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A micro–macro scale approach for thermal effects in ferroelectrics

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Abstract

The influence of thermal fields on the electromechanical behavior of ferroelectric ceramics under cyclic electric loading is presented. To predict the temperature effect, a 3D micromechanical model for tetragonal domain switching is extended by including thermal effects. Numerical simulations were done through the finite element program Abaqus with the help of a user-defined element. Besides external heat sources, a change in temperature is considered by internal heat generated due to domain switching. Material properties are assumed to be linearly dependent on the temperature. The temperature influence on the behavior of ferroelectrics is shown by means of the strain and polarization hysteresis loops. The model shows a good qualitative agreement with the experimental results available in the literature.

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References

  1. Chen, H.S., Pei, Y.M., Liu, B., Fang, D.N.: Rate dependant heat generation in single cycle of domain switching of lead zirconate titanate via in-situ spontaneous temperature measurement. Appl. Phys. Lett. 102(24), 242912 (2013)

    Article  ADS  Google Scholar 

  2. Görnandt, A., Gabbert, U.: Finite element analysis of thermopiezoelectric smart structures. Acta Mech. 154(1–4), 129–140 (2002)

    Article  MATH  Google Scholar 

  3. Huber, J., Fleck, N., Landis, C., McMeeking, R.: A constitutive model for ferroelectric polycrystals. J. Mech. Phys. Solids 47(8), 1663–1697 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. Ikeda, T.: Fundamentals of Piezoelectricity. Oxford University Press, Oxford (1996)

    Google Scholar 

  5. Kamlah, M., Liskowsky, A.C., McMeeking, R.M., Balke, H.: Finite element simulation of a polycrystalline ferroelectric based on a multidomain single crystal switching model. Int. J. Solids Struct. 42(9–10), 2949–2964 (2005)

    Article  MATH  Google Scholar 

  6. Kim, S.J.: A constitutive model for thermo-electro-mechanical behavior of ferroelectric polycrystals near room temperature. Int. J. Solids Struct. 48(9), 1318–1329 (2011)

    Article  MATH  Google Scholar 

  7. Kim, S.J.: Macroscopic comparison of ferroelectric domain switching processes in a PZT wafer at high temperatures. Curr. Appl. Phys. 11(3), S200–S207 (2011)

    Google Scholar 

  8. Kozinov, S., Kuna, M.: Micromechanical simulation of ferroelectric domain processes at crack tips. Arch. Appl. Mech. 88, 1–15 (2018)

    Article  Google Scholar 

  9. Kozinov, S., Kuna, M.: Simulation of fatigue damage in ferroelectric polycrystals under mechanical/electrical loading. J. Mech. Phys. Solids 116, 150–170 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  10. Li, Q., Kuna, M.: Inhomogeneity and material configurational forces in three dimensional ferroelectric polycrystals. Eur. J. Mech. A Solids 31(1), 77–89 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Mauck, L.D., Lynch, C.S.: Thermo-electro-mechanical behavior of ferroelectric materials part I: a computational micromechanical model versus experimental results. J. Intell. Mater. Syst. Struct. 14(9), 587–602 (2003)

    Article  Google Scholar 

  12. Pathak, A., McMeeking, R.M.: Three-dimensional finite element simulations of ferroelectric polycrystals under electrical and mechanical loading. J. Mech. Phys. Solids 56(2), 663–683 (2008)

    Article  ADS  MATH  Google Scholar 

  13. Sakai, T., Kawamoto, H.: Durability properties of piezoelectric stack actuator. Jpn. J. Appl. Phys. 37(9S), 5338 (1998)

    Article  ADS  Google Scholar 

  14. Senousy, M., Rajapakse, R., Gadala, M.: A temperature-dependent two-step domain-switching model for ferroelectric materials. Acta Mater. 57(20), 6135–6145 (2009)

    Article  Google Scholar 

  15. Shang, F., Kuna, M., Scherzer, M.: A finite element procedure for three-dimensional analysis of thermopiezoelectric structures in static applications. Tec. Mech. 22(3), 235 (2002)

    Google Scholar 

  16. Weiland, L.M., Lynch, C.S.: Thermo-electro-mechanical behavior of ferroelectric materials part II: introduction of rate and self-heating effects. J. Intell. Mater. Syst. Struct. 14(10), 605–621 (2003)

    Article  Google Scholar 

  17. Wen, B., Zhang, Y., Liu, X., Ma, L., Wang, X.: Temperature-dependent ferroelectric hysteresis properties of modified lead zirconate titanate ceramics. J. Mater. Sci. 47(10), 4299–4304 (2012)

    Article  ADS  Google Scholar 

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Correspondence to Omar El Khatib.

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Communicated by Andreas Öchsner.

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El Khatib, O., Kozinov, S. & Kuna, M. A micro–macro scale approach for thermal effects in ferroelectrics. Continuum Mech. Thermodyn. 31, 1439–1452 (2019). https://doi.org/10.1007/s00161-019-00760-8

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  • DOI: https://doi.org/10.1007/s00161-019-00760-8

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