Constitutive modelling of strength and plasticity of nanocrystalline metallic materials

A phase mixture model is proposed to describe the deformation behaviour of a nanocrystalline metallic material. The deformation behaviour of the crystallite phase is described by constitutive equations based on dislocation density evolution and includes a contribution from diffusion controlled plastic flow. The dislocation glide contribution to the plastic strain rate is considered to vanish below a certain critical grain size. The grain boundary material, which is treated as a separate phase, is considered to deform by a diffusional mechanism, resulting in a viscous Newtonian behaviour. The strain in both phases is assumed to be the same and equal to the imposed macroscopic strain. The stress is calculated using a simple rule of mixtures. The grain size dependence of the stress-strain curves obtained is shown to be in reasonable agreement with experiments, as are the predicted strain rate effects. In particular, observed deviations from the Hall-Petch behaviour are described by the model correctly. The effect of grain size distribution is also considered. (C) 2001 Elsevier Science B.V. All rights reserved.