Relation between Third-Order Elastic Constants of Single Crystals and Polycrystals

Abstract

The approximations by Voigt, Reuss, and Hill for calculating the elastic constants of polycrystals from the elastic constants of single crystals are extended to the third‐order elastic constants. The general relations including the expressions for the third‐order elastic compliances are presented and given explicitly for cubic symmetry. They are used to calculate the polycrystalline third‐order elastic constants of eleven cubic materials. For cubic symmetry, relations for the pressure derivatives of the second‐order elastic constants in the approximations of Voigt, Reuss, and Hill are also presented, and the anisotropy of the third‐order elastic constants is discussed. It is found that for all materials considered, the anisotropy for the third‐order elastic constants is much larger than the anisotropy of the second‐order elastic constants, and that a weak correlation exists between the anisotropy of the third‐order elastic constants and of the second‐order elastic constants.