SpringerLink
Log in

Fatigue life evaluation of notched components affected by multiple factors

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

Accurately assessing the fatigue performance of components is the key to ensuring structural integrity and reliability, but there is a lack of fatigue life prediction methods that effectively couple the stress gradient effect, the non-proportional additional strengthening effect, and the size effect. Accordingly, a fatigue life prediction model for notched specimens under multiaxial loading is established by analyzing the influence of tension–torsion proportional load and tension–torsion non-proportional load on the fatigue strength of notched specimens. Firstly, based on the energy critical plane method, the location of the critical plane is determined with the help of the coordinate transformation principle. Secondly, the material constant is used to quantify the level of cyclic strengthening, and a non-proportional additional strengthening function is proposed by considering the influence of phase difference. Thirdly, the influence of the non-uniform stress field at the notch root on the fatigue life is considered, and the distribution of equivalent stress on the specific paths is extracted and normalized to give an equivalent stress gradient factor. Then, a fatigue strength reduction factor is constructed by considering the influence of different notch geometrical parameters. Finally, a fatigue life assessment method for notched specimens is proposed based on the Manson–Coffin equation. With the help of the test data of three materials, En8, Al7050-T7451, and GH4169, the method is validated and compared with the calculation results of the Manson–Coffin equation, SWT model, and FS model. The results show that the prediction accuracy of the method in this study is high, which is located in the two-fold error dispersion band, and the prediction results are better than that of the other three models.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Canada)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Data availability

No datasets were generated or analyzed during the current study.

References

  1. Branco, R., Prates, P.A., Costa, J.D., et al.: Rapid assessment of multiaxial fatigue lifetime in notched components using an averaged strain energy density approach. Int. J. Fatigue 124, 89–98 (2019)

    Article  Google Scholar 

  2. Infante, G.D., Qian, G.A., Miguelez, H., et al.: Analysis of the effect of out-of-phase biaxial fatigue loads on crack paths in cruciform specimens using XFEM. Int. J. Fatigue 123, 87–95 (2019)

    Article  Google Scholar 

  3. Liao, D., Zhu, S.P.: Energy field intensity approach for notch fatigue analysis. Int. J. Fatigue 127, 190–202 (2019)

    Article  Google Scholar 

  4. Sun, L., Zhang, X.C., Wang, R.Z., et al.: Evaluation of fatigue and creep-fatigue damage levels on the basis of engineering damage mechanics approach. Int. J. Fatigue 166, 107277 (2023). https://doi.org/10.1016/j.ijfatigue.2022.107277

    Article  Google Scholar 

  5. Wang, R.Z., Zhu, S.P., Zhang, X.C., et al.: High temperature fatigue and creep-fatigue behaviors in a Ni-based superalloy: damage mechanisms and life assessment. Int. J. Fatigue 118, 08–21 (2019)

    Article  Google Scholar 

  6. Gu, H.H., Wang, R.Z., Zhu, S.P., et al.: Machine learning assisted probabilistic creep-fatigue damage assessment. Int. J. Fatigue 156, 106677 (2022). https://doi.org/10.1016/j.ijfatigue.2021.106677

    Article  Google Scholar 

  7. Gu, H.H., Wang, R.Z., Zhang, X.C., et al.: Creep-fatigue reliability assessment for high-temperature components fusing on-line monitoring data and physics-of-failure by engineering damage mechanics approach. Int. J. Fatigue 169, 107481 (2023). https://doi.org/10.1016/j.ijfatigue.2022.107481

    Article  Google Scholar 

  8. Luo, P., Yao, W.X., Wang, Y.Y., et al.: A survey on fatigue life analysis approaches for metallic notched components under multi-axial loading. Proc. Inst. Mech. Eng. Part G J. Aerosp. Eng. 233(10), 3870–3890 (2019)

    Article  Google Scholar 

  9. Li, H.R., Peng, Y., Liu, Y., et al.: Corrected stress field intensity approach based on averaging superior limit of intrinsic damage dissipation work. J. Iron. Steel Res. Int. 25(10), 1094–1103 (2018)

    Article  Google Scholar 

  10. Groza, M., Nadot, Y., Varadi, K.: Defect size map for nodular cast iron components with ellipsoidal surface defects based on the defect stress gradient approach. Int. J. Fatigue 112, 206–215 (2018)

    Article  Google Scholar 

  11. Branco, R., Costa, J.D., Borrego, L.P., et al.: Notch fatigue analysis and life assessment using an energy field intensity approach in 7050–T6 aluminium alloy under bending-torsion loading. Int. J. Fatigue 162, 106947 (2022). https://doi.org/10.1016/j.ijfatigue.2022.106947

