Abstract
Abstract The disc under diametral compression is one of the preferred specimens for the calibration of photoelastic materials. Current calibration methods have some limitations from a metrological point of view, because they do not provide measurement uncertainties and they assume that observations are independent and with the same accuracy. In this work, a new calibration method is proposed to avoid the above-mentioned metrological limitations: The generalized least squares by Lagrange multipliers method. This methodology accepts correlated input quantities or with different accuracy through the input covariance matrix, and it provides, through a least-squares adjustment, the estimates of the quantities to be measured and their associated standard uncertainties. The application of the method shows coherent results and it also provides a chi-square value that can be used to test the consistency of the measurement model, and the normalized deviations between the input estimates and their fitted values, which are a tool to identify potential outliers. Results reveal a great influence of the radius of the specimen on the uncertainty of the stress-optic coefficient measurement, which casts serious doubt on previous affirmations about the disc in compression is preferable over other specimens.
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