Numerical simulations were used to investigate the competing grain boundary and dislocation mediated deformation mechanisms in nanocrystalline Ni with grain sizes in the range of 4 to 32nm. A 3D phase field model was presented which tracked the evolution of individual dislocations and grain boundaries. The model showed that the transition from Hall–Petch to inverse Hall–Petch, as the grain size was reduced, could not be characterized by the grain size alone and was also affected by the grain-boundary energetics. It was found that the grain size corresponding to the maximum yield stress (the transition from Hall–Petch strengthening with decreasing grain size to inverse Hall–Petch) decreased with increasing grain boundary energy. Interestingly, it was found that for grain boundaries with high cohesive energy the Hall–Petch maximum was not observed for grains in the range of 4 to 32nm.

Role of Grain Boundary Energetics on the Maximum Strength of Nanocrystalline Nickel. M.Koslowski, D.W.Lee, L.Lei: Journal of the Mechanics and Physics of Solids, 2011, 59[7], 1427-36