Mechanics of Solid Interfaces

Chapter 8

Coating-Substrate Interfaces

8.1. Thin films on massive substrates: a typical case

Apart from the native interfaces present in two-phase alloys or the reinforcement-matrix interfaces synthesized in composites, the case of thin film-substrate interfaces of functional coatings — frequently seen in current technical materials — reveals exemplary features in the simplicity of its overall geometry and its mechanical boundary conditions.

The thin surface layer shows only a negligible stiffness in bending as in traction, compared to that of the substrate. Consequently, it is obliged to follow the strains that the substrate imposes on it, at least for as long as it remains adherent and undamaged. The knowledge of the field of displacements of points on the substrate’s surface is generally used to understand the displacement field of its coating. If the constitutive law of coating material is known, with the help of some specific boundary conditions we can hope to describe the state of stress prevalent in this thin film without too much difficulty.

8.2. State of stress in a thin film-substrate specimen

As an example, we will study the case of a thin film with a thickness h_c adhering to the surface of a planar massive substrate of constant thickness h_s, as shown in Figure 8.1. The orthonormal frame chosen has a plane (x_1Ox₂) in the plane of the film-substrate interface. The substrate and its film are assumed to be very large in dimension in the direction of plane (x₁, x₂), and ...