Critical circumferential through-wall cracks according to the unloading of the cracked section under displacement-controlled bending load

The evaluation of critical circumferential through-wall crack lengths in piping is usually performed by the flow stress concept, plastic limit load method or GE-EPRI procedures. Most of these methods treat the secondary stresses, especially those caused by bending moments resulting from restrained thermal expansion, as force-controlled loads. In reality, there is a movement of the piping into the direction of the prescribed displacement and, therefore, a relaxation of the cracked section, which is due to the local rotation of the cracked section. Instead of the bending moment originating from the elastic analysis of the piping system there will be a reduced bending moment, the load decreases, the real critical through-wall crack lengths due to this displacement-controlled loading are larger than those predicted by the load controlled methods. A corresponding analytical procedure taking into account this relaxation was developed and validated by a comparison with experiments as well as finite element calculations. The procedure can be used for the evaluation of the safety of piping systems (e.g. leak-before-break analyses), if the usual methods based on force-controlled loads give unrealistic-conservative results.