  Size dependent hardness has long been reported in nanosized indentations,
however the corresponding explanation is still in exploration. In this paper,
we examine the influence of surface energy on the hardness of materials under
spherical indentation. To evaluate the ability of materials to resist
indentation, a yield hardness is defined here as the contact pressure at the
inception of material yield. It is found that this defined hardness is an
intrinsic material property depending only on the yield strength and Poisson
ratio in conventional continuum mechanics. Then, the impact of surface energy
on the yield hardness is analyzed through finite element simulations. By using
the dimensional analysis, the dependences of the yield hardness and critical
indent depth at yield initiation on surface energy have been achieved. When the
yield strength is comparable to the ratio of surface energy density to indenter
radius, surface energy will alter the yield hardness and the critical indent
depth. As the size of indenter decreases to nanoscale, both the yield hardness
and the indent depth will increase significantly. This study provides a
possible clarification to the size dependence of hardness and a potential
approach to measure the yield strength and surface energy of solids through
nanosized indentations.
