A universal model for the load–displacement relation in an elastic coated spherical contact

•A coated spherical contact problem was studied theoretically.•A universal dimensionless load–displacement relation was found.•An effective modulus of elasticity that is based on mechanical properties alone was defined.

A finite element analysis was used in order to investigate the elastic contact of a coated sphere compressed by a rigid flat. Different coating and substrate geometrical and mechanical properties were analyzed to obtain a universal dimensionless model for the load–displacement relation. Both hard and soft coatings were considered. Dimensionless parameters, which control the behavior of the elastically loaded coated sphere, were identified. A proper normalization of the dimensional load and displacement was found resulting in a universal model. This model also provides a universal expression for the effective modulus of elasticity that is based only on mechanical properties of the coating and the substrate.