Estimation of Elastic Modulus with Multiple Indenters

Abstract

The conventional Oliver-Pharr method of estimating elastic modulus shows reasonably good accuracy, but errors occur due to inaccuracies in the actual contact area.

To resolve this issue, this study proposed a new method to estimate the elastic modulus using two different indenters without additional equipment or complicated calibration. We aimed to estimate the elastic modulus using the theoretical indentation depth, without the consideration of sink-in / pile-up effect.

A numerical indentation test was performed using Berkovich and spherical indenters, and the theoretical contact area and initial unloading slope of the indentation load-depth curve were calculated to derive c-ratio based on the correction factor c. Numerical validation using finite element analysis for various material properties of J₂ and pressure-dependent hardening models showed that the method estimates the elastic modulus with R ² = 98 %, outperforming the conventional method.

Microindentation tests were conducted on copper, Al1050, SS304 specimens for experimental validation. The estimated elastic moduli with proposed method showed good agreement with those from tensile tests with an error of 7 %.

This study proposed a new method for estimating elastic modulus that overcomes the limitations of the conventional method, which is difficult to accurately measure the actual contact area at maximum load, and has high applicability to various materials by using the correction factor c.