Mechanics of Time-Dependent Materials

, Volume 14, Issue 4, pp 329–345 | Cite as

Constitutive modeling of the mechanical behavior of high strength ferritic steels for static and dynamic applications

  • Farid H. AbedEmail author


A constitutive relation is presented in this paper to describe the plastic behavior of ferritic steel over a broad range of temperatures and strain rates. The thermo-mechanical behavior of high strength low alloy (HSLA-65) and DH-63 naval structural steels is considered in this study at strains over 40%. The temperatures and strain rates are considered in the range where dynamic strain aging is not effective. The concept of thermal activation analysis as well as the dislocation interaction mechanism is used in developing the flow model for both the isothermal and adiabatic viscoplastic deformation. The flow stresses of the two steels are very sensitive to temperature and strain rate, the yield stresses increase with decreasing temperatures and increasing strain rates. That is, the thermal flow stress is mainly captured by the yield stresses while the hardening stresses are totally pertained to the athermal component of the flow stress. The proposed constitutive model predicts results that compare very well with the measured ones at initial temperature range of 77 K to 1000 K and strain rates between 0.001 s−1 and 8500 s−1 for both steels.


Constitutive relations Temperature and strain rate effect High strength ferritic steel (HSS) Plasticity/viscoplasticity 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abed, F.H., Voyiadjis, G.Z.: Plastic deformation modeling of AL-6XN stainless steel at low and high strain rates and temperatures using a combination of BCC and FCC mechanisms of metals. Int. J. Plast. 21, 1618–1639 (2005a) CrossRefzbMATHGoogle Scholar
  2. Abed, F.H., Voyiadjis, G.Z.: A consistent modified Zerilli-Armstrong flow stress model for BCC and FCC metals for elevated temperatures. Acta Mech. 175, 1–18 (2005b) CrossRefzbMATHGoogle Scholar
  3. Børvik, T., Hopperstad, O.S., Berstad, T., Langseth, M.: A computational model of viscoplasticity and ductile damage for impact and penetration. Eur. J. Solid Mech. A 20, 685–712 (2001) CrossRefGoogle Scholar
  4. Guo, W.G., Nemat-Nasser, S.: Flow stress of Nitronic-50 stainless steel over a wide range of strain rates and temperatures. Mech. Mater. 38, 1090–103 (2006) CrossRefGoogle Scholar
  5. Hecker, S.S., Stout, M.G., Staudhammer, K.P., Smith, J.L.: Effects of strain state and strain rate on deformation induced transformation in 304 stainless steel. I. Magnetic measurements and mechanical behavior. Metall. Trans. A 13A, 619–626 (1982) Google Scholar
  6. Ishikawa, K., Tanimura, S.: Strain rate sensitivity of flow stress at low temperature in 304N stainless steel. Int. J. Plast. 8, 947–958 (1992) CrossRefGoogle Scholar
  7. Johnson, G.R., Cook, W.H.: A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: Proceedings of the Seventh International Symposium on Ballistic, pp. 541–547. The Hague, The Netherlands (1983) Google Scholar
  8. Kapoor, R., Nemat-Nasser, S.: Determination of temperature rise during high strain rate deformation. Mech. Mater. 27, 1–12 (1998) CrossRefGoogle Scholar
  9. Klepaczko, J.R.: Modeling of structural evolution at medium and high strain rates, FCC and BCC metals. In: Constitutive Relations and Their Physical Basis, pp. 387–395 (1987) Google Scholar
  10. Klepaczko, J.R., Rezaig, B.: A numerical study of adiabatic shear bending in mild steel by dislocation mechanics based constitutive relations. Mech. Mater. 24, 125–139 (1996) CrossRefGoogle Scholar
  11. Klopp, R.W., Clifton, R.J., Shawki, T.: Pressure-shear impact and the dynamic viscoplastic response of metals. Mech. Mater. 4, 375–385 (1985) CrossRefGoogle Scholar
  12. Kocks, U.F., Argon, A.S., Ashby, M.F.: Thermodynamics and kinetics of slip. Prog. Mater. Sci. 19 (1975) Google Scholar
  13. Kocks, U.F., Maddin, R.: Observations on the deformation of niobium. Acta Metall. 4, 92 (1956) CrossRefGoogle Scholar
  14. Krauss, G.: Microstructures, Processing, and Properties of Steel. ASM Handbook 1, pp. 126–139 (1990) Google Scholar
  15. Militzer, M., Hawbolt, E.B., Meadowcroft, T.R.: Microstructural model for hot strip rolling of high-strength low alloy steels. Metall. Trans. A 31A, 1247–1259 (2000) CrossRefGoogle Scholar
  16. Nemat-Nasser, S., Isaacs, J.: Direct measurement of isothermal flow stress of metals at elevated temperatures and high strain rates with application to Ta and Ta-W alloys. Acta Metall. 45, 907–919 (1997) Google Scholar
  17. Nemat-Nasser, S., Guo, W.G.: Thermomechanical response of DH-36 structural steel over a wide range of strain rates and temperatures. Mech. Mater. 35, 1023–47 (2003) CrossRefGoogle Scholar
  18. Nemat-Nasser, S., Guo, W.G.: Thermomechanical response of HSLA-65 steel plates: experiments and modelling. Mech. Mater. 37, 379–405 (2005) CrossRefGoogle Scholar
  19. Orowan, E.: Discussion in Symposium on Internal Stresses in Metals and Alloys, p. 451. Institute of Metals, London (1948) Google Scholar
  20. Perzyna, P.: Fundamental problems in viscoplasticity. Adv. Appl. Mech. 9, 243–377 (1966) CrossRefGoogle Scholar
  21. Stout, M.G., Follansbee, P.S.: Strain rate sensitivity, strain hardening, and yield behavior of 304L stainless steel. Trans. ASME, J. Eng. Mater. Technol. 108, 119–132 (1986) CrossRefGoogle Scholar
  22. Taylor, G.I.: Plastic strain in metals. J. Inst. Met. 62, 307–324 (1938) Google Scholar
  23. Voyiadjis, G.Z., Abed, F.H.: Microstructures based models for bcc and fcc metal with temperature and strain rate dependency. Mech. Mater. 37, 355–378 (2005a) CrossRefGoogle Scholar
  24. Voyiadjis, G.Z., Abed, F.H.: Effect of dislocation density evolution on the thermo-mechanical response of metals with different crystal structures at low and high strain rates and temperatures. Arch. Mech. 57, 299–343 (2005b) zbMATHGoogle Scholar
  25. Voyiadjis, G.Z., Abed, F.H.: Implicit algorithm for finite deformation hypoelsto-viscoplasticity in FCC metals. Int. J. Numer. Methods Eng. 67, 933–955 (2006) CrossRefzbMATHGoogle Scholar
  26. Wang, W.M., Sluys, L.J., de Borst, R.: Viscoplasticity for instabilities due to strain softening and strain-rate softening. Int. J. Numer. Methods Eng. 40, 3839–3864 (1997) CrossRefzbMATHGoogle Scholar
  27. Zener, C., Hollomom, J.H.: High speed deformation of metals. J. Appl. Phys. 15, 22–32 (1944) CrossRefGoogle Scholar
  28. Zerilli, F.J., Armstrong, R.W.: Dislocation-mechanics-based constitutive relations for material dynamics calculation. J. Appl. Phys. 5, 1816–1825 (1987) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, B. V. 2010

Authors and Affiliations

  1. 1.Department of Civil EngineeringAmerican University of Sharjah (AUS)SharjahUnited Arab Emirates

Personalised recommendations