非等温条件下非比例循环粘塑性本构描述

为了描述在非等温非比例循环加载下的循环变形行为，本文提出了一个考虑材料非比例循环附加硬化效应、非比例循环加载历史效应和温度历史效应的粘塑性本构模型．在该模型中，引入了具有三种不同演化速率的背应力演化方程；定义了新的非比例度；为了反映非比例循环历史和温度历史的影响，引入了表现各向同性变形阻力Ｑａｓｍ，并对各向同性的表现变形阻力引入了具有先前加载历史记忆的演化方程．将本文模型用于１Ｃｒ１８Ｎｉ９Ｔｉ不锈钢高温循环变形行为描述，其预言结果与实验结果吻合得很好．     

考虑细观变形特征的镁合金宏观本构模型及数值模拟

为了能有效描述镁合金宏观各向异性塑性行为,考虑了滑移、孪生、去孪生三种细观变形模式的特点,给出了相应的硬化函数;根据VonMises屈服准则,发展了一种镁合金宏观本构模型及其迭代算法。模型将变形模式的开启与晶粒取向相关联,同时针对镁合金孪生变形时引起的晶粒重新定向问题,描述了一种晶向偏转的方法。在此基础上编写了ABAQUS/UMAT材料用户子程序;利用开发的本构模型,开展了单轴拉伸、单轴压缩、单轴循环拉压加载条件下镁合金塑性行为的数值模拟,并对随机织构下的镁合金板材轧制过程进行了有限元仿真实验。模拟结果表明:单轴拉伸、单轴压缩和循环加载情形下的镁合金宏观硬化行为与实验结果基本吻合;轧制后镁合金板材表现出了应力-应变不均匀特性,多晶织构演化结果与实验结果基本一致。说明文中所提出的宏观本构模型、晶向偏转模型能够有效描述镁合金的宏观塑性行为和织构演化。     

基于晶体塑性理论研究铝材料高压高应变率下的强度特性

为了了解金属材料在极端加载下复杂动态响应过程中的多种机制和效应，重点针对Al材料在高压、高应变率加载下的塑性变形机制，在经典晶体塑性模型的基础上，对其中的非线性弹性、位错动力学和硬化形式进行改进，建立适用于高压、高应变率加载下的热弹-黏塑性晶体塑性模型。该模型可以较好地描述单晶铝和多晶铝材料屈服强度随压力的变化过程，相比宏观模型，用该模型还获得了多晶Al材料在冲击加载下的织构演化规律，揭示了织构择优取向行为和压力的关系。     

非比例循环塑性内时本构关系研究

在Valanis的内时本构理论的框架中,引入内结构张量以反映由于非比例加载而引起金属材料的附加等向强化及异向强化效应,同时提出材料强化程度的度量采用沿路径法线方向的塑性应变分量来描述.这些考虑的有效性已经通过用所建模型对304不锈钢材料在一些典型非比例循环加载路径下的响应进行的理论预测得到了验证;将该模型应用于U71Mn材料室温单轴棘轮行为描述中,结果显示内结构张量的引入不仅能较好地反映应变控制下的非比例附加效应,而且也能较好地反映应力控制下塑性应变的累积及变化率.     

镁合金晶体塑性本构模型与非均匀孪生变形分析

微结构演化对镁合金材料力学性能有着显著的影响，为了揭示镁合金宏观塑性各向异性特性与非均匀孪生变形的关系，开展了不同路径下的单轴加载试验以及采用含滑移、孪生机制的晶体塑性本构模型对试验条件下的镁合金变形行为进行数值模拟研究。文中本构模型描述了滑移与孪生变形机制以及晶格转动的机制，同时研究采用三维微结构代表性有限元模型，其包含晶粒尺寸、晶向和晶界倾角等微结构参数。研究结果表明，轧制镁合金具有强烈的宏观塑性各向异性行为，并对这种镁合金塑性各向异性行为的模拟结果以及多晶织构的模拟演化结果与试验测量进行对比，结果都基本吻合。对孪生非均匀变形模拟分析表明，镁合金宏观塑性各向异性行为与滑移、孪生变形机制的不同启动组合紧密相关，同时多晶体内应力的非均匀分布受到孪生变形的严重影响。而不同晶粒尺寸的晶粒所发生的孪生变形有比较大的差异，造成孪晶变体在晶粒内的分布极不均匀。本研究可为通过微结构的合理配置来设计和控制材料的力学性能提供理论依据.     

