On the Constitutive Models for Ultra-High Strain Rate Deformation of Metals

  • Hossein Sedaghat
  • Weixing Xu
  • Liangchi ZhangEmail author
  • Weidong Liu


Ultra-high strain rate deformation (> 104 s−1) is common in high speed manufacturing and impact engineering. However, a general constitutive model suitable for describing the material deformation at ultra-high strain rates is still unavailable. The purpose of this study is of two-folds. The first is to systematically evaluate the performances of four typical constitutive models, Johnson-Cook (J-C), Khan-Huang-Liang (KHL), Zerilli-Armstrong (Z-A), and Gao-Zhang (G-Z), in predicting the dynamic behaviors of materials. The second is to obtain an improved constitutive model to better describe the deformation of materials under ultra-high strain rates. To this end, high strain rate tests were carried out on different crystalline structures, i.e., BCC, FCC, and HCP over a wide range of strain rate from 102 s−1 to 1.5 × 104 s−1. It was found that before the critical strain rate, around 104 s−1, all of the previous models can predict the flow stresses. When the strain rate passes a critical point, however, these models fail to predict the sudden upsurge of the flow stresses. The improved model developed in this paper, by considering the dislocation drag mechanism, can successfully characterize the dynamic behaviours of materials over the whole range of strain rates.

Key words

Ultra high strain-rate Constitutive model Dislocations Drag mechanism 



This research was financially supported by an ARC Discovery Project (DP170100567) and was undertaken with the assistance of resources provided at the NCI National Facility systems at the Australian National University and Intersect Australia Ltd.


