Effect of machine stiffness on interpreting contact force-indentation depth curves in adhesive elastic contact experiments

Dry adhesion plays a critical role in many fields, including the locomotion of some insects and failure of microelectromechanical systems. The Dupre's work of adhesion of a contact interface is an important metric of dry adhesion. It is often measured by applying the Johnson-Kendall-Roberts (JKR) theory [1] to contact force-indentation depth curves that are measured using an atomic force microscope (AFM), or an instrument modeled after it. The JKR theory has been exceptionally successful in interpreting contact force-indentation depth measurements and explaining adhesive, elastic contact phenomena, such as the pull in and pull-off instabilities. However, in many cases the JKR theory predicts a lower magnitude for the pull-off force than what is experimentally measured, and it does not capture the finite changes in the indentation depth that occur during the pull-in and pull-off instabilities. In those cases, applying the JKR theory to calculate the work of adhesion from only the measured pull-off force is likely to give highly inaccurate results. We believe that these discrepancies occur because the classical JKR theory ignores the machine stiffness which, in the case of AFM-type instruments, is the stiffness of the mechanical structure that connects the tip to the translation stage, which moves the tip towards and away from the substrate. In this paper, we present a model that is related to, but more general than, the JKR theory that accounts for the machine stiffness. This model explains the experimental data better than the JKR theory in the cases where the JKR theory displays the aforementioned discrepancies. We consider both the first order necessary and the higher order sufficiency conditions while deriving the solutions in our model. (C) 2019 Elsevier Ltd. All rights reserved.