Investigating the limits of polycrystal plasticity modeling

A material model which describes the rate-dependent crystallographic slip of FCC metals has been implemented into a quasistatic, large deformation, nonlinear finite element code developed at Sandia National Laboratories. The resultant microstructure based elastic–plastic deformation model has successfully performed simulations of realistic looking 3-D polycrystalline microstructures generated using a Potts-model approach. These simulations have been as large as 50,000 elements composed of 200 randomly oriented grains. This type of model tracks grain orientation and predicts the evolution of sub-grains on an element by element basis during deformation of a polycrystal. Simulations using this model generate a large body of informative results, but they have shortcomings. This paper attempts to examine detailed results provided by large scale highly resolved polycrystal plasticity modeling through a series of analyses. The analyses are designed to isolate issues such as rate of texture evolution, the effect of mesh refinement and comparison with experimental data. Specific model limitations can be identified with lack of a characteristic length scale and oversimplified grain boundaries within the modeling framework.     

Propagation and scattering of ultrasonic waves in polycrystals with arbitrary crystallite and macroscopic texture symmetries

A general ultrasonic attenuation model for a polycrystal with arbitrary macroscopic texture and triclinic ellipsoidal grains is described with proper accounting for the anisotropic Green’s function for the reference medium. The texture and the ellipsoidal grain frames in the model are independent and the wave propagation direction is arbitrary. The attenuation coefficients are obtained in the Born approximation accompanied by the Rayleigh and stochastic asymptotes. The scattering model displays statistical anisotropy due to two independent factors: (1) shape of the oriented grains and (2) preferred crystallographic orientation of the grains leading to macroscopic anisotropy of the homogenized reference medium. The model is applicable to most single phase polycrystalline materials that may occur as a result of thermomechanical manufacturing processes leading to different macrotextures and elongated-shaped grains. It predicts the strength of ultrasonic scattering and its dependence on frequency and propagation direction as a function of grain shape, grain crystallographic symmetry and macroscopic texture parameters and provides the texture-induced dependence of macroscopic ultrasonic velocity on propagation angle. It considers proper wave polarizations due to macroscopic anisotropy and scattering-induced transformations of waves with different polarizations. Competing effects of grain shape and texture on the attenuation are observed. In contrast to the macroscopically isotropic case, where in the stochastic regime the attenuation is highest in the direction of the longest ellipsoidal axis of the grain, the wave attenuation in the elongation direction may be suppressed or amplified by the texture with different effects on the quasilongitudinal and quasitransverse waves. The frequency behavior is also interestingly affected by texture: a hump in the total attenuation coefficient is found for the fast quasitransverse wave which is purely the result of macroscopic anisotropy and the existence of two quasitransverse waves; this hump is not observed in the macroscopically isotropic case. Striking differences of the texture effect on the directional dependences of the attenuation coefficients are found at low versus high frequencies.     

基于微结构损伤的珠光体材料本构行为研究

珠光体材料由许多随机取向的珠光体团组成，每一珠光体团又由铁素体片和渗碳体片交替 叠合而成. 实验表明具有较小片层间距的珠光体材料具有较高的强度和寿命. 通过分析构成 珠光体团的各相及界面的损伤特征，利用损伤耗散功的概念，得到了铁素体、渗碳体与界面 损伤的具有统一形式的演化规律，将其嵌入基于细片层微结构和非经典塑性理论的珠光体团 的弹塑性本构方程，利用Hill自洽方法，得到了珠光体材料的损伤本构描述. 所得到的损 伤本构描述显含表征微结构特征的片层间距，容易证明具有较小片层间距的珠光体材料具有 较好的综合力学性能. 对珠光体材料的拉伸和循环拉压特性进行了分析，得到了与实验一 致的结果.     

