A dislocation pile-up model for the yield stress of a composite

Abstract

A numerical model to simulate yielding in a composite is developed for the transmission of slip across a dissimilar interface through the formation of co-planar dislocation arrays in both phases. A pile-up of dislocations in the soft phase is assumed to nucleate dislocations in the hard phase in which movement is dictated by lattice friction stress. The polycrystalline composite yield stress is calculated by determining the equilibrium positions of the dislocation arrays as a function of the length scales, elastic constants and Burgers vectors in the two phases, with particular reference to melt oxidized Al-Al₂O₃, in which homophase boundaries are absent, and to the commercially important system Co-WC. The hardness values predicted from this model are in good agreement with experimentally measured values in the above systems. The implications of these results for the design of hard composite microstructures are elucidated.