织构材料X射线应力分析的线性方程组

织构材料因弹性呈现各向异性，经典Ｘ射线残余应力分析法不再适用．借助取向分布函数（ＯＤＦ）分析法，由单晶的弹性性质按织构计权平均预估材料的宏观弹性各向异性，根据广义虎克定律获得求解所需应力－应变线性方程组．为了方便实际应用，深入讨论了该线性方程组的组建问题，导出对应任何测量方向的方程式系数均为一固定宏观试样坐标系下弹性常数张量元的线性组合，该组合系数仅与测量方向有关，而与材料本身的弹性性质及织构无关．对一些通常采用的测量方向，提供了适用于具有正交试样对称的织构材料确定方程组系数所需的数据，归纳了这些数据的取值规律．所述方法可适用于任何晶体结构对称的织构材料及三维应力状态，并可推广至正交对称外的其他试样对称的织构材料．

Simultaneous Linear Equations of X-ray Stress Analysis for Textured Materials

ODFs may be used as weight functions to predict macroscopically anisotropic elastic properties of the materials from the corresponding properties of single crystals and then to obtain simultaneous linear equations expressing approximately real stress strain relationship. Discussion was focused on the build up of the linear equations. It is proved that the coefficients of all the equations are linearly combined by the tensor elements of elastic constants with respect to a fixed sample coordinate system. The combination coefficients are dependent on neither the elastic properties nor the textures of materials themselves. The values of the combination coefficients were calculated in some special measured directions for the textured materials with orthorhombic sample symmetry. And some behaviours of the values were induced. The application of the method can also be extended for the textured materials with other sample symmetries in addition to orthorhombic symmetry.