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An integrated Johnson–Cook and Zerilli–Armstrong model for material flow behavior of Ti–6Al–4V at high strain rate and elevated temperature

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Abstract

The Johnson–Cook (JC) model can give an accurate estimate of the flow stress at the low strain rate and temperature, but fails to predict the flow stress under high strain rate and elevated temperature due to the complex relationship among strain, strain rate and temperature. The Zerilli–Armstrong (ZA) model is capable to provide a higher prediction accuracy of material flow stress, but is unable to describe the material behavior above the limitation temperature (0.6Tm). In this research, an integrated JC–ZA model, which considers the grain size, strain hardening, strain rate hardening, thermal softening and the coupled effects of strain, strain rate and temperature, is proposed. The effects of strain rate and temperature on the flow stress of Ti–6Al–4V are investigated by quasi-static tensile test and dynamic split Hopkinson pressure bar test. It is proved that the integrated JC–ZA model has a similar accuracy with JC model at low strain rate and temperature with a prediction error of 2.180–2.358%, and a higher accuracy at high strain rate and elevated temperature with a prediction error in the range of 0.174–2.358%. Through this research, an accurate model by integrating JC model and ZA model for the flow stress of Ti–6Al–4V is given.

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References

  1. Poondla N, Srivatsan TS, Patnaik A, Petraroli M (2009) A study of the microstructure and hardness of two titanium alloys: commercially pure and ti-6al-4v. J. Alloys Compd. 486:162–167

    Article  Google Scholar 

  2. Kotkunde N, Krishnamurthy HN, Puranik P, Gupta AK, Singh SK (2014) Microstructure study and constitutive modeling of Ti-6Al-4V alloy at elevated temperatures. Mater Des 54:96–103

    Article  Google Scholar 

  3. Donachie MJ Jr (1988) Titanium: a technical guide. ASM International, Metals Park, pp 353–365

    Google Scholar 

  4. Wessel JK (2004) Handbook of advanced materials. Wiley, Somerset

    Book  Google Scholar 

  5. Yang X, Liu CR (1999) Machining Titanium and its alloys. Mach. Sci. Technol. 3:107–139

    Article  Google Scholar 

  6. Sima M, Ozel T (2010) Modified material constitutive models for serrated chip formation simulations and experimental validation in machining of titanium alloy Ti-6Al-4V. Int. J. Mach. Tool Manuf. 50:943–960

    Article  Google Scholar 

  7. Byrne G, Dornfeld D, Denkena B (2003) Advancing cutting technology. Ann CIRP. Manuf. Technol. 52:483–507

    Article  Google Scholar 

  8. Ozel T, Sima M, Srivastava AK, Kaftanoglu B (2010) Investigations on the effects of multi-layered coated inserts in machining Ti–6Al–4V alloy with experiments and finite element simulations. Ann CIRP. Manuf. Technol. 59:77–82

    Article  Google Scholar 

  9. Lin YC, Chen XM (2011) A critical review of experimental results and constitutive descriptions for metals and alloys in hot working. Mater Des 32:1733–1759

    Article  Google Scholar 

  10. Johnson GR, Cook WH (1983) A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: Proceedings of the 7th international symposium on ballistics, The Hague, The Netherlands, pp 541–547

  11. Johnson GR, Cook WH (1985) Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Eng Fract Mech 21:31–48

    Article  Google Scholar 

  12. Gao CY, Zhang LC (2010) A constitutive model for dynamic plasticity of FCC metals. Mater Sci Eng, A 527:3138–3143

    Article  Google Scholar 

  13. Kotkunde N, Deole AD, Gupta AK, Singh SK (2014) Comparative study of constitutive modeling for Ti-6Al-4V alloy at low strain rates and elevated temperatures. Mater Des 55:999–1005

    Article  Google Scholar 

  14. Zhang DN, Shangguan QQ, Xie CJ, Liu F (2015) A modified Johnson–Cook model of dynamic tensile behaviors for 7075-T6 aluminum alloy. J. Alloys Compd. 619:186–194

    Article  Google Scholar 

  15. Tan JQ, Zhan M, Liu S, Huang T, Guo J, Yang H (2015) A modified Johnson–Cook model for tensile flow behaviors of 7050-T7451 aluminum alloy at high strain rates. Mater Sci Eng, A 631:214–219

    Article  Google Scholar 

  16. Zerilli FJ, Armstrong RW (1987) Dislocation‐mechanics‐based constitutive relations for material dynamics calculations. J Appl Phys 61:1816–1825

