Study on constitutive behavior of Ti-45Nb alloy under transversal ultrasonic vibration-assisted compression

Abstract

Ultrasonic vibration technology has been widely applied in plastic forming processes due to its advantages of material properties improvement. In this study, a transverse ultrasonic vibration-assisted compression (TUVC) system with the range of vibration amplitude from 16 to 48 µm is developed to compress the difficult-to-deformation materials. The experiment found that the temperature of the compressed sample with the vibration amplitude of 38 µm arrived at 164 ℃, hence the current constitutive models are deficient for the description of TUVC deformation behavior with the large vibration amplitudes. The results show that the flow stress declines under the coupling action of volume effect and surface effect, especially the amplitude is larger than 38 µm. To accurately depict the constitutive behavior of titanium alloy under TUVC, a hybrid constitutive model considering the difference of softening mechanism was proposed based on crystal plasticity theory, and the predicted curves are in good agreement with experimental results. Finally, the microstructure further revealed the differences of softening mechanism in TUVC, and numerous secondary α phase was precipitated. Consequently, the studies provide an insight into the deformation mechanism of TUVC and promote the application of ultrasonic vibration-assisted forming for the difficult-to-deformation alloy.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Availability of data and material

Data transparency.

Code availability

No software application or custom code.

References

  1. 1.

    Blaha F, Langenecker B. Elongation of zinc monocrystals under ultrasonic action. Die Naturwissenschaften. 1955;42:556.

    Article  Google Scholar 

  2. 2.

    Djavanroodi F, Ahmadian H, Naseri R, Koohkan K, Ebrahimi M. Experimental investigation of ultrasonic assisted equal channel angular pressing process. Arch Civ Mech Eng. 2016;16(3):249–55.

    Article  Google Scholar 

  3. 3.

    Nie H, Chi C, Chen H, Li X, Liang W. Microstructure evolution of Al/Mg/Al laminates in deep drawing process. J Mater Res Technol. 2019;8:5325–35.

    Article  Google Scholar 

  4. 4.

    Cheng CC, Wu YL. Diagnosis of multi-stage injection molding process by ultrasonic technology at a T-shape extension nozzle. J Mater Process Technol. 2020;282:116650.

    Article  Google Scholar 

  5. 5.

    Lou Y, Liu X, He J, Long M. Ultrasonic-assisted extrusion of ZK60Mg alloy micropins at room temperature. Ultrasonics. 2018;83:194–202.

    Article  Google Scholar 

  6. 6.

    Verma GC, Pandey PM, Dixit US. Estimation of workpiece-temperature during ultrasonic-vibration assisted milling considering acoustic softening. Int J Mech Sci. 2018;140:547–56.

    Article  Google Scholar 

  7. 7.

    Tang J, Liu D, Tang C, Zhang X, Xiong H, Tang B. Tribology behavior of double-glow discharge Mo layers on titanium alloy in aviation kerosene environment. Trans Nonferrous Metals Soc China. 2012;22:1967–74.

    Article  Google Scholar 

  8. 8.

    Bong HJ, Yoo DH, Kim D, Kwon Y-N, Lee J. Correlative study on plastic response and formability of Ti-6Al-4V sheets under hot forming conditions. J Manuf Process. 2020;58:775–86.

    Article  Google Scholar 

  9. 9.

    Liu T, Lin J, Guan Y, Xie Z, Zhu L, Zhai J. Effects of ultrasonic vibration on the compression of pure titanium. Ultrasonics. 2018;89:26–33.

    Article  Google Scholar 

  10. 10.

    Liu S, Shan X, Guo K, Yang Y, Xie T. Experimental study on titanium wire drawing with ultrasonic vibration. Ultrasonics. 2018;83:60–7.

    Article  Google Scholar 

  11. 11.

    Zhao J, Liu Z. Investigations of ultrasonic frequency effects on surface deformation in rotary ultrasonic roller burnishing Ti-6Al-4V. Mater Des. 2016;107:238–49.

