单晶有限变形的热力耦合计算模型

以弹性变形梯度作为基本变量,结合热力学理论构造了单晶有限变形的热、力耦合计算模型。该模型考虑了温度、变温速率以及塑性耗散等条件对单晶有限变形的影响,相对于传统的以弹性变形梯度为基本变量的晶体塑性模型,算法能够体现温度效应的影响。采用隐式的积分方法对建立的控制方程进行计算以保证求解过程的稳定。以1100Al单晶为例计算了不同升温、降温速率,以及不同应变率影响下的材料应力-应变的响应。结果表明,模型能较好地反映变温过程中,单晶各向异性性质的演化以及应力、应变之间关系的变化。     

有限变形下单晶变温本构模型

本文构造了单晶热弹粘塑性的本构模型,模拟材料在不同温度下的力学行为。该模型以晶体热运动学作为分析变形的基础,即考虑温度变化情况下总体变形梯度的乘式分解,建立温度影响下的以弹性变形梯度为基本变量的控制方程来描述单晶材料的变形,算法采用隐式积分方法来求解控制方程以保证计算的稳定性。模型能反映单晶材料变形过程中温度对应力-应变响应的影响。     

多晶体变形、应力的不均匀性及宏观响应

从单晶滑移变形分析的角度探讨多晶体塑性变形和应力的不均匀性及宏观力学响应：建议了 一种当前构形下以应力为基本变量的单晶黏塑性增量迭代计算方法；用Voronoi晶粒集合体 模型研究多晶体由于晶粒几何及取向的随机性造成的变形和应力的不均匀性, 进行了多晶集 合体的宏观响应和晶粒位向演化数值分析. 结果表明：(1)多晶体内等效塑性应变和应力分量在统计上呈现高斯分布，在应变硬化过程中, 随着塑性变形增加多晶体微观应力的统计变异系数会越来越大；(2)用Voronoi模型计算可得到沿最大剪应力方向的滑移变形带；(3)多晶体内最高三轴拉应力一般出现在晶界特别是三晶交界处；(4)Voronoi模型能用于织构分析.     

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。     

晶粒数量对多晶集合体初始各向异性的影响

Taylor类多晶晶体粘塑性模型被用于研究晶粒数量对随机分布多晶体拉伸塑性各向异性的影响。分别沿包含不同晶粒数量的多晶集合体的各方向进行单向拉伸数值模拟实验，得到多晶集合体各方向在一定等效应变下的等效应力，并用云图和等高线表示在多晶体的参考球面上。定义了描述多晶集合体各向异性程度的参考指标。讨论了三种确定晶体随机取向的方法。计算结果表明：晶粒数量有限的多晶集合体的应力应变响应仍有一定的各向异性，且随着晶粒数量增多，多晶集合体的各向异性程度降低；就所包含晶粒数相同的多晶集合体来说，在确定晶粒随机取向时，选取不同的方法对它的各向异性程度也有一定的影响。     

热粘塑性体的积分—微分型本构关系

应用ИЛЪЮШИН关于应力是五维偏应变空间变形历史的泛函的概念和Ｖａｌａｎｉｓ有关内时理论的描述，本文提出，对热粘塑性体，应力可设为应变、应变率和温度历史泛；并应用Ｍｉｌｌｅｒ和其它一些作者有关内变量演化方程的描述，由此建立了热粘塑性体的积分－微分型本构方程这一积分－微分型本构关系大体和Ｍｉｌｌｅｒ微分型模型等价。对１０２０钢的单轴本构响应进行了数值模拟，和Ｔａｎａｋａ与Ｍｉｌｌｅｒ的分析及一些实     

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。     

热粘塑性体的积分－微分型本构关系

应用　　　关于应力是五维偏应变空间变形历史的泛函的概念和Ｖａｌａｎｉｓ有关内＊时理论的描述，本文提出，对热粘塑性体，应力可设为应变、应变率和温度历史的泛函；并应用Ｍｉｌｌｅｒ和其它一些作者有关内变量演化方程的描述，由此建立了热粘塑性体的积分－微分到本构方程．这一积分－微分型本构关系大体和Ｍｉｌｌｅｒ微分型模型等价．对１０２０钢的单轴本构响应进行了数值模拟，和Ｔａｎａｋａ与Ｍｉｌｌｅｒ的分析及一些实验结果符合较好．     

