Stress Intensity Factor Solutions for Internal Longitudinal Semi-Circular Surface Flaws in a Cylinder Under Arbitrary Loading

TLDR

Semi‑circular surface flaws in pressure‑vessel cylinders are a key concern in vessel design. The study aims to map the stress‑intensity factor distribution around a longitudinal semi‑circular flaw in a cylinder with Ri/t = 10 under arbitrary loading. Finite‑element analysis with a macro‑element of over 1600 degrees of freedom and Parks’ stiffness‑derivative method were used to compute displacement and stress‑intensity factors for six crack depths (a/t = 0.10–0.90) under four loading profiles (constant, linear, quadratic, cubic). Derived nondimensional magnification factors for the stress‑intensity distribution agree with published data within 5 %.

Abstract

The behavior of semi-circular surface flaws in cylinders is of interest in the technology of pressure vessels. The object of this study is to determine the stress intensity factor distribution around the crack front under arbitrary loading conditions for a longitudinal semi-circular flaw with Ri/t = 10; where Ri is the inside radius of the cylinder, and t is the cylinder thickness. Six crack depths are studied under various loading conditions: a/t = 0.10, 0.25, 0.50, 0.65, 0.80, and 0.90, where a is the circular flaw radius. In general, the finite element method is used to determine the displacement solution. Parks’ stiffness derivative method is used to find the stress intensity factor distribution around the semi-circle. The immediate crack tip geometry is modeled by use of a “macro-element” containing over 1600 degrees of freedom. Four separate loadings are considered: 1) constant, 2) linear, 3) quadratic, and 4) cubic crack surface pressure. From these loadings, nondimensional magnification factors are derived to represent the resulting stress intensity factors. Comparisons are made with other investigators and results agree within 5 percent of published results.