Abstract
The plane, bending and antiplane strain elastostatic problems for two bonded half planes containing an arbitrarily oriented semi-infinite crack meeting the interface, are examined. A simple analogy between the interfacial continuity conditions for the plane and bending problems is derived and its implications are discussed. Using the eigenfunction-expansion method the crack tip stress singularities for various crack orientations and material combinations are compared for the three problems. It is shown that, under certain conditions, singularities are no longer present in the stress field. In the case of the antiplane strain problem subsequent paths of crack propagation are predicted.
Résumé
On examine des problèmes élasto-statiques en déformation plane, de flexion, et antiplanaire rencontrés dans deux demi-plans solidaires comportant, dans leur interface, une fissure semi-infinie orientée arbitrairement. On tire une analogie simple entre les conditions de continuité et interfaciales qui se présentent dans le cas des problèmes plans et flexionnels; ses implications sont discutées. En utilisant une méthode d'expansion d'une eigenfonction, on peut comparer les singularités de contraintes aux extrémités de la fissure, pour diverses orientations de la fissure et de combinaisons de matériaux différents. On montre que, sous certaines conditions, le champ de contraintes peut ne plus présenter de singularités. On peut par ailleurs prédire les chemins de la propagation d'une fissure dans le cas d'une déformation antiplanaire.
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Fenner, D.N. Stress singularities in composite materials with an arbitrarily oriented crack meeting an interface. Int J Fract 12, 705–721 (1976). https://doi.org/10.1007/BF00037917
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DOI: https://doi.org/10.1007/BF00037917