    Article  Google Scholar 

  17. Gao CY, Zhang LC, Yan HX (2011) A new constitutive model for HCP metals. Mater Sci Eng, A 528:4445–4452

    Article  Google Scholar 

  18. Lennon AM, Ramesh KT (2004) The influence of crystal structure on the dynamic behavior of materials at high temperatures. Int J Plast 20:269–290

    Article  MATH  Google Scholar 

  19. Liu R, Melkote S, Pucha R, Morehouse J, Man XL, Marusich T (2013) An enhanced constitutive material model for machining of Ti-6Al-4V alloy. J Mater Process Technol 213:2238–2246

    Article  Google Scholar 

  20. Samantaray D, Mandal S, Borah U, Bhaduri AK, Sivaprasad PV (2009) A thermo-viscoplastic constitutive model to predict elevated temperature flow behaviour in a titanium modified austenitic stainless steel. Mater Sci Eng, A 526:1–6

    Article  Google Scholar 

  21. Lin YC, Chen XM (2010) A combined Johnson–Cook and Zerilli–Armstrong model for hot compressed typical high-strength alloy steel. Comput Mater Sci 49:628–633

    Article  Google Scholar 

  22. Arisoy YM, Ozel T (2015) Prediction of machining induced microstructure in Ti–6Al–4V alloy using 3-D FE-based simulations: Effects of tool micro-geometry, coating and cutting conditions. J Mater Process Technol 220:1–26

    Article  Google Scholar 

  23. Rotella G, Umbrello D (2014) Finite element modeling of microstructural changes in dry and cryogenic cutting of Ti6Al4V alloy. Ann CIRP. Manuf. Technol. 63:69–72

    Article  Google Scholar 

  24. Khan AS, Suh YS, Kazmi R (2004) Quasi-static and dynamic loading responses and constitutive modeling of titanium alloys. Int J Plast 20:2233–2248

    Article  MATH  Google Scholar 

  25. Zerilli FJ, Armstrong RW (1996) Constitutive relations for titanium and Ti-6Al-4V. AIP Conf Proc 370:315–318

    Article  Google Scholar 

  26. Nadai A, Manjoine MJ (1941) High-speed tension tests at elevated temperatures. J Appl Mech 8:A77–A91

    Google Scholar 

  27. Khan AS, Zhang HY, Takacs L (2000) Mechanical response and modeling of fully compacted nanocrystalline iron and copper. Int J Plast 16:1459–1476

    Article  MATH  Google Scholar 

  28. Farrokh B, Khan AS (2009) Grain size, strain rate, and temperature dependence of flow stress in ultra-fine grained and nanocrystalline Cu and Al: synthesis, experiment, and constitutive modeling. Int J Plast 25:715–732

    Article  MATH  Google Scholar 

  29. Lee WS, Lin CF (1998) High-temperature deformation behaviour of Ti6Al4V alloy evaluated by high strain-rate compression tests. J Mater Process Technol 75:127–136

    Article  Google Scholar 

  30. Xue Q, Meyers MA, Nesterenko VF (2002) Self-organization of shear bands in titanium and Ti–6Al–4V alloy. Acta Mater 50:575–596

    Article  Google Scholar 

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Acknowledgements

This work has been financed by National Basic Research Program of China (No. 2015CB059900) and National Natural Science Foundation of China (No. 51375050). The authors would also like to thank the support from Fok Ying-Tong Education Foundation for Young Teachers in the Higher Education Institutions of China (No. 151052).

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Authors and Affiliations

  1. School of Mechanical Engineering, Beijing Institute of Technology, Beijing, 100081, China

    Jiangtao Che & Junjie Wu

  2. Key Laboratory of Fundamental Science for Advanced Machining, Beijing Institute of Technology, Beijing, 100081, China

    Tianfeng Zhou, Zhiqiang Liang & Xibin Wang

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  1. Jiangtao Che
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  2. Tianfeng Zhou
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  3. Zhiqiang Liang
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Correspondence to Zhiqiang Liang.

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Technical Editor: André Cavalieri.

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Che, J., Zhou, T., Liang, Z. et al. An integrated Johnson–Cook and Zerilli–Armstrong model for material flow behavior of Ti–6Al–4V at high strain rate and elevated temperature. J Braz. Soc. Mech. Sci. Eng. 40, 253 (2018). https://doi.org/10.1007/s40430-018-1168-7

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  • DOI: https://doi.org/10.1007/s40430-018-1168-7

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