The size-dependent mechanical response of a simple model microstructure was investigated by using continuum dislocation-based Cosserat and strain-gradient models for crystal plasticity. The governing equations and closed-form analytical solutions for plastic slip and lattice rotation were directly compared. The microstructure consisted 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 were shown to develop in the soft channels; either because of the bowing of dislocations or due to pile-up formation. The generalized continuum non-local models were 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 into the non-local models turned out to be the counterparts of the equilibrium equation for bowed dislocations.

Plastic Slip Distribution in Two-Phase Laminate Microstructures - Dislocation-Based versus Generalized-Continuum Approaches. S.Forest, R.Sedláček: Philosophical Magazine, 2003, 83[2], 245-76