一个考虑循环应变幅值历史效应的粘塑性本构模型

本文提出了一个考虑材料应变幅值历史效应的粘塑性本构模型。在该模型中，引入了三个具有不同演化速率的背应力演化方程；建立了非弹性应变幅值历史记忆模型，对各向同性变形阻力，引入了具有先前加载历史记忆的演化方程。将本文模型用于１Ｃｒ１８Ｎｉ９Ｔｉ不锈钢循环变形行为描述中，其预言结果与实验结果吻合得很好，表明该模型能很好地描述材料的循环应变幅值历史下的循环变形行为。     

304不锈钢室温单轴循环棘轮行为的粘塑性本构描述

在统一粘塑性循环本构模型的框架下对循环硬化的304不锈钢的单轴棘轮行为进行了本构描述。模型中通过随动硬化背应力演化和各向同性变形阻力演化对304不锈钢在非对称应力循环下的循环附加硬化和循环流动特性进行了分析，同时考虑了加载历史对循环棘轮行为的影响。将模型应用于304不锈钢室温单轴循环棘轮行为及其对加载历史依赖性的描述中，预言结果与实验结果吻合较好。     

复杂加载条件下的砂土本构模型

试验表明,饱和砂土的应力应变关系具有显著的密度以及压力依存性,上述两点构成了描述砂土静力加载下变形特性无法忽视的因素.此外,在循环加载等复杂加载作用下,砂土还会表现出明显的应力诱导各向异性以及相变转换特性.基于在e-p空间中存在唯一的临界状态线这一基本假定,通过在e-p空间中引入当前状态点与临界状态线的距离R来作为反映密度与压力依存特性的状态参量,将变相应力比以及峰值应力比表达为状态参量的指数函数,将上述应力比参量引入到统一硬化参量中可准确地反映初始状态下围压、密度对于单调加载下应力应变关系的影响规律,能描述砂土剪缩、剪胀,应变软化、硬化等特性.采用非相关联流动法则,p-q空间中采用水滴型屈服面,塑性势面为椭圆面,松砂在单调加载下的静态液化现象也可描述.为反映循环加载下塑性体积应变的累积特性以及塑形偏应变的滞回特性,在循环加载下将状态参量R表达为应力比参量,并在硬化参数中引入描述应力诱导各向异性特性的旋转硬化部分,所提模型可有效地描述循环加载下剪切模量的衰减特性、刚度衰化性质、强度减小特性,在不排水约束作用下,则会产生往返活动性现象.通过一系列的模型模拟与试验结果对比,验证了本构模型的有效性及适用性.     

考虑塑性应变记忆恢复的循环棘轮本构模型研究

在统一粘塑性循环本构理论框架下,以Ohno-Abdel-Karim非线性随动硬化模型为基础,建立了一个循环本构模型。模型通过引入塑性应变幅值记忆效应,并在塑性应变记忆项中加入恢复系数,提高了对循环硬化材料单轴棘轮行为的预言能力。将模型应用于316L不锈钢单轴棘轮行为的描述中,模拟不同平均应力、应力幅值下的棘轮应变,均与实验数据吻合较好,证明本文改进的本构模型能合理地描述循环硬化材料的单轴棘轮行为。     

晶体塑性变形离散滑移模型及有限元分析

基于韧性单晶体实验现象，建立了描述晶体塑性变形的离散滑移模型．该模型的主要特点是：晶体滑移变形在宏观上是不均匀的，滑移带的分布是离散的．利用晶体塑性理论对模型进行了有限变形有限元分析，计算结果揭示了晶体滑移的离散行为，模拟的应力 应变曲线与实验曲线相吻合     

Finite element analysis of grain-by-grain deformation by crystal plasticity with couple stress

