Fatigue strength prediction methodology of shot-peened materials

  • Mohamed BenkhettabEmail author
  • Hocine Guechichi
  • Salah-Eddine Benkabouche


Shot peening is used to enhance fatigue strength, but it is usually neglected by manufacturing design. The main purpose of the present work is to suggest strategies capable of making connection between the process conditions and the fatigue strength. In the present paper, fatigue lives of shot-peened parts were predicted. A new multiaxial HCF model, based on the Crossland criterion, was proposed; it integrates the favourable effects of shot peening that are the combined effect of compressive residual stresses and strain hardening. The plastic strain field accounts for the strain hardening. In order to compute residual stress and equivalent plastic strain profiles due to the repeated impacts, we have modelled and simulated, through a finite element method, the impact of the shot dynamics resulting from the process. The relaxation of induced compressive residual stresses, over the fatigue life, has been considered. For the purpose of spotlighting the capability of the present methodology, the predictions were compared with existing experimental data. This study demonstrates that the single effect of stabilized residual stress is not sufficient to explain the full enhancement of fatigue resistance. The proposed fatigue criterion provides a conservative prediction in terms of endurance limit.


Shot peening Residual stress Strain hardening Fatigue strength Simulation Fatigue criterion 



Two dimensions


Three dimensions


Compressive residual stress


Strain hardening factor


Elastic modulus


Finite element method

f−1, t−1

Endurance limits in fully reversed bending and torsion, respectively

f−1(N), t−1(N)

Fatigue limits at fatigue life N in fully reversed bending and torsion, respectively


Coefficient of friction


High-cycle fatigue


Low-cycle fatigue


Number of cycles to failure (fatigue life)


Knee point


Maximum hydrostatic pressure during the loading


Maximum hydrostatic stress due to the alternating loading


Maximum hydrostatic stress due to the monotonic loading


Strain hardening quantity


Shot radius


Residual stress


Strain hardening


Stabilized relaxed stress

[ t−1(N)]eq

Equivalent fatigue limit, at fatigue life N, in torsion for peened material

[ t−1(N)]

Fatigue limit, at fatigue life N, in torsion for unpeened material


Shot velocity (m/s)

X, Y, Z



Hardened surface layer

α, β

Material parameters in Crossland criterion

\( {\varepsilon}_{eq}^P(Y) \)

Equivalent plastic strain

\( \overline{\overline{\varSigma}} \)

Total stress tensor

\( \overline{\overline{\sigma}},{\sigma}_{eq} \)

Applied stress tensor and equivalent stress, respectively

\( {\overline{\overline{\sigma}}}_a \)

Applied stress amplitude tensor

σe, ν

Yield strength and Poison’s ratio, respectively

\( {\sigma}_{eq}^{\mathrm{max}} \)

Maximum equivalent stress

\( {\overline{\overline{\sigma}}}_m \)

Mean stress tensor

\( {\overline{\overline{\sigma}}}_R,{\sigma}_R \)

Residual stress tensor and residual stress, respectively


Square root of the amplitude of the second invariant of the stress deviator tensor



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Copyright information

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

Authors and Affiliations

  • Mohamed Benkhettab
    • 1
    Email author
  • Hocine Guechichi
    • 1
  • Salah-Eddine Benkabouche
    • 1
  1. 1.Laboratoire d’Elaboration et Caractérisation Physico Mécanique et Métallurgique des Matériaux, Department of Mechanics, Faculty of Science and TechnologyMostaganem UniversityMostaganemAlgeria

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