A multiscale gradient theory for single crystalline elastoviscoplasticity

Abstract

Explicit volume averaging procedures are used to motivate a gradient-type description of single crystalline elastoviscoplasticity. Upon regarding local elastic and plastic deformation gradients within the crystal as continuously differentiable fields, we arrive at a three-term multiplicative decomposition for the volume-averaged deformation gradient, consisting of a recoverable elastic term associated with the average applied stress and average lattice rotation, an inelastic term associated with the average plastic velocity gradient, and a (new) third term reflecting the presence of the residual microelastic deformation gradient within the volume and providing a representation of the kinematics of grain subdivision via formation of low-angle subgrain boundaries, for example. A variant of the classical Eshelby stress tensor provides the driving force for homogenized viscoplastic flow, with slip resistances dictated by densities of geometrically necessary and statistically stored dislocations. Distinctive features of the continuum model include coupling of internal elastic strain energy densities associated with residual and applied stresses, dependency of the single crystalline effective elastic moduli upon evolution of lattice substructure, and a characteristic length potentially based upon both the size of the crystal element used in volume averaging and the grain subdivision measure.