Journal of Materials Engineering and Performance

, Volume 27, Issue 3, pp 1058–1072 | Cite as

Evaluation of Strain–Life Fatigue Curve Estimation Methods and Their Application to a Direct-Quenched High-Strength Steel

  • M. Dabiri
  • M. Ghafouri
  • H. R. Rohani Raftar
  • T. Björk


Methods to estimate the strain–life curve, which were divided into three categories: simple approximations, artificial neural network-based approaches and continuum damage mechanics models, were examined, and their accuracy was assessed in strain–life evaluation of a direct-quenched high-strength steel. All the prediction methods claim to be able to perform low-cycle fatigue analysis using available or easily obtainable material properties, thus eliminating the need for costly and time-consuming fatigue tests. Simple approximations were able to estimate the strain–life curve with satisfactory accuracy using only monotonic properties. The tested neural network-based model, although yielding acceptable results for the material in question, was found to be overly sensitive to the data sets used for training and showed an inconsistency in estimation of the fatigue life and fatigue properties. The studied continuum damage-based model was able to produce a curve detecting early stages of crack initiation. This model requires more experimental data for calibration than approaches using simple approximations. As a result of the different theories underlying the analyzed methods, the different approaches have different strengths and weaknesses. However, it was found that the group of parametric equations categorized as simple approximations are the easiest for practical use, with their applicability having already been verified for a broad range of materials.


artificial neural network continuum damage mechanics high-strength steel low-cycle fatigue life prediction 



American Iron and Steel Institute


Artificial neural network


American Society for Testing and Materials


Backpropagation algorithm


Continuum damage mechanics


Carbon equivalent value


Brinell hardness


Vickers hardness


Low-cycle fatigue


Reduction in area


Society of Automotive Engineers


Strain amplitude variation



Fatigue strength exponent


Fatigue ductility exponent


Constant parameter

C1, C2

Material constants


Damage variable


Critical damage


Damage corresponding to N cycles


Initial damage


Young’s modulus


Effective Young’s modulus


Strength coefficient


Cyclic strength coefficient


Strain hardening exponent


Cyclic strain hardening exponent


Number of cycles


Transition fatigue life


Reversals to failure


Correlation coefficient


Endurance limit

\(\Delta \varepsilon\)

Strain range


Strain amplitude


Elastic strain

\(\varepsilon_{ est }\)

Estimated strain


Experimental strain


True fracture strain


Plastic strain

\(\varepsilon_{\text{f}}^{{\prime }}\)

Fatigue ductility coefficient


Threshold strain


Nominal stress

\(\tilde{\sigma }\)

Effective stress


Average strength


True fracture strength


Ultimate tensile strength


Yield strength

\(\sigma_{\text{f}}^{{\prime }}\)

Fatigue strength coefficient

\(\sigma_{\text{y}}^{{\prime }}\)

Cyclic yield strength



This study was performed as part of the Breakthrough Steels and Applications (BSA) program funded by the Finnish Funding Agency for Innovation (TEKES) and the Digital, Internet, Materials and Engineering Co-Creation (DIMECC) platform.


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Copyright information

© ASM International 2018

Authors and Affiliations

  1. 1.Laboratory of Steel StructuresLappeenranta University of TechnologyLappeenrantaFinland
  2. 2.Department of Mechanical Engineering, Science and Research BranchIslamic Azad UniversityTehranIran

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