Validation of contact mechanics models for Atomic Force Microscopy via Finite Elements Analysis and nanoindentation experiments

TL;DR

This study validates contact mechanics models for AFM nanoindentation on elastic samples, demonstrating the effectiveness of corrected Hertz and Sneddon models through finite element simulations and experiments, ensuring accurate Young's modulus measurements.

Contribution

It introduces and validates a corrected Hertz model and a new linearized Sneddon model for improved accuracy in AFM nanoindentation analysis of elastic samples.

Findings

Corrected Hertz model accurately measures Young's modulus at large indentations.

Validation of a new linearized Sneddon model for spherical indenter.

Finite element simulations support the experimental results.

Abstract

In this work, we have validated the application of Hertzian contact mechanics models and corrections for the analysis of force vs indentation curves, acquired using spherical indenters on linearly elastic samples, by means of finite elements simulations and AFM nanomechanical measurements of polyacrylamide gels possessing a thickness gradient. We have systematically investigated the impact of both large indentations and vertical spatial confinement (bottom effect) on the accuracy of the nanomechanical analysis performed with the Hertz model for the parabolic indenter compared to the Sneddon model for the spherical indenter. We demonstrated the accuracy of the combined correction of large indentation and bottom effects for the Hertz model proposed in the literature in the framework of linearized force vs indentation curves acquired using spherical indenters, as well as a validation of a new linearized form of the Sneddon model. Our results show that the corrected Hertz model allows to accurately quantify the Young's modulus of elasticity of linearly elastic samples with variable thickness at arbitrarily large indentations.