Acta Mechanica Solida Sinica

, Volume 31, Issue 3, pp 369–382 | Cite as

Constitutive Model for the Thermo-viscoplastic Behavior of Hexagonal Close-Packed Metals with Application to Ti–6Al–4V Alloy

  • Yunfei Li
  • Xiangguo Zeng
Original Paper


In this paper, a new physically based constitutive model is developed for hexagonal close-packed metals, especially the Ti–6Al–4V alloy, subjected to high strain rate and different temperatures based on the microscopic mechanism of plastic deformation and the theory of thermally activated dislocation motion. A global analysis of constitutive parameters based on the Latin Hypercube Sampling method and the Spearman’s rank correlation method is adopted in order to improve the identification efficiency of parameters. Then, an optimal solution of constitutive parameters as a whole is obtained by using a global genetic algorithm composed of an improved niche genetic algorithm, a global peak determination strategy and the local accurate search techniques. It is concluded that the proposed constitutive modal can accurately describe the Ti–6Al–4V alloy’s dynamic behavior because the prediction results of the model are in good agreement with the experimental data.


Hexagonal close-packed metals Physically based constitutive model Dislocation motion High strain rate Ti–6Al–4V 



The authors gratefully acknowledge the financial support by the National Natural Science Foundation of China Academy of Engineering Physics and the jointly set-up “NSAF” joint fund under Contract No. U1430119.


  1. 1.
    Zhang J, Wang Y, Zan X, Wang Y. The constitutive response of Ti–6.6Al–3.3Mo–1.8Zr–0.29Si alloy at high strain rates and elevated temperatures. J Alloys Compd. 2015;647:97–104.CrossRefGoogle Scholar
  2. 2.
    Majorell A, Strivatsa S, Picu RC. Mechanical behavior of Ti–6Al–4V at high and moderate temperatures—part I: experimental results. Mater Sci Eng A. 2002;326:297–305.CrossRefGoogle Scholar
  3. 3.
    Lee WS, Lin CF. Plastic deformation and fracture behavior of Ti–6Al–4V alloy loaded with high strain rate under various temperatures. Mater Sci Eng A. 1998;241:48–59.CrossRefGoogle Scholar
  4. 4.
    Chiou ST, Tsai HL, Lee WS. Impact mechanical response and micro structural evolution of Ti alloy under various temperatures. J Mater Process Technol. 2009;209:2282–94.CrossRefGoogle Scholar
  5. 5.
    Khan AS, Suh YS, Kazmi R. Quasi-static and dynamic loading responses and constitutive modeling of titanium alloys. Int J Plast. 2004;20:2233–48.CrossRefzbMATHGoogle Scholar
  6. 6.
    Arsecularatne JA, Zhang LC. Assessment of constitutive equations used in machining. Key Eng Mater. 2004;274–276:277–82.Google Scholar
  7. 7.
    Zerilli PJ, Armstrong RW. Dislocation-mechanics-based constitutive relations for material dynamics calculations. J Appl Phys. 1987;61:1816–25.CrossRefGoogle Scholar
  8. 8.
    Nemat-Nasser S, Li YL. Flow stress of FCC poly-crystals with application to OFHC Cu. Acta Mater. 1998;46:565–77.CrossRefGoogle Scholar
  9. 9.
    Follansbee PS, Kocks UF. A constitutive description of the deformation of copper based on the use of mechanical threshold stress as an internal state variable. Acta Metall. 1988;36:81–93.CrossRefGoogle Scholar
  10. 10.
    Follansbee PS, Gray GT III. An analysis of low temperature, low and high-rate deformation of Ti–6Al–4V. Metall Trans A. 1989;20:863–74.CrossRefGoogle Scholar
  11. 11.
    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.CrossRefGoogle Scholar
  12. 12.
    Zerilli FJ, Armstrong RW. Constitutive equation for HCP metals and high strength alloy steels. In: Rajapakse Y, Vinson JR, editors. High strain rate effects on polymer, metal and ceramic matrix composites and other advanced materials. San Francisco: ASME International Mechanical Engineering Congress and Exposition; 1995. p. 121–6.Google Scholar
  13. 13.
    Seo S, Min O, Yang H. Constitutive equation for Ti–6Al–4V at high-temperatures measured using the SHPB technique. Int J Impact Eng. 2005;31:735–54.CrossRefGoogle Scholar
  14. 14.
    Zhan H, Wang G, Kent D, Dargusch M. Constitutive modeling of the flow behavior of \(\alpha +\beta \) titanium alloy at high strain rates and elevated temperatures using the Johnson–Cook and modified Zerilli–Armstrong models. Mater Sci Eng A. 2014;612:71–9.CrossRefGoogle Scholar
  15. 15.
    Macdougall DAS, Harding J. A constitutive relation and failure criterion for Ti6Al4V alloy at impact rates of strain. J Mech Phys Solids. 1999;47:1157–85.CrossRefzbMATHGoogle Scholar
  16. 16.
    Regazzoni G, Kocks UF, Follansbee PS. Dislocation kinetics at high strain rates. Acta Metall. 1987;35:2865–75.CrossRefGoogle Scholar
  17. 17.
    Majorell A, Srivatsa S, Picu RC. Mechanical behavior of Ti–6Al–4V at high and moderate temperatures-part II: constitutive modeling. Mater Sci Eng A. 2002;326:306–16.CrossRefGoogle Scholar
  18. 18.
    Gao CY, Zhang LC, Yan HX. A new constitutive model for HCP metals. Mater Sci Eng A. 2011;528:4445–52.CrossRefGoogle Scholar
  19. 19.
    Peierls PE. The size of a dislocation. Proc Phys Soc. 1940;52:34–7.CrossRefGoogle Scholar
  20. 20.
    Orowan E. Problems of plastic gliding. Proc Phys Soc. 1940;52:8–22.CrossRefGoogle Scholar
  21. 21.
    Johnson WG, Gilman JJ. Dislocation velocities, dislocation densities, and plastic flow in lithium fluoride crystals. J Appl Phys. 1959;30:129–44.CrossRefGoogle Scholar
  22. 22.
    Sheng Y, Zeng XG, Han TX, Chen J. Parameter sensitivity analysis and identification method for dynamic constitutive relationship of titanium alloy. J Sichuan Univ. 2015;47:110–7.Google Scholar
  23. 23.
    Simpson TW, Lin DKJ. Sampling strategies for computer experiments: design and analysis. Int J Reliab Appl. 2001;2(3):209–40.Google Scholar
  24. 24.
    Sheng Y, Yi Y, Wei Y. An improved genetic algorithm of fast realization in multimodal function optimization. J Southwest Univ Sci Technol. 2009;24:85–90.Google Scholar
  25. 25.
    Kocks UF, Argon AS, Ashby MF. Thermodynamics and kinetics of slip. Prog Mater Sci. 1975;19:1–281.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2018

Authors and Affiliations

  1. 1.Institute of Systems EngineeringChina Academy of Engineering PhysicsMianyangChina
  2. 2.College of Architecture and EnvironmentSichuan UniversityChengduChina

Personalised recommendations