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Shapes of Deterministic Cracks Obtained under Shear

  • H. J. Herrmann
Chapter
Part of the Ettore Majorana International Science Series book series (EMISS)

Abstract

Cracks are grown in a system submitted to external shear by solving the full Lamé equation on a two-dimensional lattice. One finds that deterministic fracture patterns are in general branched and can be fractal. This effect is due to the competition between the direction of global stress and the local growth direction imposed by the lattice anisotropy.

Keywords

Fractal Dimension Stress Corrosion Global Stress Break Beam Memory Factor 
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References

  1. 1.
    See e.g. H. Liebowitz (ed.), Fracture, Vols. I–VII, (Academic Press, New York, 1984)Google Scholar
  2. 2.
    H.J. Herrmann in Random Fluctuations and Pattern Growth, eds. H.E. Stanley and N. Ostrowsky (Kluwer, Dordrecht, 1988), p.149CrossRefGoogle Scholar
  3. 3.
    L. de Arcangelis, S. Redner and H.J. Herrmann, J. Physique Lett. 46, L585 (1985)CrossRefGoogle Scholar
  4. P.M. Duxbury, P.D. Beale and P.L. Leath, Phys. Rev. Lett. 57, 1052 (1986)PubMedCrossRefGoogle Scholar
  5. P.M. Duxbury and P.L. Leath, J. Phys. A 20, L411 (1987)CrossRefGoogle Scholar
  6. P.D. Beale and D.J. Srolovitz, Phys. Rev. B 37, 5500 (1988) and references thereinCrossRefGoogle Scholar
  7. 4.
    B. Kahng, G.G. Batrouni, S. Redner, L. de Arcangelis and H.J. Herrmann, Phys. Rev. B 37, 7625 (1988)CrossRefGoogle Scholar
  8. H.J. Herrmann, A. Hansen and S. Roux, Phys. Rev. B 39, 637 (1989) and references thereinCrossRefGoogle Scholar
  9. 5.
    T.A. Witten and L.M. Sander, Phys. Rev. Lett. 47, 1400 (1981)CrossRefGoogle Scholar
  10. L. Niemeyer, L. Pietronero and H.J. Wiesmann, Phys. Rev. Lett. 52, 1033 (1984)CrossRefGoogle Scholar
  11. 6.
    E. Louis, F. Guinea and F. Flores in Fractals in Physics eds. L. Pietronero and E. Tossatti (Elsevier, Amsterdam, 1986), p.117Google Scholar
  12. E. Louis and F. Guinea, Europhys. Lett. 3, 871 (1987)CrossRefGoogle Scholar
  13. 7.
    E.L. Hinrichsen, A. Hansen and S. Roux, Europhys. Lett. 8, 1 (1989); P. Meakin, G. Li, L.M. Sander, E. Louis and F. Guinea, J.Phys. A to be publishedCrossRefGoogle Scholar
  14. 8.
    L.D. Landau and E.M. Lifshitz, Theory of Elasticity (Pergamon, Oxford, 1986)Google Scholar
  15. 9.
    S. Roux and E. Guyon, J. Physique Lett. 46, L999 (1985)CrossRefGoogle Scholar
  16. 10.
    G.G. Batrouni and A. Hansen, J. Stat. Phys. 52, 747 (1988)CrossRefGoogle Scholar
  17. 11.
    C. Tang, Phys. Rev. A, 31, 1977 (1985)PubMedCrossRefGoogle Scholar
  18. J. Szép, J. Cserti and J. Kertész, J. Phys. A 18, L413 (1985)Google Scholar
  19. J. Nittmann and H.E. Stanley, Nature 321, 661 (1986)CrossRefGoogle Scholar
  20. 12.
    J. Kertész and T. Vicsek, J. Phys. A 19, L257 (1986)CrossRefGoogle Scholar
  21. 13.
    J. Fernandez, F. Guinea and E. Louis, J. Phys. A 21, L301 (1988)CrossRefGoogle Scholar
  22. 14.
    B.B. Mandelbrot and T. Vicsek, J. Phys. A to be publishedGoogle Scholar
  23. 15.
    H.J. Herrmann, J. Kertész and L. de Arcangelis, in preparationGoogle Scholar
  24. 16.
    F. Family, D.E. Platt and T. Vicsek, J. Phys. A 20, L1177 (1987)CrossRefGoogle Scholar
  25. 17.
    J.P. Eckmann, P. Meakin, I. Procaccia and R. Zeitak, Phys. Rev. A preprintGoogle Scholar
  26. 18.
    M.J. Blackburn, W.H. Smyrl and J.A. Feeney, in Stress Corrosion in High Strength Steels and in Titanium and Aluminium Alloys, ed. B.F. Brown (Naval Res. Lab., Washington, 1972), p.344Google Scholar
  27. 19.
    H. Takayasu in Fractals in Physics, eds. L. Pietronero and E. Tossatti (Elsevier, Amsterdam, 1986), p. 181Google Scholar
  28. H. Takayasu, Phys. Rev. Lett. 54, 1099 (1985)PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1989

Authors and Affiliations

  • H. J. Herrmann
    • 1
  1. 1.SPhTCEN SaclayGif sur YvetteFrance

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