A method for linking thermally activated dislocation mechanisms of yielding with continuum plasticity theory

Abstract

This work combines classical continuum mechanics, the continuously dislocated continuum theory as developed by Kröner and Bilby with discrete dislocation theory to develop quantities that permit models involving interactions between individual dislocations to be incorporated into a description of multiaxial yielding of a material. Two quantities distinguish this approach from earlier efforts: firstly, a dislocation mobility tensor relating the velocity of a dislocation configuration to the net Peach–Koehler force on the configuration and, secondly, a vector quantity representing the dislocation content of the materials. The theory of thermally activated motion of dislocations past obstacles is employed to relate the dislocation velocity to stress by a stress-dependent mobility tensor whose components are determined by the nature of the interaction of the moving dislocation with the obstacle. An example is presented in which the obstacle is a forest dislocation that affects a gliding dislocation through mutual interaction of their stress fields. The development leads to a quantity that can be used as a plastic potential for the construction of an associated flow law.