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**Published:** Jan 1985

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**Source: **STP868-EB

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 *K*^{1} 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.

**Keywords:**

elastic-plastic fracture mechanics, finite element analysis, stress intensity factor, crack tip opening displacement, J, -integral, semi-elliptical surface crack, pressure vessel, small-scale yielding

**Author Information:**

Aurich, D *Bundesanstalt für Materialprüfung (BAM), Berlin,*

Brocks, W *Bundesanstalt für Materialprüfung (BAM), Berlin,*

Noack, H-D *Bundesanstalt für Materialprüfung (BAM), Berlin,*

Veith, H *Bundesanstalt für Materialprüfung (BAM), Berlin,*

**Committee/Subcommittee:** E08.08

**DOI:** 10.1520/STP34277S