Closed form stress intensity factors for a semi-elliptical crack in a thick-walled cylinder under thermal stress

In this paper the steady state thermoelasticity problem in a thick-walled cylinder containing an internal axial semi-elliptical crack is solved analytically. Thermal and mechanical boundary conditions are prescribed on the inner and outer surfaces of the cylinder. The steady state solution of the thermoelasticity problem is derived analytically and then, the stress intensity factors are extracted for the semi-elliptical crack using the weight function method. The results show to be in accordance with that cited in the literature in the special cases. It is shown that the critical point of the crack front displaces from the deepest to the surface points at certain geometries for an internally pressurized cylinder, which can indicate the point of starting the crack growth. However, in an internally heated pressurized cylinder, the surface points are always in closure mode and the deepest point is always the critical point in the geometries in which it falls in the opening mode.