Simulation of the Hall–Petch effect in ultra-fine grained copper

The evolution of the yield and flow stress in polycrystals with characteristic grain sizes ranging from 2  μ m down to 500 nm is studied by two-dimensional dislocation dynamics simulations. The results obtained are consistent with a Hall–Petch relationship. In addition, a linear relation is found between the rate of increase of the dislocation density and the inverse of the grain size. As a consequence, the size effect in this grain size range is found to be governed by the reduction in dislocation mean-free path induced by grain boundaries rather than by dislocation nucleation.