The limit-load solution for a thick-wall pipe with a circumferential crack under combined tension and bending loads

摘要

In the context of limit load analysis, a pipe with a circumferential through-wall crack or part-through crack has been analyzed for combined axial and bending loads. Most of the analyses developed so far are for thin-wall pipes, and almost all analyses for part-through cracks were developed for an inner crack. Although the limit load solution for a thick-wall pipe with a circumferential part-through inner crack is available in the literature for the combined axial and bending load, the corresponding solution for an outer crack on a thick-wall pipe has not been reported. In addition, there are inconsistencies in the reported closed-form solution for an inner crack on the thick-wall pipe. The objective of this paper is to present the correct limit-load solution for a thick-wall pipe under the combined axial and bending loads for a circumferential part-through inner crack, and to present the corresponding solution for a part-through outer crack for the same thick-wall pipe. Simplifications are then carried out systematically for cases (1) only with an axial or bending load, (2) for part-through flawed thin-wall pipes, (3) for through-wall flawed thin-wall pipes, and (4) for a composite crack geometry, i.e., a 360-degree inner crack with a portion through-wall, to connect the solution developed here to the solutions for various special cases which have been reported in the literature.