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Fatigue life prediction model of metallic materials considering crack propagation and closure effect

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Abstract

To consider the effect of crack closure on the mechanical properties of metals, the fatigue life of metal specimens is predicted based on energy dissipation model. The main feature of the model consists in considering the relationship between the total failure energy and the energy density increment. The total failure energy model considers the fatigue crack size and stress amplitude. It is assumed the energy density increment gradually decreases and tends to be stable. The influence of crack closure effect is considered. According to the law of metal fatigue characteristics, a new mathematical model for predicting fatigue life is established.

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Abbreviations

\( b \) :

Fatigue strength exponent

\( c \) :

The fatigue ductility exponent

\( \Delta \sigma \) :

Stress range

\( \sigma_{a} \) :

Maximum tensile stress

\( a_{\text{c}} \) :

Critical crack size

\( a{}_{0} \) :

Initial crack size

\( n \) :

Strain hardening exponent

\( n^{\prime } \) :

Cyclic strain hardening exponent

\( \varepsilon_{\text{f}} \) :

Fracture ductility

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

Cyclic fatigue ductility coefficient

\( \Delta \varepsilon_{\text{p}} \) :

Plastic strain range

\( \Delta \varepsilon_{{{\text{p}}Z}} \) :

Plastic strain increment under equivalent stress increment

\( \alpha \) :

Equivalent strain increment parameter

\( W_{\text{p}} \) :

Plastic strain energy

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

Cyclic fatigue strength coefficient

\( \delta {\text{W}} \) :

One-cycle plastic strain energy increment

\( K^{\prime } \) :

Cyclic stress intensity coefficient

\( W_{\text{pf}} \) :

Total failure energy

\( \sigma_{b} \) :

Ultimate tensile strength

\( K_{\text{theff}} \) :

Effective initial stress intensity factor

\( K_{I} \) :

Stress intensity factor

\( \sigma_{\text{f}} \) :

Fracture strength

\( N_{\text{f}} \) :

Fatigue life

References

  1. Zhu SP, Hao YZ, de Oliveira Correia JA, Lesiuk G, de Jesus AM (2019) Nonlinear fatigue damage accumulation and life prediction of metals: a comparative study. Fatigue Fract Eng Mater Struct 42(6):1271–1282

    Google Scholar 

  2. Feng L (2016) Fiber metal layer board fatigue property analysis based on strain energy density method. Mech Eng Autom 6:129–131

    Google Scholar 

  3. Wu JN, Yan SZ, Li JL, Gu YX (2016) Mechanism reliability of bistable compliant mechanisms considering degradation and uncertainties: modeling and evaluation method. Appl Math Model 40(23–24):10377–10388

    MATH  Google Scholar 

  4. Liu XT, Zhang MH, Wang HJ, Luo J, Tong JC, Wang XL (2020) Fatigue life analysis of automotive key parts based on improved peak‐over‐threshold method. Fatigue Fract Eng Mater Struct 43(8):1824–1836

    Google Scholar 

  5. He JC, Zhu SP, Liao D, Niu XP (2020) Probabilistic fatigue assessment of notched components under size effect using critical distance theory. Eng Fract Mech 235:107150

    Google Scholar 

  6. Liu XT, Kan FH, Wang HJ, Xin XF, Wang ZQ, Huang H (2020) Fatigue life prediction of clutch sleeve based on abrasion mathematical model in service period. Fatigue Fract Eng Mater Struct 43(3):488–501

    Google Scholar 

  7. Geng SL, Liu XT, Liang ZQ, Wang YS, Wang XL (2020) Tolerance analysis and evaluation of uncertain automatic battery replacement system. Struct Multidiscip Optim 61(1):239–252

    Google Scholar 

  8. Wang ML, Liu XT, Wang XL, Wang YS (2018) Probabilistic modeling of unified S-N curves for mechanical parts. Int J Damage Mech 27(7):979–999

    Google Scholar 

  9. Wang HJ, Liu XT, Zhang MH, Wang YS, Wang XL (2019) Prediction of material fatigue parameters for low alloy forged steels considering error circle. Int J Fatigue 121:135–145

