Determination and Uncertainty Propagation of Sensitivity Coefficients in Rockwell Hardness Measurements

In the field of hardness measurements, a problem arises when trying to understand how different measurement parameters (such as speed of the indenter, force, maximum displacement, thermal drift, etc.) affect the outcome of the measurement itself. Because the mathematical model defining hardness scales do not consider such factors, the simplest way to include additional influence parameters in the mathematical model is to introduce them linearly via sensitivity coefficients, which are obtained experimentally and thus characterized by uncertainties. However, uncertainties of the sensitivity coefficients are in general not considered in the evaluation of the combined standard uncertainty of the hardness measurements. In this paper a general procedure is presented and applied to practical case-studies on HRA and HRC hardness measurements. In this field, the international definitions (standards) state each sensitivity coefficient for influence parameters about specific reference values: additional (generally neglected) uncertainty contributions reflect how much the measurements fail to be performed at exactly the prescribed reference values. Indeed, in the second case-study presented in this paper, we have found that the expanded uncertainty obtained via the proposed method is about 50 % larger than the one reported in the example of the international guidelines. This result highlights the importance of considering the uncertainties of the sensitivity coefficients when evaluating the combined standard uncertainty of any measurement.