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Fatigue crack growth in metallic components: Numerical modelling and analytical solution

  • D'Angela, Danilo (Department of Structures for Engineering and Architecture, University of Naples Federico II) ;
  • Ercolino, Marianna (School of Engineering, University of Greenwich, Central Avenue)
  • Received : 2020.11.03
  • Accepted : 2021.07.14
  • Published : 2021.09.10

Abstract

The paper presents innovative approaches for the simulation of fatigue crack growth (FCG) in metallic compact tension (CT) specimens using finite element (FE) analysis and analytical solution. FE analysis is performed in ABAQUS using the extended finite element method (XFEM) coupled with the direct cyclic low-cycle fatigue (LCF) approach. Novel methods are developed for the computation of the numerical crack growth by processing the analysis outputs. The numerical modelling is validated by considering past experimental data. The analytical solution for the fatigue life evaluation is formally reviewed, and novel fatigue damage descriptors are defined. The influence of the main sample/testing features on numerical and analytical fatigue life is extensively assessed by a parametric study. The discrepancy between the numerical and analytical estimations of the fatigue life of the components is investigated and correlated to the features of the testing/modelling. A statistical-based correction factor is finally proposed in order to enhance the analytical solution.

Keywords

Acknowledgement

Computation for the work presented in this paper was supported by the University of Greenwich High Performance Computer resources (https://www.gre.ac.uk/it-and-library/hpc). The project was funded by the University of Greenwich under Seedling 2016 and REF 2017/2018 funds.

