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http://dx.doi.org/10.3795/KSME-A.2014.38.11.1245

Estimation of Fatigue Crack Growth using Gamma Process Model  

Park, Sung Ho (Defense Systems Test Center, Agency for Defense Development)
Kim, Jae Hoon (Dept. of Mechanical Design Engineering, Choongnam Nat'l Univ.)
Publication Information
Transactions of the Korean Society of Mechanical Engineers A / v.38, no.11, 2014 , pp. 1245-1256 More about this Journal
Abstract
The physical nature of fatigue shows the considerable amount of scatter from intrinsic and extrinsic factors. In this study, some degradation models, such as the gamma process model, were reviewed in terms of uncertainties associated with the continuous, gradual, and monotonic nature of fatigue crack growth. Statistically varying fatigue crack growth data obtained from Lu and Meeker were used as an example to demonstrate the use of the gamma process model. This model can describe the condition and lifetime as statistical distribution curves whose shapes vary with cycles. From the skewness of the statistical distribution curves, it was confirmed that the median is suitable for being considered as the expected life. The use of the gamma process model enables the optimum replacement period and percentile life to be employed as criteria for preventive maintenance policy.
Keywords
Fatigue Crack Growth; Gamma Process; Fatigue Life; Optimal Replacement Period; Percentile Life;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
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1 van Noortwijk, J.M. and Pandey, M.D., 2005, "Gamma Processes for Time-Dependent Reliability of Structures," Proceedings of European Safety and Reliability Conference, pp. 1457-1464.
2 van Noortwijk, J.M., 2009, "A Survey of the Application of Gamma Processes in Maintenance," Reliability Engineering & System Safety, Vol. 94, pp. 2-21.   DOI   ScienceOn
3 van Noortwijk, J.M., Cooke, R.M. and Kok, M., 1995, "A Bayesian Failure Model Based on Isotropic Deterioration," European Journal of Operational Research, Vol. 82, No. 2, pp. 270-282.   DOI   ScienceOn
4 van Noortwijk, J.M. and Pandey, M.D., 2003, "A Stochastic Deterioration Process for Time-Dependent Reliability Analysis," Proceedings of the Eleventh IFIP WG 7.5 Working Conference on Reliability and Optimization of Structural Systems, pp. 259-265.
5 Park, S.H. and Kim, J.H., 2013, "The Stockpile Reliability of Propelling Charge for Performance and Storage Safety Using Stochastic Process," J. Korean Soc. Qual. Manag., Vol. 4, No. 1, pp. 135-148.   과학기술학회마을   DOI   ScienceOn
6 Antonisamy, B., Christopher, S. and Samuel, P.P., 2010, Biostatistics: Principles and Practice, Tata McGraw Hill, New Delhi.
7 Pandey, M.D., Yuan, X.-X. and van Noortwijk J.M., 2009, "The Influence of Temporal Uncertainty of Deterioration on Life-Cycle Management of Structures," Structure and Infrastructure Engineering, Vol. 5, No. 2, pp. 145-156.   DOI   ScienceOn
8 Paris, P.C. and Erdogan, F., 1960, "A critical Analysis of Crack Propagation Laws," Journal of Basic Engineering, Vol. 85, pp. 528-534.
9 Forman, R.G., Keary, V.E. and Engle, R.M., 1967, "Numerical Analysis of Crack Propagation in Cyclic Loaded Structures," Journal of Basic Engineering, Vol. 89, pp. 459-464.   DOI
10 Yang, J.N. and Manning, S.D., 1996, "A Simple Second Order Approximation for Stochastic Crack Growth Analysis," Engineering Facture Mechanics, Vol. 53, No. 5, pp. 677-686.   DOI   ScienceOn
11 Kim, S.J., Yoon, S.H., Jeon, C.H. and Kim, I.S., 2000, "A Study on Estimation of the Probability Distribution of Fatigue Crack Growth Life for Steel," Journal of Ocean Engineering and Technology, Vol. 14, No. 4, pp. 73-78.
