated. In the numerical analyses, an elastoplastic constitutive model with isotropic hardening and the Cockcroft–Latham fracture criterion is adopted to predict the observed behaviour. The strain hardening parameters are obtained from a standard uniaxial tensile test for small and moderate strains, while the shear test is used to determine the strain hardening for large strains and to calibrate the fracture criterion. Finite Element (FE) calculations with shell and brick elements are performed using the non-linear FE code LS–DYNA. The local strains in the shear zone and the nominal shear stress-elongation characteristics obtained by experiments and FE simulations are compared, and, in general, good agreement is obtained. It is demonstrated how the strain hardening at large strains and the Cockcroft–Latham fracture criterion can be calibrated from the in-plane shear test with the aid of non-linear FE analyses. An erratum to this article can be found at     

基于三维DIC方法的高强钢拉伸力学性能测定

高强度钢在建筑等工程领域发挥着极为重要的作用,因此准确测定其力学性能具有至关重要的意义．鉴于传统机械引伸计在小尺寸试样变形测试中的不便性,利用三维数字图像相关(3D-DIC)方法,对8.8级螺栓和Q690钢这两类试样在单轴拉伸试验全过程中的变形进行了测试,分别得到了应力-应变曲线、弹性模量、屈服强度、强度极限、断后延伸率和断面收缩率,由于试样在屈服阶段应变增加而应力基本不变,因此同时研究了该阶段中试样从弹性变形演化到塑性变形的发展规律．实验结果表明三维DIC在小尺寸试样力学性能测试方面具有很强的优越性,可用来灵活地测量变形并研究变形的演化规律．     

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...     

Correlation between swift effects and tension–compression asymmetry in various polycrystalline materials

The Swift phenomenon, which refers to the occurrence of permanent axial deformation during monotonic free-end torsion, has been known for a very long time. While plastic anisotropy is considered to be its main cause, there is no explanation as to why in certain materials irreversible elongation occurs while in others permanent shortening is observed.In this paper, a correlation between Swift effects and the stress–strain behavior in uniaxial tension and compression is established. It is based on an elastic–plastic model that accounts for the combined influence of anisotropy and tension–compression asymmetry. It is shown that, if for a given orientation the uniaxial yield stress in tension is larger than that in compression, the specimen will shorten when twisted about that direction; however, if the yield stress in uniaxial compression is larger than that in uniaxial tension, axial elongation will occur. Furthermore, it is shown that on the basis of a few simple mechanical tests it is possible to predict the particularities of the plastic response in torsion for both isotropic and initially anisotropic materials. Unlike other previous interpretations of the Swift effects, which were mainly based on crystal plasticity and/or texture evolution, it is explained the occurrence of Swift effects at small to moderate plastic strains. In particular, the very good quantitative agreement between model and data for a strongly anisotropic AZ31–Mg alloy confirm the correlation established in this work between tension–compression asymmetry and Swift effects. Furthermore, it is explained why the sign of the axial plastic strains that develop depends on the twisting direction.     

Effect of triaxial stress constraint on the deformation and fracture of polymers

One purpose of this paper is to give a brief overview on the research status of deformation, fracture and toughening mechanisms of polymers, including experimental, theoretical and numerical studies. Emphasis is on the more recent progresses of micromechanics of rubber particle cavitation and crazing, and the development of fracture criteria for ductile polymers. The other purpose is to study the effect of triaxial stress constraint on the deformation and fracture behavior of polymers. Polycarbonate (PC), acrylonitrile-butadienestyrene (ABS) and PC/ABS alloy are considered in this investigation. A series of circumferentially blunt-notched bars are used to experimentally generate different triaxial stress fields. The fracture surfaces of specimens with different notch radius are examined by scanning electron microscope (SEM) to study the fracture and toughening mechanisms of polymer alloy. It is shown that the triaxial stress constraint has a significant effect on the deformation, fracture and toughening of PC, ABS and PC/ABS alloy. We will also discuss the extent to which a micromechanics criterion proposed by the first author can serve as a fracture criterion for ductile polymers. A new ductile fracture parameter is emphasized, which can be employed to evaluate the fracture ductility of polymers. Stress state independence of the parameter for the PC, ABS and PC/ABS alloy has been experimentally verified. The project supported by the National Natural Science Foundation of China (10125212), the Trans-Century Training Program Foundation and the Key Research Fund of the Education Ministry of China (01159)     

