Multiscale modeling of the effective viscoplastic behavior of $\protect \mathrm{Mg}_2\protect \mathrm{SiO}_4$ wadsleyite: bridging atomic and polycrystal scales

O. Castelnau; K. Derrien; S. Ritterbex; P. Carrez; P. Cordier; H. Moulinec

doi:10.5802/crmeca.61

Multiscale modeling of the effective viscoplastic behavior of

{Mg}_{2} {SiO}_{4}

wadsleyite: bridging atomic and polycrystal scales

O. Castelnau ¹ ; K. Derrien ¹; S. Ritterbex ^2,³; P. Carrez ³; P. Cordier ^4,³; H. Moulinec ⁵

¹ Laboratoire PIMM, Arts et Metiers Institute of Technology, CNRS, Cnam, HESAM University, 151 boulevard de l’Hopital, 75013 Paris, France
² Geodynamics Research Center, Ehime University, 2-5 Bunkyo-cho, Matsuyama 790-8577, Japan
³ Univ. Lille, CNRS, INRAE, Centrale Lille, UMR 8207 - UMET - Unité Matériaux et Transformations, F-59000 Lille, France
⁴ Institut Universitaire de France, 1 rue Descartes, 75005 Paris, France
⁵ Aix Marseille Univ, CNRS, Centrale Marseille, LMA UMR 7031, Marseille, France

Comptes Rendus. Mécanique, Contributions in mechanics of materials, Volume 348 (2020) no. 10-11, pp. 827-846.

Abstract

The viscoplastic behavior of polycrystalline ${Mg}_{2} {SiO}_{4}$ 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.

Received: 2020-07-21
Revised: 2020-11-15
Accepted: 2020-11-17
Published online: 2021-01-13

DOI: 10.5802/crmeca.61

Keywords: Earth mantle, Multiscale modelling, Dislocations, Polycrystal, Viscoplasticity

Author's affiliations:

O. Castelnau ¹; K. Derrien ¹; S. Ritterbex ^{2, 3}; P. Carrez ³; P. Cordier ^{4, 3}; H. Moulinec ⁵

¹ Laboratoire PIMM, Arts et Metiers Institute of Technology, CNRS, Cnam, HESAM University, 151 boulevard de l’Hopital, 75013 Paris, France
² Geodynamics Research Center, Ehime University, 2-5 Bunkyo-cho, Matsuyama 790-8577, Japan
³ Univ. Lille, CNRS, INRAE, Centrale Lille, UMR 8207 - UMET - Unité Matériaux et Transformations, F-59000 Lille, France
⁴ Institut Universitaire de France, 1 rue Descartes, 75005 Paris, France
⁵ Aix Marseille Univ, CNRS, Centrale Marseille, LMA UMR 7031, Marseille, France

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {O. Castelnau and K. Derrien and S. Ritterbex and P. Carrez and P. Cordier and H. Moulinec},
     title = {Multiscale modeling of the effective viscoplastic behavior of $\protect \mathrm{Mg}_2\protect \mathrm{SiO}_4$ wadsleyite: bridging atomic and polycrystal scales},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {827--846},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {348},
     number = {10-11},
     year = {2020},
     doi = {10.5802/crmeca.61},
     language = {en},
}

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O. Castelnau; K. Derrien; S. Ritterbex; P. Carrez; P. Cordier; H. Moulinec. Multiscale modeling of the effective viscoplastic behavior of $\protect \mathrm{Mg}_2\protect \mathrm{SiO}_4$ wadsleyite: bridging atomic and polycrystal scales. Comptes Rendus. Mécanique, Contributions in mechanics of materials, Volume 348 (2020) no. 10-11, pp. 827-846. doi : 10.5802/crmeca.61. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.61/

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