Structural Reliability Prediction Using Acoustic Emission-Based Modeling of Fatigue Crack Growth
Abstract
:1. Introduction
2. Experimental Approach
Noise Reduction
3. Analysis of Experimental Data and Results
3.1. Crack Growth Measurement
3.2. Test of Homogeneity
3.3. Probabilistic Model Development
3.3.1. Bayesian Data Analysis
3.3.2. Error and Uncertainty
- (a)
- Aleatory uncertainty: Also known as inherent uncertainty, aleatory uncertainty is a natural randomness of a quantity such as uncertainty in the material features. Generally, there are different factors during manufacturing of a material that cause random variation of the material properties from experiment to experiment [30]. To minimize aleatory uncertainty, test data of specimens from the same material lot (test samples coming from the same sheet of Al7075-T6 or Ti-6-4) were used. It should be noted that this physical variation is inherent to experiments and cannot be eliminated.
- (b)
- Epistemic uncertainties: This uncertainty is the result of limited information or incomplete information due to finite experimental data or a limited number of observed data points. The addition of experiments corresponding with each loading condition in the parameter estimation process can help reduce epistemic uncertainty bounds for the estimated model parameters. Two types of epistemic uncertainty are discussed below:
3.3.2.1. Model Error Estimation
3.4. Model Validation
4. Conclusions
Author Contributions
Conflicts of Interest
References
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Test Reference | Material | Loading Frequency (Hz) | Loading Ratio | Maximum Force (lbf) | Maximum Force (kN) |
---|---|---|---|---|---|
CT1 | Al7075-T6 | 10 | 0.1 | 500 | 2.22 |
CT2 | Al7075-T6 | 10 | 0.1 | 500 | 2.22 |
CT3 | Al7075-T6 | 10 | 0.3 | 500 | 2.22 |
CT4 | Al7075-T6 | 10 | 0.3 | 500 | 2.22 |
CT5 | Al7075-T6 | 10 | 0.5 | 500 | 2.22 |
CT6 | Al7075-T6 | 10 | 0.5 | 500 | 2.22 |
CT7 | Al7075-T6 | 2 | 0.1 | 500 | 2.22 |
CT8 | Al7075-T6 | 2 | 0.1 | 500 | 2.22 |
CT9 | Al7075-T6 | 7 | 0.1 | 500 | 2.22 |
CT10 | Al7075-T6 | 7 | 0.1 | 500 | 2.22 |
CT11 | Al7075-T6 | 10 | 0.1 | 500 | 2.22 |
CT12 | Al7075-T6 | 10 | 0.1 | 500 | 2.22 |
CT13 | Ti-6Al-4V | 5 | 0.1 | 900 | 4 |
CT14 | Ti-6Al-4V | 5 | 0.1 | 900 | 4 |
CT15 | Ti-6Al-4V | 5 | 0.1 | 900 | 4 |
Test | Frequency | R | α1 | α2 |
---|---|---|---|---|
CT1 | 10 | 0.1 | 0.03 | −11.46 |
CT2 | 10 | 0.1 | 0.03 | −11.17 |
CT3 | 10 | 0.3 | 0.03 | −11.09 |
CT4 | 10 | 0.3 | 0.02 | −12.01 |
CT5 | 10 | 0.5 | 0.03 | −11.97 |
CT6 | 10 | 0.5 | 0.02 | −11.77 |
CT7 | 2 | 0.1 | 0.02 | −10.88 |
CT8 | 2 | 0.1 | 0.05 | −13.86 |
CT9 | 7 | 0.1 | 0.02 | −10.86 |
CT10 | 7 | 0.1 | 0.02 | −10.74 |
CT11 | 10 | 0.1 | 0.04 | −12.91 |
CT12 | 10 | 0.1 | 0.04 | −13.41 |
Material | α1 | α2 | ε ~ N(με,s) | s ~ N(μs,σs) | ||
---|---|---|---|---|---|---|
µε | μs | σs | ||||
Al7075-T6 | 0.03 | −11.319 | 0 | 0.86 | 0.057 | |
Ti-6Al-4V | 0.006 | −4.971 | 0 | 0.24 | 0.010 |
Parameter | Mean | Standard Deviation | 2.5% | Median | 97.5% |
---|---|---|---|---|---|
bm | 0.009 | 0.011 | −0.013 | 0.009 | 0.031 |
sm | 0.059 | 0.008 | 0.045 | 0.058 | 0.078 |
Fm | 1.011 | 0.061 | 0.894 | 1.009 | 1.141 |
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Keshtgar, A.; Sauerbrunn, C.M.; Modarres, M. Structural Reliability Prediction Using Acoustic Emission-Based Modeling of Fatigue Crack Growth. Appl. Sci. 2018, 8, 1225. https://doi.org/10.3390/app8081225
Keshtgar A, Sauerbrunn CM, Modarres M. Structural Reliability Prediction Using Acoustic Emission-Based Modeling of Fatigue Crack Growth. Applied Sciences. 2018; 8(8):1225. https://doi.org/10.3390/app8081225
Chicago/Turabian StyleKeshtgar, Azadeh, Christine M. Sauerbrunn, and Mohammad Modarres. 2018. "Structural Reliability Prediction Using Acoustic Emission-Based Modeling of Fatigue Crack Growth" Applied Sciences 8, no. 8: 1225. https://doi.org/10.3390/app8081225