The effect of specimen size on the uniaxial deformation response of planar single crystals and polycrystals was investigated using discrete dislocation plasticity. The dislocations were all of edge character and modelled as line singularities in a linear elastic material. The lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation were incorporated through a set of constitutive rules. Grain boundaries were modelled as impenetrable to dislocations. Two types of polycrystalline materials were considered: one that only has grains with a single orientation while the other has a checker-board arrangement of two types of grains which were rotated 90° with respect to each other. The single crystals displayed a strong size dependence with the flow strength increasing with decreasing specimen size. In sufficiently small single crystal specimens, the nucleation rate of the dislocations was approximately equal to the rate at which the dislocations exit the specimens so that below a critical specimen size the flow strength was set by the strength of the initially present Frank–Read sources. On the other hand, grain boundaries acting as barriers to plastic deformation in polycrystalline specimens of the same size lead to a more diffuse deformation pattern and to a nearly size-independent response.

Size Effects in Uniaxial Deformation of Single and Polycrystals - a Discrete Dislocation Plasticity Analysis. D.S.Balint, V.S.Deshpande, A.Needleman, E.Van der Giessen: Modelling and Simulation in Materials Science and Engineering, 2006, 14[3], 409-22