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A new, direct approach toward modeling thermo-coupled fatigue failure behavior of metals and alloys

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Abstract

The objective of this study is two-fold. Firstly, new finite strain elastoplasticity models are proposed from a fresh standpoint to achieve a comprehensive representation of thermomechanical behavior of metals and alloys over the whole deformation range up to failure. As contrasted with the usual elastoplasticity models, such new models of much simpler structure are totally free, in the sense that both the yield condition and the loading—unloading conditions need not be introduced as extrinsic coercive conditions but are automatically incorporated as inherent constitutive features into the models. Furthermore, the new models are shown to be thermodynamically consistent, in a further sense that both the specific entropy function and the Helmholtz free energy function may be presented in explicit forms, such that the thermodynamic restriction stipulated by Clausius—Duhem inequality for the intrinsic dissipation may be identically satisfied. Secondly, it is then demonstrated that the thermo-coupled fatigue failure behavior under combined cyclic changes of stress and temperature may be derived as direct consequences from the new models. This novel result implies that the new model can directly characterize the thermo-coupled fatigue failure behavior of metals and alloys, without involving any usual damage-like variables as well as any ad hoc additional criteria for failure. In particular, numerical examples show that, under cyclic changes of temperature, the fatigue characteristic curve of fatigue life versus temperature amplitude may be obtained for the frst time from model prediction both in the absence and in the presence of stress. Results are in agreement with the salient features of metal fatigue failure.

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References

  1. L Pook, Metal Fatigue, Springer, Berlin, 2007.

    MATH  Google Scholar 

  2. Walker, K.P., Research and development program for non-linear structural modeling with advanced time-temperature dependent constitutive relationships. NASA CR-165553, 1981.

  3. Swanson, G., Linask, I., and Nissley, D., Life prediction and constitutive models for engine hot section anisotropic materials program. NASA CR-174952, 1986.

  4. P.L.C. Rolls-Royce, Predictive methods for combined cycle fatigue in gas turbine blades, in: European (Sixth RTD Framework Programme) Project, London, 2011.

  5. J.W. Hutchinson, A.G. Evans, Mechanics of materials: top-down approaches to fracture, Acta Mater. 48 (2000) 125–135.

    Article  Google Scholar 

  6. B.N. Cox, H.J. Gao, D. Gross, D. Rittel, Modern topics and challenges in dynamic fracture, J. Mech. Phys. Solids 53 (2005) 565–596.

    Article  MathSciNet  Google Scholar 

  7. D. Krajcinovic, Damage Mechanics, Elsevier, Amsterdam, 2003.

    MATH  Google Scholar 

  8. M. Brünig, A continuum damage model based on experiments and numerical simulations—a review, in: H. Altenbach, T. Matsuda, D. Okumura (Eds.), From Creep Damage Mechanics to Homogenization Methods—A Liber Amicorum to Celebrate the Birthday of Nobutada Ohno, Advanced Structural Materials Series, Springer, Berlin, 2015, pp. 19–35.

    Google Scholar 

  9. S. Suresh, second ed, Fatigue of Materials, Cambridge University Press, Cambridge, 1998.

    Book  Google Scholar 

  10. N.E. Frost, K.J. Marsh, L.P. Pook, Metal Fatigue, Dover Publications, Inc., New York, 1999.

    Google Scholar 

  11. H. Xiao, Thermo-coupled elastoplasticity model with asymptotic loss of the material strength, Int. J. Plast. 63 (2014) 211–228.

    Article  Google Scholar 

  12. V. Firouzdor, M. Rajabi, E. Nejati, F. Khomamizadeh, Effect of microstructural constituents on the thermal fatigue life of A319 aluminum alloy, Mater. Sci. Eng. A 454 (2007) 528–535.

    Article  Google Scholar 

  13. Y.D. Huang, N. Hort, H. Dieringa, P. Maier, K.U. Kainer, Investigations on thermal fatigue of aluminum-and magnesium-alloy based composites, Int. J. Fatigue 28 (2006) 1399–1405.

