The Elastic Anisotropy of Crystals

Abstract

Essentially, the elastic properties of all the known crystals are anisotropic. This paper presents a convenient method to describe the degree of the elastic anisotropy in a given cubic crystal and then discusses its practical values. On the basis of the well‐known Voigt and Reuss schemes to average the single‐crystal elastic constants for polycrystalline behavior, the degree of elastic anisotropy has been defined as A* = [3(A−1)²]/[3(A−1)²+25A], where A is the usual anisotropy factor given by A = 2c₄₄/(c₁₁−c₁₂). It is shown that the present A* has the folowing properties of practical importance: (a) A* is zero for the crystals of the elastic isotropy, i.e., A = 1. (b) For an anisotropic crystal, A* is a single‐valued measure of the elastic anisotropy regardless of whether A < 1 or A > 1. (c) A* gives a relative magnitude of the actual elastic anisotropy possessed by a crystal.