Thermal problem of curvilinear cracks in bonded dissimilar materials with a point heat source

Abstract

Boundary value problems for a circular-arc crack embedded in dissimilar materials under the application of a point heat source are formulated and solved in closed form. Based on the Hubert problem formulation and a special technique of analytic continuation, exact solutions of the temperature and temperature gradient are obtained in an explicit form. It is found that the temperature gradients or heat fluxes near the crack tips of a curved crack possess the characteristic inverse square-root singularity in terms of the radial distance away from the crack tip which is the same as those obtained for a straight crack between dissimilar materials. Due to this singular behavior, the heat flux intensity factor is introduced to measure the thermal energy intensification cumulated in the vicinity of the crack tip. Numerical results for the temperature and heat flux intensity factor are provided in graphic form. It is shown that the thermal system having a smaller crack length would make the heat flux intensity factor lower. Consequently, the thermal energy intensification is diminished.