An alternative physical explanation of the Hall–Petch relation

Abstract A new physical model to explain the Hall–Petch relation is proposed. The main assumption is that the Hall-Petch slope ( k y ), is proportional to the work required to eject dislocations from grain boundaries. The model predicts a traditional Hall–Petch relation down to a grain size of about 5 μm, below which a deviation from linearity is observed. The strengthening peaks in the vicinity of 30 nm, and further grain refinement leads to softening. A semi-empirical equation is developed, which takes into account the effects of grain boundary strain energy. The model is applicable to both equiaxed and non-equiaxed grain structures.