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用广义球谐函数的级数推导晶体取向分布的Roe法被应用到分析轧制立方材料的织构。对立方晶体对称的和正交物理对称的材料,推导了作为广义球谐函数基础的增广雅可毕多项式到第十六阶。级数的展开式在第十六阶的截断应该允许处理具有最大值为17倍无规强度和在半最大值处的最小角宽度为34°的织构。发展了一种数值方法,它允许从一纽有限的数据点近似估计积分方程。对工业用钢阐明了这个方法,并用这个方法说明了脱碳的Fe—3％Si合金的初次再结晶织构。
The Roe method, which deduces the crystal orientation distribution using the series of generalized spherical harmonic functions, is applied to the texture analysis of rolled cubic materials. For the symmetric and orthorhombic material of cubic crystal, the augmented Jacobi polynomial which is the basis of the generalized spherical harmonic function is deduced to the sixteenth order. The truncation of the expansions of the series at the sixteenth order should allow the processing of textures having a maximum randomness of 17 times the intensity and a minimum angular width of 34 ° at half maximum. A numerical method has been developed that allows approximations of integral equations from a limited number of data points. This method is elucidated for industrial steels and uses this method to demonstrate the primary recrystallization texture of the decarburized Fe-3% Si alloy.