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利用Ｘ射线衍射测定材料的残余应力时，织构的存在引起材料宏观弹性各向异性，从而导致εψ－ｓｉｎ２ψ关系丧失线性．为了获取这类材料应力分析的近真应力－应变关系，必须定量地考虑材料中晶粒择优取向对宏观弹性性质的影响．近年来在织构ＯＤＦ分析法的基础上，相继提出适于织构材料应力分析的数学方法，本文详尽地阐述了这种方法的基本原理，并尽可能提供了所需数学处理的细节．所述方法也力图博采众长，以期尽量减少测试和计算的工作量．
When X-ray diffraction is used to measure the residual stress of the material, the existence of texture causes the macroscopic elastic anisotropy of the material, resulting in a loss of linearity of the εψ-sin2ψ relationship. In order to obtain the near-true stress-strain relationship of stress analysis of such materials, the influence of the preferred orientation of grains in the material on the macroscopic elastic properties must be considered quantitatively. In recent years, based on the texture ODF analysis method, mathematical methods suitable for stress analysis of textured materials have been put forward one after another. This paper elaborates the basic principle of this method and provides the details of the mathematical processing as much as possible. The approach also seeks to draw upon the general public with a view to minimizing the workload of testing and computing.