Interface behavior of a thin-film bonded to a graded layer coated elastic half-plane

The interface behavior of a thin-film adhering to an elastic half-plane with an arbitrarily graded transition layer is analyzed by a linearly unified model when the interface between the thin-film and the graded layer is subjected to a mismatch strain. A series of continuous but piecewise linear functions are adopted to describe different graded variation laws of the transition layer's modulus. The fundamental solution of a graded-layer coated half-plane under a pair of normal and tangential concentrated forces is obtained first, and then the mismatch problem of a thin-film bonded to an elastic half-plane with an arbitrarily graded transition layer is further investigated. Solving the obtained integral governing equation of Cauchy singularity leads to the interfacial shear stress, the normal stress in the film, as well as the stress intensity factor near the bonded edge. It is found that the interfacial mechanics of a thin-film bonded to a graded layer is significantly affected by varying gradient law, stiffness of the film, ratio of shear modulus and length scale of the graded transition layer. The results should be helpful for the design of systems with thin-films and functional graded materials and could guide engineers to choose proper graded materials for particular applications.