A Probabilistic Treatment of Microstructural Effects on Fatigue Crack Growth of Large Cracks

Abstract

A probabilistic model has been developed for treating the effects of microstructural variation on the fatigue crack growth response of large cracks in structural alloys. The proposed methodology is based on a microstructure-based fatigue crack growth law that relates the crack growth rate, da/dN, to the dislocation barrier spacing, yield stress, fatigue ductility coefficient, Young’s modulus, and the dislocation cell size or crack jump distance. Probabilistic treatment of these microstructure-dependent variables has led to a fatigue crack growth law that includes explicitly the randomness of the yield stress, fatigue ductility coefficient, and the dislocation barrier spacing in the response equation. Applications of the probabilistic crack growth model to structural reliability analyses for steels and Ti-alloys are illustrated, and the probabilistic sensitivities of individual random variables are evaluated.