Thickness effect on the indentation of an elastic layer

Sneddon's solution has been used in indentation tests to analyze elastic behavior of materials, in which the result ignores the effect of specimen thickness. However, in the real situation, the specimen thickness especially for thin films may not be negligible when the ratio of contact radius to the specimen thickness is larger than one. An analytical solution of the load-displacement relationship was derived for the indentation problem of an elastic layer by a rigid flat-ended cylindrical indenter. To obtain the closed-form solution, frictionless condition was used at contact interfaces. The contact force is found to be inversely proportional to the film thickness and independent of the contact radius if the contact radius is much larger than the film thickness. Then the effect of adhesion between the elastic layer and the indenter was addressed and an analytical solution of the pull-off force was obtained. The pull-off force is a function the layer thickness and Poisson's ratio, which increases with Poisson's ration and the ratio of the contact radius to the layer thickness.