Crack front stability for a tunnel-crack propagating along its plane in mode $ \mathbf{2+3}$

Véronique Lazarus; Jean-Baptiste Leblond

doi:10.1016/S1631-0721(02)01481-X

Crack front stability for a tunnel-crack propagating along its plane in mode

2 + 3

[Stabilité du front d'une fissure en forme de fente infinie se propageant dans son plan en mode

2 + 3

]

Véronique Lazarus ¹ ; Jean-Baptiste Leblond ¹

¹ Laboratoire de modélisation en mécanique, Université Pierre et Marie Curie, 8, rue du Capitaine Scott, 75015 Paris, France

Comptes Rendus. Mécanique, Volume 330 (2002) no. 6, pp. 437-443.

Résumé
Abstract

Les auteurs ont récemment étudié la stabilité de la forme rectiligne du front d'une fissure en forme de fente infinie se propageant dans son plan en conditions de mode mixte 2+3. Les extrema de la perturbation du front, supposée sinusoı̈dale, et du taux de restitution d'énergie étaient supposés coı̈ncider, ce qui imposait une certaine différence de phase entre les perturbations des deux parties du front. Le but de ce travail est de lever cette contrainte. Le système dépend du temps si bien que la question de la stabilité soulève des problèmes de définition. On montre notamment que pour une définition appropriée de la stabilité, certaines perturbations se développent de manière « instable » si leur longueur d'onde est supérieure à une valeur critique dépendant de la largeur moyenne de la fissure, du coefficient de Poisson et du rapport de mixité.

The authors recently studied stability of the straight configuration of the front of a tunnel-crack propagating along its plane in mixed mode 2+3 conditions. Coincidence of the extrema of the supposedly sinusoidal crack front perturbation and the energy release rate was assumed, which imposed a certain phase difference between the perturbations of the two parts of the front. The aim of this paper is to relax this constraint. The system is time-dependent so that the stability issue is prone to problems of definition. It is notably shown that for some appropriate definition of stability, certain perturbations develop “unstably” if their wavelength is larger than some critical value depending on mean crack width, Poisson's ratio and mode mixity.

Reçu le : 2002-02-14
Accepté le : 2002-04-23
Publié le : 2002-01-01

DOI : 10.1016/S1631-0721(02)01481-X

Keywords: configurational stability, crack front, tunnel-crack, coplanar propagation, mixed mode
Mots-clés : stabilité configurationnelle, front de fissure, fente infinie, propagation coplanaire, mode mixte

Affiliations des auteurs :

Véronique Lazarus ¹ ; Jean-Baptiste Leblond ¹

¹ Laboratoire de modélisation en mécanique, Université Pierre et Marie Curie, 8, rue du Capitaine Scott, 75015 Paris, France

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     author = {V\'eronique Lazarus and Jean-Baptiste Leblond},
     title = {Crack front stability for a tunnel-crack propagating along its plane in mode $ \mathbf{2+3}$},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {437--443},
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     doi = {10.1016/S1631-0721(02)01481-X},
     language = {en},
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Véronique Lazarus; Jean-Baptiste Leblond. Crack front stability for a tunnel-crack propagating along its plane in mode $ \mathbf{2+3}$. Comptes Rendus. Mécanique, Volume 330 (2002) no. 6, pp. 437-443. doi : 10.1016/S1631-0721(02)01481-X. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(02)01481-X/

Bibliographie
Cité par

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