准D5晶粒各向异性集合的弹性本构研究

多晶体金属材料由微小晶粒集合而成，晶粒的物理性质和金属的微结构决定了该多晶体材料的宏观力学性质．常见金属多晶体材料的晶粒有面心立方、体心立方和密排六方结构．基于Voigt模型，Morris和Sayers给出了立方晶粒正交集合的弹性本构关系，Huang则给出了立方晶粒各向异性集合的弹性本构关系．假设一材料是由大量的准D5晶粒集合而成(称为准多D5晶体)，利用准D5晶粒的对称性研究D5晶粒弹性本构关系，然后基于Voigt模型和Reuss模型分别推导出准D5晶粒各向异性集合的有效弹性刚度张量和有效弹性柔度张量．在本文中，品粒取向分布函数(ODF)w(R)用来描述多晶体中的晶粒取向为R的可能性密度，给出了弹性本构与织构系数之间的关系表达式．

Constitutive Relation of Anisotropic Aggregate of Quasi-D5 Crystallites

A polycrystal is an aggregate of tiny crystallites separated by grain boundaries.The physical properties of the crystallites and the microstructures of the polycrystal,which include grain orientations and grain boundary structure,determine macroscopic properties of the polycrystal. Metals often consist of cubic crystals or hexagonal crystals.Using Voigt model, Morris and Sayers gave elastic constitutive tensor for an orthorhombic aggregate of cubic crystallites;however,Huang derived elastic constitutive tensor for an anisotropic aggregate of cubic crystallites.Assuming a material to be an anisotropic aggregate of many tiny quasi- D_5 crystallites,we study elastic constitutive relation of quasi- D_5 crystals and then get the effective elastic stiffness tensor and the effective softness tensor for an anisotropic aggregate of quasi- D_5 crystallites under Voigt model and Reuss model,respectively.In this paper,we use the (ODF) w( R) (the orientation distribution function) to describe the probability density of finding a crystallite with orientation R and find relations between elastic constitutive tensors and the texture coefficients.