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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)
  • Received : 2018.11.26
  • Accepted : 2019.01.21
  • Published : 2019.02.25

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

Acknowledgement

Supported by : Korea Agency for Infrastructure Technology Advancement (KAIA)

References

  1. ASCE Committee on Fatigue and Fracture Reliability (1982), "Fatigue reliability: Introduction", J. Struct. Div., 108(1), 3. https://doi.org/10.1061/JSDEAG.0005869
  2. Bannantine, J., Corner, J. and Handrock, J. (1990), Fundamentals of Metal Fatigue Analysis, Englewood Cliffs, Prentice Hall, New Jersey, U.S.A.
  3. Bathias, C. (1999), "There is no infinite fatigue life in metallic materials", Fatig. Fract. Eng. Mater. Struct., 22(7), 559-565. https://doi.org/10.1046/j.1460-2695.1999.00183.x
  4. British Standard Institution (2015), Guide on Methods for Assessing the Acceptability of Flaws in Metallic Structures, British Standard Institution.
  5. 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. https://doi.org/10.1061/(ASCE)0733-9445(1997)123:3(277)
  6. Dong, P. (2005), "A robust structural stress method for fatigue analysis of offshore/marine structures", J. Offsh. Mech. Arct., 127(1), 68-74. https://doi.org/10.1115/1.1854698
  7. 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. https://doi.org/10.1016/j.ress.2012.06.011
  8. 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. https://doi.org/10.1111/j.1460-2695.2008.01322.x
  9. 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.
  10. Irwin, G.R. (1957), "Analysis of stresses and strains near the end of a crack traversing a plate", J. Appl. Mech., 24, 361-364. https://doi.org/10.1115/1.4011547
  11. Juvinall, R.C. and Marshek, K.M. (2006). Fundamentals of Machine Component Design, John Wiley & Sons, New York, U.S.A.
  12. 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. https://doi.org/10.1080/15732479.2010.539060
  13. Karamchandani, A., Dalane, J.I. and Bjerager, P. (1992), "Systems reliability approach to fatigue of structures", J. Struct. Eng., 118(3), 684-700. https://doi.org/10.1061/(ASCE)0733-9445(1992)118:3(684)
  14. 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.
  15. Lalanne, C. (2010), Mechanical Vibration and Shock Analysis, Fatigue Damage, John Wiley & Sons.
  16. Lee, Y.J. and Cho, S. (2016), "SHM-based probabilistic fatigue life prediction for bridges based on FE model updating", Sensors, 16(3), 317. https://doi.org/10.3390/s16030317
  17. 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. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000286
  18. 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. https://doi.org/10.1016/j.ress.2012.05.007
  19. Lee, Y.J. and Song, J. (2014), "System reliability updating of fatigue-induced sequential failures", J. Struct. Eng., 140(3), 04013074.
  20. 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. https://doi.org/10.3390/s17040936
  21. 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.
  22. Lee, Y.L., Barkey, M.E. and Kang, H.T. (2011), Metal Fatigue Analysis Handbook: Practical Problem-Solving Techniques for Computer-Aided Engineering, Elsevier.
  23. Manson, S.S. (1966), "Interfaces between fatigue, creep, and fracture", Int. J. Fract. Mech., 2(1), 327-327. https://doi.org/10.1007/BF00698478
  24. 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. https://doi.org/10.1016/0025-5416(82)90084-2
  25. Millwater, H.R. and Wieland, D.H. (2010). "Probabilistic sensitivity-based ranking of damage tolerance analysis elements", J. Aircraft, 47(1), 161-171. https://doi.org/10.2514/1.44498
  26. Miner, M.A. (1945). "Cumulative damage in fatigue", J. Appl. Mech., 12(3), 159-164. https://doi.org/10.1115/1.4009458
  27. 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. https://doi.org/10.1115/1.1286601
  28. Newman, J.C. (1998), "The merging of fatigue and fracture mechanics concepts: A historical perspective", Prog. Aerosp. Sci., 34(5), 347-390. https://doi.org/10.1016/S0376-0421(98)00006-2
  29. 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. https://doi.org/10.1016/j.engfailanal.2014.04.003
  30. Paris, P. and Erdogan, F. (1963), "A critical analysis of crack propagation laws", J. Basic Eng., 85(4), 528-533. https://doi.org/10.1115/1.3656900
  31. 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. https://doi.org/10.1016/j.marstruc.2017.04.006
  32. 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. https://doi.org/10.1016/j.jcsr.2014.04.021
  33. Radhakrishnan, V.M. (1980), "Quantifying the parameters in fatigue crack propagation", Eng. Fract. Mech., 13(1), 129-141. https://doi.org/10.1016/0013-7944(80)90048-X
  34. 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.
  35. 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. https://doi.org/10.1016/0013-7944(79)90015-8
  36. Schutz, W. (1996), "A history of fatigue", Eng. Fract. Mech., 54(2), 263-300. https://doi.org/10.1016/0013-7944(95)00178-6
  37. 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. https://doi.org/10.1046/j.1460-2695.2002.00463.x
  38. 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. https://doi.org/10.1016/0951-8320(95)00123-9
  39. 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. https://doi.org/10.1016/j.ijfatigue.2006.11.015
  40. Sorensen, J.D. (2009), "Framework for risk-based planning of operation and maintenance for offshore wind turbines", Wind Energy, 12(5), 493-506. https://doi.org/10.1002/we.344
  41. 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.
  42. 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.
  43. Straub, D. (2011), "Reliability updating with equality information", Probabilist. Eng. Mech., 26(2), 254-258. https://doi.org/10.1016/j.probengmech.2010.08.003
  44. Suresh, S. (1998), Fatigue of Materials. Cambridge university press, Cambridge, U.K.
  45. 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. https://doi.org/10.1016/S1644-9665(12)60045-4
  46. Tada, H., Paris, P.C. and Irwin, G.R. (2000), The Stress Analysis of Cracks Handbook, 3rd Edition, ASME Press.
  47. VDME (2003), Analytical Strength Assessment of Components in Mechanical Engineering: FKM-Guideline, VDMA.
  48. 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. https://doi.org/10.1115/1.3443666
  49. Weibull, W. (2013), Fatigue Testing and Analysis of Results, Elsevier.
  50. Wirsching, P.H. (1983), Statistical Summaries of Fatigue Data for Design Purposes, NASA, Washington, D.C., U.S.A.
  51. Zhao, Z., Haldar, A. and Breen Jr, F.L. (1994), "Fatigue-reliability evaluation of steel bridges", J. Struct. Eng., 120(5), 1608-1623. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:5(1608)

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