Plastic deformation in 2-dimensional monophase and composite materials was studied by using a discrete dislocation dynamics method. The dislocations were represented by line defects in a linear elastic medium, and their interaction with boundaries or second-phase elastic particles was incorporated by means of a complementary finite-element solution. The formulation included a set of simple constitutive rules for modelling the lattice resistance to dislocation glide, as well as the generation, annihilation and pinning of dislocations at point obstacles. Attention was focussed upon the predicted strain hardening of these materials when only a single slip system was active. When the particle morphology was such as to require geometrically necessary dislocations, hardening in the composite materials exhibited a distinct size-effect. This effect was weaker than that which was predicted by simple analytical estimates that were based upon geometrically necessary dislocations.

Discrete Dislocation Simulations and Size-Dependent Hardening in Single Slip. H.Cleveringa, E.Van der Giessen, A.Needleman: Journal de Physique IV, 1998, 8[4], 83-92