Orientation Distribution Functions for Microstructures of Heterogeneous Materials(Ⅱ)-Crystal Distribution Functions and Irreducible Tensors Restricted by Various Material Symmetries
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摘要: 目的是建立三维晶体定向分布函数(CODF)的张量傅立叶展开的显式表示.与三维ODF的傅立叶展开的第m项系数仅对应单个m阶对称无迹张量不同,三维CODF的傅立叶展开的第m项系数一般由2m+1个m阶对称无迹张量组成.随后还建立了在各种宏观和微观对称性下三维CODF的张量傅立叶展开的约束形式,表明大多数对称性下的约束形式中的m阶不可约张量数目明显少于2m+1.这些结果是通过对各种点群对称性约束下二维和三维不可约张量的约束形式的研究得到的.Abstract: The explicit representations for tensorial Fourier expansion of 3-D crystal orientation distribution functions(CODFs) are established.In comparison with that the coefficients in the m th-term of the Fourier expansion of a 3-D ODF make up just a single irreducible m th order tensor,the coefficients in the m th term of the Fourier expansion of a 3-D CODF constitute generally so many as 2m+1 irreducible m th order tensors.Therefore,the restricted forms of tensorial Fourier expansions of 3-D CODFs imposed by various microand macro-scopic symmetries are further established,and it is shown that in most cases of symmetry the restricted forms of tensorial Fourier expansions of 3-D CODFs contain remarkably reduced numbers of m th order irreducible tensors than the number 2m+1.These results are based on the restricted forms of irreducible tensors imposed by various pointgroup symmetries,which are also thoroughly investigated in the present part in both 2and 3-D spaces.
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