An analytical finite-strain parametrization for texture evolution in deforming olivine polycrystals
TypeArticles dans des revues avec comité de lecture
Progressive deformation of upper mantle rocks via dislocation creep causes their constituent crystals to take on a non-random orientation distribution (crystal preferred orientation or CPO). The resulting anisotropy of the rock's elastic properties can be observed by seismic techniques, and provides a means to constrain mantle convective flow patterns. Existing methods for calculating the evolution of CPO in deforming olivine-dominated rocks rely on unwieldy discrete representations of the crystal orientation distribution in terms of a large number (103-104) of individual grains. Here we propose a more efficient method in which CPO is represented using three continuous analytical functions (structured basis functions or SBFs), each of which represents a virtual CPO produced by the action of just one of the three dominant slip systems of olivine. The SBFs are then combined using an appropriate weighting scheme to represent a realistic CPO that results from the simultaneous activity of all three slip systems. We assume that olivine CPO is a unique function of the finite strain experienced by the aggregate, which implies that the weights of the SBFs depend only on the two ratios of the lengths of the axes of the finite strain ellipsoid (FSE) and the two ratios of the strengths (critical resolved shear stresses) of the slip systems. Our preferred set of weighting coefficients is obtained by least-squares fitting of the SBF expansion to the predictions of a kinematic model (solved by the method of characteristics) in which the amplitudes of the crystallographic spins do not increase with strain. Calculation of CPO using this model is ≈107 times faster than full homogenization approaches such as the second-order self-consistent model, and the result fits the characteristics-based solution with a variance reduction ≥ 88.6 per cent for equivalent strains up to 0.9. Finally, we propose a simple modification of the FSE that prevents the CPO from becoming singular at large strains.
Files in this item
Showing items related by title, author, creator and subject.
Analytical parametrization of self-consistent polycrystal mechanics: Fast calculation of upper mantle anisotropy GOULDING, Neil J.; RIBE, Neil M.; CASTELNAU, Olivier; WALKER, Andrew M. (Oxford University Press on behalf of The Royal Astronomical Society., 2015)Progressive deformation of upper mantle rocks via dislocation creep causes their constituent crystals to take on a non-random orientation distribution (crystallographic preferred orientation or CPO) whose observable ...
Multiscale modeling of upper mantle plasticity: From single-crystal rheology to multiphase aggregate deformation RATERRON, Paul; DETREZ, Fabrice; CASTELNAU, Olivier; BOLLINGER, Caroline; CORDIER, Patrick; MERKEL, Sébastien (ELSEVIER, 2014)We report a first application of an improved second-order (SO) viscoplastic self-consistent model for multiphase aggregates, applied to an olivine + diopside aggregate as analogue for a dry upper mantle peridotite deformed ...
The evolution with strain of the stored energy in different texture components of cold-rolled if steel revealed by high resolution X-ray diffraction WAUTHIER-MONNIN, Aurélie; CHAUVEAU, T; CASTELNAU, Olivier; RÉGLÉ, H; BACROIX, Brigitte (ELSEVIER, 2015)During the deformation of low carbon steel by cold-rolling, dislocations are created and stored in grains depending on local crystallographic orientation, deformation, and deformation gradient. Orientation dependent ...
A self-consistent estimate for linear viscoelastic polycrystals with internal variables inferred from the collocation method VU, QH; BRENNER, Renald; CASTELNAU, Olivier; MOULINEC, H; SUQUET, P (IOP PUBLISHING, 2012)The correspondence principle is customarily used with the Laplace–Carson transform technique to tackle the homogenization of linear viscoelastic heterogeneous media. The main drawback of this method lies in the fact that ...
MASSON, Renaud; BRENNER, Renald; CASTELNAU, Olivier (ELSEVIER, 2012)An approximate self-consistent modelling is proposed to estimate the effective viscoelastic response of polycrystals presenting an ageing constitutive behaviour. This approach makes use of the equivalence between the ...