A model for the inverse Hall–Petch relation of nanocrystalline materials

We propose a composite model to explain the phenomena of strength softening with decreasing the grain size, which was reported in some nanocrystalline (nc) materials. We assume that a nc material consists of a grain interior and an amorphous grain-boundary layer. The grain interior deforms elastically under external stresses, while the plastic deformation of the grain-boundary layer was governed by a Maxwellʹs equation. Based on this model, it will be shown that the strength of a nc material decreases linearly with decreasing the grain size, when the grain size is below a certain threshold. The model is compared with the experimental data from the published studies on nc Cu and Ni. The predictions of relevant creep mechanisms for nc materials are also discussed.