Thin-coating contact mechanics with adhesion

An elementary theory for a rigid spherical indenter contacting a thin, linear elastic coating that is bonded to a rigid substrate was developed. This theory predicts that contact area varies as the square root of the compressive load in contrast to Hertz theory where contact area varies as the two-thirds power of the compressive load. Finite element analysis confirmed an approximate square root dependence of contact area on compressive load when the coating thickness-to-indenter radius ratio is less than 0.1 and when the coating Poisson’s ratio is less than 0.45. Thin-coating contact mechanics theories that use either the Derjaguin-Muller-Toporov (DMT) approximation or the Johnson-Kendall-Roberts (JKR) approximation were also developed. In addition, a finite element simulation capability that includes adhesion was developed and verified. Illustrative finite element simulations that include adhesion were then performed for a thin elastic coating (rigid indenter/substrate). Results were compared with the thin-coating contact theories and the transition from DMT-like to JKR-like response was examined.