Early Post-yield Contact Behavior of Rigid Sphere Against the Elastic–Plastic Half-Space

The elastic–plastic contact theory states that the early stage of the elastic–plastic contact is mainly dominated by elastic deformation because the plastic deformation zone is completely surrounded by elastic material. Therefore, contact behavior still manifests elasticity at the early stage of plastic deformation. However, it is still unclear which contact parameters rampant by the elastic theory at early post-yield deformation stage. The application range for the elastic contact theory is obscure. To probe the above indicated hidden phenomenon, a comprehensive investigation was conducted by the finite element method for a rigid sphere contacting an elastic-perfectly plastic half-space. The responses of contact force, contact indentation, contact pressure and the contact radius were computed for a wide array of practical materials with different Poisson’s ratio. According to the force-indentation relationship, the limiting range of the elastic theory was obtained and described by an indentation range when the deviation of the simulated contact force with the result of the Hertz contact theory is less than 3%. The relation of the limiting indentation with \(E^{*} /\sigma_{Y}\) (where \(E^{*}\) is the effective elastic modulus and \(\sigma_{Y}\) the yield stress) was presented by fitting approach from simulations. This research features a valuable reference for the initial failure or destruction of mechanical components.