La génération de fissures hertziennes de forme conique par des contacts mécaniques apparaît souvent comme un cas dʼécole pour étudier la rupture des matériaux fragiles. Cependant, la simulation de ce phénomène physique nʼest pas triviale, car la plupart des modèles analytiques prédisent des angles de fissuration différents de ceux observés expérimentalement. Cette différence a pu être expliquée par des modélisations éléments finis reposant sur des algorithmes de remaillage très spécifiques, engendrant malheureusement un certain nombre de limitations pratiques. Dans cet article, nous proposons dʼutiliser la méthode des éléments finis étendus pour représenter ce phénomène. Lʼangle de propagation obtenu est en très bon accord avec les résultats de la littérature, et la différence observée avec les modèles analytiques peut sʼexpliquer par une modification du champ de contraintes au cours de la propagation. Nous montrons aussi que les résultats obtenus sont robustes, cʼest-à-dire quʼils ne dépendent pas ou très peu de paramètres numériques tels que la taille des éléments ou la longueur dʼextension de fissure. En conclusion, la technique X-FEM apparaît comme très efficace et suffisamment précise pour modéliser la rupture en cône de Hertz.
Hertzian cone cracks are nowadays a scholarly case making it possible to understand fracture of materials. However, the simulation of this physical phenomenon is not trivial and most theoretical models lead to the prediction of cone crack angles different from those observed experimentally. In the past, finite-element models have been developed based on a re-meshing procedure to explain this difference successfully, but with some limitations due the algorithms used. In this paper, we propose to use the X-FEM method to model Hertzian cone crack propagation with a 2D axisymmetric approach. The effect of various numerical parameters, such as mesh size or time step, is investigated and it is shown that they do not have a great impact on the crack angle result. The analysis of the stress field induced leads us to understand the difference in terms of cone crack angle based on the pre-existing stress field and those experimentally observed. As a conclusion, X-FEM is very efficient to reproduce faithfully several characteristics of the Hertzian cone crack phenomenon in a very simple manner.
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Mots clés : Fissuration en cône, Indentation, Matériaux fragiles, X-FEM, Verres silicatés, Contact mécanique
David Y. Tumbajoy-Spinel 1 ; Éric Feulvarch 2 ; Jean-Michel Bergheau 2 ; Guillaume Kermouche 1
@article{CRMECA_2013__341_9-10_715_0,
author = {David Y. Tumbajoy-Spinel and \'Eric Feulvarch and Jean-Michel Bergheau and Guillaume Kermouche},
title = {2D axisymmetric {X-FEM} modeling of the {Hertzian} cone crack system},
journal = {Comptes Rendus. M\'ecanique},
pages = {715--725},
publisher = {Elsevier},
volume = {341},
number = {9-10},
year = {2013},
doi = {10.1016/j.crme.2013.09.004},
language = {en},
}
TY - JOUR AU - David Y. Tumbajoy-Spinel AU - Éric Feulvarch AU - Jean-Michel Bergheau AU - Guillaume Kermouche TI - 2D axisymmetric X-FEM modeling of the Hertzian cone crack system JO - Comptes Rendus. Mécanique PY - 2013 SP - 715 EP - 725 VL - 341 IS - 9-10 PB - Elsevier DO - 10.1016/j.crme.2013.09.004 LA - en ID - CRMECA_2013__341_9-10_715_0 ER -
%0 Journal Article %A David Y. Tumbajoy-Spinel %A Éric Feulvarch %A Jean-Michel Bergheau %A Guillaume Kermouche %T 2D axisymmetric X-FEM modeling of the Hertzian cone crack system %J Comptes Rendus. Mécanique %D 2013 %P 715-725 %V 341 %N 9-10 %I Elsevier %R 10.1016/j.crme.2013.09.004 %G en %F CRMECA_2013__341_9-10_715_0
David Y. Tumbajoy-Spinel; Éric Feulvarch; Jean-Michel Bergheau; Guillaume Kermouche. 2D axisymmetric X-FEM modeling of the Hertzian cone crack system. Comptes Rendus. Mécanique, Volume 341 (2013) no. 9-10, pp. 715-725. doi : 10.1016/j.crme.2013.09.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2013.09.004/
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