Multiple cracking of thin films due to residual stress combined with bending stress

Multiple cracking of brittle films deposited on the relatively soft substrate was commonly observed in different applications. In this paper, multiple film cracking in the film/substrate systems was analyzed. The system was subjected to the combination of the residual stresses and the applied bending stress. First, a simply analytical model was developed to derive the closed-form solutions for the stress distribution and redistribution due to the edge effects in the film segment. Second, the energy and strength criteria were adopted to perform the analysis on the multiple film cracking on the basis of the knowledge on the residual stress distribution. Third, the case of Yttria-stabilized zirconia film/Inconel 617 substrate system was used to illustrate the implementation of this model. The predicted crack density against the applied strain was compared with the existing experimental measurements. The relationship between the fracture energy and the film strength was obtained.