Plastic slip distribution in two-phase laminate microstructures: Dislocation-based versus generalized-continuum approaches

The size-dependent mechanical response of a simple model microstructure is investigated using continuum dislocation-based, Cosserat and strain-gradient models of crystal plasticity. The governing equations and closed-form analytical solutions for plastic slip and lattice rotation are directly compared. The microstructure consists of a periodic succession of hard (elastic) and soft (elastoplastic single-crystal) layers, subjected to single glide perpendicular to the layers. In the dislocation-based approach, inhomogeneous plastic deformation and lattice rotation are shown to develop in the soft channels, either because of bowing of dislocations or owing to pile-up formation. The generalized continuum non-local models are found to be able to reproduce the plastic slip and lattice rotation distribution. In particular, a correspondence was found between the generalized-continuum results and line tension effects; the additional or higher- order balance equations introduced in the non-local models turn out to be the counterparts of the equilibrium equation for bowed dislocations. The relevance and possible physical interpretation of additional or higher-order interface conditions responsible for the inhomogeneous distribution of plastic slip and lattice rotations are discussed.