    Article  Google Scholar 

  12. He, J.C., Zhu, S.P., Liao, D., et al.: Probabilistic fatigue assessment of notched components under size effect using critical distance theory. Eng. Fract. Mech. 235, 107150 (2020). https://doi.org/10.1016/j.engfracmech.2020.107150

    Article  Google Scholar 

  13. Luo, P., Yu, M., Wen, C.L.: A strain energy density field method to predict the life of metallic notched components under multiaxial fatigue loading. J. Phys. Conf. Ser. (2024). https://doi.org/10.1088/1742-6596/2686/1/012011

    Article  Google Scholar 

  14. Liao, D., Zhu, S.P., Qian, G.A.: A strain energy density field method to predict the life of metallic notched components under multiaxial fatigue loading. Int. J. Mech. Sci. 163, 38–50 (2019)

    Article  Google Scholar 

  15. Zhou, J., Tan, Z.C., Cao, L.W., et al.: An improved critical plane-energy multiaxial fatigue life prediction model considering shear mean stress. J. Mech. Sci. Technol. 37(05), 2333–2341 (2023)

    Article  Google Scholar 

  16. Zhang, X.L., Huang, H.Z., Zhang, X.L., et al.: A multiaxial probabilistic fatigue life prediction method for nickel-based single crystal turbine blade considering mean stress correction. Qual. Reliab. Eng. Int. 39(05), 1735–1755 (2023)

    Article  Google Scholar 

  17. Sun, J.Y., Qian, G.A., Li, J.H., et al.: A framework to simulate the crack initiation and propagation in very-high-cycle fatigue of an additively manufactured AlSi10Mg alloy. J. Mech. Phys. Solids (2023). https://doi.org/10.1016/j.jmps.2023.105293

    Article  MathSciNet  Google Scholar 

  18. Zhang, Z.B., Zhan, M., Fu, M.W.: Microstructural and geometrical size effects on the fatigue of metallic materials. Qual. Reliab. Eng. Int. 218, 107058 (2022). https://doi.org/10.1016/j.ijmecsci.2021.107058

    Article  Google Scholar 

  19. He, J.C., Zhun, S.P., Gao, J.W., et al.: Microstructural size effect on the notch fatigue behavior of a Ni-based superalloy using crystal plasticity modelling approach. Int. J. Plast. 172, 103857 (2023). https://doi.org/10.1016/J.IJPLAS.2023.103857

    Article  Google Scholar 

  20. Li, K.S., Wang, R.Z., Wang, J., et al.: Investigation of creep-fatigue crack initiation by using an optimal dual-scale modelling approach. Int. J. Fatigue 172, 107621 (2023). https://doi.org/10.1016/j.ijfatigue.2023.107621

    Article  Google Scholar 

  21. Hua, F.L., Liu, J.H., Pan, X.M., et al.: Research on multiaxial fatigue life of notched specimens based on Weibull distribution and Bayes estimation. Int. J. Fatigue 166, 107271 (2023). https://doi.org/10.1016/j.ijfatigue.2022.107271

    Article  Google Scholar 

  22. Liu, J.H., Zi, R., Wei, Y.B., et al.: A stress gradient-based fatigue life prediction method for multiaxial notched specimen considering additional hardening effect. Int. J. Press. Vessels Pip. 195, 104597 (2021). https://doi.org/10.1016/J.IJPVP.2021.104597

    Article  Google Scholar 

  23. Tang, Y.H., Song, Y.X., Yin, G.F., et al.: Notch fatigue life prediction model considering stress gradient influence depth and weight function. Metals 13(03), 539 (2023). https://doi.org/10.3390/met13030539

    Article  Google Scholar 

  24. Zhao, H., Liu, J.H., Hua, F.H., et al.: Multiaxial fatigue life prediction model considering stress gradient and size effect. Int. J. Press. Vessels Pip. 199, 104703 (2022). https://doi.org/10.1016/J.IJPVP.2022.104703

    Article  Google Scholar 

  25. Zhong, B., Wang, Y.R., Wei, D.S., et al.: Multiaxial fatigue life prediction for powder metallurgy superalloy FGH96 based on stress gradient effect. Int. J. Fatigue 109, 26–36 (2018)

    Article  Google Scholar 

  26. Lamba, H.S., Sidebottom, O.M.: Cyclic plasticity for nonproportional paths: part 1—cyclic hardening, erasure of memory, and subsequent strain hardening experiments. J. Eng. Mater. Technol. 100(01), 96–103 (1978)

    Article  Google Scholar 

  27. Xu, L., Wang, R.Z., Wang, J., et al.: On multiaxial creep–fatigue considering the non-proportional loading effect: Constitutive modeling, deformation mechanism, and life prediction. Int. J. Plast. 155, 103337 (2022). https://doi.org/10.1016/j.ijplas.2022.103337

