The geometrically non-linear scale dependent response of polycrystal face-centered cubic metals was modelled by an enhanced crystal plasticity framework based upon the evolution of several dislocation density types and their distinct physical influence on the mechanical behavior. The isotropic hardening contribution follows from the evolution of statistically stored dislocation densities during plastic deformation, where the determination of the slip resistance was based upon the mutual short range interactions between all dislocation types, i.e. including the geometrically necessary dislocation densities. Moreover, the geometrically necessary dislocations introduced long range interactions by means of a back-stress measure, opposite to the slip system resolved shear stress. The grain size dependent mechanical behavior of a limited collection of grains under plane stress loading conditions was determined using the finite element method. Each grain was subdivided into finite elements and an additional expression, coupling the geometrically necessary dislocation densities to spatial crystallographic slip gradients, renders the geometrically necessary dislocation densities to be taken as supplemental nodal degrees of freedom. Consequently, these densities could be uncoupled at the grain boundary nodes, allowing for the introduction of grain boundary dislocations based upon the lattice mismatch between neighboring grains and enabling the obstruction of crystallographic slip perpendicular to the grain boundary.

Scale Dependent Crystal Plasticity Framework with Dislocation Density and Grain Boundary Effects. L.P.Evers, W.A.M.Brekelmans, M.G.D.Geers: International Journal of Solids and Structures, 2004, 41[18-19], 5209-30