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

  • Dominique Leguillon
  • Eric Martin
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 


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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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