Stability of circumferential through-cracks in ductile pipes

An analysis of tearing instability is presented for a pipe with a circumferential through-crack. Loading conditions consisting of a large external axial force and a bending moment, together with an internal pressure, have been considered. The mechanical behavior of the material is assumed to be elastic perfectly-plastic. Instability has been studied under fixed grip conditions, following the application of loads which correspond to the plastic limit load of the cracked cross-section. The values of the applied tearing modulus have been expressed in terms of geometrical factors such as pipe length, pipe radius, and the length of the crack. Numerical examples have been calculated to obtain an estimate of the critical value of the length-to-radius ratio, for the case that the tearing modulus of the material is known.