Channel cracking in thin films on substrates of finite thickness

Solutions are presented for the elastic plane-strain problem of a crack in a coating on a compliant substrate of finite thickness. Analysis of the problem shows that substrate thickness has a significant effect on the steady-state energy release rate for channel cracks. This is so over a wide range of elastic mismatch between film and substrate, but is especially important if the substrate is more compliant than the film. Relaxation of the film stress due to elastic deformation of the substrate also plays an important role. If the substrate is clamped around the edge, as would be the case for a coated membrane, the stress in the coating cannot relax and the energy release rate for channel cracking increases significantly with decreasing substrate thickness. If the film stress is allowed to relax, however, the driving force for cracking is reduced as the substrate thickness decreases. The results from this study are used to evaluate the change in curvature of a film/substrate assembly due to channel cracking, a quantity that is of interest for the experimental determination of stresses in thin films. An expression for the elastic extension of the substrate due to channel cracking is derived making it possible to evaluate the effect of cracking on the mechanical behavior of bilayer membranes. It is expected that the present study may lead to the development of new experimental techniques for measuring the fracture toughness of thin coatings.