On the distribution and scatter of fatigue lives obtained by integration of crack growth curves: Does initial crack size distribution matter?

By integrating the simple deterministic Paris' law from a distribution of initial defects, in the form of a Frechet extreme value distribution, it was known that a distribution of Weibull distribution of fatigue lives follows exactly. However, it had escaped previous researchers that the shape parameter of this distribution tends to very high values (meaning the scatter is extremely reduced) when Paris' exponent m approaches 2, leading to the exponential growth of cracks with number of cycles. In view of the fact that values close to m = 2 are of great importance in materials for example used for primary aircraft structures as recognized by some certification requirements (and the so-called "lead crack" methodology), we believe this conclusion may have some immediate relevance for damage tolerance procedures, or certification methods where accurate description of scatter is required. Indeed, we extend the result also to the case when Paris' constant C is distributed, and give also an estimate of the level of scatter expected in propagation life in the most general case when C, m are both random variate along with the defect size distribution, based on first transforming them to uncorrelated form C-0, m, and validate this with the famous Virkler set of data. We finally discuss that from known typical values of fatigue life scatter of aeronautical alloys, it is very likely that an important contribution comes from short crack growth.