On the adhesion mechanics of multi-layer elastic systems

Local-probe instruments such as surface force apparatus or atomic force microscope are routinely used to extract the mechanical properties of thin-layers by subjecting them to indentation loading. Inadvertently, at these micro- or nano-indentation loads, the adhesive surface forces operating between the indenter and the thin-layer will contribute to the deformation. The well-established Johnson–Kendal–Roberts (JKR) theory is applied to extract the surface energy of the contacting solids. For this thin-layer system, the JKR theory should be an error as it is based on the indentation of an elastic half-space with an elastic sphere. A continuum mechanics approach coupled with non-dimensional analysis and finite elements simulation is presented to explain the indentation process of multi-layer elastic systems under the presence of adhesion. The emphasis is on spherical and flat punch probes. Computations of contact size and contact stiffness as a function of load are presented for a range of values of adhesion energies.