International Journal of Fracture

, Volume 141, Issue 1–2, pp 291–312 | Cite as

A failure criterion for brittle elastic materials under mixed-mode loading

  • Zohar Yosibash
  • Elad Priel
  • Dominique Leguillon
Original Article


The failure criterion of Leguillon at reentrant corners in brittle elastic materials (Leguillon 2002, Eur J Mech A/Solids 21: 61–72; Leguillon et al. (2003), Eur J Mech A—Solids 22(4): 509–524) validated in (Yosibash et al. 2004, Int J Fract 125(3–4): 307–333) for mode I loading is being extended to mixed mode loading and is being validated by experimental observations. We present an explicit derivation of all quantities involved in the computation of the failure criterion. The failure criterion is validated by predicting the critical load and crack initiation angle of specimens under mixed mode loading and comparison to experimental observations on PMMA (polymer) and Macor (ceramic) V-notched specimens.


Failure initiation Mixed-mode fracture Generalized stress intensity factors V-notch 


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  1. Blum, H, Dobrowolski, M 1982On finite element methods for elliptic equations on domains with cornersComputing285363MATHMathSciNetCrossRefGoogle Scholar
  2. Dunn, ML, Hui, C, Labossiere, P, Lin, Y 2001Small scale geometric and material features at geometric discontinuities and their role in fracture analysisInt J Fract110101121CrossRefGoogle Scholar
  3. Dunn, ML, Suwito, W, Cunningham, S 1997aFracture initiation at sharp notches: Correlation using critical stress intensitiesInt J Solids Struct3438733883CrossRefGoogle Scholar
  4. Dunn, ML, Suwito, W, Cunningham, S, May, CW 1997bFracture initiation at sharp notches under mode I, mode II, and mild mixed mode loadingInt J Fract84367381CrossRefGoogle Scholar
  5. Fett, T 1996Failure of brittle materials near stress singularitiesEng Fract Mech53511518CrossRefGoogle Scholar
  6. Hashin, Z 1996Finite thermoelastic fracture criterion with application to laminate cracking analysisJ Mech Phys Solids4411291145CrossRefGoogle Scholar
  7. Kanninen, MF, Popelar, CH 1985Advanced fracture mechanicsOxford University PressNew-York, NY, USAMATHGoogle Scholar
  8. Labossiere, P, Dunn, M, Cunningham, S 2002Application of bimaterial interface corner failure mechanics to silicon/glass anodic bondsJ Mech Phys Solids50405433MATHCrossRefGoogle Scholar
  9. Lazzarin, P, Zmabardi, R 2001A finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp V-shaped notchesInt J Fract112275298CrossRefGoogle Scholar
  10. Leguillon, D 2002Strength or toughness? a criterion for crack onset at a notchEur J Mech A/Solids216172MATHCrossRefGoogle Scholar
  11. Leguillon, D, Laurencin, J, Dupeux, M 2003Failure initiation in an epoxy joint between two steel platesEur J Mech A—Solids22509524MATHCrossRefGoogle Scholar
  12. Leguillon D, Siruguet K (2002) Finite fracture mechanics Application to the onset of a crack at a bimaterial corner. In: Wales B and Karihaloo (eds.) IUTAM symposium on analytical and computational fracture mechanics of non-homogeneous materials (Cardiff, 18–22 June 2001), solid mechanics and its applications, vol 97. Kluwer Academic Publishers, Dordrecht, pp 11–18Google Scholar
  13. Leguillon, D, Yosibash, Z 2003Crack onset at a V-Notch. Influence of the notch tip radiusInt J Fract122121CrossRefGoogle Scholar
  14. Mohammed, I, Liechti, K 2000Cohesive zone modeling of crack nucleation at bimaterial cornersJ Mech Phys Solids48735764MATHCrossRefGoogle Scholar
  15. Reedy, JED 2000Connection between interface corner and interfacial fracture analyses of an adhesively-bonded butt jointInt J Solids Struct3724292442MATHCrossRefGoogle Scholar
  16. Seweryn, A 1994Brittle fracture criterion for structures with sharp notchesEng Fract Mech47673681CrossRefGoogle Scholar
  17. Seweryn, A, Lukaszewicz, A 2002Verification of brittle fracture criteria for elements with V-shaped notchesEng Fract Mech6914871510CrossRefGoogle Scholar
  18. Seweryn, A, Poskrobko, S, Mróz, Z 1997Brittle fracture in plane elements with sharp notches under mixed-mode loadingJ Eng Mech123535543CrossRefGoogle Scholar
  19. Szabó BA, Babuška I (1988) Computation of the amplitude of stress singular terms for cracks and reentrant corners. In: CTA (ed) Fracture mechanics: nineteenth Symposium. ASTM STP 969, ASTM, Philadelphia, pp 101–124Google Scholar
  20. Taylor, D, Cornetti, P, Pugno, N 2005The fracture mechanics of finite crack extensionEng Fract Mech7210211038CrossRefGoogle Scholar
  21. Yosibash, Z, Adan, O, Shneck, R, Atlas, H 2003Thermo-mechanical failure criterion at the micron scale in electronic devicesInt J Fract1224764CrossRefGoogle Scholar
  22. Yosibash, Z, Bussiba, A, Gilad, I 2004Failure criteria for brittle elastic materialsInt J Fract125307333CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  • Zohar Yosibash
    • 1
  • Elad Priel
    • 1
  • Dominique Leguillon
    • 2
  1. 1.Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical EngineeringBen-Gurion University of the NegevBeer-ShevaIsrael
  2. 2.LMM-CNRS UMR7607Universite Pierre et Marie CurieParis Cedex 05France

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