12 Kim, S.J., 2003, "Characteristics of Parameters for the Distribution of Fatigue Crack Growth Lives Under Constant Stress Intensity Factor Control," Journal of Ocean Engineering and Technology, Vol. 17, No. 2, pp. 54-59.
13 Yang, J.N., Salivar, G.C. and Annis, Jr., C.G., 1983, "Statistical Modeling of Fatigue Crack Growth in a Nickel-Based Superalloy," Engineering Fracture Mechanics, Vol. 18, No. 2, pp. 257-270.   DOI   ScienceOn
14 Lee, O.S., 2008, Introduction to Stochastic Process, 3rd Ed., Kyungmoonsa, Seoul, pp. 41-91.
15 Edirisinghe, R., Setunge, S. and Zhang, G., 2011, "Application of Gamma Process for Deterioration Prediction of Buildings from Discrete Condition Data," SRI LANKAN Journal of Applied Statistics, Vo. 12, pp. 13-25.
16 Kim, J.K. and Shim, D.S., 1996, "A Stochastic Analysis of Variation in Fatigue Crack Growth of 7075-T6 Al Alloy," Tran. of the KSME(A), Vol. 20, No. 7, pp. 2159-2166.   과학기술학회마을
17 Lee, O.S., 1998, "Fatigue Life Prediction by Statistical Approach Under Constant Amplitude Loading," KSME International Journal, Vol. 12, No. 1, pp. 67-72.   DOI
18 Seo, C.M., 2011, Fatigue and Fracture Mechanics, Wonchang, Incheon, pp. 1-16.
19 Shim, D.S. and Kim, J.K., 1998, "A stochastic Analysis on Variation of Fatigue Crack Propagation due to Thickness Effect," Trans. Korean Soc. Mech. Eng. A, Vol. 22, No. 8, pp. 1523-1532.
20 Tanaka, K., Hoshide, T. and Nakata, M., 1983, "Elastic-Plastic Crack Propagation Under High Cyclic Stresses," ASTM STP 803, p.707.
21 Lados, D.A. and Apelian, D., 2006, "The Effect of Residual Stress on the Fatigue Crack Growth Behavior of Al-Si-Mg Cast Alloys-Mechanisms and Corrective Mathematical Models," Metallurgical and Materials Transactions A, Vol. 37A, pp.133-145.
22 Makhlouf, K. and Jones, J.W., 1993, "Effects of Temperature and Frequency on Fatigue Crack Growth in 18% Cr Ferritic Stainless Steel," Int. J. Fatigue, Vol. 15, No. 3, pp.163-171.   DOI   ScienceOn
23 Bogdanoff, J.L. and Kozin, F., 1985, Probabilistic Models of Cumulative Damage, Wiley-Interscience, New York.
24 Bradshaw, F.J. and Wheeler, C., 1969, "The Influence of Gaseous Environment and Fatigue Frequency on the Growth of Fatigue Cracks in some Aluminum Alloys," International Journal of Fracture Mechanics, Vol. 5, No. 4, 255-268.
25 Brotzu, A., Cavallini, A., Felli, F. and Marchetti, M., 1998, "Influence of Corrosion on Fatigue Crack Growth Propagation of Aluminium Lithium Alloys," Fatigue in the Presence of Corrosion Workshop, pp.8-1-8-12.
26 Lu, C.J. and Meeker, W.Q., 1993, "Using Degradation Measures to Estimate a Time-to-Failure Distribution," Technometrics, Vol. 35, No. 2, pp. 161-174.   DOI   ScienceOn
27 Kim, J.K. and Kim, D.S., 1995, "A Probabilistic Analysis for Fatigue Cumulative Damage and Fatigue Life in CFRP Composites Containing a Circular Hole," Tran. of KSME, Vol. 19, No. 7, pp. 1915-1926.   과학기술학회마을