Advertisement

Acta Mechanica Solida Sinica

, Volume 20, Issue 1, pp 1–12 | Cite as

A simple constitutive model for ferroelectric ceramics under electrical/mechanical loading

  • Li Yu
  • Shouwen Yu
  • Xiqiao Feng
Article

Abstract

A simple phenomenological model is developed for describing the macroscopic constitutive response of ferroelectric materials based on consideration of the fact that domain switching is a progressive evolution process with loading. The volume fraction of domain switching is taken as an internal variable, which is derived from the domain nucleation theory. The proposed theory can simulate the dielectric hysteresis, reversed butterfly hysteresis, nonlinear strain-stress hysteresis, as well as electric displacement-stress relation of ferroelectric materials. Its comparison with experimental results and two other theoretical models reveals that the model presented can well predict the nonlinear hysteresis of ferroelectrics under electrical or mechanical loading.

Key words

ferroelectrics gradual domain switching constitutive laws electromechanical coupling 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Jaffe, B., Cook, W.R. and Jaffe, H., Piezoelectric Ceramics. London and New York: Academic Press, 1971.Google Scholar
  2. 2.
    Picinin, A., Lente, M.H., Eiras, J.A. and Rino, J.P., Theoretical and experimental investigations of polarization switching in ferroelectric materials. Phys. Rev. B, 2004, 69, 064117.CrossRefGoogle Scholar
  3. 3.
    Hwang, S.C., Lynch, C.S. and McMeeking, R.M., Ferroelectric/ ferroelastic interactions and a polarization switching model. Acta Metall. Mater., 1995, 43: 2073–2084.CrossRefGoogle Scholar
  4. 4.
    Lu, W., Fang, D.N., Li, C.Q. and Hwang, K.C., Nonlinear electric-mechanical behavior and micromechanics modeling of ferroelectric domain evolution. Acta Mater., 1999, 47: 2913–2926.CrossRefGoogle Scholar
  5. 5.
    Li, F.X. and Fang, D.N., Effects of lateral stress on the electromechanical response of ferroelectric ceramics: experiments versus model. J. Intell. Mat. Syst. Struct., 2005, 16: 583–588.CrossRefGoogle Scholar
  6. 6.
    Chen, X., Fang, D.N. and Hwang, K.C., Micromechanics simulation of ferroelectric polarization switching. Acta Mater., 1997, 45: 3181–3189.CrossRefGoogle Scholar
  7. 7.
    Hwang, S.C., Huber, J.E., McMeeking, R.M. and Fleck, N.A., The simulation of switching in polycrystalline ferroelectric ceramics. J. Appl. Phys., 1998, 83: 1530–1540.CrossRefGoogle Scholar
  8. 8.
    Chen, W. and Lynch, C.S., A micro-electro-mechanical model for polarization switching of ferroelectric materials. Acta Mater., 1998, 46: 5303–5311.CrossRefGoogle Scholar
  9. 9.
    Cheng, J.Q., Wang, B. and Du, S.Y., A statistical model for predicting effective electroelastic properties of polycrystalline ferroelectric ceramics with aligned defects. Int. J. Solids Struc., 2000, 37: 4763–4781.CrossRefGoogle Scholar
  10. 10.
    Li, J. and Weng, G.J., A theory of domain switch for the nonlinear behavior of ferroelectrics. Proc. R. Soc. Lond., 1999, A455: 3493–3511.CrossRefGoogle Scholar
  11. 11.
    Li, J. and Weng, G.J., A micromechanics-based hysteresis model for ferroelectric ceramics. J. Intell. Mat. Syst. Struct., 2001, 12: 79–91.CrossRefGoogle Scholar
  12. 12.
    Huber, J.E., Fleck, N.A., Landis, C.M. and McMeeking, R.M., A constitutive model for ferroelectric polycrystals. J. Mech. Phys. Solids, 1999, 47: 1663–1697.MathSciNetCrossRefGoogle Scholar
  13. 13.
    Huber, J.E. and Fleck, N.A., Multi-axial electrical switching of a ferroelectric: theory versus experiment. J. Mech. Phys. Solids, 2001, 49: 785–811.CrossRefGoogle Scholar
  14. 14.
    Landis, C.M., Fully coupled, Multi-axial, symmetric constitutive laws for polycrystalline ferroelectric ceramics. J. Mech. Phys. Solids, 2002, 50: 127–152.CrossRefGoogle Scholar
  15. 15.
    Chen, P.J. and Peercy, P.S., One-dimensional dynamic electromechanical constitutive relations of ferroelectric materials. Acta Mech., 1979, 31: 231–241.MathSciNetCrossRefGoogle Scholar
  16. 16.
    Bassiouny, E. and Maugin, G.A., Thermodynamical formulation for coupled electromechanical hysteresis effects -III. Parameter Identification. Int. J. Eng. Sci., 1989, 27: 975–987.MathSciNetCrossRefGoogle Scholar
  17. 17.
    Cocks, C.F. and McMeeking, R.M., A phenomenological constitutive law for the behaviour of ferroelectric ceramics. Ferroelectrics, 1999, 228: 219–228.CrossRefGoogle Scholar
  18. 18.
    Kamlah, M. and Tsakmakis, C., Phenomenogical modeling of the non-linear electromechanical coupling in ferroelectrics. Int. J. Solids. Struc., 1999, 36: 669–695.CrossRefGoogle Scholar
  19. 19.
    Landis, C.M. and McMeeking, R.M., A phenomenological constitutive law for ferroelastic switching and a resulting asymptotic crack tip solution. J. Intell. Mat. Syst. Struct., 1999, 10: 155–163.CrossRefGoogle Scholar
  20. 20.
    Zhong, W.L., The Physics of Ferroelectrics. Beijing: Science Press, 1996 (in Chinese).Google Scholar
  21. 21.
    Wang, J., Shi, S.H., Chen, L.Q., Li, Y.L. and Zhang, T.Y., Phase field simulations of ferroelectric/ferroelastic polarization switching. Acta Mater., 2004, 52: 749–764.CrossRefGoogle Scholar
  22. 22.
    Miller, R.C. and Weinreich, G., Mechanism for the sidewise motion of 180° domain walls in Barium Titanate. Phys. Rev., 1960, 117: 1460.CrossRefGoogle Scholar
  23. 23.
    Wang, T.C. and Liu, F., Seminar on nonlinear constitutive relation for ferroelectric materials. Beijing: Academy of Sciences of China, 2004.Google Scholar
  24. 24.
    Merz, W.J., Switching time in ferroelectric BaTiO3 and its dependence on crystal thickness. J. Appl. Phys., 1956, 27: 938–943.CrossRefGoogle Scholar
  25. 25.
    Lines, M.E. and Glass, A.M., Principles and Applications of Ferroelectrics and Related Materials. Oxford: Oxford University Press, 1977.Google Scholar
  26. 26.
    Lynch, C.S., The effect of uniaxial stress on the electro-mechanical response of 8/65/35 PLZT. Acta Mater., 1996, 44: 4137–4148.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2007

Authors and Affiliations

  • Li Yu
    • 1
  • Shouwen Yu
    • 1
  • Xiqiao Feng
    • 1
  1. 1.Department of Engineering MechanicsTsinghua UniversityBeijingChina

Personalised recommendations