The fatigue limit: An analytical solution to a Monte Carlo problem

A new extreme value distribution based on log-normally distributed defects is presented. From this, an analytical solution to the random defect Monte Carlo problem in form of a distribution function characterizing the fatigue limit of an arbitrary component is derived. Surface defects, defined as internal defects intersecting a free surface, are incorporated into the model through an original analytical approach. The presented model is physically based and simple to implement and apply. Furthermore, the model was applied to a series of fatigue limit experiments found in the literature. The fatigue limit predictions were in good agreement with experimental results.