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.