References

  1. Agathos, K., Chatzi, E. and Bordas, S.P.A. (2018), "Multiple crack detection in 3D using a stable XFEM and global optimization", Comput. Mech., 62(4), 835-852. https://doi.org/10.1007/s00466-017-1532-y.
  2. Agathos, K.A. and Chatzi, E. (2016), "Introduction to the extended finite element method", Institute of Structural Engineering, Zurich, Switzerland.
  3. Ashari, S.E. and Mohammadi, S. (2010), "Modeling delamination in composite laminates using XFEM by new orthotropic enrichment functions", IOP Conf. Ser.: Mater. Sci. Eng., 10, 012240. https://doi.org/10.1088/1757-899X/10/1/012240.
  4. ASTM International (2015), ASTM E647-15e1, Standard Test Method for Measurement of Fatigue Crack Growth Rates, ASTM International, West Conshohocken, Pennsylvania.
  5. Belytschko, T. and Black, T. (1999), "Elastic crack growth in finite elements with minimal remeshing", Int. J. Numer. Meth. Eng., 45(5), 601-620. https://doi.org/10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S.
  6. Bergara, A., Dorado, J.I., Martin-Meizoso, A. and Martinez-Esnaola, J.M. (2017), "Fatigue crack propagation in complex stress fields: Experiments and numerical simulations using the Extended Finite Element Method (XFEM)", Int. J. Fatig., 103, 112-121. https://doi.org/10.1016/j.ijfatigue.2017.05.026.
  7. Bhattacharya, S., Singh, I.V. and Mishra, B.K. (2013), "Fatigue-life estimation of functionally graded materials using XFEM", Eng. Comput., 29(4), 427-448. https://doi.org/10.1007/s00366-012-0261-2.
  8. D'Angela, D. and Ercolino, M. (2018), "Finite element analysis of fatigue response of nickel steel compact tension samples using ABAQUS", Procedia Struct. Integ., 13, 939-946. https://doi.org/10.1016/j.prostr.2018.12.176.
  9. De Jesus, A.M.P., Matos, R., Fontoura, B.F.C., Rebelo, C., Simoes da Silva, L. and Veljkovic, M. (2012), "A comparison of the fatigue behavior between S355 and S690 steel grades", J. Constr. Steel Res., 79, 140-150. https://doi.org/10.1016/j.jcsr.2012.07.021.
  10. Deliktas, B. and Mizamkhan, A. (2014), "Modeling nonlinear behavior of gusset plates in the truss based steel bridges", Struct. Eng. Mech., 51(5), 809-821. https://doi.org/10.12989/SEM.2014.51.5.809.
  11. Djebli, A., Aid, A., Bendouba, M., Amrouche, A., Benguediab, M. and Benseddiq, N. (2013), "A non-linear energy model of fatigue damage accumulation and its verification for Al-2024 aluminum alloy", Int. J. Nonlin. Mech., 51, 145-151. https://doi.org/10.1016/j.ijnonlinmec.2013.01.007.
  12. Gallagher, J. (1983), Damage Tolerant Design Handbook. A Compilation of Fracture and Crack-Growth Data for High-Strength Alloys, MCIC-HB-01R, University of Dayton Research Institute, Dayton, Ohio.
  13. Griffith, A.A. (1921), "The phenomena of rupture and flow in solids", Philos. Tran. Royal Soc. A: Math. Phys. Eng. Sci., 221(582-593), 163-198. https://doi.org/10.1098/rsta.1921.0006.
  14. Hasni, H., Alavi, A.H., Jiao, P. and Lajnef, N. (2017), "Detection of fatigue cracking in steel bridge girders: A support vector machine approach", Arch. Civil Mech. Eng., 17(3), 609-622. https://doi.org/10.1016/j.acme.2016.11.005.
  15. Hedayati, E. and Vahedi, M. (2014), "Using extended finite element method for computation of the stress intensity factor, crack growth simulation and predicting fatigue crack growth in a Slant-Cracked Plate of 6061-T651 aluminum", World J. Mech., 4(01), 24-30. https://doi.org/10.4236/wjm.2014.41003.
  16. Hua, C.T. and Socie, D.F. (1984), "Fatigue damage in 1045 steel under constant amplitude biaxial loading", Fatig. Fract. Eng. Mater. Struct., 7(3), 165-179. https://doi.org/10.1111/j.1460-2695.1984.tb00187.x.
  17. Hudson, C.M. (1969), "Effect of stress ratio on Fatigue-Crack Growth in 7075-T6 and 2024-T3 aluminum-alloy specimens", NASA Technical Note NASA TN D-5390, Langley Research Center, Hampton, Virginia.
  18. Hulton, A.W. and Cavallaro, P.V. (2016), "Composite failures: A comparison of experimental test results and computational analysis using XFEM", NUWC-NPT Technical Report 12,218, Naval Undersea Warfare Center Division, Newport, Rhode Island.
  19. Imam, B. and Chryssanthopoulos, M.K. (2010), "A review of metallic bridge failure statistics", Bridge Maintenance, Safety and Management: Proceedings of the Fifth International IABMAS Conference, Philadelphia, Pennsylvania, July.
  20. 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
