复合材料蠕变本构关系及实验测定Ⅰ.本构关系

蠕变是复合材料最重要的力学性能之一,实验表明:复合材料在蠕变条件下的变形可以分为弹性变形、粘弹性变形和粘塑性变形.应用不可逆过程的热力学和广义变量的概念可以分析材料的蠕变变形.本文首先回顾了热力学的基本方程;基于Schapery本构关系的假设和思路推导了蠕变本构关系的一般形式,其中包括弹性变形、粘弹性变形和粘塑性变形;考虑到广义力选取的不唯一性,本文提出了广义力选取的原则以使得到的本构关系尽可能地简单;由此本文给出了复合材料的一维蠕变,各向同性复合材料的二维蠕变和纤维增强复合材料平面内的蠕变的本构关系.     

沥青砂混合料粘弹塑力学特性研究

在0.1MPa、0.15MPa、0.2MPa、0.25MPa和0.3MPa下进行了沥青砂试样单轴压缩和蠕变实验,分析了其压缩和蠕变性质,根据变形机理提出了粘弹塑本构模型可由粘弹性和粘塑性的两个子模型串联构成,通过对粘塑性子模型中粘性系数进行改进,理论推导了模型蠕变本构方程,确定了模型参数,并求得模型参数与加载应力函数关系。进行模型预测与实验结果对比,结果表明:该模型能够描述沥青砂试样在不同应力下蠕变变形的3个阶段,反映了沥青砂混合料粘弹塑变形特点。     

Bammann-Chiesa-Johnson粘塑性本构模型的参数识别方法与验证

Bammann-Chiesa-Johnson(BCJ)粘塑性本构模型对材料力学响应的再现和预测能力强烈依赖于其模型参数的确定,而模型参数的确定往往是通过反分析方法来进行。由于BCJ粘塑性模型包含了应变、应变率和温度耦合效应以及加载路径和温度历史,其常数多达18个,所以寻找最佳的模型参数识别值十分繁琐。针对BCJ本构模型参数复杂、识别困难的问题,本文基于参数的物理意义,在准静态、蠕变及动态加载试验基础上,通过模型参数解耦分离、粒子群智能优化的方法分6步对18个材料常数进行识别,并用识别结果对1060纯铝动态加载试验力学响应进行模拟,模拟结果与试验结果符合良好。通过定量化误差分析,证明了BCJ粘塑性模型对实验数据的预测具有较高精度,该模型参数识别方法科学可行。     

硬聚氯乙烯的粘塑性本构模型与裂纹扩展行为

建立材料的粘塑性本构模型,进行粘塑性裂纹扩展试验,是开展聚合物粘塑性裂纹扩展问题研究的基础.采用恒定应变速率的方法,对硬聚氯乙烯进行低应变速率下的拉伸试验,确定各应变速率下应力与应变的关系曲线.实验数据表明,该材料的力学性能对应变速率有依赖性,与时间相关,是典型的粘塑性材料.根据实验测得的不同应变速率下应力-应变关系的曲线族,对实验数据进行多元回归分析,确定有关的材料常数,建立了硬聚氯乙烯材料Bailey-Norton公式形式的粘塑性本构模型.进行硬聚氯乙烯的粘塑性裂纹扩展试验研究,得到了裂纹长度增量与时间的关系.     

岩体粘塑性模型参数的反分析

基于弹—粘塑性有限元方法,探讨了通过反分析来确定P.Perzyna粘塑性本构模型中反映岩体粘塑性变形的流动系数和屈服函数的函数的方法,并用实测数据检验了这一反分析方法的可行性。     

用T积分研究硬聚氯乙烯粘塑性裂纹扩展

采用作者建立的硬聚氯乙烯的粘塑性本构模型,以CT试样为研究对象进行粘塑性有限元分析,并在此基础上编程计算T积分,然后再用T积分与实验所得的裂纹扩展速率关联.研究结果显示,描述蠕变延性材料和蠕变脆性材料粘塑性裂纹扩展速率的控制参量是不同的.T积分不适合作为硬聚氯乙烯粘塑性裂纹扩展的控制参量.     

VPF用粘性介质粘弹塑性本构模型及参数确定

为确定粘性介质压力成形所采用的粘性传力介质的材料模型及其参数,对粘性介质剪切蠕变-回复实验结果进行分析,提出采用粘弹塑性材料模型描述粘性介质变形行为.将粘性介质的总变形分解为弹性分量、粘弹性分量和粘塑性分量,对实验结果进行拟合分析,分别确定了粘性介质变形的各个应变分量与应力之间的关系,最终建立了所选用的粘性介质粘弹塑性模型,为数值模拟粘性介质变形行为提供了依据.     

