The Hall–Petch and inverse Hall–Petch relations and the hardness of nanocrystalline metals

We review some of the factors that influence the hardness of polycrystalline materials with grain-sizes less than 1 µm. The fundamental physical mechanisms that govern the hardness of nanocrystalline materials are discussed. The recently proposed dislocation curvature model for grain size dependent strengthening and the 60-year old Hall-Petch relationship are compared. For grains less than 30 nm in size, there is evidence for a transition from dislocation-based plasticity to grain boundary sliding, rotation or diffusion as the main mechanism responsible for hardness. The evidence surrounding the inverse Hall-Petch phenomenon is found to be inconclusive due to processing artefacts, grain growth effects and errors associated with the conversion of hardness to yield strength in nanocrystalline materials