Size-dependent yield hardness induced by surface energy

Abstract

Size-dependent hardness has long been reported in nanosized indentations, however the corresponding explanation is still in exploration. In this work, the influence of surface energy on the hardness of materials under spherical indentation is examined. To evaluate the ability of materials to resist indentation, we define a yield hardness as the contact pressure at the inception of yield. It is found that this defined hardness is an intrinsic material property depending only on the yield strength and Poisson’s ratio in conventional continuum mechanics. Then, the impact of surface energy on the yield hardness is investigated by finite element simulations. Through dimensional analysis, the dependences of the yield hardness and the critical indent depth on surface energy have been achieved. When the yield strength is comparable to the ratio of surface energy density to indenter radius, both the yield hardness and the critical indent depth will be affected significantly by surface energy. 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.