A new method was presented for the accurate calculation of self and mutual interactions between dislocation loops. Loops of arbitrary shape were segmented, with appropriate parametric equations representing the dislocation line vector. Field equations for infinitesimal linear elasticity were developed on the basis of isotropic elastic Green's tensor functions. The accuracy and speed of the method were illustrated by calculating the stress field around a typical (110)-[111] slip loop in a body-centered cubic crystal. The method was shown to be highly accurate, for short-range dislocation interactions, with no loss of computational speed when compared with analytical evaluations of the stress field for short linear segments. The calculations of self-forces and energies for curved segments were certain to be accurate, because of the continuity of line curvature on the loop.

Curved Parametric Segments for the Stress Field of 3-D Dislocation Loops. N.M.Ghoniem: Journal of Engineering Materials and Technology, 1999, 121[2], 136-42