Dimensional Changes in Crystals Caused by Dislocations

Abstract

According to the classical linear elasticity theory, if one or more dislocations are introduced into a body of elasticmaterial, the average value of each of the infinitesimal strain components is zero; in particular, the change in volume is zero. This result seems not to be in accord with experimental data on cold worked metals. In this paper we use nonlinear elasticity theory to show how changes in the average dimensions of elastic bodies, either isotropic or anisotropic, resulting from the introduction of dislocations, can be calculated. In particular, we derive an explicit relation between the resultant change in volume, the stored energy, and the pressure derivatives of the elastic moduli.