Macroscopic theory and nonlinear finite element analysis of micromechanics of single crystals at finite strains

The present paper is concerned with an efficient framework for a nonlinear finite element procedure for the macroscopic rate-independent and rate-dependent analysis of micromechanics of metal single crystals undergoing finite elastic-plastic deformations which is based on the assumption that inelastic deformation is solely due to crystallographic slip. The formulation relies on a multiplicative decomposition of the material deformation gradient into incompressible elastic and plastic as well as a scalar valued volumetric part. Furthermore, the crystal deformation is described as arising from two distinct physical mechanisms, elastic deformation due to distortion of the lattice and crystallographic slip due to shearing along certain preferred lattice planes in certain preferred lattice directions. Macro- and microscopic stress measures are related to Green’s macroscopic strains via a hyperelastic constitutive law based on a free energy potential function, whereas plastic potentials expressed in terms of the generalized Schmid stress lead to a normality rule for the macroscopic plastic strain rate. Estimates of the microscopic stress and strain histories are obtained via a highly stable and very accurate semi-implicit scalar integration procedure which employs a plastic predictor followed by an elastic corrector step, and, furthermore, the development of a consistent elastic-plastic tangent operator as well as its implementation into a nonlinear finite element program will also be discussed. Finally, the numerical simulation of finite strain elastic-plastic tension tests is presented to demonstrate the efficiency of the algorithm.     

Nonlinear constitutive equations for transient creep of viscoelastic polymers including the effect of hydrostatic pressure

The behaviour of polymers is known to be significantly influenced by the hydrostatic pressure in creep deformation or elastic-plastic deformation. The effect of the third stress invariant on the nonlinear viscoelastic deformation is much smaller than that of the hydrostatic pressure. In this paper, a constitutive equation for transient creep is proposed, which includes the effect of the hydrostatic pressure on the yield function. The creep and plastic strains or the creep strain rate converge to zero with increasing hydrostatic pressure. The proposed constitutive equation is in good agreement with the actual creep data of cellulose nitrate and cellulose acetate, under various combinations of superimposed tensile and hydrostatic loadings.     

Behavior of PVC and HDPE under highly triaxial stress states: An experimental and numerical study

This paper addresses the deformation of axisymmetric tensile bars, made of mineral-filled PVC and HDPE, with and without pre-machined notch. The purpose of the study is both to investigate the mechanical behavior under various stress triaxialities, induced by different notch radii, and the capabilities of a phenomenological constitutive model. The yield stress and the plastic dilation have been chosen as the key response parameters from the tests in order to evaluate the yield function and the flow potential of the constitutive model. It is found that the yield stress and the plastic dilation of the mineral-filled PVC are highly sensitive to hydrostatic pressure. The yield stress of the HDPE hardly changes, while the plastic dilation increases with increasing stress triaxiality. The experimentally observed plastic dilation of both materials is related to void growth. The constitutive model reproduces force–displacement relationships for both materials with reasonable accuracy. However, the numerical simulations underestimate the plastic dilation for high stress triaxialities.     

Two-scale analysis for deformation-induced anisotropy of polycrystalline metals

The anisotropic macroscopic mechanical behavior of polycrystalline metals is characterized by incorporating the microscopic constitutive model of single crystal plasticity into the two-scale modeling based on the mathematical homogenization theory, which enables us to derive both micro- and macro-scale governing equations. The two-scale simulations are conducted to evaluate the macroscopic anisotropy induced by microscopic plastic deformation histories of the polycrystalline aggregate. In the simulations, the representative volume element (RVE) composed of several crystal grains is uniformly loaded in one direction, unloaded to macroscopically zero stress in a certain stage of deformation and then re-loaded in the different directions. The last re-loading calculations provide different macroscopic responses of the RVE, which can be the appearance of material anisotropy. We then try to examine the effects of the intergranular and intragranular behaviors on the anisotropy by means of various illustrations of microscopic plastic deformation process without referring to the change of crystallographic orientations.     

