The orientation distribution of crystallites in a polycrystal can be described by the orientation distribution function(ODF) . The ODF can be expanded under the Wigner D-bases. The expanded coefficients in the ODF are called the texture coefficients. In this paper,we use the Clebsch-Gordan expression to derive an explicit expression of the elasticity tensor for an anisotropic cubic polycrystal. The elasticity tensor contains three material constants and nine texture coefficients. In order to measure the nine texture coefficients by ultrasonic wave,we give relations between the nine texture coefficients and ultrasonic propagation velocities. We also give a numerical example to check the relations.
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.
