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

Under applied mechanical forces, strong mutual interaction or other thermod ynamic forces, dislocation shapes became highly curved. We present here a n ew method for accurate computations of self and mutual interactions between dislocation loops. In this method, dislocation loops of arbitrary shapes a l-e segmented with appropriate parametric equations representing the disloc ation line vector Field equations of infinitesimal linear elasticity ar-e d eveloped on the basis of isotropic elastic Green's tensor functions. The ac curacy and computational speed of the method are illustrated by computing t he stress field around a typical (110)-[111] slip loop in a BCC crystal. Th e method is shown to be highly accurate for close-range dislocation interac tions without any loss of computational speed when compared to analytic eva luations of the stress field for short linear segments. Moreover, computati ons of self-forces and energies of curved segments are guaranteed to be acc urate, because of the continuity, of line curvature on the loop.