Determination of Steady State Thermal Stress Intensity Factors for Semi-Elliptical Circumferential Cracks in Cylinders

In this paper, the closed-form stress intensity factors are calculated at the deepest point of a circumferential semi-elliptical crack located at the inner surface of a cylinder. The cylinder is subjected to pressure (internal and external) and the inner surface of the cylinder is subjected to convection cooling. To solve the problem, initially, a weight function is derived for the deepest point of the circumferential semi-elliptical crack using two reference loads. Then, the steady state solution of the thermoelasticity problem is derived and, finally, the stress intensity factors are extracted using the weight function method. For some special cases of loading, the results of the present theory are compared with available solutions in the literature indicating an acceptable agreement. Moreover, the effects of crack relative depth and aspect ratio and heat transfer type on the thermal stress intensity factors are studied. The extracted results demonstrate that for some cases of loading and crack geometry, shallow cracks are more critical than deep ones and the solution of conduction heat transfer is more conservative than the forced convection one.