Simulated small-angle scattering patterns for a plastically deformed model composite material

Abstract

The small-angle scattering patterns predicted by discrete dislocation plasticity versus local and non-local continuum plasticity theory are compared in a model problem. The problem considered is a two-dimensional model composite with elastic reinforcements in a crystalline matrix subject to macroscopic shear. Only single slip is permitted in the matrix material. Emphasis is on the relationship between characteristics of the scattering patterns and the dislocation structures that can develop as a function of the composite morphology. The computed small-angle scattering patterns clearly distinguish between the different dislocation structures that arise for different composite morphologies. Many features of the small-angle scattering patterns are also reproduced by continuum slip plasticity theory, although the local features due to the discreetness of the individual dislocations are not. The non-local hardening description that gives the best fit with the overall stress-strain response is found to also give the best agreement between the non-local continuum and the discrete dislocation scattering patterns.