Advertisement

Multiaxial Fatigue Limit Criterion of Metals

A Mesoscopic Scale Approach
  • I. V. Papadopoulos
Part of the International Centre for Mechanical Sciences book series (CISM, volume 392)

Abstract

In the present article attention is focused on the problem of the fatigue limit criterion, which is the extension of the usual concept of the uniaxial fatigue limit under multiaxial stress conditions. The intensity of the cyclic loads at the fatigue limit level is usually low such that the behaviour of the component remains apparently elastic at the macroscopic scale. However, it is experimentally observed that even is absence of detectable plastic strains, some metals grains located in the most stresses zones of a component suffer plastic slip. This irreversible process that takes place at the grain scale of the metal is responsible for crack initiation under high-cycle fatigue loading. Investigation of this phenomenon necessitates the introduction of the mesoscopic scale of material description (i.e. the scale of the metal grains of a metallic aggregate), in addition to the usual macroscopic scale of continuum mechanics. Within the framework of the mesoscopic scale approach, the local stresses and strains acting at the level of the metal grains are linked to the usual macroscopic stresses and strains with the help of Lin-Taylor assumption. The elaborated fatigue limit criterion is essentially defined as a restraint to be applied on the plastic strain accumulated by a cyclic loading in those crystals of the metallic aggregate that undergone plastic slip. Comparison of the predictions of the proposed criterion against experimental results obtained under proportional and non-proportional multiaxial stress conditions shows good agreement.

Keywords

Fatigue Limit Resolve Shear Stress Kinematic Hardening Mesoscopic Scale Accumulate Plastic Strain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Walgraef, D. and Aifantis, E. C. (1985). Dislocation patterning in fatigued metals as a result of dynamic instabilities. J. Appl Physics. Vol. 58, 688–691.CrossRefGoogle Scholar
  2. 2.
    Klesnil, M. and Lukas, P. (1992). Fatigue of metallic materials. Elsevier, Amsterdam.Google Scholar
  3. 3.
    Tanaka, K. and Mura, T. (1981). A disclocation model for fatigue crack initiation. Trans. ASME, J. Appl. Mech. Vol. 48, 97–103.CrossRefMATHGoogle Scholar
  4. 4.
    Lin, T. H. and Ito, Y. M. (1969). Mechanics of a fatigue crack nucleation mechanism. J. Mech. Phys. Solids Vol. 17, 515–523.Google Scholar
  5. 5.
    Mura, T. and Nakasone, Y. (1990). A theory of fatigue crack initiation in solids. Trans. ASME, J. Appl. Mech. Vol. 57, 1–6.CrossRefGoogle Scholar
  6. 6.
    Venkataraman, G., Chung, Y.W., Nakasone, Y. and Mura, T. (1990) Free energy formulation of fatigue crack initiation along persistent slip bands: Calculation of S-N curves and crack depths. Acta metall. mater. Vol. 38, 31–40.CrossRefGoogle Scholar
  7. 7.
    Gough, H. J. (1933). Crystalline structure in relation to failure of metals — Especially by fatigue. Eigth Edgar Marburg Lecture 33. Proceedings ASTM. Google Scholar
  8. 8.
    Dang Van, K. (1973). Sur la résistance à la fatigue des métaux. Thèse de Doctorat es Sciences. Science et Techniques de l Armement. Vol. 47, 647–722.Google Scholar
  9. 9.
    Papadopoulos, I. V. (1987). Fatigue polycyclique des métaux: Une nouvelle approche. Thèse de Doctorat. Ecole Nationale des Ponts et Chaussées, Paris.Google Scholar
  10. 10.
    Papadopoulos, I. V. and Dang Van, K. (1988). Sur la nucléation des fissures en fatigue polycyclique sous chargement multiaxial. Arch. Mech. Vol. 40, 759–774.Google Scholar
  11. 11.
    Basinski, Z. S. and Basinski, S. J. (1992). Fundamental aspects of low amplitude cyclic deformation in face-centred cubic crystals. Progress in Material Science. Vol. 36, 89–148.CrossRefGoogle Scholar
  12. 12.
    Orowan, E. (1939). Theory of the fatigue of metals. Proceedings of the Royal Academy-A. Vol. 171, 79–106.CrossRefMATHGoogle Scholar
  13. 13.
    Frost, N.E. and Dugdale, D.S. (1957). Fatigue tests on notched mild steel plates with measurements of fatigue cracks. J. Mech. Phys. Solids. Vol. 5, 182–192.CrossRefGoogle Scholar
  14. 14.
    Miller, K.J. and de los Rios, E.R. (editors) (1992). Short fatigue cracks. ESIS Publication 13. Mechanical Engineering Publications, London.Google Scholar
  15. 15.
    Sines, G. and Ohgi G. (1981). Fatigue criteria under combined stresses or strains. Trans. ASME, J. Engng Mater. Tech. Vol. 103, 82–90.CrossRefGoogle Scholar
  16. 16.
    Crossland, B. (1956). Effect of large hydrostatic pressures on the torsional fatigue strength of an alloy steel. In Proc. Int. Conf. on Fatigue of Metals, London-New York Institution of Mechanical Engineers, London, 138–149.Google Scholar
  17. 17.
    Papadopoulos, I.V. and Panoskaltsis, V. (1996). Invariant formulation of a gradient dependent multiaxial high-cycle fatigue criterion. Engng Fract. Mech. Vol. 55, 513–528.CrossRefGoogle Scholar
  18. 18.
    Gough, H.J., Pollard, H.V. and Clenshaw, W.J. (1951). Some experiments on the resistance of metals to fatigue under combined stress. Reports and Memoranda No 2522, Aeronautical Research Counsil. His Majesty’s Stationary Office, London.Google Scholar
  19. 19.
    Sines, G. (1959). Behaviour of metals under complex static and alternating stresses. In Metal Fatigue (G. Sines and J.L. Waisman Eds). McGraw Hill, New York, 145–169.Google Scholar
  20. 20.
    Froustey, C. and Lasserre, S. (1989). Multiaxial fatigue endurance of 30NCD16 steel. Int. J. Fatigue. Vol. 11, 169–175.CrossRefGoogle Scholar
  21. 21.
    Papadopoulos, I.V, Davoli, P., Gorla, C., Filippini, M. and Bernasconi, A. (1997). A comparative study of multiaxial high-cycle fatigue criteria for metals. Int. J. Fatigue. Vol. 19, 219–235.CrossRefGoogle Scholar
  22. 22.
    Zenner, H., Heidenreich, R. and Richter, I.Z. (1985). Dauerschwingfestigkeit bei nichtsynchroner mehrachsinger beanspruchung. Werkstofftech. Vol. 16, 101–112.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 1999

Authors and Affiliations

  • I. V. Papadopoulos
    • 1
  1. 1.European CommissionJoint Research CentreIspraItaly

Personalised recommendations