Probabilistic Aspects of the Growth and Detection of Fatigue Cracks

For engineering structures, fatigue, and more specifically fatigue life prediction, is a problem of great interest. The first part of this dissertation focuses on the importance of probabilistic methods in structural health management in general, and how they can be applied to fatigue failure prognosis. Paris' law, using measured values of the parameters in the law, has been used to forecast fatigue crack growth from an assumed initial probability distribution of crack lengths, represented by a truncated lognormal distribution. The evolution of this distribution with the number of cycles has been determined, and the probability of the existence of a crack larger than an undesirable value, but smaller than the value where failure may occur, has been calculated. In addition, inspections have been modeled using three typical probability of detection curves, and the effect of an inspection has been evaluated. The probability of detection concept has also been extended using a Bayesian approach to include the effect of the number of elapsed cycles and the stress range of each cycle. All statistics considered in this dissertation have been evaluated for a surface-breaking crack in a half-space and a cracked rivet hole in a lap joint, both under cyclic tensile loading.;The second part of this dissertation focuses on an aspect of the diagnosis of fatigue cracks. The acoustic emission from fatigue crack growth has been calculated using the reciprocity relation, again for a surface-breaking crack in a half-space and a cracked rivet hole in a lap joint. This result, which is a stochastic quantity because the amount of crack growth is stochastic, is used to calculate the probability of detection of an acoustic wave emitted by the crack growth for these cases.