An accurate solution of a hemisphere contact against a rigid flat under varying elastic moduli and yield strengths and comparison with previous model

The contact behavior of hemisphere pressed by a rigid flat is analyzed based on the finite element method under the condition of independent varying elastic moduli (E) and yield strengths (Y). The contact behavior is related to the ratio of E/Y. The mean contact pressure (p*) first increases and then decreases with the increasing interference, and this trend is more obvious for the contact of materials with the comparatively small ratio of E/Y. The end of the elastoplastic range or the inception of the fully plastic range is determined according to the interference corresponding to the peak value of the p*. The contact load and area in elastoplastic and fully plastic ranges are determined by the interference and the ratio of E/Y. Then, a new contact model to accurately predict the contact load and area for a wide range of E and Y is proposed, and compared with the previous models. The correctness of the current model is verified by the experimental measurement results recorded in previous literature.