A multiscale approach to modelling size effect in crystal plasticity is presented. At the microscale, 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.

The question of the description of the elastic fields of dislocations and of the plastic strains generated by their motion is central to the connection between dislocation-based and continuum approaches of plasticity. In the present work, the homogenization of the elementary shears produced by dislocations is discussed within the frame of a discrete-continuum numerical model. In the latter, a dislocation dynamics simulation is substituted for the constitutive form traditionally used in finite element calculations. As an illustrative example of the discrete-continuum model, the stress field of single dislocations is obtained as a solution of the boundary value problem. The hybrid code is also shown to account for size effects originating from line tension effects and from stress concentrations at the tip of dislocation pile-ups. ? 2001 Elsevier Science Ltd. All rights reserved.

The solution is given for the state of stress induced in an infinite plane by a uniform distribution of edge dislocations present over a general triangle. This provides the basis of a ?perturbation element? for modelling macroscopic plastic flow, providing a systematic and internally consistent way of developing a plasticity solution from an underlying elasticity solution to a problem.