    Google Scholar 

  10. Esin A (1968) The microplastic strain energy criterion applied to fatigue. Basic Eng 90(1):28–31

    Google Scholar 

  11. Esin A, Jones WJD (1966) A theory of fatigue based on the microstructural accumulation of strain energy*1. Nucl Eng Des 4(3):292–298

    Google Scholar 

  12. Tchankov DS, Vesselinov KV (1998) Fatigue life prediction under random loading using total hysteresis energy. Inc J Pressure Vessel Pi 75(13):955–962

    Google Scholar 

  13. Xiao T, De W, Hao X (1989) Investigation of cyclic hysteresis energy in fatigue failure process. Int J Fatigue 11(5):353–359

    Google Scholar 

  14. Liakat M, Khonsari MM (2014) Rapid estimation of fatigue entropy and toughness in metals. Mater Des 62:149–157

    Google Scholar 

  15. Huffman P, Ferreira J, Correia JAFO, Jesus AMPD, Glinka G (2017) Fatigue crack propagation prediction of a pressure vessel mild steel based on a strain energy density model. Frat Ed Integr Strut 42:170–180

    Google Scholar 

  16. Lesiuk G, Szata M, Rozumek D, Marciniak Z, Correia J, De Jesus A (2018) Energy response of s355 and 41cr4 steel during fatigue crack growth process. J Strain Anal Eng Des 53(8):663–675

    Google Scholar 

  17. Correia JAFO, Huffman PJ, De Jesus AMP (2018) Probabilistic fatigue crack initiation and propagation fields using the strain energy density. Strength Mater 2018(50):620–635

    Google Scholar 

  18. Lesiuk G, Szata M, Rozumek D, Marciniak Z, Jesus AMPD (2017) Energy description of fatigue crack growth process-theoretical and experimental approach. Procedia Struct Integr 5:904–911

    Google Scholar 

  19. Yang B, Liaw PK, Morrison M, Liu CT, Buchanan RA, Huang JY (2005) Temperature evolution during fatigue damage. Intermetallics 13(3):419–428

    Google Scholar 

  20. Risitano A, Risitano G (2013) Cumulative damage evaluation in multiple cycle fatigue tests taking into account energy parameters. Int J Fatigue 48:214–222

    Google Scholar 

  21. Meneghetti G (2007) Analysis of the fatigue strength of a stainless steel based on the energy dissipation. Int J Fatigue 29(1):81–94

    Google Scholar 

  22. Meneghetti G, Ricotta M (2012) The use of the specific heat loss to analyse the low-and high-cycle fatigue behaviour of plain and notched specimens made of a stainless steel. Eng Fract Mech 81:2–16

    Google Scholar 

  23. Ye DY, Wang ZL (2001) A new approach to low-cycle fatigue damage based on exhaustion of static toughness and dissipation of cyclic plastic strain energy during fatigue. Int J Fatigue 23(8):679–687

    Google Scholar 

  24. Wang HJ, Liu XT, Wang XL, Wang YS (2019) Numerical method for estimating fatigue crack initiation size using elastic-plastic fracture mechanics method. Appl Math Model 73:365–377

    MathSciNet  MATH  Google Scholar 

  25. Meneghetti G, Ricott M (2017) Evaluating the heat energy dissipated in a small volume surrounding the tip of a fatigue crack. Int J Fatigue 3:424–431

    Google Scholar 

  26. Stowell E (1966) A study of the energy criterion for fatigue. Nucl Eng Des 3:32–40

    Google Scholar 

  27. Correia JAFO, Blasón S, De Jesus AMP, Canteli AF, Moreira PMGP, Tavares PJ (2016) Fatigue life prediction based on an equivalent initial flaw size approach and a new normalized fatigue crack growth model. Eng Fail Anal 69:15–28

    Google Scholar 

  28. Vshivkov AN, Iziumova AY, Panteleev IA, Ilinykh AV, Wildemann VE, Plekhov OA (2019) The study of a fatigue crack propagation in titanium Grade 2 using analysis of energy dissipation and acoustic emission data. Eng Fract Mech 210:312–319

    Google Scholar 

  29. Wojciech M, Tadeusz L, Norbert M (2018) Energy-based fatigue failure characteristics of materials under random bending loading in elastic-plastic range. Fatigue Fract Eng Mater Struct 41(2):249–259

