Surface effect on the partial-slip contact of a nano-sized flat indenter

The partial-slip contact at nano-scale is always influenced by a surface effect. A new model based on the Gurtin-Murdoch (G-M) surface elasticity theory is proposed in this paper to study the partial-slip contact behavior of a rigid flat nano-indenter on an elastic half-space. The surface effect in the partial-slip contact is characterized via a non-classical boundary condition involving a surface-induced normal traction related to the residual surface stress and a surface-induced tangential traction related to the surface elasticity, the influences of which on stress and displacement fields and the stick-slip state at the contact surface are investigated. It is found that, with the increase of residual surface stress, both the normal pressure and vertical and horizontal displacements in the contact zone decrease, the relative slip between indenter and substrate reduces and the stick region is enlarged. Such effects are basically attributed to the action of the surface-induced normal traction opposite to the externally applied compression. However, the increase of surface elastic constants is conductive to the relative slip and results in a shrinkage of the stick region, which is attributed to the action of the surface-induced tangential traction opposite to the frictional stress. An interesting phenomenon is further unveiled that, when the frictional coefficient increases, the dominant role in affecting the stick-slip state changes from the surface-induced tangential traction to the normal one, thus inspiring a feasible route to manipulate the surface effect by tuning the frictional coefficient of substrate. The present research enables one to better understand the partial-slip contact behavior of nano-indenters, which is of guiding value for anti-wear designs in nano-mechanical devices.