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Equivalent Plastic Strain Gradient Plasticity with Grain Boundary Hardening and Comparison to Discrete Dislocation Dynamics

The gradient crystal plasticity framework of Wulfinghoff et al. [53] incorporating an equivalent plastic strain and grain boundary yielding, is extended with additional grain boundary hardening. By comparison to averaged results from many discrete dislocation dynamics (DDD) simulations of an aluminum type tricrystal under tensile loading, the new hardening parameter in the continuum model is calibrated. It is shown that although the grain boundaries (GBs) in the discrete simulations are impenetrable, an infinite GB yield strength corresponding to microhard GB conditions, is not applicable in the continuum model. A combination of a finite GB yield strength with an isotropic bulk Voce hardening relation alone also fails to model the plastic strain profiles obtained by DDD. Instead, a finite GB yield strength in combination with GB hardening depending on the equivalent plastic strain at the GBs is shown to give a better agreement to DDD results. The differences in the plastic strain profiles obtained in DDD simulations by using different orientations of the central grain could not be captured, indicating that the misorientation dependent elastic interaction of dislocations reaching over the GBs should be included in the continuum model.