A two-dimensional model composite, composed of elastic reinforcement in a crystalline matrix, was analyzed. It was subjected to macroscopic shear, and the effect was investigated in terms of discrete dislocation plasticity and conventional continuum slip crystal plasticity. In the former case, the dislocations were modelled as line defects in a linear elastic medium. At each loading stage, superposition was used to represent the solution in terms of an infinite-medium solution for the discrete dislocations; plus a complimentary solution that enforced the boundary conditions. The latter was non-singular, and was obtained from a linear-elastic finite-element solution. Lattice resistance to dislocation motion, dislocation nucleation and dislocation annihilation were incorporated into the formulation via a set of constitutive rules. Obstacles which could lead to dislocation pile-ups were also accounted for. Results were presented for materials having a single slip system. A reinforcement size-effect was revealed by the discrete-dislocation based analysis, whereas the continuum slip results were size-independent. The discrete-dislocation results indicated higher average reinforcement stress levels than did the corresponding continuum-slip calculations. Averaging of the stress fields over regions of increasing size was used to obtain some insight into the transition from discrete-dislocation controlled to continuum behavior.

Comparison of Discrete Dislocation and Continuum Plasticity Predictions for a Composite Material. H.H.M.Cleveringa, E.Van der Giessen, A.Needleman: Acta Materialia, 1997, 45[8], 3163-79