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 via elasticity. Constitutive rules were used which accounted for key short-range dislocation interactions. These included junction formation and dynamic source and obstacle creation. Two-dimensional calculations were performed which could treat high dislocation densities and strains of up to 0.1. Attention was focussed on the effect of dimensional constraints upon plastic flow and hardening. Specimen dimensions ranging from hundreds of nm to tens of μm were considered. The results revealed a marked size-dependence of the flow strength and work-hardening rate at the micron-scale. Taylor-like hardening was shown to be insufficient as an explanation for the flow stress to scale with the specimen dimensions. The predicted size effect was associated with the emergence, at sufficient resolution, of a signed dislocation density. Correlations between the macroscopic flow stress and macroscopic measures of dislocation density were sought. The most accurate one was found to be a correlation that was based upon two state variables: the total dislocation density and an effective scale-dependent measure of the 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