The Stress Field of Rectangular Prismatic Dislocation Loops

Abstract

A closed-form analytical solution for the resolved shear stress field of an elongated rectangular dislocation loop is obtained. The stress field plays a significant role in modelling of dislocation patterns. Assuming the linear isotropic elasticity, the stress fields for the loops with infinitesimal and fine heights are derived. The standard methods of calculation are used: in the former case the integration of the stress field of infinitesimal loops is applied, in the latter case the summation of stress fields of four straight dislocation segments forming the loop is utilized. The obtained stress solution for the loop with the finite height is compared with the much simpler analytical formula for the stress field of the loop of the infinitesimal height and the range of validity of the infinitesimal height approximation is determined.