Stress intensity factor for a longitudinal semi-elliptical crack in a thick-walled cylinder under hyperbolic thermal loading

In this paper, the stress intensity factor for a longitudinal semi-elliptical crack in the internal surface of a thick-walled cylinder is derived analytically and numerically. The cylinder is assumed enough long and subjected to the axisymmetric cooling thermal shock on the internal surface. The uncoupled thermoelasticity governing equations for an uncracked cylinder are solved analytically. The non-dimensional hyperbolic heat equation is solved using separation of variables method. The weight function method is implemented to obtain the stress intensity factor for the deepest and surface points of the crack. Results show the different behavior of the crack under hyperbolic thermal shock. At a short time after the thermal shock, the stress intensity factor at the deepest point –especially for shallow cracks- for hyperbolic model is significantly greater than Fourier one. The stress intensity factor at the deepest point is greater as the crack is narrower for both models. Unlike mechanical loading, the greatest stress intensity factor may occur at the surface point. According to the results, assumption of adequate heat conduction model for structure design under transient thermal loading is critical.