Contribution of the nucleation and recovery of disconnections to shear viscosity in diffusional creep

According to the principles of diffusional creep, the normal and tangent components of the velocity jumps between adjacent grains arise from, respectively, the climbing and sliding of disconnections along grain boundaries. Stationary deformation thus implies a balance between nucleation and recovery of moving disconnections. The model considers a periodic lattice of hexagonal grains with nucleation of disconnection multipoles at triple junctions. The strain energy coupled to the population of climbing disconnections is calculated by inferring that the internal strain field associated to disconnection pile-ups brings a distribution of tractions along GBs that is consistent with the field of diffusion potential gradient that drives disconnection climb. It follows that the distribution of the density of climbing disconnections is parabolic and that the dissipation due to the nucleation and recovery of climbing disconnections is equal to 50% of the dissipation arising from diffusion fluxes. These results hold for both Nabarro-Herring creep and Coble creep. The analysis of the disconnection nucleation process highlights the sources of non-Newtonian behaviour and the existence of a threshold stress as an intrinsic feature of diffusional creep.