Bayesian analysis for determination and uncertainty assessment of strength and crack growth parameters of brittle materials

Abstract

To determine the strength and the crack growth parameters of brittle materials, the common approach is to first evaluate the strength and then the crack growth parameters. When the parameters are needed for different temperatures, the procedure is repeated for each temperature of interest. Since the number of test specimens is generally small, the separated analysis of strength and crack growth parameters for each tested temperature leads to large parameters uncertainty. In order to improve the accuracy of the parameters, we propose a Bayesian method that allows to combine all strength and lifetime data obtained at different temperatures and determine the distribution of all material parameters in a single analysis. The results obtained from the analysis of measured skutterudite data show that in comparison to the standard approach the presented method significantly reduces the material parameters uncertainty and therefore is well adapted for a reduced number of samples.