Mechanism-based discrete dislocation plasticity was used to investigate the effect of size upon micron scale crystal plasticity under conditions of macroscopically homogeneous deformation. Long-range interactions among dislocations were naturally incorporated through elasticity. Constitutive rules were used which account for key short-range dislocation interactions. These included junction formation and dynamic source and obstacle creation. Two-dimensional calculations were carried out which could handle high dislocation densities and large strains up to 0.1. The focus was laid on the effect of dimensional constraints on plastic flow and hardening processes. Specimen dimensions ranging from hundreds of nanometers to tens of microns were considered. The findings revealed a strong size-dependence of flow strength and work-hardening rate at the micron scale. Taylor-like hardening was shown to be insufficient as a rationale for the flow stress scaling with specimen dimensions. The predicted size effect was associated with the emergence, at sufficient resolution, of a signed dislocation density. Heuristic correlations between macroscopic flow stress and macroscopic measures of dislocation density were sought. Most accurate among those was a correlation based upon two state variables: the total dislocation density and an effective, scale-dependent measure of signed density.

Size Effects under Homogeneous Deformation of Single Crystals - a Discrete Dislocation Analysis. P.J.Guruprasad, A.A.Benzerga: Journal of the Mechanics and Physics of Solids, 2008, 56[1], 132-56