Advertisement

Stochastic Cumulative Models for Fatigue

  • K. Sobczyk
Part of the International Centre for Mechanical Sciences book series (CISM, volume 334)

Abstract

This chapter is devoted to modelling of fatigue crack growth via cumulative jump stochastic processes. A wide class of such processes can be represented in the form of a stochastic integral with respect to counting Poisson measure in particular, such processes take a form of a random sum of random components. The cumulative jump processes are adopted as a model-process for fatigue crack growth in engineering materials subjected to random loading and other uncertainties. After brief presentation of the previous author’ results, the extension of the approach to a more general situation where elementary crack increments are mutually correlated is shown. The use of Morgenstern model for the joint probability distribution leads to approximate characterization of the crack size. The results quantify the effect of the correlation in crack’s increments on statistics of a crack size and show the features analogous to those in existing experimental data. In the last part of the chapter a stochastic cumulative jump model of fatigue crack growth with retardation is presented.

Keywords

Fatigue Crack Fatigue Crack Growth Crack Size Crack Growth Retardation Dependent Random Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Itagaki H. and Shinozuka M., Application of the Monte Carlo Technique to fatigue Analysis under Random Loading, in: Probabilistic Aspects of Fatigue (Ed. Heller R.A.) Amer. Soc. for Testing and Materials, STP511, Philadelphia, PA, 1972.Google Scholar
  2. 2.
    Sobczyk K. and Trebicki J., Modelling of Random Fatigue by Cumulative Jump Processes, Eng. Fract. Mech., Vol. 34, No. 2, pp. 477–493, 1989.CrossRefGoogle Scholar
  3. 3.
    Sobczyk K. and Trçbicki J., Cumulative Jump—Correlated Model for Fatigue, Eng. Fract. Mech., Vol. 40, No 1, pp. 201–210, 1991.CrossRefGoogle Scholar
  4. 4.
    Ditlevsen O. and Sobczyk K., Random Fatigue Crack Growth with Retardation, Eng. Fract. Mech., Vol. 34, No 2, pp. 861–878, 1986.CrossRefGoogle Scholar
  5. 5.
    Morgenstern D., Einfache Beispiele Zweidimensionaler Verteilungen, Miteilingsblatt fur Math. Statik, Vol. 8, pp. 234–235, 1956.MathSciNetMATHGoogle Scholar
  6. 6.
    Kotz S., Multivariate Distribution at a Cross Road, in: Statistical Distributions in Scientific Work (eds. Patial, G.P., et al.) Reidel Publ. Comp., Dordrecht, Vol. 1, pp. 247–270, 1975.Google Scholar
  7. 7.
    Liu P.L. and Der Kiureghian A., Multivariate Distribution Model with Prescribed marginals and Covariances, Probab. Eng, Mech., Vol. 1, No 2, pp. 105–112, 1986.Google Scholar
  8. 8.
    Virkler D.A., Hillberry B.M., and Goel P.K., The Statistical Nature of Fatigue Crack Propagation, Journal Eng. Material and Techn., ASME, Vol. 101, pp. 148–153, 1979.CrossRefGoogle Scholar
  9. 9.
    Sobczyk K. and Trgbicki J., Maximum Entropy Principle in Stochastic Dynamics, Prob. Eng. Mech., Vol. 5, No 3, 1990.Google Scholar
  10. 10.
    Crandall S.H. and Mark W.D., Random vibration in mechanical systems, Academic Press, New York, 1963.Google Scholar
  11. 11.
    Scharton T.D. and Crandall S.H., Fatigue failure under complex stress histories, Trans. ASME J. Basic Eng., Vol. 88, Ser. D., No 1, p. 247–251, 1966.CrossRefGoogle Scholar
  12. 12.
    Wei R.P. and Shih T.T., Delay in fatigue crack growth, Trans. ASME. J.Basic Eng., Ser. D., Vol. 94, No 1., p. 181–186, 1972.Google Scholar
  13. 13.
    Stouffer D.C. and Williams J.F., A model for fatigue crack growth with a variables stress intensity factor, Eng. Frac. Mech, Vol. 11 p. 525–536, 1979.CrossRefGoogle Scholar
  14. 14.
    Bernard P.J., Lindley T.C. and Richards C.E., Mechanisms of overload retardation during fatigue crack propagation, in: Fatigue Crack Growth under Spectrum Loads, ASTM STP 595, 1976.Google Scholar
  15. 15.
    Jones R.E., Fatigue crack growth retardation after single-cycle peak overload in Ti/6A1/4V titanium alloy, Eng. Fract. Mech., Vol. 5 pp. 585–604, 1973.CrossRefGoogle Scholar
  16. 16.
    Schijve J., Observations on the prediction of fatigue crack growth propagation under variable-amplitude loading, in: Fatigue Crack Growth under Spectrum Loads. ASTM STP 595, 1976.Google Scholar
  17. 17.
    Robin C., Louah M. and Pluvinage G., Influence of an overload on fatigue crack growth in steels, fatigue Eng. Mat. Struct., Vol. 6 p. 1–13, 1983.CrossRefGoogle Scholar
  18. 18.
    Porter T.R., Method of analysis and prediction for variable amplitude fatigue crack growth, Eng. Fract. Mech. Vol. 4 pp. 717–736, 1972.CrossRefGoogle Scholar
  19. 19.
    Broek D. and Smith S.H., The prediction of fatigue crack growth under flight-by-flight loading, Eng. Fracture Mech., Vol. 11, p. 123–141, 1979.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 1993

Authors and Affiliations

  • K. Sobczyk
    • 1
  1. 1.Polish Academy of SciencesWarsawPoland

Personalised recommendations