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The European Physical Journal Special Topics

, Volume 146, Issue 1, pp 341–356 | Cite as

Slow crack growth: Models and experiments

  • S. Santucci
  • L. Vanel
  • S. CilibertoEmail author
Article

Abstract.

The properties of slow crack growth in brittle materials are analyzed both theoretically and experimentally. We propose a model based on a thermally activated rupture process. Considering a 2D spring network submitted to an external load and to thermal noise, we show that a preexisting crack in the network may slowly grow because of stress fluctuations. An analytical solution is found for the evolution of the crack length as a function of time, the time to rupture and the statistics of the crack jumps. These theoretical predictions are verified by studying experimentally the subcritical growth of a single crack in thin sheets of paper. A good agreement between the theoretical predictions and the experimental results is found. In particular, our model suggests that the statistical stress fluctuations trigger rupture events at a nanometric scale corresponding to the diameter of cellulose microfibrils.

Keywords

Stress Intensity Factor Crack Length European Physical Journal Special Topic Critical Length Free Energy Density 
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.

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References

  1. H.J. Herrmann, S. Roux, Statistical Models for the Fracture of Disordered Media (Elsevier, Amsterdam, 1990) Google Scholar
  2. M.J. Alava, P.K.N.N. Nukala, S. Zapperi, Adv. Phys. 55, 349 (2006) Google Scholar
  3. S.S. Brenner, J. Appl. Phys. 33, 33 (1962) Google Scholar
  4. S.N. Zhurkov, Int. J. Fract. Mech. 1, 311 (1965) Google Scholar
  5. L. Golubovic, S. Feng, Phys. Rev. A 43, 5223 (1991) Google Scholar
  6. Y. Pomeau, C.R. Acad. Sci. Paris II 314, 553 (1992); C.R. Mécanique 330, 1 (2002) Google Scholar
  7. A. Buchel, J.P. Sethna, Phys. Rev. Lett. 77, 1520 (1996); Phys. Rev. E 55, 7669 (1997) Google Scholar
  8. K. Kitamura, I.L. Maksimov, K. Nishioka, Phil. Mag. Lett. 75, 343 (1997) Google Scholar
  9. S. Roux, Phys. Rev. E 62, 6164 (2000) Google Scholar
  10. R. Scorretti, S. Ciliberto, A. Guarino, Europhys. Lett. 55, 626 (2001) Google Scholar
  11. S. Santucci, L. Vanel, R. Scorretti, A. Guarino, S. Ciliberto, Europhys. Lett. 62, 320 (2003) Google Scholar
  12. R.A. Schapery, Encyclopedia of Material Science and Engineering (Pergamon, Oxford, 1986), p. 5043 Google Scholar
  13. J.S. Langer, Phys. Rev. Lett. 70, 3592 (1993) Google Scholar
  14. A. Chudnovsky, Y. Shulkin, Int. J. Fract. 97, 83 (1999) Google Scholar
  15. P. Paris, F. Erdogan, J. Basic Eng. 89, 528 (1963) Google Scholar
  16. A.A. Griffith, Phil. Trans. Roy. Soc. Lond. A 221, 163 (1920) Google Scholar
  17. B. Lawn, T. Wilshaw, Fracture of Brittle Solids (Cambridge University Press, Cambridge, 1975) Google Scholar
  18. L. Pauchard, J. Meunier, Phys. Rev. Lett. 70, 3565 (1993) Google Scholar
  19. S. Ciliberto, A. Guarino, R. Scorretti, Physica D 158, 83 (2001) Google Scholar
  20. B. Diu, C. Guthmann, D. Lederer, B. Roulet, Physique Statistique (Herrmann, Paris, 1989), p. 272 Google Scholar
  21. M. Marder, Phys. Rev. E 54, 3442 (1996) Google Scholar
  22. R. Thomson, Solid State Physics, edited by H. Ehrenreich, D. Turnbull (Academic, New York, 1986), vol. 39, p. 1 Google Scholar
  23. D. Stauffer, Introduction to Percolation Theory (Taylor & Francis, London, 1991) Google Scholar
  24. S. Santucci, P.-P. Cortet, S. Deschanel, L. Vanel, S. Ciliberto, Europhys. Lett. 74, 595 (2006) Google Scholar
  25. S. Santucci, L. Vanel, S. Ciliberto, Phys. Rev. Lett. 93, 095505 (2004) Google Scholar
  26. A. Guarino, S. Ciliberto, A. Garcimartìn, Europhys. Lett. 47, 456 (1999) Google Scholar
  27. H.F. Jakob, S.E. Tschegg, P. Fratzl, J. Struct. Biol. 113, 13 (1994) Google Scholar
  28. P.-P. Cortet, L. Vanel, S. Ciliberto, Europhys. Lett. 74, 602 (2006) Google Scholar
  29. J. Kierfeld, V.M. Vinokur, Phys. Rev. Lett. 96, 175502 (2006) Google Scholar
  30. E. Bouchbinder, I. Procaccia, S. Santucci, L. Vanel, Phys. Rev. Lett. 96, 055509 (2006) Google Scholar
  31. S. Santucci, K.J. Måloy, A. Delaplace, J. Mathiesen, A. Hansen, J.O. Haavig Bakke, J. Schmittbuhl, L. Vanel, P. Ray, Phys. Rev. E. 75, 016104 (2007) Google Scholar
  32. F. Bueche, J. App. Phys. 28, 784 (1957) Google Scholar
  33. N. Mallick, P.-P. Cortet, S. Santucci, S. Roux, L. Vanel, Phys. Rev. Lett. (2006) (submitted) Google Scholar
  34. P.P. Cortet, S. Santucci, L.Vanel, S. Ciliberto, Europhys. Lett. 71, 1 (2005) Google Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  1. 1.Laboratoire de Physique, CNRS UMR 5672Lyon Cedex 07France

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