Influence of frictional contact on indentation of elastic layer under surface energy effects

Abstract

The paper examines the influence of frictional contact on an indentation problem of a finite-thickness elastic layer under a rigid flat-ended cylindrical indenter considering surface energy effects based on Coulomb friction model. The continuum-based approach corresponding to the complete version of Gurtin-Murdoch surface elasticity model is adopted to demonstrate the influence from surface energy. Normal and radial displacement boundary conditions in the contact region corresponding to the frictional indentation problem is formulated in the term of integral equations by employing the relevant displacement Green's function obtained by the use of Hankel integral transform. The contact tractions are solved by applying a collocation technique together with the assumption of a piecewise distribution for the tractions within each discretized annular ring element. The accuracy of proposed solution scheme is validated with existing solutions from classical continuum mechanics for frictional indentation problem of an elastic half-space. Selected numerical results are presented to demonstrate the influence of friction effects on the elastic fields of the layer under the influence of surface energy. It is found that the consideration of frictional contact makes the layer stiffer when compared to the frictionless indentation, and the influence of friction effect is smaller when the surface energy effects are accounted for. In addition, the elastic fields of the layer are clearly size-dependent and the elastic layer becomes stiffer with the presence of surface stresses.