The prediction of the length of sub-critical cracks is important for damage tolerant structures, because there exist a crack length at which the structure will fail. Since the crack growth process is not deterministic, the predicted crack length is represented by a distribution. Getting an accurate crack length distribution is the basis of reliability analysis. An accurate prediction reduces the risk of failure of a structure and the cost of maintenance, by providing an optimized inspection interval based on the reliability of the structure. In this dissertation, both fatigue and stress corrosion cracks (SCC) are considered.;In the first part of this dissertation, Chapters 2 and 3, a comprehensive SCC growth analysis is presented, and the reliability of a structure containing an SCC has been assessed. Two SCC growth mechanisms, anodic dissolution (AD) and hydrogen embrittlement (HE), were considered to determine the SCC growth rate of AA7050-T6 for a surface-breaking crack with a blunt tip in an aqueous environment. The relative contribution of each mechanism and their interactions have been quantitatively assessed. Results show that AD provides critical conditions for HE, which explains in part a step-wise propagation of the crack. Finally the total crack growth rate due to the combined effects of AD and HE has been determined, and numerical results have been compared with experimental data, and a calculation of the crack growth rate for a practical configuration has been presented.;Using the result of SCC growth analysis with important but uncertain factors, probabilistic SCC growth analysis has been developed, and the reliability of the cracked structure has been determined. Based on the data from designed computer experiments, the computer code developed in Chapter 2 to conduct deterministic SCC growth analysis has been represented by metamodels together with a Gaussian process regression. Through sensitivity analysis, important variables which need to be calibrated have been identified. A dynamic Bayesian network (DBN) model and a Monte Carlo simulation (MCS) have been utilized to quantify uncertainties. Statistical parameters of input variables have been obtained by a machine learning technique. The calibrated model has been validated using Bayesian hypothesis testing. Since the DBN model yields a probability of detection (POD) comparable to the probability based on binary validation data, the probabilistic model with calibrated parameters is expected to be a good representation of the growth of an SCC. The results also show that reliability largely depends on the accuracy of flaw detection methods and on the critical crack length.;The second part of this dissertation, Chapter 4, focuses on an application of the framework developed in the first part to a structure containing a fatigue crack. A more realistic nondestructive inspection (NDI) model based on the eddy current inspection (ECI) response of both the actual rotor blade and bolt hole specimens containing cracks of known lengths was incorporated in the DBN model to predict the reliability of a jet engine compressor rotor blade containing a fatigue crack. The detection threshold and the POD curve were determined. A DBN model was used to quantify uncertainties. The model includes a realistic ECI response model, so that it is possible to consider all relevant inspection data types. Factors which contribute the most to the variation of crack length have been determined by sensitivity analysis, and have been calibrated using the field inspection data. Part of the inspection data was used to validate the calibrated model, and a Bayes factor of 9.93 which corresponds to a confidence level of 91% was obtained. Based on the control level for the reliability index, betactrl=3, and the reliability indices calculated from the calibrated model, the recommended interval for the first inspection has been determined as 1600h. This interval is smaller than the actual current interval which is 3200h.
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