Closed Form Expressions for Fracture Mechanics Analysis of Cracked Pipes

Abstract

Closed form stress intensity factor (K1) expressions are presented for cracks in pipes subjected to a variety of loading conditions. The loadings considered are: 1) axial tension, 2) remotely applied bending moment, and 3) internal pressure. Expressions are presented for circumferential and axial cracks, and include both part-through and through-wall crack geometries. The closed form K1 expressions are valid for pipe radius to wall thickness ratio between 5 and 20.

Stress intensity factors for circumferential through‐wall cracks in thin‐walled cylindrical shells subjected to tension and torsion

“…Zahoor's solution is only intended for 5 ≤ R m / t ≤ 20. For R m / t = 10, it agrees with the FEM results, while for long cracks in thinner cylinders, it becomes increasingly more conservative, also as intended …”

“…This interpolated solution has been shown to agree very well with FE results by Forman, Hickman, and Shivakumar and extended finite element method (XFEM) results by Zarrinzadeh, Kabir, and Deylami . Zahoor generated an alternative, conservative version of Sander's interpolated solution, limited to 5 ≤ R m / t ≤ 20, which was included in Zahoor's Ductile Fracture Handbook…”

“…The FEM results are compared with five solutions found in the literature. Sanders' long crack solution and Zahoor's solution are included because they are given in handbooks . Takahashi and Shim et al performed extensive reviews of available solutions, each proposing an interpolation of certain FE solutions.…”

“…Dimensionless shape factor F I for tensile loading. Comparison between closed‐form solutions by Shim et al , Takahashi, and Zahoor, Sanders' interpolated (INT) and long crack (LC) solutions, and finite element method (FEM) results obtained here [Colour figure can be viewed at wileyonlinelibrary.com]…”

“…It is convenient to define the membrane component of the stress intensity factors for the circumferential through‐wall crack as follows, with F I and F II being dimensionless geometry factors: The stress intensity factors do also have a bending component, because of the through‐thickness variation of the stresses near the crack tip. These bending components have been shown to be very small in both tension and torsion according to the shallow shell theory and are usually neglected in the case of tensile loading . FE results suggest that these bending components are significant for the case of torsion however.…”