Fracture modelling of WC-Co hardmetals using crystal plasticity theory and the Gurson model

The behaviour of edge cracks under Mode I loading in the WC–Co material system is studied using the finite element method (FEM). This work focuses on ductile failure mechanisms in the Co binder. A micromechanical approach is taken whereby Co layers are modelled explicitly. An embedding technique is employed. Crystal plasticity theory and J₂ flow theory are used to represent plastic deformation in Co ligaments. Areas of high hydrostatic stress, triaxiality and accumulated slip or effective plastic strain are identified within the binder material. The Gurson model is used to model crack growth in the Co ligaments. Fracture resistance curves are obtained giving a relationship between macroscopic material behaviour and microscopic failure mechanisms. Factors effecting the crack growth in single and multiple ligaments are identified.     

Multiscale prediction of mechanical behavior of ferrite–pearlite steel with numerical material testing

Multiscale mechanical behaviors of ferrite–pearlite steel were predicted using numerical material testing (NMT) based on the finite element method. The microstructure of ferrite–pearlite steel is regarded as a two‐component aggregate of ferrite crystal grains and pearlite colonies. In NMT, the macroscopic stress–strain curve and the deformation state of the microstructure were examined by means of a two‐scale finite element analysis method based on the framework of the mathematical homogenization theory. The microstructure of ferrite–pearlite steel was modeled with finite elements, and constitutive models for ferrite crystal grains and pearlite colonies were prepared to describe their anisotropic mechanical behavior at the microscale level. While the anisotropic linear elasticity and the single crystal plasticity based on representative characteristic length have been employed for the ferrite crystal grains, the constitutive model of a pearlite colony was newly developed in this study. For that reason, the constitutive behavior of the pearlite colony was investigated using NMT on a smaller scale than the scale of the ferrite–pearlite microstructure, with the microstructure of the pearlite colony modeled as a lamellar structure of ferrite and cementite phases with finite elements. On the basis of the numerical results, the anisotropic constitutive model of the pearlite colony was formulated based on the normal vector of the lamella. The components of the anisotropic elasticity were estimated with NMT based on the finite element method, where the elasticity of the cementite phase was numerically evaluated with a first‐principles calculation. Also, an anisotropic plastic constitutive model for the pearlite colony was formulated with two‐surface plasticity consisting of yield functions for the interlamellar shear mode and yielding of the overall lamellar structure. After addressing the microscopic modeling of ferrite–pearlite steel, NMT was performed with the finite element models of the ferrite–pearlite microstructure and with the microscopic constitutive models for each of the components. Finally, the results were compared with the corresponding experimental results on both the macroscopic response and the microscopic deformation state to ascertain the validity of the numerical modeling. Copyright © 2011 John Wiley & Sons, Ltd.     

Relationship between burgers vectors of dislocations and plastic strain localization patterns in compression-strained alkali halide crystals

Plastic strain localization patterns in compression-strained alkali halide (NaCl, KCl, and LiF) crystals have been studied using a double-exposure speckle photography technique. The main parameters of strain localization autowaves at the linear stages of deformation hardening in alkali halide crystals have been determined. A quantitative relationship between the macroscopic parameters of plastic flow localization and microscopic parameters of strained alkali halide crystals has been established.     

Modeling of Nonlinear Mechanical Behavior for 3D Needled C/C-SiC Composites Under Tensile Load

This paper established a macroscopic constitutive model to describe the nonlinear stress–strain behavior of 3D needled C/C-SiC composites under tensile load. Extensive on- and off-axis tensile tests were performed to investigate the macroscopic mechanical behavior and damage characteristics of the composites. The nonlinear mechanical behavior of the material was mainly induced by matrix tensile cracking and fiber/matrix debonding. Permanent deformations and secant modulus degradation were observed in cyclic loading-unloading tests. The nonlinear stress–strain relationship of the material could be described macroscopically by plasticity deformation and stiffness degradation. In the proposed model, we employed a plasticity theory with associated plastic flow rule to describe the evolution of plastic strains. A novel damage variable was also introduced to characterize the stiffness degradation of the material. The damage evolution law was derived from the statistical distribution of material strength. Parameters of the proposed model can be determined from off-axis tensile tests. Stress–strain curves predicted by this model showed reasonable agreement with experimental results.     

