考虑损伤的内变量黏弹--黏塑性本构方程

基于Rice不可逆内变量热力学框架,在约束构型空间中讨论材料的蠕变损伤问题.通过给定具体的余能密度函数和内变量演化方程推导出考虑损伤的内变量黏弹--黏塑性本构方程.通过模型相似材料单轴蠕变加卸载试验对一维情况下的本构方程进行参数辨识和模型验证,本构方程能很好地描述黏弹性变形和各蠕变阶段.不同的蠕变阶段具有不同的能量耗散特点.受应力扰动后,不考虑损伤的材料系统能自发趋于热力学平衡态或稳定态.在考虑损伤的整个蠕变过程中,材料系统先趋于平衡态再背离平衡态发展.能量耗散率可作为材料系统热力学状态偏离平衡态的测度;能量耗散率的时间导数可用于表征系统的演化趋势;两者的域内积分值可作为结构长期稳定性的评价指标.     

考虑损伤的内变量黏弹-黏塑性本构方程

基于Rice 不可逆内变量热力学框架,在约束构型空间中讨论材料的蠕变损伤问题. 通过给定具体的余能密度函数和内变量演化方程推导出考虑损伤的内变量黏弹-黏塑性本构方程. 通过模型相似材料单轴蠕变加卸载试验对一维情况下的本构方程进行参数辨识和模型验证,本构方程能很好地描述黏弹性变形和各蠕变阶段.不同的蠕变阶段具有不同的能量耗散特点. 受应力扰动后,不考虑损伤的材料系统能自发趋于热力学平衡态或稳定态. 在考虑损伤的整个蠕变过程中,材料系统先趋于平衡态再背离平衡态发展. 能量耗散率可作为材料系统热力学状态偏离平衡态的测度;能量耗散率的时间导数可用于表征系统的演化趋势;两者的域内积分值可作为结构长期稳定性的评价指标.      

基于分形理论的高强混凝土动态损伤本构关系

基于高强混凝土（HSC）试块在SHPB冲击实验中的分形损伤演化规律,推导了HSC的分形损伤变量表达式,标定了HSC裂纹的分形维数范围。然后参考ZWT模型,并结合HSC实验过程中的应变率相关性、动态损伤特性及近似恒应变率,推导了分形损伤演化的HSC动态损伤本构方程。采用4组应变率工况下的C60、C80混凝土应力-应变曲线对本构方程进行验证,理论曲线和实验曲线吻合较好。     

考虑微观结构特征长度演化的内变量黏塑性本构模型

在金属晶体材料高应变率大应变变形过程中,存在强烈的位错胞尺寸等微观结构特征长度细化现象,势必对材料加工硬化、宏观塑性流动应力产生重要影响。基于宏观塑性流动应力与位错胞尺寸成反比关系,提出了一种新型的BCJ本构模型。利用位错胞尺寸参数,修正了BCJ模型的流动法则、内变量演化方程,引入了考虑应变率和温度相关性的位错胞尺寸演化方程,建立了综合考虑微观结构特征长度演化、位错累积与湮灭的内变量黏塑性本构模型。应用本文模型,对OFHC铜应变率在10-4~103 s-1、温度在298~542 K、应变在0~1的实验应力-应变数据进行了预测。结果表明:在较宽应变率、温度和应变范围内,本文模型的预测数据与实验吻合很好;与BCJ模型相比,对不同加载条件下实验数据的预测精度均有较大程度的提高,最大平均相对误差从9.939%减小为5.525%。     

