Evaluation of uncertainty in the measurement of the crack-tip stress field using photoelasticity

Photoelasticity has always played an important role in the experimental study of fracture mechanics. It can, with a degree of simplicity, be used to measure the parameters that characterize the crack-tip stress field. The so-called over-deterministic method is the most widely used in that regard. Although that particular method functions correctly, it has some metrological limitations: no measurement uncertainties are provided, observations are assumed to be independent and of equal accuracy, and its results may be skewed due to the misalignment of the coordinate axes in the data collection. In this article, it is shown that these limitations no longer apply when using the generalized least squares by Lagrange multipliers method. It provides not only an estimate of the quantities to be measured, as the over-deterministic method, but also a fitted estimate of the value of each input quantity; the covariance matrix of all these estimates from which both the standard uncertainties and correlation coefficients can be calculated; 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 tools to identify potential outliers.