Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
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.
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.
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.
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.
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.
D. Slavic, H. Sehitoglu, Constitutive models suitable for thermal loading, J. Eng. Mater. Technol. 108 (1986) 303–312.
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.
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.
M. Abdel-Karim, N. Ohno, Kinematic hardening model suitable for ratchetting with steady-state., Int. J. Plast. 16 (2000) 225–240.
P.J. Armstrong, C.O. Fredrick, A mathematical representation of the multiaxial Bauschinger effect., Report No. RD/B/N 73), CEGB, 1966.
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.
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.
N. Ohno, J.-D. Wang, Kinematic hardening rules for simulation of ratcheting behaviour, Eur. J. Mech. A/Solids 13 (1994) 519–531.
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.
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.
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.
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.
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.
J.L. Chaboche, A review of some plasticity and viscoplasticity constitutive theories., Int. J. Plast. 24 (2008) 1642–1693.
Y. Jiang, H. Sehitoglu, Modeling of cyclic ratcheting plasticity, part I: development of constitutive relations., J. Appl. Mech. 63 (3) (1996) 720–725.
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.
M.E. Gurtin, E. Fried, L. Anand, The Mechanics and Thermodynamics of Continua, Cambridge University Press, 2010.
M. Jirasek, Z. Bazant, Inelastic Analysis of Structures, Wiley, 2001.
S. Balasubramanian, L. Anand, Elasto-viscoplastic constitutive equations for polycrystalline FCC materials at low homologous temperatures, J. Mech. Phys. Solids 50 (2002) 101–126.
U.F. Kocks, Laws for work-hardening and low-temperature creep., J. Eng. Mater. Technol. 98 (1976) 76–85.
H.J. Frost, M.F. Ashby, Deformation-Mechanism Maps, Pergamon Press, 1982.
S. Nemat-Nasser, Plasticity: A Treatise on the Finite Deformation of Heterogneous Inelastic Materials, Cambridge University Press, 2004.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Luk-Cyr, J., Paquet, D., Lanteigne, J. et al. A unified plasticity methodology for rate- and temperature-sensitive alloys exhibiting a non-linear kinematic hardening behavior. Acta Mech. Solida Sin. 30, 27–37 (2017). https://doi.org/10.1016/j.camss.2016.09.001
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1016/j.camss.2016.09.001