Experimental characterization of the intragranular strain field in columnar ice during transient creep

A digital image correlation (DIC) technique has been adapted to polycrystalline ice specimens in order to characterize the development of strain heterogeneities at an intragranular scale during transient creep deformation (compression tests). Specimens exhibit a columnar microstructure so that plastic deformation is essentially two-dimensional, with few in-depth gradients, and therefore surface DIC analyses are representative of the whole specimen volume. Local misorientations at the intragranular scale were also extracted from microstructure analyses carried out with an automatic texture analyzer before and after deformation. Highly localized strain patterns are evidenced by the DIC technique. Local equivalent strain can reach values as much as an order of magnitude larger than the macroscopic average. The structure of the strain pattern does not evolve with strain in the transient creep regime. Almost no correlation between the measured local strain and the Schmid factor of the slip plane of the underlying grain is observed, highlighting the importance of the mechanical interactions between neighboring grains resulting from the very large viscoplastic anisotropy of ice crystals. Finally, the experimental microstructure was introduced in a full-field fast Fourier transform polycrystal model; simulated strain fields are a good match with experimental ones

Evidence of 3D strain gradients associated with tin whisker growth

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

Elasto-viscoplastic behavior of polycrystalline ice

Une technique de corrélation d’images numériques (DIC) a été adaptée à l’étuded’échantillons de glace polycristalline colonnaire, afin de caractériser le développementdes hétérogénéités de déformation à une échelle intragranulaire au cours du fluage transitoireen compression. Ces hétérogénéités sont dues à la grande anisotropie viscoplastiquedu cristal de glace (avec un seul plan de glissement facile pour les dislocations), qui estresponsable d’interactions fortes entre les grains voisins lorsque l’échantillon se déforme,et de la mise en place de fortes contraintes internes. L’orientation particulière des plans deglissement et la structure colonnaire des échantillons, sans gradient de microstructure dansl’épaisseur, permet de considérer la déformation plastique essentiellement dans le plan.Les champs de déformation mesurés en surface peuvent donc être considérés en premièreapproximation comme représentatifs de tout le volume de l’échantillon. Les orientationscristallographiques, et désorientations locales à l’échelle intragranulaire, ont également étémesurées avec un analyseur optique de texture, avant et après déformation.De très fortes localisations de la déformation sont mises en évidence par la DIC;les déformations équivalentes locales peuvent atteindre plus de dix fois la valeur macroscopique.La structure des motifs de localisation évolue peu durant le régime de fluagetransitoire et elle est caractérisée par des bandes de localisation qui traversent l’échantillonobliquement, sur des distances allant jusqu’à dix fois la taille des grains. La corrélationentre le facteur de Schmid du plan de glissement d’un grain et sa déformation locale esttrès faible : l’agencement local des grains et les interactions intergranulaires jouent doncun rôle primordial dans la