SpringerLink
Log in

Corrected stress field intensity approach based on averaging superior limit of intrinsic damage dissipation work

  • Original Paper
  • Published:
Journal of Iron and Steel Research International Aims and scope Submit manuscript

Abstract

Corrected stress field intensity obtained by averaging the superior limit of intrinsic damage dissipation work in critical domain, which considers thoroughly thermodynamic consistency within irreversible thermodynamic framework, was proposed for predictions of high-cycle fatigue endurance limits. Simultaneously, the effects of mean stress, additional hardening behavior related to non-proportional loading paths and stress gradients on multiaxial high-cycle fatigue are taken into account in the proposed approach. The approach is an extension of the general stress field intensity. For a better comparison, existing multiaxial high-cycle fatigue criteria were employed to predict the endurance limits of different metallic materials subjected to different multiaxial loading paths, and it is shown that present proposal performs better from statistical value of error indexes, which make the proposed approach of corrected stress field intensity and its associated concepts provide a new conception to predict endurance limits of multiaxial high-cycle fatigue with high accuracy.

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 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

Similar content being viewed by others

Abbreviations

c :

Coefficient considering the influence of stress gradients on the high-cycle fatigue strength

D :

Internal damage variable

\( \mathop D\limits^{ \cdot } \) :

Damage evolution rate

\( D_{\text{c}} \) :

Critical value of damage

E :

Elastic modulus (MPa)

f − 1 :

Endurance limit in reversed rotative bending (MPa)

f − 1 N :

Conditional endurance limit in reversed rotative bending (MPa)

g :

Function of Helmholtz free energy (J m−3)

\( K_{\text{m}} \), K 1, K 2 :

Reduced material parameters

K 3 :

Pure torsion fatigue strength coefficient (MPa)

K 4 :

Rotative bending fatigue strength coefficient (MPa)

M :

A material parameter associated with damage evolution model

N :

Number of cycles (cycle)

\( N_{\text{f}} \) :

Predicted life solely considering a point in the critical domain (cycle)

\( N_{\text{fp}} \) :

Predicted life considering the total critical domain (cycle)

p − 1 :

Endurance limit in reversed plane bending (MPa)

p − 1 N :

Conditional endurance limit in reversed plane bending (MPa)

\( \mathop {q_{i} }\limits^{ \cdot } \) :

Vector of heat flux (J s−1 m−1)

\( \mathop {q_{i,i} }\limits^{ \cdot } \) :

Transition rate of heat flux gradient (J s−1)

\( Q_{\text{cycle}} \) :

Intrinsic dissipation (J m−3)

r :

Radius vector within polar coordinates (m)

R :

Radius of smooth specimen (m)

R γ :

Three-axis factor

s :

State entropy (J K−1 m−3)

\( \mathop s\limits^{ \cdot } \) :

Evolution rate of state entropy (J K−1 s−1 m−3)

S :

Total cross-sectional area for element (m−2)

\( S_{\text{D}} \) :

Total area of all micro-cracks and cavities for element (m−2)

S ijkl :

The fourth-order elastic stiffness tensor (MPa)

T :

Temperature (K)

\( \mathop T\limits^{ \cdot } \) :

Temperature transition rate (K s−1)

T i :

Temperature gradients (K m−1)

V :

Volume of the critical domain (m3)

Y :

Generalized force of damage driving (MPa)

Y i :

Discrete sequence toward generalized force of damage driving (MPa)

Y max (Y min):

Maximum (minimum) generalized force of damage driving in one cycle (MPa)

\( \sigma_{\text{damage}} \) :

Corrected stress field intensity resulting from homogenization toward the superior limit of intrinsic damage dissipation work in critical domain (MPa)

σ ij :

Stress tensor (MPa)

\( \sigma_{\text{eq}} \) :

Von Mises equivalent stress (MPa)

\( \sigma_{\text{m}} \) :

Hydrostatic stress (MPa)

\( \sigma_{\text{eqa}} \) :

Equivalent stress amplitude considering the effect of mean stress and additional hardening on multiaxial high-cycle fatigue endurance limits (MPa)

\( \sigma_{\text{a}} \) :

Normal stress amplitude (MPa)

σ − 1 :

Endurance limit in reversed tension (MPa)

σ − 1 N :

Conditional endurance limit in reversed tension (MPa)

θ :

Angle vector within polar coordinates (rad)

\( \varepsilon_{ij}^{p} \, \) :

Micro-plastic strain tensor

\( \mathop {\varepsilon_{ij}^{p} }\limits^{ \cdot } \) :

Micro-plastic strain rate tensor

ɛ e ij (ɛ e kl ):

Elastic strain tensor

\( \mathop {\varepsilon_{ij}^{e} }\limits^{ \cdot } \) :

Elastic strain rate tensor

ρ :

Material density (kg m−3)

ρ max :

Radius of the critical domain (m)

〈·〉max :

Maximum value in symbol

ν :

Poisson ratio

α, β 0 :

Material parameters dependent on S–N curve in reversed tension

β 1 :

Material parameter dependent on S–N curve in reversed torsion

β 2 :

Material parameter dependent on S–N curve in rotative bending

\( \delta D_{\text{i}} \) :

Increment of internal damage

\( \tau_{\text{a}} \) :