在冲击载荷作用下弹塑性圆板的反直观动力行为数值分析

对周边简支理想弹塑性圆板受脉冲载荷作用时的动力行为进行了数值计算与分析,揭示了板类结构反直观动力行为的客观存在性．通过分析发现,随着脉冲强度的增加,存在几个窄的载荷区域,板的响应是反直观的,而且在此附近,结构参数、载荷等因素的微小改变将导致响应模式的很大差异,表明反直观行为对这些参数的极其敏感性．进一步计算表明,这一特殊的动力行为主要与板内力间的相互耦合作用密切相关,同时,卸载后的结构反弹到另一侧时发生较大的反向塑性变形,导致能量的进一步耗散,使板呈现反常的动力响应．这一现象是几何与材料两种非线性相互作用的结果。     

确定微纳米尺度金属薄膜拉伸分叉点的实验研究

为了确定微纳米尺度金属薄膜的拉伸分叉点,本文使用磁控溅射镀膜技术,在PI(聚酰亚胺)基底上沉积500nm厚的铜薄膜,制作薄膜/基底结构拉伸试件。在单轴拉伸作用下,通过测量拉伸加载过程中铜薄膜的电阻变化情况,得到薄膜电阻随应变变化的关系,并与理论推导的结果进行对比分析,从而确定了塑性阶段理论曲线与实验曲线分离的点,即铜薄膜的分叉点。以此为基础,研究了铜薄膜在单轴拉伸作用下的分叉行为。研究结果表明,沉积于PI基底上的微纳米尺度铜薄膜在单轴拉伸下,经过弹性变形阶段后,很快就发生分叉,然后产生破坏,而塑性变形阶段和局部化阶段较短;弹性阶段薄膜的电阻变化速率很小,塑性阶段薄膜的电阻变化速率稍有增大,而当薄膜表面开始出现微裂纹后,电阻变化速率急剧增大。     

基于塑性体积应变的岩石损伤变形特性实验研究

为分析岩石塑性变形与损伤的关系,在定义岩石的初始损伤和临界损伤,提出塑性体积应变分析方法,从而以塑性体积应变为损伤变量,采用归一化方法建立岩石的损伤本构模型。采用递增循环加载实验确定岩石损伤本构模型中的弹性卸载模量和弹性应变比例系数两个参数。通过实验和理论分析得出:当荷载较小时,普通单轴压缩状态下岩石损伤随荷载的增加具有减小趋势,荷载超过一定数值后,岩石损伤才开始增加;单轴递增循环压缩状态下当循环荷载大于约35%峰值强度后,卸载后岩石的损伤具有增加的趋势,小于该荷载之前具有减小的趋势。整个加载过程的理论应力-应变曲线能很好地与实验结果相吻合,在循环加载区间理论结果还能体现出岩石实验结果中的回滞环。     

Role of elasticity in elastic–plastic fracture: Analytical bi-linear crack-tip fields and finite element analysis

A solution for Model-I plane strain crack tip fields in a bi-linear elastic–plastic material is presented. The elastic–plastic Poisson's ratio is introduced to characterize the influence of elastic deformation on the near tip constraint. Attention is focused on the distribution of elastic/plastic strain energy in the sensitive region of the forward sector ahead of a crack tip. The present study shows that the elastic strain energy can be higher than the plastic strain energy in this sensitive sector while large amount of the plastic strain energy develops outside this sector around the crack tip. The effect of elastic deformation in this sensitive region on the structure of crack-tip fields is considerable and the assumption in some important solutions for crack-tip fields reported in literature that the elastic deformation is small and can be ignored is therefore not physically reasonable. Besides, finite element analysis is carried out to validate the analytical solution and good agreement between them is found. It is seen that the present solution with T-stress can properly describe the crack-tip fields under various constraints for different specimens and an analytical relation is established between the critical value of J-integral, J_c, and T-stress for elastic–plastic fracture.     

