Numerical Analysis of the Transient Thermal Stress Intensity Factors in Cylinders Containing an External Circumferential Semi-Elliptical Crack

Document Type : Regular Paper


1 Faculty of Aerospace Engineering, Malek-Ashtar University of Technology, Tehran, Iran

2 Department of Mechanical Engineering, College of Engineering, Islamic Azad University, Tehran, Iran


In this paper, the transient thermal stress intensity factors for circumferential semi-elliptical crack located on the external surface of the cylinder are determined numerically. The internal surface of the cylinder is exposed to ultra-cold fluid, and the external wall is kept at a constant temperature. The three-dimensional finite element method in ABAQUS software and singular elements in the crack front has been used. In order to ensure the accuracy of the modelling process, stress intensity factors on the cylinder containing the semi-elliptical crack under mechanical loading for different geometric dimensions of the cylinder are extracted, and the results are evaluated with available data. In the research process, transient thermal stress has been modelled using an uncoupled thermoelasticity model in the quasi-static state. Also, the thermal stress results in steady-state are compared to the existing analytical data and, excellent agreement is achieved. Finally, transient thermal stress intensity factors are presented for different values of cylinder radius ratio and various relative depths and aspect ratios of the crack.


Main Subjects

[1] X. B. Lin, R. A. Smith, (1998). Fatigue growth prediction of internal surface cracks in pressure vessels. Journal Pressure Vessel Technology, ASME, 120:17–23.
[2] Raju, I.S., Newman, J.C. (1986).  Stress intensity factors for circumferential surface cracks in pipes and rods. In Fracture Mechanics: Seventeenth Volume, ed. J. Underwood, R. Chait, C. Smith, D. Wilhem, W. Andrews, and J. Newman (West Conshohocken, PA: ASTM International), 789–805.
[3] Carpinteri, A., Brighenti R., Spagnoli, A. (1998). Part-through cracks in pipes under cyclic bending. Nuclear Engineering and Design. 185:1–10.
[4] Carpinteri, A., Brighenti R., (1998). Circumferential surface flaws in pipes under cyclic axial loading. Engineering Fracture Mechanics. 60:383–396. Doi:10.1016/S0013-7944(98)00036-8
[5] Carpinteri, A., Brighenti R., Spagnoli, A. (2000). External surface cracks in shells under cyclic internal pressure. Fatigue Fracture Engineering Materials and Structures. 23:467–476.
[6] A. Carpinteri, R. Brighenti and S. Vantadori, (2003). Circumferentially notched pipe with an external surface crack under complex loading. International Journal of Mechanical Sciences. 45:1929–1947.
[7] Ligoria, S.A., Knight G.S., Ramachandra Murthy, D.S., (2005). Three-dimensional finite element analysis of a semi-elliptical circumferential surface crack in a carbon steel pipe subjected to a bending moment. Journal of Strain Analysis. 40:525–533. Doi:10.1243/030932405X16052
[8] Shahani, A.R., Habibi, S.E. (2007). Stress intensity factors in hollow cylinder containing a circumferential semi-elliptical crack subjected to combined loading. International Journal of Fatigue. 291:128–140. Doi:10.1016/j.ijfatigue.2006.01.017
[9] Shahani, A.R., Mohammadi Shodja M., Shahhosseini, A. (2010). Experimental investigation and finite element analysis of fatigue crack growth in pipes containing a circumferential semi-elliptical crack subjected to bending. Experimental Mechanics. 50:563–573.
[10] Fillery, B.P.  Hu, X.Z. (2012). Compliance based assessment of stress intensity factor in cracked hollow cylinders with finite boundary restraint: Application to thermal shock part II. Engineering Fracture Mechanics. 79:18–35.
