Enhancement of adhesion strength in viscoelastic unsteady contacts

We present a general energy approach to study the unsteady adhesive contact of viscoelastic materials. Under the assumption of infinitely short-range adhesive interactions, we exploit the principle of virtual work to generalize Griffith’s local energy balance at contact edges to the case of a non-conservative (viscoelastic) material, subjected to a generic contact time–history. We apply the proposed energy balance criterion to study the approach–retraction motion of a rigid sphere in contact with a viscoelastic half-space. A strong interplay between adhesion and viscoelastic hysteretic losses is reported which can lead to strongly increased adhesion strength, depending on the loading history. Specifically, two different mechanisms are found to govern the increase of pull-off force during either approach–retraction cycles and approach – full relaxation – retraction tests. In the former case, hysteretic losses occurring close to the circular perimeter of the contact play a major role, significantly enhancing the energy release rate. In the latter case, instead, the pull-off enhancement mostly depends on the glassy response of the whole (bulk) material which, triggered by the fast retraction after relaxation, leads to a sort of ‘frozen’ state and results in a flat-punch-like detachment mechanism (i.e., constant contact area). In this case, the JKR theory of adhesive contact cannot be invoked to relate the observed pull-off force to the effective adhesion energy, i.e. the energy release rate $G$, and strongly overestimates it. Therefore, a rigorous mathematical procedure is also proposed to correctly calculate the energy release rate in viscoelastic dissipative contacts.