压力敏感材料中的空洞长大研究及其在页岩及高分子材料中的应用（英文）

主要研究压力敏感材料中含内压的空洞长大,如页岩或者高分子材料。采用数值方法研究含内压空洞的对称和非对称球形和柱形胞元的宏观力学行为。结果表明,压力敏感性及其空洞内压将极大影响空洞的形核与长大。在球形胞元情形中未出现柱形胞元的单轴拉伸现象。将胞元有限变形的数值计算结果与基于近期提出的考虑压力敏感材料中空洞长大的塑形力学模型的分析结果进行了对比。     

超塑性材料约束胀形中的空洞损伤与变形局部化

将含有二阶段空洞长大模型的本构关系引入大变形刚黏塑性有限元中，研究了空洞敏感材料向锥台形凹模内超塑约束胀形时空洞化损伤与变形局部化行为，详细阐述静水背压Ｐｈ、初始空洞长大速率β＿０以及模具几何形状（锥角θ，模腔高度Ｈｐ）对局部化以及空洞断裂行为的影响，给出实现完全贴模条件下Ｐｈ－θ，Ｐｈ－β＿０，Ｈｐ－θ以及Ｐｈ－Ｈｐ间临界关系。     

热局部非平衡条件下含柱形空洞横观各向同性饱和多孔介质的热应力分析

提出了一个热局部非平衡条件下横观各向同性多孔介质的弹性力学模型,研究了含柱形空洞的无限大多孔介质在冷对流边界条件下的孔隙压力和固相热应力.应用Laplace变换反演法数值分析了热局部非平衡及材料的各向异性对孔隙压力和固相热应力的影响.结果表明:孔隙压力和固相热应力随着横向热膨胀系数的增大而显著增大,而弹性模量的各向异性对孔隙压力和固相热应力的影响则是微弱的.同时,结果还证实了在Biot数为中等值范围内,热局部非平衡效应是非常明显的.     

受有两级空洞损伤时韧性材料的力学行为

本文利用大应变有限元方法研究了两级空洞对韧性材料的损伤作用.模型是以轴对称圆柱基体作为胞元,内含一初始的球型空洞.基体内的应力/应变随胞元外载的增大而达到临界状态,从而在围绕初级空洞的基体内将萌生次级空洞.后者是由空单元实现的.两级空洞的交互作用被证明将促进材料中的空洞化现象从而加速损伤并导至材料的总体弹性模量值在临近破断时急剧下降.     

动态冲击下铝板中不同深度空洞演化的有限元分析

通过建立样品厚度为飞片厚度2倍的铝板撞击有限元模型,采用Johnson-Cook本构方程研究了纯铝材料中不同深度空洞的演化过程.研究结果表明:微空洞从杂质周围形核并呈近球形长大;由于靶板不同深度拉伸应力的峰值以及加载持续时间不同,空洞的长大速率与其在靶板的位置有关;由于冲击过程中没有形成三向拉应力,材料表面的空洞长大速度为零;靶板中间层位置首先出现拉伸应力,最先开始长大,靶板中间层位置的三向拉应力最大且作用时间较长,空洞长大速度最快;从靶板中间往两表面的方向,空洞依次开始长大,长大速度逐渐减小;模拟结果与实验观察结果相符,为研究动态冲击下空洞的演化提供参考.     

基于球形压入法提取材料的塑性力学参数

基于球形压入的工作方式,重点研究材料塑性力学参数的表征方法. 首先,通过对球压入可测量的综合评价,选取能量比(可释放功和压入总功之比)作为主要分析参数; 其次,利用孔洞模型、量纲分析和数值模拟等工具,定义特定的代表性应变,建立起能量比和材料塑性力学参数之间的关系式, 由此,提出一种能提取材料屈服应力和硬化指数的力学表征方法,该方法避免了对接触半径的测量,确保了方法的可操作性,并通过参数重组提高其稳定性; 最后,选用45号钢和6061铝合金进行压入试验,与拉伸试验结果比对显示: 该方法识别的塑性力学参数能满足工程测试需要.      

含空洞非线性材料的本构势和空洞扩展率

本文基于体胞模型的解析分析,分析了含空洞非线性材料的宏观本构势,得到了各种幂硬化指数下宏观应力和基体平均流变应力之间的相关曲线.当基体是遵循经典塑性全量理论时,这些曲线方程就是一簇依赖于空洞体积比和硬化指数的屈服面方程.当基体是粘性体时,这些方程就是粘性约束方程.通过曲线拟合的方法,本文发展了修正的Gurson方程,使之适合于不同硬化指数的情况.最后本文计算了粘性体中空洞的相对扩展率,结果与已有体胞模型的数值模拟计算结果相当一致.     