SiCp/Al复合材料增强颗粒尺寸效应的细观分析

运用Voronoi方法建立了反映金属基颗粒增强复合材料(MMCp)微结构的多晶集合体代表性单元(RVE);采用Taylor关系推导了包含颗粒结构尺寸和体积分数参数的位错滑移硬化函数;建立了由300个平均粒度约为20μm的晶粒组成的多晶集合体代表性单元,并对MMCp3.5-5、MMCp3.5-10、MMCp10-5、MMCp10-10四种具有不同粒径和体积分数的铝基SiC颗粒增强复合材料在宏观均匀变形条件下的应力应变响应进行了数值模拟。计算结果表明:复合材料的应力应变模拟曲线与试验曲线吻合得较好,说明所推导的模型和硬化模式能够合理地描述颗粒增强尺度效应的变化趋势;多晶体模型也能够合理地表现复合材料内部应力应变在空间分布上的细观不均匀性。数值模拟结果反映了颗粒增强区承载着较大的载荷份额,而非颗粒存在区(基体)则承受着高达18%的应变,在两个区域的交界处出现了高达310MPa的应力集中,与已有文献试验观测的结果比较吻合。     

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%。     

A new integration algorithm for finite deformation of thermo-elasto-viscoplastic single crystals

An algorithm for integrating the constitutive equations in thermal framework is presented, in which the plastic deformation gradient is chosen as the integration variable. Compared with the classic algorithm, a key feature of this new approach is that it can describe the finite deformation of crystals under thermal conditions. The obtained plastic deformation gradient contains not only plastic defor- mation but also thermal effects. The governing equation for the plastic deformation gradient is obtained based on ther- mal multiplicative decomposition of the total deformation gradient. An implicit method is used to integrate this evo- lution equation to ensure stability. Single crystal 1 100 aluminum is investigated to demonstrate practical applications of the model. The effects of anisotropic properties, time step, strain rate and temperature are calculated using this integration model.     

延性单晶非均匀变形的三维有限元模拟

对延性单晶在拉伸载荷作用下的应变局域化和颈缩等非均匀变形过程进行了三维有限元数值模拟。将相关晶体塑性本构模型及一种新的数值积分方法补充到ABAQUS6.1商用有限元软件中。该方法的特点是，利用晶体塑性的动力学方程，获得一个关于晶体弹性变形梯度的演化方程，采用半隐式积分方案进行求解。本文推导出一种新的应力变本构矩阵。按此方式更新本构矩阵，计算速度和计算稳定性大大提高。加载方式，边界条件和变形程度等因素影响着滑移系的启动状况，这是平面模型所不能预测的。本文利用三维有限元方法模拟了不同取向下滑移系的启动状况，全面地考虑了FCC单晶材料12个可能滑移系在变形过程中的启动状况，合理地模拟了FCC面心立方单晶沿不同取向加载时晶轴旋转导致的应变局域化和颈缩等非均匀变形过程。     

Self-consistent modeling of large plastic deformation, texture and morphology evolution in semi-crystalline polymers

A self-consistent model for semi-crystalline polymers is proposed to study their constitutive behavior, texture and morphology evolution during large plastic deformation. The material is considered as an aggregate of composite inclusions, each representing a stack of crystalline lamellae with their adjacent amorphous layers. The deformation within the inclusions is volume-averaged over the phases. The interlamellar shear is modeled as an additional slip system with a slip direction depending on the inclusion's stress. Hardening of the amorphous phase due to molecular orientation and, eventually, coarse slip, is introduced via Arruda-Boyce hardening law for the corresponding plastic resistance. The morphology evolution is accounted for through the change of shape of the inclusions under the applied deformation gradient. The overall behavior is obtained via a viscoplastic tangent self-consistent scheme. The model is applied to high density polyethylene (HDPE). The stress-strain response, texture and morphology changes are simulated under different modes of straining and compared to experimental data as well as to the predictions of other models.     

Bending of single crystal microcantilever beams of cube orientation: Finite element model and experiments

The aim of this work is to investigate the microstructure evolution, stress-strain response and strain hardening behavior of microscale beams. For that purpose, two single crystal cantilever beams in the size dependent regime were manufactured by ion beam milling and beams were bent with an indenter device. A crystal plasticity material model for large deformations was implemented in a finite element framework to further investigate the effect of boundary constraints. Simulations were performed using bulk material properties of single crystal copper without any special treatment for the strain gradients. The difference between the slopes of the experimental and the simulated force displacement curves suggested negligible amount of strain gradient hardening compared to the statistical hardening mechanisms.     

