The interfacial behavior of an axisymmetric film bonded to a graded inhomogeneous substrate

With the development of high-tech applications such as thermal barrier coatings, stretchable and flexible electronics, etc, the key film/substrate systems are more commonly involving three-dimensional axisymmetric problems with graded inhomogeneous substrates. In these film/substrate systems, the effects of geometric and material factors of both the films and the substrates on the interfacial behavior are urgently needed to be uncovered. Herein, a novel theoretical axisymmetric model of an elastic film bonded to a graded substrate is proposed and solved by using Hankel integral transformation and orthotropic polynomials. The interfacial shear stress and the corresponding shear stress intensity factor as well as radial stresses and hoop stresses of both the film and the graded substrate are obtained. It is found that the present model works well to predict the interfacial behavior between an axisymmetric film and a graded substrate. Compared with cases with homogeneous substrates, choosing graded substrates can reduce the risk of edge fracture on the surface of the substrate. A film with a smaller elastic modulus and thickness is advantageous for the interface reliability of the film/substrate system under a thermal load. The results should be useful for not only understanding the load transfer mechanism of axisymmetric film/substrate system, but also providing a valuable guidance to optimize film/substrate structures in various practical and potential applications.