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 nanocrystal line (tic) materials. We assume that a tic material consists of a grain interior and an amorphous grain-boundary layer. The grain interior deforms elastically tinder external stresses, while the plastic deformation of the grain-boundary layer was governed by a Maxwell's equation. Based on this model, it will be shown that the strength of a tic 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 tic Cu and Ni. The predictions of relevant creep mechanisms for tic materials are also discussed. (c) 2005 Elsevier B.V. All rights reserved.