Simulation de fissures courbes en trois dimensions avec extraction directe des facteurs d'intensité des contraintes : En vue de l'identification de lois de propagation de fatigue

It is necessary to understand the behavior of structures up to their failure to enhance their design. The mechanisms and phenomena undergoing failure vary according to the considered material and boundary conditions. We consider homogeneous materials for which cracks propagate in a context where behavior nonlinearities are not dominants. These conditions are matched for brittle and quasi-brittle materials and for some fatigue cracks. For the former, the main source of dissipation is the crack propagation which can be seen as the generation of a new free-surface. For the later, there is many applications where, in one loading cycle, the nonlinearities remains confined around the crack tip. The linear elastic fracture mechanics theory is then a pertinent model to approximate the structure behavior. Under such hypotheses, a singularity appears in the crack tip vicinity. The Williams' series expansion is computed from the asymptotic study of plane and anti-plane states. The stress is singular at the crack tip and the order of this singularity is one out of two. The singularity amplitude is quantified by the stress intensity factors (SIF), one for each of the three loading modes. In 3D, the crack shape is potentially complex (front curvature and non-planar crack), and no general asymptotic series expansion exists. In this PhD thesis, the 2D Williams' series in displacements are used and regularized with a finite element evolution along the front. From this 3D definition of the asymptotic fields in the crack tip vicinity, a numerical method for direct estimation of the SIF (DEK-FEM) is extended to 3D. This method is based on domain decomposition, the two domains are bounded in a weak sense on their interface. In the crack tip vicinity, the mechanical fields are approximated by a truncation of the asymptotic series expansion. Therefore, appropriate fields are used to deal with the singularity, and the associated degrees of freedom are directly the asymptotic coefficients. Among these coefficients are the SIF and the T-stresses. To bridge the scales between the structure and the crack front singularity and to increase the numerical efficiency, this method is embedded in a localized X-FEM multigrids approach. The proposed method is shown to provide an accurate evaluation of the SIF and T-stresses evolution. This approach has been developed in combination of an experimental post-processing method (full field displacement measurement through image correlation) based on the same asymptotic series expansion. The 3D images can be obtained for in situ fatigue experiments by X-ray microtomography and reconstruction. The crack geometry and the SIF are then provided by image correlation and regularization based on Williams series expansion. These data can be used for identifying a 3D fatigue crack growth law. The efficiency of the method is illustrated in 2D.La compréhension du comportement de structures jusqu'à leur ruine est nécessaire pour concevoir au mieux ces structures. Selon le matériau et les sollicitations considérées, les mécanismes physiques à l'origine de la rupture changent. Nous nous intéresserons à des matériaux homogènes pour lesquels la ruine passe par le développement de fissures autour desquelles les non-linéarités de comportement n'ont pas un rôle dominant. Ces conditions sont réunies pour les matériaux fragiles pour lesquels la source principale de dissipation est la génération non réversible d'une surface libre, et pour certaines fissures de fatigue. Sur un cycle de chargement, il existe de nombreuses applications pour lesquelles les non-linéarités restent confinées. La théorie de la mécanique linéaire élastique de la rupture est alors un modèle pertinent pour approcher le comportement de la structure. Sous ces hypothèses, le front de la fissure introduit une singularité. L'étude asymptotique de cette singularité dans des situations plane et anti-plane permet de définir les séries de Williams. La singularité est alors d'ordre un demi et elle est quantifiée par les facteurs d'intensité des contraintes (FIC) pour chacun des trois modes de sollicitations. En 3D, la fissure peut avoir une géométrie complexe, et aucune expression générale de la singularité n'existe. Dans cette thèse, les séries de Williams en déplacements sont utilisées et régularisées le long du front au sens des éléments finis. À partir de cette définition 3D des séries asymptotiques en pointe de fissure, une méthode d'extraction directe des FIC (DEK-FEM) est étendue au cas 3D. Le domaine est décomposé en deux domaines, raccordés en moyenne sur l'interface. Au voisinage du front, les champs mécaniques sont approchés par une troncature des champs asymptotiques. La singularité est donc traitée avec des champs adaptés, et les degrés de liberté associés sont directement les coefficients asymptotiques. Parmi ces coefficients asymptotiques, on retrouve les FIC et les T-stresses. Pour des raisons d'efficacité numérique et pour pouvoir relier l'échelle de la structure à l'échelle de la fissure, cette méthode est intégrée dans un contexte multigrilles localisées X-FEM. Ainsi nous montrons que cette approche permet une bonne évaluation des évolutions des FIC et du T-stress. Cette méthode est développée en parallèle d'une stratégie de post-traitement expérimental (mesure de champs de déplacements par corrélation d'images) basée sur les mêmes séries asymptotiques. Les images tridimensionnels d'un essai de fatigue in situ sont obtenues par micro-tomographie à rayons X et reconstruction. La corrélation et la régularisation basées sur les séries asymptotiques permettent d'obtenir la géométrie de la fissure et les FIC pour pouvoir identifier des lois de propagation de fissures 3D en fatigue. L'efficacité de cette méthode en parallèle d'une simulation DEK-FEM est illustrée en 2D

