The role of plastic deformation of rough surfaces in the size-dependent hardness

In this study, we propose a bearing ratio model for nanoindentation of rough surfaces. During an indentation test, the work done by an applied indentation load contains the bulk work and the surface work. The surface work causes plastic deformation of an indented rough surface and thus dissipates energy, which is necessary to form an impression on a solid. The energy dissipation occurring at the indented surface is among the factors that cause the Indentation Size Effect (ISE) at the micro/nanometer scales. In particular, the surface effect predominates when the indentation depth is shallow. Good agreement is found between the theoretical and experimental results of the size-dependent hardness, indicating that the surface effect plays an important role in size-dependent hardness.