distribution spatiale des déformations. A l’échelle du grain, lesfortes désorientations de réseau ont été associées aux composantes locales du déplacement.On a montré en particulier que les distorsions sous forme de ”bandes en genou” (ou kinkbands) étaient corrélées à un déplacement le long de l’axe c du grain, mesuré par DIC.Les microstructures expérimentales ont été implémentées dans un modèle plein champFFT qui simule le comportement élasto-viscoplastique des polycristaux (code CraFT).Les champs de déformation simulés présentent globalement les mêmes caractéristiquesque les champs expérimentaux. En particulier, la majorité des zones de localisation dela déformation sont bien reproduites, spatialement et en intensité. Cependant, il n’a pasété possible de reproduire le comportement macroscopique des échantillons à la décharge.La déformation retardée effective est d’un ordre de grandeur inférieure à celle mesuréeexpérimentalement. Il est probable que cette limitation soit liée à l’e↵et du champ descontraintes internes, généré par la structure des champs de dislocations, et qui n’a pas étépris en compte dans la loi de comportement.A Digital Image Correlation (DIC) technique has been adapted to polycrystalline icespecimens in order to characterize the development of strain heterogeneities at an intra-granular scale during transient creep deformation. These heterogeneities are due to thestrong viscoplastic anisotropy of the ice single crystal (with only one easy glide planefor dislocations), inducing strong mechanical interactions between adjacent grains duringdeformation, and the establishment of strong internal stresses. Specimens exhibit a co-lumnar microstructure so that plastic deformation is essentially 2-D with few in-depthgradients, and therefore surface DIC analyses are representative for the whole specimenvolume. Local misorientations at the intragranular scale were also extracted from mi-crostructure analyses carried out with an automatic texture analyzer before and afterdeformation. Highly localized strain patterns are evidenced by the DIC technique. Localequivalent strain can reach values as high as one order of magnitude larger than the ma-croscopic average. The structure of the strain pattern does not evolve signicantly withstrain during the transient creep regime. Almost no correlation was measured betweenthe local strain and the Schmid factor of the slip plane of the underlying grain ; thishighlights the importance of the mechanical interactions between neighboring grains. Atthe grain scale, the strong lattice misorientations have been associated to the local com-ponents of the displacement. In particular, kink band distortions could be correlated to adisplacement along the c-axis measured by DIC. The experimental microstructures wereintroduced into a full-eld FFT model that simulates the behaviour of elasto-viscoplasticpolycrystals (CraFT code). The simulated deformation elds present globally the samecharacteristics as the experimental ones. Most of the localization bands are well repro-duced, spatially and quantitatively. However, we could not reproduce the macroscopicbehaviour of the specimens upon unloading. The predicted recovery eective strain is oneorder of magnitude lower than the measured one. This limitation might be linked withthe internal stress eld induced by the dislocation structure, which is not explicitly takeninto account in the local constitutive relation