Dynamic crack propagation with a variational phase-field model: limiting speed, crack branching and velocity-toughening mechanisms

International audienceWe address the simulation of dynamic crack propagation in brittle materials using a regularized phase-field description, which can also be interpreted as a damage-gradient model. Benefiting from a variational framework, the dynamic evolution of the mechanical fields are obtained as a succession of energy minimizations. We investigate the capacity of such a simple model to reproduce specific experimental features of dynamic in-plane fracture. These include the crack branching phenomenon as well as the existence of a limiting crack velocity below the Rayleigh wave speed for mode I propagation. Numerical results show that, when a crack accelerates , the damaged band tends to widen in a direction perpendicular to the propagation direction, before forming two distinct macroscopic branches. This transition from a single crack propagation to a branched configuration is described by a well-defined master-curve of the apparent fracture energy Γ as an increasing function of the crack velocity. This Γ(v) relationship can be associated, from a macroscopic point of view, with the well-known velocity-toughening mechanism. These results also support the existence of a critical value of the energy release rate associated with branching: a critical value of approximately 2Gc is observed i.e. the fracture energy contribution of two crack tips. Finally, our work demonstrates the efficiency of the phase-field approach to simulate crack propagation dynamics interacting with heterogeneities, revealing the complex interplay between heterogeneity patterns and branching mechanisms

Variational phase field model for dynamic brittle fracture

Simulating crack nucleation and propagation remains a challenging problematic because of the complexity of crack patterns observed in fracture mechanics experiments. Whereas some numerical methods aim at explicitly tracking the crack front evolution, an interesting alternative is offered by continuous approaches of brittle fracture which consist in representing the crack topology using a continuous field varying from 0 (sound material) to 1 (fully cracked material) across an internal length scale. This « phase field » approach benefits from a variational framework, strongly related to gradient damage models, and can be seen as a regularization of the variational approach to fracture developed by Francfort and Marigo in 1998. Moreover, it does not require any a priori knowledge of the crack path or topology, its evolution being driven only by energy minimization. Using such an approach combined to a finite-element discretization, the present work aims at providing some insights on crack propagation in a dynamic context. More specifically, crack branching (splitting of a single crack in two or more cracks) is a characteristic phenomenon of dynamic brittle fracture which still lacks a sound theoretical explanation. Numerical simulations will help us better understand some aspects of the branching phenomenon, especially the role played by material heterogeneities in the onset or delay of crack branching

Direct observation of the displacement field and microcracking in a glass by means of X-ray tomography during in situ Vickers indentation experiment

International audienceThe actual displacement field in a glass during an in-situ Vickers indentation experiment was determined by means of X-ray tomography, thanks to the addition of 4 vol % of X-ray absorbing particles, which acted as a speckle to further proceed through digital volume correlation. This displacement was found to agree well with the occurrence of densification beneath the contact area. The intensity of the densification contribution (Blister field proposed by Yoffe) was characterized and provides evidence for the significant contribution of densification to the mechanical fields. Densification accounts for 27% of the volume of the imprint for the studied glass, that is expected to be less sensitive to densification than amorphous silica or window glass. A major consequence is that indentation cracking methods for the evaluation of the fracture toughness, when they are based on volume conservation, as in the case of Hill-Eshelby plastic inclusion theory, are not suitable to glass. The onset for the formation of the subsurface lateral crack was also detected. The corresponding stress is z 14 GPa and is in agreement with the intrinsic glass strength

