International Journal of Fracture

, Volume 132, Issue 2, pp 175–196 | Cite as

A numerical analysis of constraint effects in fatigue crack growth by use of an irreversible cohesive zone model

  • B. Wang
  • T. Siegmund


The analysis of constraint effects in fatigue crack growth in multi-layer structures is discussed. The process of material separation under cyclic loading is described by a cohesive zone model (CZM) with an irreversible constitutive relationship. The traction–separation behavior does not follow a predefined path, but is dependent on the evolution of the damage dependent cohesive zone properties. A modified boundary layer model is used in simulations of fatigue crack growth along the centerline crack of the metal layer sandwiched between two elastic substrates. Fatigue crack growth is computed for a series of values of metal layer thickness under constant and variable amplitude loading conditions. The results of the computations demonstrate that certain combinations of load magnitude, layer thickness and material properties results in significant constrain effects in fatigue crack growth. The influence of these constraint effects on fatigue crack growth rates and on crack closure processes is determined. The evolutions of the traction–separation law, the accumulated and current plastic zones, as well as the stress fields during the crack propagation are discussed.


Cohesive zone model constraint cyclic loading fatigue crack growth multilayer structures 


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  1. Barenblatt, G.I. 1962The mathematical theory of equilibrium cracks in brittle fractureAdvances in Applied Mechanics755129CrossRefMathSciNetGoogle Scholar
  2. Cannon, R.M., Dalgleish, B.J., Dauskardt, R.H., Oh, T.S, Ritchie, R.O. 1991Cyclic fatigue-crack propagation along ceramic/metal interfacesActa Metallurgica et Materialia3921452156Google Scholar
  3. Dauskardt, R.H., Lane, M., Ma, Q., Krishna, N 1998Adhesion and debonding ofmulti-layer thin film structures.Engineering Fracture Mechanics61141162Google Scholar
  4. Deshpande, V.S., Needleman, A., Giessen, E. 2002Discrete dislocation modeling of fatigue crack propagation.Acta Materialia50831846Google Scholar
  5. Dugdale, D.S. 1960Yielding of steel sheets containing slits.Journal of the Mechanicsand Physics of Solids8100104ADSGoogle Scholar
  6. de-Andrés, A., Pérez, J.L., Ortiz, M. 1999Elastoplastic finite element analysis of three-dimensional fatigue crack growth in aluminum shafts subjected to axial loading.International Journal of Solids and Structures3622312258MATHGoogle Scholar
  7. Evans, A.G., Hutchinson, J.W. 1995The thermomechanical integrity of thin films and multilayers.Acta Metallurgica et Materialia4325072530Google Scholar
  8. Gilbert, C.J., Ritchie, R.O. 1998Transient fatigue crack behavior in a monolithic silicon nitride ceramic.Engineering Fracture Mechanics60303313Google Scholar
  9. Hutchinson, J.W., Evans, A.G. 2000Mechanics of materials: top-down approaches to fractureActa Materialia48125135Google Scholar
  10. Kruzic, J.J., McNaney, J.M., Cannon, R.M., Ritchie, R.O. 2004Effects of plastic constraint on the cyclic and static fatigue behavior of metal/ceramic layered structuresMechanics of Materials365772Google Scholar
  11. Lane, M., Dauskardt, R.H., Vainchtein, A., Gao, H. 2000Plasticity contributionsto interface adhesion in thin-film interconnect structuresJournal of Materials Research1527582769ADSGoogle Scholar
  12. Lemaitre, J. 1996A Course on Damage MechanicsSpringer-VerlagBerlinMATHGoogle Scholar
  13. Lin, G., Kim, Y.J., Cornec, A., Schwalbe, K.H 1997Fracture toughness of a constrained metal layer.Computational Materials Science93647Google Scholar
  14. McNaney, J.M., Cannon, R.M., Ritchie, R.O. 1996Fracture and fatigue-crack growth along aluminum-alumina interfaces.Acta Materialia1247134728Google Scholar
  15. Needleman, A. 1990An analysis of decohesion along an imperfect interface.International Journal of Fracture422140Google Scholar
  16. Nguyen, O., Repetto, E.A., Ortiz, M., Radovitzky, R.A. 2001A cohesive model of fatigue crack growthInternational Journal of Fracture110351369Google Scholar
  17. Paris, P.C., Gomez, M.P., Anderson, W.P 1961A rational analytic theory of fatigue.The Trend in Engineering13914Google Scholar
  18. Roe, K.L. and Siegmund, T. (2001). Simulation of interface fatigue crack growth via a fracture process zone model. In: Computational Fluids and Solid Mechanics, Proceedings of the 1st MIT Conference on Computational Fluids and Solid Mechanics, (Edited by K.J. Bathe), Elsevier, Boston, pp. 435–437.Google Scholar
  19. Roe, K.L., Siegmund, T. 2003An irreversible cohesive zone model for interface fatigue crack growth simulationEngineering Fracture Mechanics70209232Google Scholar
  20. Roychowdhury, S., Dodds, R.H. 2003A numerical investigation of 3-D small-scale yielding fatigue crack growthEngineering Fracture Mechanics7023632383Google Scholar
  21. Siegmund, T. 2004A numerical study of transient fatigue crack growth by use of an irreversible cohesive zone modelInternational Journal of Fatigue9929939Google Scholar
  22. Stüwe, H.-P., Pippan, R. 1992On the energy balance of fatigue crack growthComputers & Structures441317ADSGoogle Scholar
  23. Suresh S. (1998). Fatigue of Materials. Cambridge University PressGoogle Scholar
  24. Tvergaard, V., Hutchinson, J.W. 1992The relation between crack growth resistance and fracture process parameters in elastic-plastic solidsJournal of the Mechanics and Physics of Solids4013771397MATHADSGoogle Scholar
  25. Tvergaard, V., Hutchinson, J.W. 1993The influence of plasticity on mixed mode interface toughnessJournal of the Mechanics and Physics of Solids4111191135MATHADSGoogle Scholar
  26. Tvergaard, V., Hutchinson, J.W. 1994Toughness of an interface along a thin ductile layer joining elastic solidsPhilosophical MagazineA70641656ADSGoogle Scholar
  27. Tvergaard, V., Hutchinson, J.W. 1996On the toughness of ductile adhesive jointsJournal of the Mechanics and Physics of Solids44789800ADSGoogle Scholar
  28. Varias, A.G., Suo, Z., Shin, C.F. 1991Ductile failure of a constrained metal foilJournal of the Mechanics and Physics of Solids39963986ADSGoogle Scholar
  29. Yang, B., Mall, S., Ravi-Chandar, K. 2001A cohesive zone model for fatigue crack growth in quasibrittle materialsInternational Journal of Solids and Structures3839273944MATHGoogle Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.School of Mechanical EngineeringPurdue UniversityWest LafayetteUSA

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