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.