Complex unloading behavior: Nature of the deformation and its consistent constitutive representation

Complex (nonlinear) unloading behavior following plastic straining has been reported as a significant challenge to accurate springback prediction. More fundamentally, the nature of the unloading deformation has not been resolved, being variously attributed to nonlinear/reduced modulus elasticity or to inelastic/“microplastic” effects. Unloading-and-reloading experiments following tensile deformation showed that a special component of strain, deemed here “Quasi-Plastic-Elastic” (“QPE”) strain, has four characteristics. (1) It is recoverable, like elastic deformation. (2) It dissipates work, like plastic deformation. (3) It is rate-independent, in the strain rate range 10⁻⁴-10⁻²/s, contrary to some models of anelasticity to which the unloading modulus effect has been attributed. (4) To first order, the evolution of plastic properties occurs during QPE deformation. These characteristics are as expected for a mechanism of dislocation pile-up and relaxation. A consistent, general, continuum constitutive model was derived incorporating elastic, plastic, and QPE deformation. Using some aspects of two-yield-function approaches with unique modifications to incorporate QPE, the model was implemented in a finite element program with parameters determined for dual-phase steel and applied to draw-bend springback. Significant differences were found compared with standard simulations or ones incorporating modulus reduction. The proposed constitutive approach can be used with a variety of elastic and plastic models to treat the nonlinear unloading and reloading of metals consistently for general three-dimensional problems.     

Numerical analysis and elastic–plastic deformation behavior of anisotropically damaged solids

The present paper is concerned with the numerical modelling of the large elastic–plastic deformation behavior and localization prediction of ductile metals which are sensitive to hydrostatic stress and anisotropically damaged. The model is based on a generalized macroscopic theory within the framework of nonlinear continuum damage mechanics. The formulation relies on a multiplicative decomposition of the metric transformation tensor into elastic and damaged-plastic parts. Furthermore, undamaged configurations are introduced which are related to the damaged configurations via associated metric transformations which allow for the interpretation as damage tensors. Strain rates are shown to be additively decomposed into elastic, plastic and damage strain rate tensors. Moreover, based on the standard dissipative material approach the constitutive framework is completed by different stress tensors, a yield criterion and a separate damage condition as well as corresponding potential functions. The evolution laws for plastic and damage strain rates are discussed in some detail. Estimates of the stress and strain histories are obtained via an explicit integration procedure which employs an inelastic (damage-plastic) predictor followed by an elastic corrector step. Numerical simulations of the elastic–plastic deformation behavior of damaged solids demonstrate the efficiency of the formulation. A variety of large strain elastic–plastic-damage problems including severe localization is presented, and the influence of different model parameters on the deformation and localization prediction of ductile metals is discussed.     

Suppressed plastic deformation at blunt crack-tips due to strain gradient effects

Large deformation gradients occur near a crack-tip and strain gradient dependent crack-tip deformation and stress fields are expected. Nevertheless, for material length scales much smaller than the scale of the deformation gradients, a conventional elastic–plastic solution is obtained. On the other hand, for significant large material length scales, a conventional elastic solution is obtained. This transition in behaviour is investigated based on a finite strain version of the Fleck–Hutchinson strain gradient plasticity model from 2001. The predictions show that for a wide range of material parameters, the transition from the conventional elastic–plastic to the elastic solution occurs for length scales ranging from 0.001 times the size of the plastic zone to a length scale of the same order of magnitude as the plastic zone.