The effect of contact conditions and material properties on the elasticity terminus of a spherical contact

The fundamental problem of elastic–plastic normally loaded contact between a deformable sphere and a rigid flat is analyzed under perfect slip and full stick conditions for a wide range of the sphere mechanical properties. The effect of these properties on failure inception is investigated by finding the critical interference and normal loading as well as the location of the first plastic yield or brittle failure. The analysis is based on the analytical Hertz solution under frictionless slip condition and on a numerical solution under stick condition. The failure inception is determined by using either the von Mises criterion of plastic yield or the maximum tensile stress criterion of brittle failure. For small values of the Poisson’s ratio the behavior in stick, when high tangential stresses prevail in the contact interface, is much different than in slip. For high values of the Poisson’s ratio the tangential stresses under stick condition are low and the behavior of the failure inception in stick and slip is similar.