Grain-size effect in viscoplastic polycrystals at moderate strains

This work deals with the prediction of grain-size dependent hardening in FC C and BCC polycrystalline metals at moderately high strains (2-30%). The mo del considers 3-D, polycrystalline aggregates of purely viscoplastic crysta ls, and simulates quasi-static deformation histories with a hybrid finite e lement method implemented for parallel computation. The hardening response of the individual crystals is considered to be isotropic, but modified to i nclude a physically motivated measure of lattice incompatibility which is s upposed 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 conside rations. The grain-size effect in FCC polycrystals and development of Stage IV hardening in a BCC material are examined. Though the grain-size does no t enter explicitly into the constitutive model, an inverse relationship bet ween 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 transi tion to Stage IV (linear) hardening upon saturation of Stage III (parabolic ) hardening. (C) 2000 Elsevier Science Ltd. All rights reserved.