3D curved crack simulation with direct generalized K-factors estimation : Toward fatigue crack growth law identification

La compréhension du comportement de structures jusqu'à leur ruine est nécessaire pour concevoir au mieux ces structures. Selon le matériau et les sollicitations considérées, les mécanismes physiques à l'origine de la rupture changent. Nous nous intéresserons à des matériaux homogènes pour lesquels la ruine passe par le développement de fissures autour desquelles les non-linéarités de comportement n'ont pas un rôle dominant. Ces conditions sont réunies pour les matériaux fragiles pour lesquels la source principale de dissipation est la génération non réversible d'une surface libre, et pour certaines fissures de fatigue. Sur un cycle de chargement, il existe de nombreuses applications pour lesquelles les non-linéarités restent confinées. La théorie de la mécanique linéaire élastique de la rupture est alors un modèle pertinent pour approcher le comportement de la structure. Sous ces hypothèses, le front de la fissure introduit une singularité. L'étude asymptotique de cette singularité dans des situations plane et anti-plane permet de définir les séries de Williams. La singularité est alors d'ordre un demi et elle est quantifiée par les facteurs d'intensité des contraintes (FIC) pour chacun des trois modes de sollicitations. En 3D, la fissure peut avoir une géométrie complexe, et aucune expression générale de la singularité n'existe. Dans cette thèse, les séries de Williams en déplacements sont utilisées et régularisées le long du front au sens des éléments finis. À partir de cette définition 3D des séries asymptotiques en pointe de fissure, une méthode d'extraction directe des FIC (DEK-FEM) est étendue au cas 3D. Le domaine est décomposé en deux domaines, raccordés en moyenne sur l'interface. Au voisinage du front, les champs mécaniques sont approchés par une troncature des champs asymptotiques. La singularité est donc traitée avec des champs adaptés, et les degrés de liberté associés sont directement les coefficients asymptotiques. Parmi ces coefficients asymptotiques, on retrouve les FIC et les T-stresses. Pour des raisons d'efficacité numérique et pour pouvoir relier l'échelle de la structure à l'échelle de la fissure, cette méthode est intégrée dans un contexte multigrilles localisées X-FEM. Ainsi nous montrons que cette approche permet une bonne évaluation des évolutions des FIC et du T-stress. Cette méthode est développée en parallèle d'une stratégie de post-traitement expérimental (mesure de champs de déplacements par corrélation d'images) basée sur les mêmes séries asymptotiques. Les images tridimensionnels d'un essai de fatigue in situ sont obtenues par micro-tomographie à rayons X et reconstruction. La corrélation et la régularisation basées sur les séries asymptotiques permettent d'obtenir la géométrie de la fissure et les FIC pour pouvoir identifier des lois de propagation de fissures 3D en fatigue. L'efficacité de cette méthode en parallèle d'une simulation DEK-FEM est illustrée en 2D.It is necessary to understand the behavior of structures up to their failure to enhance their design. The mechanisms and phenomena undergoing failure vary according to the considered material and boundary conditions. We consider homogeneous materials for which cracks propagate in a context where behavior nonlinearities are not dominants. These conditions are matched for brittle and quasi-brittle materials and for some fatigue cracks. For the former, the main source of dissipation is the crack propagation which can be seen as the generation of a new free-surface. For the later, there is many applications where, in one loading cycle, the nonlinearities remains confined around the crack tip. The linear elastic fracture mechanics theory is then a pertinent model to approximate the structure behavior. Under such hypotheses, a singularity appears in the crack tip vicinity. The Williams' series expansion is computed from the asymptotic study of plane and anti-plane states. The stress is singular at the crack tip and the order of this singularity is one out of two. The singularity amplitude is quantified by the stress intensity factors (SIF), one for each of the three loading modes. In 3D, the crack shape is potentially complex (front curvature and non-planar crack), and no general asymptotic series expansion exists. In this PhD thesis, the 2D Williams' series in displacements are used and regularized with a finite element evolution along the front. From this 3D definition of the asymptotic fields in the crack tip vicinity, a numerical method for direct estimation of the SIF (DEK-FEM) is extended to 3D. This method is based on domain decomposition, the two domains are bounded in a weak sense on their interface. In the crack tip vicinity, the mechanical fields are approximated by a truncation of the asymptotic series expansion. Therefore, appropriate fields are used to deal with the singularity, and the associated degrees of freedom are directly the asymptotic coefficients. Among these coefficients are the SIF and the T-stresses. To bridge the scales between the structure and the crack front singularity and to increase the numerical efficiency, this method is embedded in a localized X-FEM multigrids approach. The proposed method is shown to provide an accurate evaluation of the SIF and T-stresses evolution. This approach has been developed in combination of an experimental post-processing method (full field displacement measurement through image correlation) based on the same asymptotic series expansion. The 3D images can be obtained for in situ fatigue experiments by X-ray microtomography and reconstruction. The crack geometry and the SIF are then provided by image correlation and regularization based on Williams series expansion. These data can be used for identifying a 3D fatigue crack growth law. The efficiency of the method is illustrated in 2D

