Thermal stresses in a solid containing parallel circular cracks

This paper presents an analysis of the steady-state thermal stresses and displacements in an infinite elastic medium containing two or more parallel coaxial circular cracks. A “perturbation” technique is employed to reduce the problem of finding the temperature and the induced stresses to integral equations of Fredholm type which may be solved by numerical means or iterations. Two types of prescribed thermal conditions are considered. The first is concerned with a uniform flow of heat disturbed by insulated cracks and the second deals with stress-free cracks whose surfaces are exposed to identical amounts of heat. The details of the analysis are illustrated by considering the case of two cracks symmetrically located about the mid plane of the solid. When the cracks are of equal radii, iterative solutions of the governing integral equations are derived and used to determine expressions for the stress-intensity factors (opening and edge-sliding modes), displacements of crack surfaces and other quantities of physical interest which are valid for widely spaced cracks.