Asymptotic Behavior of a Strain Percolation Model for a Deforming Metal

  • Y. Shim
  • L. E. Levine
  • R. Thomson
  • D. E. Kramer
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 90)


In this paper, we present a recent advance in theoretical understanding of a deforming metal, using a strain percolation model which possibly explains spasmodic, fine slip line burst events occurring in the metal. The model addresses how the additional strain nucleated in a cell propagates through a dislocation cell structure, and predicts that near the critical point, the system exhibits critical power-law behavior. It is found that although the model displays long-transient behavior associated with the initial strain in the model, asymptotically critical behavior observed in the system is well explained by standard percolation theory. The long-transient behavior suggests that finite-size effects could be an important factor for the stress-strain relation in the metal. A detailed study reveals that the universal aspects of the model, i.e., the evolution into an initial condition- independent, critical state, arise from collective behavior of a huge number of self- organizing critical cells that develop the minimum or at least marginally stable strain


Slip Plane Total Strain Strained Cell Initial Strain Universal Behavior 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    D. Hull and D.J. Bacon: Introduction to dislocations (Butterworth-Heinemann, Woburn 1999)Google Scholar
  2. 2.
    M.-C. Miguel, A. Vespignani, S. Zapperi, J. Weiss, and J.-R. Grasso: Nature 410, 667 (2001)ADSCrossRefGoogle Scholar
  3. 3.
    J. Weiss, J.-R. Grasso, M.-C. Miguel, A. Vespignani, and S. Zapperi: Mater. Sci. Eng. A 309–310, 360 (2001)Google Scholar
  4. 4.
    M.-C. Miguel, A. Vespignani, S. Zapperi, J. Weiss, and J.-R. Grasso: Mater. Sci. Eng. A 309–310, 324 (2001)Google Scholar
  5. 5.
    J.G. Sevillano, I.O. Arizcorreta, and L.P. Kubin: Mater. Sci. Eng. A 309–310, 393 (2001)Google Scholar
  6. 6.
    S. Zapperi and M. Zaiser: Mater. Sci. Eng. A 309–310, 348 (2001)Google Scholar
  7. 7.
    H. Mughrabi, T. Ungar, W. Kienle, and M. Wilkens: Philos. Mag. A 53, 793 (1986)ADSCrossRefGoogle Scholar
  8. 8.
    L.P. Kubin, in Materials science and technology: a comprehensive treatment. Ed. by R.W. Cahn, P. Haasen, E.J. Kramer (VCH, Weinheim 1993) Vol.6, Chap. 4Google Scholar
  9. 9.
    P. Hähner, K. Bay, and M. Zaiser: Phys. Rev. Lett. 81, 2470 (1998)ADSCrossRefGoogle Scholar
  10. 10.
    I. Groma and B. Bako: Phys. Rev. Lett. 84, 1487 (2000)ADSCrossRefGoogle Scholar
  11. 11.
    M. Zaiser and P. Hähner: Mater. Sci. Eng. A 270, 299 (1999); M. Zaiser, K. Bay, and P. Hähner: Acta Mater. 47, 2463 (1999)CrossRefGoogle Scholar
  12. 12.
    P. Hähner: Acta Matter. 44, 2345 (1996); Appl. Phys. A 62, 473 (1996)CrossRefGoogle Scholar
  13. 13.
    M. Zaiser: Mater. Sci. Eng. A 309–310, 304 (2001)Google Scholar
  14. 14.
    R. Thomson and L.E. Levine: Phys. Rev. Lett. 81, 3884 (1998)ADSCrossRefGoogle Scholar
  15. 15.
    P. Bak, C. Tang, and K. Wiesenfeld: Phys. Rev. Lett. 59, 381 (1987)MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    R. Thomson, L.E. Levine, and D. Stauffer: Physica A 283, 307 (2000)ADSCrossRefGoogle Scholar
  17. 17.
    D. Stauffer and A. Aharony: Introduction to Percolation Theory. (Taylor and Francis, London 1994)Google Scholar
  18. 18.
    R. Thomson, L.E. Levine, and Y. Shim, to be published.Google Scholar
  19. 19.
    P.L. Leath: Phys. Rev. B 14, 5046 (1976)ADSCrossRefGoogle Scholar
  20. 20.
    Y. Shim, L.E. Levine, and R. Thomson: Mater. Sci. Eng. A 309–310, 340 (2001)Google Scholar
  21. 21.
    L.E. Levine, R. Thomson, M.F. Savage, D.E. Kramer, and Y. Shim: “Single-Crystal Plasticity: Statistical Physics and Experiments”, in Plasticity, Damage and Fracture at Macro, Micro and Nano Scales. Ed. by A.S. Khan and O. Lopez-Pamies (Neat Press, Fulton 2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Y. Shim
    • 1
    • 2
  • L. E. Levine
    • 2
  • R. Thomson
    • 2
  • D. E. Kramer
    • 2
  1. 1.Center for Simulation PhysicsUniversity of GeorgiaAhtensUSA
  2. 2.Materials Science and Engineering LaboratoryNational Institute of Standards and TechnologyGaithersburgUSA

Personalised recommendations