Comptes Rendus
no. 7-8
Surface mechanics: facts and numerical models
Experimental and numerical analysis of fretting crack formation based on 3D X-FEM frictional contact fatigue crack model
[Simulation expérimentale et numérique X-FEM de fissures tridimensionnelles de fatigue avec contact et frottement. Application au fretting]
Emilien Pierres1 ; Marie-Christine Baietto1  ; Anthony Gravouil1
1 INSA-Lyon, LaMCoS, CNRS UMR5259, bâtiment Jean-dʼAlembert, 18, 20, rue des Sciences, 69621 Villeurbanne cedex, France
Comptes Rendus. Mécanique, Volume 339 (2011) no. 7-8, pp. 532-551.

De nos jours, la méthode des éléments finis étendus couplée aux techniques de fonctions de niveau (level-set) a été appliquée avec succès à un grand nombre dʼapplications et en particulier à la simulation de la propagation de fissures de fatigue tridimensionnelles. En effet, la géométrie de la fissure ne doit pas être maillée explicitement. La plupart des difficultés liées à la génération de maillages complexes autour de la fissure et les opérations de re-maillage et de projection de champs lors de la propagation sont donc évitées. Un modèle 3D à deux échelles, celle de la structure et celle de de la fissure, développé dans le cadre X-FEM est présenté dans ce papier. Il permet lʼutilisation dʼune discrétisation raffinée de lʼinterface de la fissure, adaptée à lʼéchelle des non linéarités de contact avec frottement et indépendante du maillage éléments finis sous-jacent. Une formulation faible stabilisée à trois champs est également proposée afin dʼéviter les oscillations possibles dans la solution locale liées à la condition LBB en cas de glissement tangentiel. Deux exemples numériques simples en trois dimensions sont présentés. Ils visent à illustrer les capacités et le niveau élevé de précision du modèle X-FEM proposé. Enfin, le modèle est intégré dans une démarche globale couplant expérimenation et simulation numérique pour prédire la durée de vie de composants en fatigue. Des essais de fretting menés pour des conditions de chargement induisant lʼinitiation et la propagation de fissures sont simulés numériquement. Les conditions de chargement et les faciès de fissuration 3D sont utilisés comme données dʼentrée dans le modèle numérique X-FEM. Les conditions de contact et frottement à lʼinterafce des fissures sont déterminées au cours dʼun cycle de fretting et les facteurs dʼintensité de contraintes en mode I, II et III sont calculés. Cette simulation démontre la capacité de modèle à faire face aux défis posés par les problèmes réels complexes et la possibilité de réaliser une prédiction en fatigue tribologique des composants de structures.

Nowadays, numerical simulation of 3D fatigue crack growth is easily handled using the eXtended Finite Element Method coupled with level set techniques. The finite element mesh does not need to conform to the crack geometry. Most difficulties associated to complex mesh generation around the crack and the re-meshing steps during the possible propagation are hence avoided. A 3D two-scale frictional contact fatigue crack model developed within the X-FEM framework is presented in this article. It allows the use of a refined discretization of the crack interface independent from the underlying finite element mesh and adapted to the frictional contact crack scale. A stabilized three-field weak formulation is also proposed to avoid possible oscillations in the local solution linked to the LBB condition when tangential slip is occurring. Two basic three-dimensional numerical examples are presented. They aim at illustrating the capacities and the high level of accuracy of the proposed X-FEM model. Stress intensity factors are computed along the crack front. Finally an experimental 3D ball/plate fretting fatigue test with running conditions inducing crack nucleation and propagation is modeled. 3D crack shapes defined from actual experimental ones and fretting loading cycle are considered. This latter numerical simulation demonstrates the model ability to deal with challenging actual complex problems and the possibility to achieve tribological fatigue prediction at a design stage based on the fatigue crack modeling.

Publié le :
DOI : 10.1016/j.crme.2011.05.011
Keywords: X-FEM, Fatigue, Fretting, Frictional contact
Mot clés : X-FEM, Fatigue, Fretting, Contact frottement
Emilien Pierres 1 ; Marie-Christine Baietto 1 ; Anthony Gravouil 1

1 INSA-Lyon, LaMCoS, CNRS UMR5259, bâtiment Jean-dʼAlembert, 18, 20, rue des Sciences, 69621 Villeurbanne cedex, France 
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Emilien Pierres; Marie-Christine Baietto; Anthony Gravouil. Experimental and numerical analysis of fretting crack formation based on 3D X-FEM frictional contact fatigue crack model. Comptes Rendus. Mécanique, Volume 339 (2011) no. 7-8, pp. 532-551. doi : 10.1016/j.crme.2011.05.011. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2011.05.011/

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