Phenomenological model for the macroscopical material behavior of ferroelectric ceramics

Journal of the Mechanics and Physics of Solids

Volumn 55, Issue 10, 2007, Pages 2106-2141

  Mehling, V ^a   Tsakmakis, Ch ^a   Gross, D ^a  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Electromechanical coupling; Ferroelectricity; Phenomenological modeling; Piezoelectricity; Thermodynamical modeling

Indexed keywords

ANISOTROPY; CONSTITUTIVE MODELS; ELECTROMECHANICAL COUPLING; ENERGY BARRIERS; FERROELECTRICITY; PIEZOELECTRICITY; POLYCRYSTALLINE MATERIALS;

INTERNAL STATE VARIABLES; PHENOMENOLOGICAL MODELING; THERMODYNAMICAL MODELING;

FERROELECTRIC CERAMICS;

EID: 34548626603     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2007.03.008     Document Type: Article

References (38)

1. Allik H., and Hughes T.J.R. Finite element method for piezoelectric vibration. Int. J. Numer. Methods Eng. 2 (1970) 151-157
2. Bassiouny E., and Maugin G.A. Thermomechanical formulation for coupled electromechanical hysteresis effects-III. Parameter identification, IV. Combined electromechanical loading. Int. J. Eng. Sci. 27 (1989) 975-1000
3. Bassiouny E., Ghaleb A.F., and Maugin G.A. Thermomechanical formulation for coupled electromechanical hysteresis effects-I. Basic equations, II. Poling of ceramics. Int. J. Eng. Sci. 26 (1988) 1279-1306
4. Boehler, J.P., 1987. Representations for isotropic and anisotropic non-polynomial tensor functions. In: Boehler, J.P. (Ed.), Applications of tensor functions in solid mechanics, CISM Courses No. 292. Springer, Berlin.
5. Cao H., and Evans A.G. Nonlinear deformation of ferroelectric ceramics. J. Am. Ceram. Soc. 74 4 (1993) 890-896
6. Chen P.J. Three dimensional dynamic electromechanical constitutive relations for ferroelectric materials. Int. J. Solids Struct. 16 (1980) 1059-1067
7. Chen P.J., and Peercy P.S. One dimensional dynamic electromechanical constitutive relations of ferroelectric materials. Acta Mech. 31 (1979) 231-241
8. Cocks A.C.F., and McMeeking R.M. A phenomenological constitutive law of the behaviour of ferroelectric ceramics. Ferroelectrics 228 (1999) 219-228
9. Coleman B.D., and Gurtin M.E. Thermodynamics with internal state variables. J. Chem. Phys. 47 2 (1967) 597-613
10. Coleman B.D., and Noll W. The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Ration. Mech. Anal. 13 (1963) 167-178
11. Fett T., Müller S., Munz D., and Thun G. Nonsymmetry in the deformation behaviour of PZT. J. Mater. Sci. Lett. 17 (1998) 261-265
12. Fett T., Munz D., and Thun G. Multiaxial deformation behavior of PZT from torsion tests. J. Am. Chem. Soc. 86 8 (2003) 1427-1429
13. Fröhlich, A., 2001. Mikromechanisches Modell zur Ermittlung effektiver Materialeigenschaften von piezoelektrischen Polykristallen. Dissertation, Fakultät für Maschinenbau der Universität Karlsruhe(TH), FZ Karlsruhe.
14. Hall D.A., Steuwer A., Cherdhirunkorn B., Mori T., and Withers P.J. A high energy synchrotron X-ray study of crystallographic texture and lattice strain in soft lead zirconate titanate ceramics. J. Appl. Phys. 96 8 (2004) 4245-4252
15. Hall D.A., Steuwer A., Cherdhirunkorn B., Withers P.J., and Mori T. Micromechanics of residual stress and texture developement due to poling in polycrystalline ferroelectric ceramics. J. Mech. Phys. Solids 53 (2005) 249-260
16. Huber J.E., and Fleck N.A. Multi-axial electric switching of a ferroelectric: theory versus experiment. J. Mech. Phys. Solids 49 (2001) 785-811
17. Hwang S.C., and McMeeking R.M. A finite element model of ferroelastic polycrystals. Int. J. Solids Struct. 36 (1999) 1556-1641
