A Model for Junction Growth of a Spherical Contact

The evolution of the contact area (junction growth) of an elastic-plastic preloaded spherical contact subjected to an additional tangential loading is investigated theoretically. The normal preloading leads to the formation of a junction that can support additional tangential load. A gradual increase of this tangential load, while the normal preload remains constant, can incept plasticity of the contact zone in case the initial normal preload was elastic or enhance an existing one, thus lowering the tangential stiffness of the junction. Finally, the tangential stiffness approaches zero which corresponds to sliding inception (i.e. loss of stability). The evolution of the contact area during the tangential loading prior to sliding inception reveals an essential junction growth which depends on the magnitude of the normal preload. The mechanism causing this junction growth seems to be new points of the sphere surface, which originally lay outside of the initial contact area that are coming into contact with the rigid flat during the tangential loading. A theoretical relation is developed for the dependence of junction growth on the normal preload, which correlates well with some limited experiments.