Rigid–plastic crystal plasticity with the rate-sensitive constitutive behavior of a slip system has been formulated within the framework of a two-dimensional finite element method to predict the grain-by-grain deformation of single- and polycrystalline FCC metals. For that purpose, individual grains are represented by several numbers of finite elements to describe the sub-grain deformation behavior, and couple stress has been introduced into the equilibrium equation to be able to describe the size effect as well as to prevent mesh-dependent predictions. A modified virtual work-rate principle with an approximate interface constraint has been suggested to use a C ⁰-continuous element in the finite element implementation, and the couple stress work-rate has been formulated on the basis of an assumed constitutive behavior. Simulated plane-strain compressions of a single crystal cube show that the shearing and the deformation load are closely related to the imbedded lattice orientation of the crystal grain, and that the sub-grain deformation and the load magnitude can be controlled by the couple stress hardening. It is also confirmed that almost the same predictions are obtained for different mesh systems by considering the couple stress hardening. Simulated plane-strain compressions of a bi-crystal show considerably curved grain-by-grain surface profiles after large reduction for several combinations of the imbedded lattice orientation. The high couple stress hardening predicted around grain boundaries is supposed to be related to the grain size effect. It is also supposed that consideration of couple stress is necessary to predict the sub-grain or the grain-by-grain deformation, and the couple stress hardening may be used to describe the state of microstructures in grain.     

Crystal plasticity model with enhanced hardening by geometrically necessary dislocation accumulation

A strain gradient dependent crystal plasticity approach is used to model the constitutive behaviour of polycrystal FCC metals under large plastic deformation. Material points are considered as aggregates of grains, subdivided into several fictitious grain fractions: a single crystal volume element stands for the grain interior whereas grain boundaries are represented by bi-crystal volume elements, each having the crystallographic lattice orientations of its adjacent crystals. A relaxed Taylor-like interaction law is used for the transition from the local to the global scale. It is relaxed with respect to the bi-crystals, providing compatibility and stress equilibrium at their internal interface. During loading, the bi-crystal boundaries deform dissimilar to the associated grain interior. Arising from this heterogeneity, a geometrically necessary dislocation (GND) density can be computed, which is required to restore compatibility of the crystallographic lattice. This effect provides a physically based method to account for the additional hardening as introduced by the GNDs, the magnitude of which is related to the grain size. Hence, a scale-dependent response is obtained, for which the numerical simulations predict a mechanical behaviour corresponding to the Hall-Petch effect. Compared to a full-scale finite element model reported in the literature, the present polycrystalline crystal plasticity model is of equal quality yet much more efficient from a computational point of view for simulating uniaxial tension experiments with various grain sizes.     

A combined experimental-numerical approach for elasto-plastic fracture of individual grain boundaries

The parameters for a crystal plasticity finite element constitutive law were calibrated for the aluminum–lithium alloy 2198 using micro-column compression testing on single crystalline volumes. The calibrated material model was applied to simulations of micro-cantilever deflection tests designed for micro-fracture experiments on single grain boundaries. It was shown that the load–displacement response and the local deformation of the grains, which was measured by digital image correlation, were predicted by the simulations. The fracture properties of individual grain boundaries were then determined in terms of a traction–separation-law associated with a cohesive zone. This combination of experiments and crystal plasticity finite element simulations allows the investigation of the fracture behavior of individual grain boundaries in plastically deforming metals.     

Microstructure-sensitive modeling of polycrystalline IN 100

A rate dependent, microstructure-sensitive crystal plasticity model is formulated for correlating the mechanical behavior of a polycrystalline Ni-base superalloy IN 100 at 650 °C. This model has the capability to capture first order effects on the stress–strain response due to (a) grain size, (b) γ′ precipitate size distribution, and (c) γ′ precipitate volume fraction. Experimental fatigue data with variable strain rates are used to calibrate the model for several distinct IN 100 microstructures (grain size, precipitate size distributions and volume fractions) obtained from thermomechanical processing. Physically based hardening laws are employed to evolve the dislocation densities for each slip system, taking into consideration the dislocation interaction mechanisms.     

晶粒的取向和变形性质对双晶体循环变形影响的模拟研究

应用晶体细观力学方法，分析了双晶体循环变形过程中组元晶粒取向及其变形性质（Ｂａｕｓｃｈｉｎｇｅｒ效应和循环硬化）的影响，发现双晶体的反向屈服及循环硬化行为为主要由组元晶粒性质支配，晶间内应力的影响是次要的，晶粒取向对宏微观应力应变行为有重要的影响，取向对称性较弱或罗硬差别较大的双晶体晶界影响较大。     

Grain size effects in multiphase steels assisted by transformation-induced plasticity

