Abstract
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.
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Abbreviations
- AISI:
-
American Iron and Steel Institute
- ANN:
-
Artificial neural network
- ASTM:
-
American Society for Testing and Materials
- BPA:
-
Backpropagation algorithm
- CDM:
-
Continuum damage mechanics
- CEV:
-
Carbon equivalent value
- HB:
-
Brinell hardness
- HV:
-
Vickers hardness
- LCF:
-
Low-cycle fatigue
- RA:
-
Reduction in area
- SAE:
-
Society of Automotive Engineers
- SAV:
-
Strain amplitude variation
- b :
-
Fatigue strength exponent
- c :
-
Fatigue ductility exponent
- C :
-
Constant parameter
- C 1, C 2 :
-
Material constants
- D :
-
Damage variable
- D c :
-
Critical damage
- D N :
-
Damage corresponding to N cycles
- D 0 :
-
Initial damage
- E :
-
Young’s modulus
- E′ :
-
Effective Young’s modulus
- K :
-
Strength coefficient
- K′ :
-
Cyclic strength coefficient
- n :
-
Strain hardening exponent
- n′ :
-
Cyclic strain hardening exponent
- N :
-
Number of cycles
- N t :
-
Transition fatigue life
- 2N f :
-
Reversals to failure
- R :
-
Correlation coefficient
- S e :
-
Endurance limit
- \(\Delta \varepsilon\) :
-
Strain range
- \(\varepsilon_{\text{a}}\) :
-
Strain amplitude
- \(\varepsilon_{\text{e}}\) :
-
Elastic strain
- \(\varepsilon_{ est }\) :
-
Estimated strain
- \(\varepsilon_{\text{exp}}\) :
-
Experimental strain
- \(\varepsilon_{\text{f}}\) :
-
True fracture strain
- \(\varepsilon_{\text{p}}\) :
-
Plastic strain
- \(\varepsilon_{\text{f}}^{{\prime }}\) :
-
Fatigue ductility coefficient
- \(\varepsilon_{0}\) :
-
Threshold strain
- \(\sigma\) :
-
Nominal stress
- \(\tilde{\sigma }\) :
-
Effective stress
- \(\sigma_{\text{ave}}\) :
-
Average strength
- \(\sigma_{\text{f}}\) :
-
True fracture strength
- \(\sigma_{\text{u}}\) :
-
Ultimate tensile strength
- \(\sigma_{\text{y}}\) :
-
Yield strength
- \(\sigma_{\text{f}}^{{\prime }}\) :
-
Fatigue strength coefficient
- \(\sigma_{\text{y}}^{{\prime }}\) :
-
Cyclic yield strength
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Acknowledgments
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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Appendices
Appendix 1
See Table 6.
Appendix 2
Figure 12 shows regression analysis of estimated reversals to failure by the ANN-based model at \(\Delta \varepsilon\)/2 = 2% versus experimental fatigue lives for the data set. The figure includes (a) training, (b) validation, (c) testing and (d) all data points. The values of correlation coefficients at all strain ranges are summarized in Table 7. The correlation coefficient values of test points (6 random materials at each strain range) are all within satisfactory levels.
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Dabiri, M., Ghafouri, M., Rohani Raftar, H.R. et al. Evaluation of Strain–Life Fatigue Curve Estimation Methods and Their Application to a Direct-Quenched High-Strength Steel. J. of Materi Eng and Perform 27, 1058–1072 (2018). https://doi.org/10.1007/s11665-018-3215-z
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DOI: https://doi.org/10.1007/s11665-018-3215-z