International Journal of Fracture

, Volume 209, Issue 1–2, pp 187–202 | Cite as

Prediction of multi-cracking in sub-micron films using the coupled criterion

Original Paper


Sub-micron films deposited on a flexible substrate are now commonly used in electronic industry. The main damaging mode of these systems is a multi-cracking of the film under the action of thermal and mechanical stresses. This multi-cracking phenomenon is described using the coupled criterion based on the simultaneous fulfilment of an energy and a stress criteria. The coupled criterion is implemented in a representative volume element and it allows to decide whether the stress or the energy condition governs the cracking mechanism. It is found that the energy conditions predominates for very thin films whereas the stress condition can take place for thicker films. The initial density of cracks is determined and is in good agreement with the experimental measures. Further subdivisions, when increasing the load, are also predicted. Moreover, under some conditions, a master curve can rule the density of cracks function of the applied strain, showing a good agreement between predictions and experiments for a wide range of film thicknesses.


Thin films Brittle fracture Residual stresses 


  1. Ambrico JM, Begley MR (2002) The role of initial flaw size, elastic compliance and plasticity in channel cracking of thin films. Thin Solid Films 419:144–153CrossRefGoogle Scholar
  2. Andersons J, Modniks J, Leterrier Y, Tornare G, Dumont P, Manson J-AE (2008) Evaluation of toughness by finite fracture mechanics from crack onset strain of brittle coatings on polymers. Theor Appl Fract Mech 49:151–157CrossRefGoogle Scholar
  3. Beuth JL, Klingbeil NW (1996) Cracking of thin films bonded to elastic-plastic substrates. J Mech Phys Solids 44:1411–1428CrossRefGoogle Scholar
  4. Bordet H, Ignat M, Dupeux M (1998) Analysis of the mechanical response of film on substrate systems presenting rough interfaces. Thin Solid Films 315:207–213CrossRefGoogle Scholar
  5. Chen Z, Cotterell B, Wang W (2002) The fracture of brittle thin films on compliant substrates in flexible displays. Eng Fract Mech 69:597–603CrossRefGoogle Scholar
  6. Crawford GP (2005) Flexible flat panel displays. Wiley series in display technology. Wiley, HobokenCrossRefGoogle Scholar
  7. Evans AG, Hutchinson GW (1995) The thermomechanical integrity of thin films and multi-layers, Acta Metal Mater 43:2507–2530CrossRefGoogle Scholar
  8. Freund LB, Suresh S (2004) Thin film materials. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  9. Fu Y, Zhang XC, Xuan FZ, Tu ST, Wang ZD (2013) Multiple cracking of thin films due to residual stress combined with bending stress. Comput Mater Sci 73:113–119CrossRefGoogle Scholar
  10. Hashin Z (1996) Finite thermoelastic fracture criterion with application to laminate cracking analysis. J Mech Phys Solids 44:1129–1145CrossRefGoogle Scholar
  11. He MY, Hutchinson JW (1989) Crack deflection at an interface between dissimilar elastic materials. Int J Solids Struct 25:1053–1067CrossRefGoogle Scholar
  12. Hsueh CH, Yanaka M (2003) Multiple film cracking in film/substrate systems with residual stresses and unidirectional loading. J Mater Sci 38:1809–1817CrossRefGoogle Scholar
  13. Hu MS, Evans AG (1989) The cracking and decohesion of thin films on ductile substrates. Acta Metall 37:917–925CrossRefGoogle Scholar
  14. Jansson NE, Leterrier Y, Manson J-AE (2006a) Modeling of multiple cracking and decohesion of a thin film on a polymer substrate. Eng Fract Mech 73:2614–2626CrossRefGoogle Scholar
  15. Jansson NE, Leterrier Y, Medico L, Manson JAE (2006b) Calculation of adhesive and cohesive fracture toughness of a thin brittle coating on a polymer substrate. Thin Solids Films 515:2097–2105CrossRefGoogle Scholar
  16. Leguillon D (2002) Strength or toughness? A criterion for crack onset at a notch. Eur J Mech A/Solids 21:61–72CrossRefGoogle Scholar
  17. Leguillon D, Sanchez-Palencia E (1992) Fracture in heterogeneous materials, weak and strong singularities. In: Ladeveze P, Zienkiewicz OC (eds) New advances in computational structural mechanics, vol 32. Studies in applied mechanics. Elsevier, Amsterdam, pp 423–434Google Scholar
  18. Leguillon D, Martin E (2014) Mathematical methods and models in composites, computational and experimental methods in structures. In: Mantic V (ed) Crack nucleation at stress concentration points in composite materials—application to the crack deflection by an interface. Imperial College Press, London, pp 401–424Google Scholar
  19. Leguillon D, Martin E, Sevecek O, Bermejo R (2015) Application of the coupled stress-energy criterion to predict the fracture behaviour of layered ceramics designed with internal compressive stresses. Eur J Mech A/Solids 54:94–104CrossRefGoogle Scholar
  20. Leguillon D, Lafarie-Frenot MC, Pannier Y, Martin E (2016) Prediction of the surface cracking pattern of an oxidized polymer induced by residual and bending stresses. Int J Solids Struct 91:89–101CrossRefGoogle Scholar
  21. Leguillon D, Li J, Martin E (2017) Multi-cracking in brittle thin layers and coatings using a FFM model. Eur J Mech A/Solids 63:14–21CrossRefGoogle Scholar
  22. Ramsey PM, Chandler HW, Page TF (1991) Bending test to estimate through-thickness strength and interfacial shear strength in coated systems. Thin Solid Films 201:81–89CrossRefGoogle Scholar
  23. Thouless MD (1990) Crack spacing in brittle films on elastic substrate. J Am Ceram Soc 73:2144–2146CrossRefGoogle Scholar
  24. Timm DH, Guzina BB, Voller VR (2003) Prediction of thermal crack spacing. Int J Solids Struct 40:125–142CrossRefGoogle Scholar
  25. Weissgraeber P, Leguillon D, Becker W (2016) A review of finite fracture mechanics: crack initiation at singular and non-singular stress-raisers. Arch Appl Mech 86:375–401CrossRefGoogle Scholar
  26. Yanaka M, Miyamoto T, Tsukahara Y, Takeda N (1999) In situ observation and analysis of multiple cracking phenomena in thin glass layers deposited on polymer films. Compos Interfaces 6:409–424CrossRefGoogle Scholar
  27. Ye T, Suo Z, Evans AG (1992) Thin film cracking and the role of substrate and interface. Int J Solids Struct 29:2639–2648CrossRefGoogle Scholar
  28. Zhang XC, Xuan FZ, Zhang YK, Tu ST (2008) Multiple film cracking in film/substrate systems with mismatch strain and applied strain. J Appl Phys 104:063520CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  1. 1.Institut Jean le Rond d’Alembert, CNRS UMR 7190Sorbonne UniversitésParisFrance
  2. 2.Laboratoire des Composites Thermo-Structuraux, CNRS UMR 5801Université de BordeauxPessacFrance

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