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。     

泡沫塑料包装衬垫缓冲性能建模

本文从非线性粘弹性物质的多重积分型本构方程出发,引入塑性应变,推导了粘弹塑性物质的微分型本构方程.进一步考虑材料的损伤特性,建立了泡沫塑料包装衬垫的缓冲性能模型.根据在一种跌落高度、衬垫厚度和静态应力组合条件下的国产可发聚苯乙烯沫泡塑料的连续多次跌落冲击试验数据,识别了其缓冲性能模型参数.动力学计算与试验结果的比较表明,该模型能较好地反映可发聚苯乙烯泡沫塑料包装衬垫在连续多次跌落冲击过程中的加速度、速度、位移变化,冲击能量的吸收性和塑性变形等基本特性.并且仅根据在一种组合条件下的试验数据所识别的这一模型,在其它组合条件下其缓冲性能与试验结果也吻合较好.     

VPF粘性介质粘弹性本构关系研究

为研究粘性介质的力学性能对板材变形的影响,通过剪切蠕变-回复和松弛试验分析了甲基乙烯基粘性介质的流变性能.实验结果表明粘性介质可以简化为线性粘弹性材料.建立了粘性介质的积分型粘弹性本构方程,并结合剪切蠕变-回复过程的有限元分析确定了方程中的材料参数.利用该本构方程对粘性介质压力胀形过程进行了有限元分析,模拟结果与试验结果对比表明,所建立的本构方程可以较好的预测板材的变形过程.     

循环荷载作用下粉砂岩疲劳流变损伤模型研究

针对现有流变模型难以有效描述循环荷载作用下岩石变形及疲劳损伤演化特征等问题,开展了粉砂岩循环加卸载试验,分析了不同上限荷载下岩石的流变规律与疲劳特性。基于Kachanov蠕变损伤理论建立损伤变量,引入一个带应变触发和应力阈值的黏塑性元件,与Burgers模型串联构建循环荷载作用下岩石疲劳流变损伤模型;将正弦波应力函数替换流变微分本构方程中的恒定应力,推导岩石在循环荷载下的一维、三维微分型损伤本构方程,再根据叠加原理得到模型的黏弹塑性流变损伤方程。适用性验证表明,新建模型不仅可以精确地反映循环加卸载过程中粉砂岩的衰减、稳态流变阶段,还可以有效地描述上限荷载高于疲劳强度时的加速流变阶段。通过粉砂岩疲劳损伤流变全过程定量化分析,提出加速流变阶段的临界损伤阈值和破坏失稳判据,并给出加速流变阶段的启始时间、持续时间及疲劳寿命预测方法,模型对岩体工程长期稳定性评价具有一定的理论指导意义。     

Efficiency of Power Dissipation and Instability Criterion for Processing Maps in Hot Forming

The processing maps are a superimposition of iso-efficiency contour map and flow instability map, which are used to design hot working processing conditions in a wide variety of materials. In order to construct the processing maps, the efficiency of power dissipation and an instability criterion taking into account the contribution of strain and microstructure evolution are proposed based on a set of microstructure-based viscoplastic constitutive equations. In viscoplastic constitutive equations, the grain size of matrix phase and the dislocation density are taken as internal state variables. And, the material constants in present equations can be identified by a genetic algorithm (GA)-based objective optimization technique. Isothermal compression of Ti-6Al-4V alloy is conducted on a Thermecmaster-Z simulator with different deformation temperatures, strain rates and height reductions so as to establish the processing maps by using the present model. The primary a grain size is measured at an OLYMPUS PMG3 microscope with the quantitative metallography image analysis software. Based on the experimental results, the processing maps of Ti-6Al-4V alloy are constructed at different strains. The processing maps show that the instability domains and the efficiency of power dissipation vary as the strain increases. The comparison between the processing maps of present study and that based on Prasad's theory shows that the present processing maps can more efficiently describe the deformation behavior and provide more appropriately physical interpretation and optimize processing conditions accurately.     

