Plastic flow in a composite: a comparison of nonlocal continuum and discrete dislocation predictions

A two-dimensional model composite with elastic reinforcements in a crystall ine matrix subject to macroscopic sheer is considered using both discrete d islocation plasticity and a nonlocal continuum crystal plasticity theory. O nly single slip is permitted in the matrix material. The discrete dislocati on results are used as numerical experiments, and we explore the extent to which the nonlocal crystal plasticity theory can reproduce their behavior. In the nonlocal theory, the hardening rate depends on a particular strain g radient that provides a measure of plastic (or elastic) incompatibility. Th is nonlocal formulation preserves the classical structure of the incrementa l boundary value problem. Two composite morphologies are considered; one gi ves rise to relatively high composite hardening and a dependence of the str ess-strain response on size while the other exhibits nearly ideally plastic composite response and size independence. The predictions of the nonlocal plasticity model are confronted with the results of the discrete dislocatio n calculations for the overall composite stress-strain response and the pha se averages of stress. Material parameters are found with which the nonloca l continuum plasticity formulation predicts trends that are in good accord with the discrete dislocation plasticity simulations. (C) 2001 Elsevier Sci ence Ltd. All rights reserved.