The displacement, and strain–stress fields of a general circular Volterra dislocation loop

Abstract

A closed-form analytical solution for the displacement, and strain–stress fields of a circular Volterra dislocation loop having a glide and prismatic components is obtained. Assuming linear elasticity and infinite isotropic material, the displacement field is found by integrating the Burgers displacement equation for a circular dislocation loop. The strain field is subsequently obtained and stresses follow from Hooke's law. The field equations are expressed in terms of complete elliptic integrals of the first, second, and/or third elliptic integrals. The general loop solution is, from the principle of superposition, the additive sum of the prismatic and glide solutions.