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), although micro-scale surface characteristics such as grain boundaries are not considered. The material is modeled as elastic-perfectly plastic. The numerical results are compared to other existing models of spherical contact, including the fully plastic truncation model (often attributed to Abbott and Firestone) and the perfectly elastic case (known as the Hertz contact). This work finds that the fully plastic average contact pressure, or hardness, commonly approximated to be a constant factor of about three times the yield strength, actually varies with the deformed contact geometry, which in turn is dependent upon the material properties (e.g., yield strength). The current work expands on previous works by including these effects and explaining them theoretically. Experimental and analytical results have also been shown to compare well with the current work. The results are fit by empirical formulations for a wide range of interferences (displacements which cause normal contact between the sphere and rigid flat) and materials for use in other applications.

In typical metallic contacts, stresses are very high and result in yielding of the material. Therefore, the study of contacts which include simultaneous elastic and plastic deformation is of critical importance. This work reviews the current state-of-the-art in the modeling of single asperity elastic–plastic contact and, in some instances, makes comparisons to original findings of the authors. Several different geometries are considered, including cylindrical, spherical, sinusoidal or wavy, and axisymmetric sinusoidal. As evidenced by the reviewed literature, it is clear that the average pressure during heavily loaded elastic–plastic contact is not governed by the conventional hardness to yield strength ratio of approximately three, but rather varies according to the boundary conditions and deformed geometry. For spherical contact, the differences between flattening and indentation contacts are also reviewed. In addition, this paper summarizes work on tangentially loaded contacts up to the initiation of sliding. As discussed briefly, the single asperity contact models can be incorporated into existing rough surface contact model frameworks. Depending on the size of a contact, the material properties can also effectively change, and this topic is introduced as well. In the concluding discussion, an argument is made for the value of studying hardening and other failure mechanisms, such as fracture as well as the influence of adhesion on elastic–plastic contact.