A general numerical method to solve for dislocation configurations

The shape of a mechanically equilibrated dislocation line is of considerabl e interest in the study of plastic deformation of metals and alloys. A gene ral numerical method for finding such configurations in arbitrary stress fi elds has been developed. Analogous to the finite-element method (FEM), a ge neral dislocation line is approximated by a series of straight segments (el ements) bounded by nodes. The equilibrium configuration is found by minimiz ing the system energy with respect to nodal positions using a Newton-Raphso n procedure. This approach, termed the finite-segment method (FSM), confers several advantages relative to segment-based, explicit formulations. The u tility, generality, and robustness of the FSM is demonstrated by analyzing the Orowan bypass mechanism and a model of dislocation generation and equil ibration at misfitting particles. Energy differences from previous analytic al methods based on simple loop shapes are significant, up to XO pet. Expli cit expressions for the coordinate transformations, energies, and forces re quired for numerical implementation are presented.