Effects of surface stress on the indentation response of an elastic half-space

Nanoindentation technique, which is based on Hertzian contact theory and Sneddon's solutions for the contact between a rigid indenter and an elastic half-space, has been widely investigated due to its practical importance in localized mechanical test of submicron structures. However, both the Hertzian contact theory and Sneddon's solutions do not take into account the contribution of surface stress to contact deformation. In this work, we study the effect of surface stress without the out-of-plane term on the indentation deformation of an elastic half-space by rigid, axisymmetric indenters, including flat-ended cylindrical, conical and spherical indenters. In contrast to classical theories, which are based on physically admissible condition of finite normal stress at contact edge, an alternative condition of geometrical continuity at contact edge is used to determine the contact radius. The numerical results reveal the combinational effects of the surface stress and Poisson's ratio on the load-displacement relationship for the indentation of the elastic half-space. The surface stress causes significant change in shear stress and modest variation in normal stress in the direction normal to the surface of the elastic half-space. The numerical method used in this work offers a feasible approach to study the effect of surface stress on the contact deformation of elastic substrates.