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Inverse method for identifying the underlying crack distribution in plates with random strengths

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Summary

In the current investigation we seek to identify the underlying crack number and crack length distributions in brittle plates with a known strength distribution. The inverse problem in probabilistic fracture mechanics is defined, and the numerical procedure to solve the inverse problem is constructed. The simulation process of generating simulated plates containing simulated random cracks is elaborated. The maximum strain energy release rate criterion (G max) is applied to each simulated random crack to find the crack strength. The strength of the simulated plate is equated to the strength of the weakest simulated crack in the plate based on the weakest link notion. The underlying crack number and crack length distributions are obtained by minimizing the difference between the simulated plate strengths and the known plate strengths. The gamma, lognormal and two-parameter Weibull distributions are employed for the underlying crack length distribution, and are compared in order to identify the best choice. Numerical examples demonstrate that the three PDFs are all acceptable for reasons to be explained. In the appendix, the direct problem in probabilistic fracture mechanics is presented as part of the demonstration of a method for using the crack distribution identified in the inverse problem to predict the strength and the probability of fracture in a practical application.

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References

  1. Jayatilaka, A. De S., Trustrum, K.: Statistical approach to brittle fracture. J. Material Sci.12, 1426–1430 (1977).

    Google Scholar 

  2. Jayatilaka, A. De S., Trustrum, K.: Application of a statistical method to brittle fracture in biaxial loading systems. J. Material Sci.12, 2043–2048 (1977).

    Google Scholar 

  3. Nicholson, D. W., Ni, P.: Extreme value probabilistic theory for mixed-mode brittle fracture. Engng. Fract. Mech.58, 121–132 (1977).

    Google Scholar 

  4. Ahn, Y., Nicholson, D. W.: Probabilistic theory of mixed-mode fracture in brittle plates with random cracks. Proc. Int. Conf. Fracture and Damage Mech. (M. Aliabadi, ed). University of London 1999.

  5. Ahn, Y., Nicholson, D. W.: Probabilistic theory of fracture in brittle plates with random cracks, including scatter inK IC. Submitted for publication.

  6. Ni, P.: Probabilistic theory for mixed-mode brittle fracture and fatigue with random cracks, Ph. D. Dissertation, University of Central Florida 1996.

  7. Sih, G. C.: Strain energy density factor applied to mixed mode crack problems. Int. J. Fract.10, 305–321 (1974)

    Google Scholar 

  8. Shi, G. C., Macdonald, B.: Fracture mechanics applied to engineering problems — Strain energy density criterion. Engng. Fract. Mech.6, 361–386 (1974).

    Google Scholar 

  9. Hudak, S. J., et al.: A. comparison of single-cycle versus multiple-cycle proof testing strategies. NASA Contractor Report No. 4318, Washington D. C., 1990.

  10. Harris, D. O.: Probabilistic fracture mechanics. In: Probabilistic structural mechanics handbook (C. Sundararajan, ed.). New York: Chapman and Hall 1995.

    Google Scholar 

  11. Ichikawa, M., Tanaka, S.: A critical analysis of the relationship between the energy release rate and the stress intensity factors for non-coplanar crack extension under combined mode loading. Int. J. Fract.18, 19–28 (1982).

    Google Scholar 

  12. Ahn, Y., Nicholson, D. W.: Mixed-mode fracture by maximum strain energy release rate criterion, In: Proc. 1st Canadian Conference on Nonlinear Solid Mechanics (Croitoro, E., ed.), Victoria, Canada, July 1999. Victoria: University of Victoria Press 1999.

    Google Scholar 

  13. Erdogan, F., Sih, G. C.: On the crack extension in plates under loading and transverse shear. ASME J. Basic Engng85, 519–527 (1963).

    Google Scholar 

  14. Mann, N. R., Schafer, R. E., Singpurwalla, N. D.: Methods for statistical analysis of reliability and life data. New York: Wiley 1974.

    Google Scholar 

  15. McClave, J. T. et al.: Statistics. New Jersey: Prentice-Hall 1997.

    Google Scholar 

  16. Knuth, D. E.: Seminumerical algorithms. New Jersey: Addison-Wesley 1981.

    Google Scholar 

  17. Press, W. H. et al.: Numerical recipes in C. Cambridge: Cambridge University Press 1988.

    Google Scholar 

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Author notes

  1. Y. Ahn, D. W. Nicholson, M. C. Wang & P. Ni

    Present address: Department of Mechanical, Materials and Aerospace Engineering, University of Central Florida, 32816, Orlando, FI, USA

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    1. Y. Ahn
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    2. D. W. Nicholson
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    3. M. C. Wang
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    4. P. Ni
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    Ahn, Y., Nicholson, D.W., Wang, M.C. et al. Inverse method for identifying the underlying crack distribution in plates with random strengths. Acta Mechanica 144, 137–154 (2000). https://doi.org/10.1007/BF01170171

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