Abstract
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.
Highlights
The plastic anisotropy of a material is often described by a yield surface
The twofold rotation symmetry axis that is meant here belongs to the sample symmetry of the texture, not to the crystal symmetry (see e.g. Bunge (1982))
This means that a tremendous number of distinct strain rate tensors must be considered when trying to cover all possible deformation modes within a certain angular resolution. Such a method has been developed (Mols et al, 1984). After using it for some time, it was concluded that i) the textures of the considered samples most had at least a twofold symmetry axis; ii) most stress states that were of some practical interest, and for which plane sections of the yield locus had to be made, were such that this twofold symmetry axis was a principal direction of stress
Summary
The plastic anisotropy of a material is often described by a yield surface. It is the geometrical representation of the stress states for which plastic yielding occurs. Suppose that an anisotropic sample possesses a twofold rotation axis of symmetry, at least with regard to those material properties that control plastic anisotropy. This axis will be a principal direction of strain when it is a principal direction of stress. Because of condition (6), it has only five independent components This means that a tremendous number of distinct strain rate tensors must be considered when trying to cover all possible deformation modes within a certain angular resolution. Such a method has been developed (Mols et al, 1984). The M-values which are needed for the data bank can be constructed by means of a Taylor-Bishop-Hill model or by means of the relaxed Taylor-Bishop-Hill theory, for metals with flat elongated grains (Van Houtte, 1984b)
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