[Un modèle simple de faïençage thermique utilisant le critère couplé]
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.
Accepté le :
Publié le :
Mots-clés : Mécanique des solides, Mécanique de la rupture, Fissuration thermique
Dominique Leguillon 1
@article{CRMECA_2013__341_6_538_0,
author = {Dominique Leguillon},
title = {A simple model of thermal crack pattern formation using the coupled criterion},
journal = {Comptes Rendus. M\'ecanique},
pages = {538--546},
publisher = {Elsevier},
volume = {341},
number = {6},
year = {2013},
doi = {10.1016/j.crme.2013.04.002},
language = {en},
}
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/
[1] Crack patterns in ceramic plates after quenching, J. Am. Ceram. Soc., Volume 93 (2010), pp. 3006-3008
[2] A fracture mechanics approach to the effects of UV-degradation on polypropylene, J. Mater. Sci., Volume 23 (1988), pp. 1580-1590
[3] Shrinkage star-shaped cracks: Explaining the transition from 90 degrees to 120 degrees, Europhys. Lett., Volume 89 (2010) | DOI
[4] Craquelures dans les couches picturales des peintures dʼart, Reflets de la Physique, Volume 3 (2007), pp. 5-9
[5] Scaling behaviour of thermal shock crack patterns and tunnelling cracks driven by cooling or drying, J. Mech. Phys. Solids, Volume 58 (2010), pp. 1411-1421
[6] A study of the mechanism of formation and numerical simulations of crack patterns in ceramics subjected to thermal shock, Acta Mater., Volume 60 (2012), pp. 4540-4550
[7] A variational approach to thermal cracks, Beijing, China, August 19–24 (2012)
[8] Crack patterns obtained by unidirectional drying of a colloidal suspension in a capillary tube: experiments and numerical simulations using a two–dimensional variational approach, Int. J. Fract. (2013) (submitted for publication) | DOI
[9] Revisiting brittle fracture as an energy minimization problem, J. Mech. Phys. Solids, Volume 46 (1998), pp. 1319-1342
[10] Strength or toughness? A criterion for crack onset at a notch, Eur. J. Mech. A, Solids, Volume 21 (2002), pp. 61-72
[11] Multiple failures in or around a stiff inclusion embedded in a soft matrix under a compressive loading, Eur. J. Mech. A, Solids, Volume 28 (2009), pp. 668-679
[12] The Stress Analysis of Cracks Handbook, ASME Press, New York, 2000
[13] Monolithic catalyst preparation for CNG applications. On the influence of the starting material on the washcoat quality, Cracow, Poland, 8–10 Sept. (2010)
[14] The use of the point load test for the rapid estimation of mode I fracture toughness, Int. J. Rock Mech. Min. Sci., Volume 36 (1999), pp. 257-263
[15] The strengthening effect caused by an elastic contrast – Part I: The bimaterial case, Int. J. Fract., Volume 179 (2013), pp. 157-167
[16] From craquelures to spiral crack patterns: influence of layer thickness on the crack patterns induced by desiccation, Soft Matter (2011) | DOI
[17] Conduction of heat in solids, Oxford University Press, Oxford, Great Britain, 1959
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