The grain size dependence of the flow strength of polycrystals was analyzed using plane strain, discrete dislocation plasticity. Dislocations were modelled as line singularities in a linear elastic solid and plasticity occurred through the collective motion of large numbers of dislocations. Constitutive rules were used to model lattice resistance to dislocation motion, as well as dislocation nucleation, dislocation annihilation and the interaction with obstacles. The materials analyzed consisted of micron-scale grains having either one or three slip systems and two types of grain arrangements: either a checker-board pattern or randomly dispersed with a specified volume fraction. Calculations were carried out for materials with either a high density of dislocation sources or a low density of dislocation sources. In all cases, the grain boundaries were taken to be impenetrable to dislocations. A Hall–Petch type relation was predicted with Hall–Petch exponents ranging from ≈0.3 to ≈1.6 depending on the number of slip systems, the grain arrangement, the dislocation source density and the range of grain sizes to which a Hall–Petch expression was fit. The grain size dependence of the flow strength was obtained even when no slip incompatibility exists between grains suggesting that slip blocking/transmission governs the Hall–Petch effect in the simulations.

Discrete Dislocation Plasticity Analysis of the Grain Size Dependence of the Flow Strength of Polycrystals. D.S.Balint, V.S.Deshpande, A.Needleman, E.Van der Giessen: International Journal of Plasticity, 2008, 24[12], 2149-72