Curved Parametric Segments for the Stress Field of 3-D Dislocation Loops

Abstract

Under applied mechanical forces, strong mutual interaction or other thermodynamic forces, dislocation shapes become highly curved. We present here a new method for accurate computations of self and mutual interactions between dislocation loops. In this method, dislocation loops of arbitrary shapes are segmented with appropriate parametric equations representing the dislocation line vector. Field equations of infinitesimal linear elasticity are developed on the basis of isotropic elastic Green’s tensor functions. The accuracy and computational speed of the method are illustrated by computing the stress field around a typical (110)-[111] slip loop in a BCC crystal. The method is shown to be highly accurate for close-range dislocation interactions without any loss of computational speed when compared to analytic evaluations of the stress field for short linear segments. Moreover, computations of self-forces and energies of curved segments are guaranteed to be accurate, because of the continuity of line curvature on the loop.