Parametric dislocation dynamics: A thermodynamics-based approach to investigations of mesoscopic plastic deformation

A thermodynamics-based variational method is developed to establish the equ ations of motion for three-dimensional (3D) interacting dislocation loops. The approach is appropriate for investigations of plastic deformation at th e mesoscopic scale by direct numerical simulations. A fast sum technique fo r determination of elastic field variables of dislocation ensembles is util ized to calculate forces acting on generalized coordinates of arbitrarily c urved loop segments. Each dislocation segment is represented by a parametri c space curve of specified shape functions and associated degrees of freedo m. Kinetic equations for the time evolution of generalized coordinates are derived for general 3D climb/glide motion of curved dislocation loops. It i s shown that the evolution equations for the position (P), tangent (T), and normal (N) vectors at segment nodes are sufficient to describe general 3D dislocation motion. When crystal structure constraints are invoked, only tw o degrees of freedom per node are adequate for constrained glide motion. A selected number of applications are given for: (1) adaptive node generation on interacting segments, (2) variable time-step determination for integrat ion of the equations of motion, (3) dislocation generation by the Frank-Rea d mechanism in fee, bcc, and de crystals, (4) loop-loop deformation and int eraction, and (5) formation of dislocation junctions.