Assessment of partly circumferential cracks in pipes Article Received: 01 October 2004 Accepted: 13 January 2005 DOI:
Cite this article as: Wallbrink, C.D., Peng, D. & Jones, R. Int J Fract (2005) 133: 167. doi:10.1007/s10704-005-0628-0 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 References Bergman, M. 1995 Stress intensity factors for circumferential surface cracks in pipes Fatigue and Fracture of Engineering Materials and Structures 18 1155 1172 Google Scholar
BS 7910:1999 (2000). – Guide on methods for assessing the acceptability of flaws in metallic structures: London.
Carpinteri, A., Brighenti, R. 1998 Circumferential surface flaws in pipes under cyclic axial loading Engineering Fracture Mechanics 60 383 396 Google Scholar Carpinteri, A., Brighenti, R. 2000 Three-parameter model for fatigue behaviour of circumferential surface flaws in pipes International Journal of Mechanical Sciences 42 1255 1269 Google Scholar Chen, D.H., Nisitani, H., Mori, K. 1991 Tension or bending of cylindrical vessels with a surface crack Nippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers Part A 57 1710 1714 Google Scholar Cordes, R.D., Joseph, P.F. 1994 Surface and internal cracks in a residually stressed plate International Journal of Fracture 68 287 314 Google Scholar Dai, Y., Roedig, M., Altes, J. 1991 Calculation of the stress intensity factor for a partial circumferentially cracked tube loaded in bending by using the shell line-spring model Fatigue and Fracture of Engineering Materials and Structures 14 11 23 Google Scholar Delale, F., Erdogan, F. 1982 Application of the line-spring model to a cylindrical shell containing a circumferential or axial part-through crack Journal of Applied Mechanics, Transactions ASME 49 97 102 Google Scholar
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.
Jones, R., Peng, D., Pitt, S., Wallbrink, C. 2004 Weight functions, CTOD, and related solutions for cracks at notches Engineering Failure Analysis 11 79 114 Google Scholar Joseph, P.F., Cordes, R.D., Erdogan, F. 1995 Surface cracks in toroidal shells Nuclear Engineering and Design 158 263 276 Google Scholar Lin, X.B., Smith, R.A. 1998 Fatigue growth simulation for cracks in notched and unnotched round bars International Journal of Mechanical Sciences 40 405 419 Google Scholar Lin, X.B., Smith, R.A. 1999 Shape evolution of surface cracks in fatigued round bars with a semicircular circumferential notch International Journal of Fatigue 21 965 973 Google Scholar Nehari, Z. 1975Conformal Mapping Dover Publications: Inc New York, USA 273 275 Google Scholar
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.
Peng D. (2002). Methods for failure assessment of structures and applications to shape optimisation. In: Mechanical Engineering: Monash University Melbourne.
Poette, C., Albaladejo, S. 1991 Stress intensity factors and influence functions for circumferential surface cracks in pipes Engineering Fracture Mechanics 39 641 650 Google Scholar Pook, L.P. 1994 Some implications of corner point singularities Engineering Fracture Mechanics 48 367 378 Google Scholar
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.
Rice J.R. and Levy N. (1972). The part-through surface crack in an elastic plate.
Journal of Applied Mechanics Transactions ASME: 185–194. Sih, G.C., Lee, Y.D. 1989 Review of triaxial crack border stress and energy behavior Theoretical and Applied Fracture Mechanics 12 1 17 Google Scholar Tseng, A.A. 1980 Three-dimensional finite element analysis of the three-point bend specimen Engineering Fracture Mechanics 13 939 943 Google Scholar Vijayakumar, K., Atluri, S.N. 1981 Embedded elliptical crack, in an infinite solid, subject to arbitrary crack-face tractions Journal of Applied Mechanics Transactions ASME 48 88 96 Google Scholar Wunsch, D.A. 1994Complex Variables with Applications Addison-Wesley Publishing Company Inc UK 491 508 Google Scholar Xian-ming, K., Si-tao, Z., Zhen-yuan, C. 1989 Studies on stress intensity factor K/sub I/ of surface cracks in a cylinder under remote tension loads Engineering Fracture Mechanics 33 105 111 Google Scholar
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.