Analysis of shear localization in porous materials based on a lower bound approach

The conditions for shear localization in porous materials are examined based on the lower bound approach proposed by the present authors. The influence of void nucleation and material inhomogeneity on the critical strain to localization is investigated and an improved plastic strain controlled nucleation criterion is proposed which makes it possible to include the influence of hydrostatic stress and avoid the ambiguity caused by the non-normality flow rule. The constitutive behavior of porous materials (including the yield loci, the void growth rate and the stress-strain curve) is also examined and comparison is made between the theoretical result and the experiment. Finally the instability and fracture of sintered CP Ti alloy and AISI4340 steels is analyzed and results are compared with the experiment.     

On the nature of plastic deformation generated by hydrostatic pressure in silicon single crystals

Macroscopic plastic deformation of silicon single crystals, caused by annealing at hydrostatic pressure and high temperature, was studied by X-ray topography and transmission electron microscopy. The analysis is given of elastic and thermal properties of material around surface cracks and scratches from which deformation process is propagated. The idea of elastic misfit between damaged self-strained material at cracks and scratches and defect-free silicon matrix, is introduced. On the basis of theoretical and experimental data it is concluded that the plastic deformation of silicon at high pressure consists of two processes. The first is a loss of coherency of cracks and scratches by the emission of dislocations at misfitting second phase precipitates present in silicon. The second is the macroscopic yielding from incoherent cracks and scratches at lower elastic strain energies.The presented mechanism explains also the deformation behaviour of silicon crystals subjected to tensile stress at high temperatures; the generation and propagation of dislocations at oxide precipitates before the macroscopic yielding [3].     

混凝土材料的粘塑性损伤统一本构模型

发展了只适用于金属类材料的粘塑性统一本构理论,借助经典塑性理论的基本法则,建立了无屈服面和无破坏面的混凝土材料的粘塑性损伤统一本构模型。放弃了传统统一本构模型的静水压不影响非弹性变形和无非弹性体积膨胀的基本假设;发展了间断的经典塑性乘子,使其为连续函数,并提出了相应的构造方法,拓展定义了其物理意义。数值模拟显示,此本构模型能够模拟混凝土材料的率相关性质、在压缩载荷作用下的体积膨胀现象和由损伤引起的应力软化和刚度退化现象。     

Construction of a constitutive model in calculations of pressure-dependent material

To make constitutive modeling of materials more approaching reality, a new theory is proposed, in which a corresponding constitutive model can be constructed and characterized experimentally via two steps, one relates to the characterization of yielding behavior of material, and the second relates to the characterization of plastic flow of material deformation. The constitutive model involves two functions, yield function and plastic potential. A relationship between two functions is suggested, therefore, a corresponding plastic potential can be easily created after we have an appropriate yield function. To consider the non-isotropic hardening feature of strength differential in the constitutive model, the concept of equivalent hardening state is introduced, and then, multi-experimental flow stresses can be addressed in the model. When pressure sensitive materials are taken as an example in discussions, the Drucker–Prager yield function is employed to express the yielding behavior of material and a differently experimental characterization of the model is created as the corresponding plastic potential to describe the feature of plastic flow of material. This simple constitutive model can reproduce three sets of experimental results; including two flow-stresses and the volumetric plastic strain. The constitutive model can also well predict stress–strain relations with different pressures loaded on the material. Study shows that the feature of plastic flow is not that sensitive to the pressure loaded on the material when the yielding stress is.     

