International Journal of Fracture

, Volume 173, Issue 2, pp 91–104 | Cite as

A cohesive crack model coupled with damage for interface fatigue problems

Original Paper


An semi-analytical formulation based on the cohesive crack model is proposed to describe the phenomenon of fatigue crack growth along an interface. Since the process of material separation under cyclic loading is physically governed by cumulative damage, the material deterioration due to fatigue is taken into account in terms of interfacial cohesive properties degradation. More specifically, the damage increment is determined by the current separation and a history variable. The damage variable is introduced into the constitutive cohesive crack law in order to capture the history-dependent property of fatigue. Parametric studies are presented to understand the influences of the two parameters entering the damage evolution law. An application to a pre-cracked double-cantilever beam is discussed. The model is validated by experimental data. Finally, the effect of using different shapes of the cohesive crack law is illustrated


Cohesive crack model Fatigue damage Interface Double cantilever beam 


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  1. ASTM G 168 (2000) Standard practice for making and using precracked double beam stress corrosion specimens. ASTM Annual Book of ASTM Standards, vol 03.02Google Scholar
  2. Bouvard JL, Chaboche JL, Feyel F, Gallerneau F (2009) A cohesive zone model for fatigue and creep-fatigue crack growth in single crystal superalloys. Int J Fatigue 31: 868–879CrossRefGoogle Scholar
  3. Carpinteri A (1985) Interpretation of the Griffith instability as a bifurcation of the global equilibrium. In: Shah S (ed) Application of fracture mechanics to cementitious composites (Proceedings of NATO advanced research workshop, Evanston, USA). Martinus Nijhoff, Dordrecht, pp 287–316Google Scholar
  4. Carpinteri A, Di Tommaso A, Fanelli M (1985) Influence of material parameters and geometry on cohesive crack propagation. In: Wittmann FH (ed) Fracture toughness and fracture energy of concrete. Elsevier, Amsterdam, pp 117–135Google Scholar
  5. Carpinteri A, Paggi M, Zavarise G (2008) The effect of contact on the decohesion of laminated beams with multiple microcracks. Int J Solids Struct 45: 129–143CrossRefGoogle Scholar
  6. Chaboche JL, Lesne PM (1988) A non-linear continuous fatigue damage model. Fatigue Fract Eng Mater Struct 11: 1–7CrossRefGoogle Scholar
  7. Chaboche JL (1988) Continuum damage mechanics: part I-general concepts. J Appl Mech 55: 59–64CrossRefGoogle Scholar
  8. Chaboche JL (1988) Continuum damage mechanics: part II-Damage growth, crack initiation, and crack growth. J Appl Mech 55: 65–72CrossRefGoogle Scholar
  9. Cornetti P, Pugno N, Carpinteri A, Taylor D (2006) Finite fracture mechanics: a coupled stress and energy failure criterion. Eng Fract Mech 73: 2021–2033CrossRefGoogle Scholar
  10. de-Andrés A, Pérez JL, Ortiz M (1999) Elastoplastic finite element analysis of three-dimensional fatigue crack growth in aluminum shafts subjected to axial loading. Int J Solids Struct 36: 2231–2258CrossRefGoogle Scholar
  11. Dowling NE, Begley JA (1976) Fatigue crack growth during gross plasticity and the J-integral. ASTM STP 590: 82–103Google Scholar
  12. Elices M, Planas J, Guinea GV (2000) Fracture mechanics applied to concrete. In: Freutes M, Elices M, Martin-Meizoso A, Martmez-Esnaola JM (eds) Fracture mechanics: applications and challenges. ESIS publication 26. Elsevier, AmsterdamGoogle Scholar