  21. Irwin, G.R. (1961), "Plastic zone near a crack and fracture toughness", Proceedings of the 7th Sagamore Ordnance Materials Research Conference on Mechanical and Metallurgical Behavior of Sheet Materials, New York, New York State, August.
  22. Jiang, S. and Du, C. (2017), "Study on dynamic interaction between crack and inclusion or void by using XFEM", Struct. Eng. Mech., 63(3), 329-345. https://doi.org/10.12989/sem.2017.63.3.329.
  23. Jiang, Z. and Xiang, J. (2020), "Method using XFEM and SVR to predict the fatigue life of plate-like structures", Struct. Eng. Mech., 73(4), 455-462. https://doi.org/10.12989/sem.2020.73.4.455.
  24. Jovicic, G., Zivkovic, M., Jovicic, N., Milovanovic, D. and Sedmak, A. (2010), "Improvement of algorithm for numerical crack modelling", Arch. Civil Mech. Eng., 10(3), 19-35. https://doi.org/10.1016/S1644-9665(12)60134-4.
  25. Kalfarisi, R., Wu, Z.Y. and Soh, K. (2020), "Crack detection and segmentation using deep learning with 3d reality mesh model for quantitative assessment and integrated visualization", J. Comput. Civil Eng., 34(3), 04020010. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000890.
  26. Khelil, F., Aour, B., Belhouari, M. and Benseddiq, N. (2013), "Modeling of fatigue crack propagation in aluminum alloys using an energy based approach", Eng., 3(4), 488-496. https://doi.org/10.48084/etasr.329.
  27. Kim, S.K., Lee, C.S., Kim, J.H., Kim, M.H., Noh, B.J., Matsumoto, T. and Lee, J.M. (2015), "Estimation of fatigue crack growth rate for 7% nickel steel under room and cryogenic temperatures using damage-coupled finite element analysis", Metal., 5(2), 603-627. https://doi.org/10.3390/met5020603.
  28. Kim, Y.W., Jin Oh, D., Lee, J.M., Noh, B.J., Sung, H.J. ando, R., Matsumoto, T. and Hyun Kim, M. (2016), "An experimental study for fatigue performance of 7% nickel steels for type b liquefied natural gas carriers", J. Offsh. Mech. Arct. Eng., 138(3), 031401. https://doi.org/10.1115/1.4032706.
  29. Krueger, R. (2004), "Virtual crack closure technique: History, approach, and applications", Appl. Mech. Rev., 57(2), 109. https://doi.org/10.1115/1.1595677.
  30. Kucharski, P., Lesiuk, G., Czaplinski, T., Fratczak, R. and Maciejewski, L. (2016), "Numerical estimation of stress intensity factors and crack propagation in lug connector with existing flaw", Fatigue Failure and Fracture Mechanics XXVI AIP Conference Proceedings, Fojutowo, Poland, May.
  31. Kumar, S., Singh, I.V. and Mishra, B.K. (2015), "A homogenized XFEM approach to simulate fatigue crack growth problems", Comput. Struct., 150, 1-22. https://doi.org/10.1016/j.compstruc.2014.12.008.
  32. Lee, G.C., Mohan, S.B., Huang, C. and Fard, B.N. (2013), "A Study of U.S. bridge failures (1980-2012)", Technical Report MCEER-13-0008, University at Buffalo State University of New York, Buffalo, New York.
  33. Lee, Y.L., Barkey, M.E. and Kang, H.T. (2012), "Metal fatigue analysis handbook: Practical problem-solving techniques for computer-aided engineering", Butterworth-Heinemann, Waltham, Massachusetts.
  34. Li, C.Q., Yang, W. and Shi, W. (2020), "Corrosion effect of ferrous metals on degradation and remaining service life of infrastructure using pipe fracture as example", Struct. Infrastr. Eng., 16(4), 583-598. https://doi.org/10.1080/15732479.2019.1663221.
  35. Li, H. and Yuan, H. (2013), "Cohesive zone modelling of low cycle fatigue cracks in cracked and notched specimens", Fatig. Fract. Eng. Mater. Struct., 36(12), 1246-1257. https://doi.org/10.1111/ffe.12061.
  36. Liu, G., Zhou, D., Bao, Y., Ma, J. and Han, Z. (2017), "Multiscale simulation of major crack/minor cracks interplay with the corrected XFEM", Arch. Civil Mech. Eng., 17(2), 410-418. https://doi.org/10.1016/j.acme.2016.12.001.
  37. London, T., De Bono, D.M. and Sun, X. (2015), "An evaluation of the low cycle fatigue analysis procedure in abaqus for crack propagation: numerical benchmarks and experimental validation", SIMULIA UK Regional Users Meeting, London, United Kingdom, November.
  38. Melson, J.H. (2014), "Fatigue crack growth analysis with finite element methods and a monte carlo simulation", Master's Dissertation, Virginia Polytechnic Institute and State University, Blacksburg, Virginia.
  39. Moes, N., Dolbow, J. and Belytschko, T. (1999), "A finite element method for crack growth without remeshing", Int. J. Numer. Meth. Eng., 46(1), 131-150. https://doi.org/10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J.
