Numerical Analysis of the Effect of External Circumferential Cracks in Transition Thickness Zone of Pressurized Pipes Using XFEM – Elastic-Plastic Behavior

Document Type: Research Paper


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

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



The elastic-plastic behavior of the material is considered to analyze the effect of an external circumferential crack on a pipe with thickness transition and double slopes. Using the extended finite element method (XFEM), the J-integral of 3D cracks were investigated and compared between straight pipes and pipes with thickness transition and different slopes. Considering internal pressure, this work highlighted the investigation of a 3D crack problem in a thickness transition pipe with a double slope, In the extended finite element method (XFEM), the level sets and the enrichment zone were defined. A crack is easily modeled by enrichment functions. The comparison between the values of the J-integral showed that the pipe containing thickness transition with double slopes is more sensitive to the considered cracks, more precisely, the parameters of the first thickness transition have more influence on the variation of J-integral than the parameters of the second thickness transition. The decreasing of the angle of the slopes and the increase of the ratio of the thicknesses is one effective method of reducing the J-integral.


[1] Rahman S., Ghadiali N., Wilcowski G.M., Moberg F., Brickstad B., 1998, Crack-opening-area analysis for circumferential trough-wall cracks restrain of bending thickness transition and weld residual stresses, International Journal of Pressure Vessels and Piping 75: 397-415.
[2] Électricité de F., 1997, RSE-M: Règles de Surveillance en Exploitation des Matériels Mécaniques des Ilots Nucléaires REP, Edition AFCEN.
[3] Abdelkader S., Saıd H., 2006, Numerical study of elliptical cracks in cylinders with a thickness transition, International Journal of Pressure Vessels and Piping 83: 35-41.
[4] Abdelkader S., Saıd H., 2006, Comparison of semi-elliptical cracks in cylinders with a thickness transition and in a straight cylinder – Elastic-plastic behavior, Engineering Fracture Mechanics 73: 2685-2697.
[5] Wessel E.T., Murrysville P.A., Server W.L., Kennedy E.L., 1991, Primer: Fracture Mechanics in the Nuclear Power Industry, EPRI Report, NP-5792-SR.
[6] CEA: The French Alternative Energies and Atomic Energy Commission, Commissariat à L’Energie Atomique (France)’,
[8] Chapuliot S., Lacire M.H., 1999, 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 1999 :395-106.
[9] Le Delliou P., Porte P., Code RSE-M: calcul simplifié du paramètre J pour un défaut axisymétrique débouchant en surface externe d’une transition d’épaisseur, RAPPORT EDF HT-2C/99/025/A.
[10] Idapalapati S., Xiao Z.M., Yi D., Kumar S.B., 2012, Fracture analysis of girth welded pipelines with 3D embedded cracks subjected to biaxial loading conditions, Engineering Fracture Mechanics 96: 570-587.
[11] Xiao Z., Zhang Y., Luo J., 2018, Fatigue crack growth investigation on offshore pipelines with three-dimensional interacting cracks, Geoscience Frontiers 9(6): 1689-1698.
[12] Salmi H., El Had Kh., El Bhilat H., Hachim A., 2019, Numerical analysis of the effect of external circumferential elliptical cracks in transition thickness zone of pressurized pipes using XFEM, Journal of Applied and Computational Mechanics 5(5): 861-874.
[13] Salmi H., El Had Kh., El Bhilat H., Hachim A., 2019, Numerical modeling and comparison study of elliptical cracks effect on the pipes straight and with thickness transition exposed to internal pressure, using XFEM in elastic behavior, Journal of Computational and Applied Research in Mechanical Engineering 5(5):861-874.
[14] Szu-Ying W., Bor-Jiun T., Jien-Jong Ch., 2015, Elastic-plastic finite element analyses for reducers with constant-depth internal circumferential surface cracks, International Journal of Pressure Vessels and Piping 131: 10-14.
[15] Zhibo M., Zhao Y., 2018,Verification and validation of common derivative terms approximation in meshfree numerical scheme, Journal of Computational and Applied Research in Mechanical Engineering 4(3): 231-244.
[16] Yazdani M., 2018, A novel modification of decouple scaled boundary finite element method in fracture mechanics problems, JCARME 7(2): 243-260.
[17] Surendran M., Pramod A.L.N., Nataraj S., 2019, Evaluation of fracture parameters by coupling the edge-based smoothed finite element method and the scaled boundary finite element method, Journal of Computational and Applied Research in Mechanical Engineering 5(3): 540-551.
[18] Moës N., Gravouil A., Belytschko T., 2002, 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: 2549-2568.
[19] Belytschko T., Black T., 1999, Elastic crack growth in finite elements with minimal remeshing, International Journal for Numerical Methods in Engineering 45: 601-620.
[20] Stolarska M., Chopp D., Moes N., Belytschko T., 2001, Modelling crack growth by level sets in the extended finite element method, International Journal for Numerical Methods in Engineering 51: 943-960.
[21] Kumar S., Singh I.V., Mishra B.K., 2013, Numerical investigation of stable crack growth in ductile materials using XFEM, Procedia Engineering 64: 652-660.
[22] Malekan M., Khosravi A., Cimini Jr C.A.,2019, Deformation and fracture of cylindrical tubes under detonation loading: A review of numerical and experimental analyses, International Journal of Pressure Vessels and Piping 173: 114-132.
[23] Sharma K., Singh I.V., Mishra B.K., Bhasin V., 2014, Numerical modeling of part-through cracks in pipe and pipe bend using XFEM, Procedia Materials Science 6: 72-79.
[24] Kwang S.W., Prodyot B., 2004, J-integral and fatigue life computations in the incremental plasticity analysis of large scale yielding by p-version of F.E.M., Structural Engineering & Mechanics 17(1): 51-68.
[25] Guangzhong L., Guangzhong L., Dai Z., Jin M., Zhaolong H., 2016, Numerical investigation of mixed-mode crack growth in ductile material using elastic-plastic XFEM, Journal of the Brazilian Society of Mechanical Sciences and Engineering 38: 1689-1699.
[26] Liu X., Lu Z.X., Chen Y., Sui Y. L., Dai L.H., 2018, Failure assessment for the high-strength pipelines with constant-depth circumferential surface cracks, Hindawi Advances in Materials Science and Engineering 36835: 1-11.
[27] Irwin G.R., 1961, Plastic zone near a crack and fracture toughness, Sagamore Research Conference Proceedings 4: 63-78.
[28] 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.
[29] Kumar V., German M., 1988, Elastic-Plastic Fracture Analysis of Through-Wall and Surface Flaws in Cylinders, EPRI Topical Report, NP-5596, Electric Power Research Institute, Palo Alto, CA.
[30] Van V., Krystyn J., 2006, Mechanical Behavior of Materials.
[31] Sukumar N., Chopp D.L., Moran B., 2003, Extended finite element method and fast marching method for three-dimensional fatigue crack propagation, Engineering Fracture Mechanics 70: 29-48.
[32] Eshelby J.D., 1956, The continuum theory of lattice defects, Solid State Physics 3: 79-144.
[33] Mahaffey R.M., Van Vuuren S.J., 2014, Review of pump suction reducer selection: Eccentric or concentric reducers, Journal of the South African Instituti Engineering 56(3): 65-76.
[34] EL-Gharib J., 2009, Macro commande MACR_ASCOUF_MAIL, Code Aster Clé: U4.CF.10, Révision: 1122, Document diffusé sous licence Gnufdl.