An Elastic-plastic Finite Element Analysis of Two Interfering Hemispheres Sliding in Frictionless Contact

A vast amount of previous work on hemispherical contact is almost solely dedicated to quasi-static normal loading (axisymmetric 2D models). Some scarce work exists on tangential loading but it is limited to full stick conditions. The sliding of interfering bodies is considerably distinct. Hence, the objective of this work is to investigate two hemispheres sliding across each other, subject to an interference that is large enough to deform their surfaces permanently, during and after contact. Similar (steel-on-steel) and dissimilar (aluminum-on-copper) materials are investigated using a 3D finite element analysis (FEA). The behavior and outcomes are vastly different from previously reported work. Results include the formation and propagation of the von Mises stresses, the deformations, the contact areas, and the energy loss even with friction being absent. The results are normalized so that they may be applied to any scale (from macro to micro contacts); the main intention, however, is to apply the results to interfering asperities in rough surfaces that are sliding. The effectiveness of that normalization is discussed. Empirical equations for the net energy loss, the permanent residual deformations (damage), and the effective coefficient of friction (in frictionless sliding) are given as functions of the interference. Lastly, some FEA results are favorably compared to those obtained from a semi-analytical method, but these are only limited to a few special cases that the latter is able to solve.