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

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.