JKR adhesion in cylindrical contacts

Planar JKR adhesive solutions use the half-plane assumption and do not permit calculation of indenter approach or visualization of adhesive force–displacement curves unless the contact is periodic. By considering a conforming cylindrical contact and using an arc crack analogy, we obtain closed-form indenter approach and load–contact size relations for a planar adhesive problem. The contact pressure distribution is also obtained in closed-form. The solutions reduce to known cases in both the adhesion-free and small-contact solution (Barquins, 1988) limits. The cylindrical system shows two distinct regimes of adhesive behavior; in particular, contact sizes exceeding the critical (maximum) size seen in adhesionless contacts are possible. The effects of contact confinement on adhesive behavior are investigated. Some special cases are considered, including contact with an initial neat-fit and the detachment of a rubbery cylinder from a rigid cradle. A comparison of the cylindrical solution with the half-plane adhesive solution is carried out, and it indicates that the latter typically underestimates the adherence force. The cylindrical adhesive system is novel in that it possesses stable contact states that may not be attained even on applying an infinite load in the absence of adhesion.