Unloading of an elastic–plastic loaded spherical contact

The process of unloading of an elastic–plastic loaded sphere in contact with a rigid flat is studied by finite element method. The sphere material is assumed isotropic with elastic-linear hardening. The numerical simulations cover a wide range of material properties and sphere radius. The contact load, stresses, and deformation in the sphere during both loading and unloading, are calculated for a wide range of interferences. Analytical dimensionless expressions are presented for the unloading load–deformation relation, the residual interference and the residual curvature of the sphere after complete unloading. A new measure termed elastic–plastic loading index is introduced to indicate the plasticity level of the loaded sphere. Some ideas regarding reversibility of the unloading process and elasticity of multiple loading unloading are also presented.