Axisymmetric indentation of an incompressible elastic thin film

Indentation has been used to measure material properties in small volumes. This work presents a rigorous analysis of an incompressible elastic thin film indented by a rigid spherical or conical indenter under conditions that the contact radius is much larger than the film thickness and the contact condition between the indenter and the film is frictionless. Closed-form solutions for the load-displacement relationship and the contact stiffness are derived in terms of the ratio of the contact radius to the film thickness and material properties. It turns out that they are different from those obtained for the indentation of an elastic half-space. The contact stiffness is proportional to the contact area and inversely proportional to the film thickness for the frictionless boundary condition between the film and the substrate. For perfect bonding between the film and the substrate, the contact stiffness is proportional to the square of the contact area and inversely proportional to the cube of the film thickness. The results provide a guideline for measuring the elastic constants of thin films and determining the degree of adhesion between a thin film and a stiffer substrate.