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9 results on '"Phase-field models of fracture"'

1. On the loss of symmetry in toughness dominated hydraulic fractures.

Author

Tanné, Erwan, Bourdin, Blaise, and Yoshioka, Keita

Subjects
*FRACTURE mechanics, *HYDRAULIC fracturing, *SYMMETRY, *FRACTURE toughness, *DAMAGE models, *ROCK deformation
Abstract

Fracking, or hydraulic fracturing, is a ubiquitous technique for generating fracture networks in rocks for enhanced geothermal systems or hydrocarbon extraction from shales. For decades, models, numerical simulation tools, and practical guidelines have been based on the assumption that this process generates networks of self-similar parallel cracks. Yet, some field and laboratory observations show asymmetric crack growth, and material heterogeneity is routinely attributed for it. Here, we show that simultaneous growth of multiple parallel cracks is impossible and that a single crack typically propagates asymmetrically in toughness dominated hydraulic fracturing, in which viscous dissipation of the fluid is negligible. In other words, loss of symmetry is a fundamental feature of hydraulic fracturing in a toughness dominated regime and not necessary the result of material heterogeneities. Our findings challenge the assumptions of symmetrical growth of hydraulic fractures commonly made in practice, and point to yet another instability other than material heterogeneity. [ABSTRACT FROM AUTHOR]

Published
2022
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2. A variational phase-field model for hydraulic fracturing in porous media.

Author

Chukwudozie, Chukwudi, Bourdin, Blaise, and Yoshioka, Keita

Subjects
*POROUS materials, *HYDRAULIC fracturing, *PHASE transitions, *MECHANICAL behavior of materials, *FRACTURE mechanics
Abstract

Abstract Rigorous coupling of fracture–porous medium fluid flow and topologically complex fracture propagation is of great scientific interest in geotechnical and biomechanical applications. In this paper, we derive a unified fracture–porous medium hydraulic fracturing model, leveraging the inherent ability of the variational phase-field approach to fracture to handle multiple cracks interacting and evolving along complex yet, critically, unspecified paths. The fundamental principle driving the crack evolution is an energetic criterion derived from Griffith's theory. The originality of this approach is that the crack path itself is derived from energy minimization instead of additional branching criterion. The numerical implementation is based on a regularization approach similar to a phase-field model, where the cracks location is represented by a smooth function defined on a fixed mesh. The derived model shows how the smooth fracture field can be used to model fluid flow in a fractured porous medium. We verify the proposed approach in a simple idealized scenario where closed form solutions exist in the literature. We then demonstrate the new method's capabilities in more realistic situations where multiple fractures turn, interact, and in some cases, merge with other fractures. Highlights • A unified fracture - porous medium flow model has been proposed, which is regularized with a phase-field variable consistent with the fracture mechanics regularization without defining extra variables or level set functions. • The methodology to compute the crack opening displacement using the gradient of the phase-field variable has been derived using the Gamma-convergence approximation. • Additionally, we point out erroneous crack opening displacement computation under deformed domain, which has not been discussed before, and propose an approach to mitigate this error. • The proposed model has been verified in the toughness dominated regime of hydraulic fracturing. [ABSTRACT FROM AUTHOR]

Published
2019
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3. On the loss of symmetry in toughness dominated hydraulic fractures

Author

Tanné, E., Bourdin, B., Yoshioka, Keita, Tanné, E., Bourdin, B., and Yoshioka, Keita

Abstract

Fracking, or hydraulic fracturing, is a ubiquitous technique for generating fracture networks in rocks for enhanced geothermal systems or hydrocarbon extraction from shales. For decades, models, numerical simulation tools, and practical guidelines have been based on the assumption that this process generates networks of self-similar parallel cracks. Yet, some field and laboratory observations show asymmetric crack growth, and material heterogeneity is routinely attributed for it. Here, we show that simultaneous growth of multiple parallel cracks is impossible and that a single crack typically propagates asymmetrically in toughness dominated hydraulic fracturing, in which viscous dissipation of the fluid is negligible. In other words, loss of symmetry is a fundamental feature of hydraulic fracturing in a toughness dominated regime and not necessary the result of material heterogeneities. Our findings challenge the assumptions of symmetrical growth of hydraulic fractures commonly made in practice, and point to yet another instability other than material heterogeneity.

