A generalized Anderson–Darling test for the goodness-of-fit evaluation of the fracture strain distribution of acrylic glass

Acrylic glasses, as well as mineral glasses, exhibit a high variability in tensile strength. To cope with this uncertainty factor for the dimensioning of structural parts, modeling of the stress-strain behavior and a proper characterization of the varying fracture stress or strain are required. For the latter, this work presents an experimental and mathematical methodology. Fracture strains from 50 quasi-static tensile tests, locally analyzed using digital image correlation, form the sample. For the assignment of an occurrence probability to each experiment, an evaluation of existing probability estimators is conducted, concerning their ability to fit selected probability distribution functions. Important goodness-of-fit tests are introduced and assessed critically. Based on the popular Anderson-Darling test, a generalized form is proposed that allows a free, hitherto not possible, choice of the probability estimator. To approach the fracture strains population, the combination of probability estimator and distribution function that best reproduces the experimental data is determined, and its characteristic progression is discussed with the aid of fractographic analyses.