Constitutive model for rate dependent behavior of ferroelectric materials

A constitutive model for rate dependent behavior of ferroelectric materials is developed from a one-dimensional switching model [Ikeda et al., Proc. SPIE, 7289 (2009), 728905]. The one-dimensional switching model has the following three features. (i) Several ferroelectric variants can be considered, such as 0-degree, 90-degree, 180-degree, and initial mixed variants. (ii) Required switching energy is approximated as a sum of two exponential functions of volume fraction of the variants. (iii) A specimen is assumed to be comprised of grains with infinitesimal size, and relationship between two grains regarding the required switching energy is unchanged independently of switching directions. Accordingly, the switching proceeds one-dimensionally. To take into account loading rate effects, a function of volume fraction rate is added to the required switching energy. That makes energy barrier higher at higher rates. To verify validity of the present model, electro-mechanical behavior of a thin PZT plate is measured at various loading rates and simulated using the present model. Result shows the present model can capture the influence of electric loading rate on responses of electric displacement and strain, such that remnant polarization decreases and coercive field increases with increasing the loading rate.

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