Abstract
Three dimensional linear elastic fracture mechanics analyses of the problem of an internally pressurised thick-walled cylinder with a semi-elliptical surface crack are carried out using the Boundary Integral Equation method. The cases treated are for ratios of external to internal cylinder radii of 2 and 3, with maximum crack depths ranging from 20% to 80% of the wall thickness. For a typical crack, the predicted value of stress intensity factor decreases slightly along the crack front moving away from the point of deepest penetration, reaching a minimum before increasing rapidly as the free internal surface of the cylinder is approached. The results presented will be of considerable use in the prediction of residual or safe life of, for example, chemical reactor tubes known to be cracked to a certain depth.
Résumé
Une analyse tri-dimensionnelle élastique et linéaire en mécanique de rupture du problème d'un cylindre à paroi épaisse soumis à pression interne et comportant une fissure de surface semi-elliptique a été effectuée en utilisant la méthode d'équation intégrale aux limites. Les cas envisagés dans l'étude sont relatifs à des rapports des rayons de cylindre externe et interne de 2 et de 3 avec des profondeurs maximum de fissure s'étalant de 20% à 80% de l'épaisseur de paroi. Dans le cas d'une fissure typique, la valeur prédite pour le facteur d'intensité des contraintes décroit légèrement le long du front de la fissure lorsque l'on se meut du point de pénétration le plus profond, et passe par un minimum pour ensuite s'accroître rapidement lorsqu'on approche de la surface libre interne du cylindre. Les résultats présentés s'avèreront d'une aide considérable pour prédire la vie résiduelle ou la durée de service fiable, par exemple, de tubes de réacteur chimique dont on sait qu'ils sont fissurés sur une certaine profondeur.
Similar content being viewed by others
References
O.L. Bowie,Journal of Mathematics and Physics, 35 (1956) 60–71
O.L. Bowie & C.E. Freese,Engineering Fracture Mechanics, 4 (1972) 315–321
O.L. Bowie & D.M. Neal, “A Modified Mapping Collocation Technique for Accurate Calculation of Stress Intensity Factors”, Technical Report, AMMRC TR 69–28 (1969)
R.W.E. Shannon,International Journal of Pressure Vessels and Piping, 2 (1974) 19
G.R. Irwin,Journal of Applied Mechanics, Transactions of ASME, 84-Series F (1962) 651–654
J.R. Rice & N. levy, “The Part-Through Surface Crack in an Elastic Plate”, Technical Report, NASA NGL 40–002–080/3 (1970)
R.C. Shah & A.S. Kobayashi, inThe Surface Crack: Physical Problems and Computational Solutions (edited by J.L. Swedlow), ASME (1972) 79–124
F.W. Smith, ibid, loc. cit. 125–152
J.R. Rice, ibid, loc. cit. 171–185
J.H. Underwood, inStress Analysis and Growth of Crack, ASTM STP 513 (1972) 59–70
A.S. Kobayashi, N. Polvanich, A.F. Emery & W.J. Love, inComputational Fracture Mechanics (edited by E.F. Rybicki and S.E. Benzley), ASME (1975), 121–132
P.V. Marcal, inThe Surface Crack: Physical Problems and Computational Solutions (edited by J.L. Swedlow), ASME (1972), 187–202
M.F.S. Pereira, “Three Dimensional Linear Elastic Fracture Mechanics Analysis of Thick-Walled Pressure Vessel Components”, Ph.D. Thesis, University of London (1977)
W.S. Blackburn & T.K. Hellen, “Calculation of Stress Intensity Factors for Elliptical and Semi-Elliptical Cracks in Blocks and Cylinders”, Technical Report, CEGB RD/B/N3103 XE032 (1974)
W.S. Blackburn & T.K. Hellen,International Journal for Numerical Methods in Engineering, 11 (1977) 211–229
J.J. McGowan & M. Raymund, ASTM STP 677 (in press)
J. Heliot, R.C. Labbens & A. Pellissier-Tanon, ASTM STP 677 (in press)
N. Atluri & K. Kathiresan,Nuclear Engineering and Design, 51 (1979) 163–176
C.L. Tan & R.T. Fenner,Journal of Strain Analysis, 13 (1978) 213–219
T.A. Cruse, inThe Surface Crack: Physical Problems and Computational Solutions (edited by J.L. Swedlow), ASME (1972) 153–170
T.A. Cruse,Computers and Structures, 4 (1974) 741–754
T.A. Cruse & G.J. Meyers,Proceedings of American Society of Civil Engineers, Journal of Structures Division, 103 (1977) 309–320
T.A. Cruse & P.M. Besuner,Journal of Aircraft, 12 (1975) 369–375
J.M. Boissenot, inProceedings IAEA Symposium-Vienna (1977)
D. Lange, inProceedings of the 1st International Conference in Numerical Methods in Fracture Mechanics, Swansea (editors: A.R. Luxmore and D.R.J. Owen) (1978) 115–127
T.A. Cruse,International Journal of Solids and Structures, 5 (1969) 1259–1274
J.C. Lachat & J.O. Watson,International Journal for Numerical Methods in Engineering, 10 (1976) 991–1005
J.C. Lachat & J.O. Watson,Computer methods in Applied Mechanics and Engineering, 10 (1977) 273–289
S.K. Chan, I.S. Tuba & W.K. Wilson,Engineering Fracture Mechanics, 2 (1970) 1–17
R.H. Gallagher, inProceedings of the 1st International Conference in Numerical Methods in Fracture Mechanics, Swansea (editors: A.R. Luxmoore and D.R.J. Owen) (1978) 1–25
O.C. Zienkiewicz,The Finite Element Method, McGraw Hill (1977)
K. Nishioka & K. Hitawaka, inProceedings of 2nd International Conference on High Pressure Engineering, Brighton 1975 (edited by H.L.D. Pugh) (1977) 325–330
C.L. Tan & P.S.J. Crofton, Unpublished results
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tan, C.L., Fenner, R.T. Stress intensity factors for semi-elliptical surface cracks in pressurised cylinders using the boundary integral equation method. Int J Fract 16, 233–245 (1980). https://doi.org/10.1007/BF00013380
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00013380