Analysis of the effect of temperature on Vickers, Brinell, and Knoop hardness measurements

In 2023, the European Association of National Metrology Institutes (EURAMET) launched project 22RPT01 TracInd BVK-H. Project's main objective is to improve the traceability and reliability of hardness measurements using optical measurement methods, namely Brinell, Vickers, and Knoop (BVK) tests. One of the outcomes of this initiative is to assess how hardness measurements can be affected by possible influencing variables. Within this framework, this thesis tries to determine the sensitivity coefficients and related uncertainties for BVK methods that link hardness to the temperature at which the test is performed. The temperature range (15-35°C) used is that permitted in ISO standards for end users, such as a company's testing laboratory. The experimental campaign was carried out in the laboratories of the National Institute of Metrological Research (INRiM), with primary machines and performed after the design of active and passive temperature controls. Assuming a linear relationship between temperature and hardness, the data analysis was conducted using two different approaches, which proved to be compatible. The first statistical method proposed is Weighted Total Least Square (WTLS), which allowed the estimation of sensitivity coefficients and the Normalized chi squared value, an indicator of the goodness of the model. The second methodology used was a Monte Carlo simulation applied to linear regression, followed by an assessment of significance with respect to the heterogeneity of the hardness block. Finally, it is possible to appreciate a relationship between hardness and temperature even for this narrow range. All sensitivity coefficients found are between 0 and -3 HV/°C. Moreover, the analysis suggests that the hardness level of the block does not influence the variation relative to the change in test temperature.