Basic singular thermoelastic solutions for a crack

Abstract

Basic, singular solutions of plane thermoelasticity for an infinite medium with a crack are studied and furnished in this article. By these solutions, thermal stresses and thermal stress intensity factors in the cracked medium, under the action of a point thermal inclusion or a point heat source, can simply and exactly be evaluated. These solutions are obtained by the use of the complex function method and some quadrature techniques. In the case of a heat source, exact expressions for the temperature distribution are also derived, and some dislocation solutions are employed to obtain the final expressions for thermal stresses and thermal stress intensity factors. A number of definite integrals, with logarithmic functions as main components in their integrands, have been treated rigorously to obtain exact and closed form formulas of evaluation. This kind of definite integral is characteristic in the thermoelastic analysis of cracked bodies. Numerical values for stress intensity factors and temperature distributions are worked out and presented in tabular or graphic form.