[Mécanique de la rupture finie en 3D sous chargement en mode I : la fissure elliptique plane]
The determination of the remote stress causing crack propagation in an infinite 3D domain with an embedded flat elliptical crack is here revisited in the framework of the Coupled Criterion of Finite Fracture Mechanics. We started reviewing Linear Elastic Fracture Mechanics approaches, which differ by accounting for different infinitesimal crack growths. Then, we provide the solution based on Finite Fracture Mechanics: if the elliptical flaw is sufficiently small, the crack grows along iso-stress lines. For larger sizes, other crack growths may take place. Thus, the present investigation shows that assuming an iso-stress crack front may effectively provide the exact Finite Fracture Mechanics solution, particularly for small defects; on the other hand, it can be wrong for larger size, providing moreover un-conservative predictions. However, for the geometry at hand, it yields failure stress estimates differing from the actual one by a few percents. Thus, the iso-stress assumption, conjectured by Leguillon [D. Leguillon, “An attempt to extend the 2D coupled criterion for crack nucleation in brittle materials to the 3D case”, Theor. Appl. Fract. Mech. 74 (2014), pp. 7–17]—implying strong simplifications in the numerical implementation of the coupled criterion in 3D problems—seems to be largely justified by the present results. Moreover, regardless of the initial crack size, the finite growth predicted by the model results in a new elliptical crack shape closer to the circular one, meaning the eccentricity consistently decreases as the crack propagates.
La détermination de la contrainte à distance provoquant la propagation d’une fissure dans un domaine 3D infini contenant une fissure elliptique plane est ici revisitée dans le cadre du Critère Couplé de la Mécanique de la Rupture Finie. Nous commençons par passer en revue les approches de la Mécanique Linéaire de la Rupture, qui diffèrent selon la prise en compte de différentes croissances infinitésimales de la fissure. Ensuite, nous présentons la solution basée sur la Mécanique de la Rupture Finie : si le défaut elliptique est suffisamment petit, la fissure croît le long de lignes iso-contraintes. Pour des tailles plus grandes, d’autres modes de croissance de fissure peuvent se produire. Ainsi, cette étude montre que supposer un front de fissure iso-contraintes peut effectivement fournir la solution exacte en Mécanique de la Rupture Finie, en particulier pour les petits défauts ; en revanche, cela peut être erroné pour des défauts de plus grande taille, entraînant de surcroît des prédictions non conservatrices. Toutefois, pour la géométrie considérée, cela donne des estimations de contrainte de rupture ne différant que de quelques pourcents de la valeur réelle. Ainsi, l’hypothèse d’iso-contraintes, avancée par Leguillon [D. Leguillon, “An attempt to extend the 2D coupled criterion for crack nucleation in brittle materials to the 3D case”, Theor. Appl. Fract. Mech. 74 (2014), pp. 7-17], impliquant des simplifications importantes dans l’implémentation numérique du critère couplé dans des problèmes 3D, semble largement justifiée par les résultats présents. En outre, quelle que soit la taille initiale de la fissure, la croissance finie prédite par le modèle aboutit à une nouvelle forme elliptique de la fissure, plus proche d’un cercle, ce qui signifie que l’excentricité diminue systématiquement au fur et à mesure de la propagation de la fissure.
