The dependence of shear yield strength on grain size was analyzed using discrete dislocation dynamics. Plastic deformation was modelled through the motion of edge dislocations in an elastic solid. 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. Single slip was assumed within each grain and a checkerboard-like arrangement of grains was used as a unit cell for the polycrystal. Doubly-periodic pure shear calculations were carried out for planar polycrystals with grain sizes in the range of 0.2 to 5μm and for 2 values of initial dislocation source density that differ by an order of magnitude. The offset flow strength varies with grain size, d, as d−n, with n = 0.40 or 0.45; depending upon the source density. The value of the offset flow strength was higher for the low source density polycrystal. Furthermore, for each initial source density, the flow strength was found to scale roughly with dislocation density.

A Discrete Dislocation Plasticity Analysis of Grain-Size Strengthening. D.S.Balint, V.S.Deshpande, A.Needleman, E.Van der Giessen: Materials Science and Engineering A, 2005, 400-401, 186-90