Multiscale modelling of size effect in fcc crystals: discrete dislocation dynamics and dislocation-based gradient plasticity

A multiscale approach to modelling size effect in crystal plasticity is presented. At the rnicroscale, discrete dislocation dynamics (DD) coupled with finite element (FE) analysis allows the rigorous treatment of a broad range of micro-plasticity problems with minimal phenomenological assumptions. At the macroscale, a gradient crystal plasticity model, which incorporates scale-dependence by introducing the density of geometrically necessary dislocations (GNDs) in the expression of mean glide path length, is used. As a case study, bending of micro-sized single crystal beams is considered and the correspondence between the predictions of both models is made. In its current framework, the macroscale model did not capture the experimentally observed effect of specimen size on the initial yield stress. With this effect naturally captured in the corresponding DD analysis, the absence of a density-independent size effect in the expression for the strength of slip systems was concluded. In an independent work on the tensile loading of micrometer-sized polycrystals [1], a size effect, physically rooted in the size and location of Frank-Read sources (FRS) relative to grain boundaries, was identified. This effect can be generalized in the context of dislocation-interface interactions, typically missing to one degree or another, in current,gradient crystal plasticity models and can, in principle, be used to understand the initial yield size-dependence in single crystal bending identified through DD analysis.