THERMOELASTIC PROBLEM OF CURVILINEAR CRACK WITH A POINT HEAT-SOURCE

Boundary value problems for a circular-arc crack embedded in an infinite medium due to a point heat source are formulated and solved in closed form. Based on the Hilbert problem formulation and a special technique of contour integration, exact solutions of a semicircular crack are obtained in an explicit form. It is found that the thermal stresses or temperature gradient near the tips of a curved crack always possess the characteristic inverse square-root singularity in terms of the radial distance away from the crack tip under the application of a heat source. The simultaneous existence of mode-I and mode-II stress intensity factors are shown in this article to be dependent on the strength of a heat source, heat conductivity, as well as thermal and elastic isotropy. The nonnegative mode-I stress intensity factor is found to be present in this article for the application of the heat sink, which validates the fully open crack assumption.