Loading-Unloading of an Elastic-Plastic Adhesive Spherical Contact

A numerical solution is presented for a single load-unload cycle of an adhesive contact between an elastic-plastic sphere and a rigid flat. The interacting forces between the sphere and the flat are obtained through connecting non-linear spring elements having force-displacement behavior that obeys the Lennard-Jones potential. Linear kinematic hardening (with tangent modulus of 2% and 5% of the Young’s modulus) rather than isotropic hardening is assumed for the sphere material to account for possible secondary plastification during the unloading. The well known Tabor parameter and a plasticity parameter are shown to be the two main dimensionless parameters governing the problem. The effects of these two parameters on the load-approach curves, on the plastically deformed sphere profiles and on the plastic strain fields inside the sphere are presented, showing different modes of separation during the unloading.