Multiscale Modeling of Nanocrystalline Materials: A Variational Approach

This paper presents a variational multi‐scale constitutive model in the finite deformation regime capable of capturing the mechanical behavior of nanocrystalline (nc) fcc metals. The nc‐material is modeled as a two‐phase material consisting of a grain interior (GI) phase and a grain boundary (GB) phase. A rate‐independent isotropic porous plasticity model is employed to describe the GB phase, whereas a crystal‐plasticity model which accounts for the transition from partial dislocation to full dislocation mediated plasticity is employed for the GI phase. Assuming the rule of mixtures, the overall behavior of a given grain is obtained via volume averaging. The scale transition from a single grain to a polycrystal is achieved by Taylor‐type homogenization. It is shown that the proposed model is able to capture the inverse Hall‐Petch effect. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)