考虑应变率效应的混凝土随机损伤本构模型研究

混凝土材料组分复杂且具有随机分布的特点, 其受力力学行为不可避免地存在非线性和随机性. 同时, 在动力荷载作用下, 混凝土材料具有不可忽视的率敏感性. 为了综合反映混凝土受力力学行为中的非线性、随机性与率敏感性, 本文从对材料的纳-微观裂纹扩展分析入手, 引入速率过程理论描述纳观裂纹的扩展速率, 并研究了对应的能量耗散过程. 在此基础上通过裂纹层级模型将纳观分析推演到微观尺度, 建立了微观能量耗散的基本表达式. 进而与微-细观随机断裂模型相结合, 形成了混凝土纳-微-细观随机损伤本构模型. 同时, 基于速率相关势垒的分析, 揭示了动力强度的提高源自加载速率和原子键断裂速率的竞争机制. 据此, 假定微裂纹间相互作用与应变率比值的相关关系以建立微弹簧能量耗散速率与应变率的联系, 实现了从静力本构模型向动力本构模型的扩展. 数值算例表明, 建议模型能够同时反映混凝土材料力学行为中的非线性、随机性和率敏感性. 最后通过与相关试验结果的对比, 验证了建议模型的正确性.      

混凝土材料冲击特性的研究

基于混凝土材料强冲击加载下的试验研究，提出了两种损伤型动态本构模型： 损伤型黏弹性本构模型和损伤与塑性耦合的本构模型. 通过模型计算结果与冲击试验结果的 比较可发现，随着冲击速度的提高，混凝土材料内部产生了显著的塑性变形，由此 损伤型黏弹性本构模型的应用就存在一些不足. 而损伤与塑性耦合的本构模型由于考虑了裂 纹扩展引起的材料强度和刚度的弱化，以及微空洞缺陷塌陷引起的塑性变形，因而能更好地 用于模拟强冲击载荷作用下混凝土材料的冲击响应特性.     

混凝土WW三参数率相关动态本构模型

根据一致粘塑性模型理论，结合所做的混凝土单轴动力特性试验，对常用的混凝土本构模型Willam—Warnke三参数模型进行改进，引入应变率的影响，推导了Willam—Warnke材料的动态率相关本构模型；并与试验的应力应变曲线进行比较，结果表明本文模型能够较好地反应混凝土的动力特性；最后，通过对一受冲击荷载的简支梁进行计算，并与线弹性及率无关塑性结果进行比较，结果表明考虑了应变率的影响后梁的动力特性发生了较大的变化。     

考虑微缺陷形状的细片层状珠光体钢的损伤本构模型

基于非经典塑性理论和连续介质损伤力学,利用在一个特殊坐标系下基于椭球形孔洞模型得到的可考虑孔洞形状变化混合强化材料的损伤演化率得到了铁素体相的损伤本构方程,通过混合物理论利用铁素体和渗碳体相各自本构关系并考虑其几何特征得到了珠光体团的损伤本构模型。进而采用Hill自洽方法,得到了珠光体材料的宏观损伤本构描述,发展了相应的数值方法与程序。讨论了孔洞形状对材料损伤的影响,并对典型珠光体双相材料BS11在非对称循环加载史下的弹塑性响应特性进行了分析,得到了与实验较为一致的结果。     

脆性固体非弹性和软化性能的损伤本构模拟

本文概要地介绍了作者近年来在脆性固体粘塑性损伤本构模型方面的工作。首先，通过假设损伤率依赖于粘塑性应变率和应力变化率，提出了一个考虑损伤演化及其对材料力学性能的影响的粘塑性损伤本构模型。     

沥青混合料的粘弹性疲劳损伤模型研究

从沥青混合料的黏弹性本构模型出发，按应变等效假设 将损伤引进本构模型，推导周期应力条件下含损伤的耗散能表达式，进而得到黏弹性损伤演 化方程和疲劳方程；该模型可以综合反映应力、加载频率和温度的影响，适合用来分析沥青 路面的疲劳损伤问题；利用MTS开展了沥青混合料的疲劳损伤试验，确定了相应的黏弹性疲 劳损伤模型参数，据此开展了模型验证，结果表明模型与实测值之间相关性很好.     

A new free energy for plastic damage analysis

This work presents a new free energy for the ductile plastic damage analysis. The derivation here is based on the ductile plastic damage model proposed by Lemaitre and the examination of the plastic strain of a damaged material. The result given here can be used for the damage evolution law derived from the potential of dissipation.     