  13. Hertzberg RW (1995) Deformation and fracture mechanics of engineering materials. Wiley, New YorkGoogle Scholar
  14. Kachanov LM (1958) On the time to failure under creep conditions. Izvestia Akademii Nauk SSSR, Otdelenie tekhnicheskich nauk 8: 26–31Google Scholar
  15. Krajcinovich D (1984) Continuum damage mechanics. Appl Mech Rev 37: 1–6Google Scholar
  16. Lemaitre J, Plumtree A (1979) Application of damage concept to predict creep-fatigue failures. ASME J Eng Mater Technol 101(3): 284–292CrossRefGoogle Scholar
  17. Lemaitre J (1996) A course on damage mechanics. Springer, BerlinCrossRefGoogle Scholar
  18. Leguillon D (2002) Strength or toughness? A criterion for crack onset at a notch. Eur J Mech A/Solids 21: 61–72CrossRefGoogle Scholar
  19. Maiti S, Geubelle PH (2005) A cohesive model for fatigue failure of polymers. Eng Fract Mech 72: 691–708CrossRefGoogle Scholar
  20. Maiti S, Geubelle PH (2006) Cohesive modelling of fatigue crack retardation in polymers: crack closure effect. Eng Fract Mech 73: 22–41CrossRefGoogle Scholar
  21. Mostovoy S, Ripling EJ (1975) Flaw tolerance of a number of commercial and experimental adhesives. Plenum Press, New YorkGoogle Scholar
  22. Neumann P (1974) The geometry of slip processes at a propagating fatigue crack-II. Acta Metal 22: 1167–1178CrossRefGoogle Scholar
  23. Needleman A (1990) An analysis of tensile decohesion along an interface. J Mech Phys Solids 38: 289–324CrossRefGoogle Scholar
  24. Needleman A (1990) An analysis of decohesion along an imperfect interface. Int J Fract 42: 21–40CrossRefGoogle Scholar
  25. Nguyen O, Repetto EA, Ortiz M, Radovitzky RA (2001) A cohesive model of fatigue crack growth. Int J Fract 110: 351–369CrossRefGoogle Scholar
  26. Paris PC, Gomez MP, Anderson WP (1961) A rational analytic theory of fatigue. Trend Eng 13: 9–14Google Scholar
  27. Pirondi A, Nicoletto G (2004) Fatigue crack growth in bonded DCB specimens. Eng Fract Mech 71: 859–871CrossRefGoogle Scholar
  28. Roe KL, Siegmund T (2003) An irreversible cohesive zone model for interface fatigue crack growth simulation. Eng Fract Mech 70: 209–232CrossRefGoogle Scholar
  29. Suo Z, Bao G, Fan B (1992) Delamination R-curve phenomena due to damage. J Mech Phys Solids 40: 1–16CrossRefGoogle Scholar
  30. Skibo MD, Hertzberg RW, Manson JA, Kim SL (1977) On the generality of discontinuous fatigue crack growth in glassy polymers. J Mater Sci 12: 531–542CrossRefGoogle Scholar
  31. Taylor D, Cornetti P, Pugno N (2005) The fracture mechanics of finite crack extension. Eng Fract Mech 72: 1021–1038CrossRefGoogle Scholar
  32. Wang J (1992) A continuum damage mechanic model for low-cycle fatigue failure of metals. Eng Fract Mech 41: 437–441CrossRefGoogle Scholar
  33. Wang T, Lou Z (1990) A continuum damage model for weld heat affected lone under low cycle fatigue loading. Eng Fract Mech 37: 825–829CrossRefGoogle Scholar
  34. Williams J, Hadavinia H (2002) Analytical solutions for cohesive zone models. J Mech Phys Solids 50: 809–825CrossRefGoogle Scholar
  35. Xu XP, Needleman A (1993) Void nucleation by inclusion debonding in a crystal matrix. Model Simul Mater Sci Eng 1: 111–132CrossRefGoogle Scholar
  36. Yang B, Mall S, Ravi-Chandar K (2001) A cohesive zone model for fatigue crack growth in quasibrittle materials. Int J Solids Struct 38: 3927–3944CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of Structural Engineering and GeotechnicsPolitecnico di TorinoTorinoItaly

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