Calculation of the Yield Locus of Textured Polycrystals Using the Taylor and the Relaxed Taylor Theory

Several authors have proposed methods which use the Taylor–Bishop–Hill theory in order to calculate the yield surface of textured samples of which the O.D.F. is known. The purpose of this paper is to show how these methods can be generalized while keeping the computational effort within reasonable limits. It must be emphasized that the new method produces “true” plane sections of the yield locus instead of so-called “principle strain yield loci.” A theorem that permits the exploitation of the sample symmetry is demonstrated. After a general description of the method, it is explained how the theorem can be used in order to restrict the number of deformation modes that must be considered. The next section discusses how a data bank of Taylor factors can be constructed. The full-constraint Taylor theory as well as the relaxed Taylor theory are considered. In the next section, it is explained how the plane sections through the multidimensional yield locus are generated. A few applications are finally discussed, including a study of the elongation of a torsion sample of which the O.D.F. has been measured.