Comptes Rendus
Fatigue growth of embedded elliptical cracks using Paris-type law in a hybrid weight function approach
Comptes Rendus. Mécanique, Volume 336 (2008) no. 4, pp. 390-397.

A hybrid weight function method (HWFM), improving the calculation of the stress intensity factor (SIF) in mode I, has recently been proposed and validated in the static case [B.K. Hachi, S. Rechak, M. Haboussi, M. Taghite, Modélisation des fissures elliptiques internes par hybridation de fonctions de poids, C. R. Mecanique 334 (2006) 83–90]. In the present Note, the hybridization approach is presented for the fatigue crack growth prediction of embedded elliptical crack in infinite bodies. Hence, Paris's law of crack propagation is incorporated into the developed hybridization-based computer code, along with two degrees of freedom technique for managing the crack evolution and the cracked structure fatigue life. Simulations of the evolution of elliptical cracks (in infinite bodies) of different configurations (ellipse axes ratio, maximum crack advance) corresponding to fatigue and brittle fracture have been conducted. Comparisons with other numerical methods such as the classical weight function method (WFM) or the extended finite element methods (X-FEM) show the pertinence of the HWFM in the treatment of an aspect of fatigue cracking problems.

Une méthode, basée sur l'hybridation des fonctions de poids, a récemment été proposée pour améliorer le calcul du facteur d'intensité de contrainte (FIC) en mode I sous chargement statique, [B.K. Hachi, S. Rechak, M. Haboussi, M. Taghite, Modélisation des fissures elliptiques internes par hybridation de fonctions de poids, C. R. Mecanique 334 (2006) 83–90]. On se propose dans cette présente Note, d'appliquer l'approche d'hybridation pour décrire la propagation de fissures elliptiques internes dans un milieu infini. La loi de propagation de Paris est alors incorporée dans le code de calcul développé sur la base de l'hybridation, dans le cadre d'une approche à deux degrés de liberté pour gérer l'évolution de la forme de la fissure. Pour valider cette méthode, des simulations de l'évolution des fissures elliptiques internes de différentes configurations (rapport des axes, avance maximum de la fissure) correspondant à la rupture par fatigue ou fragile ont été réalisées. Elles ont permis de montrer, après comparaisons avec d'autres méthodes numériques telles que la méthode des fonctions de poids ou la méthode des éléments finis étendue, la pertinence de l'approche d'hybridation dans le traitement d'un aspect de la fissuration en fatigue.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2008.01.008
Keywords: Fatigue, Fatigue elliptical crack growth, Hybridization, Weight function, Paris law, Two degrees of freedom method
Mot clés : Fatigue, Propagation de fissure elliptique par fatigue, Hybridation, Fonction de poids, Loi de Paris, Méthode à de deux degrés de liberté

Brahim El Khalil Hachi 1; Said Rechak 2; Mohamed Haboussi 3; M'barek Taghite 3; Gérard Maurice 3

1 Departement of Electromechanical Engineering, C.U. Djelfa, BP 3117 Ain-Cheih, 17000, Djelfa, Algeria
2 LGMD, Departement of Mechanical Engineering, E.N.P., BP 182 Harrach 16200, Algiers, Algeria
3 LEMTA, Nancy-University, CNRS, 2, avenue de la Forêt de Haye, BP 160, 54504 Vandœuvre cedex, France
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Brahim El Khalil Hachi; Said Rechak; Mohamed Haboussi; M'barek Taghite; Gérard Maurice. Fatigue growth of embedded elliptical cracks using Paris-type law in a hybrid weight function approach. Comptes Rendus. Mécanique, Volume 336 (2008) no. 4, pp. 390-397. doi : 10.1016/j.crme.2008.01.008. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2008.01.008/

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