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 ...
ROBACH, Odile; KIRCHLECHNER, Christoph; MICHA, Jean Sébastien; ULRICH, M. Olivier; BIQUARD, Xavier; GEAYMOND, M. Olivier; CASTELNAU, Olivier; BORNERT, Michel; PETIT, Johann; BERVEILLER, Sophie; SICARDY, Olivier; VILLANOVA, Julie; RIEUTORD, François (mperial College Press, 2014)This book highlights emerging diffraction studies of strain and dislocation gradients with mesoscale resolution, which is currently a focus of research at laboratories around the world. While ensemble-average diffraction ...
On the Accuracy of Elastic Strain Field Measurements by Laue Microdiffraction and High-Resolution EBSD: a Cross-Validation Experiment PLANCHER, Emeric; PETIT, Johann; MAURICE, Claire; FAVIER, Véronique; SAINTOYANT, Lucie; LOISNARD, Dominique; RUPIN, N.; MARIJON, Jean Baptiste; ULRICH, Olivier; BORNERT, Michel; MICHA, Jean Sébastien; ROBACH, Odile; CASTELNAU, Olivier (Springer New York LLC, 2016)Determining the accuracy of elastic strain measurements in plastically deformed alloys is an experimental challenge. To develop a novel cross-validation procedure, a controlled elasto-plastic strain gradient was created ...
Combining Laue microdiffraction and digital image correlation for improved measurements of the elastic strain field with micrometer spatial resolution PETIT, Johann; BORNERT, Michel; HOFMANN, Felix A.; ROBACH, Odile; MICHA, Jean Sébastien; ULRICH, Olivier; LE BOURLOT, Christophe; FAURIE, Damien; KORSUNSKY, Alexander; CASTELNAU, Olivier (Elsevier, 2012)The X-ray Laue microdiffraction technique, available at beamline BM32 on the synchrotron ESRF, is ideally suited for probing the field of elastic strain (and associated stress) in deformed polycrystalline materials with a ...
DJAZIRI, Soundes; THIAUDIÈRE, Dominique; GEANDIER, Guillaume; RENAULT, Pierre Olivier; LE BOURHIS, Éric; GOUDEAU, P; CASTELNAU, Olivier; FAURIE, D (Elsevier, 2010)The deformation behaviour of 150. nm thick W/Cu nanocomposite deposited on polyimide substrates has been analysed under equi-biaxial tensile testing coupled to X-ray diffraction technique. The experiments were carried out ...