Calibration of photoelastic materials with the disc under diametral compression

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.