Role of Poisson's ratio mismatch on the crack path in glass matrix particulate composites

International audienceThe improvement of the mechanical properties of glass matrix particulate composites has been extensively studied in the past 40 years. Emphasis has mostly been placed on the influence of mismatches of the elastic moduli and coefficient of thermal expansion. However, little attention was paid to Poisson's ratio so far, although we show by means of analytical analysis and finite element method (FEM) that it has a major influence on the stress field distribution, the stress intensity factor and thus on the crack path in the vicinity of the inclusion. Due to local stress changes, crack front pinning and bridging phenomena are predicted in the case of adhesive particles with smaller than the one of the matrix. Nevertheless, when located close to the surface, such particles might play the role of stress concentrators. Glass offers a unique opportunity to vary composition and properties in a continuous manner, hence opening a new realm of possibilities for tuning Poisson's ratio to improve the resistance the glass composite opposes to crack extension

Variational phase field model for brittle fracture : insights on dynamic crack branching and propagation in heterogeneous media

International audienceSimulating crack nucleation and propagation remains a challenging problematic because of the complexity of crack patterns observed in fracture mechanics experiments. Whereas some numerical methods aim at explicitly tracking the crack front evolution, an interesting alternative is offered by continuous approaches of brittle fracture which consist in representing the crack topology using a continuous field varying from 0 (sound material) to 1 (fully cracked material) accross an internal length scale. This « phase field » approach benefits from a variational framework, strongly related to gradient damage models, and can be seen as a regularization of the variational approach to fracture developed by Francfort and Marigo in 1998. Moreover, it does not require any a priori knowledge of the crack path or topology, its evolution being driven only by energy minimization.Using such an approach combined to a finite-element discretization, the present work aims at providing some insights on crack propagation in a dynamic context. More specifically, crack branching (splitting of a single crack in two or more cracks) is a characteristic phenomenon of dynamic brittle fracture which still lacks a sound theoretical explanation. Numerical simulations will help us better understand some aspects of the branching phenomenon, especially the role played by material heterogeneities in the onset or delay of crack branching

Adaptation of the single edge precracked beam procedure to the determination of the toughness of glass

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Simulation multi-échelles de fissures 3D à front courbe avec estimation directe des coefficients asymptotiques

International audienceÀ partir des hypothèses de la mécanique de la rupture, la méthode proposée identifie les coefficients asymptotiques le long d'un front courbe, lors de la résolution du problème considéré. Parmi ces coefficients on retrouve notamment les facteurs d'intensité des contraintes et le T -stress. Une portion du domaine autour du front est discrétisée avec les séries asymptotiques. Elle est raccordée au sens faible au reste du domaine qui est traité avec une méthode X-FEM standard. Enfin, cette méthode est insérée dans un algorithme multigrilles localisées pour améliorer son efficacité numérique