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A criterion for high-cycle fatigue life and fatigue limit prediction in biaxial loading conditions

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Abstract

This paper presents a criterion for high-cycle fatigue life and fatigue strength estimation under periodic proportional and non-proportional cyclic loading. The criterion is based on the mean and maximum values of the second invariant of the stress deviator. Important elements of the criterion are: function of the non-proportionality of fatigue loading and the materials parameter that expresses the materials sensitivity to non-proportional loading. The methods for the materials parameters determination uses three S–N curves: tension–compression, torsion, and any non-proportional loading proposed. The criterion has been verified using experimental data, and the results are included in the paper. These results should be considered as promising. The paper also includes a proposal for multiaxial fatigue models classification due to the approach for the non-proportionality of loading.

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References

  1. Ellyin, F., Golos, K., Xia, Z.: In-phase and out-of-phase multiaxial fatigue. J. Eng. Mater. Technol. ASME 113, 112–118 (1991)

    Article  Google Scholar 

  2. Socie, D.: Multiaxial fatigue damage models. J. Eng. Mater. Technol. ASME 109, 293–298 (1987)

    Article  Google Scholar 

  3. McDiarmid, D.L.: Fatigue under out-of-phase bending and torsion. Fatigue Fract. Eng. Mater. Struct. 9, 457–475 (1986)

    Article  Google Scholar 

  4. Nishihara, T., Kawamoto, M.: The strength of metals under combined alternating bending and torsion with phase difference. Trans. Jpn. Soc. Mech. Eng. 12, 44–53 (1947)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  6. Garud, Y.S.: Multiaxial fatigue—a survey of the state of the art. J. Test. Eval. 9, 165–178 (1981)

    Google Scholar 

  7. Macha, E.: Simulation investigations of the position of fatigue fracture plane in materials with biaxial loads. Materwiss. Werksttech. 20, 132–136 (1989)

    Article  Google Scholar 

  8. Macha, E.: Generalized fatigue criterion of maximum shear and normal strains on the fracture plane for materials under multiaxial random loadings. Materwiss. Werksttech. 22, 203–210 (1991)

    Article  Google Scholar 

  9. Fatemi, A., Socie, D.F.: Critical plane approach to multiaxial fatigue damage including out-of-phase loading. Fatigue Fract. Eng. Mater. Struct. 11, 149–165 (1988)

    Article  Google Scholar 

  10. Chen, X., Xu, S., Huang, D.: Critical plane-strain energy density criterion for multiaxial low-cycle fatigue life under non-proportional loading. Fatigue Fract. Eng. Mater. Struct. 22, 679–686 (1999)

    Article  Google Scholar 

  11. Łagoda, T., Macha, E., Bedkowski, W.: A critical plane approach based on energy concepts: application to biaxial random tension–compression high-cycle fatigue regime. Int. J. Fatigue 21, 431–443 (1999)

  12. Sonsino, C.M.: Multiaxial fatigue of welded joints under in- phase and out-of-phase local strains and stresses. Int. J. Fatigue 17, 55–70 (1995)

    Article  Google Scholar 

  13. Papadopoulos, I.: Long life fatigue under multiaxial loading. Int. J. Fatigue 23, 839–849 (2001)

    Article  Google Scholar 

  14. Li, B., Reis, L., de Freitas, M.: Comparative study of multiaxial fatigue damage models for ductile structural steels and brittle materials. Int. J. Fatigue 31, 1895–1906 (2009)

    Article  Google Scholar 

  15. Wolfenden, A., Lee, Y.-L., Chiang, Y.J.: Fatigue predictions for components under biaxial reversed loading. J. Test. Eval. 19, 359 (1991)

    Article  Google Scholar 

  16. Wu, M., Itoh, T., Shimizu, Y., et al.: Low cycle fatigue life of Ti6Al4V alloy under non-proportional loading. Int. J. Fatigue 44, 14–20 (2012)