18. Ikeda T. Fundamentals of Piezoelectricity (1990), Oxford University Press, Oxford, New York, Tokyo
19. Jaffe B., Cook W.R., and Jaffe H. Piezoelectric ceramics. Non-Metallic Solids vol. 3 (1971), Academic Press, London
20. Jona F., and Shirane G. Ferroelectric Crystals (1993), Dover Publications Inc, New York (Originally published: Pergamon Press, Oxford, New York, 1962)
21. Kamlah M. Ferroelectric and ferroelastic piezoceramics-modeling of electromechanical hysteresis phenomena. Continuum Mech. Thermodyn. 13 4 (2001) 219-268
22. Kamlah M., and Jiang Q. A constitutive model for ferroelectric PZT ceramics under uniaxial loading. Smart Mater. Struct. 8 (1999) 441-459
23. Kamlah, M., Wang, Z., 2003. A thermodynamically and microscopically motivated constitutive model for piezoceramics. Wissenschaftliche Berichte FZKA 6880 FZ Karlsruhe, Institut für Materialforschung.
24. Landis, C.M., 1999. Self-consistent and phenomenological constitutive models for ferroelectric ceramics. Ph.D. Thesis, University of California.
25. Landis C.M. Fully coupled, multi-axial, symmetric constitutive laws for polycrystalline ferroelectric ceramics. J. Mech. Phys. Solids 50 (2002) 127-152
26. Landis C.M. On the strain saturation conditions for polycrystalline ferroelastic materials. J. Appl. Mech. 70 (2003) 470-478
27. Landis C.M. Non-linear constitutive modeling of ferroelectrics. Curr. Opinion Solid State Mater. Sci. 8 (2004) 59-69
28. Landis C.M., and McMeeking R.M. A phenomenological constitutive law for ferroelastic switching and a resulting asymptotic crack tip solution. J. Intelligent Mater. Syst. Struct. 10 (1999) 155-163
29. Landis C.M., Wang J., and Sheng J. Micro-electromechanical determination of the possible remanent strain and polarization states in polycrystalline ferroelectrics and the implications for phenomenological constitutive theories. J. Intelligent Mater. Syst. Struct. 15 (2004) 513-525
30. Lu W., Fang D.-N., Li C.Q., and Hwang K.-C. Nonlinear electric-mechanical behavior and micromechanics modelling of ferroelectric domain evolution. Acta Mater. 47 10 (1999) 2913-2926
31. Lupascu D.C., and Rödel J. Fatigue in bulk lead zirconate titanate actuator materials. Adv. Eng. Mater. 7 10 (2005) 882-898
32. Lynch C.S. The effect of uniaxial stress on the electro-mechanical response of 8/65/35 PLZT. Acta Mater. 44 10 (1996) 4137-4148
33. Mehling, V., Tsakmakis, Ch., Gross, D., 2005. A simple fully coupled three-dimensional phenomenological model for ferroelectric ceramics. In: Papadrakis, M., Oñate, E., Schrefler, B. (Eds.), Proceedings of the ECCOMAS Thematic Conference on Computational Methods for Coupled Problems in Science and Engineering, ECCOMAS Barcelona, International Center for Numerical Methods in Engineering (CIMNE).
34. Schröder J., and Gross D. Invariant formulation of the electromechanical enthalpy function of transversely isotropic piezoelectric materials. Arch. Appl. Mech. 73 (2004) 533-552
35. Shieh J., Huber J.E., and Fleck N.A. An evaluation of switching criteria for ferroelectrics under stress and electric field. Acta Mater. 51 (2003) 6123-6137
36. Simo J.C., and Hughes T.J.R. Computational inelasticity. Interdisciplinary Applied Mathematics vol. 7 (1997), Springer, New York, Heidelberg, Berlin
37. Zhou, D., 2003. Experimental investigation of non-linear constitutive behavior of PZT piezoceramics, Dissertation, Fakultät für Maschinenbau der Universität Karlsruhe(TH), FZ Karlsruhe.
38. Zhou D., Kamlah M., and Munz D. Effects of bias electric fields on the non-linear ferroelastic behavior of soft lead zirconate titanate piezoceramics. J. Am. Ceram. Soc. 88 4 (2005) 867