Approximate Expression for Stress Distribution in Film Subjected to Indentation by Spherical Indenter (The Case of a Very Thin Film)

In electronic devices, magnetic disks and micromechanical sysems, thin films coated on substrates are widely used. In order to develop a method for evaluation of their fracture strengths by means of indentation by a small spherical indenter, it is necessary to study the stress distribution in a film subjected to such indentation. In this paper, an approximate expression for the elastic stress distribution is derived for the case where the film thickness is much smaller than the radius of the contact area. A finite-element analysis is also carried out to examine the accuracy of the approximate expression.