Micromechanical modeling of the elasto-viscoplastic behavior of semi-crystalline polymers

A micromechanically based constitutive model for the elasto-viscoplastic deformation and texture evolution of semi-crystalline polymers is developed. The model idealizes the microstructure to consist of an aggregate of two-phase layered composite inclusions. A new framework for the composite inclusion model is formulated to facilitate the use of finite deformation elasto-viscoplastic constitutive models for each constituent phase. The crystalline lamellae are modeled as anisotropic elastic with plastic flow occurring via crystallographic slip. The amorphous phase is modeled as isotropic elastic with plastic flow being a rate-dependent process with strain hardening resulting from molecular orientation. The volume-averaged deformation and stress within the inclusions are related to the macroscopic fields by a hybrid interaction model. The uniaxial compression of initially isotropic high density polyethylene (HDPE) is taken as a case study. The ability of the model to capture the elasto-plastic stress-strain behavior of HDPE during monotonic and cyclic loading, the evolution of anisotropy, and the effect of crystallinity on initial modulus, yield stress, post-yield behavior and unloading-reloading cycles are presented.     

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.     

Modeling multi-axial deformation of planar anisotropic elasto-plastic materials,part I: Theory

In sheet metal forming processes local material points can experience multi-axial and multi-path loadings. Under such loading conditions, conventional phenomenological material formulations are not capable to predict the deformation behavior within satisfying accuracy. While micro-mechanical models have significantly improved the understanding of the deformation processes under such conditions, these models require large sets of material data to describe the micromechanical evolution and quite enormous computation expenses for industrial applications. To reduce the drawbacks of phenomenological material models under the multi-path loadings a new anisotropic elasto-plastic material formulation is suggested. The model enables the anisotropic yield surface to grow (isotropic hardening), translate (kinematic hardening) and rotate (rotation of the anisotropy axes) with respect to the deformation, while the shape of the yield surface remains essentially unchanged.Essentially, the model is formulated on the basis of an Armstrong–Frederick type kinematic hardening, the plastic spin theory for the reorientation of the symmetry axes of the anisotropic yield function, and additional terms coupling these expressions. The capability of the model is illustrated with multi-path loading simulations in ‘tension-shear’ and ‘reverse-shear’ to assess its performance with ‘cross’ hardening and ‘Bauschinger’ effects.     

球化退火态重载车轮钢CL70磨损性能及组织演化

对CL70重载车轮钢进行球化退火获得球状珠光体组织. 将组织为片状珠光体和球状珠光体的CL70分别与U75V钢轨钢在滚动摩擦磨损试验机上以相同参数进行干摩擦纯滚动试验. 使用称重法测量磨损量、利用带电子背散射衍射附件的扫描电子显微镜及显微硬度计对两种组织形态的试样运行表面进行组织及硬度变化情况的观察与分析. 结果表明:球状珠光体组织磨损性能不及片状珠光体组织. 二者的磨损机制和强化机制不同，片状珠光体组织以疲劳磨损为主，通过塑性变形和晶粒不断细化至纤维状再到纳米晶，位错不断累积并达到良好的强化效果. 球状珠光体组织以黏着磨损为主，只有铁素体和少量渗碳体变形和碎化，硬度提升主要来自于渗碳体颗粒周围的位错集中，硬化效果较差.      

Fast texture updates in fcc polycrystal plasticity based on a linear active-set-estimate of the lattice spin

The paper presents a framework for a fast computational estimate of the texture evolution in fcc polycrystals. The underlying basis is a Taylor-type approach of rigid-plasticity for fcc crystals, where the decision of slip activity is based on a purely geometric argument in terms of the rate of total deformation. This approach allows a purely kinematic estimate of the texture evolution completely independent of the hardening response of the single crystal grains. We show that such a geometric estimate of the orientation microstructure provides very good approximations when compared with Taylor-type models of rigid viscoplasticity or elasto-plasticity of fcc crystals. It is shown for several deformation modes of polycrystalline aggregates that the geometric approach predicts the texture evolution very well in the range of large strains. In contrast to standard approaches for the analysis of texture, the proposed new method is extremely robust and very fast even for a high number of discrete grain orientations. As a consequence, such an approach provides a perfect base for large scale computations of anisotropy development in polycrystals.     

