Residual stresses and strains in a two-dimensional model composite which consisted of elastic reinforcements in a crystalline matrix were analyzed. The composite was subjected to macroscopic shear and was then unloaded. Plane-strain conditions, and single slip on slip planes parallel to the shear direction, were assumed. The dislocations were modelled as line defects in a linear elastic medium. At each stage of loading, superposition was used to represent the solution in terms of the infinite medium solution for the discrete dislocations. An image solution enforced the boundary conditions. This was non-singular and was deduced from a linear elastic finite-element solution. Lattice resistance to dislocation motion, dislocation nucleation and dislocation annihilation were incorporated via a set of constitutive rules. Obstacles which could lead to dislocation pile-ups were also accounted for. Considerable reverse plasticity was found when the reinforcement arrangement was such that all slip planes were cut by particles, and when the unloading rate was equal to the loading rate. When unloading took place at a very high rate, the unloading slope was essentially elastic; but relaxation of the dislocation structure occurred in the unloaded state. Predictions of the discrete dislocation formulation for residual stresses, residual strains and strain variance were compared with the corresponding predictions which were obtained using conventional continuum slip crystal plasticity. The effect of particle size, as predicted by the discrete dislocation description, was also addressed.

A Discrete Dislocation Analysis of Residual Stresses in a Composite Material. H.H.M.Cleveringa, E.Van der Giessen, A.Needleman: Philosophical Magazine A, 1999, 79[4], 893-920