    Article  Google Scholar 

  28. Ye, W.L., Zhu, S.P., Niu, X.P., et al.: Fatigue life prediction of notched components under size effect using critical distance theory. Theor. Appl. Fract. Mech. 121, 103519 (2022). https://doi.org/10.1016/J.TAFMEC.2022.103519

    Article  Google Scholar 

  29. Zhu, S.P., Wu, Y.L., Yi, X.J., et al.: Probabilistic fatigue assessment of notched components under size effect using generalized weakest-link model. Int. J. Fatigue 162, 107005 (2022). https://doi.org/10.1016/j.ijfatigue.2022.107005

    Article  Google Scholar 

  30. Brown, M.W., Miller, K.J.: A theory for fatigue failure under multiaxial stress-strain conditions. Arch Proc. Inst. Mech. Eng. 20, 745–755 (1973)

    Article  Google Scholar 

  31. Kandil, F.A., Brown, M.W., Miller, K.J.: Biaxial low-cycle fatigue fracture of 316 stainless steel at elevated temperature. Microcomput. Des. Appl. 280, 205–210 (1982)

    Google Scholar 

  32. Wang, C.H., Brown, M.W.: A path-independent parameter for fatigue under proportional and non-proportional loading. Fatigue Fract. Eng. Mater. Struct. 16(12), 1285–1297 (1993)

    Article  Google Scholar 

  33. Smith, K.N., Watson, P., Topper, T.H.: Stress-strain function for the fatigue of metals. J. Mater. Sci. 5(04), 767–778 (1970)

    Google Scholar 

  34. Fatemi, A., Socie, D., et al.: A critical plane approach to multiaxial fatigue damage including out-of-phase loading. Fatigue Fract. Eng. Mater. Struct. 11(03), 149–165 (1988)

    Article  Google Scholar 

  35. Liu, J.H., Lu, J.M., Zhou, F., et al.: Multiaxial fatigue life prediction model for notched specimen based on modified energy gradient and critical plane method. Theor. Appl. Fract. Mech. 125, 103880 (2023). https://doi.org/10.1016/j.tafmec.2023.103880

    Article  Google Scholar 

  36. Liu, J.H., Hua, F.L., Lang, S.S., et al.: Evaluation of fatigue strength on multiaxial notched specimenss considering failure probability. Int. J. Fatigue 156, 106649 (2022). https://doi.org/10.1016/j.ijfatigue.2021.106649

    Article  Google Scholar 

  37. Itoh, T., Nakata, T., Sakane, M., et al.: Nonproportional low cycle fatigue of 6061 aluminum alloy under 14 strain paths. Eur. Struct. Integr. Soc. 25, 41–54 (1999)

    Article  Google Scholar 

  38. Borodii, M.V., Shukaev, S.M.: Additional cyclic strain hardening and its relation to material structure, mechanical characteristics, and lifetime. Int. J. Fatigue 29(06), 1184–1191 (2007)

    Article  Google Scholar 

  39. Shamsaei, N., Fatemi, A.: Effect of microstructure and hardness on non-proportional cyclic hardening coefficient and predictions. Mater. Sci. Eng. 527(12), 3015–3024 (2010)

    Article  Google Scholar 

  40. Itoh, T., Yang, T.: Material dependence of multiaxial low cycle fatigue lives under non-proportional loading. Int. J. Fatigue 33(08), 1025–1031 (2011)

    Article  Google Scholar 

  41. Kida, S., Itoh, T., Sakane, M., et al.: Dislocation structure and non-proportional hardening of type 304 stainless steel. Fatigue Fract. Eng. Mater. Struct. 20, 1375–1386 (1997)

    Article  Google Scholar 

  42. Gates, N., Fatemi, A.: Notch deformation and stress gradient effects in multiaxial fatigue. Theor. Appl. Fract. Mech. 84, 03–25 (2016)

    Article  Google Scholar 

  43. Wu, Y.L., Zhu, S.P., He, J.C., et al.: Assessment of notch fatigue and size effect using stress field intensity approach. Int. J. Fatigue 149, 106279 (2021). https://doi.org/10.1016/j.ijfatigue.2021.106279

    Article  Google Scholar 

  44. Amjad, M., Fatemi, A.: Multiaxial fatigue behavior of thermoplastics including mean stress and notch effects: experiments and modeling. Int. J. Fatigue 136, 105571 (2020). https://doi.org/10.1016/j.ijfatigue.2020.105571

