A dislocation density tensor-based crystal plasticity framework

The present contribution addresses a crystal plasticity formulation which incorporates hardening effects that are related to the presence of geometrically necessary dislocations. To this end, higher gradient contributions are introduced as additional arguments of the energy function based on microstructural considerations. Extending the derivations presented in Kaiser and Menzel (2019) for a purely phenomenological, associated type plasticity model to crystal plasticity, it is shown that the higher gradient contributions in terms of dislocation density tensors give rise to the balance equation of a generalised stress field together with non-ambiguous constitutive boundary conditions. This stress field can be shown to be energetically conjugated to the plastic flow and is additively composed of two parts: the classic stress field and a back-stress type stress field which is closely related to incompatibilities in the plastic deformation field and hence interpretable in terms of geometrically necessary dislocations. For a specific model which features twelve slip systems the constitutive response on material point level is studied in a first step before finite element based simulations, which are motivated by experimental findings on copper micro wires, are analysed in two- and three-dimensional settings