A discrete dislocation analysis of residual stresses in a composite material

Abstract

Abstract Residual stresses and strains in a two-dimensional model composite consisting of elastic reinforcements in a crystalline matrix are analysed. The composite is subject to macroscopic shear and then unloaded. Plane-strain conditions and single slip on slip planes parallel to the shear direction are assumed. The dislocations are modelled as line defects in a linear elastic medium. At each stage of loading, superposition is used to represent the solution 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 lattice resistance to dislocation motion, dislocation nucleation and dislocation annihilation are incorporated into the formulation through a set of constitutive rules. Obstacles leading to possible dislocation pile-ups are also accounted for. Considerable reverse plasticity is found when the reinforcement arrangement is such that all s...