Response to loading and stiffness of coated substrates indented by spheres

Simulations of spherical indentation of a substrate coated with a protective layer have been performed in the elastic deformation range. They provide key responses that can be used to examine the load resistance of a coated substrate. The key responses result in diagrams indicating whether yielding or fracture occurs first. In this kind of diagram, the ratio of coating fracture strength to substrate yield is related to the contact radius in indentation. As it is difficult to determine the contact radius experimentally, the latter has been found numerically and has also been approximated analytically. The analytical approximation plays an important role as it identifies the general loading condition for various sphere radii. This approximation can be extended to predicting the unloading curve which allows the elastic properties of a coated substrate to be determined.