Internal length scale and grain boundary yield strength in gradient models of polycrystal plasticity: How do they relate to the dislocation microstructure?

Gradient plasticity provides an effective theoretical framework to interpret heterogeneous and irreversible deformation processes on micron and submicron scales. By incorporating internal length scales into a plasticity framework, gradient plasticity gives access to size effects, strain heterogeneities at interfaces, and characteristic lengths of strain localization. To relate the magnitude of the internal length scale to parameters of the dislocation microstructure of the material, 3D discrete dislocation dynamics (DDD) simulations were performed for tricrystals of different dislocation source lengths (100, 200, and 300 nm). Comparing the strain profiles deduced from DDD with gradient plasticity predictions demonstrated that the internal length scale depends on the flow-stress-controlling mechanism. Different dislocation mechanisms produce different internal lengths. Furthermore, by comparing a gradient plasticity framework with interfacial yielding to the simulations it was found that, even though in the DDD simulations grain boundaries (GBs) were physically impenetrable to dislocations, on the continuum scale the assumption of plastically deformable GBs produces a better match of the DDD data than the assumption of rigid GBs. The associated effective GB strength again depends on the dislocation microstructure in the grain interior.