The Surface and Thickness Effects on Two-Dimensional Nanocontact Behaviors of a Finite-Sized Elastic Layer

Abstract The nanoscale contact behavior of an elastic layer with a finite thickness is significantly influenced by the effects of not only surface but also layer thickness. Using the elasticity theory based on the surface energy density as well as the Fourier transformation technique, the two-dimensional frictionless contact problem of a rigid nanoindenter with a flat or cylindrical shape on a finite elastic layer is investigated. Integral solutions of stresses and displacements in the finite elastic layer are obtained, which take into account the effects of both surface and layer thickness. It is found that the surface effect results in a hardening of the finite elastic layer, which is basically due to the opposite action of the surface-induced normal traction to the externally applied compression. The decrease of layer thickness induces an increase of the normal stress and a decrease of the normal displacement in the contact region because of the constraint of the rigid substrate to the layer deformation. An interesting finding is also unveiled that the surface effect could effectively eliminate the bulging behavior in a very thin layer. Furthermore, an indentation hardness including the coupling effects of surface and thickness in the finite elastic layer is predicted, which increases with either an enhancing surface effect or a decrease of the layer thickness. The present research should be helpful for designs and performance evaluations of layer-substrate structures in practical engineering, such as coatings and microelectronic devices.