Anisotropic damage law of evolution

A formulation for anisotropic damage is established in the framework of the principle of strain equivalence. The damage variable is still related to the surface density of microcracks and microvoids and, as its evolution is governed by the plastic strain, it is represented by a second order tensor and is orthotropic. The coupling of damage with elasticity is written through a tensor on the deviatoric part of the energy and through a scalar taken as its trace on the hydrostatic part. The kinetic law of damage evolution is an extension of the isotropic case. Here, the principal components of the damage rate tensor are proportional to the absolute value of principal components of the plastic strain rate tensor and are a nonlinear function of the effective elastic strain energy. The proposed damage evolution law does not introduce any other material parameter. Several series of experiments on metals give a good validation of this theory. The coupling of damage with plasticity and the quasi-unilateral conditions of partial closure of microcracks naturally derive from the concept of effective stress. Finally, a study of strain localization makes it possible to determine the critical value of the damage at mesocrack initiation.     

含孔复合材料层合板静拉伸损伤演化的实验和表征方法

为了深入探究复合材料层合板结构的损伤机理和损伤演化,应用声发射技术和图像相关技术同步实时监测含孔碳纤维复合材料层合板试样在静拉伸过程中的损伤演化。实验结果表明,试样表面应变场呈现局部化特征。对应变集中带在加载方向的应变值进行了统计分析,获得了应变场的特征统计量(标准差)随加载的演化模型。层合板损伤时产生声发射信号的峰值频率大小能够有效区分复合材料的损伤模式,由此,建立了基于损伤模式累积声发射数的损伤演化模型。通过对应变场演化模型和声发射损伤演化模型的分析,可以将复合材料的损伤演化分为损伤初始阶段、损伤平稳扩展期、损伤严重阶段三个部分。统计分析结果表明:在损伤严重阶段,基于声发射事件数的各种损伤的损伤变量和局部应变场标准差快速增长,因此局部应变场统计标准差可以作为后期局部损伤严重程度的识别指标。     

Simulation of failure under cyclic plastic loading by damage models

The purpose of this work is to simulate the evolution of ductile damage and failure involved by plastic strain reversals using damage models based on either continuum damage mechanics (CDM) or porosity evolution. A low alloy steel for pressure vessels (20MnMoNi55) was chosen as reference material. The work includes both experimental and simulation phases. The experimental campaign involves different kinds of specimens and testing conditions. First, monotonic tensile tests have been performed in order to evaluate tensile and ductile damage behaviour. Then, the cyclic yielding behaviour has been characterized performing cyclic plasticity tests on cylindrical bars. Finally, cyclic loading tests in the plastic regime have been made on different round notched bars (RNBs) to study the evolution of plastic deformation and damage under multiaxial stress conditions. The predictions of the different models were compared in terms of both, the specimens macroscopic response and local damage. Special emphasis was laid on predictions of the number of cycles prior to final failure and the crack initiation loci.     

压缩载荷作用下岩石的细观损伤和塑性研究

建立岩石微裂纹扩展的细观力学模型,研究了岩石的细观损伤和塑性性质.压缩载荷下微裂纹尖端翼裂纹稳定扩展表征岩石的细观损伤,采用应变能密度准则求解复合型断裂的翼裂纹扩展长度,微裂隙统计的二参数Weibull函数模型反映绝对体积应变对微裂纹分布数目影响,进而用翼裂纹扩展所表征的应力释放体积和微裂纹数目来表示含有微裂隙的岩石损伤演化变量;宏观塑性屈服函数采用Voyiadjis等的等效塑性应变的硬化函数,反映了塑性内变量对硬化函数的影响;建立岩石模型的本构关系及其数值算法,并用回映隐式积分算法编制了模型的本构程序.分析弹塑性损伤模型的围压对岩石损伤的影响,并从围压和短微裂隙长度等因素分析模型的岩石的损伤和宏观塑性特性.     

