The strengthening of metallic alloys which resulted from dislocation/particle interactions was investigated with regard to the initiation and propagation of shear bands, and a dislocation model was presented in order to explain these phenomena. It consisted of a discontinuous tilt wall which originally contained N infinite straight dislocations. The wall interacted with rigid particles and bowed out between them as these particles acted as pinning points. At a critical stress, the bow-out became unstable and its front propagated to form a shear band. An analytical solution was obtained for the increase in elastic strain energy which occurred as the tilt wall bowed out between the 2 rigid particles. The bow-out configuration was approximated by using a finite number of straight-line segments. The critical state at the onset of instability was obtained by minimizing the free energy. This led to an estimate of the flow stress and of its dependence upon the particle spacing. It was found that the predictions of the model were in good agreement with published experimental data.

M.Rhee, J.P.Hirth, H.M.Zbib: Acta Metallurgica et Materialia, 1994, 42[8], 2645-55