International Journal of Fracture

, Volume 154, Issue 1–2, pp 195–209 | Cite as

Interaction between cracking, delamination and buckling in brittle elastic thin films

  • W. P. Vellinga
  • M. Van den Bosch
  • M. G. D. Geers
Open Access
Original Paper


A discrete lattice based model for the interaction of cracking, delamination and buckling of brittle elastic coatings is presented. The model is unique in its simultaneous incorporation of the coating and of disorder in the interface and material properties, leading to realistic 3D bending (and buckling) behavior. Results are compared to the literature. In the case of cracking, the key role of a stress transfer correlation length ξ in establishing a scaling behavior for the brittle fracture of thin films is shown to extend to all geometrical and material properties involved. In the scaling regime of crack density in uniaxial tension cracking and delamination are found to occur simultaneously. In uniaxial tension of films with an internal biaxial compressive stress, the predicted initiation of buckles above delaminated areas near crack edges in the model is remarkably similar to experimental results.


Cracking Delamination Buckling Lattice model 



This work was financed by SENTER/IOP under grant IOT97002.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution,and reproduction in any medium, provided the original author(s) and source are credited.


  1. Alava MJ, Nukala PKKV, Zapperi S (2006) Statistical models of fracture. Adv Phys 55: 349–476CrossRefADSGoogle Scholar
  2. Audoly B (1999) Stability of straight delamination blisters. Phys Rev Lett 83(20): 4124–4127CrossRefADSGoogle Scholar
  3. Bernstein N, Hess DW (2003) Lattice trapping barriers to brittle fracture. Phys Rev Lett 91: 025501PubMedCrossRefADSGoogle Scholar
  4. Beuth JL (1992) Cracking of thin bonded films in residual tension. Int J Solids Struct 29(13): 1657–1675CrossRefGoogle Scholar
  5. Gille G (1984) Investigations on mechanical behaviour of brittle wear-resistant coatings, II: theory. Thin Solid Films 111: 201–218CrossRefADSGoogle Scholar
  6. Gille G, Wetzig K (1983) Investigations on mechanical behaviour of brittle wear-resistant coatings, I: experimental results. Thin Solid Films 110: 37–54CrossRefGoogle Scholar
  7. Handge UA, Sokolov IM, Blumen A (1997) Fragmentation of viscoelastic surface layers. Europhys Lett 40(3): 275–280CrossRefADSGoogle Scholar
  8. Handge UA, Leterrier Y, Manson JAE, Sokolov IM, Blumen A (1999) An analysis of disorder in thin silicon oxide coatings. Europhys Lett 48(3): 280–285CrossRefGoogle Scholar
  9. Handge UA, Sokolov IM, Blumen A (2000a) Universal scaling and nonlinearity in surface layer fragmentation. Phys Rev E 61(3): 3216–3219CrossRefADSGoogle Scholar
  10. Handge UA, Leterrier Y, Sokolov IM, Blumen A (2000b) Two scaling domains in mutiple cracking phenomena. Phys Rev E 62(6): 7807–7810CrossRefADSGoogle Scholar
  11. Handge UA, Sokolov IM, Blumen A (2001) Disorder and plasticity in the fragmentation of coatings. Phys Rev E 64: 016109CrossRefADSGoogle Scholar
  12. He MY, Evans AG, Hutchinson JW (1998) Effects of morphology on the decohesion of compressed thin films. Mat Sci Eng A 245: 5168–181CrossRefGoogle Scholar
  13. Hornig T, Sokolov IM, Blumen A (1996) Patterns and scaling in surface fragmentation processes. Phys Rev E 54(4): 4293–4298CrossRefADSGoogle Scholar
