On the consideration of interactions between dislocations and grain boundaries in crystal plasticity finite element modeling – Theory, experiments, and simulations

We suggest a dislocation based constitutive model to incorporate the mechanical interaction between mobile dislocations and grain boundaries into a crystal plasticity finite element framework. The approach is based on the introduction of an additional activation energy into the rate equation for mobile dislocations in the vicinity of grain boundaries. The energy barrier is derived by using a geometrical model for thermally activated dislocation penetration events through grain boundaries. The model takes full account of the geometry of the grain boundaries and of the Schmid factors of the critically stressed incoming and outgoing slip systems and is formulated as a vectorial conservation law. The new model is applied to the case of 50% (frictionless) simple shear deformation of Al bicrystals with either a small, medium, or large angle grain boundary parallel to the shear plane. The simulations are in excellent agreement with the experiments in terms of the von Mises equivalent strain distributions and textures. The study reveals that the incorporation of the misorientation alone is not sufficient to describe the influence of grain boundaries on polycrystal micro-mechanics. We observe three mechanisms which jointly entail pronounced local hardening in front of grain boundaries (and other interfaces) beyond the classical kinematic hardening effect which is automatically included in all crystal plasticity finite element models owing to the change in the Schmid factor across grain boundaries. These are the accumulation of geometrically necessary dislocations (dynamic effect; see [Ma A, Roters F, Raabe D. A dislocation density based constitutive model for crystal plasticity FEM including geometrically necessary dislocations. Acta Mater 2006;58:2169–79]), the resistance against slip penetration (dynamic effect; this paper), and the change in the orientation spread (kinematic effect; this paper) in the vicinity of grain boundaries.