Simulated small-angle scattering patterns for a plastically deformed modelcomposite material

The small-angle scattering patterns predicted by discrete dislocation plast icity versus local and non-local continuum plasticity theory are compared i n a model problem. The problem considered is a two-dimensional model compos ite with elastic reinforcements in a crystalline matrix subject to macrosco pic shear. Only single slip is permitted in the matrix material. Emphasis i s on the relationship between characteristics of the scattering patterns an d the dislocation structures that can develop as a function of the composit e morphology. The computed small-angle scattering patterns clearly distingu ish between the different dislocation structures that arise for different c omposite morphologies. Many features of the small-angle scattering patterns are also reproduced by continuum slip plasticity theory, although the loca l features due to the discreteness of the individual dislocations are not. The non-local hardening description that gives the best fit with the overal l stress-strain response is found to also give the best agreement between t he non-local continuum and the discrete dislocation scattering patterns.