Hétérogénéités de déformation au cours du fluage transitoire de la glace polycristalline. Mesures par corrélation d'images numériques et modélisation

A Digital Image Correlation (DIC) technique has been adapted to polycrystalline icespecimens in order to characterize the development of strain heterogeneities at an intra-granular scale during transient creep deformation. These heterogeneities are due to thestrong viscoplastic anisotropy of the ice single crystal (with only one easy glide planefor dislocations), inducing strong mechanical interactions between adjacent grains duringdeformation, and the establishment of strong internal stresses. Specimens exhibit a co-lumnar microstructure so that plastic deformation is essentially 2-D with few in-depthgradients, and therefore surface DIC analyses are representative for the whole specimenvolume. Local misorientations at the intragranular scale were also extracted from mi-crostructure analyses carried out with an automatic texture analyzer before and afterdeformation. Highly localized strain patterns are evidenced by the DIC technique. Localequivalent strain can reach values as high as one order of magnitude larger than the ma-croscopic average. The structure of the strain pattern does not evolve signicantly withstrain during the transient creep regime. Almost no correlation was measured betweenthe local strain and the Schmid factor of the slip plane of the underlying grain ; thishighlights the importance of the mechanical interactions between neighboring grains. Atthe grain scale, the strong lattice misorientations have been associated to the local com-ponents of the displacement. In particular, kink band distortions could be correlated to adisplacement along the c-axis measured by DIC. The experimental microstructures wereintroduced into a full-eld FFT model that simulates the behaviour of elasto-viscoplasticpolycrystals (CraFT code). The simulated deformation elds present globally the samecharacteristics as the experimental ones. Most of the localization bands are well repro-duced, spatially and quantitatively. However, we could not reproduce the macroscopicbehaviour of the specimens upon unloading. The predicted recovery eective strain is oneorder of magnitude lower than the measured one. This limitation might be linked withthe internal stress eld induced by the dislocation structure, which is not explicitly takeninto account in the local constitutive relation.Une technique de corrélation d’images numériques (DIC) a été adaptée à l’étuded’échantillons de glace polycristalline colonnaire, afin de caractériser le développementdes hétérogénéités de déformation à une échelle intragranulaire au cours du fluage transitoireen compression. Ces hétérogénéités sont dues à la grande anisotropie viscoplastiquedu cristal de glace (avec un seul plan de glissement facile pour les dislocations), qui estresponsable d’interactions fortes entre les grains voisins lorsque l’échantillon se déforme,et de la mise en place de fortes contraintes internes. L’orientation particulière des plans deglissement et la structure colonnaire des échantillons, sans gradient de microstructure dansl’épaisseur, permet de considérer la déformation plastique essentiellement dans le plan.Les champs de déformation mesurés en surface peuvent donc être considérés en premièreapproximation comme représentatifs de tout le volume de l’échantillon. Les orientationscristallographiques, et désorientations locales à l’échelle intragranulaire, ont également étémesurées avec un analyseur optique de texture, avant et après déformation.De très fortes localisations de la déformation sont mises en évidence par la DIC;les déformations équivalentes locales peuvent atteindre plus de dix fois la valeur macroscopique.La structure des motifs de localisation évolue peu durant le régime de fluagetransitoire et elle est caractérisée par des bandes de localisation qui traversent l’échantillonobliquement, sur des distances allant jusqu’à dix fois la taille des grains. La corrélationentre le facteur de Schmid du plan de glissement d’un grain et sa déformation locale esttrès faible : l’agencement local des grains et les interactions intergranulaires jouent doncun rôle primordial dans la distribution spatiale des déformations. A l’échelle du grain, lesfortes désorientations de réseau ont été associées aux composantes locales du déplacement.On a montré en particulier que les distorsions sous forme de ”bandes en genou” (ou kinkbands) étaient corrélées à un déplacement le long de l’axe c du grain, mesuré par DIC.Les microstructures expérimentales ont été implémentées dans un modèle plein champFFT qui simule le comportement élasto-viscoplastique des polycristaux (code CraFT).Les champs de déformation simulés présentent globalement les mêmes caractéristiquesque les champs expérimentaux. En particulier, la majorité des zones de localisation dela déformation sont bien reproduites, spatialement et en intensité. Cependant, il n’a pasété possible de reproduire le comportement macroscopique des échantillons à la décharge.La déformation retardée effective est d’un ordre de grandeur inférieure à celle mesuréeexpérimentalement. Il est probable que cette limitation soit liée à l’e↵et du champ descontraintes internes, généré par la structure des champs de dislocations, et qui n’a pas étépris en compte dans la loi de comportement

Hétérogénéités de déformation au cours du fluage transitoire de la glace polycristalline. Mesures par corrélation d'images numériques et modélisation

