Modelling size effects using 3D density-based dislocation dynamics

Abstract

We use density-based continuity equations to model strain patterns and size effects in confined plastic flow, namely, shearing of thin films and microbending. To this end, we use a representation in terms of coupled equations for the densities of screw and edge components. We show how these equations derive from a more general formulation in a higher-dimensional configuration space, and discuss relations with other density-based approaches proposed in the past. The new element here is the incorporation into previous continuum formulations of geometrical features and interactions of dislocation lines that cannot be neglected or ‘averaged out’ within a three-dimensional setting of plasticity at the micron and nano-scales.

Acknowledgements

We acknowledge the support of the Commission of the European Communities under contracts MRTN-CT-2003-506434 (SizeDepEn) and HPRN-CT 2002-00198, and of EPSRC under Grant No. GR/S20406/01.

Notes

†The notion of a ‘mesoscopic’ internal-stress field is motivated by the fact that this stress field is defined on the same scale as the dislocation density measure ρ and the plastic strain γ. If ρ and γ are considered as smooth averages over volume elements containing many dislocations, the same holds for τ_mf.