In order to study the effect of a difference, between the shear moduli of a particle and a matrix, upon flow stress and work-hardening, a numerical approach based upon discrete dislocation simulations was developed. The image stress upon dislocations, which was caused by a second-phase impenetrable particle, was used. The glide of a dislocation line, of initially screw type, through a channel between 2 spherical particles with a differing shear modulus, was simulated. A shear stress was applied incrementally to the slip plane, and the equilibrium position of the dislocation line was calculated for the given applied stress. It was found that the flow stress, at which the dislocation by-passed the obstacles by bowing between a pair of particles, varied as (ΔG/Gm)α, where Gm was the shear modulus of the matrix and ΔG was the difference between the shear moduli. Here, α was found to be less than unity, and the effect of ΔG increased as the radius of the spherical particles increased. The stress increment which was required to force a dislocation to glide, between particles which had Orowan loops remaining from previous slip, became higher as the particle became harder. It was found that dislocations could bypass particles, by cross-slip, as soon as a critical number of Orowan loops surrounding the particles was reached. The image stress field around the particle, produced by a difference between the shear moduli, appeared to enhance the cross-slip probability.

Dislocation-Impenetrable Precipitate Interaction - a Three-Dimensional Discrete Dislocation Dynamics Analysis. C.S.Shin, M.C.Fivel, M.Verdier, K.H.Oh: Philosophical Magazine, 2003, 83[31], 3691-704