Fracture Mechanics Analysis of a Pressure Vessel with a Semi-Elliptical Surface Crack Using Elastic-Plastic Finite Element Calculations

Elastic-plastic three-dimensional finite element (FE) calculations were performed on a semi-elliptical inner surface crack of a pressure vessel using the FE program ADINA. The pressure was increased until the ligament yielded entirely. The variations of the stress intensity factor K of the J-integral and of the crack tip opening displacement (CTOD) along the crack front are presented and discussed.

The stress intensity factors K₁ calculated by extrapolation from stresses and displacements and by the energy release rate agree well within a tolerance of about 10%. As in linear elasticity, the plastic part of the J-integral can also be described by a power law of the applied load. The normal stresses in the crack opening direction in the ligament meet a power function (J/r) as the two-dimensional HRR (Hutchinson-Rice-Rosengren) field equations postulate. The exponent is not a material constant, however, but varies along the crack front. Therefore the distribution of the crack opening stress along the crack front at a fixed distance from the crack front cannot be characterized by the J-distribution along the crack front. Neither does the singular HRR field describe the redistribution of stresses due to crack tip blunting. For the considered pressure vessel the J-integral in the elastic-plastic range can be calculated from an elastic solution if small-scale yielding corrections for plane-stress conditions are performed.