Solid angles in N dimensional space: Application of spherical volume theory to crystal yield surfaces

Abstract

A general method is presented to calculate solid angles, in N dimensional spaces, associated with a given cone of vectors. This method is applied here to a study of the shape of a facetted crystal yield surface. The case of the Bishop and Hill yield polyhedron of fcc crystals undergoing a completely imposed strain is treated in detail. The probability of activating a given type of yield vertex is obtained from the ratios for the solid angles associated with the corresponding cone of normals. Some applications of this method to polycrystal plasticity problems are outlined, with the aim of predicting the anisotropic behaviour of textured polycrystals. © 1989.