A continuum model for slip transfer at grain boundaries

Using a continuous representation of dislocations in elastoplastic polycrystals, we investigate slip transfer at grain boundaries by assessing the compatibility of the slip system shear rates with tangential continuity of the plastic distortion rate tensor at these interfaces. Fulfillment of this tangential continuity condition is needed for consistency of the continuous description of dislocations in polycrystals. We show that, in f.c.c. materials at moderate temperatures, this condition unequivocally translates into constraints on the slip rates on both sides of grain boundaries. Appended to the elastoplastic boundary value problem, it allows a complete determination of the slip system shear rates. An algorithm enabling the implementation of compatible slip transfer in both the finite element methods and the spectral methods based on Fast Fourier Transforms is provided in both standard crystal plasticity and the mechanics of dislocations fields.