Indentation Hardness Measurements at Macro-, Micro-, and Nanoscale: A Critical Overview

Abstract

The Brinell, Vickers, Meyer, Rockwell, Shore, IHRD, Knoop, Buchholz, and nanoindentation methods used to measure the indentation hardness of materials at different scales are compared, and main issues and misconceptions in the understanding of these methods are comprehensively reviewed and discussed. Basic equations and parameters employed to calculate hardness are clearly explained, and the different international standards for each method are summarized. The limits for each scale are explored, and the different forms to calculate hardness in each method are compared and established. The influence of elasticity and plasticity of the material in each measurement method is reviewed, and the impact of the surface deformation around the indenter on hardness values is examined. The difficulties for practical conversions of hardness values measured by different methods are explained. Finally, main issues in the hardness interpretation at different scales are carefully discussed, like the influence of grain size in polycrystalline materials, indentation size effects at micro-and nanoscale, and the effect of the substrate when calculating thin films hardness. The paper improves the understanding of what hardness means and what hardness measurements imply at different scales.

Adaptive hard and tough mechanical response in single-crystal B1 VNx ceramics via control of anion vacancies

“…MgO is selected as substrate material because it is isostructural with VN and exhibits a sufficient film/substrate lattice mismatch (0.9%) to enable film relaxation, a necessity for the investigation of intrinsic properties. VNx(001) hardness and Young's moduli values as a function of x are quantified [21,22] via nanoindentation experiments performed on 300-nm-thick films in a Hysitron TI950 Triboindenter using a sharp Berkovich 142.3° diamond probe (tip radius ~150 nm) calibrated to an epitaxial TiN/MgO(001) sample. Nine indentations, arranged in a 3 × 3 pattern with indents separated by 10 µm, are made in each sample with a maximum tip penetration limited to 10% of the film thickness, which was verified to avoid spurious substrate effects on measured hardness values.…”

Reactive magnetron sputtering of tungsten target in krypton/trimethylboron atmosphere

“…The "rule of thumb" for nanoindentations, stating that the indenter should not penetrate more than 10% of the total film thickness, has been shown to fail in many materials (see [36] and references therein). In some of our W-B-C films, the maximum penetration depth hmax was calculated using the graphical method explained in the standard ISO 14577 Part 4 [37].…”

“…To compare reported values on elastic modulus (E) from the literature with our measured Er values, we applied the formula; 1/Er=((1-n 2 )/E)+((1-ni 2 )/Ei)) from ref. [36] and assumed: a Poisson's ratio for the sample n=0.25, a Poisson's ratio for the indenter of n=0.07, and the elastic modulus of the indenter to be Ei=1140 GPa. Figure 1a shows the elemental composition obtained from the quantitative analysis of XPS spectra for W-B-C films deposited with TMB flows of 1, 2.5, 5, 7.5, and 10 sccm at 500 o C. As observed, all films are metal-rich and where the W content decreases from ~ 93 at% to ~ 73 at% from with increasing TMB content in the plasma.…”

A quantitative analysis of the indentation fracture of fused silica

“…The fracture toughness K Ic of fused silica was set to be 0.75 MPa·m 1/2 which was measured using the double‐cantilever cleavage technique . In addition, the Poisson's ratio ν i and the Young's modulus E i of the diamond indenter were 0.07 and 1140 GPa, respectively …”