Multiple loading–unloading of an elastic–plastic spherical contact

A model for multiple repeated loading and unloading of an elastic–plastic sphere and a rigid flat is presented to cover a wide range of loading conditions far beyond the elastic limit. The sphere material is modeled as elastic linear isotropic hardening and follows the von Mises yield criterion. It is shown that although most of the plastic deformation occurs during the first loading, secondary plastic flow may evolve during the first unloading. The occurrence of this secondary plastic flow depends on the level of first loading and is strongly affected by the Poisson’s ratio and material hardening. The region of secondary plastic flow may propagate during the very first loading–unloading cycles, reaching a steady state after which the following loading–unloading cycles become fully elastic.