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http://dx.doi.org/10.12989/sem.2019.69.4.361

A new Bayesian approach to derive Paris' law parameters from S-N curve data  

Prabhu, Sreehari Ramachandra (School of Urban and Environmental Engineering, Ulsan National Institute of Science and Technology (UNIST))
Lee, Young-Joo (School of Urban and Environmental Engineering, Ulsan National Institute of Science and Technology (UNIST))
Park, Yeun Chul (Institute of Construction and Environmental Engineering, Seoul National University)
Publication Information
Structural Engineering and Mechanics / v.69, no.4, 2019 , pp. 361-369 More about this Journal
Abstract
The determination of Paris' law parameters based on crack growth experiments is an important procedure of fatigue life assessment. However, it is a challenging task because it involves various sources of uncertainty. This paper proposes a novel probabilistic method, termed the S-N Paris law (SNPL) method, to quantify the uncertainties underlying the Paris' law parameters, by finding the best estimates of their statistical parameters from the S-N curve data using a Bayesian approach. Through a series of steps, the SNPL method determines the statistical parameters (e.g., mean and standard deviation) of the Paris' law parameters that will maximize the likelihood of observing the given S-N data. Because the SNPL method is based on a Bayesian approach, the prior statistical parameters can be updated when additional S-N test data are available. Thus, information on the Paris' law parameters can be obtained with greater reliability. The proposed method is tested by applying it to S-N curves of 40H steel and 20G steel, and the corresponding analysis results are in good agreement with the experimental observations.
Keywords
Bayesian approach; fatigue crack growth; Paris' law; statistical parameter; S-N curve;
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1 Tada, H., Paris, P.C. and Irwin, G.R. (2000), The Stress Analysis of Cracks Handbook, 3rd Edition, ASME Press.
2 VDME (2003), Analytical Strength Assessment of Components in Mechanical Engineering: FKM-Guideline, VDMA.
3 Virkler, D.A., Hillberry, B. and Goel, P.K. (1979), "The statistical nature of fatigue crack propagation", J. Eng. Mater. T., 101(2), 148-153.   DOI
4 Weibull, W. (2013), Fatigue Testing and Analysis of Results, Elsevier.
5 Wirsching, P.H. (1983), Statistical Summaries of Fatigue Data for Design Purposes, NASA, Washington, D.C., U.S.A.
6 Zhao, Z., Haldar, A. and Breen Jr, F.L. (1994), "Fatigue-reliability evaluation of steel bridges", J. Struct. Eng., 120(5), 1608-1623.   DOI
7 Szata, M. and Lesiuk, G. (2009), "Algorithms for the estimation of fatigue crack growth using energy method", Arch. Civil Mech. Eng., 9(1), 119-134.   DOI
8 Bathias, C. (1999), "There is no infinite fatigue life in metallic materials", Fatig. Fract. Eng. Mater. Struct., 22(7), 559-565.   DOI
9 ASCE Committee on Fatigue and Fracture Reliability (1982), "Fatigue reliability: Introduction", J. Struct. Div., 108(1), 3.   DOI
10 Bannantine, J., Corner, J. and Handrock, J. (1990), Fundamentals of Metal Fatigue Analysis, Englewood Cliffs, Prentice Hall, New Jersey, U.S.A.
11 British Standard Institution (2015), Guide on Methods for Assessing the Acceptability of Flaws in Metallic Structures, British Standard Institution.
12 Byers, W.G., Marley, M.J., Mohammadi, J., Nielsen, R.J. and Sarkani, S. (1997), "Fatigue reliability reassessment applications: State-of-the-art paper", J. Struct. Eng., 123(3), 277-285.   DOI
13 Dong, P. (2005), "A robust structural stress method for fatigue analysis of offshore/marine structures", J. Offsh. Mech. Arct., 127(1), 68-74.   DOI
14 Dong, W., Moan, T. and Gao, Z. (2012), "Fatigue reliability analysis of the jacket support structure for offshore wind turbine considering the effect of corrosion and inspection", Reliab. Eng. Syst. Safe., 106, 11-27.   DOI
15 Dowling, N.E., Calhoun, C.A. and Arcari, A. (2009), "Mean stress effects in stress-life fatigue and the Walker equation", Fatig. Fract. Eng. M., 32(3), 163-179.   DOI
16 Kang, W.H., Lee, Y.J., Song, J. and Gencturk, B. (2012), "Further development of matrix-based system reliability method and applications to structural systems", Struct. Infrast. E., 8(5), 441-457.   DOI
17 Forman, R.G. and Mettu, S.R. (1990), Behavior of Surface and Corner Cracks Subjected to Tensile and Bending Loads in Ti-6Al-4V Alloy, NASA, Houston, Texas, U.S.A.
18 Irwin, G.R. (1957), "Analysis of stresses and strains near the end of a crack traversing a plate", J. Appl. Mech., 24, 361-364.   DOI
19 Juvinall, R.C. and Marshek, K.M. (2006). Fundamentals of Machine Component Design, John Wiley & Sons, New York, U.S.A.
20 Karamchandani, A., Dalane, J.I. and Bjerager, P. (1992), "Systems reliability approach to fatigue of structures", J. Struct. Eng., 118(3), 684-700.   DOI
21 Keating, P.B. and Fisher, J.W. (1986), Evaluation of Fatigue Tests and Design Criteria on Welded Details, NCHRP Report 286, Transportation Research Board, National Research Council, Washington, D.C., U.S.A.