    Article  Google Scholar 

  17. Itoh, T., Ozaki, T., Amaya, T., et al.: Determination of stress and strain ranges under non-proportional cyclic loading. In: 8th International Conference on Multiaxial Fatigue and Fracture (2007)

  18. Skibicki, D., Sempruch, J.: Use of a load non-proportionality measure in fatigue under out-of-phase combined bending and torsion. Fatigue Fract. Eng. Mater. Struct. 27, 369–377 (2004)

    Article  Google Scholar 

  19. Skibicki, D.: Multiaxial fatigue life and strength criteria for non-proportional loading. Materialprufung 48, 99–102 (2006)

    Google Scholar 

  20. Lee, Y.L., Tjhung, T., Jordan, A.: A life prediction model for welded joints under multiaxial variable amplitude loading histories. Int. J. Fatigue 29, 1162–1173 (2007)

  21. Susmel, L.: Multiaxial fatigue limits and material sensitivity to non-zero mean stresses normal to the critical planes. Fatigue Fract. Eng. Mater. Struct. 31, 295–309 (2008)

    Article  Google Scholar 

  22. Davoli, P., Bernasconi, A., Filippini, M., et al. Independence of the torsional fatigue limit upon a mean shear stress. Int. J. Fatigue 25, 471–480 (2003)

  23. Susmel, L., Tovo, R., Lazzarin, P.: The mean stress effect on the high-cycle fatigue strength from a multiaxial fatigue point of view. Int. J. Fatigue 27, 928–943 (2005)

    Article  MATH  Google Scholar 

  24. Carpinteri, A., Spagnoli, A., Vantadori, S., et al.: Structural integrity assessment of metallic components under multiaxial fatigue: the C–S criterion and its evolution. Fatigue Fract. Eng. Mater. Struct. 36, 870–883 (2013)

  25. Liu, Y., Mahadevan, S.: A unified multiaxial fatigue damage model for isotropic and anisotropic materials. Int. J. Fatigue 29, 347–359 (2007)

    Article  MATH  Google Scholar 

  26. Crossland, G.: Effect of large hydrostatic pressures on the torsional fatigue strength of an alloy steel. In: International Conference of Fatigue of Metals, pp. 138–149. Institute of Mechanical Engineers, London (1956)

  27. Zenner, H., Simburger, A.: On the fatigue limit of ductile metals under complex multiaxial loading. Int. J. Fatigue 22, 137–145 (2000)

    Article  Google Scholar 

  28. Kurek, M., Lagoda, T.: Fatigue life estimation under cyclic loading including out-of-parallelism of the characteristics. In: Uncertainty in Mechanical Engineering, pp. 125–132. Trans Tech Publications Ltd., Switzerland (2012)

  29. Papadopoulos, I.V., Davoli, P., Gorla, C., et al.: A comparative study of multiaxial high-cycle fatigue criteria for metals. Int. J. Fatigue 19, 219–235 (1997)

  30. Pejkowski, Ł., Skibicki, D., Sempruch, J.: High cycle fatigue behavior of austenitic steel and pure copper under uniaxial, proportional and non-proportional loading. Stroj. Vestn. J. Mech. Eng. 60, 549–560 (2014)

  31. Vu, Q.H., Halm, D., Nadot, Y.: Multiaxial fatigue criterion for complex loading based on stress invariants. Int. J. Fatigue 32, 1004–1014 (2010)

    Article  Google Scholar 

  32. Karolczuk, A.: Non-local area approach to fatigue life evaluation under combined reversed bending and torsion. Int. J. Fatigue 30, 1985–1996 (2008)

    Article  MATH  Google Scholar 

  33. Dubar, L.: Fatigue multiaxiale des aciers-passage de lendurance lendurance limitprise en compte des accidents gomtriques (1992)

  34. Mamiya, E.N., Castro, F.C., Algarte, R.D., et al.: Multiaxial fatigue life estimation based on a piecewise ruled SN surface. Int. J. Fatigue 33, 529–540 (2011)

