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

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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

References

  1. S. Manson, Fatigue: A Complex Subject—Some Simple Approximations, Exp. Mech., 1965, 5, p 193–226

    Article  Google Scholar 

  2. M. Mitchell, D. Socie, and E. Caulfield, Fundamentals of Modern Fatigue Analysis, Fracture Control Program, No. 26, University of Illinois (1977)

  3. U. Muralidharan and S. Manson, A Modified Universal Slopes Equation for Estimation of Fatigue Characteristics of Metals, J. Eng. Mater. Technol., 1988, 110, p 55–58

    Article  Google Scholar 

  4. B.T. Seeger and C. Boller, Materials Data for Cyclic Loading: Supplement 1, Elsevier, Amsterdam, 1990

    Google Scholar 

  5. J. Ong, An Improved Technique for the Prediction of Axial Fatigue Life from Tensile Data, Int. J. Fatigue, 1993, 15, p 213–219

    Article  Google Scholar 

  6. M. Roessle and A. Fatemi, Strain-Controlled Fatigue Properties of Steels and Some Simple Approximations, Int. J. Fatigue, 2000, 22, p 495–511

    Article  Google Scholar 

  7. M. Meggiolaro and J. Castro, Statistical Evaluation of Strain-Life Fatigue Crack Initiation Predictions, Int. J. Fatigue, 2004, 26, p 463–476

    Article  Google Scholar 

  8. J. Park and J. Song, New Estimation Method of Fatigue Properties of Aluminum Alloys, J. Eng. Mater. Technol., 2003, 125, p 208–214

    Article  Google Scholar 

  9. J. Park and J. Song, Detailed Evaluation of Methods for Estimation of Fatigue Properties, Int. J. Fatigue, 1995, 17, p 365–373

    Article  Google Scholar 

  10. K. Lee and J. Song, Estimation Methods for Strain-Life Fatigue Properties from Hardness, Int. J. Fatigue, 2006, 28, p 386–400

    Article  Google Scholar 

  11. J. Pujol and J. Pinto, A Neural Network Approach to Fatigue Life Prediction, Int. J. Fatigue, 2011, 33, p 313–322

    Article  Google Scholar 

  12. T. Pleune and O. Chopra, Using Artificial Neural Networks to Predict the Fatigue Life of Carbon and Low-Alloy Steels, Nucl. Eng. Des., 2000, 197, p 1–12

    Article  Google Scholar 

  13. V. Srinivasan, Low Cycle Fatigue and Creep–Fatigue Interaction Behavior of 316L(N) Stainless Steel and Life Prediction by Artificial Neural Network Approach, Int. J. Fatigue, 2003, 25, p 1327–1338

    Article  Google Scholar 

  14. K. Genel, Application of Artificial Neural Network for Predicting Strain-Life Fatigue Properties of Steels on the Basis of Tensile Tests, Int. J. Fatigue, 2004, 26, p 1027–1035

    Article  Google Scholar 

  15. R. Basan, M. Franulovic´, I. Prebil, and N. Črnjarić-Žic, Analysis of Strain-Life Fatigue Parameters and Behaviour of Different Groups of Metallic Materials, Int. J. Fatigue, 2011, 33, p 484–491

    Article  Google Scholar 

  16. S. Dhar, P. Dixit, and R. Sethuraman, A Continuum Damage Mechanics Model for Ductile Fracture, Int. J. Press. Vessels Pip., 2000, 77, p 335–344

    Article  Google Scholar 

  17. H. Costa Mattos, G. Minak, F. Di Gioacchino, and A. Soldá, Modeling the Superplastic Behavior of Mg Alloy Sheets Under Tension Using a Continuum Damage Theory, Mater. Des., 2009, 30, p 1674–1679

    Article  Google Scholar 

  18. S. Oller, O. Salomón, and E. Oñate, A Continuum Mechanics Model for Mechanical Fatigue Analysis, Comput. Simul. Mater. Sci., 2005, 32, p 175–195

    Article  Google Scholar 

  19. Y. Xiao, S. Li, and Z. Gao, A Continuum Damage Mechanics Model for High Cycle Fatigue, Int. J. Fatigue, 1998, 20, p 503–508

    Article  Google Scholar 

  20. S. Silitonga, J. Maljaars, F. Soetens, and H. Snijder, Survey on Damage Mechanics Models for Fatigue Life Prediction, HERON, 2013, 58, p 25–60

    Google Scholar 

  21. V. Dattoma, S. Giancane, R. Nobile, and F. Panella, Fatigue Life Prediction Under Variable Loading Based on a New Non-linear Continuum Damage Mechanics Model, Int. J. Fatigue, 2006, 28, p 89–95

    Article  Google Scholar 

  22. S. Giancane, R. Nobile, F. Panella, and V. Dattoma, Fatigue Life Prediction of Notched Components Based on a New Nonlinear Continuum Damage Mechanics Model, Proced. Eng., 2010, 2, p 1317–1325

    Article  Google Scholar 

  23. C.L. Chow and Y. Wei, A Model of Continuum Damage Mechanics for Fatigue Failure, Int. J. Fract., 1991, 50, p 301–316

    Article  Google Scholar 

  24. W. June, A Continuum Damage Mechanics Model for Low-Cycle Fatigue Failure of Metals, Eng. Fract. Mech., 1992, 41, p 437–441