Multiscale Dynamics of Heterogeneous Media in?the?Peridynamic Formulation

A methodology is presented for investigating the dynamics of heterogeneous media using the nonlocal continuum model given by the peridynamic formulation. The approach presented here provides the ability to model the macroscopic dynamics while at the same time resolving the dynamics at the length scales of the microstructure. Central to the methodology is a novel two-scale evolution equation. The rescaled solution of this equation is shown to provide a strong approximation to the actual deformation inside the peridynamic material. The two scale evolution can be split into a microscopic component tracking the dynamics at the length scale of the heterogeneities and a macroscopic component tracking the volume averaged (homogenized) dynamics. The interplay between the microscopic and macroscopic dynamics is given by a coupled system of evolution equations. The equations show that the forces generated by the homogenized deformation inside the medium are related to the homogenized deformation through a history dependent constitutive relation.     

橡胶材料弹性的一种新的螺旋管模型

建立统计力学模型正确描述材料微观结构与宏观力学特性之间的关系是软物质类材料的最大挑战之一,已有的橡胶材料统计模型尚存在一些不足.文章根据橡胶类材料宏观各向同性、连续均匀和不可压缩特性,结合分子链的非高斯统计模型,提出一种橡胶材料网络结构的力学特性模型.该模型将代表体元上对应点之间的传力路径用一个类螺旋管区域约束的分子链子网络来描述,螺旋管的表面随材料的宏观变形做仿射变形,分子链子网络由方向和长度随机的分子链或链段首尾链接而成,在此基础上由分子链的熵推导出描述材料宏观力学特性的本构关系.通过大量的材料测试数据对本构模型进行拟合验证,拟合结果表明该模型具有非常好的精度,并且在采用两个参数时模型具有非常高的可靠性,仅用单轴拉伸实验数据拟合模型就能准确预测全部3类实验数据.该模型使用了仿射的弯曲管假设,能从微观结构尺度上说明材料的不可压缩特性,避免了直管模型的近似性,为微观尺度的随机性和宏观的均匀性的联系提出一个新的模型.     

Spatial representation of evolving anisotropy at large strains

A phenomenological model for evolving anisotropy at large strains is presented. The model is formulated using spatial quantities and the anisotropic properties of the material is modeled by including structural variables. Evolution of anisotropy is accounted for by introducing substructural deformation gradients which are linear maps similar to the usual deformation gradient. The evolution of the substructural deformation gradients is governed by the substructural plastic velocity gradients in a manner similar to that for the continuum. Certain topics related to the numerical implementation are discussed and a simple integration scheme for the local constitutive equations is developed. To demonstrate the capabilities of the model it is implemented into a finite element code. Two numerical examples are considered: deformation of uniform plate with circular hole and the drawing of a cup. In the two examples it is assumed that initial cubic material symmetry applies to both the elastic and plastic behavior. To be specific, a polyconvex Helmholtz free energy function together with a yield function of quadratic type is adopted.     

Modeling and simulation of magnetic-shape-memory polymer composites

Composites of small magnetic-shape-memory (MSM) particles embedded in a polymer matrix have been proposed as an energy damping mechanism and as actuators. Compared to a single crystal bulk material, the production is simpler and more flexible, as both type of the polymer and geometry of the microstructure can be tuned. Compared to polycrystals, in composites the soft polymer matrix permits the active grains to deform to some extent independently; in particular the rigidity of grain boundaries arising from incompatible orientations is reduced. We study the magnetic-field-induced deformation of composites, on the basis of a continuous model incorporating elasticity and micromagnetism, in a reduced two-dimensional, plane-strain setting. The aim is to give conceptual guidance for the design of composite materials independent of the concrete macroscopic device. Thus, on the background of homogenization theory, we determine the macroscopic behavior by studying an affine-periodic cell problem. An energy descent algorithm is developed, whose main ingredients are a boundary element method for the computation of the elastic and magnetic field energies; and a combinatorial component reflecting the phase transition in the individual particles, which are assumed to be of single-domain type. Our numerical results demonstrate the behavior of the macroscopic material properties for different possible microstructures, and give suggestions for the optimization of the composite.     

