Acta Mechanica Solida Sinica

, Volume 30, Issue 1, pp 27–37 | Cite as

A unified plasticity methodology for rate- and temperature-sensitive alloys exhibiting a non-linear kinematic hardening behavior

  • Jacques Luk-Cyr
  • Daniel Paquet
  • Jacques Lanteigne
  • Henri Champliaud
  • Aurelian Vadean


In this paper, a novel unified plasticity methodology is proposed to allow the coupling of rate- and temperature-sensitivity of engineering alloys as well as the non-linear kinematic hardening behavior often observed during cyclic loading. The proposed methodology is general in the sense that an arbitrary constitutive model may be chosen for the viscoplastic part, as well as the cyclic part. We adapt our model with a physically-motivated viscoplasticity flow rule and a nonlinear kinematic hardening model. In contrast with other unified plasticity models, the simplified theory involves few material parameters that can be readily calibrated from standard mechanical tests. The capabilities of the proposed theory are demonstrated for a hot rolled annealed 304L stainless steel supplied by Vimetal Peckover. The model is tested with stress-strain curves obtained from standard tensile and cyclic uniaxial tests at various strain amplitudes and strain-rates, and good accuracy of the response is obtained for strains up to 15%, within a temperature range of 293–673 K. We note that the cyclic plasticity model in our adapted theory can be readily enhanced with ratchetting, mean stress relaxation, strain amplitude history, Masing effects or other complex capabilities.


