六角晶粒各向异性多晶体弹性本构关系的一般形式  

General Form of Constitutive Relations for Anisotropic Aggregates of Hexagonal Crystallites

作　　者：黄模佳[1] 郑腾龙[1] 

机构地区：[1]南昌大学工程力学研究所,江西南昌330031

出　　处：《南昌大学学报（理科版）》2009年第3期272-278,共7页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(10562004;10662004);高等学校博士学科点专项科研基金资助项目(20070403003);江西省自然基金资助项目(2008GZW0005);江西省教育厅科技计划项目([2006]3)

摘　　要：金属多晶体材料是大量微小立方晶粒或六角晶粒的集合体,晶格结构的各向异性导致晶粒弹性性质的各向异性,也使得六角晶粒多晶体的弹性性质与晶粒取向分布有关。多晶体的晶粒取向分布可由取向分布函数(ODF)描述,ODF在Wigner D-函数基下展开成级数形式,其展开系数为织构系数。基于Voigt模型和Reuss模型,Li和Thompson(1990)推导出六角晶粒正交集合的弹性本构关系。Man(1998)利用代数方法给出了立方晶粒正交集合本构关系的一般形式。本文利用Clebsch-Gordan表达式推导出六角晶粒各向异性多晶体的弹性本构关系,其结果适用于六角晶粒各向异性集合体,它不依赖于任何物理模型,为六角晶粒各向异性多晶体弹性本构关系的一般形式。Metal polycrystals are aggregates of numerous tiny cubic crystallites or hexagonal crystallites. Since the anisotropy of crystal lattices leads to the anisotropy of elastic properties for crystals, the elastic properties of a hexagonal polycrystal depend on not only single crystal elastic constants but also the crystalline orientation distribution. The crystalline orientation distribution can be described by the orientation distribution function （ODF）. The ODF can be expanded under Wigner D -functions and the corresponding expanded coefficients are called the texture coefficients. Based on Voigt model and Reuss model, the constitutive relation for an orthorhombic aggregate of hexagonal crystallites was derived by Li and Thompson （1990）. By an algebra method,Man （1998） gave the general form of constitutive relation for an orthorhombic aggregate of cubic crystallites. In this paper, we obtain the general expression of constitutive relation for an anisotropic aggregate of hexagonal crystallites. The general expression is model independent.

关 键 词：多晶体材料弹性本构关系 六角晶粒 ODF Clebsch—Gordan表达式 

分 类 号：O343.8[理学—固体力学]