Discrete dislocation dynamics modelling of mechanical deformation of nickel-based single crystal superalloys

Discrete dislocation dynamics (DDD) has been used to model the deformation of nickel-based single crystal superalloys with a high volume fraction of precipitates at high temperature. A representative volume cell (RVC), comprising of both the precipitate and the matrix phase, was employed in the simulation where a periodic boundary condition was applied. The dislocation Frank-Read sources were randomly assigned with an initial density on the 12 octahedral slip systems in the matrix channel. Precipitate shearing by superdislocations was modelled using a back force model, and the coherency stress was considered by applying an initial internal stress field. Strain-controlled loading was applied to the RVC in the [0 0 1] direction. In addition to dislocation structure and density evolution, global stress-strain responses were also modelled considering the influence of precipitate shearing, precipitate morphology, internal microstructure scale (channel width and precipitate size) and coherency stress. A three-stage stress-strain response observed in the experiments was modelled when precipitate shearing by superdislocations was considered. The polarised dislocation structure deposited on the precipitate/matrix interface was found to be the dominant strain hardening mechanism. Internal microstructure size, precipitate shape and arrangement can significantly affect the deformation of the single crystal superalloy by changing the constraint effect and dislocation mobility. The coherency stress field has a negligible influence on the stress-strain response, at least for cuboidal precipitates considered in the simulation. Preliminary work was also carried out to simulate the cyclic deformation in a single crystal Ni-based superalloy using the DDD model, although no cyclic hardening or softening was captured due to the lack of precipitate shearing and dislocation cross slip for the applied strain considered.     

Deformation gradient based kinematic hardening model

A kinematic hardening model applicable to finite strains is presented. The kinematic hardening concept is based on the residual stresses that evolve due to different obstacles that are present in a polycrystalline material, such as grain boundaries, cross slips, etc. Since these residual stresses are a manifestation of the distortion of the crystal lattice a corresponding deformation gradient is introduced to represent this distortion. The residual stresses are interpreted in terms of the form of a back-stress tensor, i.e. the kinematic hardening model is based on a deformation gradient which determines the back-stress tensor. A set of evolution equations is used to describe the evolution of the deformation gradient. Non-dissipative quantities are allowed in the model and the implications of these are discussed. Von Mises plasticity for which the uniaxial stress–strain relation can be obtained in closed form serves as a model problem. For uniaxial loading, this model yields a kinematic hardening identical to the hardening produced by isotropic exponential hardening. The numerical implementation of the model is discussed. Finite element simulations showing the capabilities of the model are presented.     

Nonlinear Fractional Order Viscoelasticity at Large Strains

In this paper, we formulate a fractional order viscoelastic model for large deformations and develop an algorithm for the integration of the constitutive response. The model is based on the multiplicative split of the deformation gradient into elastic and viscous parts. Further, the stress response is considered to be composed of a nonequilibrium part and an equilibrium part. The viscous part of the deformation gradient (here regarded as an internal variable) is governed by a nonlinear rate equation of fractional order. To solve the rate equation the finite element method in time is used in combination with Newton iterations. The method can handle nonuniform time meshes and uses sparse quadrature for the calculations of the fractional order integral. Moreover, the proposed model is compared to another large deformation viscoelastic model with a linear rate equation of fractional order. This is done by computing constitutive responses as well as structural dynamic responses of fictitious rubber materials.     

Nonlinear Fractional Order Viscoelasticity at Large Strains

In this paper, we formulate a fractional order viscoelastic model for large deformations and develop an algorithm for the integration of the constitutive response. The model is based on the multiplicative split of the deformation gradient into elastic and viscous parts. Further, the stress response is considered to be composed of a nonequilibrium part and an equilibrium part. The viscous part of the deformation gradient (here regarded as an internal variable) is governed by a nonlinear rate equation of fractional order. To solve the rate equation the finite element method in time is used in combination with Newton iterations. The method can handle nonuniform time meshes and uses sparse quadrature for the calculations of the fractional order integral. Moreover, the proposed model is compared to another large deformation viscoelastic model with a linear rate equation of fractional order. This is done by computing constitutive responses as well as structural dynamic responses of fictitious rubber materials.