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http://hdl.handle.net/10985/19619
Earth Mantle Rheology Inferred from Homogenization Theories, chapitre 4
CASTELNAU, Olivier; LEBENSOHN, Ricardo; CASTAEDA, Pedro Ponte; BLACKMAN, Donna
The Earth’s upper mantle is known to exhibit elastic anisotropy, which is common-ly attributed to the presence of Lattice Preferred Orientations (LPO). Such anisotropy is revealed in recordings of seismic waves that travel through the mantle with speeds that depend on propagation and/or polarization direction. The development of LPO is due to the plastic deformation of mantle minerals associated with large-scale convec-tive ﬂow. Both olivine and pyroxene crystals exhibit an orthorhombic structure and have only a few slip systems available for dislocation creep. This leads to very high viscoplastic anisotropy at the grain scale, so that an upper mantle region with strong seismic anisotropy (i.e., pronounced LPO) may also exhibit a large effective viscoplas-tic anisotropy which may manifest itself as differences in effective viscosities of up to one or two orders of magnitude depending on the loading direction. This may have a large inﬂuence on the ﬂow in (at least) some regions of the mantle [CHR 87], as was also shown for the ﬂow of ice in ice sheets [MAN 97], but the topic has received little attention [BLA 07]. The key of this issue is to understand the link between single crys-tal rheology, microstructure (in particular LPO) and associated polycrystal behavior,e.g. as attempted for polar ices [CAS 08b].
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10985/196192008-01-01T00:00:00ZCASTELNAU, OlivierLEBENSOHN, RicardoCASTAEDA, Pedro PonteBLACKMAN, DonnaThe Earth’s upper mantle is known to exhibit elastic anisotropy, which is common-ly attributed to the presence of Lattice Preferred Orientations (LPO). Such anisotropy is revealed in recordings of seismic waves that travel through the mantle with speeds that depend on propagation and/or polarization direction. The development of LPO is due to the plastic deformation of mantle minerals associated with large-scale convec-tive ﬂow. Both olivine and pyroxene crystals exhibit an orthorhombic structure and have only a few slip systems available for dislocation creep. This leads to very high viscoplastic anisotropy at the grain scale, so that an upper mantle region with strong seismic anisotropy (i.e., pronounced LPO) may also exhibit a large effective viscoplas-tic anisotropy which may manifest itself as differences in effective viscosities of up to one or two orders of magnitude depending on the loading direction. This may have a large inﬂuence on the ﬂow in (at least) some regions of the mantle [CHR 87], as was also shown for the ﬂow of ice in ice sheets [MAN 97], but the topic has received little attention [BLA 07]. The key of this issue is to understand the link between single crys-tal rheology, microstructure (in particular LPO) and associated polycrystal behavior,e.g. as attempted for polar ices [CAS 08b].Multiscale modeling of the effective viscoplastic behavior of Mg 2 SiO 4 wadsleyite: bridging atomic and polycrystal scales
http://hdl.handle.net/10985/19938
Multiscale modeling of the effective viscoplastic behavior of Mg 2 SiO 4 wadsleyite: bridging atomic and polycrystal scales
CASTELNAU, Olivier; DERRIEN, Katell; RITTERBEX, S.; CARREZ, P.; CORDIER, P.; MOULINEC, H.
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.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10985/199382020-01-01T00:00:00ZCASTELNAU, OlivierDERRIEN, KatellRITTERBEX, S.CARREZ, P.CORDIER, P.MOULINEC, H.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.Huge local elastic strains in bulk nanostructured pure zirconia materials
http://hdl.handle.net/10985/19947
Huge local elastic strains in bulk nanostructured pure zirconia materials
ORS, Taylan; GOURAUD, Fanny; MICHEL, Vincent; HUGER, Marc; GEY, Nathalie; MICHA, Jean-Sébastien; CASTELNAU, Olivier; GUINEBRETIÈRE, René
From the liquid state to room temperature, two successive solid-state phase transitions occur in pure zirconia. It is well-known that the last one (tetragonal to monoclinic) is martensitic and induces large volume variations and shear strains. Elastic and inelastic behaviors of zirconia-based materials are strongly influenced by this transition and the associated strain fields that it induces. Knowledge of strain and stress at the crystal scale is thus a crucial point. Using fully dense pure zirconia polycrystals obtained by a fuse casting process, we have determined at a sub-micrometric scale, by X-ray Laue microdiffraction, the strains map at room temperature in as-cast specimens and after a post elaboration high temperature thermal treatment. We observed that the fluctuation of deviatoric elastic strain is huge, the standard deviation of normal component being in the range of 1–2%. The heat treatment tends to even further increase this range of fluctuation, despite the development of a multiscale crack network formed during the cooling. Correspondingly, the associated stress level is also huge. It lies in the 5 GPa range with stress gradient amounting 1 GPa μm−1.