含石量对土石混合体压桩承载力影响的离散元分析

土石混合体是介于土体和岩体之间的一种非均质、非连续和非线性的特殊工程地质材料,其在压桩贯入过程中的承载力受含石量的影响非常显著。本文分别采用球形颗粒和非规则镶嵌组合颗粒模拟土体颗粒和块石,对不同含石量下压桩贯入过程进行离散元数值分析。计算结果表明,桩柱阻力及其波动规律在不同含石量下有很大的差别。高含石量下的阻力要明显大于低含石量下的阻力,且其波动性也更加明显。通过对土石混合体内部力链结构的细观分析,揭示了压桩贯入过程中承载力随含石量变化的内在机理。以上研究有助于分析土石混合体材料的宏观力学行为,深入研究其在复杂工程条件下的力学特性。     

初始应力状态对材料层裂破坏特性影响研究

通过对球面飞片加载条件下的应力/应变状态分析表明采用施加径向应变方法可以近似模拟球面加载的受力过程. 采用过盈配合的热装配方法对平面样品施加了径向预应变,一维平面应变气炮实验结果显示初始预应力(变)明显降低了LY12铝层裂强度. 从空洞长大基本原理出发分析了各向异性受力条件下空洞长大的路径和所消耗能量不同于各向同性应力加载.通过数值模拟对含损伤的材料本构模型进行分析,得到了材料层裂强度与其外部宏观应力场密切相关,也间接的与构型相关的结论.      

空心材料导热性能预测研究

本文建立了一种预测空心材料导热性的方法。研究了空心材料的导热性。用柱形空心材料分析了体分比和孔洞的排列方式对整体材料导热性的影响，用圆柱形、方柱形空心材料和含裂纹材料，分析了空心形状对材料导热性的影响。同他人的实验结果和某些现有的理论模型比较表明，本文方法是有效的。本文的结果能够很好地解释实验结果。     

Continuum modeling of a porous solid with pressure-sensitive dilatant matrix

The pressure-sensitive plastic response of a material has been studied in terms of the intrinsic sensitivity of its yield stress to pressure and the presence and growth of cavities. This work focuses on the interplay between these two distinctly different mechanisms and the attendant material behavior. To this end, a constitutive model is proposed taking both mechanisms into account. Using Gurson's homogenization, an upper bound model is developed for a voided solid with a plastically dilatant matrix material. This model is built around a three-parameter axisymmetric velocity field for a unit sphere containing a spherical void. The void is also subjected to internal pressure; this can be relevant for polymeric adhesives permeated by moisture that vaporizes at elevated temperatures. The plastic response of the matrix material is described by Drucker–Prager's yield criterion and an associated flow rule. The resulting yield surface and porosity evolution law of the homogenized constitutive model are presented in parametric form. Using the solutions to special cases as building blocks, approximate models with explicit forms are proposed. The parametric form and an approximate explicit form are compared against full-field solutions obtained from finite element analysis. They are also studied for loading under generalized tension conditions. These computational simulations shed light on the interplay between the two mechanisms and its enhanced effect on yield strength and plastic flow. Among other things, the tensile yield strength of the porous solid is greatly reduced by the internal void pressure, particularly when a liquid/vapor phase is the source of the internal pressure.     

The size dependence of micro-toughness in ductile fracture

Micro-toughness in ductile fracture is defined as the plastic work dissipated per unit fracture surface area in the material separation processes of void growth and coalescence. A micromechanics model for the estimation of the size dependence of micro-toughness in ductile fracture is presented. Size effects are incorporated in the model using the conventional mechanism-based strain gradient plasticity (CMSG) theory. A finite element model of an axisymmetric representative unit cell with an initial spherical void is used to validate model predictions. Two characteristic length scales emerge from the model. The initial void radius sets the scale for the initial spherical void growth. For the subsequent void coalescence, the scale is set by the width of the intervoid ligament. Energy dissipation in ductile fracture is found to be dominated by the mechanisms of coalescence, and the micro-toughness in ductile fracture is found to be size dependent for dimple sizes approximately one order of magnitude larger than the material length scale.     