基于动态再结晶37CrS4特种钢的流变应力预测模型

使用Gleeble-1500D热模拟实验机对37CrS4特种钢进行单道次热压缩实验,研究了37CrS4钢在950~1100℃和0.01 s^-1~10 s^-1条件下的热压缩流变应力行为。结果表明：这种钢的真应力应变曲线出现了明显的高温塑性变形动态再结晶行为;热变形后的微观组织为典型的板条状马氏体,发生动态再结晶行为的临界应变值与峰值应变比值为0.77162,拟合相关性R²=0.9576;其软化机制为动态回复与动态再结晶的共同作用。引入Zener-Hollomon参数(Z参数)建立再结晶动力学模型,得到了37CrS4特种钢基于动态回复、动态再结晶的分段式流变应力本构模型。本构模型的平均相关性R²=0.9756,分段式本构模型的预测应力与实验应力具有较高的一致性,能较为准确的预测37CrS4高温塑性变形时流变应力的变化。     

Modeling multiaxial impact behavior of a glassy polymer

In many applications of polymers, impact performance is a primary concern. Impact tests experimentally performed on molding prototypes yield useful data for a particular structural and impact loading case. But, it is generally not practical in terms of time and cost to experimentally characterize the effects of a wide range of design variables. A successful numerical model for impact deformation and failure of polymers can provide convenient and useful guidelines on product design and therefore decrease the disadvantages that arise from purely experimental trial and error. Since the specimen geometry and loading mode for multiaxial impact test provides a close correlation with practical impact conditions and can conveniently provide experimental data, the first step of validating a numerical model is to simulate this type of test. In this paper, we create a finite element analysis model using ABAQUS/Explicit to simulate the deformation and failure of a glassy ABS (acrylonitrile-butadiene-styrene) polymer in the standard ASTM D3763 multiaxial impact test. Since polymers often exhibit different behavior in uniaxial tensile and compression tests, the uniaxial compression or tensile tests are generally not representative of the three-dimensional deformation behavior under impact loading. A hydrostatic pressure effect (controlled by the parameter γ) is used to generalize a previously developed constitutive model ("DSGZ" model) so that it can describe the entire range of deformation behavior of polymers under any monotonic loading modes. The generalized DSGZ model and a failure criterion are incorporated in the FEA model as a user material subroutine. The phenomenon of thermomechanical coupling during plastic deformation is considered in the analysis. Impact load vs. displacement and impact energy vs. displacement curves from FEA simulation are compared with experimental data. The results show good agreement. Finally, equivalent stress, strain, strain rate and temperature distributions in the polymer disk are presented. Electronic Publication     

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.     

Constitutive relationship and hot deformation behavior of Armco-type pure iron for a wide range of temperature

The hot deformation behavior and constitutive relationship of Armco-type pure iron were investigated using isothermal compression tests with a wide range of temperature and strain rate ranging from 923 to 1523 K, and 0.1 to 10 s⁻¹, respectively. When deformed with a single phase, the flow stress of Armco-type pure iron increases accompanied by the increase of strain rate and the decrease of deformation temperature. Instability phenomenon of Armco-type pure iron appears when deformed with dual phase. γ-Fe undergoes completed discontinuous dynamic recrystallization (dDRX) at all hot deformation conditions. α-Fe undergoes uncompleted dDRX process at high temperature and low strain rate, however, dynamic recovery (DRV) process is the main restoration process for α-Fe at low temperature and high strain rate. The modified Arrhenius-type constitutive equation considering strain compensation is used to describe the flow stress of γ-Fe and α-Fe. From correlation coefficient (R), root mean square error (RMSE) and average absolute relative error (AARE), the predictability of the constitutive equation for the two phases of Armco-type pure iron was evaluated.     

Disorder is good for you: the influence of local disorder on strain localization and ductility of strain softening materials

We formulate a generic concept model for the deformation of a locally disordered, macroscopically homogeneous material which undergoes irreversible strain softening during plastic deformation. We investigate the influence of the degree of microstructural heterogeneity and disorder on strain localization (formation of a macroscopic shear band) in such materials. It is shown that increased microstructural heterogeneity delays strain localization and leads to an increase of the plastic regime in the macroscopic stress–strain curves. The evolving strain localization patterns are characterized.