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Finite Fracture Mechanics for Fractal Cracks

  • Arash Yavari
  • Michael P. Wnuk
Conference paper
Part of the Iutam Bookseries book series (IUTAMBOOK, volume 10)

Abstract

We extend the recently developed Quantized Fracture Mechanics (QFM) by Pugno and Ruoff (2004) for fractal cracks. Using an equivalent smooth blunt crack for a given fractal crack, we show that assuming that radius of curvature of the corresponding blunt crack is a material property, the crack roughens while propagating, i.e., fractal dimension at the crack tip is a monotonically increasing function of the nominal crack length. In other words, the presence of the Mirror-Mist-Hackle phenomenon for fractal cracks is analytically demonstrated.

Keywords

Fractal Dimension Stress Intensity Factor Crack Length Energy Release Rate Short Crack 
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. 1.
    Balankin, A.S. (1997). Physics of fracture and mechanics of self-affine cracks. Engineering Fracture Mechanics, 57(2),135–203.Google Scholar
  2. 2.
    Barenblatt, G. I. (1987), Dimensional Analysis, Gordon and Breach, New York.Google Scholar
  3. 3.
    Bažant, Z. P. and Yavari, A. (2005) Is the cause of size effect on structural strength fractal or energetic-statistical? Engineering Fracture Mechanics, 72:1-31.CrossRefGoogle Scholar
  4. 4.
    Borodich, F.M. (1992). Fracture energy in a fractal crack propagating in concrete or rock. Doklady Akademii Nauk, 325, 1138–1141.Google Scholar
  5. 5.
    Borodich, F.M. (1997). Some fractal models of fracture. Journal of the Mechanics and Physics of Solids, 45(2),239–259.zbMATHCrossRefGoogle Scholar
  6. 6.
    Cherepanov, G. P., Balankin, A.S., and Ivanova, V. S. (1995). Fractal fracture mechanics – A review. Engineering Fracture Mechanics, 51(6),997–1033.CrossRefGoogle Scholar
  7. 7.
    Cornetti, P., Pugno, N., Carpinteri, A. and Taylor, D. (2006) Finite fracture mechanics: A coupled stress and energy failure criterion. Engineering Fracture Mechanics, 73:2021-2033.CrossRefGoogle Scholar
  8. 8.
    Creager, M. and Paris, P.C. (1967). Elastic field equations for blunt cracks with reference to stress corrosion cracking. International Journal of Fracture, 3,247–252.Google Scholar
  9. 9.
    Goldshteˇn, R.V. and Mosolov, A.A. (1992). Cracks with a fractal surface. Soviet Physics Doklady, 38(8),603–605.Google Scholar
  10. 10.
    Goldshteˇn, R.V. and Mosolov, A.A. (1991). Fractal cracks. Journal of Applied Mathematics and Mechanics, 56(4),563–571.CrossRefGoogle Scholar
  11. 11.
    Griffith, A.A. (1921). The phenomenon of rupture and flow in solids. Philosophical Transactions of the Royal Society of London, A221,163–198.Google Scholar
  12. 12.
    Ippolito, M., Mattoni, A., Colombo, L. and Pugno, N. (2006) Role of lattice discreteness on brittle fracture: Atomistic simulations versus analytical models. Physical Review B, 73:104111.CrossRefGoogle Scholar
  13. 13.
    Irwin, G.R. (1958). Fracture I, Handbuck der Physik VI, Flügge Ed., 558–590, Springer.Google Scholar
  14. 14.
    Mosolov, A.A. (1991). Cracks with fractal surfaces. Dokl. Akad. Nauk SSSR, 319(4),840–844.MathSciNetGoogle Scholar
  15. 15.
    Novozhilov, V.V. (1969) On a necessary and sufficient criterion for brittle strength. Journal of Applied Mathematics and Mechanics-USSR, 33:212-222.Google Scholar
  16. 16.
    Orowan, E. (1955) Energy criteria of fracture. Welding Journal, 34: S157-S160.Google Scholar
  17. 17.
    Pugno, N. and Ruoff, R. S. (2004). Quantized fracture mechanics. Philosophical Magazine, 84(27),2829–2845.CrossRefGoogle Scholar
  18. 18.
    Pugno, N., Peng, B. and Espinosa, H. D. (2005) Predictions of strength in MEMS components with defects - a novel experimental-theoretical approach. International Journal of Solids and Structures, 42:647-661.zbMATHCrossRefGoogle Scholar
  19. 19.
    Pugno, N. (2006) Dynamic quantized fracture mechanics. International Journal of Fracture, 140:159-168.zbMATHCrossRefGoogle Scholar
  20. 20.
    Taylor, D. and Cornetti, P. and Pugno, N. (2005) The fracture mechanics of finite crack extension. Engineering Fracture Mechanics, 72:1021-1038.CrossRefGoogle Scholar
  21. 21.
    Wnuk, M.P., and Yavari, A. (2003). On estimating stress intensity factors and modulus of cohesion for fractal cracks. Engineering Fracture Mechanics, 70,1659–1674.CrossRefGoogle Scholar
  22. 22.
    Wnuk, M. P. and Yavari, A. (2005) A correspondence principle for fractal and classical cracks. Engineering Fracture Mechanics, 72:2744-2757.CrossRefGoogle Scholar
  23. 23.
    Wnuk, M. P. and Yavari, A. (2008) Discrete fractal fracture mechanics. Engineering Fracture Mechanics, 75(5):1127-1142.CrossRefGoogle Scholar
  24. 24.
    Xie, H. (1989). The fractal effect of irregularity of crack branching on the fracture toughness of brittle materials. International Journal of Fracture, 41,267–274.CrossRefGoogle Scholar
  25. 25.
    Xie, H. and Sanderson, D.J. (1995). Fractal effects of crack propagation on dynamic stress intensity factors and crack velocities. International Journal of Fracture, 74,29–42.CrossRefGoogle Scholar
  26. 26.
    Yavari, A., Hockett, K.G., and Sarkani, S. (2000). The fourth mode of fracture in fractal fracture mechanics. International Journal of Frcture, 101(4),365–384.CrossRefGoogle Scholar
  27. 27.
    Yavari, A. (2002) Generalization of Barenblatt’s cohesive fracture theory for fractal cracks. Fractals-Complex Geometry Patterns and Scaling in Nature and Society, 10:189-198.zbMATHCrossRefGoogle Scholar
  28. 28.
    Yavari, A., Sarkani, S., and Moyer, E.T. (2002). The mechanics of self-similar and self-affine fractal cracks. International Journal of Fracture, 114,1–27.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Arash Yavari
    • 1
  • Michael P. Wnuk
  1. 1.School of Civil and Environmental EngineeringGeorgia Institute of TechnologyAtlanta

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