Skip to main content
SpringerLink
Log in

Probabilistic Fatigue Life Framework of Notched Specimens Based on the Weibull Distribution Under Multiaxial Loading

  • Published:
Acta Mechanica Solida Sinica Aims and scope Submit manuscript

Abstract

In engineering applications, the notch effect and size effect significantly influence the evaluation of fatigue performance in components, necessitating special attention in life prediction. This study proposes a new probabilistic model, based on the theory of critical distance (TCD), to predict fatigue life, with the aim of quantitatively assessing the impact of notch effect and size effect. The stress distribution on the critical plane is first characterized using a sixth-order multinomial function, and the relative stress gradient function is utilized to calculate the value of the critical distance. Furthermore, the effect of the ratio of shear strain to normal strain on fatigue life under multiaxial loading is considered. Additionally, the integration of the Weibull distribution into the TCD is employed for conducting probabilistic modeling of fatigue life. Finally, fatigue experiments are conducted on notched specimens of Q355D steel, demonstrating that the life prediction results under 50% survival probability are superior to the traditional TCD method.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

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

Availability of Data and Materials

All data generated or analyzed during this study are included in this published article.

References

  1. Liao D, Zhu SP, Correia JAFO, Jesus AMPD, Calçada R. Computational framework for multiaxial fatigue life prediction of compressor discs considering notch effects. Eng Fract Mech. 2018;202:423–35.

    Article  Google Scholar 

  2. Branco R, Prates PA, Costa JD, Borrego LP, Berto F, Kotousov A, Antunes FV. Rapid assessment of multiaxial fatigue lifetime in notched components using an averaged strain energy density approach. Int J Fatigue. 2019;124:89–98.

    Article  Google Scholar 

  3. Baumgartner J, Lipp K, Bruder T, Kaufmann H. Design methods for reliable fatigue assessment of PM components. Materialwiss Werkstofftech. 2011;42(10):894–903.

    Article  CAS  Google Scholar 

  4. Liao D, Zhu SP. Energy field intensity approach for notch fatigue analysis. Int J Fatigue. 2019;127:190–202.

    Article  CAS  Google Scholar 

  5. Mäde L, Schmitz S, Gottschalk H, Beck T. Combined notch and size effect modeling in a local probabilistic approach for LCF. Comput Mater Sci. 2018;142:377–88.

    Article  Google Scholar 

  6. Liao D, Zhu SP, Correia JAFO, Jesus AMPD, Berto F. Recent advances on notch effects in metal fatigue: a review. Fatigue Fract Eng Mater Struct. 2020;43(4):637–59.

    Article  Google Scholar 

  7. Qian GA, Wang MT, Wang L. High cycle fatigue life prediction by local stress-strain method. J Mech Strength. 2004;26:275–7.

    Google Scholar 

  8. Gao T, Tong Y, Zhan Z, Mei W, Hu W, Meng Q. Development of a non-local approach for life prediction of notched specimen considering stress/strain gradient and elastic-plastic fatigue damage. Int J Damage Mech. 2022;31(7):1057–81.

    Article  Google Scholar 

  9. Qiao H, Hao X. Two-parameter nominal stress approach. Int J Fatigue. 1995;17(5):339–41.

    Article  Google Scholar 

  10. Taylor D. The theory of critical distances. Eng Fract Mech. 2006;75(7):1696–705.

    Article  Google Scholar 

  11. Zeng Y, Li M, Zhou Y, Li N. Development of a new method for estimating the fatigue life of notched specimens based on stress field intensity. Theoret Appl Fract Mech. 2019;104:102339.

    Article  Google Scholar 

  12. Hu XP, Xin PP, Song YD. Probabilistic fatigue life prediction method for notched specimens based on the weakest-link theory. Mech Sci Technol Aerosp Eng. 2013;32(2):164–9.

    Google Scholar 

  13. Li Z, Shi D, Li S, Yang X, Miao G. A systematical weight function modified critical distance method to estimate the creep-fatigue life of geometrically different structures. Int J Fatigue. 2019;126:6–19.

    Article  Google Scholar 

  14. Liao D, Zhu SP, Keshtegar B, Qian G, Wang Q. Probabilistic framework for fatigue life assessment of notched components under size effects. Int J Mech Sci. 2020;181:105685.

    Article  Google Scholar 

  15. Ai Y, Zhu SP, Liao D. Probabilistic modelling of notch and size effect of components under fatigue loadings. Procedia Struct Integr. 2019;22:70–7.

    Article  Google Scholar 

  16. Lei WS, Qian G, Yu Z, Berto F. Statistical size scaling of compressive strength of quasi-brittle materials incorporating specimen length-to-diameter ratio effect. Theoret Appl Fract Mech. 2019;104:102345.

    Article  Google Scholar 

  17. Liu JH, Zhao H, Ran Y, Hua FL, Zi R. Multiaxial fatigue life prediction model with relative stress gradient and size effect. Fatigue Fract Eng Mater Struct. 2022;45(12):3701–15.

    Article  Google Scholar 

  18. He JC, Zhu SP, Liao D, Niu XP. Probabilistic fatigue assessment of notched components under size effect using critical distance theory. Eng Fract Mech. 2020;235:107150.

    Article  Google Scholar 

  19. Lanning DB, Nicholas T, Palazotto A. The effect of notch geometry on critical distance high cycle fatigue predictions. Int J Fatigue. 2005;27:1623–7.

    Article  CAS  Google Scholar 

  20. Hu X, Jia X, Bao Z, Song Y. Effect of notch geometry on the fatigue strength and critical distance of TC4 titanium alloy. J Mech Sci Technol. 2017;31:4727–37.

