Predictive approach of high-cycle fatigue limit of finished turned AISI 316L steel

  • R. GrissaEmail author
  • F. Zemzemi
  • S. Manchoul
  • R. Seddik
  • R. Fathallah


This paper presents a global approach in order to predict the high-cycle fatigue (HCF) limit of turned parts. The multi-axial fatigue criteria of both Crossland and Dang Van are adapted for the case of machined parts. Thereby, the machined surface conditions which are residual stresses, superficial damage, and hardening, are taken into account in the both criteria. The suggested approach is conducted for turned AISI 316L stainless steel for various machining parameters. Otherwise, three types of cyclic loading, which are traction, torsion, and combined traction-torsion loadings, are applied onto the machined surface so as to investigate their effects on the HCF performance. The applicability of the used fatigue criteria and their efficiency in the prediction of the HCF indicator are discussed. A critical assessment of the beneficial or unbeneficial effects of each surface condition on the fatigue strength is investigated. The obtained results are physically consistent and are in good concordance with the available experimental investigations.


High-cycle fatigue performance Fatigue criteria Residual stresses Machining conditions Cyclic loading Surface conditions 



superficial damage after machining


new yield strength after machining

\( {\sigma}_{y_0} \)

initial yield strength of the material


residual stresses in the circumferential directions


residual stresses in the axial directions

\( {\underset{\_}{\underset{\_}{\sigma}}}_{RS}(y) \)

residual stress tensor

\( {\sigma}_{\mathrm{eqDV}}^M \)

equivalent stress of the Dang Van criterion for the machined material

\( {\sigma}_{\mathrm{eqCr}}^M \)

equivalent stress of the Crossland criterion for the machined material

\( \underset{\_}{\underset{\_}{\sigma }}\left(y,t\right) \)

total cyclic loading tensor at an instant t and for y depth

\( {\underset{\_}{\underset{\_}{\sigma}}}_{\mathrm{app}}\left(y,t\right) \)

applied cyclic loading tensor at an instant t and for y depth

αD, βD

material parameters defining the Dang Van criterion

αC, βC

material parameters defining the Crossland criterion


fatigue limit in tensile loadings before machining (MPa)


fatigue limit in torsion loadings before machining (MPa)


fatigue limit in tensile loadings after machining (MPa)


fatigue limit in torsion loadings after machining (MPa)


amplitude of the tensile stress (MPa)


amplitude of the torsion stress (MPa)


average stress in tensile loadings (MPa)


average stress in torsion loadings (MPa)


load ratio


maximal tensile stress (MPa)


minimal tensile stress (MPa)

\( {\hat{\tau}}^{\mathrm{a}} \)

Tresca shear stress (MPa)

J2, a

amplitude of the second invariant

\( {I}_{\mathrm{Cr}}^M\;\left(\%\right) \)

HCF indicator of the Crossland criterion

\( {I}_{\mathrm{DV}}^{\mathrm{M}}\;\left(\%\right) \)

HCF indicator of the Dang Van criterion


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  • R. Grissa
    • 1
    • 2
    Email author
  • F. Zemzemi
    • 3
  • S. Manchoul
    • 1
    • 2
  • R. Seddik
    • 1
    • 2
  • R. Fathallah
    • 1
    • 2
  1. 1.Unité de Génie de Production Mécanique et Matériaux (UGPM2-UR17ES43), National Engineering School of SfaxUniversity of SfaxSfaxTunisia
  2. 2.National Engineering School of SousseUniversity of SousseSousseTunisia
  3. 3.Laboratory of Mechanics of Sousse, National Engineering School of SousseUniversity of SousseSousseTunisia

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