An elasto-plastic solution for channel cracking of brittle coating on polymer substrate

In this article, an elasto-plastic channel-cracking model is presented to study the open-mode fracture of a thin layer brittle coating grown on a polymer substrate. A linear elastic shear interlayer is introduced to describe the stress transfer from the elasto-plastic substrate to the brittle coating, on basis of the shear-lag principle. The channel cracking behavior involves three stages: elastic, elasto-plastic and plastic stages, which are solved in a continuous manner based on the deformation status of the substrate. Explicit solutions are derived for the mutli-stage cracking process. Corresponding experimental tests for a titanium oxide (TiO₂) coating on a poly (ethylene terephthalate) substrate are conducted. The fracture toughness of the coating layer is estimated based on the crack spacing versus layer thickness relationship at certain strain levels. This method is found to be more reliable than the traditional methods using crack onset strain. Parametric studies of the fracture energy release rate for the coating and interfacial compliance of the thin film system are conducted, through which the effect of plastic deformation on the channel cracking behavior is studied extensively. The results indicate that the tangent modulus of the substrate controls the evolution curvature of crack spacing where a smaller tangent modulus corresponds to a slower saturation of crack spacing. The energy release rate also varies significantly with the properties of the interlayer. The study highlights the necessity of an elasto-plastic model for the thin film systems of brittle coating on a plastic substrate.