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

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Faculty of Science and Technology, Sidi Mohamed Ben Abdellah University, Fez 30000, Morocco
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Laboratory of Systems Engineering and Applications (LISA), National School of Applied Sciences of Fez, Sidi Mohamed Ben Abdellah University, Fez 30000, Morocco
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Department of Mechanical Engineering, Imperial College London, Exhibition Rd., London SW7 2AK, UK
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Design, Manufacturing & Engineering Management, University of Strathclyde, Glasgow G1 1XJ, UK
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National School of Applied Sciences of Safi, University Cadi Ayad, Marrakesh 40000, Morocco
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Department of Industrial and Manufacturing Engineering, University of Engineering and Technology, Lahore 54890, Pakistan
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Department of Industrial and Systems Engineering, Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Korea
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Author to whom correspondence should be addressed.
Mathematics 2021, 9(5), 507; https://doi.org/10.3390/math9050507
Received: 23 January 2021 / Revised: 15 February 2021 / Accepted: 22 February 2021 / Published: 2 March 2021
(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems)
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. View Full-Text
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MDPI and ACS Style

Yakoubi, K.; Montassir, S.; Moustabchir, H.; Elkhalfi, A.; Pruncu, C.I.; Arbaoui, J.; Farooq, M.U. An Extended Finite Element Method (XFEM) Study on the Elastic T-Stress Evaluations for a Notch in a Pipe Steel Exposed to Internal Pressure. Mathematics 2021, 9, 507. https://doi.org/10.3390/math9050507

AMA Style

Yakoubi K, Montassir S, Moustabchir H, Elkhalfi A, Pruncu CI, Arbaoui J, Farooq MU. An Extended Finite Element Method (XFEM) Study on the Elastic T-Stress Evaluations for a Notch in a Pipe Steel Exposed to Internal Pressure. Mathematics. 2021; 9(5):507. https://doi.org/10.3390/math9050507

Chicago/Turabian Style

Yakoubi, Khadija, Soufiane Montassir, Hassane Moustabchir, Ahmed Elkhalfi, Catalin I. Pruncu, Jamal Arbaoui, and Muhammad U. Farooq 2021. "An Extended Finite Element Method (XFEM) Study on the Elastic T-Stress Evaluations for a Notch in a Pipe Steel Exposed to Internal Pressure" Mathematics 9, no. 5: 507. https://doi.org/10.3390/math9050507

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