Sets of Multiple Cracks in Solids with Application to the Fatigue Life and Reliability Prediction

  • V. V. Bolotin
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)

Summary

A generalized probabilistic model is developed for the fatigue life and reliability prediction of structures containing a set of non-interacting cracks. The main point is a comprehensive use of the concept of Poisson random sets throughout all the stages of the analysis. The model includes both initial and newborn cracks and crack-wise defects. Macrocracks initiation is considered as a result of dispersed damage accumulation. Inspection, repair and replacement of structural elements are included into the consideration also. The resuts may be interpreted as a fargoing generalization of Weibull distribution [1].

Keywords

Fatigue Manifold Transportation 

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References

  1. 1.
    Weibull, W.: A statistical theory of strength of materials. Proc. Roy. Swedish Inst.Engng Res., Stockholm, 151 (1939).Google Scholar
  2. 2.
    Болотин, B. B.: Расределеление времен до разрушенения при случайных. Прикладная механика и техничоокая Физика (1980) 149–158Google Scholar
  3. 3.
    Болотин, B. B.: Статистические методы B строитөлъной механикө. Москва: Стройиздат 1961 (І-е изд.) 1965 (2-е изд.). Eng. transl.: Statistical methods in structural mechanics. San Francisco: Holden-Day 1969. German transi.: Wahrschheinlichkeitsmethoden zur Berechnung von Konstruktionen. Berlin: VEB Verlag fur Bauwesen 1981.Google Scholar
  4. 4.
    Болотин, B. B.: методы төории вөроятностей и теории надеҗности в расчетах сооруҗений. Москва: Стройиздат 1971 (І-е изд.) 1982 (2-e изд.). Engl.transi.: Bolotin, V.V.: Application of the methods of the theory of probability and the theory of reliability to analysis of structures. Springfield: NTIS US Dept of Commerce, 1974.Google Scholar
  5. 5.
    Bolotin, V.V.: Reliability of Structures. In: Trends in Solid Mechanics, Delft University Press 1979.Google Scholar
  6. 6.
    Болотин, B. B.: о σезопасних размерах трөшин при случайном нагруҗении. Известия АН СССР, Механика твердого тела (1980) 124–130Google Scholar
  7. 7.
    Когаев, B. П. :Расчеты на прочность при нагрузках, переменних во времени. Москва: Машиностроение 1977, 232.Google Scholar
  8. 8.
    Болотин, B. B.: О прогнозировании надеҗностд и долговөчности машин. Машиноведение (1977) 86–93.Google Scholar
  9. 9.
    Болотин, B. B.: Случайные колеσания упругих систем. Москва: Наука 1979.Google Scholar
  10. 10.
    Панасюк, B. B., Андройкив, А.Е., Ковчик, С.Е.: Методы опөнки трешиностоикости конструкпионых материалов. Киев: Наукова думка 1977.Google Scholar
  11. 11.
    Dover, W.D., Hibberd, R.D.: The influence of mean stress and amplitude distribution on random load fatigue crack growth. Engng Fracture Mech. 9 (1977) 251–263.CrossRefGoogle Scholar
  12. 12.
    Mc Cartney, L.N, Cooper, R.M.: A new method of analysing fatigue crack propagation data. Engng Fracture Mech. 9 (1979) 273–290.CrossRefGoogle Scholar
  13. 13.
    Bolotin, V.V.: Stochastic model of fracture with applications to the reliability theory. In: Structural Safety and Reliability/Eds. Moan, T., Shinozuka, M. Amsterdam, Oxford, New York: Elsevier 1981, 31–56.Google Scholar
  14. 14.
    Болотин, B. B.:уравнөния роста усталостных трешин. Известия АН СССР, Механика твердого төла, 4 (1983) 153–160.Google Scholar
  15. 15.
    Graham, T.W., Tetelman, A.S.: The use of crack size distribution and crack detection for determining the probability of fatigue failure. AIAA/ASME/SAE 15-th Structures, Structural Dynamics and Materials Conference. AIAA Paper N 74394 (1974).Google Scholar
  16. 16.
    Yang, J.-N., Trapp, W.J.: Reliability analysis of aircraft structures under random loading and periodic inspection. AIAA Journal 12 (1974) 1623–1630.Google Scholar
  17. 17.
    Jouris, G.M., Shaffer, D.H.: A procedure for estimating the probability of flaw nondetection. Nucl.Engng and Design 48 (1978) 517–521.CrossRefGoogle Scholar
  18. 18.
    Gallagher, J.P., Grandt, A.F.Jr., Crane, R.L.: Tracking potentional crack growth damage. Journal of Aircraft (1978) 435–442.Google Scholar
  19. 19.
    Heller, R.A., Stevens, G.H.: Bayesian estimation of crack initiation times from service data. Journal of Aircraft 15 (1978) 794–798.CrossRefGoogle Scholar
  20. 20.
    Fardis, M.N., Cornell, C.A.: Containment linear seismic reliability under statistical uncertainty. Nucl.Engng and Design 49 (1978) 279–294.CrossRefGoogle Scholar
  21. 21.
    Engesvik, K.N., Moan, T.: Probabilistic analysis of the uncertainty in the fatigue capacity of welded joints. Engng Fracture Mech. 18 (1983) 743–762.CrossRefGoogle Scholar
  22. 22.
    Schaller, G.L.: Impact of probability risk assessement of containment. Nucl. Engng and Design 69 (1983) 399–402.Google Scholar
  23. 23.
    Wirsching, P.H.: Fatigue reliability in welded joints of offshore structures. In: Proc. of 11-th Offshore Technology Conference, Houston 1979, 197–204.Google Scholar
  24. 24.
    Ditlevsen, O.: Reliability against defect generated fracture. Journal of Structural Mechanics 9 (1981) 115–137.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag, Berlin, Heidelberg 1985

Authors and Affiliations

  • V. V. Bolotin
    • 1
  1. 1.Institute of Mechanical EngineeringUSSR Academy of SciencesMoscowRussia

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