Abstract
On the basis of the steady-state two-dimensional theory of thermoelasticity, the influence of an insulated circular hole on the thermal stress singularities at the tips of a line crack, whose surface is cooled, is discussed. The crack is located arbitrarily in an infinite matrix. The method of continuous distribution of dislocations is extended by newly introducing a continuous distribution of quasi-Volterra dislocations corresponding to line heat sources. Replacing the crack by the continuous distributions of quasi-Volterra dislocations and edge dislocations, we obtain a set of simultaneous singular integral equations for dislocation density functions. By means of this method, the thermal stress singularities at the crack tips are estimated exactly and the stress intensity factors can be readily evaluated. The variations of the stress intensity factors and the initial direction of crack extension with the distance of the crack from the insulated circular hole and the angle of inclination of the crack are shown graphically.
Résumé
Sur la base d'une théorie bidimensionnelle en état statique de la thermoélasticité, on discute l'influence d'un trou circulaire sur les singularités des contraintes thermiques aux extrémités d'une fissure linéaire dont la surface est refroidie. La fissure est localisée arbitrairement dans une matrice infinie. La méthode de distribution continue des dislocations est généralisée par l'introduction d'une distribution continue de dislocations du type quasi Volterra correspondant à des sources de chaleur en ligne. En remplaçant la fissure par des distributions continues de dislocations du type quasi Volterra et par des dislocations-coin, on obtient une série d'intégrales singulières simultanées correspondant aux fonctions de densité de dislocations. Par cette méthode, les singularités de contraintes thermiques aux extrémités d'une fissure sont estimées de façon exacte et les facteurs d'intensité de contraintes peuvent être évaluées aisément. Les variations des facteurs d'intensité des contraintes ainsi que la direction initiale de l'extension de la fissure suivant la distance de la fissure à partir d'un trou circulaire isolé et l'angle d'inclinaison de la fissure sont exprimés graphiquement.
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Sekine, H. Influence of an insulated circular hole on thermal stress singularities at tips of a crack. Int J Fract 13, 133–149 (1977). https://doi.org/10.1007/BF00042556
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DOI: https://doi.org/10.1007/BF00042556