Abstract
A model is constructed to analyze more carefully the energy release rate for Williams' blister test. The model, which consists of an interface crack between two elastic layers, is loaded by uniform internal pressure. The singular integral equations for the dislocation densities are derived and solved using numerical quadrature and the energy release rate is calculated directly from the dislocation densities. Both the two-dimensional and axisymmetric penny-shaped crack problems are considered, and it is noted that there are significant differences between these two cases. It is found that in some cases crack propagation will not be catastrophic.
Résumé
On établit un modèle mathématique en vue d'analyser de manière plus soignée le taux de relaxation d'énergie dans le test de coupelle proposé par Williams. Le modèle représente une fissure d'interface entre deux couches clastiques, et est soumis à une pression interne uniforme. On déduit les intégrales singulières caractérisant les densités de dislocation, et on les résoud par quadrature numérique, pour ensuite calculer les taux de relaxation d'énergie directement à partir de ces densités de dislocation. Sont à la fois considérés les problèmes de fissures circulaires bidimensionnelle, et axisymétrique. On observe des différences significatives entre ces deux variantes. On trouve également que, dans certains cas, la propagation d'une fissure peut ne pas être brutale.
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Farris, T.N., Keer, L.M. Williams' blister test analyzed as an interface crack problem. Int J Fract 27, 91–103 (1985). https://doi.org/10.1007/BF00040388
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DOI: https://doi.org/10.1007/BF00040388