Published
2022

4. Crack nucleation in variational phase-field models of brittle fracture.

Author

Tanné, E., Li, T., Bourdin, B., Marigo, J.-J., and Maurini, C.

Subjects
*NUCLEATION, *BRITTLE fractures, *CRACK propagation (Fracture mechanics), *COMPUTER simulation, *CRYSTAL structure, *STRENGTH of materials
Abstract

Phase-field models, sometimes referred to as gradient damage or smeared crack models, are widely used methods for the numerical simulation of crack propagation in brittle materials. Theoretical results and numerical evidences show that they can predict the propagation of a pre-existing crack according to Griffith’ criterion. For a one-dimensional problem, it has been shown that they can predict nucleation upon a critical stress, provided that the regularization parameter be identified with the material’s internal or characteristic length. In this article, we draw on numerical simulations to study crack nucleation in commonly encountered geometries for which closed-form solutions are not available. We use U- and V-notches to show that the nucleation load varies smoothly from that predicted by a strength criterion to that of a toughness criterion when the strength of the stress concentration or singularity varies. We present validation and verification numerical simulations for both types of geometries. We consider the problem of an elliptic cavity in an infinite or elongated domain to show that variational phase field models properly account for structural and material size effects. Our main claim, supported by validation and verification in a broad range of materials and geometries, is that crack nucleation can be accurately predicted by minimization of a nonlinear energy in variational phase field models, and does not require the introduction of ad-hoc criteria. [ABSTRACT FROM AUTHOR]

Published
2018
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5. On crack opening computation in variational phase-field models for fracture

Author

Yoshioka, Keita, Naumov, Dmitri, Kolditz, Olaf, Yoshioka, Keita, Naumov, Dmitri, and Kolditz, Olaf

Abstract

Phase-field models for fracture have gained exceptional popularity in the last couple of decades and have been extended into areas well beyond brittle quasi-static fracture propagation to ductile, dynamic, or hydraulic fracturing. Despite the significant theoretical advancements in these more complex physical settings, little attention has been paid to the quantification of crack opening displacement to date as most applications do not explicitly require the crack opening displacement for the morphological evolution of cracks. However, one of the exemptions would be hydraulic fracturing where the crack propagation is driven by the fluid pressure which strongly depends on the crack opening displacement.In this study, we look into two known approaches, a line integral and a level-set method, for crack opening computation mainly from an implementation point of view. Firstly, we derive an approximation of a discontinuous function field in the variational phase-field setting which is then applied to obtain the crack opening (displacement jump) and verify the approximation against a closed solution. We then propose a “certain distance from the crack” required for the level-set function using a one-dimensional analysis. Finally, we compare these approaches under several different conditions such as crack alignment to the mesh or under loading (asymmetric displacement field) and investigate the convergence with respect to the mesh size.

Published
2020

6. A variational phase-field model for hydraulic fracturing in porous media

Author

Chukwudozie, C., Bourdin, B., Yoshioka, Keita, Chukwudozie, C., Bourdin, B., and Yoshioka, Keita

Abstract

Rigorous coupling of fracture–porous medium fluid flow and topologically complex fracture propagation is of great scientific interest in geotechnical and biomechanical applications. In this paper, we derive a unified fracture–porous medium hydraulic fracturing model, leveraging the inherent ability of the variational phase-field approach to fracture to handle multiple cracks interacting and evolving along complex yet, critically, unspecified paths. The fundamental principle driving the crack evolution is an energetic criterion derived from Griffith’s theory. The originality of this approach is that the crack path itself is derived from energy minimization instead of additional branching criterion. The numerical implementation is based on a regularization approach similar to a phase-field model, where the cracks location is represented by a smooth function defined on a fixed mesh. The derived model shows how the smooth fracture field can be used to model fluid flow in a fractured porous medium. We verify the proposed approach in a simple idealized scenario where closed form solutions exist in the literature. We then demonstrate the new method’s capabilities in more realistic situations where multiple fractures turn, interact, and in some cases, merge with other fractures.