[11] Ghajar, R., Abbaspour Niasani M., Saeidi Googarchin, H., (2014). Explicit expressions of stress intensity factor for external semi-elliptical circumferential cracks in a cylinder under mechanical and thermal loads. Modares Mechanical Engineering. 14:90-98. (In Persian)
[12] Abbaspour Niasani M., Ghajar, R., Saeidi Googarchin, H.,  Sharifi, S.M.H., (2017).  Crack growth pattern prediction in a thin walled cylinder based on closed form thermo-elastic stress intensity factors. Journal of Mechanical Science and Technology. 31:1603–1610.
[13] Nabavi, S.M., Montazer Torbati, E., Jamal-Omidi, M. (2020). Weight function for an external circumferential semielliptical crack in a cylinder. Fatigue Fracture Engineering Materials and Structures. 43:1487–1499. doi:10.1111/ffe.13224
[14] Fakhri, O.M., Kareem, A.K., Ismail, A.E.,  Jamian, S., Nemah, M.N., (2019).  Mode I SIFs for internal and external surface semi-elliptical crack located on a thin cylinder. Test Engineering and Management. 81:586–596.
[15] Al-Moayed, O.M., Kareem, A.K., Ismail, A.E., Jamian, S., Nemah, M.N., (2019). Distribution of Mode I stress intensity factors for single circumferential semi-elliptical crack in thick cylinder. International Journal of Integrated Engineering. 11:102–111.
[16] Al-Moayed, O.M., Kareem, A.K., Ismail, A.E., Jamian, S., Nemah, M.N., (2020). Influence coefficients for a single superficial cracked thick cylinder under torsion and bending moments. International Journal of Integrated Engineering. 12:132–144.
[17] Qian, X., Li, T., (2010). Effect of residual stresses on the linear-elastic KI–T field for circumferential surface flaws in pipes. Engineering Fracture Mechanics. 77:2682–2697. Doi:10.1016/j.engfracmech.2010.06.014
[18] Miyazaki, K., Mochizuki, M., (2011). The effects of residual stress distribution and component geometry on the stress intensity factor of surface crack. Journal of Pressure Vessel Technology. 133:1–7.
[19] Zareei, A., Nabavi, S.M., (2016).  Weight function for circumferential semi-elliptical cracks in cylinders due to residual stress fields induced by welding. Archive of Applied Mechanics. 86:1219–1230.
[20] Zareei, A., Nabavi, S.M., (2016).  Calculation of stress intensity factors for circumferential semi-elliptical cracks with high aspect ratio in pipes. International Journal of Pressure Vessels and Piping. 146:32–38. Doi: 10.1016/j.ijpvp.2016.05.008
[21] Nabavi, S.M., Shahmorady, M.B. (2020). Stress intensity factors for circumferential semi-elliptical cracks in cylinders subjected to forced convection heat transfer. International Journal of Integrated Engineering. 12:232–239.
[22] Paarmann, M., Sander, M., (2020). Analytical determination of stress intensity factors in thick walled thermally loaded components. Engineering Fracture Mechanics. 235, e107125.
[23] Banks-Sills, L., (1991). Application of the finite element to linear elastic fracture mechanic. Applied Mechanics Review. 44:447–461. Doi: 10.1115/1.3119488
[24] Anderson, T.L., (2017). Fracture Mechanics- Fundamentals and Applications, 4th Edition, Boca Raton, CRC Press.
[25] Institute AP. API 579-1/ASME FFS-1. Fitness-for-service. 2nd Edition, 2007.
[26] Laham S. Stress intensity factor and limit load. Handbook, British Energy Generation Limited, 1998.
[27] Bergman, M. (1995). Stress intensity factors for circumferential surface cracks in pipes. Fatigue Fracture Engineering Materials and Structures. 18:1155–1172.
[28] Hetnarski R.B., Eslami M.R. (2019). Thermal stresses: advanced theory and applications. 2nd Edition, Springer.
[29] Alipour, K. Nabavi, S.M., Bakhshan, M., Rahimi, F., Zareei, H., (2013) Thermal stresses solutions in cylinders due to steady state forced convection heat transfer. 13th Conference of Iranian Aerospace Society, Tehran, University of Tehran, Faculty of New Science and Technology.