Elastoplastic analysis of surface cracks in pressure vessels using slip-line theory

The paper considers the aspects of engineering application of SLF theory to long surface cracks in pressure vessels. Green's upper-bound SLF for a bend specimen with deep wedge-shaped notch of small flank angle is adopted to analyse the remaining ligament of the cracked section. The SLF involves only one unknown variable, i.e., the radius of a circular slip-line arc, which can be evaluated from the equilibrium condition across the ligament. The stress distribution across the ligament is easily computed by Hencky's theorem and the respective stress resultants produce the boundary conditions for the solution of the neighboring elastic material. The elastic solution readily yields the rotation of the crack edges, COA, and it in turn geometrically defines the applied CTOD. Comparison has proved their relation to the stress resultants identical with that following from the customary single plastic hinge model when Tresca's yield condition prevails and the tensile side plastic constraint factor of the hinge model is chosen as 1.7. The SLF approach is demonstrated for an internal circumferential surface crack subjected to thermal gradient and axial load representative of overpressurization and emergency cooling conditions of a pressure vessel. Analytical formulas relating COA and CTOD to applied loading are derived and CTOD-R curve based stable crack propagation is solved iteratively. Generic numerical results are presented for COA and CTOD under arbitrary loading combination. The risk of crack growth initiation appears to increase with the linear dimensions of the pressure vessel, but remains small for a chosen BWR application. For a long axial surface crack the approach agrees with a previous plastic hinge analysis by Ranta-Maunus et al. suggesting instability under certain combinations of thermal gradient and internal pressure. (orig./HP)