Plastic Yield Conditions for Adhesive Contacts Between a Rigid Sphere and an Elastic Half-Space

Hertz contact theory allows the onset of yielding to be predicted for those contacts in which the effect of adhesion can be neglected. However, in microscale contacts, such as those that occur in microelectromechanical systems (MEMS), yielding will occur for lower loads than those predicted by Hertz. For such cases, the Johnson–Kendall–Roberts (JKR), Derjaguin–Muller–Toporov (DMT), and Greenwood–Johnson (GJ) theories extend the Hertz theory to include the effect of adhesion. The present study gives yield conditions for the JKR, DMT, and Greenwood–Johnson theories of adhesion. Attention is first focused on the initiation of yield along the axis of symmetry of an elastic half-space contacted by a rigid sphere. The results show that the critical loads for the three adhesion theories are close together, but differ significantly from that predicted by Hertz. In fact, it is possible for yielding to occur due to adhesion alone, without an external load. A curve-fit formula is given for the yield load as a function of an adhesion parameter for different Poisson’s ratios. Results are then obtained for the onset of plastic deformation away from the axis of symmetry using the Greenwood–Johnson theory of adhesion.