Discrete dislocation simulations and size dependent hardening in single slip

Plastic deformation in two-dimensional monophase and composite materials is studied using a discrete dislocation dynamics method. In this method, dislocations are represented by line defects in a linear elastic medium, and their interactions with boundaries or second-phase elastic particles are incorporated through a complementary finite element solution. The formulation includes a set of simple constitutive rules to model the lattice resistance to dislocation glide, as well as the generation, annihilation and pinning of dislocations at point obstacles. The focus is on the predicted strain hardening of these materials when only a single slip system is active. When the particle morphology is such as to require geometrically necessary dislocations, hardening in the composite materials exhibits a distinct size effect. This size effect is weaker than that predicted by simple analytical estimates based on geometrically necessary dislocations.