An Elastic-Plastic Spherical Contact Model Under Combined Normal and Tangential Loading

Spherical contact under combined normal and tangential loading has been investigated by many researchers, and some physically based criteria were proposed to capture the sliding inception, e.g., the local yielding criterion of the Kogut-Etsion (KE) model and the tangential stiffness criterion of the Brizmer-Kligerman-Etsion (BKE) model. In this work, by utilizing the maximum frictional shear stress criterion for the sliding inception, a finite element model for obliquely loaded spherical contact has been developed, which realized a friction transition from the KE model to the BKE model, with an increasing normal approach. The stress, strain, tangential force, normal force, and contact area during tangential loading are investigated using different models. It was found that with an elastic normal displacement preload, material failure is initiated on the surface, while with an elastic-plastic normal displacement preload the failure is initiated under the surface and then extends to the surface with the increasing tangential load. With an elastic-plastic normal displacement preload, there is an obvious normal force release during tangential loading. Different from the full stick model, both the Coulomb friction model and the proposed model are partial slip models in nature. However, the Coulomb friction is more empirically determined with some arbitrary friction coefficient, whereas the proposed model is based on physics parameters. Furthermore, both the Coulomb friction model and the proposed model predict a lower tangential force at the same tangential displacement, a slower growth of the contact area under elastic normal displacement preload, and a faster growth of the contact area under an elastic-plastic normal displacement preload compared to the full stick model.