Induced anisotropy in large ice shields: theory and its homogenization

For polycrystalline ice, an isothermal flow law is derived from microscopic considerations concerning constitutive equations and kinematic assumptions. On the basis of an elasto-plastic decomposition of the deformation gradient on the grain level and by assuming a continuous distribution of different orientated grains in the vicinity of each material point the classical macroscopic field quantities are obtained by calculating the weighted mean values of the associated microscopic quantities. The weighting function is represented by a so called Orientation Distribution Function (ODF). For the general two dimensional (plane and rotationally symmetric) flow regime analytical representations of the ODF are derived under the assumption of a uniform stress distribution over all polycrystals (Sachs-Condition) and a plane or rotationally symmetric orientation distribution. Additionally, the influence of the macroscopic constitutive relations on the microscopic level is restricted to isotropic parts only. Simple examples are used to demonstrate the ability of the ODF to perform the evolving texture. The microscopic constitutive relation for the dissipation potential is assumed to be an objective function of the stress deviator and is expressed as a polynomial law up to the power , as proposed by Lliboutry (1993). A second order structure tensor which depends on the ODF is introduced to consider induced anisotropy. The resulting macro fluidities (inverse viscosities) are then calculated from the analytical representation of the ODF for the case of uniaxial loading underlying linear and nonlinear material behaviour. Received March 30, 1998     

A brick model for asperity sintering and creep of APS TBCs

A micromechanical model is developed for the microstructural evolution of an air plasma sprayed (APS), thermal barrier coating: discrete, brick-like splats progressively sinter together at contacting asperities and also undergo Coble creep within each splat. The main microstructural features are captured: the shape, orientation and distribution of asperities between disc-shaped splats, and the presence of columnar grains within each splat. Elasticity is accounted for at the asperity contacts and within each splat, and the high contact compliance explains the fact that APS coatings have a much lower modulus (and thermal conductivity) than that of the parent, fully dense solid. The macroscopic elastic, sintering and creep responses are taken to be transversely isotropic, and remain so with microstructural evolution. Despite the large number of geometric and kinetic parameters, the main features of the behaviour are captured by a small number of characteristic material timescales: these reveal the competition between the deformation mechanisms and identify the rate controlling processes for both free and constrained sintering. The evolution of macroscopic strain, moduli and asperity size is compared for free and constrained sintering, and the level of in-plane stress within a constrained coating is predicted.     

A variational multiscale constitutive model for nanocrystalline materials

This paper presents a variational multi-scale constitutive model in the finite deformation regime capable of capturing the mechanical behavior of nanocrystalline (nc) fcc metals. The nc-material is modeled as a two-phase material consisting of a grain interior phase and a grain boundary effected zone (GBAZ). A rate-independent isotropic porous plasticity model is employed to describe the GBAZ, whereas a crystal-plasticity model which accounts for the transition from partial dislocation to full dislocation mediated plasticity is employed for the grain interior. The constitutive models of both phases are formulated in a small strain framework and extended to finite deformation by use of logarithmic and exponential mappings. Assuming the rule of mixtures, the overall behavior of a given grain is obtained via volume averaging. The scale transition from a single grain to a polycrystal is achieved by Taylor-type homogenization where a log-normal grain size distribution is assumed. It is shown that the proposed model is able to capture the inverse Hall-Petch effect, i.e., loss of strength with grain size refinement. Finally, the predictive capability of the model is validated against experimental results on nanocrystalline copper and nickel.     

Model of plastic anisotropy evolution with texture-dependent yield surface

Model of evolution of plastic anisotropy due to crystallographic texture development, in metals subjected to large deformation processes, is presented. The model of single grain with the regularized Schmid law proposed by Gambin is used. Evolution of crystallographic texture during drawing, rolling and pure shear is calculated. Phenomenological texture-dependent yield surface for polycrystalline sheets is proposed. Evolution of this yield surface is compared with evolution of phenomenological higher order yield surfaces proposed by Hill and Barlat with Lian for drawing, rolling and pure shear processes. The change of the Hill yield surface and the Barlat–Lian yield surface is obtained by replacing material parameters present in these conditions by texture-dependent functions.