Abstract
Certain problems in which a cooled rigid punch indents an elastic half-space have no steady state solution. A simple model is described in which it is shown that this paradox is avoided by the assumption of a thermal resistance varying inversely with contact pressure. A limiting case of this system retains linearity and introduces a state of “imperfect” contact in which contact pressure is negligible but there is significant thermal contact resistance.
This approach is generalized to permit the formulation of three dimensional contact problems and one such problem is solved for an axisymmetric geometry. Particular results are given for the identation of a half-space by a cooled rigid sphere.
Résumé
Les problèmes de contact thermoélastiques pour un demi-espace entaillé par un poinçon rigide refroidi n'ont pas parfois de solution établie. On décrit un modèle simple demontrant qu'on évite ce paradoxe en supposant une résistance thermique varient en raison inverse du pression de contact. On retiens linearité avec un cas limitatif de ce système en introduisant une condition de contact “imparfait” ou le pression de contact est négligeable mais il y a de la résistance thermique de contact significative.
On généralise cette méthode pour permetter la formulation des problèmes de contact thermique dans trois dimensions et un problème de ce type est résolu en cas de symetrie axiale. On donne des resultats particulières pour le demi-espace entaillé par une sphère rigide refroidie.
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Barber, J.R. Contact problems involving a cooled punch. J Elasticity 8, 409–423 (1978). https://doi.org/10.1007/BF00049190
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DOI: https://doi.org/10.1007/BF00049190