The evolution of voids in the plasticity strain hardening gradient materials

The main aim of this paper is to opens out the meso-mechanism of void growth and coalescence in the matrix materials with graded strain-hardening exponent distribution. For this end, detailed finite element computations of a representative cylindrical cell containing a spherical void have been carried out. According to the FE analyses, significant effects of the strain-hardening exponent gradient (SEG) in the matrix on the void growth and coalescence are revealed: (1) In the homogeneous materials, the void growth and coalescence are slightly dependent on the strain-hardening exponent, however, the SEG distribution in the matrix can increase remarkably the void growth rate and decrease seriously the void coalescence strain. (2) The critical void shapes in the homogeneous materials are mainly governed by the macroscopic stress triaxiality, but due to earlier plastic flow localization in the softer matrix layer, the SEG distribution in the matrix has very significant effects on the deformed void shapes, especially when the stress triaxiality is lower. (3) When the triaxial stress levels are lower, in the homogeneous materials, the shape change mode of the void evolution is dominate so the void growth rate is very low; however, the SEG distribution in the matrix can bring the volume change mode out, as a result of increasing the void growth rate. (4) Comparisons of the numerical results with the existing damage model indicate that the classic damage model cannot give satisfying prediction to the void growth in both the homogeneous strain-hardening matrix and the SEG materials. On the basis of large numbers of numerical computations, a new damage model, which can uniformly describe the void growing in the homogeneous and plasticity gradient materials, is suggested. A mass of element computations have validated that the new damage model can give satisfying agreement with the FE results of cell model.     

Void growth and coalescence in single crystals

Void growth and coalescence in single crystals are investigated using crystal plasticity based 3D finite element calculations. A unit cell involving a single spherical void and fully periodic boundary conditions is deformed under constant macroscopic stress triaxiality. Simulations are performed for different values of the stress triaxiality, for different crystal orientations, and for low and high work-hardening capacity. Under low stress triaxiality, the void shape evolution, void growth, and strain at the onset of coalescence are strongly dependent on the crystal orientation, while under high stress triaxiality, only the void growth rate is affected by the crystal orientation. These effects lead to significant variations in the ductility defined as the strain at the onset of coalescence. An attempt is made to predict the onset of coalescence using two different versions of the Thomason void coalescence criterion, initially developed in the framework of isotropic perfect plasticity. The first version is based on a mean effective yield stress of the matrix and involves a fitting parameter to properly take into account material strain hardening. The second version of the Thomason criterion is based on a local value of the effective yield stress in the ligament between the voids, with no fitting parameter. The first version is accurate to within 20% relative error for most cases, and often more accurate. The second version provides the same level of accuracy except for one crystal orientation. Such a predictive coalescence criterion constitutes an important ingredient towards the development of a full constitutive model for porous single crystals.     

Void growth and coalescence in ductile solids with stage III and stage IV strain hardening

State of the art ductile fracture models often rely on simple power laws to describe the strain hardening of the matrix material. Power laws do not distinguish between the two main stages of hardening observed in polycrystals, referred to as stage III and stage IV hardening, and which emerge from the evolution of the dislocation substructure. The aim of this study is to couple a physics based strain hardening law including these two stages to a micromechanics based ductile damage model. One of the main motivations is that, the stage IV constant hardening rate stage, occurring only at large strain, will be attained in most ductile failure problems if not at the overall level of deformation, at least locally around the growing voids. Furthermore, proper modelling of the stage III involving dislocation storage and recovery terms and the transition to stage IV provides a link with the underlying physical mechanisms of deformation and with the microstructure. First, in order to evaluate the effects of the stage III and stage IV hardening on void growth and coalescence, an extensive parametric study is performed on two-dimensional (2D) axisymmetric finite element (FE) unit cell calculations, using a Kocks-Mecking type hardening law. The cell calculations demonstrate that accounting for the stage IV hardening can have a profound effect on delaying void coalescence and increasing the ductility. The magnitude of the recovery term during stage III has also a significant effect on the void growth rate. Then, the Kocks-Mecking law is incorporated into the Gologanu-Leblond-Devaux (GLD) porous plasticity model supplemented by two different versions of the Thomason void coalescence criterion. The predictions of the damage model are in good agreement with the results of the FE calculations in terms of the stress-strain curves, the evolution of void shape and porosity, as well as the strain value at the onset of void coalescence.     

