Plastic Flow in a Composite: A Comparison of Nonlocal Continuum and Discrete Dislocation Predictions

A two-dimensional model composite with elastic reinforcements in a crystalline matrix subject to macroscopic shear is considered using both discrete dislocation plasticity and a nonlocal continuum crystal plasticity theory. Only single slip is permitted in the matrix material. The discrete dislocation 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 gradient that provides a measure of plastic (or elastic) incompatibility. This nonlocal formulation preserves the classical structure of the incremental boundary value problem. Two composite morphologies are considered; one gives rise to relatively high composite hardening and a dependence of the stress-strain response on size, while the other exhibits nearly ideally plastic composite response and size independence. The predictions of the two plasticity models for the overall composite stress-strain response and for the phase averages of stress are compared. Material parameters are found with which the nonlocal continuum plasticity formulation predicts trends that are in good accord with the discrete dislocation plasticity simulations.