    Article  Google Scholar 

  12. 12.

    Zhou H, Cui H, Qin Q-H, Wang H, Shen Y. A comparative study of mechanical and microstructural characteristics of aluminium and titanium undergoing ultrasonic assisted compression testing. Mater Sci Eng A. 2017;682:376–88.

    Article  Google Scholar 

  13. 13.

    Sedaghat H, Xu W, Zhang L. Ultrasonic vibration-assisted metal forming: constitutive modelling of acoustoplasticity and applications. J Mater Process Technol. 2019;265:122–9.

    Article  Google Scholar 

  14. 14.

    Xie Z, Guan Y, Lin J, Zhai J, Zhu L. Constitutive model of 6063 aluminum alloy under the ultrasonic vibration upsetting based on Johnson-Cook model. Ultrasonics. 2019;96:1–9.

    Article  Google Scholar 

  15. 15.

    Prabhakar A, Verma GC, Krishnasamy H, Pandey PM, Lee MG, Suwas S. Dislocation density based constitutive model for ultrasonic assisted deformation. Mech Res Commun. 2017;85:76–80.

    Article  Google Scholar 

  16. 16.

    Yao Z, Kim G-Y, Wang Z, Faidley L, Zou Q, Mei D, Chen Z. Acoustic softening and residual hardening in aluminum: modeling and experiments. Int J Plast. 2012;39:75–87.

    Article  Google Scholar 

  17. 17.

    Zerilli FJ, Armstrong RW. Dislocation-mechanics-based constitutive relations for material dynamics calculations. J Appl Phys. 1987;61:1816–25.

    Article  Google Scholar 

  18. 18.

    Nemat-Nasser S, Guo WG, Nesterenko VF, Infrakanti SS, Gu YB. Dynamic response of conventional and hot isostatically pressed Ti–6Al–4V alloys: experiments and modeling. Mech Mater. 2001;33:425–39.

    Article  Google Scholar 

  19. 19.

    Gao CY, Zhang LC. Constitutive modelling of plasticity of fcc metals under extremely high strain rates. Int J Plast. 2012;32–33:121–33.

    Article  Google Scholar 

  20. 20.

    Gao CY, Zhang LC, Yan HX. A new constitutive model for HCP metals. Mater Sci Eng A. 2011;528:4445–52.

    Article  Google Scholar 

  21. 21.

    Orowan E. Problems of plastic gliding. Proc Phys Soc. 1940;52:8.

    Article  Google Scholar 

  22. 22.

    Kocks U. Constitutive behaviour based on crystal plasticity. Berlin: Springer; 1987.

    Google Scholar 

  23. 23.

    Patra A, Zhu T, McDowell DL. Constitutive equations for modeling non-Schmid effects in single crystal bcc-Fe at low and ambient temperatures. Int J Plast. 2014;59:1–14.

    Article  Google Scholar 

  24. 24.

    Gu B-P, Hu X, Zhao L, Kong D-J, Yang Z-S, Lai J-T, Pan L. Effect of multidimensional ultrasonic-assisted pulsed-laser surface irradiation on residual stress in AISI 1045 steel. J Clean Prod. 2017;143:1183–90.

    Article  Google Scholar 

  25. 25.

    Pohlman R, Lehfeldt E. Influence of ultrasonic vibration on metallic friction. Ultrasonics. 1966;4:178–85.

    Article  Google Scholar 

  26. 26.

    Kumari M, Ray KK. Effect of the mode of deformation on activation volume of a material. Mater Sci Eng A. 2016;650:335–44.

    Article  Google Scholar 

  27. 27.

    Choi I-C, Brandl C, Schwaiger R. Thermally activated dislocation plasticity inbody-centered cubic chromium studied by high-temperature nanoindentation. Acta Mater. 2017;140:107–15.

    Article  Google Scholar 

  28. 28.

