The evolution of the flow stress under shear deformation, for grain sizes ranging from about 11 to 1µm, was examined by using 2-dimensional discrete dislocation dynamics. Grain boundaries were assumed to be the only sources of dislocation nucleation and also the only obstacles to dislocation motion. The analysis was confined to a single-slip system within each grain; with various orientations with respect to the slip systems of neighboring grains. Simulations were carried out for 2 sets of system sizes. In the first set of simulations, the grain morphology was maintained constant and the simulation unit cell-size was varied from 25µm x 25µm to 2.5µm x 2.5µm. In a second set of simulations, the simulation unit-cell size was maintained at 25µm x 25µm and the grain size was varied. For the grain-size ranges considered, an inverse relationship was observed between the grain size and the 0.2% offset flow stress. This was in the form of a Hall-Petch relationship, with a d-1/2 dependence; although there was some uncertainty as to the exponent. The evolution of the flow stress lay within a narrow band, when expressed as a function of the dislocation density; divided by the dislocation source density. This suggested a scaling with respect to the grain size.

The Effects of Grain Size and Dislocation Source Density on the Strengthening Behaviour of Polycrystals - a Two-Dimensional Discrete Dislocation Simulation. S.B.Biner, J.R.Morris: Philosophical Magazine, 2003, 83[31], 3677-90