Development of a dislocation density based constitutive model for crystal plasticity FEM with special regard to grain boundaries

Plastic deformation of metals is mainly caused by crystallographic slip of dislocations. Therefore, physical constitutive models use dislocation densities as state variables in opposition to empirical models which mostly use the accumulated strain as state variable. In the talk it is demonstrated how evolution laws for the dislocation densities can be derived and how the stress-strain relationship can be evaluated on the basis of the Orowan equation. The framework of crystal plasticity FEM offers a link between the physical process of dislocation slip and the most powerful tool in continuum mechanics the FEM. It will therefore also be shown how a dislocation density based model can be extended for the incorporation into crystal plasticity FE simulations. The model is applied to the deformation of Aluminium single and bicrystals. In these examples the importance of the treatment of strain gradients and the grain boundary becomes obvious. Therefore, the local dislocation density model is extended to a nonlocal one in a physically sound manner. The final model is capable of predicting the local deformation behaviour of the Al bicrystals much more precisely than a phenomenological viscoplastic crystal plasticity model.