The work investigates the importance of the K-T approach in the modelling of pressure cracked structures. T-stress is the constant in the second term of the Williams expression; it is often negligible, but recent literature has shown that there are cases where T-stress plays the role of opening the crack, also T-stress improves elastic modeling at the point of crack. In this research study, the most important effects of the T-stress are collected and analyzed. A numerical analysis was carried out by the extended finite element method (X-FEM) to analyze T-stress in an arc with external notch under internal pressure. The different stress method (SDM) is employed to calculate T-stress. Moreover, the influence of the geometry of the notch on the biaxiality is also examined. The biaxiality gave us a view on the initiation of the crack. The results are extended with a comparison to previous literature to validate the promising investigations.

For a long time, cracked structures have triggered various researchers to develop a structural integrity approach and design models to address the fracture problems. In the present study, a pipeline with an axial semi-elliptical surface defect was examined in detail. Recent works have highlighted the use of the classical finite element method (CFEM) as numerical tools to solve the fracture mechanics; however, this approach comes with a few difficulties in the modelling aspects. To overcome this issue, we proposed the use of the extended finite element method (XFEM), which was implemented in the commercial version of Abaqus software. Moreover, we have used the results based on this technique in the volumetric method to estimate the stress intensity factors (SIFs). Then, this parameter was employed to build the failure assessment diagram (FAD). The FAD curve was used in the current investigation because it is one of the conventional methods for the evaluation of flaws in steel pipes. The XFEM simulations enable us to draw an FAD curve that can be used as a practical reference for defect evaluation in pipeline systems in the industrial world.

The aim of this study is to investigate the problem of pipe cracking based on T-stress analysis and the influence of other parameters, using a numerical computation performed by extended isogeometric analysis (X-IGA). This article examines the T-stress, which defines the second term of the Williams’ series expansion. T-stress provides effective elastic modeling at the crack tip. Using the extended iso-geometric analysis (X-IGA), we determined the distribution of T-stress at the crack tip in a pipe under internal pressure as a function of internal pressure, crack size, and Poisson’s ratio. To validate the promising findings, the results are expanded with a comparison to the extended finite element (X-FEM) method and existing research in this field, and we obtained an error between 0.2% and 4.6%. This work demonstrated the significance of T-stress in fracture description, the effect of Poisson’s ratio and size on T-stress, and that X-IGA provided accurate numerical results by precisely describing the geometry of the crack and enriching it.