Duality of the S–N fatigue curve caused by competing failure modes in a titanium alloy and the role of Poisson defect statistics

The mechanism of the duality of the S–N fatigue data (S is stress and N is cycles to failure) or the grouping of data into two distinct S–N curves as a result of two competing failure modes, occurring during fatigue of some α + β microstructures of the metastable beta-titanium alloy Ti–10V–2Fe–3Al, is quantitatively assessed in this research. The competing failure modes result in two separate fatigue curves in this material: one for failures from surface-nucleated cracks and the other for the subsurface-nucleated. The consequence of this behavior is that one can not predict exactly how a specimen or component would fail, regardless of the number of samples tested. This work discusses in detail the microstructural conditions that trigger this phenomenon in the titanium alloy studied. Based on Poisson defect statistics and Monte-Carlo simulations, it is shown that this phenomenon can arise from a Poisson spatial pattern of low populations of microscale defects. An interesting finding is that there should be a combination of average defect density and specimen area at which this phenomenon is observable in any material having sparsely populated and Poisson-distributed defects. The complete analysis presented here also helps to explain the duality of fatigue failures caused by competing failure modes observed in steels and superalloys.