多晶体中的晶粒取向分布可通过取向分布函数(orientation distribution function,ODF)表示.取向分布函数(ODF)可在Wigner D-函数基下展开,其展开系数称为织构系数.利用Clebsch-Gordan表达式推导出立方晶粒各向异性集合多晶体的弹性张量显表达式,该弹性张量表达式包含3个材料常数和9个织构系数.为了织构系数的超声波测定,给出了这9个织构系数与超声波速之间的关系式,并通过一个算例来验证这个关系式.
Some physical properties of crystals differ indirection n because crystal lattices are often anisotropic.A polycrystal is an aggregate of numerous tiny crystallites.Unless the polycrystal is an isotropic aggregate of crystallites,the physical properties of the polycrystal vary with n.The direction-dependent functions (DDF) for crystals andpolycrystals are introduced to describe the variations of thephysical properties in direction n. Until now there are fewpapers dealing systematically with relations between theDDF and the crystalline orientation distribution. Herein wegive general expressions of the DDF for crystals and polycrystals.We discuss the applications of the DDF in describingthe physical properties of crystals and polycrystals.
An orthorhombic polycrystal is an orthorhombic aggregate of tiny crystallites. In this paper, we study the effect of the crystalline mean shape on the constitutive relation of the orthorhombic polycrystal. The crystalline mean shape and the crystalline orientation arrangement are described by the crystalline shape function (CSF) and the orientation distribution function (ODF), respectively. The CSF and the ODF are expanded as an infinite series in terms of the Wigner D-functions. The expanded coefficients of the CSF and the ODF are called the shape coefficients sm0l and the texture coefficients cmnl respectively. Assuming that Ceff in the constitutive relation depends on the shape coefficients sm0l and the texture coefficients cmnl, by the principle of material frame-indifference we derive an analytical expression for Ceff up to terms linear in sm0l and cmnl , and the expression would be applicable to the polycrystal whose texture is weak and whose crystalline mean shape has weak anisotropy. Ceff contains six unspecified material constants (λ, μ, c, s1, s2, s3), five shape coefficients (s020, s220, s400, s420, s440), and three texture coefficients (c400, c420, c440). The results based on the perturbation approach are used to determine the five material constants approximately. We also find that the shape coefficients s2m0 and s4m0 are all zero if the crystalline mean shape is a cuboid. Some examples are given to compare our computational results.
