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Strength of Materials

, Volume 49, Issue 6, pp 760–768 | Cite as

Probabilistic Distribution of Crack Length in the Case of Multiple Fracture

  • S. R. IgnatovichEmail author
  • V. S. Krasnopol’skii
Article
  • 49 Downloads

A model describing crack length distribution is proposed on the basis of experimental laws governing the formation and growth of fatigue cracks in a flat specimen with multiple stress raisers. The density of this distribution corresponds to that of Pareto and can be used to describe the accumulation of scattered defects in a wide range of cracking scale. The critical values of Pareto distribution exponent, which correspond to the limit states of the multiple fracture of solid bodies, have been substantiated.

Keywords

multiple fracture formation and growth of fatigue cracks crack length distribution crack coalescence 

References

  1. 1.
    L. R. Botvina and G. I. Barenblatt, “Self-similarity of damage cumulation,” Strength Mater., 17, No. 12, 1653–1663 (1985).CrossRefGoogle Scholar
  2. 2.
    L. R. Botvina, Fracture Kinetics of Structural Materials [in Russian], Nauka, Moscow (1989).Google Scholar
  3. 3.
    L. R. Botvina, Fracture: Kinetics, Mechanisms, General Laws [in Russian], Nauka, Moscow (2008).Google Scholar
  4. 4.
    A. Carpinteri, G. Lacidogna, and S. Puzzi, “Prediction of cracking evolution in full scale structures by the b-value analysis and Yule statistics,” Fiz. Mesomekh., 11, No. 3, 75–87 (2008).Google Scholar
  5. 5.
    V. V. Bolotin, Life of Machines and Structures [in Russian], Mashinostroenie, Moscow (1990).Google Scholar
  6. 6.
    S. R. Ignatovich and N. I. Bouraou, “The reliability of detecting cracks during nondestructive testing of aircraft components,” Russ. J. Nondestruct. Test., 49, No. 5, 294–300 (2013).CrossRefGoogle Scholar
  7. 7.
    S. R. Ignatovich, “Predicting the merging of disperse defects,” Strength Mater., 24, No. 2, 202–211 (1992).Google Scholar
  8. 8.
    S. R. Ignatovich, A. G. Kucher, A. S. Yakushenko, and A. V. Bashta, “Modeling of coalescence of dispersed surface cracks. Part 1. Probabilistic model for crack coalescence,” Strength Mater., 36, No. 2, 125–133 (2004).CrossRefGoogle Scholar
  9. 9.
    S. R. Ignatovich, “Probabilistic model of multiple-site fatigue damage of riveting in airframes,” Strength Mater., 46, No. 3, 336–344 (2014).CrossRefGoogle Scholar
  10. 10.
    S. R. Ignatovich and E. V. Karan, “Fatigue crack growth kinetics in D16AT aluminum alloy specimens with multiple stress concentrators,” Strength Mater., 47, No. 4, 586–594 (2015).CrossRefGoogle Scholar
  11. 11.
    V. T. Troshchenko and L. A. Khamaza, Mechanics of Nonlocalized Fatigue Damage of Metals and Alloys [in Russian], Pisarenko Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev (2016).Google Scholar
  12. 12.
    S. Barter, L. Molent, N. Goldsmith, and R. Jones, “An experimental evaluation of fatigue crack growth,” Eng. Fail. Anal., 12, 99–128 (2005).CrossRefGoogle Scholar
  13. 13.
    L. Molent, R. Jones, S. Barter, and S. Pitt, “Recent developments in fatigue crack growth assessment,” Int. J. Fatigue, 28, 1759–1768 (2006).CrossRefGoogle Scholar
  14. 14.
    D. A. Virkler, B. M. Hillberry, and P. K. Goel, “The statistical nature of fatigue crack propagation,” J. Eng. Mater. Technol., 101, No. 2, 148–153 (1979).CrossRefGoogle Scholar
  15. 15.
    Y. C. Tong, Literature Review on Aircraft Structural Risk and Reliability Analysis, Technical Report DSTO-TR-1110, Aeronautical and Maritime Research Laboratory (2001).Google Scholar
  16. 16.
    S. R. Ignatovich, E. V. Karan, and V. S. Krasnopol’skii, “Crack length distribution in a riveted joint of on aircraft structure in the case of multiple site damage,” Fiz.-Khim. Mekh. Mater., 49, No. 2, 109–116 (2013).Google Scholar
  17. 17.
    S. R. Ignatovich, “Distribution of defect dimensions in loading solids,” Strength Mater., 22, No. 9, 1295–1301 (1990).CrossRefGoogle Scholar
  18. 18.
    I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products [in Russian], Nauka, Moscow (1971).Google Scholar
  19. 19.
    M. E. J. Newman, “Power laws, Pareto distributions and Zipf’s law,” Contemp. Phys., 46, No. 5, 323–351 (2005).CrossRefGoogle Scholar
  20. 20.
    V. A. Vladimirov, Yu. L. Vorob’ev, G. G. Malinetskii, et al., Risk Control. Risk, Sustainable Development, and Synergetics [in Russian], Nauka, Moscow (2000).Google Scholar
  21. 21.
    A. Carpinteri, G. Lacidogna, G. Niccolini, and S. Puzzi, “Critical defect size distributions in concrete structures detected by the acoustic emission technique,” Meccanica, 43, 349–363 (2008).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.National Aviation UniversityKievUkraine

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