Une technique de corrélation d images numériques (DIC) a été adaptée à l étuded échantillons de glace polycristalline colonnaire, afin de caractériser le développementdes hétérogénéités de déformation à une échelle intragranulaire au cours du fluage transitoireen compression. Ces hétérogénéités sont dues à la grande anisotropie viscoplastiquedu cristal de glace (avec un seul plan de glissement facile pour les dislocations), qui estresponsable d interactions fortes entre les grains voisins lorsque l échantillon se déforme,et de la mise en place de fortes contraintes internes. L orientation particulière des plans deglissement et la structure colonnaire des échantillons, sans gradient de microstructure dansl épaisseur, permet de considérer la déformation plastique essentiellement dans le plan.Les champs de déformation mesurés en surface peuvent donc être considérés en premièreapproximation comme représentatifs de tout le volume de l échantillon. Les orientationscristallographiques, et désorientations locales à l échelle intragranulaire, ont également étémesurées avec un analyseur optique de texture, avant et après déformation.De très fortes localisations de la déformation sont mises en évidence par la DIC;les déformations équivalentes locales peuvent atteindre plus de dix fois la valeur macroscopique.La structure des motifs de localisation évolue peu durant le régime de fluagetransitoire et elle est caractérisée par des bandes de localisation qui traversent l échantillonobliquement, sur des distances allant jusqu à dix fois la taille des grains. La corrélationentre le facteur de Schmid du plan de glissement d un grain et sa déformation locale esttrès faible : l agencement local des grains et les interactions intergranulaires jouent doncun rôle primordial dans la distribution spatiale des déformations. A l échelle du grain, lesfortes désorientations de réseau ont été associées aux composantes locales du déplacement.On a montré en particulier que les distorsions sous forme de bandes en genou (ou kinkbands) étaient corrélées à un déplacement le long de l axe c du grain, mesuré par DIC.Les microstructures expérimentales ont été implémentées dans un modèle plein champFFT qui simule le comportement élasto-viscoplastique des polycristaux (code CraFT).Les champs de déformation simulés présentent globalement les mêmes caractéristiquesque les champs expérimentaux. En particulier, la majorité des zones de localisation dela déformation sont bien reproduites, spatialement et en intensité. Cependant, il n a pasété possible de reproduire le comportement macroscopique des échantillons à la décharge.La déformation retardée effective est d un ordre de grandeur inférieure à celle mesuréeexpérimentalement. Il est probable que cette limitation soit liée à l e et du champ descontraintes internes, généré par la structure des champs de dislocations, et qui n a pas étépris en compte dans la loi de comportement.A Digital Image Correlation (DIC) technique has been adapted to polycrystalline icespecimens in order to characterize the development of strain heterogeneities at an intra-granular scale during transient creep deformation. These heterogeneities are due to thestrong viscoplastic anisotropy of the ice single crystal (with only one easy glide planefor dislocations), inducing strong mechanical interactions between adjacent grains duringdeformation, and the establishment of strong internal stresses. Specimens exhibit a co-lumnar microstructure so that plastic deformation is essentially 2-D with few in-depthgradients, and therefore surface DIC analyses are representative for the whole specimenvolume. Local misorientations at the intragranular scale were also extracted from mi-crostructure analyses carried out with an automatic texture analyzer before and afterdeformation. Highly localized strain patterns are evidenced by the DIC technique. Localequivalent strain can reach values as high as one order of magnitude larger than the ma-croscopic average. The structure of the strain pattern does not evolve signicantly withstrain during the transient creep regime. Almost no correlation was measured betweenthe local strain and the Schmid factor of the slip plane of the underlying grain ; thishighlights the importance of the mechanical interactions between neighboring grains. Atthe grain scale, the strong lattice misorientations have been associated to the local com-ponents of the displacement. In particular, kink band distortions could be correlated to adisplacement along the c-axis measured by DIC. The experimental microstructures wereintroduced into a full-eld FFT model that simulates the behaviour of elasto-viscoplasticpolycrystals (CraFT code). The simulated deformation elds present globally the samecharacteristics as the experimental ones. Most of the localization bands are well repro-duced, spatially and quantitatively. However, we could not reproduce the macroscopicbehaviour of the specimens upon unloading. The predicted recovery eective strain is oneorder of magnitude lower than the measured one. This limitation might be linked withthe internal stress eld induced by the dislocation structure, which is not explicitly takeninto account in the local constitutive relation.SAVOIE-SCD - Bib.électronique (730659901) / SudocGRENOBLE1/INP-Bib.électronique (384210012) / SudocGRENOBLE2/3-Bib.électronique (384219901) / SudocSudocFranceF

Hétérogénéités de déformation et mécanismes de recristallisation. Cas de la glace "2D-1/2"

International audienc

Experimental characterization of the intragranular strain field in columnar ice during transient creep