Published
2019

7. Modèles variationnels à champ de phase pour la rupture de type fragile et ductile : nucléation et propagation

Author

Tanne, Erwan, Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Université Paris-Saclay, Jean-Jacques Marigo, and Blaise Bourdin

Subjects
Modèles d’endommagement à gradient, Fracturation hydraulique, Variational approach, Ductile fracture, [SPI.MECA.MSMECA]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Materials and structures in mechanics [physics.class-ph], Hydraulic fracturing, Stabilité des fissures, Crack stability, Plasticity model, Gradient damage models, Nucléation de fissure, Phase-field models of fracture, Approche variationnelle, Size effects in brittle materials, Modèles à champ de phase pour la rupture, Effet d’échelle dans les matériaux fragiles, Modèles de plasticités, Crack nucleation, Rupture ductile
Abstract

Phase-field models, sometimes referred to as gradient damage, are widely used methods for the numerical simulation of crack propagation in brittle materials. Theoretical results and numerical evidences show that they can predict the propagation of a pre-existing crack according to Griffith’s criterion. For a one- dimensional problem, it has been shown that they can predict nucleation upon a critical stress, provided that the regularization parameter is identified with the material’s internal characteristic length.In this work, we draw on numerical simulations to study crack nucleation in commonly encountered geometries for which closed-form solutions are not available. We use U- and V-notches to show that the nucleation load varies smoothly from the one predicted by a strength criterion to the one of a toughness criterion when the strength of the stress concentration or singularity varies. We present validation and verification of numerical simulations for both types of geometries. We consider the problem of an elliptic cavity in an infinite or elongated domain to show that variational phase field models properly account for structural and material size effects.In a second movement, this model is extended to hydraulic fracturing. We present a validation of the model by simulating a single fracture in a large domain subject to a control amount of fluid. Then we study an infinite network of pressurized parallel cracks. Results show that the stimulation of a single fracture is the best energy minimizer compared to multi-fracking case. The last example focuses on fracturing stability regimes using linear elastic fracture mechanics for pressure driven fractures in an experimental geometry used in petroleum industry which replicates a situation encountered downhole with a borehole called burst experiment.The last part of this work focuses on ductile fracture by coupling phase-field models with perfect plasticity. Based on the variational structure of the problem we give a numerical implementation of the coupled model for parallel computing. Simulation results of a mild notch specimens are in agreement with the phenomenology of ductile fracture such that nucleation and propagation commonly reported in the literature.; Les simulations numériques des fissures fragiles par les modèles d’endommagement à gradient deviennent main- tenant très répandues. Les résultats théoriques et numériques montrent que dans le cadre de l’existence d’une pre-fissure la propagation suit le critère de Griffith. Alors que pour le problème à une dimension la nucléation de la fissure se fait à la contrainte critique, cette dernière propriété dimensionne le paramètre de longueur interne.Dans ce travail, on s’attarde sur le phénomène de nucléation de fissures pour les géométries communément rencontrées et qui ne présentent pas de solutions analytiques. On montre que pour une entaille en U- et V- l’initiation de la fissure varie continument entre la solution prédite par la contrainte critique et celle par la ténacité du matériau. Une série de vérifications et de validations sur diffèrent matériaux est réalisée pour les deux géométries considérées. On s’intéresse ensuite à un défaut elliptique dans un domaine infini ou très élancé pour illustrer la capacité du modèle à prendre en compte les effets d’échelles des matériaux et des structures.Dans un deuxième temps, ce modèle est étendu à la fracturation hydraulique. Une première phase de vérification du modèle est effectuée en stimulant une pré-fissure seule par l’injection d’une quantité donnée de fluide. Ensuite on étudie la simulation d’un réseau parallèle de fissures. Les résultats obtenus montrent qu’il a qu’une seule fissure qui se propage et que ce type de configuration minimise mieux l’énergie la propagation d’un réseau de fractures. Le dernier exemple se concentre sur la stabilité des fissures dans le cadre d’une expérience d’éclatement à pression imposée pour l’industrie pétrolière. Cette expérience d’éclatement de la roche est réalisée en laboratoire afin de simuler les conditions de confinement retrouvées lors des forages.La dernière partie de ce travail se concentre sur la rupture ductile en couplant le modèle à champ de phase avec les modèles de plasticité parfaite. Grâce à l’approche variationnelle du problème on décrit l’implantation numérique retenue pour le calcul parallèle. Les simulations réalisées montrent que pour une géométrie légèrement entaillée la phénoménologie des fissures ductiles comme par exemple la nucléation et la propagation sont en concordances avec ceux reportées dans la littérature.

