The mechanics of contact and adhesion of periodically rough surfaces

An analytical model based on the Johnson-Kendall-Roberts (JKR) theory of ad hesion was used to study the contact mechanics and adhesion of periodically rough surfaces. The relation of the applied load to the contact area and t he work of adhesion W was found in closed form for arbitrary surface profil es. Our analysis showed that when the parameter alpha = 2/pi beta root 2W r ho /E* > alpha* [where alpha* is a numerical constant of order, one beta on e is the aspect ratio of a typical surface profile (or asperity), and rho i s the number of asperities per unit length], the surfaces will jump into co ntact with each other with no applied load, and the contact area will conti nue to expand until the two surfaces are in full. contact. The theory was t hen extended to the non-JKR regime in which the region where the surface fo rces act is no longer confined to a small region near the contact zone. Exa ct solution was also obtained for this case. An exact analysis of the effec t of entrapped air on the mechanics of adhesion and contact was also enacte d. The results showed that interaction between asperities should be taken i nto consideration in contact-mechanics models of adhesion or friction. (C) 2001 John Wiley & Sons, Inc.