Size dependent yield hardness induced by surface energy

TL;DR

This paper investigates how surface energy influences the size-dependent hardness in nanoscale indentations, revealing that surface energy significantly affects yield hardness and critical indentation depth at small scales.

Contribution

It introduces a finite element simulation approach combined with dimensional analysis to quantify the impact of surface energy on yield hardness and indentation size effects.

Findings

Surface energy alters yield hardness when comparable to material strength.

Yield hardness and critical indent depth increase at nanoscale sizes.

Size dependence of hardness can be explained by surface energy effects.

Abstract

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.