The interface behavior of a thin piezoelectric film bonded to a graded substrate

A theoretical model of a thin piezoelectric film bonded to a graded substrate under an in-plane electrical loading is established, in which the shear modulus of the graded substrate is assumed to vary exponentially in the thickness direction. Two kinds of interface behavior is analyzed, one is the perfect interface and the other is the imperfect interface. Based on the equilibrium equation and the interfacial boundary conditions, the governing equations are obtained with the help of Fourier transformation for both the perfectly and imperfectly bonded interface problems, which are further solved by the collocation method. The interfacial shear stress and the axial stress as well as the stress intensity factors at both ends of the piezoelectric film and tips of debonded parts are achieved and analyzed. It is found that the interface shear and the normal stress in the piezoelectric film can be reduced by a relative small inhomogeneity parameter of the graded substrate, a relative large effective Young's modulus of the piezoelectric film or a relative short length of the film. Furthermore, the longer the interior debonding length at the interface, the stronger the stress concentration at the debonding tips will be. All the results should be useful for the design of piezoelectric film/substrate systems in real applications.