Crack initiation lives

Y. Kondo, Prediction of fatigue crack initiation life based on pit growth. Corrosion 45, 7 (1989). 

Since fatigue cracks often start at a random surface imperfection, considerable scatter occurs in fatigue data, increasing with the increasing lifetime wherever crack initiation occupies most of the fatigue life of a specimen. When a line of the best fit is drawn from the available data points on an S-N curve, this represents the mean life expected at any given stress level or the stress that would cause, say, 50% of the product failures in a given number of cycles. 

Saintier, N., Multiaxial fatigue life of a natural rubber crack initiation mechanisms and local fatigue life criterion, Ph.D. dissertation, Ecole des Mines de Paris, 2001. 

Fatigue failure in metals is known to consist of crack initiation and growth. Crack initiation starts with dislocation movement. Submicrocracks are then formed at slip bands. They subsequently grow and coalesce to form a crack of detectable size (short crack) to complete the crack initiation process [12]. This is then followed by the growth of a single crack until final rupture. The period of crack initiation and submicrocrack growth covers most of the fatigue life. 

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