    Article  Google Scholar 

  21. Yang X, Wang J, Liu J. High temperature LCF life prediction of notched DS Ni-based superalloy using critical distance concept. Int J Fatigue. 2011;33(11):1470–6.

    Article  CAS  Google Scholar 

  22. Susmel L. The theory of critical distances: a review of its applications in fatigue. Eng Fract Mech. 2008;75(7):1706–24.

    Article  Google Scholar 

  23. Shirani M, Härkegård G. Fatigue life distribution and size effect in ductile cast iron for wind turbine components. Eng Fail Anal. 2011;18(1):12–24.

    Article  CAS  Google Scholar 

  24. Liu X, Wu Q, Su S, Wang Y. Evaluation and prediction of material fatigue characteristics under impact loads: review and prospects. Int J Struct Integr. 2022;13(2):251–77.

    Article  Google Scholar 

  25. Zhang Y, Liu X, Lai J, Wei Y, Luo J. Corrosion fatigue life prediction of crude oil storage tank via improved equivalent initial flaw size. Theoret Appl Fract Mech. 2021;114:103023.

    Article  Google Scholar 

  26. Wu ZK, Wu SC, Qian WJ, Zhang HO, Zhu HB, Chen QY, Zhang ZX, Guo F, Wang JS, Withers PJ. Structural integrity issues of additively manufactured railway components: progress and challenges. Eng Fail Anal. 2023;149:107265.

  27. Zhang Y, Su C, Liu X. Notch-based probabilistic fatigue analysis of automobile transmission gear considering size effect. Theoret Appl Fract Mech. 2023;125:103882.

    Article  ADS  CAS  Google Scholar 

  28. Wu SC, Xu ZW, Kang GZ, He WF. Probabilistic fatigue assessment for high-speed railway axles due to foreign object damages. Int J Fatigue. 2018;117:90–100.

    Article  Google Scholar 

  29. Liu X, Wang R, Hu D, Mao J. A calibrated weakest-link model for probabilistic assessment of LCF life considering notch size effects. Int J Fatigue. 2020;137:105631.

    Article  Google Scholar 

  30. Ai Y, Zhu SP, Liao D, Correia JAFO, Jesus AMPD, Keshtegar B. Probabilistic modelling of notch fatigue and size effect of components using highly stressed volume approach. Int J Fatigue. 2019;127:110–9.

    Article  Google Scholar 

  31. Liu JH, Pan XM, Li YT, Chen XC. A two-point method for multiaxial fatigue life prediction. Acta Mech Solida Sin. 2022;35(2):316–27.

    Article  Google Scholar 

  32. Susmel L, Taylor D. A novel formulation of the theory of critical distances to estimate lifetime of notched components in the medium-cycle fatigue regime. Fatigue Fract Eng Mater Struct. 2010;30(7):567–81.

    Article  Google Scholar 

  33. Wang R, Li D, Hu D, Meng F, Liu H, Ma Q. 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. 2017;95:8–17.

    Article  CAS  Google Scholar 

  34. Liu JH, Wang J, He YB, Lu JM, Pan XM, Li B. Multiaxial fatigue life prediction of notched specimens based on multidimensional grey Markov theory. Eng Fract Mech. 2023;293:109689.

    Article  Google Scholar 

  35. Qylafku G, Azari Z, Kadi N. Application of a new model proposal for fatigue life prediction on notches and key-seats. Int J Fatigue. 1999;21(8):753–60.

    Article  Google Scholar 

  36. Susmel L, Taylor D. An elasto-plastic reformulation of the theory of critical distances to estimate lifetime of notched components failing in the low/medium-cycle fatigue regime. J Eng Mater Technol. 2010;132(2):021002.

    Article  Google Scholar 

  37. Kim JK, Kim DS, Takeda N. Notched strength and fracture criterion in fabric composite plates containing a circular hole. J Compos Mater. 1995;29(7):982–98.

    Article  Google Scholar 

  38. Huang J, Yang XG, Shi DQ, Wang JK, Hu XA. Low cycle fatigue life prediction of notched DZ125 component based on combined critical distance-critical plane approach. J Mech Eng. 2013;49(22):109–15.

    Article  Google Scholar 

Download references

Acknowledgements

We thank all the students in the fatigue strength group for their helpful discussions on this paper.

Funding

This research was supported by the National Natural Science Foundation of China (Grant Number 52365016), Gansu Province Young Doctor Fund Project (Grant Number 2023QB-030), and Lanzhou University of Technology Graduate Research Exploration Project.

Author information

Authors and Affiliations

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

    Jie Wang, Jianhui Liu, Jumei Lu, Yingbao He, Xuemei Pan & Ziyang Zhang

Authors
  1. Jie Wang
    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. Yingbao He
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xuemei Pan
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Ziyang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

JW was involved in the investigation, data analysis, methodology, and writing-original draft; JL contributed to the funding acquisition, supervision, and conceptualization; JL assisted in the methodology and conceptualization, YH and XP performed the data analysis, and ZZ was involved in the review and editing.

Corresponding author

Correspondence to Jianhui Liu.

Ethics declarations

Conflict of interest

The authors have no conflicts of interest to declare.

Consent for Publication

The authors of this paper give their consent for its publication in Acta Mechanica Solida Sinica.

Ethics Approval and Consent to Participate

The present paper does not report on or involve the use of any animal or human data or tissue.

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

Wang, J., Liu, J., Lu, J. et al. Probabilistic Fatigue Life Framework of Notched Specimens Based on the Weibull Distribution Under Multiaxial Loading. Acta Mech. Solida Sin. (2024). https://doi.org/10.1007/s10338-024-00472-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10338-024-00472-w

Keywords

Search

Navigation