Évaluation métrologique d'algorithmes de corrélation d'images numériques

Cet article rend compte d'un travail collectif mene au sein du GT1 du GDR CNRS 2519, Mesure de champs et identification en mécanique des solidesOptical full field measurement techniques based on digital image correlation get more and more popular. We propose a methodology for the assessment of the metrological performances of the image processing algorithms that constitute their central component, the knowledge of which is required for a global assessment of the whole measurement system. It is based on the generation of synthetic images representative of real speckle patterns, deformed according to a sinusoidal displacement field with varying amplitude and period, and the statistical analysis of the discrepancies between imposed and measured values. It has been applied to various softwares used in the french community. Results show general tendencies rather independent from the implementations but strongly correlated with the assumptions of the underlying algorithms. Various error regimes are identified, for which the dependence of the accuracy with the parameters of the algorithms, such as correlation window size or shape functions can be precised

Mesure 3d de champs cinématiques dans le cas d'un contraste non uniformément réparti.

Les techniques de corrélation d'image numérique ont récemment été étendues afin de pouvoir analyser des séquences d'images tridimensionnelles, obtenues par exemple par microtomographie X. La résolution et la résolution spatiale des champs de déformation mesurés dépendent directement de la répartition, de la taille et du contraste local des marqueurs utilisés pour réaliser l'appariement des images. Lorsqu'il est présent, le contraste naturel issu des hétérogénéités intrinsèques au matériau peut directement fournir ces marqueurs [1]. Lorsque celui-ci fait défaut, des marqueurs supplémentaires peuvent être ajoutés, mais leur répartition spatiale est difficile à maîtriser [2]. Dans les deux cas, le contraste local peut être fortement non-uniforme, contrairement à ce qui peut être obtenu avec un mouchetis de peinture en corrélation d'image de surface. Habituellement le calcul du critère de ressemblance est réalisé sur des sous-domaines espacés régulièrement. Cette discrétisation spatiale homogène facilite le post-traitement des données mais ne permet pas toujours une exploitation optimale du signal. En effet, les domaines de corrélation ne sont a priori pas centrés sur les marqueurs présentant le meilleur contraste, ce qui peut conduire à des erreurs de mesure. Il est proposé ici de déterminer la position des points de mesure (centre des domaines de corrélation) en fonction de plusieurs critères quantifiant la qualité du signal présent dans l'image. Les premières applications seront réalisées sur le matériau présenté dans [2] : des essais de traction sur une éprouvette entaillée en aluminium marqué par des inclusions de cuivre, puis sur le même matériau renforcé avec de larges particules sphériques de Zircone-Silice. Enfin, la déformation d'un alliage d'Aluminium-Cuivre en cours de solidification [3] sera analysée malgré un contraste local peu abondant dans la structure. [1] Bay ,Smith ,Fyhrie ,Saad, Digital volume correlation : three-dimensional strain mapping using X-ray tomography, Experimental Mechanics, 1999. [2] Bornert ,Chaix ,Doumalin ,Dupré ,Fournel, Jeulin, Maire, Moreaud, Moulinec, Mesure tridimensionnelle de champs cinématiques par imagerie volumique pour l'analyse des matériaux et des structures. Instrumentation, Mesure, Métrologie, 2004. [3] Limodin, Salvo, Suery, Dimichiel, In-situ investigation by X-Ray tomography of the overall and local microstructural changes occurring during partial remelting of an Al-15.8wt%Cu alloy, Acta Materialia, 2007

Second-order estimates of the self-consistent type for viscoplastic polycrystals

The ‘second–order’ homogenization procedure of Ponte Castañeda is used to propose new estimates of the self–consistent type for the effective behaviour of viscoplastic polycrystals. This is accomplished by means of appropriately generated estimates of the self–consistent type for the relevant ‘linear thermoelastic comparison composite’, in the homogenization procedure. The resulting nonlinear self–consistent estimates are the only estimates of their type to be exact to second order in the heterogeneity contrast, which, for polycrystals, is determined by the grain anisotropy. In addition, they satisfy the recent bounds of Kohn and Little for two–dimensional power–law polycrystals, which are known to be significantly sharper than the Taylor bound at large grain anisotropy. These two features combined, suggest that the new self–consistent estimates, obtained from the second–order procedure, may be the most accurate to date. Direct comparison with other self–consistent estimates, including the classical incremental and secant estimates, for the special case of power–law creep, appear to corroborate this observation

