*Article* **An Extended Finite Element Method (XFEM) Study on the Elastic T-Stress Evaluations for a Notch in a Pipe Steel Exposed to Internal Pressure**

**Khadija Yakoubi 1, Soufiane Montassir 1, Hassane Moustabchir 2, Ahmed Elkhalfi 1, Catalin Iulian Pruncu 3,4,\*, Jamal Arbaoui <sup>5</sup> and Muhammad Umar Farooq 6,7**


**Abstract:** 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.

**Keywords:** T-stress; X-FEM; notch; pipe; stress difference method (SDM)