  40. Nguyen, Q., Park, S. and Nguyen, T. (2014), "Validation of material constants for low-cycle fatigue modeling", ASME International Mechanical Engineering Congress and Exposition, Montreal, Canada. https://doi.org/10.1115/IMECE2014-39267.
  41. Pandey, V.B., Singh, I.V., Mishra, B.K., Ahmad, S., Venugopal Rao, A. and Kumar, V. (2019), "A new framework based on continuum damage mechanics and XFEM for high cycle fatigue crack growth simulations", Eng. Fract. Mech., 206, 172-200. https://doi.org/10.1016/j.engfracmech.2018.11.021.
  42. Paris, P. and Erdogan, F. (1963), "A critical analysis of crack propagation laws", J. Basic Eng., 85(4), 528. https://doi.org/10.1115/1.3656900.
  43. Pathak, H., Singh, A. and Singh, I.V. (2013), "Fatigue crack growth simulations of 3-D problems using XFEM", Int. J. Mech. Sci., 76, 112-131. https://doi.org/10.1016/j.ijmecsci.2013.09.001.
  44. Razmi, J. (2016), "Fracture mechanics-based and continuum damage modeling approach for prediction of crack initiation and propagation in integral abutment bridges", J. Comput. Civil Eng., 30(4), 04015061. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000535.
  45. Said Schicchi, D., Hoffmann, F., Hunkel, M. and Lubben, T. (2017), "Numerical and experimental investigation of the mesoscale fracture behaviour of quenched steels: Numerical and Experimental Investigation of the Mesoscale Fracture Behaviour of Quenched Steels", Fatig. Fract. Eng. Mater. Struct., 40(4), 556-570. https://doi.org/10.1111/ffe.12518.
  46. Schijve, J. (2003), "Fatigue of structures and materials in the 20th century and the state of the art", Int. J. Fatig., 25(8), 679-702. https://doi.org/10.1016/S0142-1123(03)00051-3.
  47. Sedmak, A. (2018), "Computational fracture mechanics: An overview from early efforts to recent achievements", Fatig. Fract. Eng. Mater. Struct., 41(12), 2438-2474. https://doi.org/10.1111/ffe.12912.
  48. Shi, J., Chopp, D., Lua, J., Sukumar, N. and Belytschko, T. (2010), "Abaqus implementation of extended finite element method using a level set representation for three-dimensional fatigue crack growth and life predictions", Eng. Fract. Mech., 77(14), 2840-2863. https://doi.org/10.1016/j.engfracmech.2010.06.009.
  49. Simulia (2016), Abaqus/CAE User's Manual Version 6.14, Dassault Systemes Simulia Corp., Providence, Rhode Island.
  50. Singh, I.V., Mishra, B.K., Bhattacharya, S. and Patil, R.U. (2012), "The numerical simulation of fatigue crack growth using extended finite element method", Int. J. Fatig., 36(1), 109-119. https://doi.org/10.1016/j.ijfatigue.2011.08.010.
  51. Stephens, R.I. and Fuchs, H.O. (2001), Metal Fatigue in Engineering, Wiley, New York.
  52. Stolarska, M., Chopp, D.L., Moes, N. and Belytschko, T. (2001), "Modelling crack growth by level sets in the extended finite element method", Int. J. Numer. Meth. Eng., 51(8), 943-960. https://doi: 10.1002/nme.201.
  53. Sun, B., Xu, Y.L., Wang, F.Y., Li, Z. and Zhu, Q. (2019), "Multiscale fatigue damage prognosis for long-span steel bridges under vehicle loading", Struct. Infrastr. Eng., 15(4), 524-538. https://doi.org/10.1080/15732479.2018.1562478.
  54. Ural, A., Krishnan, V.R. and Papoulia, K.D. (2009), "A cohesive zone model for fatigue crack growth allowing for crack retardation", Int. J. Solid. Struct., 46(11-12), 2453-2462. https://doi.org/10.1016/j.ijsolstr.2009.01.031.
  55. Valvo, P.S. (2012), "A revised virtual crack closure technique for physically consistent fracture mode partitioning", Int. J. Fract., 173(1), 1-20. https://doi.org/10.1007/s10704-011-9658-y.
  56. Wang, C., Wang, Y., Cui, B., Duan, L., Ma, N. and Feng, J. (2020), "Numerical simulation of distortion-induced fatigue crack growth using extended finite element method", Struct. Infrastr. Eng., 16(1), 106-122. https://doi.org/10.1080/15732479.2019.1650076.
  57. Wardhana, K. and Hadipriono, F.C. (2003), "Analysis of recent bridge failures in the United States", J. Perform. Constr. Facil., 17(3), 144-150. https://doi.org/10.1061/(ASCE)0887-3828(2003)17:3(144)
  58. Zehnder, A.T. (2012), Fracture Mechanics, Lecture Notes, Applied and Computational Mechanics, Springer, Dordrecht, Netherlands. https://doi.org/10.1007/978-94-007-2595-9.
  59. Zhan, Z., Hu, W., Li, B., Zhang, Y., Meng, Q. and Guan, Z. (2017), "Continuum damage mechanics combined with the extended finite element method for the total life prediction of a metallic component", Int. J. Mech. Sci., 124-125, 48-58. https://doi.org/10.1016/j.ijmecsci.2017.03.002.