Second-order estimates of the self-consistent type for viscoplastic polycrystals

The ‘second–order’ homogenization procedure of Ponte Castañeda is used to propose new estimates of the self–consistent type for the effective behaviour of viscoplastic polycrystals. This is accomplished by means of appropriately generated estimates of the self–consistent type for the relevant ‘linear thermoelastic comparison composite’, in the homogenization procedure. The resulting nonlinear self–consistent estimates are the only estimates of their type to be exact to second order in the heterogeneity contrast, which, for polycrystals, is determined by the grain anisotropy. In addition, they satisfy the recent bounds of Kohn and Little for two–dimensional power–law polycrystals, which are known to be significantly sharper than the Taylor bound at large grain anisotropy. These two features combined, suggest that the new self–consistent estimates, obtained from the second–order procedure, may be the most accurate to date. Direct comparison with other self–consistent estimates, including the classical incremental and secant estimates, for the special case of power–law creep, appear to corroborate this observation

Évaluation métrologique d'algorithmes de corrrélation d'images numériques

Les techniques optiques d'extensométrie de champ utilisant la corrélation d'images numériques connaissent une popularité grandissante. On propose une méthodologie d'évaluation des performances métrologiques des traitements d'images qui en constituent la composante centrale, dont la connaissance est nécessaire pour une bonne maîtrise de l'ensemble du dispositif de mesure. Elle repose sur la synthèse d'images représentatives de mouchetis réels, déformées selon un champ de déplacement sinusoïdal, d'amplitude et de période variables, et l'analyse statistique des écarts entre valeurs imposées et mesurées. Elle a été mise en œuvre sur plusieurs outils logiciels utilisés dans la communauté française. Les résultats révèlent des tendances générales relativement indépendantes des implémentations mais fortement corrélées aux hypothèses des algorithmes sous-jacents. Divers régimes d'erreur sont mis en évidence, pour lesquels on peut préciser la dépendance des incertitudes vis-à-vis des paramètres des algorithmes, comme la taille de la fenêtre de corrélation et la forme de la transformation locale

Micromechanical modeling of the elastic behavior of unidirectional CVI SiC/SiC composites

International audienceThe elastic behavior of SiC/SiC composite is investigated at the scale of the tow through a micromechanical modeling taking into account the heterogeneous nature of the microstructure. The paper focuses on the sensitivity of transverse properties to the residual porosity resulting from the matrix infiltration process. The full analysis is presented stepwise, starting from the microstructural characterization to the study of the impact of pore shape and volume fraction. Various Volume Elements (VEs) of a virtual microstructure are randomly generated. Their microstructural properties are validated with respect to an experimental characterization based on high definition SEM observations of real materials, using various statistical descriptors. The linear elastic homogenization is performed using finite elements calculations for several VE sizes and boundary conditions. Important fluctuations of the apparent behavior, even for large VEs, reveal that scales are not separated. Nevertheless, a homogeneous equivalent behavior is estimated by averaging apparent behaviors of several VEs smaller than the Representative Volume Element (RVE). Therefore, the impact of the irregular shape of the pores on the overall properties is highlighted by comparison to a simpler cylindrical porous microstructure. Finally, different matrix infiltration qualities are simulated by several matrix thicknesses. A small increase in porosity volume fraction is shown to potentially lead to an important fall of transverse elastic moduli together with high stress concentrations

Caractérisation et modélisation du comportement mécanique de matériaux composites SiC/SiC

National audienceLes composites SiC/SiC sont envisagés comme matériaux de coeur des réacteurs nucléaires de 4e génération. Leur comportement mécanique à été étudié par le biais d'essais biaxés, ayant permis la construction et l'identification d'un modèle d'endommagement ainsi que son implantation dans un code éléments finis

Approche multi-échelle du comportement mécanique des matériaux composites SiC/SiC : comportement élastique à l'échelle du toron