含热冲击预损伤的陶瓷基复合材料损伤本构模型

陶瓷基复合材料结构在服役过程中不可避免地经受热冲击(较高的热应力梯度)而产生热机械损伤, 因此, 建立含循环热冲击预损伤材料的损伤本构模型, 以描述材料在热机械载荷作用下的力学行为, 对材料结构损伤容限设计与结构完整性评估非常重要. 本文首先对经历了循环热冲击的材料进行单调拉伸损伤实验, 发现对于含循环热冲击预损伤的材料, 其弹性模量的下降与所施加的应变直接相关. 然后在连续介质损伤力学的框架下, 基于平面应力假设, 建立了含循环热冲击预损伤材料的损伤演化模型, 该模型所涉及的参数可通过一个偏轴(45$^\circ$)以及两个正轴(平行于两个主方向)的单调拉伸试验获得. 最后, 采用经典塑性理论对由基体损伤引起的非弹性应变进行了描述. 本文所提出的应变损伤宏观模型可以描述陶瓷基复合材料在热机械载荷作用下的损伤演化, 同时弥补了含预损伤的陶瓷基复合材料在机械载荷下损伤本构模型在理论及实验研究方面的不足.      

A physico-mechanical approach to modeling of metal forming processes—part I: theoretical framework

A combined physico-mechanical approach to research and modeling of forming processes for metals with predictable properties is developed. The constitutive equations describing large plastic deformations under complex loading are based on both plastic flow theory and continuum damage mechanics. The model which is developed in order to study strongly plastically deformed materials represents their mechanical behavior by taking micro-structural damage induced by strain micro-defects into account. The symmetric second-rank order tensor of damage is applied for the estimation of the material damage connected with volume, shape, and orientation of micro-defects. The definition offered for this tensor is physically motivated since its hydrostatic and deviatoric parts describe the evolution of damage connected with a change in volume and shape of micro-defects, respectively. Such a representation of damage kinetics allows us to use two integral measures for the calculation of damage in deformed materials. The first measure determines plastic dilatation related to an increase in void volume. A critical amount of plastic dilatation enables a quantitative assessment of the risk of fracture of the deformed metal. By means of an experimental analysis we can determine the function of plastic dilatation which depends on the strain accumulated by material particles under various stress and temperature-rate conditions of forming. The second measure accounts for the deviatoric strain of voids which is connected with a change in their shape. The critical deformation of ellipsoidal voids corresponds to their intense coalescence and to formation of large cavernous defects. These two damage measures are important for the prediction of the meso-structure quality of metalware produced by metal forming techniques. Experimental results of various previous investigations are used during modeling of the damage process.      

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.     

Stochastic damage model for concrete based on energy equivalent strain

Starting with the framework of conventional elastoplastic damage mechanics, a class of stochastic damage constitutive model is derived based on the concept of energy equivalent strain. The stochastic damage model derived from the parallel element model is adopted to develop the uniaxial damage evolution function. Based on the expressions of damage energy release rates (DERRs) conjugated to the damage variables thermodynamically, the concept and its tensor formulations of energy equivalent strain is proposed to bridge the gap between the uniaxial and the multiaxial constitutive models. Furthermore, a simplified coupling model is proposed to consider the evolution of plastic strain. And the analytical expressions of the constitutive model in 2-D are established from the abstract tensor expression. Several numerical simulations are presented against the biaxial loading test results of concrete, demonstrating that the proposed models can reflect the salient features for concrete under uniaxial and biaxial loading conditions.     

增量型各向异性损伤理论与数值分析

考虑到目前各向异性损伤理论存在一些不足,该文在增量型各向异性损伤理论的框架下,引入二阶对称张量,构造四阶对称有效损伤张量,建立了有效应力方程．类似于塑性流动分析方法,定义了增量弹性应力．应变关系．利用von Mises塑性屈服准则,并考虑各向异性损伤效应,推导出四阶对称的弹．塑性变形损伤刚度张量,其对称性反映了材料的固有特性．根据物体的变形和现时损伤状态,构造了材料损伤演化方程,方程中各项具有明确的物理意义．通过对A12024-T3金属薄板单向拉伸的有限元分析,确定了损伤演化参数,验证了损伤演化方程的正确性．此外还对含孔口薄板做有限元模拟,讨论了反力—位移曲线的变化规律以及它所揭示变形性质,给出了损伤场的分布规律。