Survivability of a Pipeline with a Surface Crack Taking into Account Biaxial Constraint of Deformations Along Its Front

Abstract

A method for assessing the survivability of a pipeline with a longitudinal surface semi-elliptical normal separation crack, located away from a transverse weld, taking into account biaxial strain restraint along its front, is proposed. At present there are no publications that predict the growth of such a crack while accounting for the T_xx and T_zz stresses, which are the non‑singular terms in the Williams expansion for stresses at the crack front in three‑dimensional bodies. For simulation of fatigue crack growth a modified Paris law was used, in which the range of the conventional stress intensity factor (SIF) is replaced by the range of an effective SIF. In the expression for the effective SIF, in addition to the conventional SIF, the T_xx and T_zz stresses are included. The proposed two‑parameter approach allows one to account for deformation constraint in the crack plane: in the direction normal to the front, by introducing T_xx stresses into the expression for the effective SIF, and in the longitudinal direction, by introducing T_zz stresses. The expression for the effective SIF was previously obtained by the authors by refining the maximum tangential stress failure criterion. It is assumed that the tangential stresses in the pre‑failure zone are equal to the local strength of the material. The size of the pre‑failure zone and the local material strength are determined taking T_xx and T_zz stresses into account. Numerical simulation was performed in the finite‑element environment ANSYS Workbench. To build the finite‑element model in the vicinity of the crack front, degenerated 15‑node wedge singular elements derived from SOLID186 were used; these have a built‑in capability to compute the SIF and T_xxstresses. A special APDL macro was developed to compute the T_zz stresses and the effective SIF along the crack front. It is shown that the traditional single‑parameter approach based on the Paris law does not allow one to account for biaxial deformation constraint when assessing pipeline survivability, since, unlike the effective SIF, the conventional SIF for a longitudinal semi‑elliptical crack depends only on the circumferential stresses. It was established that for surface cracks of the same initial depth, increasing the half‑length reduces the pipeline life. Moreover, the life predicted using the standard single‑parameter Paris law is approximately 30% lower than that obtained from the two‑parameter analysis.