    Article  Google Scholar 

  25. N. Bonora, Low Cycle Fatigue Life Estimation for Ductile Metals Using a Nonlinear Continuum Damage Mechanics Model, Int. J. Solids Struct., 1998, 35, p 1881–1894

    Article  Google Scholar 

  26. B. Bhattacharya and B. Ellingwood, A New CDM-Based Approach to Structural Deterioration, Int. J. Solids Struct., 1999, 36, p 1757–1779

    Article  Google Scholar 

  27. J. Kömi, P. Karjalainen, and D. Porter, Direct-Quenched Structural Steels, Encyclopedia of Iron, Steel, and Their Alloys, CRC Press, Boca Raton, 2016, p 1109–1125

    Book  Google Scholar 

  28. Standard Test Method for Strain-Controlled Fatigue Testing, ASTM Standard E606. American Society for Testing and Materials, West Conshohocken (2013)

  29. Standard practice for statistical analysis of linear or linearized stress-life (S–N) and strain-life (ε − N) fatigue data, ASTM Standard E739. American Society for Testing and Materials, West Conshohocken (2004)

  30. M. Dabiri, M. Isakov, T. Skriko, and T. Björk, Experimental Fatigue Characterization and Elasto-Plastic Finite Element Analysis of Notched Specimens Made of Direct-Quenched Ultra-High Strength Steel, Proc. Inst. Mech. Eng, Part C, 2017, 231, p 4209–4226

    Article  Google Scholar 

  31. R. Basan, D. Rubeša, M. Franulović, and B. Križan, A Novel Approach to the Estimation of Strain Life Fatigue Parameters, Proced. Eng., 2010, 2, p 417–426

    Article  Google Scholar 

  32. E.J. Pavlina and C. Van Tyne, Correlation of Yield Strength and Tensile Strength with Hardness for Steels, J. Mater. Eng. Perform., 2008, 17, p 888–893

    Article  Google Scholar 

  33. R. Basan, MATDAT Material Properties Database (2017). http://www.matdat.com. Accessed 30 March 2017

  34. S. Murakami, Continuum Damage: A Continuum Mechanics Approach to the Analysis of Damage and Fracture, Springer, Berlin, 2012

    Book  Google Scholar 

  35. L. Kachanov, Introduction to Continuum Damage Mechanics, Martinus Nijhoff, The Hague, 1986

    Book  Google Scholar 

  36. J. Lemaitre, A Continuous Damage Mechanics Model for Ductile Fracture, J. Eng. Mater. Tech., 1985, 170, p 83–89

    Article  Google Scholar 

  37. J. Bennantine, J. Comer, and J. Handrock, Fundamentals of Metal Fatigue Analysis, Prentice Hall, Upper Saddle River, 1990

    Google Scholar 

  38. Y. Upadhyaya and B. Sridhara, Fatigue Life Prediction: A Continuum Damage Mechanics and Fracture Mechanics Approach, Mater. Des., 2012, 35, p 220–224

    Article  Google Scholar 

  39. J. Lemaitre, A Course on Damage Mechanics, Springer, Berlin, 1992

    Book  Google Scholar 

  40. T. Marohnić and R. Basan, Study of Monotonic Properties’ Relevance for Estimation of Cyclic Yield Stress and Ramberg–Osgood Parameters of Steels, J. Mater. Eng. Perform., 2016, 25, p 4812–4823

    Article  Google Scholar 

  41. M. Dabiri, M. Ghafouri, H. Rohani Raftar, and T. Björk, Neural Network-Based Assessment of the Stress Concentration Factor in a T-Welded Joint, Constr. Steel Res., 2017, 128, p 567–578

    Article  Google Scholar 

  42. R. Basan, D. Rubeša, M. Franulović, and T. Marohnić, Some Considerations on the Evaluation of Methods for the Estimation of Fatigue Parameters from Monotonic Properties, Proced. Eng., 2015, 101, p 18–25

    Article  Google Scholar 

  43. Hartman, Robust Model for Fatigue Life Estimation from Monotonic Properties Data for Steels, University of Waterloo, Waterloo, 2013

    Google Scholar 

  44. B. Bhattacharya and B. Ellingwood, Continuum Damage Mechanics Analysis of Fatigue Crack Initiation, Int. J. Fatigue, 1998, 20, p 631–639

    Article  Google Scholar 

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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.

Author information

Authors and Affiliations

  1. Laboratory of Steel Structures, Lappeenranta University of Technology, P.O. Box 20, 53851, Lappeenranta, Finland

    M. Dabiri, M. Ghafouri & T. Björk

  2. Department of Mechanical Engineering, Science and Research Branch, Islamic Azad University, P.O. Box 440902, Tehran, Iran

    H. R. Rohani Raftar

Authors
  1. M. Dabiri
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  2. M. Ghafouri
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  3. H. R. Rohani Raftar
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  4. T. Björk
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Corresponding author

Correspondence to M. Dabiri.

Appendices

Appendix 1

See Table 6.

Table 6 Mechanical properties of low-alloy steels used as a data set in implementation of the ANN-based model
Full size table

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.

Fig. 12
figure 12

Regression analysis of estimated reversals to failure by the ANN-based model at ∆ε/2 = 2% for (a) training, (b) validation, (c) testing and (d) all data points

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Table 7 Correlation coefficients of regression analyses at different strain amplitudes
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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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