A dislocation-based constitutive model was suggested which incorporated the mechanical interaction between mobile dislocations and grain boundaries into a crystal-plasticity finite-element framework. This approach was based upon the introduction of an additional activation energy into the rate equation for mobile dislocations in the vicinity of grain boundaries. The energy barrier was 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 was formulated as a vectorial conservation law. The new model was 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 were in excellent agreement with the experiments in terms of the von Mises equivalent strain distributions and textures. The study revealed that the incorporation of the misorientation alone was not sufficient to describe the influence of grain boundaries on polycrystal micro-mechanics. Three mechanisms were observed which jointly produced a marked local hardening in front of grain boundaries, and other interfaces. These were accumulation of geometrically necessary dislocations, resistance to slip penetration, and a change in the orientation spread near to grain boundaries. These were in addition to the classical kinematic hardening effect, which arose automatically in crystal-plasticity finite-element models due to a change in the Schmid factor across grain boundaries.

On the Consideration of Interactions between Dislocations and Grain Boundaries in Crystal Plasticity Finite Element Modeling – Theory, Experiments and Simulations. A.Ma, F.Roters, D.Raabe: Acta Materialia, 2006, 54[8], 2181-94