Phenomenological formulation of viscoplastic constitutive equation for polyethylene by taking into account strain recovery during unloading

A viscoplastic constitutive equation for polyethylene that properly describes significant strain recovery during unloading was proposed. The constitutive equation was formulated by combining the kinematic hardening creep theory of Malinin and Khadjinsky with the nonlinear kinematic hardening rule of Armstrong and Frederick. In order to describe the strain recovery, the nonlinear kinematic hardening rule was modified. First, a loading surface was defined in a viscoplastic strain space. A loading–unloading criterion was then introduced using the loading surface. Moreover, a new parameter was defined by the relationship between the loading surface and the current state of the viscoplastic strain, and the evolution equation of back stress was modified using this parameter, which has some value only during unloading. Experimental results for polyethylene were simulated by using the modified constitutive equations, and cyclic inelastic deformation in both uniaxial and biaxial states of stress was predicted. Finally, the validity of the above-described modification was verified, and the features of the constitutive equation and the deformation were discussed.     

Creep rupture and viscoelastoplasticity of polypropylene

Observations are reported on isotactic polypropylene in tensile tests with various strain rates, relaxation tests at various strains, and creep tests with various stresses at room temperature. Constitutive equations are derived for the viscoelastic and viscoplastic responses of semicrystalline polymers at three-dimensional deformations with small strains. The stress-strain relations involve eight material constants that are found by fitting the experimental data. The model is applied to the numerical analysis of creep failure of polypropylene under various deformation modes (uniaxial tension, equi-biaxial tension, shear, multiple-step creep tests).     

Viscoplastic response and creep failure time prediction of polymers based on the transient network model

The nonlinear viscoelastic/viscoplastic response of polymeric materials is described by a new model based on previous works in terms of monotonic loading, stress–relaxation, and creep. In the proposed analysis, following a constitutive equation of viscoelasticity, based on the transient network theory, essential modifications are introduced, which account for the nonlinearity and viscoplasticity at small elastic and finite plastic strain regime. In addition, viscoplastic response is successfully analyzed by a proper kinematic formulation, which is combined with a functional form of the rate of plastic deformation. A three-dimensional constitutive equation is then derived for an isotropic incompressible medium. This analysis is capable of capturing the main aspects of inelastic response and the instability stage taking place at the tertiary creep, related to the creep failure. Model simulations described successfully the experimental data of polypropylene, which were performed elsewhere.     

On the creep crack growth prediction by a local approach

Classical methods to predict crack growth in structures are generally based on fracture mechanics concepts. For high-temperature applications, where creep (monotonic or cyclic) or thermal stresses are present, such classical approaches lead to large difficulties. An alternative method is to calculate as accurately as possible the actual local behaviour including viscoplasticity and creep damage effects. The different levels of the possible “local approaches” are briefly reviewed and discussed; the case of creep crack growth is then studied in detail, through the use of viscoplastic constitutive equations including creep damage effect. Both the creep damage and the hardening of the metal are supposed to be isotropic, characterized respectively by the following scalar internal variables: the Kachanov's damage variable D and the cumulated viscoplastic strain p. The evolution equation of creep damage is a differential non-linear one with non-linear cumulative effect. The local states of different mechanical fields ((σ, , D) and their redistribution, due to damage effect, are accurately investigated and illustrated by various numerical examples. Finally the approach is applied to the creep of initially cracked CT specimen.     

Micromechanically Established Constitutive Equations for Multiphase Materials with Viscoelastic–Viscoplastic Phases

A model for viscoelastic–viscoplastic solids is incorporated in a micromechanical analysis of composites with periodic microstructures in order to establish closed-form coupled constitutive relations for viscoelastic–viscoplastic multiphase materials. This is achieved by employing the homogenization technique for the establishment of concentration tensors that relate the local elastic and inelastic fields to the externally applied loading. The resulting constitutive equations are sufficiently general such that viscoelastic, viscoplastic and perfectly elastic phases are obtained as special cases by a proper selection of the material parameters the phase. Results show that the viscoelastic and viscoplastic mechanisms have significant effect on the global stress-strain, relaxation and creep behavior of the composite, and that its response is strongly rate-dependent in the reversible and irreversible regimes.     

Constitutive model for cyclic deformation of perfluoroelastomers

Observations are reported in uniaxial cyclic tensile tests with a strain-controlled program on perfluoroelastomer Hyflon MFA. A constitutive model is developed for its viscoplastic response and damage at three-dimensional deformations with finite strains. Adjustable parameters in the stress–strain relations are found by fitting the experimental data. Numerical simulation demonstrates that the constitutive equations adequately describe the mechanical response of perfluoroelastomer in cyclic tests with complicated deformation programs.