For the calculation of load or residual stresses from measured strain data by means of x-rays or neutrons, the so called x-ray elastic constants are required. Usually they are calculated from the corresponding single crystal data assuming some models such as Voigt, Reuss or Kr?ner. In this paper, the finite element method is used to guarantee both, stress equilibrium and strain compatibility across the grain boundaries. The method is applicable to materials with a random texture as well as to specimens with a given texture using the information of the Orientation Distribution Function (ODF). All crystal structures are supported. The method is demonstrated on trigonal Al_2O_3 and on textured thin films of Tungsten and Niobium.
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