    Elangovan S, Semeer S, Prakasan K. Temperature and stress distribution in ultrasonic metal welding-An FEA-based study. J Mater Process Technol. 2009;209:1143–50.

    Article  Google Scholar 

  29. 29.

    Yao Z, Kim G-Y, Faidley L, Zou Q, Mei D, Chen Z. Effects of superimposed high-frequency vibration on deformation of aluminum in micro/meso-scale upsetting. J Mater Process Technol. 2012;212:640–6.

    Article  Google Scholar 

  30. 30.

    Hung J-C, Lin C-C. Investigations on the material property changes of ultrasonic-vibration assisted aluminum alloy upsetting. Mater Des. 2013;45:412–20.

    Article  Google Scholar 

  31. 31.

    Meng B, Cao BN, Wan M, Wang CJ, Shan DB. Constitutive behavior and microstructural evolution in ultrasonic vibration assisted deformation of ultrathin superalloy sheet. Int J Mech Sci. 2019;157–158:609–18.

    Article  Google Scholar 

  32. 32.

    Campbell J, Ferguson W. The temperature and strain-rate dependence of the shear strength of mild steel. Philos Mag. 1970;21:63–82.

    Article  Google Scholar 

  33. 33.

    De Vries E. Mechanics and mechanism of ultrasonic metal welding, dissertation, The Ohio State University. 2004.

  34. 34.

    Daud Y, Lucas M, Huang ZH. Superimposed ultrasonic oscillations in compression tests of aluminium. Ultrasonics. 2006;44:511–5.

    Article  Google Scholar 

  35. 35.

    Statnikov ES, Korolkov OV, Vityazev VN. Physics and mechanism of ultrasonic impact. Ultrasonics. 2006;44:533–8.

    Article  Google Scholar 

  36. 36.

    Chu Y, Li J, Zhao F, Tang B, Kou H. Flow behavior and constitutive relationship for elevated temperature compressive deformation of a high Nb containing TiAl alloy with (α2+ γ) microstructure. Mater Lett. 2018;210:58–61.

    Article  Google Scholar 

  37. 37.

    Delshadmanesh M, Khatibi G, Ghomsheh MZ, Lederer M, Zehetbauer M, Danninger H. Influence of microstructure on fatigue of biocompatible β-phase Ti-45Nb. Mater Sci Eng A. 2017;706:83–94.

    Article  Google Scholar 

  38. 38.

    Kara G, Purcek G. Growth kinetics and mechanical characterization of boride layers formed on β-type Ti-45Nb alloy. Surf Coat Technol. 2018;352:201–12.

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to acknowledge the editors and the anonymous referees for their insightful comments. This work is supported by the National Natural Science Foundation of China (51875283); the Fundamental Research Funds from COSTIND (2019-JCJQ-JJ-341); and the Aeronautical Science Foundation of China (2017ZE52052).

Funding

Wenliang Chen: National Natural Science Foundation of China (51875283). Zhenchao Qi: Fundamental Research Funds from COSTIND (2019-JCJQ-JJ-341). Zhenchao Qi: Aeronautical Science Foundation of China (2017ZE52052).

Author information

Affiliations

Authors

Contributions

XW designed the study, performed the research, analysis data, and wrote the paper. ZQ directed experiments and data processing. WC provided experimental condition, modified the paper framework.

Corresponding author

Correspondence to Zhenchao Qi.

Ethics declarations

Conflict of interest

Author Xingxing Wang declares that he has no conflict of interest. Author Zhenchao Qi declares that he has no conflict of interest. Author Wenliang Chen declares that he has no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Wang, X., Qi, Z. & Chen, W. Study on constitutive behavior of Ti-45Nb alloy under transversal ultrasonic vibration-assisted compression. Archiv.Civ.Mech.Eng 21, 31 (2021). https://doi.org/10.1007/s43452-021-00186-7

Download citation

Keywords

  • Transversal ultrasonic vibration-assisted compression
  • Surface effect
  • Flow stress
  • Constitutive behavior
  • Microstructure