Enhanced modeling of hardening in crystal plasticity for FCC metals

A crystal plasticity model for large plastic deformation of FCC metals is extended in order to be able to predict grain size dependent effects. An aggregate of grains at a material point is considered, where each grain is subdivided into a single crystal interior section and several bi-crystals, which are assumed to represent the grain boundaries, each having the crystallographic orientations of their adjacent grains. The micro-macro interaction law is taken into account by a Taylor approach, which is modified for the bi-crystal elements : compatibility as well as stress equilibrium are met at their interface. Moreover, during loading, a plastic deformation difference between the grain core and the associated bi-crystal half arises, of which a plastic strain gradient can be determined, dependent on the grain size. To maintain compatibility of the lattice between the core and the boundary, a certain amount of geometrically-necessary dislocations (GNDs) is required. These dislocations form additional obstacles to the dislocation movement supporting the ongoing plastic deformation, and accordingly introduce enhanced slip system hardening. The well-known Hall-Petch relation, indicating the empirical influence of the grain size on the flow stress, is simulated numerically.