Effect of Tabor parameter on hysteresis losses during adhesive contact

The Tabor parameter mu 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 mu > 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 mu. 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 a = 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 mu > 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.