    Article  Google Scholar 

  14. Y.G. Min, J. Bergström, X.C. Wu, L.G. Xu, Oxidation and thermal fatigue behaviors of two type hot work steels during thermal cycling, J. Iron Steel Res. Int. 20 (2013) 90–97.

    Article  Google Scholar 

  15. J. Jonas, B. Ilja, J. Erland, D. Rainer, L. Peter, Investigation on thermal fatigue of SnAgCu, Sn100C, and SnPbAg solder joints in varying temperature environments, Microelectron. Reliab. 54 (2014) 2523–2535.

    Article  Google Scholar 

  16. F. Szmytka, M. Salem, F. Rézaï-Aria, A. Oudin, Thermal fatigue analysis of automotive diesel piston: experimental procedure and numerical protocol, Int. J. Fatigue 73 (2015) 48–57.

    Article  Google Scholar 

  17. F. Ohmenhäuser, C. Schwarz, S. Thalmair, H.S. Evirgen, Constitutive modeling of the thermo-mechanical fatigue and lifetime behavior of the cast steel 1.4849, Mater. Des. 64 (2014) 631–639.

    Article  Google Scholar 

  18. T. Seifert, H. Riedel, Mechanism-based thermomechanical fatigue life prediction of cast iron. Part I: Models., Int. J. Fatigue 32 (2010) 1358–1367.

    Article  Google Scholar 

  19. E. Paffumi, K.F. Nilsson, Z. Szaraz, Experimental and numerical assessment of thermal fatigue in 316 austenitic steel pipes, Eng. Failure Anal. 47 (2015) 312–327.

    Article  Google Scholar 

  20. L. Rémy, F. Szmytka, L. Bucher, Constitutive models for bcc engineering iron alloys exposed to thermal-mechanical fatigue, Int. J. Fatigue 53 (2013) 2–14.

    Article  Google Scholar 

  21. K. Bauerbacha, M. Vormwalda, J. Rudolph, Fatigue assessment of thermal cyclic loading conditions based on a short crack approach, Proc. Eng. 2 (2013) 1569–1578.

    Article  Google Scholar 

  22. V. Levitin, High Temperature Strain of Metals and Alloys, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 1996.

    Google Scholar 

  23. R.C. Reed, The Superalloys: Fundamentals and Applications, Cambridge University Press, Cambridge, 2006.

    Book  Google Scholar 

  24. K. Otsuka, C.M. Wayman, Shape Memory Materials, Cambridge University Press, Cambridge, 1998.

    Google Scholar 

  25. J.F. Bell, The experimental foundation of solid mechanics, Encyclopedia of Physics, vol. VIa/1, Springer, Berlin, 1973.

    Google Scholar 

  26. Y.L. Bai, B. Dodd, Adiabatic Shear Localization, Pergamon, London, 1992.

  27. H. Xiao, O.T. Bruhns, A. Meyers, Free rate-independent elastoplastic equations, ZAMM-J. Appl. Math. Mech. 94 (2014) 461–476.

    Article  MathSciNet  Google Scholar 

  28. Z.L. Wang, H. Xiao, A study of metal fatigue failure as inherent features of elastoplastic constitutive equations, in: H. Altenbach, T. Matsuda, D. Okumura (Eds.), From Creep Damage Mechanics to Homogenization Methods-A Liber Amicorum to Celebrate the Brithday of Nobutada Ohno, Advanced Structural Materials Series, Springer, Berlin, 2015, pp. 529–540.

    Google Scholar 

  29. , 2016,37(2): 245–251 Z.L. Wang, H. Xiao, X.M. Wang, Direct simulation of metal fatigue failure based on new elastoplastic model, Chin. Q. Mech. 37 (2) (2016) 245–251.

    Google Scholar 

  30. H. Xiao, O.T. Bruhns, A. Meyers, Elastoplasticity beyond small deformations, Acta Mech. 182 (2006) 31–111.

    Article  Google Scholar 

  31. O.T. Bruhns, H. Xiao, A. Meyers, Self-consistent {E}ulerian rate type elasto-plasticity models based upon the logarithmic stress rate, Int. J. Plast. 15 (1999) 479–520.

