基于Voigt模型和Reuss模型的三方晶粒各向异性集合的弹性本构关系

多晶体材料的宏观力学性质与晶粒的化学成分和多晶体的微结构（晶粒的尺寸、取向分布、边界结构）有关，研究多晶体微结构与材料宏观力学性质的关系具有重要的理论意义和工程应用背景。利用三方晶粒的D3对称性给出了三方晶粒的弹性本构关系，通过引入ODF描述多晶体材料的取向分布，基于Voigt模型和Reuss模型分别找出带有织构系数影响的三方晶粒任意集合的多晶体材料弹性本构关系上、下限。

ELASTIC CONSTITUTIVE EQUATIONS OF ANISOTROPIC AGGREGATE OF TRIAANGLECRYSTALLITES UNDER VOIGT''''S MODEL AND REUSS''''MODEL

A polycrystalline material is an aggregate of tiny crystallites separated by grain boundaries.The chemical composition and the arrangement of the constituting crystallites,which includes grain orientations and grain boundary structure,determine the mechanics properties of the polycrystal.It is very important to study microstructures of polycrystals because of its engineering application.In this paper,we use the D_3 symmetry of triangle crystallites to obtain elastic constitutive relation of crystallites with D_3 symmetry.By introducing the orientation distribution function(ODF) to describe the probability density of finding a crystallite with orientation R,we derive an elastic stiffness tensor and an elastic softness tensor of an anisotropic aggregate of D_3 crystallites under Voigt's model and Reuss' model,respectively.The elastic stiffness tensor and the elastic softness tensor's inverse are the upper bound and the lower bound of the effective elastic stiffness tensor,respectively.