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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Mon, 15 Jul 2024 08:35:44 GMT2024-07-15T08:35:44ZEffective 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.Multiscale modeling of upper mantle plasticity: From single-crystal rheology to multiphase aggregate deformation
http://hdl.handle.net/10985/7989
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
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 at 10 15 s 1 shear strain rate along a 20-Ma ocean geotherm. Beside known dislocation slip systems, this SO-model version accounts for an isotropic relaxation mechanism representing ‘diffusionrelated’ creep mechanisms in olivine. Slip-system critical resolved shear stress (CRSS) are evaluated in both phases – as functions of P, T, oxygen fugacity (fO2) and strain rate – from previously reported experimental data obtained on single crystals and first-principle calculations coupled with the Peierls–Nabarro model for crystal plasticity; and the isotropic-mechanism dependence on T and P matches that of Si selfdiffusion in olivine, while its relative activity is constrained by reported data. The model reproduces well the olivine and diopside lattice preferred orientations (LPO) produced experimentally and observed in naturally deformed rocks, as well as observed sensitivities of multiphase aggregate strength to the volume fraction of the hard phase (here diopside). It shows a significant weakening of olivine LPO with increasing depth, which results from the combined effects of the P-induced [100]/[001] dislocation-slip transition and the increasing activity with T of ‘diffusion-related’ creep. This work thus provides a first quantification of the respective effects of [100]/[001] slip transition and diffusion creep on the olivine LPO weakening inducing the seismic anisotropy attenuation observed in the upper mantle.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10985/79892014-01-01T00:00:00ZRATERRON, PaulDETREZ, FabriceCASTELNAU, OlivierBOLLINGER, CarolineCORDIER, PatrickMERKEL, SébastienWe 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 at 10 15 s 1 shear strain rate along a 20-Ma ocean geotherm. Beside known dislocation slip systems, this SO-model version accounts for an isotropic relaxation mechanism representing ‘diffusionrelated’ creep mechanisms in olivine. Slip-system critical resolved shear stress (CRSS) are evaluated in both phases – as functions of P, T, oxygen fugacity (fO2) and strain rate – from previously reported experimental data obtained on single crystals and first-principle calculations coupled with the Peierls–Nabarro model for crystal plasticity; and the isotropic-mechanism dependence on T and P matches that of Si selfdiffusion in olivine, while its relative activity is constrained by reported data. The model reproduces well the olivine and diopside lattice preferred orientations (LPO) produced experimentally and observed in naturally deformed rocks, as well as observed sensitivities of multiphase aggregate strength to the volume fraction of the hard phase (here diopside). It shows a significant weakening of olivine LPO with increasing depth, which results from the combined effects of the P-induced [100]/[001] dislocation-slip transition and the increasing activity with T of ‘diffusion-related’ creep. This work thus provides a first quantification of the respective effects of [100]/[001] slip transition and diffusion creep on the olivine LPO weakening inducing the seismic anisotropy attenuation observed in the upper mantle.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.Numerical study of the relationship between the spherulitic microstructure and isothermal crystallization kinetics. Part I. 2-D
http://hdl.handle.net/10985/17535
Numerical study of the relationship between the spherulitic microstructure and isothermal crystallization kinetics. Part I. 2-D
LU, Xiaoxin; DETREZ, Fabrice; ROLAND, Sébastien
In this paper, we proposed a numerical model to study the kinetic properties and the spherulite microstructure of a semi-crystalline polymer under isothermal crystallization, which further exhibits the potential in generating the 2D spherulitic structure according to the observations obtained by experimental techniques. Two characteristic parameters are introduced, namely, characteristic length Lc and characteristic time tc, which are dependent on the growth rate, G and the nucleation rate, I. In addition, two non-dimensional parameters are introduced to model the nucleation saturation: Ld/Lc and t⋆/tc, which is related to the thickness of nucleation exclusion zone Ld, and the effective nucleation time t⋆, respectively. In 2D modeling, the kinetics are confirmed by Avrami fitting, and the effects of the four characteristic parameters on the Avrami parameter n and the crystallization half-time t0.5 are presented. The regularity of how the spherulite density or the mean radius of spherulites R change along with these parameters are also given, respectively. It shows that Lc is the prominent parameter for the size of the spherulite, and tc controls t0.5 as long as there is no nucleation saturation (Ld=0 and t⋆→∞). Besides, the existence of the nucleation saturation increases the mean radius of spherulites, but decreases n from 3 to 2 in 2-D modeling. Finally, a relationship between crystallization kinetics and microstructures is provided, giving a new perspective to estimate the nucleation rate.