In this paper, we report on a study of the surface effect on nanoindentation and introduce the apparent surface stress that represents the energy dissipated per unit area of a solid surface in a nanoindentation test. The work done by an applied indentation load contains both bulk and surface work. Surface work, which is related to the apparent surface stress and the size and geometry of an indenter tip, is necessary in the deformation of a solid surface. Good agreement is found between theoretical first-order approximations and empirical data on depth-dependent hardness, indicating that the apparent surface stress plays an important role in depth-dependent hardness. In addition, we introduce a critical indentation depth. The surface deformation predominates if the indentation depth is shallower than the critical depth, while the bulk deformation predominates when the indentation depth is deeper than the critical depth.
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