Curved parametric segments for the stress field of 3-D dislocation loops

Under applied mechanical forces, strong mutual interaction or other thermodynamic forces, dislocation shapes became 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 al-e segmented with appropriate parametric equations representing the dislocation line vector Field equations of infinitesimal linear elasticity ar-e 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.