Fri, 01 Jan 2021 00:00:00 GMThttp://hdl.handle.net/10985/199472021-01-01T00:00:00ZORS, TaylanGOURAUD, FannyMICHEL, VincentHUGER, MarcGEY, NathalieMICHA, Jean-SébastienCASTELNAU, OlivierGUINEBRETIÈRE, RenéFrom the liquid state to room temperature, two successive solid-state phase transitions occur in pure zirconia. It is well-known that the last one (tetragonal to monoclinic) is martensitic and induces large volume variations and shear strains. Elastic and inelastic behaviors of zirconia-based materials are strongly influenced by this transition and the associated strain fields that it induces. Knowledge of strain and stress at the crystal scale is thus a crucial point. Using fully dense pure zirconia polycrystals obtained by a fuse casting process, we have determined at a sub-micrometric scale, by X-ray Laue microdiffraction, the strains map at room temperature in as-cast specimens and after a post elaboration high temperature thermal treatment. We observed that the fluctuation of deviatoric elastic strain is huge, the standard deviation of normal component being in the range of 1–2%. The heat treatment tends to even further increase this range of fluctuation, despite the development of a multiscale crack network formed during the cooling. Correspondingly, the associated stress level is also huge. It lies in the 5 GPa range with stress gradient amounting 1 GPa μm−1.Evidence of 3D strain gradients associated with tin whisker growth
http://hdl.handle.net/10985/13301
Evidence of 3D strain gradients associated with tin whisker growth
HEKTOR, Johan; MARIJON, Jean-Baptiste; RISTINMAA, Matti; HALL, Stephen A.; HALLBERG, Hakan; SRINIVASAN, Iyengar; MICHA, Jean-Sébastien; ROBACH, Odile; GRENNERAT, Fanny; CASTELNAU, Olivier
We have used Differential Aperture X-ray Microscopy (DAXM) to measure grain orientations and deviatoric elastic strains in 3D around a tin whisker. The results show strain gradients through the depth of the tin coating, revealing a higher strain deeper in the Sn layer. These higher strains are explained by the volume change occurring during growth of the intermetallic phase Cu6Sn5 at the interface between the Cu substrate and the Sn coating and at grain boundaries between Sn grains.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/133012018-01-01T00:00:00ZHEKTOR, JohanMARIJON, Jean-BaptisteRISTINMAA, MattiHALL, Stephen A.HALLBERG, HakanSRINIVASAN, IyengarMICHA, Jean-SébastienROBACH, OdileGRENNERAT, FannyCASTELNAU, OlivierWe have used Differential Aperture X-ray Microscopy (DAXM) to measure grain orientations and deviatoric elastic strains in 3D around a tin whisker. The results show strain gradients through the depth of the tin coating, revealing a higher strain deeper in the Sn layer. These higher strains are explained by the volume change occurring during growth of the intermetallic phase Cu6Sn5 at the interface between the Cu substrate and the Sn coating and at grain boundaries between Sn grains.Effective viscoplastic behavior of polycrystalline aggregates lacking four independent slip systems inferred from homogenization methods; application to olivine
http://hdl.handle.net/10985/9880
Effective viscoplastic behavior of polycrystalline aggregates lacking four independent slip systems inferred from homogenization methods; application to olivine
DETREZ, Fabrice; CASTELNAU, Olivier; CORDIER, Patrick; MERKEL, Sébastien; RATERRON, Paul
Polycrystalline aggregates lacking four independent systems for the glide of dislocations can deform in a purely viscoplastic regime only if additional deformation mechanisms (such as grain boundary sliding and diffusion) are activated. We introduce an implementation of the self-consistent scheme in which this additional physical mechanism, considered as a stress relaxation mechanism, is represented by a nonlinear isotropic viscoplastic potential. Several nonlinear extensions of the self-consistent scheme, including the second-order method of Ponte-Castañeda, are used to provide an estimate of the effective viscoplastic behavior of such polycrystals. The implementation of the method includes an approximation of the isotropic potential to ensure convergence of the attractive fixed-point numerical algorithm. The method is then applied to olivine polycrystals, the main constituent of the Earth's upper mantle. Due to the extreme local anisotropy of the local constitutive behavior and the subsequent intraphase stress and strain-rate field heterogeneities, the second-order method is the only extension providing qualitative and quantitative accurate results. The effective viscosity is strongly dependent on the strength of the relaxation mechanism. For olivine, a linear viscous relaxation (e.g. diffusion) could be relevant; in that case, the polycrystal stress sensitivity is reduced compared to that of dislocation glide, and the most active slip system is not necessarily the one with the smallest reference stress due to stress concentrations. This study reveals the significant importance of the strength and stress sensitivity of the additional relaxation mechanism for the rheology and lattice preferred orientation in such highly anisotropic polycrystalline aggregates.