Evaluation of Crack Propagation in Pressure Equipment under Static Loading through Analytical, Finite Element and XFEM Approaches

¹ Higher Institute of Marine Fisheries-Agadir
² Laboratory of Energy Engineering, Materials and Systems (LEEMS), National School of Applied Sciences (ENSA), Ibn Zohr University, Agadir, Morocco.
³ Hassan II University of Casablanca (UH2C), National Higher School of Electricity and Mechanics, Laboratory of Mechanics, Engineering and Innovation, Km 8 Route d'El Jadida, B.P 5366 Maarif Casablanca 20100 Morocco
⁴ Higher Institute of Maritimes Studies, Casablanca, Morocco
⁵ Environmental, Ecological and Agro-Industrial Engineering Laboratory. Department of Biology, Faculty of Sciences and Techniques. University Sultan Moulay Slimane. Beni-Mellal, Morocco
⁶ Laboratory of Mechanics and High Energy Physics, Faculty of Sciences Aïn-Chock, Hassan II University of Casablanca, P.O. Box 5366 Maarif Casablanca 20100, Morocco

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Abstract

This study investigates the fracture behavior of pressure equipment under static loading by comparing analytical solutions, conventional FEM, and XFEM. Cylindrical and spherical structures with semi-elliptical surface cracks are analyzed to evaluate the effects of crack geometry and structural curvature on the stress intensity factor (KI). Results show that XFEM accurately captures crack behavior without complex remeshing, closely matching analytical solutions (deviation <1%), whereas FEM reliability depends strongly on mesh refinement near the crack. The stress intensity factor increases with relative crack depth (a/t) and structural curvature (decreasing R/t), with spherical structures exhibiting higher KI than cylindrical ones. Overall, the study demonstrates XFEM's efficiency for assessing structural integrity and guiding the design of safer pressure equipment in energy and environmental applications.