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.

纳米压痕早已报道了尺寸依赖性硬度，但是相应的解释仍在探索中。在这项工作中，研究了表面能对球形压痕下材料硬度的影响。为了评估材料抵抗压痕的能力，我们将屈服硬度定义为屈服开始时的接触压力。已经发现，该限定的硬度是固有的材料性质，仅取决于常规连续体力学中的屈服强度和泊松比。然后，通过有限元模拟研究了表面能对屈服硬度的影响。通过尺寸分析，获得了屈服硬度和临界压痕深度对表面能的依赖性。当屈服强度与表面能密度与压头半径之比相当时，屈服硬度和临界压痕深度都会受到表面能的显着影响。这项研究可能澄清了硬度的大小依赖性，并提供了一种通过纳米压痕测量固体的屈服强度和表面能的潜在方法。