    Google Scholar 

  30. Guo Q, Zairi F, Guo XL (2018) An intrinsic dissipation model for high-cycle fatigue life prediction. Int J Mech Sci 140:163–171

    Google Scholar 

  31. Wang RZ, Zhang XC, Tu ST, Zhu SP, Zhang CC (2016) A modified strain energy density exhaustion model for creep-fatigue life prediction. Int J Fatigue 90:12–22

    Google Scholar 

  32. Zhu SP, Liu Y, Liu Q (2018) Strain energy gradient-based LCF life prediction of turbine discs using critical distance concept. Int J Fatigue 113:33–42

    Google Scholar 

  33. Socie DF, Morrow J, Chen WC (1979) A procedure for estimating the total fatigue life of notched and cracked members. Eng Fract Mech 11(4):851–859

    Google Scholar 

  34. Mahtabi MJ, Shamsaei N (2016) A modified energy-based approach for fatigue life prediction of superelastic NiTi in presence of tensile mean strain and stress. Int J Mech Sci 117:321–333

    Google Scholar 

  35. Sedighi M, Monshi P, Joudaki J (2017) Investigation of mechanical properties and fatigue life of ECARed AA5083 aluminium alloy. Fatigue Fract Eng Mater Struct 40(3):412–422

    Google Scholar 

  36. Liao D, Zhu SP (2019) Energy field intensity approach for notch fatigue analysis. Int J Fatigue 127:190–202

    Google Scholar 

  37. Liao D, Zhu SP, Keshtegar B, Qian G, Wang QY (2020) Probabilistic framework for fatigue life assessment of notched components under size effects. Int J Mech Sci 181:105685

    Google Scholar 

  38. Liu HL, Liu HJ, Bocher P, Zhu CC, Sun ZD (2018) Effects of case hardening properties on the contact fatigue of a wind turbine gear pair. Int J Mech Sci 141:520–527

    Google Scholar 

  39. Elber W (1970) Fatigue crack closure under cyclic tension. Eng Fract Mech 2(1):37–45

    Google Scholar 

  40. Schijve J (1998) Fatigue specimens for sheet and plate material. Fatigue Fract Eng Mater Struct 21(3):347–357

    Google Scholar 

  41. Manson SS, Hrischberg MH (1963) Fatigue behavior in strain cycling in low-and intermediate-cycle range. In: Proceedings of the 10th Sagamore army materials research confidence

  42. Zheng XL, Wang H, Yan JH, Ding XW (2013) Material fatigue theory and engineering application. Science Press, Beijing

    Google Scholar 

  43. Wang XG, Crupi V, Jiang C (2017) Energy-based approach for fatigue life prediction of pure copper. Int J Fatigue 104:243–250

    Google Scholar 

  44. Budynas RG, Nisbett JK (2006) Shigley’s mechanical engineering design, 8th edn. McGraw-Hill Primis, New York

    Google Scholar 

  45. Mischke CR (1987) Prediction of stochastic endurance strength. J Vib Acoust Stress Reliab Des 109(1):113

    Google Scholar 

  46. Ling J, Pan J (1997) A maximum likelihood method for estimating P-S-N curves. Int J Fatigue 19:415–419

    Google Scholar 

  47. Tong XY, Jun WD, Hao X (1989) Investigation of cyclic hysteresis energy in fatigue failure process. Int J Fatigue 11:353–359

    Google Scholar 

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Acknowledgement

This work is supported by the National Natural Science Foundation of China (51675324).

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Authors and Affiliations

  1. School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai, 201620, China

    Que Wu, Xintian Liu, Zhiqiang Liang, Yansong Wang & Xiaolan Wang

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  1. Que Wu
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  2. Xintian Liu
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  3. Zhiqiang Liang
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  4. Yansong Wang
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  5. Xiaolan Wang
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Correspondence to Xintian Liu.

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Technical Editor: João Marciano Laredo dos Reis.

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Wu, Q., Liu, X., Liang, Z. et al. Fatigue life prediction model of metallic materials considering crack propagation and closure effect. J Braz. Soc. Mech. Sci. Eng. 42, 424 (2020). https://doi.org/10.1007/s40430-020-02512-1

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