Rheology of Earth Materials :

Closing the gap between timescales in the laboratory and in the mantle

30 August 2021 - Two new publications from F. Delannay


The work revisits the model of diffusional deformation by accounting for the dependence of the diffusion potential on grain boundary curvature.  Two case-studies are analysed: the deformation of a lattice of columnar grains, and the rotation of a grain embedded in a polycrystal.  A link is established between the curvature distribution and the transfer of diffusion fluxes across grain boundaries.  Unless grain boundary mobility is infinite, grain boundary curvature is dynamically induced by strain rate.  The classical model assuming flat grain boundaries with transfer of fluxes via triple junctions emerges as a particular case involving the implicit assumption of an infinite grain boundary mobility.  The contributions to power dissipation arising from curvature are found to scale closely as the square of grain size.  The dissipation contribution due to curvature translates into a lower bound for the apparent boundary viscosity parameter to be used in numerical simulations. 



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 work considers that moving disconnections pile-ups nucleate at triple junctions.  The internal strain field associated to disconnection pile-ups brings a distribution of GB tractions 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.  The analysis shows that the dissipation due to the nucleation and recovery of climbing disconnections is equal to 50% of the dissipation arising from diffusion fluxes.  It highlights the sources of non-Newtonian behaviour and the existence of a threshold stress as an intrinsic feature of diffusional creep.