Bayesian analysis of critical fatigue failure sources

•The inclusion size distribution from fatigue testing is filtered by fatigue process.•Observation of an inclusion limits the possible sizes of other failure sources.•The presented model has enhanced fatigue size effect prediction capabilities. A novel approach for inferring the underlying non-metallic inclusion distribution from fatigue test fractography is presented. It is shown that the non-metallic inclusion size distribution obtained from fatigue testing differs from the extreme value distributions, which do not take fatigue into account. Fatigue, as a process, acts as a filter for the observed inclusions, and by taking advantage of this allows us to extract more refined information from the fractography using statistical inference. The emphasis in this paper is on analysis of axial fatigue testing of smooth specimens. The concepts presented here apply to all fatigue testing where the data from fracture surfaces is collected.