Criteria for crack extension in cylindrical pressure vessels

This paper describes three closely related criteria for the extension of axial through-cracks in cylindrical pressure vessels: (1) a fracture-toughness criterion mainly for low- and medium-tough materials, (2) a plastic flow stress criterion for short cracks in tough materials, and (3) a modification of (1) for relatively thin-walled containers. The development couples the Folias theoretical treatment of a pressurized cylindrical shell with the fracture-toughness approach and a new plasticity correction. This correction, which is consistent with crack-tip displacement measurements, shows that the plastic-flow strength governs the extension of short cracks in vessels fabricated from tough materials. This is to be contrasted with the behavior of longer cracks or more brittle materials which depends on the fracture toughness. The formulation is extended to vessels with large radius to wall-thickness ratios, e.g., R/t > 50 by way of a simple empirical modification. In this way, estimates of critical hoop stress-crack length combinations can be derived from the vessel radius to wall-thickness ratio, and either the ordinary yield strength, the yield and ultimate strengths, or Kc without prior full-scale test experience. Such estimates are shown to be in accord with the large body of published data encompassing ductile-steel, brittle-steel, as well as aluminum- and titanium-alloy vessels.