Duality of fatigue failures of materials caused by Poisson defect statistics of competing failure modes

The statistical nature of failures of components subjected to fatigue loading is a major challenge in engineering applications. Here, we report an interesting fatigue phenomenon in which there is a 'duality' of the S-N fatigue data (S is stress and N is cycles to failure)--the grouping of data into two distinct S-N curves as a result of two competing failure modes. The proportions of failure by either mode are about the same and one cannot predict which failure mode will eventually dominate. This means that fatigue lives may be unpredictable in materials under certain application conditions and the consequences can be disastrous. Based on Poisson defect statistics and Monte Carlo simulations, we show that this phenomenon can arise from the Poisson distribution of low populations of microscale defects. An unexpected finding is that there should be a combination of average defect density and specimen area at which this phenomenon is observable in materials having sparsely populated defects.