Abstract
This paper proposes a lognormal distribution model to relate crack-length distribution to fatigue damage accumulated in aging airframes. The fatigue damage is expressed as fatigue life expended (FLE) and is calculated using the strain-life method and Miner's rule. A two-stage Bayesian updating procedure is constructed to determine the unknown parameters in the proposed semi-empirical model of crack length versus FLE. At the first stage of the Bayesian updating, the crack closure model is used to simulate the crack growth based upon generic but uncertain physical properties. The simulated crack-growth results are then used as data to update the uninformative prior distributions of the unknown parameters of the proposed semi-empirical model. At the second stage of the Bayesian updating, the crack-length data collected from field inspections are used as evidence to further update the posteriors from the first stage of the Bayesian updating. Two approaches are proposed to build the crack-length distribution for the fleet based on individual posterior crack distribution of each aircraft. The proposed distribution model of the crack length can be used to analyze the reliability of aging airframes by predicting, for instance, the probability that a crack will reach an unacceptable length after additional flight hours.
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