What is behind the inverse Hall–Petch effect in nanocrystalline materials?

An inverse Hall–Petch effect has been observed for nanocrystalline materials by a large number of researchers. This effect implies that nanocrystalline materials get softer as grain size is reduced below a critical value. Postulated explanations for this behavior include dislocation-based models, diffusion-based models, grain-boundary-shearing models and two-phase-based models. In this paper, we report an explanation for the inverse Hall–Petch effect based on the statistical absorption of dislocations by grain boundaries, showing that the yield strength is dependent on strain rate and temperature and deviates from the Hall–Petch relationship below a critical grain size.