Based on the previous limit load analytical modeling for cracked thin-walled pipe  the limit load model for thick-walled pipe had developed. There are some additional peculiarities included in proposed model. First, the radial stresses distribution and their accounting for the Tresca’s criterion. Second, the crack location and related to it the interaction of hoop stress (due to the inner pressure) and axial one (caused by local bending moment) in the limit state. Third, hoop stress redistribution with possibility of plastic hinge forming in the zone, which is opposite to the crack zone. Forth, an analysis of derived easy to use analytical formulas by comparing with results of full-scale burst test.
Local Limit Load Analytical Model for Thick-Walled Pipe With Axial Surface Defect
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Ageiev, S, Orynyak, I, Radchenko, S, & Zarazovskii, M. "Local Limit Load Analytical Model for Thick-Walled Pipe With Axial Surface Defect." Proceedings of the ASME 2014 Pressure Vessels and Piping Conference. Volume 3: Design and Analysis. Anaheim, California, USA. July 20–24, 2014. V003T03A095. ASME. https://doi.org/10.1115/PVP2014-28666
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