A digital image correlation (DIC) technique has been adapted to polycrystalline ice specimens in order to characterize the development of strain heterogeneities at an intragranular scale during transient creep deformation (compression tests). Specimens exhibit a columnar microstructure so that plastic deformation is essentially two-dimensional, with few in-depth gradients, and therefore surface DIC analyses are representative of the whole specimen volume. Local misorientations at the intragranular scale were also extracted from microstructure analyses carried out with an automatic texture analyzer before and after deformation. Highly localized strain patterns are evidenced by the DIC technique. Local equivalent strain can reach values as much as an order of magnitude larger than the macroscopic average. The structure of the strain pattern does not evolve with strain in the transient creep regime. Almost no correlation between the measured local strain and the Schmid factor of the slip plane of the underlying grain is observed, highlighting the importance of the mechanical interactions between neighboring grains resulting from the very large viscoplastic anisotropy of ice crystals. Finally, the experimental microstructure was introduced in a full-field fast Fourier transform polycrystal model; simulated strain fields are a good match with experimental ones.International audienceA digital image correlation (DIC) technique has been adapted to polycrystalline ice specimens in order to characterize the development of strain heterogeneities at an intragranular scale during transient creep deformation (compression tests). Specimens exhibit a columnar microstructure so that plastic deformation is essentially two-dimensional, with few in-depth gradients, and therefore surface DIC analyses are representative of the whole specimen volume. Local misorientations at the intragranular scale were also extracted from microstructure analyses carried out with an automatic texture analyzer before and after deformation. Highly localized strain patterns are evidenced by the DIC technique. Local equivalent strain can reach values as much as an order of magnitude larger than the macroscopic average. The structure of the strain pattern does not evolve with strain in the transient creep regime. Almost no correlation between the measured local strain and the Schmid factor of the slip plane of the underlying grain is observed, highlighting the importance of the mechanical interactions between neighboring grains resulting from the very large viscoplastic anisotropy of ice crystals. Finally, the experimental microstructure was introduced in a full-field fast Fourier transform polycrystal model; simulated strain fields are a good match with experimental ones

Stress heterogeneities in anisotropic materials - their effect on dislocation fields and post-deformational recrystallization : insights from combined experiments and numerical simulations of polycrystalline ice

We present a coupled experimental and modeling approach to better understand the role of stress field heterogeneities on deformation and post-deformational behavior in material with a high viscoplastic anisotropy e.g. polycrystalline ice. We investigate: (1) Effect of stress heterogeneities on deformation behavior and microstructural development and, (2) effect of such microstructures on post-deformational recrystallization. (1) Full-field elasto-viscoplastic modelling (CraFT) is used to predict the local stress and strain field during transient creep in a polycrystalline ice sample. Modeling input includes the experimental starting microstructure and a validated slip system dependent flow law. EBSD measurements on selected areas are used to estimate the local dislocation field utilizing the Weighted Burgers Vector (WBV) analysis. Areas of local stress concentration correlate with triple junctions and grain boundaries, originating from strain incompatibilities between differently oriented grains. In these areas, the WBV analysis shows a non-negligible c-axis component that must be related to resolved shear stress in a prismatic plane, coherent with the predicted elevated stress levels. The resultant defect structure is necessary for the formation of the observed kink bands which have a well-defined crystallographic character, lattice distortions and subgrain development. (2) The microstructures arising from (1) significantly affect post-deformational behavior. Combined post-deformational annealing experiments and numerical simulations using the microdynamic modeling platform ELLE, allow prediction of the local microstructural evolution taking recovery within grains, grain boundary migration and nucleation into account. Results from this study, can explain several of the observed features in natural ice, and help to refine large scale models.1 page(s

Multi-scale modeling of the mechanical behavior of polycrystalline ice under transient creep.

International audienceIce is a challenging material for understanding the overall behavior of polycrystalline materials and more specifically the coupling between elastic and viscous effects during transient creep. At the single crystal level, ice is an hexagonal material with a rather weak elastic anisotropy but with a strong viscoplastic anisotropy. The strain-stress curve of ice single crystals shows a softening behavior depending on the strain-rate. The strong viscous anisotropy of ice gives rise to the progressive development of intergranular and intragranular strain heterogeneities and to stress concentrations which play an important role in the understanding of the creep behavior of ice polycrystals. The single crystal constitutive relations of Castelnau et al [1] are slightly modified here for a better evolution of the reference resolved shear stress on the slip systems and to account for kinematic hardening at the single crystal level. These constitutive relations are then used in a full-field simulation performed by an elasto-viscoplastic FFT-based method. The material parameters of the model are determined by comparison with experimental data available for single crystals as well as for polycrystals

Multiscale modeling of ice deformation behavior

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 complexit