Modeling of ductile fracture: Application of the mechanism-based concepts

This paper summarizes our recent studies on modeling ductile fracture in structural materials using the mechanism-based concepts. We describe two numerical approaches to model the material failure process by void growth and coalescence. In the first approach, voids are considered explicitly and modeled using refined finite elements. In order to predict crack initiation and propagation, a void coalescence criterion is established by conducting a series of systematic finite element analyses of the void-containing, representative material volume (RMV) subjected to different macroscopic stress states and expressed as a function of the stress triaxiality ratio and the Lode angle. The discrete void approach provides a straightforward way for studying the effects of microstructure on fracture toughness. In the second approach, the void-containing material is considered as a homogenized continuum governed by porous plasticity models. This makes it possible to simulate large amount of crack extension because only one element is needed for a representative material volume. As an example, a numerical approach is proposed to predict ductile crack growth in thin panels of a 2024-T3 aluminum alloy, where a modified Gologanu–Leblond–Devaux model [Gologanu, M., Leblond, J.B., Devaux, J., 1993. Approximate models for ductile metals containing nonspherical voids – Case of axisymmetric prolate ellipsoidal cavities. J. Mech. Phys. Solids 41, 1723–1754; Gologanu, M., Leblond, J.B., Devaux, J., 1994. Approximate models for ductile metals containing nonspherical voids – Case of axisymmetric oblate ellipsoidal cavities. J. Eng. Mater. Tech. 116, 290–297; Gologanu, M., Leblond, J.B., Perrin, G., Devaux, J., 1995. Recent extensions of Gurson’s model for porous ductile metals. In: Suquet, P. (Ed.) Continuum Micromechanics. Springer-Verlag, pp. 61–130] is used to describe the evolution of void shape and void volume fraction and the associated material softening, and the material failure criterion is calibrated using experimental data. The calibrated computational model successfully predicts crack extension in various fracture specimens, including the compact tension specimen, middle crack tension specimens, multi-site damage specimens and the pressurized cylindrical shell specimen.     

Verification of the transferability of micromechanical parameters by cell model calculations with visco-plastic materials

Finite element (FE) calculations of a cylindrical cell containing a spherical hole have been performed under large strain conditions for varying triaxiality with three different constitutive models for the matrix material, i.e. rate independent plastic material with isotropic hardening, visco-plastic material under both isothermal and adiabatic conditions, and porous plastic material with a second population of voids nucleating strain controlled. The “mesoscopic” stress-strain and void growth responses of the cell are compared with predictions of the modified Gurson model in order to study the effects of varying triaxiality and strain rate on the critical void volume fraction. The interaction of two different sizes of voids was modelled by changing the strain level for nucleation and the stress triaxiality. The study confirms that the void volume fraction at void coalescence does not depend significantly on the triaxiality if the initial volume fraction of the primary voids is small and if there are no secondary voids. The strain rate does not affect f_c either. The results also indicate that a single internal variable, f, is not sufficient to characterize the fracture processes in materials containing two different size-scales of void nucleating particles.     

Coalescence of voids by internal necking: Theoretical estimates and numerical results

Upper-bound estimates and supposedly exact numerical results are obtained for the limit loads associated with cylindrical cells containing voids and subjected to boundary conditions that are consistent with post-localization kinematics in porous plastic solids. When supplemented with evolution equations for the microstructural variables, the results can be used in the modeling of void coalescence by internal necking in ductile materials.     

Constitutive models for power-law viscous solids containing spherical voids

In the analysis of non-linear porous solids, it is commonplace to employ a spherical unit cell owing to the simplicity it affords. The macroscopic constitutive response of the material is then predicted based upon either uniform traction or linear displacement/velocity boundary conditions applied to the outer surface of the cell. In this investigation, we carry out a careful computational analysis of the effect of these two types of boundary conditions on the macroscopic response of the (idealized) porous solid and in particular, we explore the sensitivity of the predicted response to the macroscopic stress, void volume fraction and material non-linearity. The numerical results are then used as a basis for establishing an approximate constitutive model that is expressed in a compact, explicit form. The study is carried out in the context of an incompressible, isotropic power-law viscous matrix material, and the computational analysis is focused on axisymmetric deformation of the unit cell. While the macroscopic strain-rate potential is found to exhibit a dependence on the third invariant of the macroscopic stress deviator, this dependence is slight (particularly for the linear displacement/velocity boundary condition) and, toward developing an approximate strain-rate potential applicable to general macroscopic stress states, a simple averaging scheme is employed to suppress the role of this quantity. Guided by the numerical results as well as by various previously proposed constitutive relations, an approximate generalized elliptic form for the macroscopic strain-rate potential is then proposed. The constitutive potential which is ultimately developed involves a fairly simple dependence upon the void volume fraction and the properties of the matrix material, yet it gives rise to predictions that agree well with the detailed unit cell calculations over the full range of properties and macroscopic stress states considered.