A simple model for stability of a long axial surface crack in a thin walled cylinder

Growth in the thickness direction of a long axial surface crack at the inner surface of a thin walled cylinder has been analyzed for loads generated by internal pressure and a thermal gradient through the wall thickness. Plane-strain deformations have been considered. It has been assumed that the cracked cross-section is fully plastic, but that the plastic zone width in the circumferential direction is very small. The cracked cross-section transmits a normal force and a bending moment, which have been considered as external forces on an equivalent cut ring element, to compute the deformation of the cracked cross-aection. An analytical expression has been derived for the crack-opening-displacement, as a function of the loads and the crack depth. Stable and unstable crack growth have been investigated on the basis of a critical crack-opening-displacement and a smoothly rising crack-opening R-curve. The condition for unstable crack growth depends primarily on the magnitude of the internal pressure. A thermal gradient by itself is less likely to cause unstable crack propagation.