2 February 1995 Micromechanical theory of the nonlinear behavior of ferroelectric ceramics
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Proceedings Volume 2427, Active Materials and Smart Structures; (1995) https://doi.org/10.1117/12.200926
Event: Symposium on Active Materials and Smart Structures: Society of Engineering Science 31st Annual Meeting, 1994, College Station, TX, United States
Ferroelectric and ferroelastic switching cause ferroelectric ceramics to depolarize and deform when subjected to excessive electric field or stress. Switching is the source of the classic butterfly shaped strain vs. electric field hysteresis loops and the corresponding electric displacement vs. electric field loops. It is also the source of a stress-strain curve with linear elastic behavior at low stress, non-linear switching strain at intermediate stress, and linear elastic behavior at high stress. In this work, a series of experiments on lead lanthanum zirconate titanate are modeled with a computer simulation of the ceramic microstructure. The polarization and strain for an individual grain are predicted from the imposed electric field and stress through a Preisach hysteresis model. The response of the bulk ceramic to applied loads is predicted by averaging the response of individual grains that are considered to be statistically random in orientation. The random orientation yields essential non-linear behavior of the observed strain and electric displacement hysteresis loops and the non-linear stress- strain curve for the polycrystalline ceramic. The linear piezoelectric effect opens up a butterfly shape to the strain vs. electric field hysteresis loop but the model fails to predict the observed effect of 90 degree(s) switching. The grain to grain residual stress and residual polarization are estimated from inclusion calculations. These are both a function of the remanent strain and remanent polarization of the ceramic. This constraint opposed switching but has little effect on the butterfly shape in the strain vs. electric field hysteresis loop.
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Christopher S. Lynch, Christopher S. Lynch, Stephen C. Hwang, Stephen C. Hwang, Robert M. McMeeking, Robert M. McMeeking, "Micromechanical theory of the nonlinear behavior of ferroelectric ceramics", Proc. SPIE 2427, Active Materials and Smart Structures, (2 February 1995); doi: 10.1117/12.200926; https://doi.org/10.1117/12.200926

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