Scale dependent crystal plasticity framework with dislocation density and grain boundary effects

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