# Microhardness Variation with Indentation Depth for Body-Centered Cubic Steels Pertinent to Grain Size and Ferrite Content

## TL;DR

This paper studies how microhardness changes with indentation depth in steels, linking it to grain size and ferrite content for better predictions.

## Contribution

A new analytical model connects microhardness to macrohardness using grain size and ferrite volume fraction.

## Key findings

- The proposed model predicts microhardness variation with 96% reliability.
- Characteristic indentation depth is explicitly linked to grain size and ferrite content.
- Normal distribution theory accounts for measurement scatter due to material heterogeneity.

## Abstract

For a micro-indentation hardness test with non-destructivity, the Nix–Gao model is widely used to describe tested hardness or microhardness variation with an indentation depth induced by indentation size effect, in which tested hardness approaches the macrohardness when the indentation depth is large enough. Based on an analysis of hardness measurements on 10 body-centered cubic steels with diverse microstructure, this paper proposes an analytical relation between microhardness to macrohardness ratio and the indentation depth by explicitly linking characteristic indentation depth (a data-fitting parameter) to grain size and ferrite volume fraction using two different methods. In addition, the normal distribution theory is incorporated to consider the inevitable scatter of identical measurements resulting from material heterogeneity and machining/testing errors. Results show that the proposed model, with 96% reliability, can effectively predict microhardness variation with the indentation depth and its scatter.