The influence of the austenitic grain size on the overall stress–strain behavior in a multiphase carbon steel is analyzed through three-dimensional finite element simulations. A recently developed multiscale martensitic transformation model is combined with a plasticity model to simulate the transformation-induced plasticity effects of a grain of retained austenite embedded in a ferrite-based matrix. Grain size effects are included via a surface energy term in the Helmholtz energy. Tensile simulations for representative orientations of the grain of retained austenite show that the initial stability of the austenite increases as the grain size decreases. Consequently, the effective strength is initially higher for smaller grains. The influence of the grain size on the evolution of the transformation process strongly depends on the grain orientation. For “hard” orientations, the transformation rate is higher for larger grains. In addition, the phase transformation is partially suppressed as the grain size decreases. In contrast, for “soft” orientations, the transformation rate is lower for larger grains. The phase transformation is more homogeneous for smaller grains and, consequently, the effective transformation strain is larger. Nevertheless, in multiphase carbon steels with a relatively low percentage of retained austenite, the influence of the austenitic grain size on the overall constitutive response is smaller than the influence of the austenitic grain orientation.     

SIMULATIONS OF MECHANICAL BEHAVIOR OF POLYCRYSTALLINE COPPER WITH NANO-TWINS

Mechanical behavior and microstructure evolution of polycrystalline copper with nano-twins were investigated in the present work by finite element simulations. The fracture of grain boundaries are described by a cohesive interface constitutive model based on the strain gradient plasticity theory. A systematic study of the strength and ductility for different grain sizes and twin lamellae distributions is performed. The results show that the material strength and ductility strongly depend on the grain size and the distribution of twin lamellae microstructures in the polycrystalline copper.     

Constitutive modeling of cyclic plasticity deformation of a pure polycrystalline copper

Cyclic plasticity experiments were conducted on a pure polycrystalline copper and the material was found to display significant cyclic hardening and nonproportional hardening. An effort was made to describe the cyclic plasticity behavior of the material. The model is based on the framework using a yield surface together with the Armstrong–Frederick type kinematic hardening rule. No isotropic hardening is considered and the yield stress is assumed to be a constant. The backstress is decomposed into additive parts with each part following the Armstrong–Frederick type hardening rule. A memory surface in the plastic strain space is used to account for the strain range effect. The Tanaka fourth order tensor is used to characterize nonproportional loading. A set of material parameters in the hardening rules are related to the strain memory surface size and they are used to capture the strain range effect and the dependence of cyclic hardening and nonproportional hardening on the loading magnitude. The constitutive model can describe well the transient behavior during cyclic hardening and nonproportional hardening of the polycrystalline copper. Modeling of long-term ratcheting deformation is a difficult task and further investigations are required.     

Crystallographic plasticity in fretting of Ti–6AL–4V

The deformation occurring under fretting conditions occurs over length scales of the same order as the grain size. Consequently, the crystallographic orientation of the grains plays a significant role in the deformation response. The cyclic deformation response in the region experiencing fretting predicted by a crystal plasticity model is compared to prediction of an initially isotropic J₂ cyclic plasticity theory with nonlinear kinematic hardening. The crystal plasticity model provides enhanced understanding of the fretting fatigue process, especially with regard to the shakedown and ratchetting limits.     

Modeling aspects of low plastic strain amplitude multiaxial cyclic plasticity in conventional and ultrafine grain nickel

Aspects of the cyclically saturated responses of initially annealed, conventional grain size (average grain diameter of approximately 50 μm) and electrodeposited, ultrafine grain (grains from 20 to 500 nm) nickel to reversed proportional and 90° out-of-phase axial-torsional, strain-controlled cycling at a nominally constant equivalent inelastic strain amplitude of approximately 100 μ strain are reported. An anisotropic, axial-torsional subspace version of Abdel-Karim and Ohno’s kinematic hardening model is presented. Within the framework of conventional small strain, rate-independent plasticity, this approach is used to model the responses. An anhysteretic, phenomenolically based, magnetomechanical model is coupled to the rate-independent plasticity model to include the cyclic magnetostriction response. The kinematic hardening parameter determination scheme, using the proportional path responses, is described. The model correlations achieved are presented and the ability of the resulting models to capture the 90° out-of-phase responses is examined. The model parameter sets, as determined from the proportional responses, require small changes to result in more accurate correlation of the 90° out-of-phase responses and the implications of this are discussed. The relative values of the model parameters between the two materials reflect the initial microstructures. Persistent mean stresses associated with mean total strains imposed are successfully modeled for the proportional strain path responses but not for the 90° out-of-phase responses.