A Finite Element Study of Elasto-Plastic Hemispherical Contact

This work presents a finite element study of elasto-plastic hemispherical contact. The results are normalized such that they are valid for macro contacts (e.g., rolling element bearings) and micro contacts (e.g., asperity contact). The material is modeled as elastic-perfectly plastic. The numerical results are compared to other existing models of spherical contact, including the fully plastic case (known as the Abbott and Firestone model) and the perfectly elastic case (known as the Hertz contact). At the same interference, the area of contact is shown to be larger for the elasto-plastic model than that of the elastic model. It is also shown, that at the same interference, the load carrying capacity of the elasto-plastic modeled sphere is less than that for the Hertzian solution. This work finds that the fully plastic average contact pressure, or hardness, commonly approximated to be a constant factor (about three) times the yield strength, actually varies with the deformed contact geometry, which in turn is dependant upon the material properties (e.g., yield strength). The results are fit by empirical formulations for a wide range of interferences and materials for use in other applications.