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10985/98802015-01-01T00:00:00ZDETREZ, FabriceCASTELNAU, OlivierCORDIER, PatrickMERKEL, SébastienRATERRON, PaulPolycrystalline aggregates lacking four independent systems for the glide of dislocations can deform in a purely viscoplastic regime only if additional deformation mechanisms (such as grain boundary sliding and diffusion) are activated. We introduce an implementation of the self-consistent scheme in which this additional physical mechanism, considered as a stress relaxation mechanism, is represented by a nonlinear isotropic viscoplastic potential. Several nonlinear extensions of the self-consistent scheme, including the second-order method of Ponte-Castañeda, are used to provide an estimate of the effective viscoplastic behavior of such polycrystals. The implementation of the method includes an approximation of the isotropic potential to ensure convergence of the attractive fixed-point numerical algorithm. The method is then applied to olivine polycrystals, the main constituent of the Earth's upper mantle. Due to the extreme local anisotropy of the local constitutive behavior and the subsequent intraphase stress and strain-rate field heterogeneities, the second-order method is the only extension providing qualitative and quantitative accurate results. The effective viscosity is strongly dependent on the strength of the relaxation mechanism. For olivine, a linear viscous relaxation (e.g. diffusion) could be relevant; in that case, the polycrystal stress sensitivity is reduced compared to that of dislocation glide, and the most active slip system is not necessarily the one with the smallest reference stress due to stress concentrations. This study reveals the significant importance of the strength and stress sensitivity of the additional relaxation mechanism for the rheology and lattice preferred orientation in such highly anisotropic polycrystalline aggregates.A self-consistent estimate for linear viscoelastic polycrystals with internal variables inferred from the collocation method
http://hdl.handle.net/10985/10144
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
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 the whole stress and strain histories have to be considered to compute the mechanical response of the material during a given macroscopic loading. Following a remark of Mandel (1966 Mécanique des Milieux Continus(Paris, France: Gauthier-Villars)), Ricaud and Masson (2009 Int. J. Solids Struct. 46 1599–1606) have shown the equivalence between the collocation method used to invert Laplace–Carson transforms and an internal variables formulation. In this paper, this new method is developed for the case of polycrystalline materials with general anisotropic properties for local and macroscopic behavior. Applications are provided for the case of constitutive relations accounting for glide of dislocations on particular slip systems. It is shown that the method yields accurate results that perfectly match the standard collocation method and reference full-field results obtained with a FFT numerical scheme. The formulation is then extended to the case of time- and strain-dependent viscous properties, leading to the incremental collocation method (ICM) that can be solved efficiently by a step-by-step procedure. Specifically, the introduction of isotropic and kinematic hardening at the slip system scale is considered.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10985/101442012-01-01T00:00:00ZVU, QHBRENNER, RenaldCASTELNAU, OlivierMOULINEC, HSUQUET, PThe 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 the whole stress and strain histories have to be considered to compute the mechanical response of the material during a given macroscopic loading. Following a remark of Mandel (1966 Mécanique des Milieux Continus(Paris, France: Gauthier-Villars)), Ricaud and Masson (2009 Int. J. Solids Struct. 46 1599–1606) have shown the equivalence between the collocation method used to invert Laplace–Carson transforms and an internal variables formulation. In this paper, this new method is developed for the case of polycrystalline materials with general anisotropic properties for local and macroscopic behavior. Applications are provided for the case of constitutive relations accounting for glide of dislocations on particular slip systems. It is shown that the method yields accurate results that perfectly match the standard collocation method and reference full-field results obtained with a FFT numerical scheme. The formulation is then extended to the case of time- and strain-dependent viscous properties, leading to the incremental collocation method (ICM) that can be solved efficiently by a step-by-step procedure. Specifically, the introduction of isotropic and kinematic hardening at the slip system scale is considered.Multiscale modeling of ice deformation behavior
