The interfacial analysis of a film bonded to a finite thickness graded substrate

The problem of an elastic film bonded to a finite-thickness graded substrate under different loading conditions is investigated, in which the shear modulus of the graded substrate is assumed to vary exponentially along its thickness and perfect adhesion is adopted at the contact interface. The governing singular integral equation for the present model is formulated analytically in terms of interfacial shear stress. With the help of the collocation method, the governing equation is further solved numerically. The interfacial shear stress, the normal stress in the film as well as the singularity near the film edges are discussed in order to evaluate the interface behaviors that are closely related to failure and destruction of the film/substrate systems. It is found that the interface behavior of the film/substrate system can be modified by tuning the material and geometric parameters of both the film and the graded substrate. Compared with cases under a non-symmetric loading and a symmetric one, the effect of some parameters is observed to be dependent of the loading type.