Extension of the Hertz model for accounting to surface tension in nano-indentation tests of soft materials

TL;DR

This paper extends the classical Hertz model for nano-indentation of soft materials by incorporating surface tension effects through a finite element model, revealing significant influence on force measurements.

Contribution

It introduces a numerical finite element approach to account for surface tension in nano-indentation, refining the Hertz model for soft materials.

Findings

Surface tension significantly affects indentation force responses.

Force vs. depth follows a power law with material-dependent constants.

Classical Hertz model validity is limited at nano-scale with soft materials.

Abstract

The contact between a spherical indenter and a solid is considered. A numerical finite element model (F. E. M) to taking into account the surface tension of the solid is presented and assessed. It is shown that for nano-indentation of soft materials, the surface tension of the solid influences significantly the reaction force due to indentation. The validity of the classical Hertz model is defined. In very good approximation, the force vs. indentation depth curve can be fitted by a power law function $F=a^\delta b$ where $F$ denotes the force acting on the indentor, $d$ the indentation depth, $a$ and $b\in\ ]1,1.5]$ are constants depending on the materials and the size of the indentor.