http://hdl.handle.net/10985/8420
Multiscale modeling of ice deformation behavior
MONTAGNAT, Maurine; CASTELNAU, Olivier; BONS, P.D; FARIA, S.H; GAGLIARDINI, O; GILLET-CHAULET, F; GRENNERAT, Fanny; GRIERA, A; LEBENSOHN, R.A.; MOULINEC, Hervé; ROESSIGER, J.; SUQUET, Pierre
Understanding the flow of ice in glaciers and polar ice sheets is of increasing relevance in a time of potentially significant climate change. The flow of ice has hitherto received relatively little attention from the structural geological community. This paper aims to provide an overview of methods and results of ice deformation modeling from the single crystal to the polycrystal scale, and beyond to the scale of polar ice sheets. All through these scales, various models have been developed to understand, describe and predict the processes that operate during deformation of ice, with the aim to correctly represent ice rheology and self-induced anisotropy. Most of the modeling tools presented in this paper originate from the material science community, and are currently used and further developed for other materials and environments. We will show that this community has deeply integrated ice as a very useful “model” material to develop and validate approaches in conditions of a highly anisotropic behavior. This review, by no means exhaustive, aims at providing an overview of methods at different scales and levels of complexity
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10985/84202013-01-01T00:00:00ZMONTAGNAT, MaurineCASTELNAU, OlivierBONS, P.DFARIA, S.HGAGLIARDINI, OGILLET-CHAULET, FGRENNERAT, FannyGRIERA, ALEBENSOHN, R.A.MOULINEC, HervéROESSIGER, J.SUQUET, PierreUnderstanding the flow of ice in glaciers and polar ice sheets is of increasing relevance in a time of potentially significant climate change. The flow of ice has hitherto received relatively little attention from the structural geological community. This paper aims to provide an overview of methods and results of ice deformation modeling from the single crystal to the polycrystal scale, and beyond to the scale of polar ice sheets. All through these scales, various models have been developed to understand, describe and predict the processes that operate during deformation of ice, with the aim to correctly represent ice rheology and self-induced anisotropy. Most of the modeling tools presented in this paper originate from the material science community, and are currently used and further developed for other materials and environments. We will show that this community has deeply integrated ice as a very useful “model” material to develop and validate approaches in conditions of a highly anisotropic behavior. This review, by no means exhaustive, aims at providing an overview of methods at different scales and levels of complexityNumerical Modeling of Iceberg Capsizing Responsible for Glacial Earthquakes
http://hdl.handle.net/10985/14082
Numerical Modeling of Iceberg Capsizing Responsible for Glacial Earthquakes
SERGEANT, Amandine; YASTREBOV, Vladislav; MANGENEY, Anne; CASTELNAU, Olivier; MONTAGNER, Jean-Paul; STUTZMANN, Eléonore
The capsizing of icebergs calved from marine‐terminating glaciers generate horizontal forces on the glacier front, producing long‐period seismic signals referred to as glacial earthquakes. These forces can be estimated by broadband seismic inversion, but their interpretation in terms of magnitude and waveform variability is not straightforward. We present a numerical model for fluid drag that can be used to study buoyancy‐driven iceberg capsize dynamics and the generated contact forces on a calving face using the finite‐element approach. We investigate the sensitivity of the force to drag effects, iceberg geometry, calving style, and initial buoyancy. We show that there is no simple relationship between force amplitude and iceberg volume, and similar force magnitudes can be reached for different iceberg sizes. The force history and spectral content varies with the iceberg attributes. The iceberg aspect ratio primarily controls the capsize dynamics, the force shape, and force frequency, whereas the iceberg height has a stronger impact on the force magnitude. Iceberg hydrostatic imbalance generates contact forces with specific frequency peaks that explain the variability in glacial earthquake dominant frequency. For similar icebergs, top‐out and bottom‐out events have significantly different capsize dynamics leading to larger top‐out forces especially for thin icebergs. For realistic iceberg dimensions, we find contact‐force magnitudes that range between 5.6 × 1011 and 2 × 1014 kg·m, consistent with seismic observations. This study provides a useful framework for interpreting glacial earthquake sources and estimating the ice mass loss from coupled analysis of seismic signals and modeling results.