A superdislocation model for the strengthening of metal matrix composites and the initiation and propagation of shear bands

Abstract

Strengthening in metallic alloys resulting from dislocation-particle interaction is investigated in connection with the initiation and propagation of shear bands. A dislocation model is presented in this work to explain these phenomena. It consists of a discontinuous tilt wall initially containing N infinite straight dislocations. The wall interacts with rigid particles and bows out between them as these particles act as pinning points. At a critical stress, the bow-out becomes unstable and its front propagates to form a shear band. An analytical solution is formulated for the increase in the elastic strain energy as the tilt wall bows out between the two rigid particles. The bow-out configuration is approximated by a finite number of straight line segments. The critical state at the onset of instability is obtained by minimizing the free energy, leading to an estimate for the flow stress and its dependence on particle spacing. The model is in good agreement with experimental data found in the literature.