Indentation load–depth relation for an elastic layer with surface tension

Abstract

The load–depth relation is a fundamental requisite in nanoindentation tests for thin layers; however, the effects of surface tension are seldom included. This paper concerns micro-/nano-sized indentation by a rigid sphere of a bonded elastic layer. The surface Green’s function with the incorporation of surface tension is first derived by applying the Hankel integral transform, and subsequently used to formulate the governing integral equation for the axisymmetric contact problem. By using a numerical method based on the Gauss–Chebyshev quadrature formula, the singular integral equation is solved efficiently. Several numerical results are presented to investigate the influences of surface tension and layer thickness on contact pressure, surface deformation, and bulk stress. It is found that when the size of contact is comparable to the ratio of surface tension to elastic modulus, the contribution of surface tension to the load–depth relation becomes quite prominent. With the help of a parametric study, explicit general expressions for the indentation load–depth relation as well as the load–contact radius relation are summarized, which provide the groundwork for practical applications.