    Article  Google Scholar 

  45. Wang, R.Q., Li, D., Hu, D.Y., et al.: A combined critical distance and highly-stressed-volume model to evaluate the statistical size effect of the stress concentrator on low cycle fatigue of TA19 plate. Int. J. Fatigue 95, 08–17 (2017)

    Article  Google Scholar 

  46. Qylafku, G., Azari, N., Kadi, N.: Application of a new model proposal for fatigue life prediction on notches and key-seats. Int. J. Fatigue 21(08), 753–760 (1999)

    Article  Google Scholar 

  47. Made, L., Schmitz, S., Gottschalk, H., et al.: Combined notch and size effect modeling in a local probabilistic approach for LCF. Comput. Mater. Sci. 142, 377–388 (2018)

    Article  Google Scholar 

  48. Peterson, R.E., Plunkett, R.: Stress concentration factors. Nav. Eng. J. 67(03), 697–708 (2010)

    Google Scholar 

  49. Faruq, N.Z., Susmel, L.: Proportional/nonproportional constant/variable amplitude multiaxial notch fatigue: cyclic plasticity, non-zero mean stresses, and critical distance/plane. Fatigue Fract. Eng. Mater. Struct. 42(09), 1849–1873 (2019)

    Article  Google Scholar 

  50. Sun, G.Q., Shang, D.G.: Prediction of fatigue lifetime under multiaxial cyclic loading using finite element analysis. Mater. Des. 31(01), 126–133 (2010)

    Article  Google Scholar 

  51. Tao, Z.Q., Shang, D.G., Sun, Y.J., et al.: Multiaxial notch fatigue life prediction based on pseudo stress correction and finite element analysis under variable amplitude loading. Fatigue Fract. Eng. Mater. Struct. 41(08), 1674–1690 (2018)

    Article  Google Scholar 

  52. Manson, S.S.: Fatigue: a complex subject—some simple approximations. Exp. Mech. 05(04), 193–226 (1965)

    Article  Google Scholar 

  53. Coffin, L.F.: A study of the effects of cyclic thermal stresses on a ductile metal. Trans. Am. Soc. Mech. Eng. 76(08), 931–950 (1954)

    Article  Google Scholar 

  54. Manson, S.S., Halford, G.R.: Multiaxial low-cycle fatigue of type 304 stainless steel. J. Eng. Mater. Technol. 99(03), 283–285 (1977)

    Article  Google Scholar 

  55. Bonacuse, P.J., Kalluri, S.: Elevated temperature axial and torsional fatigue behavior of Haynes 188. J. Eng. Mater. Technol. 117(02), 191–199 (1995)

    Article  Google Scholar 

  56. Deng, Q.Y., Zhu, S.P., Niu, X.P.: Load path sensitivity and multiaxial fatigue life prediction of metals under non-proportional loadings. Int. J. Fatigue 166, 107281 (2022). https://doi.org/10.1016/j.ijfatigue.2022.107281

    Article  Google Scholar 

  57. He, Y.B., Liu, J.H., Hua, F.L.: Low-cycle multiaxial random fatigue life prediction model based on equivalent stress transformation. Int. J. Struct. Integr. 13(05), 870–882 (2022)

    Article  Google Scholar 

  58. Tao, Z.Q., Qian, G.A., Sun, J.Y.: Multiaxial fatigue life prediction by equivalent energy-based critical plane damage parameter under variable amplitude loading. Fatigue Fract. Eng. Mater. Struct. 45(12), 3640–3657 (2022)

    Article  Google Scholar 

Download references

Funding

This study was funded by the National Natural Science Foundation of China, Grant/Award Number: 52365016; Gansu Province Young Doctor Fund Project, Grant/Award Number: 2023QB-030.

Author information

Authors and Affiliations

  1. School of Mechanical and Electrical Engineering, Lanzhou University of Technology, Lanzhou, 730050, China

    Shenglei Wu, Jianhui Liu, Jumei Lu, Yazhou Wang & Wenjun Kou

Authors
  1. Shenglei Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jianhui Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jumei Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yazhou Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Wenjun Kou
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Shenglei Wu was contributed to writing—original draft, methodology, software, investigation. Jianhui Liu was contributed to writing—review and editing, funding acquisition, resources, supervision. Jumei Lu was contributed to visualization, investigation. Yazhou Wang was contributed to data curation, formal analysis. Wenjun Kou was contributed to visualization, software, validation.

Corresponding author

Correspondence to Jianhui Liu.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wu, S., Liu, J., Lu, J. et al. Fatigue life evaluation of notched components affected by multiple factors. Arch Appl Mech 94, 1871–1889 (2024). https://doi.org/10.1007/s00419-024-02607-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-024-02607-4

Keywords

Search

Navigation