A Unified Variable-Amplitude Model for Crack Initiation and Crack Propagation

  • A. B. Chattopadhyay
  • G. Glinka
Conference paper


Fatigue crack growth under variable amplitude loading is of interest to the aerospace industry as the number of ageing aircraft in use rises. The model proposed in this paper aims to provide accurate fatigue crack growth estimates from the crack initiation phase through to final failure. Most variable amplitude fatigue crack growth models require tuning with variable amplitude fatigue crack growth data in order to provide reliable estimates for fatigue life [1, 2]. The model proposed in this paper requires only constant amplitude fatigue crack growth data in order to operate, and therefore requires much less material testing before it can be used to provide a good fatigue crack growth estimate.

The model describes the crack as having a blunted tip of radius r*, and uses the Smith-Watson-Topper model to calculate the fatigue damage in r* sized elements ahead of the crack tip. Whenever the damage in one of these elements reaches the value of one, the element breaks, and the crack is extended. The r* value is a constant for a given material in a given environment; for example: steel in air, or aluminum in salt water.

The residual stress field affecting the crack tip is what allows for the model to account for variable amplitude loading. The paper outlines a set of five rules which determine which loading cycles affect the residual stress field. By taking the residual stress field generated by each successive loading cycle into account, the model gains a structural memory. This structural memory combined with the material memory provided by the fatigue damage in the r* sized material blocks allows the model to handle a wide array of variable amplitude loading spectra.

Since the proposed fatigue crack growth model uses the Smith-Watson-Topper fatigue damage parameter to propagate the crack, it is capable of growing a crack from a r* sized notch on the order of a few microns through to the final failure. A short crack correction factor is also used, which provides a smooth transition from the short crack to long crack fatigue crack regimes.


Fatigue Life Fatigue Crack Growth Fatigue Damage Residual Stress Field Crack Increment 
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  1. 1.
    Newman, J.C.: Prediction of fatigue crack growth under variable amplitude and spectrum loading using a closure model. In: ASTM STP, vol. 761, pp. 255–277. American Society for Testing and Materials (1982)Google Scholar
  2. 2.
    Suresh, S.: Fatigue of Materials. Cambridge University Press, Cambridge (1991)Google Scholar
  3. 3.
    Landgraf, R.W., Morrow, J.D., Endo, T.: Journal of Materials 4(1), 176 (1969)Google Scholar
  4. 4.
    Smith, K.N., Watson, P., Topper, T.H.: Journal of Materials 5(4), 767–778 (1970)Google Scholar
  5. 5.
    Creager, M., Paris, P.C.: International Journal of Fatigue 3, 247–251 (1967)Google Scholar
  6. 6.
    Glinka, G.: Engineering Fracture Mechanics 21(2), 245–261 (1985)CrossRefGoogle Scholar
  7. 7.
    Lal, D.N., Weiss, V.: Metallurgical Transactions 9A, 413–426 (1978)Google Scholar
  8. 8.
    Majumder, S., Morrow, J.D.: Fracture Toughness and Slow-stable Cracking. In: STP, vol. 559, pp. 159–182. American Society for Testing and Materials (1974)Google Scholar
  9. 9.
    Chakrabortty, S.B.: Fatigue of Engineering Materials and Structures 2, 331–344 (1979)CrossRefGoogle Scholar
  10. 10.
    Glinka, G.: International Journal of Fatigue 4, 59–67 (1982)CrossRefGoogle Scholar
  11. 11.
    Irwin, G.R.: Journal of Applied Mechanics 24, 109–114 (1957)Google Scholar
  12. 12.
    Neuber, H.: Kerbspannungslehre. Springer, Berlin (1958)zbMATHGoogle Scholar
  13. 13.
    Harris, W.J.: Metallic Fatigue. Pergamon Press, London (1961)Google Scholar
  14. 14.
    Forsyth, P.J.: International Journal of Fatigue 5, 3–14 (1983)CrossRefGoogle Scholar
  15. 15.
    Glinka, G., Noroozi, A.H., Lambert, S.: International Journal of Fatigue 29, 1616–1634 (2007)zbMATHCrossRefGoogle Scholar
  16. 16.
    Mikheevskiy, S.: Elastic-Plastic Fatigue Crack Growth Analysis Under Variable Amplitude Loading Spectra. University of Waterloo, Waterloo (2009)Google Scholar
  17. 17.
    Mikheevskiy, S., Glinka, G.: International Journal of Fatigue 31, 1828–1836 (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • A. B. Chattopadhyay
    • 1
  • G. Glinka
    • 1
  1. 1.University of WaterlooCanada

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