Rotational diffusion and grain size dependent shear instability in nanostructured materials

Previous experimental observations on some nanostructured metals have indicated a transition from homogeneous to non-homogeneous plastic deformation with a reduction in grain size [Jia D, Ramesh KT, Ma E. Acta Mater 2003;51:349]. We present a model that predicts the development of shear bands in such materials under quasi-static loading rates. Motivated by microscopic observations, a grain rotation based geometric softening mechanism is implemented as an internal variable within a viscoplastic constitutive setting. The model predicts the occurrence of the shear bands at small grain sizes, whereas at larger grain sizes it predicts homogeneous plastic flow. The model also predicts the phenomenon of shear band broadening with strain, which is experimentally observed, and attributes this to the “rotational diffusion” mechanism along with the restoration of material hardening within the band following the saturation of grain reorientation. Finally, we provide a localization index that can be used to classify nanostructured metals in terms of the susceptibility to this shear band mechanism.