Frequency-dependent nonlinear electromechanical coupling behaviors of ferroelectric composites

In this paper, a frequency-dependent micromechanics-based model is developed to study the nonlinear electromechanical coupling behaviors of ferroelectric composites which in general consist of ferroelectric inclusions and a polymer matrix. The coupling behavior not only depends on the volume concentration and the shape of the inclusions, but also on the frequency of external applied field. For the frequency-dependent properties, an exponential function is introduced to evaluate the remanent polarization and coercive field of the ferroelectric phase. Then a two-level micromechanics-based model is applied to obtain the hysteresis loops and butterfly-shaped responses of the ferroelectric composites at various frequencies. The first level model deals with the single ferroelectric phase by considering the evolution of domain switches while the second level is regarding to the two-phase ferroelectric composites. To verify the developed theory, we compared the calculated results with the existing experimental data for the hysteresis of electric displacement versus electric field and the butterfly-shaped strain versus electric field of the 1–3 type of composites with PZT fibers embedded in an epoxy matrix. The comparisons between theoretical calculations and experimental data show reasonable agreement. In the meantime, the influences of the shape and the volume concentration of the inclusions to the overall effective properties of the composites have been investigated and will shed the light for the design and structure architecture of the ferroelectric composites.