Advertisement

Burst Statistics as a Criterion for Imminent Failure

  • Srutarshi Pradhan
  • Alex Hansen
  • Per C. Hemmer
Part of the Iutam Bookseries book series (IUTAMBOOK, volume 10)

Abstract

The distribution of the magnitudes of damage avalanches during a failure process typically follows a power law. When these avalanches are recorded close to the point at which the system fails catastrophically, we find that the power law has an exponent which differs from the one characterizing the size distribution of all avalanches. We demonstrate this analytically for bundles of many fibers with statistically distributed breakdown thresholds for the individual fibers. In this case the magnitude distribution Δ for the avalanche size Δ follows a power law Δ with ξ=3/2 near complete failure, and ξ=5/2 elsewhere. We also study a network of electric fuses, and find numerically an exponent 2.0 near breakdown, and 3.0 elsewhere. We propose that this crossover in the size distribution may be used as a signal for imminent system failure.

Keywords

Failure fiber bundle model fuse model burst statistics crossover 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    H. J. Herrmann and S. Roux (Eds.) Statistical Models for the Fracture of Disordered Media (Elsevier, Amsterdam, 1990).Google Scholar
  2. 2.
    B. K. Chakrabarti and L. G. Benguigui Statistical Physics and Breakdown in Disordered Systems (Oxford University Press, Oxford, 1997).zbMATHGoogle Scholar
  3. 3.
    D. Sornette, Critical Phenomena in Natural Sciences, Springer-Verlag, Berlin (2000).zbMATHGoogle Scholar
  4. 4.
    M. Sahimi, Heterogeneous Materials II: Nonlinear and Breakdown Properties,Springer-Verlag, Berlin (2003).zbMATHGoogle Scholar
  5. 5.
    P. Bhattacharyya and B. K. Chakrabarti (Eds), Modelling Critical and Catastrophic Phenomena in Geoscience, Springer, Berlin (2006).zbMATHGoogle Scholar
  6. 6.
    A. Petri, G. Paparo, A. Vespignani, A. Alippi, and M. Costantini, Phys. Rev. Lett 73, 3423 (1994).CrossRefGoogle Scholar
  7. 7.
    A. Garcimartin, A. Guarino, L. Bellon, and S. Ciliberto, Phys. Rev. Lett. 79, 3202 (1997).CrossRefGoogle Scholar
  8. 8.
    S. Pradhan, A. Hansen, and P. C. Hemmer, Phys. Rev. Lett. 95, 125501 (2005).CrossRefGoogle Scholar
  9. 9.
    S. Pradhan, A. Hansen, and P. C. Hemmer, Phys. Rev. E 74, 026106 (2006).CrossRefMathSciNetGoogle Scholar
  10. 10.
    F. T. Peirce, J. Text. Ind. 17, 355 (1926).Google Scholar
  11. 11.
    H. E. Daniels, Proc. R. Soc. Lond. A183, 405 (1945).MathSciNetGoogle Scholar
  12. 12.
    R. L. Smith, Ann. Prob. 10, 137 (1982).zbMATHCrossRefGoogle Scholar
  13. 13.
    S. L. Phoenix and R. L. Smith, Int. J. Sol. Struct. 19, 479 (1983).zbMATHCrossRefGoogle Scholar
  14. 14.
    P. C. Hemmer and A. Hansen, ASME J. Appl. Mech. 59, 909 (1992).zbMATHCrossRefGoogle Scholar
  15. 15.
    M. Kloster, A. Hansen, and P. C. Hemmer, Phys. Rev. E 56, 2615 (1997).CrossRefGoogle Scholar
  16. 16.
    S. Pradhan, P. Bhattacharyya, and B. K. Chakrabarti, Phys. Rev. E 66 016116 (2002).CrossRefGoogle Scholar
  17. 17.
    P. Bhattacharyya, S. Pradhan, and B. K. Chakrabarti, Phys. Rev. E 67, 046122 (2003).CrossRefMathSciNetGoogle Scholar
  18. 18.
    R. C. Hidalgo, Y. Moreno, F. Kun, and H. J. Herrmann, Phys. Rev. E 65, 046148 (2002).CrossRefGoogle Scholar
  19. 19.
    A. Hansen and P. C. Hemmer, Trends Stat. Phys. 1,213 (1994).Google Scholar
  20. 20.
    S. Zapperi, P. Ray, H. E. Stanley, and A. Vespignati, Phys. Rev. Lett. 85, 2865 (2000).Google Scholar
  21. 21.
    H. Kawamura, arXiv: cond-mat/0603335 (2006).Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Srutarshi Pradhan
    • 1
  • Alex Hansen
  • Per C. Hemmer
  1. 1.Department of PhysicsNorwegian University of Science and TechnologyN–7491 TrondheimNorway

Personalised recommendations