Analytical investigation of a grain boundary model that accounts for slip system coupling in gradient crystal plasticity frameworks

In this work, a physically based dislocation theory of plasticity is derived within an extended continuum mechanical context. An orientation-dependent grain boundary flow rule is introduced for the modelling of dislocation pile-up at grain boundaries and dislocation transmission through grain boundaries. With the conventional grain boundary modelling approach according to Gurtin (Gurtin. 2008 J. Mech. Phys. Solids 56, 640–662. (doi:10.1016/j.jmps.2007.05. 002)) the single-crystal consistency check for the limit case of adjacent grains that hold no misorientation is not satisfied. In order to overcome this modelling shortcoming, a slip system coupling based on a geometric measure of slip system compatibility is introduced. In order to investigate the grain boundary modelling approaches, the analytical solution of a three-phase periodic laminate is used to study the interactions of dislocations and grain boundaries within the gradient crystal plasticity framework. With the developed grain boundary model two grain boundary states, i.e. microhard and microcontrolled, are observed for misaligned grains. This allows the modelling of slip activation at grain boundaries based on the dislocation pile-up stress.