Strength of Materials

, Volume 50, Issue 1, pp 2–10 | Cite as

Effect of Cyclic Stresses Below the Endurance Limit on the Fatigue Life of 40Cr Steel

  • L. H. Zhao
  • J. Z. Feng
  • S. L. Zheng

The effect of cyclic stresses below the endurance limit on the fatigue life of 40Cr medium-strength carbon steel is studied. Conventional constant-amplitude cyclic tests and specially designed variable-amplitude ones are conducted under torsional loading at the stress ratio R = 0.1. The results show that the strengthening effect of cyclic stresses below the endurance limit can be reached if they are applied prior to the exceeding ones. Moreover, the stress amplitude, number of cycles and load sequence are found to be the three major strengthening effect-controlling factors. Generally, different cyclic stress levels exhibit different strengthening effect values, whereas the respective fatigue strength will initially rise and then drop with the number of loading cycles. The cyclic stresses of a 85% endurance limit are established to provide the maximum strengthening effect. Under multi-level cyclic loadings, the strengthening effect at different cyclic stress levels is nonlinearly growing, and the total fatigue life is strongly related to the last level of stress amplitude in the load sequence. The scatter in fatigue lives is highly dependent on the loading conditions and strengthening effect The coefficient of variance (COV) of fatigue life values exhibit the tendency to a decrease with the strengthening effect, which may improve the uniformity of the material fatigue strength characteristics.


variable amplitude load strengthening effect fatigue limit load sequence effect fatigue life 



This work was supported by the National Natural Science Foundation of China (Nos. 51375313 and 51705322), and SAIC Education Foundation Project (No. 1624).


  1. 1.
    J. Schijve, Fatigue of Structures and Materials, Springer Netherlands (2001).Google Scholar
  2. 2.
    J. Lemaitre and R. Desmorat, Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures, Springer-Verlag, Berlin–Heidelberg (2005).Google Scholar
  3. 3.
    G. Sinclair, An Investigation of the Coaxing Effect in Fatigue of Metals, Illinois University at Urbana (1952).Google Scholar
  4. 4.
    S. Teimourimanesh and F. Nilsson, “Effects of cycles below the fatigue limit on the life of a high strength steel,” J. Test. Eval., 37, No. 3, 201–204 (2009).Google Scholar
  5. 5.
    L. Zeng, Z. Li, R. Che, et al., “Mesoscopic analysis of fatigue strength property of a modified 2618 aluminum alloy,” Int. J. Fatigue, 59, 215–223 (2014).CrossRefGoogle Scholar
  6. 6.
    Y. Takahashi, H. Yoshitake, R. Nakamichi, et al., “Fatigue limit investigation of 6061-T6 aluminum alloy in giga-cycle regime,” Mater. Sci. Eng. A, 614, 243–249 (2014).CrossRefGoogle Scholar
  7. 7.
    A. B. El-Shabasy and J. J. Lewandowski, “Fatigue coaxing experiments on a Zr-based bulk-metallic glass,” Scripta Mater., 62, No. 7, 481–484 (2010).CrossRefGoogle Scholar
  8. 8.
    M. Tomozawa, P. Lezzi, R. Hepburn, et al., “Surface stress relaxation and resulting residual stress in glass fibers: A new mechanical strengthening mechanism of glasses,” J. Non-Cryst. Solids, 358, Nos. 18–19, 2650–2662 (2012).CrossRefGoogle Scholar
  9. 9.
    Y. Tanabe, T. Yoshimura, T. Watanabe, et al., “Fatigue of C/C composites in bending and in shear modes,” Carbon, 42, Nos. 8–9, 1665–1670 (2004).CrossRefGoogle Scholar
  10. 10.
    X. Lu and S. L. Zheng, “Strengthening and damaging under low-amplitude loads below the fatigue limit,” Int. J. Fatigue, 31, No. 2, 341–345 (2009).CrossRefGoogle Scholar
  11. 11.
    L. Zhao, S. Zheng, and J. Feng, “Fatigue life prediction under service load considering strengthening effect of loads below fatigue limit,” Chin. J. Mech. Eng., 27, No. 6, 1178–1185 (2014).CrossRefGoogle Scholar
  12. 12.
    A. Singh, “The nature of initiation and propagation S–N curves at and below the fatigue limit,” Fatigue Fract. Eng. Mater. Struct., 25, No. 1, 79–89 (2002).CrossRefGoogle Scholar
  13. 13.
    C. Fukuoka and Y. G. Nakagawa, “Microstructural evaluation of cumulative fatigue damage below the fatigue limit,” Scripta Mater., 34, No. 9, 1497–1502 (1996).CrossRefGoogle Scholar
  14. 14.
    S. L. Zheng and X. Lu, “Microscopic mechanism of strengthening under low-amplitude loads below the fatigue limit,” J. Mater. Eng. Perform., 21, No. 7, 1526–1533 (2012).CrossRefGoogle Scholar
  15. 15.
    X. Lu and S. L. Zheng, “Strengthening of transmission gear under low-amplitude loads,” Mater. Sci. Eng. A, 488, Nos. 1–2, 55–63 (2008).Google Scholar
  16. 16.
    M. Vormwald, “Classification of load sequence effects in metallic structures,” Procedia Engineer., 101, 534–542 (2015).CrossRefGoogle Scholar
  17. 17.
    M. Gladskyi and A. Fatemi, “Load sequence effects on fatigue crack growth in notched tubular specimens subjected to axial and torsion loadings,” Theor. Appl. Fract. Mech., 69, 63–70 (2014).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mechanical EngineeringUniversity of Shanghai for Science and TechnologyShanghaiChina
  2. 2.CMIF Key Lab for Automotive Strength and Reliability EvaluationShanghaiChina

Personalised recommendations