A multiscale multiplicative decomposition for elastoplasticity of polycrystals

A new kinematic formulation of polycrystalline elastoplasticity is proposed, based on principles of multiscale volume averaging. The homogenized macroscopic deformation gradient for an aggregate of grains consists of three terms: the elastic or recoverable deformation associated with the average stress and lattice rotation, the volume-averaged residual plastic deformation attributed to the history of dislocation glide, and an additional term consisting of residual local (mesoscopic) elastic and plastic deformation gradients associated with the single to polycrystal transition. This additional term, typically neglected in the phenomenological macroscopic multiplicative decomposition, indicates the presence of heterogeneous residual local elastoplastic deformations among constituent grains and sub-grains. Finite element simulations of deforming polycrystals, employing crystal plasticity theory for the local, mesoscopic constitutive behavior, serve to demonstrate the descriptive capabilities of the macroscopic model. Two-dimensional finite element meshes encompassing on the order of 100 grains, constructed from an enhanced optical image of a sample of polycrystalline OFHC Cu, are subjected to finite tension, compression, and shear deformation. Initial lattice misorientation distributions are varied among simulations. Positive correlation is found between the deformation gradient term associated with mesoscopic heterogeneity and the residual lattice energy density in the macroscopic stress-free intermediate configuration. Furthermore, relatively large magnitudes of effective stress and elastic energy density associated with local plastic incompatibility are found in the vicinity of high-angle grain boundaries and triple points, serving as potential driving forces for damage initiation in materials prone to intergranular separation modes.