  1. Abed, F. H. and Voyiadjis, G. Z. (2005). A consistent modified Zerilli-Armstrong flow stress model for BCC and FCC metals for elevated temperatures. Acta Mechanica 175, 1–4, 1–18.CrossRefGoogle Scholar
  2. Aziz, A. (2012). Characterising the Effective Material Softening in Ultrasonic Forming of Metals. Ph. D. Dissertation. University of Glasgow. Glasgow, UK.Google Scholar
  3. Beusink, M. (2011). Measurements and Simulations on the (Dynamic) Properties of Aluminium Alloy AA6060. Ph. D. Dissertation. Eindhoven University of Technology. Eindhoven, The Netherlands.Google Scholar
  4. Bobbili, R. and Madhu, V. (2016). Effect of strain rate and stress triaxiality on tensile behavior of Titanium alloy Ti-10-2-3 at elevated temperatures. Materials Science and Engineering: A, 667, 33–41.CrossRefGoogle Scholar
  5. Daud, Y., Lucas, M. and Huang, Z. (2007). Modelling the effects of superimposed ultrasonic vibrations on tension and compression tests of aluminium. J. Materials Processing Technology 186, 1–3, 179–190.CrossRefGoogle Scholar
  6. Follansbee, P. and Weertman, J. (1982). On the question of flow stress at high strain rates controlled by dislocation viscous flow. Mechanics of Materials 1, 4, 345–350.CrossRefGoogle Scholar
  7. Gao, C., Lu, W., Zhang, L. C. and Yan, H. (2012). A constitutive description of the thermo-viscoplastic behavior of body-centered cubic metals. Materials & Design (1980–2015), 36, 671–678.CrossRefGoogle Scholar
  8. Gao, C. and Zhang, L. C. (2010). A constitutive model for dynamic plasticity of FCC metals. Materials Science and Engineering: A 527, 13–14, 3138–3143.CrossRefGoogle Scholar
  9. Gao, C. and Zhang, L. C. (2012). Constitutive modelling of plasticity of fcc metals under extremely high strain rates. Int. J. Plasticity, 32–33, 121–133.CrossRefGoogle Scholar
  10. Gao, C., Zhang, L. C. and Yan, H. (2011). A new constitutive model for HCP metals. Materials Science and Engineering: A 528, 13–14, 4445–4452.CrossRefGoogle Scholar
  11. Johnson, G. R. and Cook, W. H. (1983). A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. Proc. 7th Int. Symp. Ballistics. The Hague, The Netherlands, 541–547.Google Scholar
  12. Khan, A. S., Baig, M., Choi, S.-H., Yang, H.-S. and Sun, X. (2012). Quasi-static and dynamic responses of advanced high strength steels: Experiments and modeling. Int. J. Plasticity, 30–31, 1–17.Google Scholar
  13. Khan, A. S. and Huang, S. (1992). Experimental and theoretical study of mechanical behavior of 1100 aluminum in the strain rate range 10−5–104 s−1. Int. J. Plasticity 8, 4, 397–424.CrossRefGoogle Scholar
  14. Khan, A. S., Suh, Y. S. and Kazmi, R. (2004). Quasi-static and dynamic loading responses and constitutive modeling of titanium alloys. Int. J. Plasticity 20, 12, 2233–2248.CrossRefGoogle Scholar
  15. Kumar, A., Hauser, F. and Dorn, J. (1968). Viscous drag on dislocations in aluminum at high strain rates. Acta Metallurgica 16, 9, 1189–1197.CrossRefGoogle Scholar
  16. Lin, Y. and Chen, X.-M. (2011). A critical review of experimental results and constitutive descriptions for metals and alloys in hot working. Materials & Design 32, 4, 1733–1759.CrossRefGoogle Scholar
  17. Lu, X. and Khonsari, M. (2007). An experimental investigation of dimple effect on the stribeck curve of journal bearings. Tribology Letters, 27, 169.CrossRefGoogle Scholar
  18. Luo, B., Li, M., Wang, G., Tan, F., Zhao, J. and Sun, C. (2017). Strain rate and hydrostatic pressure effects on strength of iron. Mechanics of Materials, 114, 142–146.CrossRefGoogle Scholar
  19. Meyer Jr, H. W. (2006). A Modified Zerilli-Armstrong Constitutive Model Describing the Strength and Localizing Behavior of Ti-6A1-4V. DTIC Document.Google Scholar
  20. Mirone, G., Corallo, D. and Barbagallo, R. (2016). Interaction of strain rate and necking on the stress-strain response of uniaxial tension tests by Hopkinson bar. Procedia Structural Integrity, 2, 974–985.CrossRefGoogle Scholar
  21. Patel, J. and Chaudhuri, A. (1963). Macroscopic plastic properties of dislocation-free germanium and other semiconductor crystals. I. Yield behavior. J. Applied Physics 34, 9, 2788–2799.CrossRefGoogle Scholar
  22. Ramesh, K. T. (2008). High Rates and Impact Experiments. Springer Handbook of Experimental Solid Mechanics. Springer, 929–960.Google Scholar
  23. Regazzoni, G., Kocks, U. and Follansbee, P. S. (1987). Dislocation kinetics at high strain rates. Acta Metallurgica 35, 12, 2865–2875.CrossRefGoogle Scholar
  24. Song, B., Chen, W., Antoun, B. and Frew, D. (2007). Determination of early flow stress for ductile specimens at high strain rates by using a SHPB. Experimental Mechanics 47, 5, 671–679.CrossRefGoogle Scholar
  25. Verleysen, P. and Peirs, J. (2017). Quasi-static and high strain rate fracture behaviour of Ti6Al4V. Int. J. Impact Engineering, 108, 370–388.CrossRefGoogle Scholar
  26. Wedberg, D. and Lindgren, L.-E. (2015). Modelling flow stress of AISI 316L at high strain rates. Mechanics of Materials 91, Part 1, 194–207.CrossRefGoogle Scholar
  27. Xu, W., Sedaghat, H. and Zhang, L. C. (2018). On the deformation behaviour of some metals under high strain rate and high frequency impact. Proc. AEPA2018, Jeju, Korea.Google Scholar
  28. Zaretsky, E. and Kanel, G. I. (2012). Effect of temperature, strain, and strain rate on the flow stress of aluminum under shock-wave compression. J. Applied Physics 112, 7, 073504.CrossRefGoogle Scholar
  29. Zerilli, F. J. and Armstrong, R. W. (1987). Dislocation-mechanics-based constitutive relations for material dynamics calculations. J. Applied Physics 61, 5, 1816–1825.CrossRefGoogle Scholar

Copyright information

© KSAE/112-05 2019

Authors and Affiliations

  • Hossein Sedaghat
    • 1
  • Weixing Xu
    • 1
  • Liangchi Zhang
    • 1
    Email author
  • Weidong Liu
    • 1
  1. 1.Laboratory for Precision and Nano Processing Technologies, School of Mechanical and Manufacturing EngineeringThe University of New South WalesSydneyAustralia

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