Effect of friction and adhesion on the load–displacement of a spherical probe in contact with a compliant incompressible elastic coating

The mechanical properties of thin films are extracted from the measured load displacement relation in a contact test conducted using micro or nano instruments. At this micro or nano force scale, the adhesion and friction operating between the test tip and thin film surface will contribute to the deformation. The well established Johnson–Kendall–Roberts (JKR) theory provided a relationship between the normal load and elastic central displacement for the adhesion contact. But because of its semi-infinite half-space hypothesis, the standard JKR theory is not applicable to thin film contact problem. Experimental verification demonstrates the numerical version of JKR theory is suitable for compliant thin film adhesion analysis, but it does not include the friction effect. In this paper, the load–displacement relation of totally bonded friction contact with adhesion is studied and compared with that of frictionless case. The practical thin film contact will lie in these two limits. The effect of friction to load and displacement seems very small except for the transition range from film to substrate response. Empirical expressions for the contact compliance are obtained from the detailed finite element study.