Metrological analysis of the four-point bending test for quantifying the photoelastic behavior of materials

In this work, a method for evaluating stress-optic coefficient measurements and their uncertainty on a four-point bending specimen is presented. Other previously used methods approached this issue by considering multiple data through an ordinary least squares fit; but they only take into account the repeatability contribution to uncertainty, so they are not consistent with the ISO-Guide to the expression of Uncertainty in Measurement. The method presented here uses a general least squares fit with which it is possible to consider all possible contributions to uncertainty. The application of the method is illustrated with an example, from which it can be seen that uncertainty has been underestimated in the results of the other methods used to date. In addition to the estimate of the stress-optic coefficient and its corresponding standard uncertainty, the method also provides a test to check the consistency of the data and an outlier identification tool.