An application of multisurface plasticity theory: yield surfaces of textured materials

Directionally dependent descriptions of material yield as determined by polycrystal plasticity computations are discrete in nature and, in principle, are available for use in large-scale application calculations employing multi-dimensional continuum mechanics codes. However, the practical side of using such detailed yield surfaces in application calculations contains some challenges in terms of algorithm development and computational efficiency. Pole figures, commonly measured by X-ray diffraction, are used to portray the distribution of crystallographic grain orientations in a polycrystalline material. The calculated orientation distribution can then be used to weight a set of discrete orientations to generate a representation of the measured texture. This discrete representation can be probed in the context of a Taylor—Bishop—Hill polycrystal calculation in order to assemble a set of deviatoric stress points that discretely map out the material's yield surface. These stress points can be fitted or tessellated into a multi-dimensional piece-wise linear representation of the yield surface for subsequent use in a continuum code constitutive algorithm. Such an algorithm that utilizes an associated flow based multisurface plasticity theory has been implemented in the three dimensional portion of the EPIC continuum mechanics code and is described in this effort.