A discrete dislocation analysis of residual stresses in a composite material

Residual stresses and strains in a two-dimensional model composite consisti ng of elastic reinforcements in a crystalline matrix are analysed. The comp osite is subject to macroscopic shear and then unloaded. Plane-strain condi tions and single slip on slip planes parallel to the shear direction are as sumed. The dislocations are modelled as line defects in a linear elastic me dium. At each stage of loading, superposition is used to represent the solu tion in terms of the infinite medium solution for the discrete dislocations and an image solution that enforces the boundary conditions, which is non- singular and obtained from a linear elastic finite-element solution. The la ttice resistance to dislocation motion, dislocation nucleation and dislocat ion annihilation are incorporated into the formulation through a set of con stitutive rules. Obstacles leading to possible dislocation pile-ups are als o accounted for. Considerable reverse plasticity is found when the reinforc ement arrangement is such that all slip planes are cut by particles and whe n the unloading rate is equal to the loading rate. When unloading takes pla ce at a very high rate, the unloading slope is essentially elastic but rela xation of the dislocation structure occurs in the unloaded state. Predictio ns of the discrete dislocation formulation for residual stresses, residual strains and the strain variance are compared with corresponding predictions obtained using conventional continuum slip crystal plasticity. The effect of particle size, as predicted by the discrete dislocation description, is also addressed.