    Article  Google Scholar 

  32. O.T. Bruhns, H. Xiao, A. Meyers, Some basic issues in traditional Eulerian formulations of finite elastoplasticity, Int. J. Plast. 19 (2003) 2007–2026.

    Article  Google Scholar 

  33. O.T. Bruhns, H. Xiao, A. Meyers, A weakened form of Ilyushin’s postulate and the structure of self-consistent Eulerian finite elastoplasticity, Int. J. Plast. 21 (2005) 199–219.

    Article  Google Scholar 

  34. H. Xiao, O.T. Bruhns, A. Meyers, The choice of objective rates in finite elastoplasticity: general results on the uniqueness of the logarithmic rate, Proc. R. Soc. London, Ser. A 456 (2000) 1865–1882.

    Article  MathSciNet  Google Scholar 

  35. H. Xiao, O.T. Bruhns, A. Meyers, A consistent finite elastoplasticity theory combining additive and multiplicative decomposition of the stretching and the deformation gradient, Int. J. Plast. 16 (2000) 143–177.

    Article  Google Scholar 

  36. H. Xiao, O.T. Bruhns, A. Meyers, Thermodynamic laws and consistent Eulerian formulations of finite elastoplasticity with thermal effects, J. Mech. Phys. Solids 55 (2007) 338–365.

    Article  MathSciNet  Google Scholar 

  37. H. Xiao, O.T. Bruhns, A. Meyers, Logarithmic strain, logarithmic spin and logarithmic rate, Acta Mech. 124 (1997) 89–105.

    Article  MathSciNet  Google Scholar 

  38. H. Xiao, Pseudo-elastic hysteresis out of recoverable finite elastoplastic flows, Int. J. Plast. 41 (2013) 82–96.

    Article  Google Scholar 

  39. H. Xiao, An explicit, direct simulation of multi-axial finite strain inelastic behavior for polymeric solids, Int. J. Plast. 71 (2015) 146–169.

    Article  Google Scholar 

  40. H. Xiao, O.T. Bruhns, A. Meyers, Finite elastoplastic J2 -flow models with strain recovery effects, Acta Mech. 210 (2010) 13–25.

    Article  Google Scholar 

  41. H. Xiao, O.T. Bruhns, A. Meyers, Phenomenological elastoplasticity view on strain recovery loops characterizing shape memory materials, ZAMM-J. Appl. Math. Mech. 90 (2010) 544–564.

    Article  MathSciNet  Google Scholar 

  42. H. Xiao, O.T. Bruhns, A. Meyers, Thermo-induced plastic flows and shape memory effects, Theor. Appl. Mech. 38 (2011) 155–207.

    Article  MathSciNet  Google Scholar 

  43. H. Xiao, An explicit, straightforward approach to modeling SMA pseudo-elastic hysteresis, Int. J. Plast. 53 (2014) 228–240.

    Article  Google Scholar 

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Authors and Affiliations

  1. Shanghai Institute of Applied Mathematics and Mechanics and State Key Laboratory for Advanced Special Steels, Shanghai University, Yanchang Road 149, 200072, Shanghai, China

    Zhaoling Wang, Hao Li, Zhengnan Yin & Heng Xiao

  2. School of Mathematics and Information Sciences, Weifang University, 261061, Shandong Province, Weifang, China

    Zhaoling Wang

Authors
  1. Zhaoling Wang
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  2. Hao Li
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  3. Zhengnan Yin
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  4. Heng Xiao
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Correspondence to Heng Xiao.

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Wang, Z., Li, H., Yin, Z. et al. A new, direct approach toward modeling thermo-coupled fatigue failure behavior of metals and alloys. Acta Mech. Solida Sin. 30, 1–9 (2017). https://doi.org/10.1016/j.camss.2016.10.001

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  • DOI: https://doi.org/10.1016/j.camss.2016.10.001

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