The survivability of a pipeline with a surface crack taking into account the biaxial constraint along its front

A method for assessing the survivability of a pipeline at a distance from a transverse weld with a longitudinal surface semi-elliptical mode I crack is proposed, taking into account the biaxial constraint along its front. A literature review has shown that there are currently no works in which the forecast of the growth of such crack is carried out taking into account the T_xx- and T_zz-stresses, which are nonsingular terms in the Williams expansion for stresses at the crack tip. To model the growth of a fatigue crack, a modified Paris formula is used, in which the range of the effective stress intensity factor (SIF) is substituted instead of the span of the usual SIF. In this case, in addition to the usual SIF, the expression for the effective SIF includes the T_xx- and T_zz-stresses. The proposed two-parameter approach allows taking into account the constraint in the crack plane in the direction perpendicular to the front, due to the introduction of T_xx-stresses into the expression for the effective SIF, and in the longitudinal direction due to the introduction of T_zz-stresses. The expression for the effective SIF was previously obtained by the authors by improving the fracture criterion of maximum tangential stresses. It is assumed that tangential stresses in the fracture process zone are equal to the local strength of the material. In this case, the size of the fracture process zone and the local strength of the material are determined taking into account the T_xx- and T_zz-stresses. Numerical simulation was performed in the finite element environment of ANSYS Workbench. To construct a mathematical model of a pipe with a semi-elliptical crack, three types of finite elements (FE) were used: 10-node tetrahedral elements SOLID187; 20-node hexahedral FE SOLID186 and 15-node wedge FE degenerated from SOLID186. The latter of which singular FEs have a built-in function for calculating the SIF and T_xx-stresses. Special macros were written in the APDL programming language to calculate the T_zz-stresses and the effective SIF along the crack front. It is shown that the use of a one-parameter approach based on the Paris formula does not allow taking into account the biaxiality of the stress state when assessing the survivability of an oil pipeline, since, unlike the effective SIF, the usual SIF for a longitudinal semi-elliptical crack depends only on circumferential stresses. It is established that for cracks of the same initial depth, the durability decreases with an increase in half-length. It is revealed that the durability predicted using the usual one-parameter Paris formula is approximately 30% underestimated, compared to the results of a two-parameter analysis.

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