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.