Finite Element Discretization of the Energy of Inclined Grain Boundaries within a Gradient Plasticity Model

A significant contribution to the overall mechanical behaviour of microstructural materials is provided by the interaction of dislocation movement and grain boundaries. As a consequence, polycrystals are observed to respond with a higher strength for smaller grain sizes, a phenomenon which can not be modeled with classical single crystal plasticity theories. Gradient plasticity theories have been developed to describe this size dependency, assuming that grain boundaries commonly either act as impenetrable obstacles or allow unrestricted dislocation movement, cf. Gurtin (2002). By means of an energetic grain boundary energy approach, the grain boundary conditions can be generalized (see, e.g., Wulfinghoff et al., 2013) to allow for a behaviour in between the two idealized limits. The additional energy contribution rises with increasing plastic flow, and consequently stores energy associated to the plastic or defect state of the grain boundary. In order to extend the in-house finite element implementation to incorporate inclined grain boundaries, a discretization strategy is developed.