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International Journal of Fracture

, Volume 142, Issue 1–2, pp 51–67 | Cite as

Material-independent crack arrest statistics: application to indentation experiments

  • Yann Charles
  • François Hild
  • Stéphane Roux
  • Damien Vandembroucq
Research Article

Abstract

An extensive experimental study of indentation and crack arrest statistics is presented for four different brittle materials (alumina, silicon carbide, silicon nitride, glass). Evidence is given that the crack length statistics is described by a universal (i.e., material independent) distribution. The latter directly derives from results obtained when modeling crack propagation as a depinning phenomenon. Crack arrest (or effective toughness) statistics appears to be fully characterized by two parameters, namely, an asymptotic crack length (or macroscopic toughnes) value and a power law size-dependent width. The experimental knowledge of the crack arrest statistics at one given scale thus gives access to its knowledge at all scales.

Keywords

Brittle fracture Crack arrest Heterogeneity Depinning Indentation Probability and statistics 

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References

  1. Bouchaud E (1997) Scaling properties of cracks. J Phys Condens Matter 9:4319–4344CrossRefADSGoogle Scholar
  2. Charles Y, Hild F (2002) Crack arrest in ceramic/steel assemblies. Int J Fract 15(3):251–272CrossRefGoogle Scholar
  3. Charles Y, Hild F, Roux S (2003) Long-term reliability of ceramics: the issue of crack arrest. ASME J Eng Mater Technol 125:333–340CrossRefGoogle Scholar
  4. Charles Y, Vandembroucq D, Hild F, Roux S (2004) Material independent crack arrest statistics. J Mech Phys Solids 52:1651–1669MATHCrossRefADSGoogle Scholar
  5. Chudnovsky A, Kunin B (1987) A probabilistic model of brittle crack formation. J Appl Phys 62:4124–4129CrossRefADSGoogle Scholar
  6. Cook RF, Lawn BR, Fairbanks CJ (1985) Microstructure-strength properties: I. Effect of crack size on toughness. J Am Ceram Soc 68:604–615Google Scholar
  7. Gao H, Rice JR (1989) A first order perturbation analysis on crack trapping by arrays of obstacles. J Appl Mech 56:828–836MATHCrossRefGoogle Scholar
  8. Glandus JC, Rouxel T (1991) Study of the Y-TZP toughness by an indentation method. Ceram Int 17:129–135CrossRefGoogle Scholar
  9. Herrmann HJ, Roux S (1990) Statistical models for the fracture of disordered media. North-HollandGoogle Scholar
  10. Jayatilaka A de S, Trustrum K (1977) Statistical approach to brittle fracture. J Mater Sci 12:1426–1430CrossRefADSGoogle Scholar
  11. Jeulin D (1994) Fracture statistics models and crack propagation in random media. Appl Mech Rev 47(1):141–150CrossRefGoogle Scholar
  12. Joanny J-F, de Gennes PG (1984) A model for contact angle hysteresis. J Chem Phys 81:552–562CrossRefADSGoogle Scholar
  13. Kurkjian CR (1985) Strength of inorganic glass. Plenum Press, New York, USAGoogle Scholar
  14. Lawn BR (1993) Fracture of brittle solids. Cambridge University Press, Cambridge, UKGoogle Scholar
  15. Lawn BR, Evans AG, Marshall DB (1980) Elastic/plastic indentation damage in ceramics: the median/radial crack system. J Am Ceram Soc 63(9–10):574–581CrossRefGoogle Scholar
  16. Ponton CB, Rawlings RD (1989a) Vickers indentation fracture toughness test – Part 1 – review of literature and formulation of standardized indentation toughness equations. Mater Sci Technol 5:865–872Google Scholar
  17. Ponton CB, Rawlings RD (1989b) Vickers indentation fracture toughness test – Part 2 – application and evaluation of standardized indentation toughness equations. Mater Sci Technol 5:961–976Google Scholar
  18. Rosso A, Krauth W (2002) Roughness at the depinning threshold for a long-range elastic string. Phys Rev E 65:025101CrossRefADSGoogle Scholar
  19. Roux S, Vandembroucq D, Hild F (2003) Effective toughness of heterogeneous brittle materials. Eur J Mech A/Solids 22:743–749MATHCrossRefMathSciNetGoogle Scholar
  20. Schmittbuhl J, Måløy KJ (1995) Direct observation of a self-affine crack propagation. Phys. Rev Lett 78: 3888–3891CrossRefADSGoogle Scholar
  21. Schmittbuhl J, Roux S, Vilotte J-P, Måløy KJ (1995) Interfacial crack pinning: effect of non-local interaction. Phys Rev Lett 74:1787–1790CrossRefADSGoogle Scholar
  22. Skoe R, Vandembroucq D, Roux S (2002) Front propagation in random media: from extremal to activated dynamics. Int J Mod Phys C 13:751–757CrossRefADSGoogle Scholar
  23. Vandembroucq D, Roux S (2004) Large scale simulations of ultrametric depinning. Phys Rev E 70:026103CrossRefADSGoogle Scholar
  24. Wang J, Gong J, Guan Z (2002) Variation in the indentation toughness of silicon nitride. Mater Lett 57:643–646CrossRefGoogle Scholar
  25. Weibull W (1939) A statistical theory of the strength of materials. Roy Swed Inst Eng Res, Report no. 151Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Yann Charles
    • 1
    • 2
  • François Hild
    • 1
  • Stéphane Roux
    • 3
  • Damien Vandembroucq
    • 3
  1. 1.LMT-CachanENS de Cachan/CNRS-UMR 8535/Université Paris 6Cachan CedexFrance
  2. 2.LPMTM, CNRS UPR-9001 / Université Paris 13VilletaneuseFrance
  3. 3.Surface du Verre et InterfacesUnité Mixte CNRS/Saint-GobainAubervilliers CedexFrance

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