Numerical Analysis of the Effect of External Circumferential Elliptical Cracks in Transition Thickness Zone of Pressurized Pipes Using XFEM

Document Type : Research Paper


1 National Higher School of Mechanics, ENSEM, Laboratory of Control and Mechanical Characterization of Materials and Structures, Casablanca, Morocco

2 Institute of Maritims Studies, Laboratory of Materials and Structures, Casablanca, Morocco


The present work investigates the effect of the elliptical three-dimensional (3D) cracks on a pipe with thickness transition, considering internal pressure. Level sets were defined using the extended finite element method (XFEM), the stress intensity factors (SIFs) of 3D cracks were investigated and compared between straight pipes and pipes with thickness transition. The results show that the XFEM is an effective tool for modeling crack in pipes. A pressurized pipe with thickness transition is more sensitive to the feature compared to the straight pipe. Parameters of the transition zone have an influence on stress intensity factors. Quantification of the SIFs associated with cracks in the transition zone of pipes with thicknesses is performed.


Main Subjects

[1] Moustabchir, H., Elhakimi, A., Hariri, S., Azari,Z., Pressure study of gas transport pipes, in the presence of defects notch type, 18 ème Congrès Français de Mécanique, Grenoble, 2007, 27-31.
[3] Hariri, S., El Hakimi, A., Azari, Z., Etude numérique et expérimentale de la nocivité des défauts dans des coques cylindriques et sphériques : aide à la détermination des facteurs de contraintes, Revue de Mécanique Appliquée et Théorique, 1(10), 2008, 1-10.
[4] Xiao, Z., Zhang, Y., Luo, J., Fatigue crack growth investigation on offshore pipelines with three-dimensional interacting cracks, Geoscience Frontiers, 9(6), 2018, 1689-1698.
[5] Idapalapati, S., Xiao, Z.M., Yi, D., Kumar, S.B., Fracture analysis of girth welded pipelines with 3D embedded cracks subjected to biaxial loading conditions, Engineering Fracture Mechanics, 96, 2012, 570-587.
[6] Broek, D., Elementary engineering fracture mechanics, Dordrecht: Kluwer, 1991.
[7] Gdoutos, E.E., Fracture mechanics-an introduction, Dordrecht: Kluwer, 1991.
[8] Le Grognec, P., Hariri, S., Afzali, M., Jaffal, H., Nocivité des défauts et propagation de fissures dans les équipements sous pression, 18 ème Congrès Français de Mécanique, 2007.
[9] Sabokrouh, M., Farahani, M., Experimental Study of the Residual Stresses in Girth Weld of Natural Gas Transmission Pipeline, Journal of Applied and Computational Mechanics, 5(2), 2019, 199-206.
[10] Vakili Tahami, F., Biglari, H., Raminnea, M., Optimum Design of FGX-CNT-Reinforced Reddy Pipes Conveying Fluid Subjected to Moving Load, Journal of Applied and Computational Mechanics, 2(4), 2016, 243-253.
[11] The French Alternative Energies and Atomic Energy Commission (CEA). ‘Commissariat a` L’Energie Atomique (France).
[13] Chapuliot, S., Lacire, M.H., Stress intensity factors for external circumferential cracks in tubes over a wide range of radius over thickness ratios. American Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication), 365, 1999, 95-106.
[14] Saffih, A., Hariri, S., Numerical study of elliptical cracks in cylinders with a thickness transition, International Journal of Pressure Vessels and Piping, 83, 2006, 35-41.
[15] Le Delliou, Calcul simplifié du paramètre J pour un défaut axisymétrique débouchant en surface externe d’une transition d’épaisseur.
[16] Moës, N., Gravouil, A., Belytschko, T., Non-planar 3D crack growth by the extended finite element and level sets; Part I:
Mechanical model, International Journal for Numerical Methods in Engineering, 53, 2002, 2549-2568.
[17] Medinas, M.T.L.F., An Extended Finite Element Method (XFEM) approach to hydraulic fractures: Modelling of oriented perforations, Master Thesis, Tecnico Lisboa, 2015.
[18] Belytschko, T., Black, T., Elastic crack growth in finite elements with minimal remeshing, International Journal for Numerical Methods in Engineering, 45, 1999, 601–620.
[19] Stolarska, M., Chopp, D., Moes, N., Belytschko, T., Modelling crack growth by level sets in the extended finite element method, International Journal for Numerical Methods in Engineering, 51, 2001, 943–960.
[20] Kamal Sharma, I., Singh, V., Mishra, B.K., Bhasin, V., Numerical Modeling of Part-Through Cracks in Pipe and Pipe Bend using XFEM, Procedia Materials Science, 6, 2014, 72-79.
[21] Kumar, S., Singh, I.V., Mishra, B.K., A coupled finite element and element-free Galerkin approach for the simulation of stable crack growth in ductile materials, Theoretical and Applied Fracture Mechanics, 70, 2014, 49-58.
[22] Cherepanov, G.P., The propagation of cracks in a continuous medium, Journal of Applied Mathematics and Mechanics, 31(3), 1967, 503-512.
[23] Rice, J.R., A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks, Journal of Applied Mechanics, 35, 1968, 379-386.
[24] Sukumar, N., Chopp, D.L., Moran, B., Extended finite element method and fast marching method for three-dimensional fatigue crack propagation, Engineering Fracture Mechanics, 70, 2003, 29-48.
[25] Eshelby, J.D., The Continuum Theory of Lattice Defects, Solid State Physics, 3, 1956, 79-144.
[26] French construction code. Construction des Appareils à Pression non soumis à l’action de la flamme, ‘the Code for Construction of unfired Pressure Vessels, Division 1, part C – design and calculation, section C2 – rules for calculating cylindrical, spherical and conical shell subjected to internal pressure, 2005, 539-622.