Grain-size effect in viscoplastic polycrystals at moderate strains

Abstract

This work deals with the prediction of grain-size dependent hardening in FCC and BCC polycrystalline metals at moderately high strains (2–30%). The model considers 3–D, polycrystalline aggregates of purely viscoplastic crystals, and simulates quasi-static deformation histories with a hybrid finite element method implemented for parallel computation. The hardening response of the individual crystals is considered to be isotropic, but modified to include a physically motivated measure of lattice incompatibility which is supposed to model, in the continuum setting, the resistance to plastic flow provided by lattice defects. The length-scale in constitutive response that is required on dimensional grounds appears naturally from physical considerations. The grain-size effect in FCC polycrystals and development of Stage IV hardening in a BCC material are examined. Though the grain-size does not enter explicitly into the constitutive model, an inverse relationship between the macroscopic flow stress and grain-size is predicted, in agreement with experimental results for deformation of FCC polycrystals having grain-sizes below 100 microns and at strains beyond the initial yield (>2%). The development of lattice incompatibility is further shown to predict a transition to Stage IV (linear) hardening upon saturation of Stage III (parabolic) hardening.