[Évaluation du taux de restitution d’énergie incrémental dans les fissures d’interface avec contact frottant et son application au critère couplé de la mécanique de la rupture finie]
A crack located in a straight and perfectly bonded interface between dissimilar isotropic linear elastic materials with a frictional contact zone adjacent to the crack tip is considered under plane strain conditions. Assuming the Coulomb friction law, the crack-tip stress singularity in such a crack is weaker than the classical square-root singularity. The main difficulty in predicting propagation of such an interface crack is that the Energy Release Rate (ERR) is zero, which is a direct consequence of this weak stress singularity at the crack tip. Therefore, the Griffith fracture criterion, which assumes infinitesimal crack advances, cannot be applied in this case. To overcome this problem a new approach to predict the propagation of an interface crack with a frictional contact zone at the crack tip, based on the Coupled stress and energy Criterion (CC) of Finite Fracture Mechanics (FFM), is proposed and analyzed. In contrast to previous approaches, the critical finite crack advance $\Delta a_\mathrm{c}$ is determined by the CC as a structural parameter given by the overall problem configuration. Two methods for calculating the incremental ERR $G_\mathrm{II} (\Delta a)$ are considered which differ in the treatment of the frictional energy dissipated along the crack advance $\Delta a$. Closed-form expressions for $G_\mathrm{II} (\Delta a)$ are derived for sufficiently large interface cracks when the most singular term of the asymptotic expansion of the elastic solution at the crack tip is dominant along the path of crack advance $\Delta a$ before the crack propagation occurs. In this case, closed-form expressions for the critical crack advance $\Delta a_\mathrm{c}$ and the critical stress intensity factor $K_\mathrm{IIc}$ are derived.
Une fissure située dans une interface droite et parfaitement adhérente entre deux matériaux isotropes linéaires élastiques dissemblables, avec une zone de contact frottant adjacente au bout de la fissure, est considérée en conditions de déformation plane. En supposant la loi de frottement de Coulomb, la singularité de contrainte à l’extrémité de la fissure est plus faible que la singularité classique en racine carrée. La principale difficulté pour prédire la propagation d’une telle fissure d’interface réside dans le fait que le taux de restitution d’énergie (TRE) est nul, ce qui découle directement de cette faible singularité de contrainte au bout de la fissure. Par conséquent, le critère de rupture de Griffith, qui suppose des avancées infinitésimales de la fissure, ne peut pas être appliqué dans ce cas. Pour surmonter ce problème, une nouvelle approche est proposée et analysée afin de prédire la propagation d’une fissure d’interface avec une zone de contact frottant à son extrémité, basée sur le critère couplé en contraintes et en énergie (CC) de la mécanique de la rupture finie (MRF). Contrairement aux approches précédentes, l’avance critique finie de la fissure $\Delta a_\mathrm{c}$ est déterminée par le critère CC comme un paramètre structurel donné par la configuration globale du problème. Deux méthodes pour calculer le TRE incrémental $G_\mathrm{II} (\Delta a)$ sont considérées, qui diffèrent dans le traitement de l’énergie de frottement dissipée au cours de l’avance de fissure $\Delta a$. Des expressions analytiques pour $G_\mathrm{II} (\Delta a)$ sont dérivées pour des fissures d’interface suffisamment longues, lorsque le terme le plus singulier du développement asymptotique de la solution élastique au voisinage de la fissure domine le long du trajet d’avance $\Delta a$, avant que la propagation ne se produise. Dans ce cas, des expressions analytiques pour l’avance critique $\Delta a_\mathrm{c}$ et le facteur d’intensité de contrainte critique $K_\mathrm{IIc}$ sont obtenues.
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Mots-clés : Fissure d’interface, modèle de contact de Comninou, loi de frottement de Coulomb, singularité faible, taux de restitution d’énergie, intégrale d’Irwin, VCCT
Enrique Graciani 1 ; Vladislav Mantič 1
CC-BY 4.0
@article{CRMECA_2025__353_G1_1365_0,
author = {Enrique Graciani and Vladislav Manti\v{c}},
title = {Evaluation of the incremental {ERR} in interface cracks with frictional contact and its application in the coupled criterion of finite fracture mechanics},
journal = {Comptes Rendus. M\'ecanique},
pages = {1365--1383},
year = {2025},
publisher = {Acad\'emie des sciences, Paris},
volume = {353},
doi = {10.5802/crmeca.319},
language = {en},
}
TY - JOUR AU - Enrique Graciani AU - Vladislav Mantič TI - Evaluation of the incremental ERR in interface cracks with frictional contact and its application in the coupled criterion of finite fracture mechanics JO - Comptes Rendus. Mécanique PY - 2025 SP - 1365 EP - 1383 VL - 353 PB - Académie des sciences, Paris DO - 10.5802/crmeca.319 LA - en ID - CRMECA_2025__353_G1_1365_0 ER -
%0 Journal Article %A Enrique Graciani %A Vladislav Mantič %T Evaluation of the incremental ERR in interface cracks with frictional contact and its application in the coupled criterion of finite fracture mechanics %J Comptes Rendus. Mécanique %D 2025 %P 1365-1383 %V 353 %I Académie des sciences, Paris %R 10.5802/crmeca.319 %G en %F CRMECA_2025__353_G1_1365_0
Enrique Graciani; Vladislav Mantič. Evaluation of the incremental ERR in interface cracks with frictional contact and its application in the coupled criterion of finite fracture mechanics. Comptes Rendus. Mécanique, Volume 353 (2025), pp. 1365-1383. doi: 10.5802/crmeca.319
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