Published
2017

8. Variational phase-field models from brittle to ductile fracture : nucleation and propagation

Author

Tanne, Erwan, Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Université Paris-Saclay, Jean-Jacques Marigo, and Blaise Bourdin

Subjects
Modèles d’endommagement à gradient, Fracturation hydraulique, Variational approach, Ductile fracture, [SPI.MECA.MSMECA]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Materials and structures in mechanics [physics.class-ph], Hydraulic fracturing, Stabilité des fissures, Crack stability, Plasticity model, Gradient damage models, Nucléation de fissure, Phase-field models of fracture, Approche variationnelle, Size effects in brittle materials, Modèles à champ de phase pour la rupture, Effet d’échelle dans les matériaux fragiles, Modèles de plasticités, Crack nucleation, Rupture ductile
Abstract

Phase-field models, sometimes referred to as gradient damage, are widely used methods for the numerical simulation of crack propagation in brittle materials. Theoretical results and numerical evidences show that they can predict the propagation of a pre-existing crack according to Griffith’s criterion. For a one- dimensional problem, it has been shown that they can predict nucleation upon a critical stress, provided that the regularization parameter is identified with the material’s internal characteristic length.In this work, we draw on numerical simulations to study crack nucleation in commonly encountered geometries for which closed-form solutions are not available. We use U- and V-notches to show that the nucleation load varies smoothly from the one predicted by a strength criterion to the one of a toughness criterion when the strength of the stress concentration or singularity varies. We present validation and verification of numerical simulations for both types of geometries. We consider the problem of an elliptic cavity in an infinite or elongated domain to show that variational phase field models properly account for structural and material size effects.In a second movement, this model is extended to hydraulic fracturing. We present a validation of the model by simulating a single fracture in a large domain subject to a control amount of fluid. Then we study an infinite network of pressurized parallel cracks. Results show that the stimulation of a single fracture is the best energy minimizer compared to multi-fracking case. The last example focuses on fracturing stability regimes using linear elastic fracture mechanics for pressure driven fractures in an experimental geometry used in petroleum industry which replicates a situation encountered downhole with a borehole called burst experiment.The last part of this work focuses on ductile fracture by coupling phase-field models with perfect plasticity. Based on the variational structure of the problem we give a numerical implementation of the coupled model for parallel computing. Simulation results of a mild notch specimens are in agreement with the phenomenology of ductile fracture such that nucleation and propagation commonly reported in the literature.; Les simulations numériques des fissures fragiles par les modèles d’endommagement à gradient deviennent main- tenant très répandues. Les résultats théoriques et numériques montrent que dans le cadre de l’existence d’une pre-fissure la propagation suit le critère de Griffith. Alors que pour le problème à une dimension la nucléation de la fissure se fait à la contrainte critique, cette dernière propriété dimensionne le paramètre de longueur interne.Dans ce travail, on s’attarde sur le phénomène de nucléation de fissures pour les géométries communément rencontrées et qui ne présentent pas de solutions analytiques. On montre que pour une entaille en U- et V- l’initiation de la fissure varie continument entre la solution prédite par la contrainte critique et celle par la ténacité du matériau. Une série de vérifications et de validations sur diffèrent matériaux est réalisée pour les deux géométries considérées. On s’intéresse ensuite à un défaut elliptique dans un domaine infini ou très élancé pour illustrer la capacité du modèle à prendre en compte les effets d’échelles des matériaux et des structures.Dans un deuxième temps, ce modèle est étendu à la fracturation hydraulique. Une première phase de vérification du modèle est effectuée en stimulant une pré-fissure seule par l’injection d’une quantité donnée de fluide. Ensuite on étudie la simulation d’un réseau parallèle de fissures. Les résultats obtenus montrent qu’il a qu’une seule fissure qui se propage et que ce type de configuration minimise mieux l’énergie la propagation d’un réseau de fractures. Le dernier exemple se concentre sur la stabilité des fissures dans le cadre d’une expérience d’éclatement à pression imposée pour l’industrie pétrolière. Cette expérience d’éclatement de la roche est réalisée en laboratoire afin de simuler les conditions de confinement retrouvées lors des forages.La dernière partie de ce travail se concentre sur la rupture ductile en couplant le modèle à champ de phase avec les modèles de plasticité parfaite. Grâce à l’approche variationnelle du problème on décrit l’implantation numérique retenue pour le calcul parallèle. Les simulations réalisées montrent que pour une géométrie légèrement entaillée la phénoménologie des fissures ductiles comme par exemple la nucléation et la propagation sont en concordances avec ceux reportées dans la littérature.

