A model for rate-dependent flow of metal polycrystals based on the slip plane lattice incompatibility

A constitutive framework that considers rate-dependent deformation and grain-size dependent work hardening of FCC and BCC metals at moderate temperature is proposed. This model considers 3-D polycrystalline aggregates of viscoplastic crystals. The hardening response of the individual single crystals is considered to be isotropic (Taylor model), but modified to include a physically-motivated measure of slip plane lattice incompatibility. In the continuum setting, a density of net dislocations is derived from the lattice incompatibility. The association of a mean free path (that distance a dislocation can move before unit length is stored) with the net dislocation density is introduced into the evolution equation for hardening. Application is made to grain-size effect in work hardening, nanoindentation, and the transition from stage III (parabolic) to stage IV (linear) hardening.