Shear stress amplitude (MPa)

τ − 1 :

Endurance limit in reversed torsion (MPa)

τ − 1 N :

Conditional endurance limit in reversed torsion (MPa)

ϕ :

Phase angle difference between tension loading and torsion loading (°)

References

  1. Y.R. Luo, C.X. Huang, Y. Guo, Q.Y. Wang, J. Iron Steel Res. Int. 19 (2012) No. 10, 47–53.

    Article  Google Scholar 

  2. C. Wang, D.G. Shang, X.W. Wang, J. Mater. Eng. Perform. 24 (2015) 816–824.

    Article  Google Scholar 

  3. A. Carpinteri, C. Ronchei, A. Spagnoli, S. Vantadori, Int. J. Fatigue 73 (2014) 120–127.

    Google Scholar 

  4. I.V. Papadopoulos, P. Davoli, C. Gorla, M. Filippini, A. Bernasconi, Int. J. Fatigue 19 (1997) 219–235.

    Article  Google Scholar 

  5. Y. Li, W.X. Yao, W. Wen, J. Mech. Strength. 24 (2002) 258–261.

    Google Scholar 

  6. W.X. Yao, Acta Mech. Solida Sin. 9 (1996) 337–349.

    Google Scholar 

  7. F. Hofmann, G. Bertolino, A. Constantinescu, M. Ferjani, J. Mech. Mater. Struct. 4 (2009) 293–308.

    Article  Google Scholar 

  8. I. Milošević, G. Winter, F. Grün, M. Kober, Procedia Eng. 160 (2016) 61–68.

    Article  Google Scholar 

  9. G. Qilafku, N. Kadi, J. Dobranski, Z. Azari, M. Gjonaj, Int. J. Fatigue 23 (2001) 689–701.

    Article  Google Scholar 

  10. D. Taylor, Int. J. Fatigue 21 (1999) 413–420.

    Article  Google Scholar 

  11. H.B. Huang, X. Chen, S.F. Weng, Chin. J. Mech. Eng. 22 (2011) 1629–1633.

    Google Scholar 

  12. N. Mitrovic, M. Milosevic, N. Momcilovic, A. Petrovic, Z. Miskovic, Key Eng. Mater. 586 (2013) 214–217.

    Article  Google Scholar 

  13. B. Li, J. L. T. Santos, M. de Freitas, Mech. Based Des. Struct. 28 (2000) 85–103.

    Google Scholar 

  14. L. Zhang, X.S. Liu, L.S. Wang, W.H. Shuang, H.Y. Fang, Trans. Nonferrous Met. Soc. China 22 (2012) 2777–2782.

    Article  Google Scholar 

  15. J. Lemaitre, Mechanics of solid materials, Cambridge University, England, 1990.

    Book  Google Scholar 

  16. X. Zhang, J. Zhao, Applied fatigue damage mechanics of metallic structural members, National Defence Industry Press, Bei**g, 1998.

    Google Scholar 

  17. A. Öchsner, Continuum damage mechanics, Springer Singapore, Berlin, 2016.

    Book  Google Scholar 

  18. Y. Yan, H.R. Li, J. Mech. Eng. 51 (2015) 135–142.

    Google Scholar 

  19. J. Lemaitre, A. Plumtree. J. Eng. Mater. 101 (1979) 284–292.

    Google Scholar 

  20. B. Crossland, In: Proceedings of International Conference on Fatigue of Metals. London, 1956, pp. 138–149.

  21. C.A. Gonçalves, J.A. Araújo, E.N. Mamiya, Int. J. Fatigue 27 (2005) 177–187.

    Article  Google Scholar 

  22. S. Holopainen, R. Kouhia, T. Saksala, Eur. J. Mech. 60 (2016) 183–195.

    Article  Google Scholar 

  23. T. Nishihara, M. Kawamoto, J. Jpn. Soc. Mech. Eng. 44 (1945) 722–723.

    Google Scholar 

  24. T. Delahay, T. Palin-Luc, Int. J. Fatigue 28 (2006) 474–484.

    Article  Google Scholar 

  25. A. Banvillet, T. Palin-Luc, S. Lasserre, Int. J. Fatigue 25 (2003) 755–769.

    Article  Google Scholar 

  26. A. Carpinteri, A. Spagnoli, Int. J. Fatigue 23 (2001) 135–145.

    Article  Google Scholar 

  27. C. Braccesi, F. Cianetti, G. Lori, D. Pioli, Int. J. Fatigue 30 (2008) 1479–1497.

    Article  Google Scholar 

  28. D.L. McDiarmid, Fatigue Fract. Eng. Mater. Struct. 9 (1987) 457–475.

    Article  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge the support provided by Key Natural Science Foundation of Hebei Province of China (E2017203161).

Author information

Authors and Affiliations

  1. National Engineering Research Center for Equipment and Technology of Cold Strip Rolling, Yanshan University, Qinhuangdao, 066004, Hebei, China

    Hao-ran Li, Yan Peng, Yang Liu & Ming Zhang

Authors
  1. Hao-ran Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yan Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ming Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yan Peng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, Hr., 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, 1094–1103 (2018). https://doi.org/10.1007/s42243-018-0157-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42243-018-0157-5

Keywords

Search

Navigation