A discrete dislocation analysis of residual stresses in a composite material
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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 slip planes are cut by particles and when the unloading rate is equal to the loading rate. When unloading takes place at a very high rate, the unloading slope is essentially elastic but relaxation of the dislocation structure occurs in the unloaded state. Predictions 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. 1999 Taylor & Francis Group, LLC.