INTERFACES IN SIZE-DEPENDENT CRYSTAL PLASTICITY

Plasticity in heterogeneous materials with small domains is governed by the interactions and reactions of dislocations and interfaces. These include reactions of existing dislocations, as well as the nucleation of dislocations at an interface. The rational for interface dominated plasticity is simple: dislocations glide through the single crystal domain with relative ease, but pile-up at interfaces, so that interface reactions become a critical step in continuing plastic deformation. While the details of dislocation reactions at interfaces take place at the atomic scale, and the behavior of dislocations in bulk is most accurately modeled by discrete dislocation dynamics, both of these models are much too expensive and impractical for analyzing the resulting bulk behavior. The need for a continuum framework for describing the plasticity across crystal interfaces, including the ubiquitous size effects, is acute. Recently developed size-dependent crystal plasticity theory [Mesarovic et al. 2010 J. Mech. Phys. Solids 58, 311-29] employ's the representation of the singular part of dislocation pile-up boundary layers as superdislocation boundary layers, or equivalently, as jumps in slip at the boundary, but internal to the crystal. These boundary superdislocations exist on two sides of an interface and react or combine to lower the total energy under certain conditions. Using this theory, we obtain solutions to simple problems of single-slip and double-slip shear of sandwiched thin film. Then, we compare the results with available discrete dislocation simulations.