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10985/140822018-01-01T00:00:00ZSERGEANT, AmandineYASTREBOV, VladislavMANGENEY, AnneCASTELNAU, OlivierMONTAGNER, Jean-PaulSTUTZMANN, EléonoreThe capsizing of icebergs calved from marine‐terminating glaciers generate horizontal forces on the glacier front, producing long‐period seismic signals referred to as glacial earthquakes. These forces can be estimated by broadband seismic inversion, but their interpretation in terms of magnitude and waveform variability is not straightforward. We present a numerical model for fluid drag that can be used to study buoyancy‐driven iceberg capsize dynamics and the generated contact forces on a calving face using the finite‐element approach. We investigate the sensitivity of the force to drag effects, iceberg geometry, calving style, and initial buoyancy. We show that there is no simple relationship between force amplitude and iceberg volume, and similar force magnitudes can be reached for different iceberg sizes. The force history and spectral content varies with the iceberg attributes. The iceberg aspect ratio primarily controls the capsize dynamics, the force shape, and force frequency, whereas the iceberg height has a stronger impact on the force magnitude. Iceberg hydrostatic imbalance generates contact forces with specific frequency peaks that explain the variability in glacial earthquake dominant frequency. For similar icebergs, top‐out and bottom‐out events have significantly different capsize dynamics leading to larger top‐out forces especially for thin icebergs. For realistic iceberg dimensions, we find contact‐force magnitudes that range between 5.6 × 1011 and 2 × 1014 kg·m, consistent with seismic observations. This study provides a useful framework for interpreting glacial earthquake sources and estimating the ice mass loss from coupled analysis of seismic signals and modeling results.An analytical finite-strain parametrization for texture evolution in deforming olivine polycrystals
http://hdl.handle.net/10985/14596
An analytical finite-strain parametrization for texture evolution in deforming olivine polycrystals
RIBE, Neil M.; HIELSCHE, Ralf; CASTELNAU, Olivier
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.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/145962019-01-01T00:00:00ZRIBE, Neil M.HIELSCHE, RalfCASTELNAU, OlivierProgressive 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.Textures in deforming forsterite aggregates up to 8 GPa and 1673 K
http://hdl.handle.net/10985/15087
Textures in deforming forsterite aggregates up to 8 GPa and 1673 K
BOLLINGER, Caroline; RATERRON, Paul; CASTELNAU, Olivier; DETREZ, Fabrice; MERKEL, Sébastien
We report results from axisymmetric deformation experiments carried out on forsterite aggregates in the deformation-DIA apparatus, at upper mantle pressures and temperatures (3.1–8.1 GPa, 1373–1673 K). We quantified the resulting lattice preferred orientations (LPO) and compare experimental observations with results from micromechanical modeling (viscoplastic second-order self-consistent model—SO). Up to 6 GPa (~185-km depth in the Earth), we observe a marked LPO consistent with a dominant slip in the (010) plane with one observation of a dominant [100] direction, suggesting that [100](010) slip system was strongly activated. At higher pressures (deeper depth), the LPO becomes less marked and more complex with no evidence of a dominant slip system, which we attribute to the activation of several concurrent slip systems. These results are consistent with the pressure-induced transition in the dominant slip system previously reported for olivine and forsterite. They are also consistent with the decrease in the seismic anisotropy amplitude observed in the Earth’s mantle at depth greater than ~200 km.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10985/150872016-01-01T00:00:00ZBOLLINGER, CarolineRATERRON, PaulCASTELNAU, OlivierDETREZ, FabriceMERKEL, SébastienWe report results from axisymmetric deformation experiments carried out on forsterite aggregates in the deformation-DIA apparatus, at upper mantle pressures and temperatures (3.1–8.1 GPa, 1373–1673 K). We quantified the resulting lattice preferred orientations (LPO) and compare experimental observations with results from micromechanical modeling (viscoplastic second-order self-consistent model—SO). Up to 6 GPa (~185-km depth in the Earth), we observe a marked LPO consistent with a dominant slip in the (010) plane with one observation of a dominant [100] direction, suggesting that [100](010) slip system was strongly activated. At higher pressures (deeper depth), the LPO becomes less marked and more complex with no evidence of a dominant slip system, which we attribute to the activation of several concurrent slip systems. These results are consistent with the pressure-induced transition in the dominant slip system previously reported for olivine and forsterite. They are also consistent with the decrease in the seismic anisotropy amplitude observed in the Earth’s mantle at depth greater than ~200 km.