  35. Verreman, Y., Guo, H.: High-cycle fatigue mechanisms in 1045 steel under non-proportional axial-torsional loading. Fatigue Fract. Eng. Mater. Struct. 30, 932–946 (2007)

    Article  Google Scholar 

  36. McDiarmid, D.L.: Multiaxial fatigue life prediction using a shear-stress based critical plane failure criterion. In: Solin, J., Marquis, G., Siljander, A., Sipila, S. (eds.) Fatigue Design, pp. 21–33. Technical Research Centre Finland, Espoo (1992)

  37. Zhao, T., Jiang, Y.: Fatigue of 7075-T651 aluminum alloy. Int. J. Fatigue 30, 834–849 (2008)

    Article  Google Scholar 

  38. Huyen, N., Flaceliere, L., Morel, F.: A critical plane fatigue model with coupled meso-plasticity and damage. Fatigue Fract. Eng. Mater. Struct. 31, 12–28 (2008)

  39. Wang, Y., Yao, W.: A multiaxial fatigue criterion for various metallic materials under proportional and nonproportional loading. Int. J. Fatigue 28, 401–408 (2006)

  40. Heidenreich, R., Zenner, H., Richter, I.: Dauerschwingfestigkeit bei mehrachsiger Beanspruchung. Forschungshefte FKM H. 105 (1983)

  41. Bernasconi, A., Foletti, S., Papadopoulos, I.: A study on combined torsion and axial load fatigue limit tests with stresses of different frequencies. Int. J. Fatigue 30, 1430–1440 (2008)

    Article  Google Scholar 

  42. Lempp, M.: Festigkeitsverhalten von Sthlen bei mehrachsiger Dauerschwingbeanspruchung durch Normalspannungen mitberlagerten phasengleichen und phasenverschobenen Schubspannungen (1977) (in German)

  43. Mamiya, E.N., Arajo, J.A., Castro, F.C.: Prismatic hull: a new measure of shear stress amplitude in multiaxial high cycle fatigue. Int. J. Fatigue 31, 1144–1153 (2009)

    Article  MATH  Google Scholar 

  44. Galtier, A.: Contribution a letude de lendommagement des aciers sous solicitations uni ou multiaxials (1993) (in French)

  45. Banvillet, A., Palin-Luc, T., Lasserre, S.:A volumetric energy based high cycle multiaxial fatigue criterion. Int. J. Fatigue 25, 755–769 (2003)

  46. Bennebach, M.: Fatigue dune fonte GS. Influence de lentaille et dun traitement de surface (1993) (in French)

  47. Palin-Luc, T.: Fatigue multiaxiale dune fonte GS sous solicitations combinees damplitude variable (1996) (in French)

  48. Palin-Luc, T., Lasserre, S.: An energy based criterion for high cycle multiaxial fatigue. Eur. J. Mech. A 17, 237–251 (1998)

    Article  MATH  Google Scholar 

  49. Morel, F., Palin-Luc, T.: A non-local theory applied to high cycle multiaxial fatigue. Fatigue Fract. Eng. Mater. Struct. 25, 649–666 (2002)

    Article  Google Scholar 

  50. Zhao, T., Jiang, Y.: Fatigue of 7075-T651 aluminum alloy. Int. J. Fatigue 30, 834–849 (2008)

    Article  Google Scholar 

  51. Ince, A., Glinka, G.: A generalized fatigue damage parameter for multiaxial fatigue life prediction under proportional and non-proportional loadings. Int. J. Fatigue 62, 34–41 (2014)

    Article  Google Scholar 

  52. Liu, Y., Mahadevan, S.: Multiaxial high-cycle fatigue criterion and life prediction for metals. Int. J. Fatigue 27, 790–800 (2005)

    Article  MATH  Google Scholar 

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Pejkowski, Ł., Skibicki, D. A criterion for high-cycle fatigue life and fatigue limit prediction in biaxial loading conditions. Acta Mech. Sin. 32, 696–709 (2016). https://doi.org/10.1007/s10409-015-0538-y

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  • DOI: https://doi.org/10.1007/s10409-015-0538-y

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