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Mots-clés : Critère couplé, Mécanique de la rupture finie, Mécanique de la fracture élastique linéaire en 3D, Fissures elliptiques, Matériaux quasi-fragile
Pietro Cornetti 1 ; Vladislav Mantič 2 ; Zohar Yosibash 3
CC-BY 4.0
@article{CRMECA_2025__353_G1_725_0,
author = {Pietro Cornetti and Vladislav Manti\v{c} and Zohar Yosibash},
title = {3D finite fracture mechanics under mode {I} loading: the flat elliptical crack},
journal = {Comptes Rendus. M\'ecanique},
pages = {725--745},
publisher = {Acad\'emie des sciences, Paris},
volume = {353},
year = {2025},
doi = {10.5802/crmeca.302},
language = {en},
}
TY - JOUR AU - Pietro Cornetti AU - Vladislav Mantič AU - Zohar Yosibash TI - 3D finite fracture mechanics under mode I loading: the flat elliptical crack JO - Comptes Rendus. Mécanique PY - 2025 SP - 725 EP - 745 VL - 353 PB - Académie des sciences, Paris DO - 10.5802/crmeca.302 LA - en ID - CRMECA_2025__353_G1_725_0 ER -
Pietro Cornetti; Vladislav Mantič; Zohar Yosibash. 3D finite fracture mechanics under mode I loading: the flat elliptical crack. Comptes Rendus. Mécanique, Volume 353 (2025), pp. 725-745. doi : 10.5802/crmeca.302. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.302/
[1] Strength or toughness? A criterion for crack onset at a notch, Eur. J. Mech. A/Solids, Volume 21 (2002), pp. 61-72 | DOI | Zbl
[2] Finite fracture mechanics: a coupled stress and e nergy failure criterion, Eng. Fract. Mech., Volume 73 (2006), pp. 2021-2033 | DOI
[3] A failure criterion for brittle elastic materials under mixed-mode loading, Int. J. Fract., Volume 141 (2006), pp. 291-312 | DOI | Zbl
[4] Mode mixity and size effect in V-notched structures, Int. J. Solids Struct., Volume 50 (2013), pp. 1562-1582 | DOI
[5] A comparison among some recent energy- and stress-based criteria for the fracture assessment of sharp V-notched components under mode I loading, Theor. Appl. Fract. Mech., Volume 71 (2014), pp. 21-30 | DOI
[6] Interface crack onset at a circular cylindrical inclusion under a remote transverse tension. Application of a coupled stress and energy criterion, Int. J. Solids Struct., Volume 46 (2009), pp. 1287-1304 | DOI | Zbl
[7] A twofold strength and toughness criterion for the onset of free-edge shear delamination in angle-ply laminates, Int. J. Solids Struct., Volume 47 (2010), pp. 1297-1305 | DOI | Zbl
[8] A finite fracture mechanics model for the prediction of the open-hole strength of composite laminates, Compos.-A: Appl. Sci. Manuf., Volume 43 (2012), pp. 1219-1225 | DOI
[9] Finite Fracture Mechanics model for mixed mode fracture in adhesive joints, Int. J. Solids Struct., Volume 50 (2013), pp. 2383-2394 | DOI
[10] Dynamic crack initiation assessment with the coupled criterion, Eur. J. Mech. A/Solids, Volume 93 (2022), 104483 | DOI | MR | Zbl
[11] Finite fracture mechanics extension to dynamic loading scenarios, Int. J. Fract., Volume 239 (2023), pp. 149-165 | DOI
[12] Fatigue limit: crack and notch sensitivity by finite fracture mechanics, Theor. Appl. Fract. Mech., Volume 105 (2020), 102407 | DOI
[13] A novel finite fracture mechanics approach to assess the lifetime of notched components, Int. J. Fatigue, Volume 173 (2023), 107659 | DOI
[14] Crack initiation at a V-notch-comparison between a brittle fracture criterion and the Dugdale cohesive model, C. R. Mèc., Volume 335 (2007), pp. 388-393 | DOI
[15] Fiber-size effects on the onset of fiber-matrix debonding under transverse tension: a comparison between cohesive zone and finite fracture mechanics models, Eng. Fract. Mech., Volume 115 (2014), pp. 96-110 | DOI
[16] Short cracks and v-notches: finite fracture mechanics vs cohesive crack model, Eng. Fract. Mech., Volume 168 (2016), pp. 2-12 | DOI
[17] Penny-shaped cracks by Finite Fracture Mechanics, Int. J. Fract., Volume 219 (2019), pp. 153-159 | DOI
[18] Finite fracture mechanics and cohesive crack model: size effects through a unified formulation, Frat. Integrità Strut., Volume 16 (2022), pp. 496-509
[19] Coupled versus energetic nonlocal failure criteria: A case study on the crack onset from circular holes under biaxial loadings, Eur. J. Mech. A/Solids, Volume 101 (2023), 105037 | DOI | MR
[20] Strength prediction of notched thin ply laminates using finite fracture mechanics and the phase field approach, Compos. Sci. Technol., Volume 150 (2017), pp. 205-216 | DOI
