Probabilistic micromechanical description of fatigue crack initiation

Abstract

In this paper the Mura-Nakasone model for fatigue crack initiation is extended to the situation where randomness in material microstructure (e.g. in grain size) and in the applied stress are important factors. The analysis and formulae presented provide a quantitative characterization of the effect of statistical scatter in grain size of the metals on the crack initiation time. Also, crack initiation time is analyzed for the situation where the applied stress is a narrow-band stationary stochastic process. The mean value, variance and probability distribution of the time to crack initiation are derived, and the results are illustrated graphically for real empirical data.