Elastic-plastic contact behavior of a sphere loaded against a rigid flat

This paper presents a contact analysis between a deformable sphere and a rigid flat by finite element method. Analysis is carried out beyond elastic limit, until the inception of plasticity for various materials with different radii. Results are compared with previous elastic-plastic models. It is found those materials with Young's modulus to yield stress (E/Y) ratio less than 300 show strikingly different contact phenomena. Equations for hardness and interference in terms of E/Y ratio for these materials are presented. Also it is noted that materials with E/Y ratio more than 300 and less than 1000 exhibit similar elastic plastic contact phenomena. New nondimensional relationships for contact load, area and contact stress for a wide range of interferences are also presented.