Unified plasticity Constitutive behavior Viscoplasticity Non-linear kinematic hardening Stainless steels 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    T.S. Byun, N. Hashimoto, K. Farrell, Temperature dependence of strain hardening and plastic instability behaviors in austenitic stainless steels, Acta Mater. 52 (2004) 3889–3899.CrossRefGoogle Scholar
  2. 2.
    E. Krempl, An experimental study of room-temperature rate-sensitivity, creep and relaxation of AISI type 304 stainless steel, J. Mech. Phys. Solids 27 (1979) 363–375.CrossRefGoogle Scholar
  3. 3.
    G. Kang, Q. Gao, L. Cai, Y. Sun, Experimental study on uniaxial and nonproportionally multiaxial ratcheting of SS304 stainless steel at room and high temperatures, Nuclear Eng. Des. 216 (2002) 13–26.CrossRefGoogle Scholar
  4. 4.
    D. Paquet, Modélisation des Contraintes Résiduelles Thermiques et étude de Leur Effet sur la vie en Fatigue de l’acier Inoxydable Austénitique 304L, École Polytechnique de Montréal, 2006 Master’s thesis.Google Scholar
  5. 5.
    D. Paquet, J. Lanteigne, M. Bernard, A new experimental method for the introduction of a predetermined amount of residual stress in fatigue test specimen, J. Appl. Mech. 79 (2012) 1–13.CrossRefGoogle Scholar
  6. 6.
    D. Slavic, H. Sehitoglu, Constitutive models suitable for thermal loading, J. Eng. Mater. Technol. 108 (1986) 303–312.CrossRefGoogle Scholar
  7. 7.
    J.L. Chaboche, D. Nouailhas, A unified constitutive model for cyclic viscoplasticity and its application to various stainless steels., J. Eng. Mater. Technol. 111 (4) (1989) 424–430.CrossRefGoogle Scholar
  8. 8.
    C.C. Englers-Pinto Jr., H. Sehitoglu, H.J. Maier, Cyclic behavior of Al319-T7B under isothermal and non-isothermal conditions, Thermomech. Fatigue Behav. Mater. ASTM STP 1428 (2003) 45–64.Google Scholar
  9. 9.
    M. Abdel-Karim, N. Ohno, Kinematic hardening model suitable for ratchetting with steady-state., Int. J. Plast. 16 (2000) 225–240.CrossRefGoogle Scholar
  10. 10.
    P.J. Armstrong, C.O. Fredrick, A mathematical representation of the multiaxial Bauschinger effect., Report No. RD/B/N 73), CEGB, 1966.Google Scholar
  11. 11.
    G Kang, Q. Gao, X.J. Yang, A visco-plastic constitutive model incorporated with cyclic hardening for uniaxial/multiaxial ratchetting of SS304 stainless steel at room temperature, Mech. Mater. 34 (2002) 521–531.CrossRefGoogle Scholar
  12. 12.
    N. Ohno, J.-D. Wang, Kinematic hardening rules with critical state of dynamic recovery. part I: formulations and basic features for ratcheting behavior., Int. J. Plast. 9 (1993) 375–403.CrossRefGoogle Scholar
  13. 13.
    N. Ohno, J.-D. Wang, Kinematic hardening rules for simulation of ratcheting behaviour, Eur. J. Mech. A/Solids 13 (1994) 519–531.zbMATHGoogle Scholar
  14. 14.
    Y. Zhu, G. Kang, Q. Kan, O. Bruhns, Y. Liu, Thermo-mechanically coupled cyclic elasto-viscoplastic constitutive model of metals: theory and application., Int. J. Plast. 79 (2016) 111–152.CrossRefGoogle Scholar
  15. 15.
    C.E.-P. Jr., H. Sehitoglu, H. Maier, T. Foglesong, Thermo-mechanical fatigue behavior of cast 319 alumnum alloys., Eur. Struct. Integr. Soc. 29 (2002) 3–13.CrossRefGoogle Scholar
  16. 16.
    G. Kang, O.T. Bruhns, K. Sai, Cyclic polycrytalline visco-plastic model for ratchetting of 316 stainless steel, Comput. Mater. Sci. 50 (2011) 1399–1405.CrossRefGoogle Scholar
  17. 17.
    N. Khutia, P. Dey, S. Sivaprasad, S. Tarafder, Development of new cyclic plasticity model for 304ln stainless steel through simulation and experimental investigation., Mech. Mater. 78 (2014) 85–101.CrossRefGoogle Scholar
  18. 18.
    N. Khutia, P. Dey, T. Hassan, An improved non proportional cyclic plasticity model for multiaxial low-cycle fatigue and ratcheting responses of 304 stainless steel., Mech. Mater. 91 (2015) 12–25.CrossRefGoogle Scholar
  19. 19.
    J.L. Chaboche, A review of some plasticity and viscoplasticity constitutive theories., Int. J. Plast. 24 (2008) 1642–1693.CrossRefGoogle Scholar
  20. 20.
    Y. Jiang, H. Sehitoglu, Modeling of cyclic ratcheting plasticity, part I: development of constitutive relations., J. Appl. Mech. 63 (3) (1996) 720–725.CrossRefGoogle Scholar
  21. 21.
    V. Do, C.-H. Lee, K.-H. Chang, A constitutive model for uniaxial/multiaxial ratcheting behavior of a duplex stainless steel, Mater. Des. 65 (2015) 1161–1171.CrossRefGoogle Scholar
  22. 22.
    M.E. Gurtin, E. Fried, L. Anand, The Mechanics and Thermodynamics of Continua, Cambridge University Press, 2010.Google Scholar
  23. 23.
    M. Jirasek, Z. Bazant, Inelastic Analysis of Structures, Wiley, 2001.Google Scholar
  24. 24.
    S. Balasubramanian, L. Anand, Elasto-viscoplastic constitutive equations for polycrystalline FCC materials at low homologous temperatures, J. Mech. Phys. Solids 50 (2002) 101–126.CrossRefGoogle Scholar
  25. 25.
    U.F. Kocks, Laws for work-hardening and low-temperature creep., J. Eng. Mater. Technol. 98 (1976) 76–85.CrossRefGoogle Scholar
  26. 26.
    H.J. Frost, M.F. Ashby, Deformation-Mechanism Maps, Pergamon Press, 1982.Google Scholar
  27. 27.
    S. Nemat-Nasser, Plasticity: A Treatise on the Finite Deformation of Heterogneous Inelastic Materials, Cambridge University Press, 2004.Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2014

Authors and Affiliations

  • Jacques Luk-Cyr
    • 1
  • Daniel Paquet
    • 2
  • Jacques Lanteigne
    • 2
  • Henri Champliaud
    • 3
  • Aurelian Vadean
    • 1
  1. 1.Department of Mechanical EngineeringEcole Polyechnique de MontrealMontreal, QCCanada
  2. 2.Institut de recherche d’Hydro-QuebecVarennes, QCCanada
  3. 3.Department of Mechanical EngineeringEcole de technologie superieureMontreal, QCCanada

Personalised recommendations