Isotropic orientation distributions of cubic crystals

摘要

The determination of the effective elastic properties of aggregates of crystalline grains with or without texture is a long standing problem. Presently, such averages are investigated and their anisotropy is quantified by an anisotropy tensor. The harmonic decomposition of foruth-order tensors is applied to both the elasticity tensors of single crystals with cubic symmetry as well as to the effective elasticity tensors of aggregates of cubic single crystals. It is shown that the anisotropic parts of the different estimates of the effective stiffnesses are irreducible. A set of four discrete crystal orientations is presented, which ensures the isotropy of the effective elastic properties, i.e., a vanishing of the harmonic parts of different averages.