International Journal of Fracture

, Volume 133, Issue 2, pp 167–181

Assessment of partly circumferential cracks in pipes

Article
  • 175 Downloads

Abstract

This paper presents a new method for predicting the stress intensity factors around a partly circumferential elliptical surface crack in a pipe. The solution is applicable to structures with both double and single curvature. The technique involves a conformal transform in conjunction with a semi-analytical approach that uses a finite element model to obtain the stress distribution in the undamaged structure. By using an indirect methodology, the model development is simplified and the analysis time is minimised. As such a coarse mesh can be used to obtain solutions for multiple crack geometries. Three examples are presented to verify this methodology. They include a partly circumferential elliptical crack under uniform tension, a pipe subject to a residual stress field, and a problem involving double curvature. For simple loading the solution compares with other published solutions to within 5% for an external crack, and to within 15% for an internal crack. For more complex loading conditions the majority of the solutions were within 5% of other published results at the deepest point, and most solutions at the surface agreed to within 15%. For the problem involving double curvature, the solutions agreed to within 4% for an internal crack, and 15% for an external crack.

Keywords

Partly circumferential crack pipes tubular structures stress intensity factor conformal transform double curvature 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bergman, M. 1995Stress intensity factors for circumferential surface cracks in pipesFatigue and Fracture of Engineering Materials and Structures1811551172Google Scholar
  2. BS 7910:1999 (2000). – Guide on methods for assessing the acceptability of flaws in metallic structures: London.Google Scholar
  3. Carpinteri, A., Brighenti, R. 1998Circumferential surface flaws in pipes under cyclic axial loadingEngineering Fracture Mechanics60383396Google Scholar
  4. Carpinteri, A., Brighenti, R. 2000Three-parameter model for fatigue behaviour of circumferential surface flaws in pipesInternational Journal of Mechanical Sciences4212551269Google Scholar
  5. Chen, D.H., Nisitani, H., Mori, K. 1991Tension or bending of cylindrical vessels with a surface crackNippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers Part A5717101714Google Scholar
  6. Cordes, R.D., Joseph, P.F. 1994Surface and internal cracks in a residually stressed plateInternational Journal of Fracture68287314Google Scholar
  7. Dai, Y., Roedig, M., Altes, J. 1991Calculation of the stress intensity factor for a partial circumferentially cracked tube loaded in bending by using the shell line-spring modelFatigue and Fracture of Engineering Materials and Structures141123Google Scholar
  8. Delale, F., Erdogan, F. 1982Application of the line-spring model to a cylindrical shell containing a circumferential or axial part-through crackJournal of Applied Mechanics, Transactions ASME4997102Google Scholar
  9. Forman R.G. and Shivakumar V. (1986). Growth behavior of surface cracks in the circumferential plane of solid and hollow cylinders. ASTM Special Technical Publication in Fracture Mechanics: Seventeenth Volume, Seventeenth National Symposium on Fracture Mechanics., Albany NY USA.Google Scholar
  10. Jones, R., Peng, D., Pitt, S., Wallbrink, C. 2004Weight functions, CTOD, and related solutions for cracks at notchesEngineering Failure Analysis1179114Google Scholar
  11. Joseph, P.F., Cordes, R.D., Erdogan, F. 1995Surface cracks in toroidal shellsNuclear Engineering and Design158263276Google Scholar
  12. Lin, X.B., Smith, R.A. 1998Fatigue growth simulation for cracks in notched and unnotched round barsInternational Journal of Mechanical Sciences40405419Google Scholar
  13. Lin, X.B., Smith, R.A. 1999Shape evolution of surface cracks in fatigued round bars with a semicircular circumferential notchInternational Journal of Fatigue21965973Google Scholar
  14. Nehari, Z. 1975Conformal MappingDover Publications: IncNew York, USA273275Google Scholar
  15. Newman J.C. and Raju I.S. (1986). Stress-Intensity Equations for Cracks in Three-Dimensional Finite Bodies Subjected to Tension and Bending Loads. In: Computational Methods in the Mechanics of Fracture (Edited by S. N. Atluri) Vol. 2 Elsevier Science Publishers, Amsterdam North-Holland 311–334.Google Scholar
  16. Peng D. (2002). Methods for failure assessment of structures and applications to shape optimisation. In: Mechanical Engineering: Monash University Melbourne.Google Scholar
  17. Poette, C., Albaladejo, S. 1991Stress intensity factors and influence functions for circumferential surface cracks in pipesEngineering Fracture Mechanics39641650Google Scholar
  18. Pook, L.P. 1994Some implications of corner point singularitiesEngineering Fracture Mechanics48367378Google Scholar
  19. Raju I.S. and Newman J.C. (1986). Stress-intensity factors for circumferential surface cracks in pipes and rods under tension and bending loads. ASTM Special Technical Publication in Fracture Mechanics: Seventeenth National Symposium on Fracture Mechanics Albany, NY, USA.Google Scholar
  20. Rice J.R. and Levy N. (1972). The part-through surface crack in an elastic plate. Journal of Applied Mechanics Transactions ASME: 185–194.Google Scholar
  21. Sih, G.C., Lee, Y.D. 1989Review of triaxial crack border stress and energy behaviorTheoretical and Applied Fracture Mechanics12117Google Scholar
  22. Tseng, A.A. 1980Three-dimensional finite element analysis of the three-point bend specimenEngineering Fracture Mechanics13939943Google Scholar
  23. Vijayakumar, K., Atluri, S.N. 1981Embedded elliptical crack, in an infinite solid, subject to arbitrary crack-face tractionsJournal of Applied Mechanics Transactions ASME488896Google Scholar
  24. Wunsch, D.A. 1994Complex Variables with ApplicationsAddison-Wesley Publishing Company IncUK491508Google Scholar
  25. Xian-ming, K., Si-tao, Z., Zhen-yuan, C. 1989Studies on stress intensity factor K/sub I/ of surface cracks in a cylinder under remote tension loadsEngineering Fracture Mechanics33105111Google Scholar
  26. Yang C.Y. (1988). Line spring method of stress intensity factor determination for surface cracks in plates under arbitrary in-plane stress. In: Fracture Mechanics: Nine-teenth Symposium(Edited by Cruse) ASTM STP 969.Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, DSTO Centre of Expertise in Structural Mechanics (CoE-SM)Monash UniversityVictoriaAustralia
  2. 2.Mechanical Engineering, Maintenance Technology InstituteMonash UniversityVictoriaAustralia
  3. 3.Department of Mechanical Engineering, Rail CRCMonash UniversityVictoriaAustralia

Personalised recommendations