[21] Toughness or strength? Regularization in phase-field fracture explained by the coupled criterion, Theor. Appl. Fract. Mech., Volume 109 (2020), 102736 | DOI
[22] Strength based regularization length in phase field fracture, Theor. Appl. Fract. Mech., Volume 124 (2023), 103728 | DOI
[23] Phase-field simulation and coupled criterion link echelon cracks to internal length in Antiplane shear, J. Mech. Phys. Solids, Volume 188 (2024), 105675 | DOI | MR
[24] A dialogue between finite fracture mechanics and phase field approaches to fracture for predicting crack nucleation at the microscale, Int. J. Fract., Volume 249 (2025), 13 | DOI
[25] An attempt to extend the 2D coupled criterion for crack nucleation in brittle materials to the 3D case, Theor. Appl. Fract. Mech., Volume 74 (2014), pp. 7-17 | DOI
[26] A 3-D failure initiation criterion from a sharp V-notch edge in elastic brittle structures, Eur. J. Mech.-A/Solids, Volume 60 (2016), pp. 70-94 | DOI | MR | Zbl
[27] A numerical study of transverse cracking in cross-ply laminates by 3D finite fracture mechanics, Compos. B: Eng., Volume 95 (2016), pp. 475-487 | DOI
[28] 3D application of the coupled criterion to crack initiation prediction in epoxy/aluminum specimens under four point bending, Int. J. Solids Struct., Volume 143 (2018), pp. 175-182 | DOI
[29] Comparison between 2D and 3D applications of the coupled criterion to crack initiation prediction in scarf adhesive joints, Int. J. Adhes. Adhes., Volume 85 (2018), pp. 69-76 | DOI
[30] The distribution of stress in the neighbourhood of a flat elliptical crack in an elastic solid, Proc. Camb. Philos. Soc., Volume 46 (1950), pp. 159-164 | DOI | MR
[31] The distribution of stress in the neighbourhood of a crack in an elastic solid, Proc. R. Soc. Lond. A, Volume 187 (1946), pp. 229-260 | MR
[32] Crack-Extension Force for a Part-Through Crack in a Plate, ASME J. Appl. Mech., Volume 29 (1962), pp. 654-661 | DOI
[33] Three-dimensional stress and displacement fields near an elliptical crack front, Int. J. Fract., Volume 109 (2001), pp. 383-401 | DOI
[34] Asymptotic solution of the elasticity equations in the vicinity of an elliptical crack front, Eng. Fract. Mech., Volume 223 (2020), 106774 | DOI
[35] Brittle fracture and fatigue propagation paths of 3D plane cracks under uniform remote tensile loading, Int. J. Fract., Volume 122 (2003), pp. 23-46 | DOI
[36] Fatigue growth prediction of elliptical cracks in welded joint structure: Hybrid and energy density approach, Theor. Appl. Fract. Mech., Volume 54 (2010), pp. 11-18 | DOI
[37] Fatigue surface crack growth behavior in flat plate and out-of-plane gusset-welded joints under biaxial cyclic loads with different phases, J. Mar. Sci. Technol., Volume 26 (2021), pp. 655-672 | DOI
[38] Energetic approach to predict the elliptical crack growth, Procedia Struct. Integr., Volume 47 (2023), pp. 873-881 | DOI
[39] A three-dimensional Finite Fracture Mechanics model to predict free edge delamination in angle-ply laminates, Eng. Fract. Mech., Volume 306 (2024), 110156 | DOI
[40] A finite fracture mechanics approach to assess the fatigue life of laminates exhibiting free edge effects, Compos. Struct., Volume 354 (2025), 118797 | DOI
[41] Predicting free edge delamination induced by thermal loading using finite fracture mechanics, Int. J. Fract., Volume 250 (2025), 110156 | DOI
[42] Stable propagation of a mode-1 planar crack in an isotropic elastic space. Comparison of the Irwin and the Griffith approaches, Problemi Attuali Dell’Analisi e Della Fisica Matematica. Atti del 20 Simposio internazionale (Taormina 15–18 Ottobre 1998) (P. E. Ricci, ed.), Aracne, Rome, 2000, pp. 167-190 | MR | Zbl
[43] On the key role of crack surface area on the lifetime of arbitrarily shaped flat cracks, Int. J. Fatigue, Volume 154 (2022), 106512 | DOI
[44] Analytical solution for fatigue crack propagation of an embedded elliptical crack, Int. J. Fract., Volume 229 (2021), pp. 245-251 | DOI
[45] Static and energetic fracture parameters for rocks and concrete, Mater. Struct., Volume 14 (1981), pp. 151-162
[46] Three-dimensional crack growth with hp-generalized finite element and face offsetting methods, Comput. Mech., Volume 46 (2010), pp. 431-453 | DOI | MR | Zbl
[47] Experimental study on 3D internal penny-shaped crack propagation in brittle materials under uniaxial compression, Deep Undergr. Sci. Eng., Volume 2 (2023), pp. 37-51 | DOI
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