22 Lalanne, C. (2010), Mechanical Vibration and Shock Analysis, Fatigue Damage, John Wiley & Sons.
23 Lee, Y.J. and Cho, S. (2016), "SHM-based probabilistic fatigue life prediction for bridges based on FE model updating", Sensors, 16(3), 317.   DOI
24 Lee, Y.J. and Song, J. (2011), "Risk analysis of fatigue-induced sequential failures by branch-and-bound method employing system reliability bounds", J. Eng. Mech., 137(12), 807-821.   DOI
25 Lee, Y.J., Song, J. and Tuegel, E.J. (2008), "Finite element system reliability analysis of a wing torque box", Proceedings of the 10th AIAA Nondeterministic Approaches Conference, Schaumburg, Illinois, U.S.A., April.
26 Lee, Y.J. and Song, J. (2012), "Finite-element-based system reliability analysis of fatigue-induced sequential failures", Reliab. Eng. Syst. Safe., 108, 131-141.   DOI
27 Lee, Y.J. and Song, J. (2014), "System reliability updating of fatigue-induced sequential failures", J. Struct. Eng., 140(3), 04013074.
28 Lee, Y.J., Kim, R.E., Suh, W. and Park, K. (2017), "Probabilistic fatigue life updating for railway bridges based on local inspection and repair", Sensors, 17(4), 936.   DOI
29 Lee, Y.L., Barkey, M.E. and Kang, H.T. (2011), Metal Fatigue Analysis Handbook: Practical Problem-Solving Techniques for Computer-Aided Engineering, Elsevier.
30 Manson, S.S. (1966), "Interfaces between fatigue, creep, and fracture", Int. J. Fract. Mech., 2(1), 327-327.   DOI
31 Moan, T. and Song, R. (2000). "Implications of inspection updating on system fatigue reliability of offshore structures", J. Offsh. Mech. Arct., 122(3), 173-180.   DOI
32 McCarver, J.F. and Ritchie, R.O. (1982), "Fatigue crack propagation thresholds for long and short cracks in Rene 95 nickel-base superalloy", Mater. Sci. Eng., 55(1), 63-67.   DOI
33 Millwater, H.R. and Wieland, D.H. (2010). "Probabilistic sensitivity-based ranking of damage tolerance analysis elements", J. Aircraft, 47(1), 161-171.   DOI
34 Miner, M.A. (1945). "Cumulative damage in fatigue", J. Appl. Mech., 12(3), 159-164.   DOI
35 Newman, J.C. (1998), "The merging of fatigue and fracture mechanics concepts: A historical perspective", Prog. Aerosp. Sci., 34(5), 347-390.   DOI
36 Oh, D.J., Lee, J.M. and Kim, M.H. (2014), "Fatigue strength assessment of Invar alloy weld joints using the notch stress approach", Eng. Fail. Anal., 42, 87-99.   DOI
37 Paris, P. and Erdogan, F. (1963), "A critical analysis of crack propagation laws", J. Basic Eng., 85(4), 528-533.   DOI
38 Pradana, M.R., Qian, X. and Swaddiwudhipong, S. (2017), "Simplified effective notch stress calculation for non-overlapping circular hollow section K-Joints", Mar. Struct., 55, 1-16.   DOI
39 Qian, X., Jitpairod, K., Marshall, P., Swaddiwudhipong, S., Ou, Z., Zhang, Y. and Pradana, M.R. (2014), "Fatigue and residual strength of concrete-filled tubular X-joints with full capacity welds", J. Constr. Steel Res., 100, 21-35.   DOI
40 Radhakrishnan, V.M. (1980), "Quantifying the parameters in fatigue crack propagation", Eng. Fract. Mech., 13(1), 129-141.   DOI
41 Sonsino, C.M. (2007), "Course of SN-curves especially in the high-cycle fatigue regime with regard to component design and safety", Int. J. Fatig., 29(12), 2246-2258.   DOI
42 Ramachandra Prabhu, S. and Lee, Y.J. (2017), "Derivation of Paris' law parameters from S-N curve data: A Bayesian approach", Proceedings of the 2017 World Congress on Advances in Structural Engineering and Mechanics, Ilsan, Korea, August.
43 Schutz, W. (1979), "The prediction of fatigue life in the crack initiation and propagation stages-a state of the art survey", Eng. Fract. Mech., 11(2), 405-421.   DOI
44 Schutz, W. (1996), "A history of fatigue", Eng. Fract. Mech., 54(2), 263-300.   DOI
45 Singh, A. (2002), "The nature of initiation and propagation S-N curves at and below the fatigue limit", Fatig. Fract. Eng. M., 25(1), 79-89.   DOI
46 Soares, C.G. and Garbatov, Y. (1996), "Fatigue reliability of the ship hull girder accounting for inspection and repair", Reliab. Eng. Syst. Safe., 51(3), 341-351.   DOI
47 Sorensen, J.D. (2009), "Framework for risk-based planning of operation and maintenance for offshore wind turbines", Wind Energy, 12(5), 493-506.   DOI
48 Sova, J.A., Crews Jr, J.H. and Exton, R.J. (1976), "Fatigue-crack initiation and growth in notched 2024-T3 specimens monitored by a video tape system", Technical Report: NASA-TN-D-8224, NASA, Washington, D.C., U.S.A.
49 Stephens, R.I., Fatemi, A., Stephens, R.R. and Fuchs, H.O. (2000), Metal Fatigue in Engineering, John Wiley & Sons, Hoboken, New Jersey, U.S.A.
50 Straub, D. (2011), "Reliability updating with equality information", Probabilist. Eng. Mech., 26(2), 254-258.   DOI
51 Suresh, S. (1998), Fatigue of Materials. Cambridge university press, Cambridge, U.K.