Probabilistic Analysis of Stress Corrosion Crack Growth and Related Structural Reliability Considerations

Abstract

The predetection evolution of stress corrosion cracking has been examined as a necessary preliminary to effective detection of such cracks. Anodic dissolution (AD) and hydrogen embrittlement (HE) have been considered to calculate the stress corrosion crack (SCC) growth in AA7050-T6 for a surface-breaking crack with blunt tip in an aqueous environment. Since these processes are not completely deterministic, several advanced statistical methods have been used to introduce probabilistic considerations. Based on the data from designed computer experiments, the computer code developed by the authors (Lee et al., 2015, “A Comprehensive Analysis of the Growth Rate of Stress Corrosion Cracks,” Proc. R. Soc. A, 471(2178), p. 20140703) to conduct deterministic stress corrosion crack growth analysis has been represented by metamodels using Gaussian process regression. Through sensitivity analysis, important variables which need to be calibrated have been identified. The dynamic Bayesian network (DBN) model and 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 well represent the growth of a stress corrosion crack. The results also show that the reliability largely depends on the accuracy of flaw detection methods and on the critical crack length.

Application of Bayesian Networks in Reliability Evaluation

“…Lee and Achenbach [55] analyzed the reliability of a jet engine compressor rotor blade with a fatigue crack by using DBNs; the structure of the DBNs was based on a fatigue crack growth model, and the parameters in the model were represented by the nodes. In [56], a similar method was used for the structural reliability analysis of stress corrosion crack growth. Straub [57] established a generic stochastic structural reliability analysis model for deterioration processes by using DBNs; the nodes represented the parameters in structural models, such as the fatigue crack growth model, and the structure of DBNs was constructed artificially.…”

“…For example, Lee and Achenbach [55] calibrated the parameters of DBNs for the reliability analysis of the rotor blade of a jet engine compressor by using an expectation maximization algorithm for the incomplete available inspection data. A similar method was used in [56] for the structural reliability analysis of stress corrosion crack growth.…”

“…Lee and Achenbach [55] used a forward-backward algorithm to achieve the exact inference of DBNs for the reliability analysis of a jet engine compressor rotor blade. A similar method was used in the structural reliability analysis of stress corrosion crack growth in [56]. In [57] and [60], a forward-backward algorithm was adopted to perform the exact inference of DBNs for a stochastic structural reliability analysis model for deterioration processes, and Straub and Kiureghian [59,61] applied exact inference algorithms to BNs for their proposed structural reliability framework by minimizing the enhanced BNs into reduced BNs.…”

“…Regarding the first type of method, Lee and Achenbach [55] validated a DBN-based model for the reliability analysis of a jet engine compressor rotor blade by using a Bayes factor and filed inspection data. For the second type of method, Lee et al [56] validated a structural reliability analysis methodology for stress corrosion crack growth by using Bayesian hypothesis testing and simulated inspection data. Groden and Collette [52] used synthetic inspection data generated by Monte Carlo simulation to validate a BN-based framework for updating structural performance and reliability of marine structures.…”

Probabilistic reliability of thermoplastic piping networks and maintenance strategy choice using Weibull distribution

“…Knowing the probability for success/failure from probability plots leads to the risk assessment using few data and helps the cost‐effective decision‐making process. Moreover, the probabilistic distribution has been used in Lee et al 13 to introduce stress corrosion cracking growth analysis. It has been shown that unlike the deterministic methods, which give a single measure per time unit, the probabilistic ones give the distribution of the predicted crack length through the outputs based on the variability of input variables, models, and measurements and get to the reliability afterwards.…”