Published
2017

9. Crack nucleation in variational phase-field models of brittle fracture

Author

Erwan Tanné, Corrado Maurini, Jean-Jacques Marigo, Tianyi Li, Blaise Bourdin, Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics Louisiana State University, Louisiana State University (LSU), Institut des Sciences de la mécanique et Applications industrielles (IMSIA - UMR 9219), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF), Institut Jean le Rond d'Alembert (DALEMBERT), Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), Mécanique et Ingénierie des Solides Et des Structures (IJLRDA-MISES), Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), National Science Foundation under Grant No. DMS-1312739 and DMS-1535076Extreme Science and Engineering Discovery Environment (XSEDE), NSF grant number ACI-1548562Sorbonnes Universites project FRZX026-SU-16-R-EMR-02-ANIS, ANR-11-IDEX-0004,SUPER,Sorbonne Universités à Paris pour l'Enseignement et la Recherche(2011), Institut Jean Le Rond d'Alembert (DALEMBERT), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-EDF R&D (EDF R&D), Centre National de la Recherche Scientifique (CNRS)-MINES ParisTech - École nationale supérieure des mines de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École polytechnique (X)

Subjects
Materials science, Characteristic length, Nucleation, Phase field models, 02 engineering and technology, [SPI.MECA.MSMECA]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Materials and structures in mechanics [physics.class-ph], [SPI.MECA.SOLID]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph], Crack growth resistance curve, 01 natural sciences, [SPI.MAT]Engineering Sciences [physics]/Materials, [SPI]Engineering Sciences [physics], Brittleness, 0203 mechanical engineering, [PHYS.MECA.SOLID]Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph], [SPI.MECA.MEMA]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of materials [physics.class-ph], Forensic engineering, 0101 mathematics, Stress concentration, size e↵ects in brittle materials, validation & verification, Computer simulation, Mechanical Engineering, gradient damage models, Fracture mechanics, Mechanics, smeared crack models, Condensed Matter Physics, size effects in brittle materials, 010101 applied mathematics, 020303 mechanical engineering & transports, Phase-field models of fracture, Mechanics of Materials, [SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph], crack nucleation
Abstract

Phase-field models, sometimes referred to as gradient damage or smeared crack models, are widely used methods for the numerical simulation of crack propagation in brittle materials. Theoretical results and numerical evidences show that they can predict the propagation of a pre-existing crack according to Griffith’ criterion. For a one-dimensional problem, it has been shown that they can predict nucleation upon a critical stress, provided that the regularization parameter be identified with the material’s internal or characteristic length. In this article, we draw on numerical simulations to study crack nucleation in commonly encountered geometries for which closed-form solutions are not available. We use U- and V-notches to show that the nucleation load varies smoothly from that predicted by a strength criterion to that of a toughness criterion when the strength of the stress concentration or singularity varies. We present validation and verification numerical simulations for both types of geometries. We consider the problem of an elliptic cavity in an infinite or elongated domain to show that variational phase field models properly account for structural and material size effects. Our main claim, supported by validation and verification in a broad range of materials and geometries, is that crack nucleation can be accurately predicted by minimization of a nonlinear energy in variational phase field models, and does not require the introduction of ad-hoc criteria.

Published
2017
Full Text
View/download PDF

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