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10985/175352019-01-01T00:00:00ZLU, XiaoxinDETREZ, FabriceROLAND, SébastienIn this paper, we proposed a numerical model to study the kinetic properties and the spherulite microstructure of a semi-crystalline polymer under isothermal crystallization, which further exhibits the potential in generating the 2D spherulitic structure according to the observations obtained by experimental techniques. Two characteristic parameters are introduced, namely, characteristic length Lc and characteristic time tc, which are dependent on the growth rate, G and the nucleation rate, I. In addition, two non-dimensional parameters are introduced to model the nucleation saturation: Ld/Lc and t⋆/tc, which is related to the thickness of nucleation exclusion zone Ld, and the effective nucleation time t⋆, respectively. In 2D modeling, the kinetics are confirmed by Avrami fitting, and the effects of the four characteristic parameters on the Avrami parameter n and the crystallization half-time t0.5 are presented. The regularity of how the spherulite density or the mean radius of spherulites R change along with these parameters are also given, respectively. It shows that Lc is the prominent parameter for the size of the spherulite, and tc controls t0.5 as long as there is no nucleation saturation (Ld=0 and t⋆→∞). Besides, the existence of the nucleation saturation increases the mean radius of spherulites, but decreases n from 3 to 2 in 2-D modeling. Finally, a relationship between crystallization kinetics and microstructures is provided, giving a new perspective to estimate the nucleation rate.A constitutive model for semi-crystalline polymer deformation involving lamellar fragmentation
http://hdl.handle.net/10985/18683
A constitutive model for semi-crystalline polymer deformation involving lamellar fragmentation
DETREZ, Fabrice; CANTOURNET, Sabine; SÉGUÉLA, Rolland
The mechanism of lamellar fragmentation in the semi-crystalline polymers with spherulitic structure, is observed at the beginning of plastic flow. It causes significant damage. This elementary mechanism is considered here as a result of plastic deformation coupled with damage, in the framework of generalized standard materials. The simplicity and the efficiency of the proposed approach come from the fact that the semi-crystalline polymers are considered as a macromolecular network bridled by intra-lamellar cohesive forces. Tensile tests and relaxation tests demonstrate the usefulness of a damage-plasticity coupled model.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10985/186832010-01-01T00:00:00ZDETREZ, FabriceCANTOURNET, SabineSÉGUÉLA, RollandThe mechanism of lamellar fragmentation in the semi-crystalline polymers with spherulitic structure, is observed at the beginning of plastic flow. It causes significant damage. This elementary mechanism is considered here as a result of plastic deformation coupled with damage, in the framework of generalized standard materials. The simplicity and the efficiency of the proposed approach come from the fact that the semi-crystalline polymers are considered as a macromolecular network bridled by intra-lamellar cohesive forces. Tensile tests and relaxation tests demonstrate the usefulness of a damage-plasticity coupled model.Multiscale framework for estimation of elastic properties of Poly ethylene terephthalate from the crystallization temperature
http://hdl.handle.net/10985/24794
Multiscale framework for estimation of elastic properties of Poly ethylene terephthalate from the crystallization temperature
LUO, Yun-Mei; DETREZ, Fabrice; CHEVALIER, Luc; LU, Xiaoxin; ROLAND, Sébastien
A 2D multiscale numerical strategy is presented in this paper. It allows to generate a representative elementary volume (REV) with a spherulitic microstructure used to predict the elastic properties of PET using a 2-scale numerical homogenization scheme. Because of the rapid crystallization kinetics of PET, DSC and optical microscopy were combined with empirical laws to estimate the crystallization kinetic parameters used to generate the REVs. Our framework allows estimating the elastic properties identified by tensile tests for several specimens crystallized at different temperatures. In addition, the comparison with mean-field models from the literature confirms that the Young's modulus of PET does not only depend on the crystallinity volume ratio but also on the crystal organization in the spherulites. The main advantage of this study is to provide a strategy for estimating the elastic properties that can be transposed to many semi-crystalline polymers with a spherulitic microstructure. Nevertheless, the numerical framework presented in the article is limited to semicrystalline polymers with a spherulitic microstructure, which crystallize under isothermal condition.
Sun, 01 Jan 2023 00:00:00 GMThttp://hdl.handle.net/10985/247942023-01-01T00:00:00ZLUO, Yun-MeiDETREZ, FabriceCHEVALIER, LucLU, XiaoxinROLAND, SébastienA 2D multiscale numerical strategy is presented in this paper. It allows to generate a representative elementary volume (REV) with a spherulitic microstructure used to predict the elastic properties of PET using a 2-scale numerical homogenization scheme. Because of the rapid crystallization kinetics of PET, DSC and optical microscopy were combined with empirical laws to estimate the crystallization kinetic parameters used to generate the REVs. Our framework allows estimating the elastic properties identified by tensile tests for several specimens crystallized at different temperatures. In addition, the comparison with mean-field models from the literature confirms that the Young's modulus of PET does not only depend on the crystallinity volume ratio but also on the crystal organization in the spherulites. The main advantage of this study is to provide a strategy for estimating the elastic properties that can be transposed to many semi-crystalline polymers with a spherulitic microstructure. Nevertheless, the numerical framework presented in the article is limited to semicrystalline polymers with a spherulitic microstructure, which crystallize under isothermal condition.