Multiscale modeling of the effective viscoplastic behavior of Mg 2 SiO 4 wadsleyite: bridging atomic and polycrystal scales

The viscoplastic behavior of polycrystalline Mg2SiO4 wadsleyite aggregates, a major high pressure phase of the mantle transition zone of the Earth (depth range: 410–520 km), is obtained by properly bridging several scale transition models. At the very fine nanometric scale corresponding to the dislocation core structure, the behavior of thermally activated plastic slip is modeled for strain-rates relevant for laboratory experimental conditions, at high pressure and for a wide range of temperatures, based on the Peierls–Nabarro–Galerkin model. Corresponding single slip reference resolved shear stresses and associated constitutive equations are deduced from Orowan’s equation in order to describe the average viscoplastic behavior at the grain scale, for the easiest slip systems. These data have been implemented in two grain-polycrystal scale transition models, a mean-field one (the recent Fully-Optimized Second-Order Viscoplastic Self-Consistent scheme of [1]) allowing rapid evaluation of the effective viscosity of polycrystalline aggregates, and a full-field (FFT based [2, 3]) method allowing investigating stress and strain-rate localization in typical microstructures and heterogeneous activation of slip systems within grains. Calculations have been performed at pressure and temperatures relevant for in-situ conditions. Results are in very good agreement with available mechanical tests conducted at strain-rates typical for laboratory experiments.This work was supported by the European Research Council under the Seventh Framework Programme (FP 7), ERC (grant number 290424 RheoMan) and under the Horizon 2020 research and innovation programme (grant number 787198 TimeMan)

Modeling dislocation glide in Mg2SiO4 ringwoodite: Towards rheology under transition zone conditions

AbstractDeformation resulting from thermally activated plastic slip is modeled in Mg2SiO4 ringwoodite at 20GPa for a wide range of temperatures. The model relies on the structures of the rate controlling 1/2〈110〉 screw dislocations which have been modeled using the Peierls–Nabarro–Galerkin method. These calculations are parametrized by density functional theory calculations of γ-surfaces of the {001},{110} and {111} planes. At finite temperatures, dislocation mobility is controlled by kink-pair nucleation on the thermally activated 1/4〈110〉 partial screw dislocations as they occur in ringwoodite. Single slip critical resolved shear stresses (CRSS) corresponding to this mechanism are deduced from Orowan’s equation. The results are found to be in reasonably good agreement with experimental data at 20GPa which show high effective flow stresses under laboratory conditions. Finally, the CRSS’s are calculated for typical mantle strain rates of ∊̇=10-16s−1 at appropriate temperatures expected in the lower transition zone. Results show that dislocation glide remains difficult and that lattice friction is not yet negligible in ringwoodite under natural conditions