Effect of Tabor parameter on hysteresis losses during adhesive contact

The Tabor parameter μ is conventionally assumed to determine the range of applicability of the classical 'JKR' solution for adhesive elastic contact of a sphere and a plane, with the variation of the contact area and approach with load, and in particular the maximum tensile force (the pull-off force) being well predicted for μ>5. Here we show that the hysteretic energy loss during a contact separation cycle is significantly overestimated by the JKR theory, even at quite large values of μ. This stems from the absence of long-range tensile forces in the JKR theory, which implies that jump into contact is delayed until the separation α=0. We develop an approximate solution based on the use of Wu's solution with van der Waals interactions for jump-in, and the JKR theory for jump out of contact, and show that for μ>5, the predicted hysteresis loss is then close to that found by direct numerical solutions using the Lennard-Jones force law. We also show how the same method can be adapted to allow for contact between bodies with finite support stiffness.