Research Papers

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

[+] Author and Article Information
Dooyoul Lee, Yonggang Huang, Jan D. Achenbach

Department of Mechanical Engineering,
McCormick School of Engineering
and Applied Science,
Northwestern University,
Evanston, IL 60208

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received September 11, 2015; final manuscript received October 20, 2015; published online November 11, 2015. Assoc. Editor: Arun Shukla.

J. Appl. Mech 83(2), 021003 (Nov 11, 2015) (9 pages) Paper No: JAM-15-1496; doi: 10.1115/1.4031899 History: Received September 11, 2015; Revised October 20, 2015

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.

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Fig. 1

Flowchart for the deterministic crack propagation analysis, where t is the time, ϕs is the potential of solution, itip is the crack tip current density, NH is the hydrogen permeation flux through the surface of the crack, ci is the concentration, Di is the diffusion coefficient, and ui is the mobility of species i

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Fig. 2

(a) and (c) Response versus Jackknife prediction, and (b) and (d) a surface generated from metamodel versus crack length (a) and applied stress (σ)

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Fig. 3

(a) Posterior SCC length distribution over time, and (b) reliability index with inspection every 30 days

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Fig. 4

Fishbone diagram for SCC growth rate variability

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Fig. 5

Bayesian network for SCC analysis

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Fig. 6

(a) Posterior SCC length distribution over time and (b) reliability index calculated from both DBN model and MCS

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Fig. 7

(a) The effect of the number of detections on Bayes factor and (b) maximum Bayes factor obtained from the posterior distribution with k = 5 and n = 10, Beta(6, 6). POD equal to 49.9% from the calibrated DBN model is indicated as a dashed line.

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Fig. 8

(a) Calibrated EApp and (b) reliability index with inspection every 30 days




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