National audienceUne approche multi-échelle a été entreprise afin d'obtenir un modèle prédictif du comportement mécanique des composites SiC/SiC. L'étude du comportement élastique à l'échelle du toron (microstructure poreuse et hétérogène), réalisée sur des microstructures générées à partir des résultats de la caractérisation microstructurale, met en évidence un problème de séparabilité des échelles. Néanmoins, une estimation du comportement homogène équivalent est proposée en première approximation

MECHANICAL BEHAVIOUR AND RUPTURE IN CLAYEY ROCKS STUDIED BY X-RAY MICRO-TOMOGRAPHY AND 3D-DIGITAL IMAGE CORRELATION

International audienceThe mechanical behaviour and the rupture of clayey rocks have been experimentally studied by performing in situ triaxial tests on a synchrotron beamline i.e. performing X-ray micro tomography scans under mechanical loading. The 3D images obtained at different steps of the test were then analysed by 3D-Digital Image Correlation method in order to measure incremental strain fields. The results allow to clearly detect the onset of shear strain localization and to characterize its development in a 3D complex pattern

Multi-scale viscoplastic behaviour of Halite: In-situ SEM full field measurements, a micro-mechanical approach

Halite geological formations are already extensively used for underground storage of hydrocarbons. For example, the entire USA federal reserve of petrol resides in deep (500 - 1000 m) artificial salt caverns, which are realized by controlled dissolution. In France, many such salt caverns are used for storage of natural gas by GDF. Salt caverns and carries are also intended to become nuclear waste repositories. At this point, salt caverns are also seriously envisaged for the daily storage of energy from renewable, but intermittent sources (photovoltaic, Aeolian), under the form of compressed air. Halite mechanical behaviour was extensively studied for the purpose of safe geothechnical applications. Halite is a ductile type rock. Its differed (time-dependent) mechanical response dominates by far, and therefore deep salt caverns experience convergence (closure), which may result in catastrophic subsidence of the overlaying geological layers. Hence, a particular attention was drawn to characterize salt single crystal creep properties (active slip systems and critical resolved shear stresses), and the rheology of poly-crystalline salt, at various temperatures, pressures, differential stresses and water contents (Ter Heege et al., 2007). But, most studies were concerned with macroscopically derived flow laws, corresponding to rather high differential stresses (as compared with those experienced on site), where crystal slip plasticity (CSP) dominates. But, many studies have also shown that halite is very sensitive to solution-precipitation creep (SPC) mechanisms, which may result in solution transfer accommodated grain boundary sliding (GBS). Conversely, some recent studies report that halite is able to flow at ambient conditions, and under very small loads, with strain rates much faster (four orders of magnitude) than those extrapolated from high stress experiments (Bérest et al., 2005). Though, the specific creep micro-mechanisms were not identified, Bérest et al. (2005) invoked possible SPC. Additionally, the effects on long term behaviour of cyclic loading (fatigue) are still poorly known. It is therefore still questionable weather it is really possible to safely extrapolate the laboratory data to the long term envisaged geotechnical applications. To answer we need i) additional experimental work in order to up date the deformation mechanism maps on the basis of better identified micro-physical mechanisms and quantification of their respective activity; and ii) numerical modelling at the scales of the material, and of the underground storage structures, in respect with the appropriated thermo-hygro-mechaniclal loadings. In the present work, we present our preliminary investigation of viscoplastic global and local responses of synthetic fine grained (50 - 500 m) halite by the means of full field measurements (FFM) of local strain by digital image correlation (DIC) during simple compression in-situ SEM (Doumalain et al., 2003). Figure 1 shows a typical loading curve obtained incrementally at the constant strain rate of c.a. 5x10-5 s-1. CSP evidenced by the development of slip lines on the free grain surfaces, and characterized by quasi-linear strain hardening, dominates the overall response up to several % of strain (microfracturing did not appear before 8 % strain). Yet, at the scale of the microstructure, the development of viscoplastic strain is heterogeneous, as shown by the strain maps obtained by DIC and corresponding to four incremental stages of the loading sequence. The heterogeneity of the strain field relates to the loading boundary conditions and to the local microstructure, such crystal size and orientation (which is characterized by electron back scattering diffraction, EBSD). Such micromechanical approach aims to provide the basis for the development of FE (finite element) computational CSP of polycrystalline halite