A simple model of thermal crack pattern formation using the coupled criterion

Dominique Leguillon

doi:10.1016/j.crme.2013.04.002

A simple model of thermal crack pattern formation using the coupled criterion
[Un modèle simple de faïençage thermique utilisant le critère couplé]

Dominique Leguillon ¹

¹ Institut Jean-Le-Rond-dʼAlembert, CNRS UMR 7190, université Pierre-et-Marie-Curie, 4 place Jussieu, 75252 Paris cedex 05, France

Comptes Rendus. Mécanique, Volume 341 (2013) no. 6, pp. 538-546.

Résumé
Abstract

Différents mécanismes (refroidissement, séchage, vieillissement) aboutissent à la formation de réseaux de fissures, appelés faïençage, à la surface de certains matériaux, quʼil est très difficile de décrire dans le détail. Nous proposons ici un modèle qui repose sur lʼutilisation du critère couplé faisant appel à deux conditions nécessaires pour la nucléation de fissures : une condition en énergie et une condition en contrainte. Ce modèle est appliqué à un exemple simple : une plaque fixée sur un support rigide et refroidie sur sa face supérieure. Au cours dʼun refroidissement lent, il met en évidence la possibilité de formation dʼun premier réseau de fissures, puis la subdivision de celui-ci. Il montre également que, lors dʼun refroidissement rapide (trempe), plus la chute en température est forte, plus le réseau de fissures est serré.

Different mechanisms (cooling, drying, and ageing) lead to the formation of crack patterns on the surface of some materials that are very difficult to describe in detail. We propose a model based on the coupled criterion using two necessary conditions for the nucleation of cracks: an energy condition and a stress condition. This model is applied to a simple example: a plate fixed to a rigid substrate and cooled down on its top face. During slow cooling, it highlights the ability of forming a first lattice of cracks and the subdivision thereof. It also shows that, in a rapid cooling (quenching), the higher the temperature drop, the tighter the cracks network.

Reçu le : 2013-02-20
Accepté le : 2013-04-08
Publié le : 2013-04-30

DOI : 10.1016/j.crme.2013.04.002

Keywords: Solid mechanics, Fracture mechanics, Thermal cracks
Mots-clés : Mécanique des solides, Mécanique de la rupture, Fissuration thermique

Affiliations des auteurs :

Dominique Leguillon ¹

¹ Institut Jean-Le-Rond-dʼAlembert, CNRS UMR 7190, université Pierre-et-Marie-Curie, 4 place Jussieu, 75252 Paris cedex 05, France

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     title = {A simple model of thermal crack pattern formation using the coupled criterion},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {538--546},
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     year = {2013},
     doi = {10.1016/j.crme.2013.04.002},
     language = {en},
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Dominique Leguillon. A simple model of thermal crack pattern formation using the coupled criterion. Comptes Rendus. Mécanique, Volume 341 (2013) no. 6, pp. 538-546. doi : 10.1016/j.crme.2013.04.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2013.04.002/

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