  14. Hutchinson JW, Suo Z (1992) Mixed mode cracking in layered materials. Adv Appl Mech 29: 63–191MATHCrossRefGoogle Scholar
  15. Hutchinson JW, He MY, Evans AG (2000) The influence of imperfections on the nucleation and propagation of buckling driven delaminations homogenization scheme. J Mech Phys Solids 48: 709–734MATHCrossRefADSGoogle Scholar
  16. Jagla EA (2007) Modeling the buckling and delamination of thin films. Phys Rev B 75: 085405CrossRefADSGoogle Scholar
  17. Klein PA, Foulk JW, Chen EP, Wimmer SA, Gao HJ (2001) Physics-based modeling of brittle fracture: cohesive formulations and the application of meshfree methods. Theor Appl Fract Mech 37: 99–166CrossRefGoogle Scholar
  18. Kitsuzenaki S (1999) Fracture patterns induced by desiccation in a thin layer. Phys Rev E 60(6): 6449–6464CrossRefADSGoogle Scholar
  19. Kouznetsova V, Geers MGD, Brekelmans WAM (2002) Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme. Int J Numer Meth Eng 54: 1235–1260MATHCrossRefGoogle Scholar
  20. Leung K-t, Neda Z (2000) Pattern formation and selection in quasistatic fracture. Phys Rev Lett 85(3): 662–666PubMedCrossRefADSGoogle Scholar
  21. Leung K-t, Josza L, Ravasz M, Neda Z (2001) Spiral cracks without twisting. Nature 410: 166PubMedCrossRefADSGoogle Scholar
  22. Meakin P (1987) A simple model for elastic fracture in thin films. Thin Solid Films 151: 165–190CrossRefADSGoogle Scholar
  23. Mezin A, Lepage J, Pacia N, Paulmier D (1989a) Étude statistique de la fissuration de revêtements. I: théorie. Thin Solid Films 172: 179–209CrossRefADSGoogle Scholar
  24. Mezin A, Pacia N, Nivoit M, Weber B (1989b) Étude statistique de la fissuration de revêtements. I: théorie. Thin Solid Films 172: 211–225CrossRefADSGoogle Scholar
  25. Morgenstern O, Sokolov IM, Blumen A (1993) Analysis of a one-dimensional fracture model. J Phys A 26: 4521–4537CrossRefADSGoogle Scholar
  26. Ostoja-Starzewski M (2002) Lattice models in micromechanics. Appl Mech Rev 55: 35–60CrossRefGoogle Scholar
  27. Skjeltorp AT, Meakin P (1988) Fracture in microsphere monolayers studied by experiment and computer simulation. Nature 335: 424–426CrossRefADSGoogle Scholar
  28. van Mier JGM (2007) Multi-scale interaction potentials (F-r) for describing britle disordered materials like cement and concrete. Int J Fract 143: 41–78CrossRefGoogle Scholar
  29. Walmann T, Malthe-Sorenssen A, Feder J, Jossang T, Meakin P (1996) Scaling relations between lengths and widths of fractures. Phys Rev Lett 77(27): 5393–5397PubMedCrossRefADSGoogle Scholar
  30. Xia CZ, Hutchinson JW (2000) Crack patterns in thin films. J Mech Phys Solids 48: 1107–1131MATHCrossRefADSGoogle Scholar
  31. Yanaka M, Tsukahara IM, Y, Nakaso N (1998) Cracking phenomena of brittle films in nanostructure composites analysed by a modified shear lag model with residual strain. J Mater Sci 33: 2111–2119CrossRefGoogle Scholar
  32. Yanaka M, Kato Y, Tsukahara IM, Y, Takeda N (1999) Effects of temperature on the multiple cracking progress of sub-micron thick glass films deposited on a polymer substrate. Thin Solid Films 355–356:337–342, 268Google Scholar

Copyright information

© The Author(s) 2008

Authors and Affiliations

  • W. P. Vellinga
    • 1
  • M. Van den Bosch
    • 2
  • M. G. D. Geers
    • 2
  1. 1.Applied PhysicsUniversity of GroningenGroningenThe Netherlands
  2. 2.Mechanical EngineeringUniversity of Technology EindhovenEindhovenThe Netherlands

Personalised recommendations