Non-uniform electric field and nonlinear piezoelectric behavior in active fiber composites

Active fiber composites (AFCs) are comprised of piezoelectric fibers (lead zirconate titanate or PZT) in an epoxy polymer. Due to the interdigitated electrode architecture of AFC, the device takes advantage of PZT's d ₃₃ piezoelectric coefficient, which is twice as high as the d ₃₁ coefficient. Despite the advantages of AFCs, such as ruggedness and flexibility, its piezoelectric performance is almost a third of PZT's, mainly because of dielectric contrast between the polymer matrix and the PZT fibers. Nonetheless, the AFCs are still of great interest because they have the potential to combine the flexibility and light weight of the polymer to the high piezoelectric performance of PZT. The objectives of this current work are to experimentally and computationally investigate the dielectric, mechanical and piezoelectric behavior of AFC with the goal of improving upon its design. Since polymers tend to have behaviors affected by their viscoelastic characteristics, especially at elevated temperatures, it is necessary to understand the coupled thermo-electro-mechanical behavior of AFCs too. Tensile tests at room temperature revealed the dependence of the properties on the loading rate; for example the Young's modulus increased by more than 75% from 0.5mm/min to 25mm/min. However, at 75°C the effect of the loading rate was not as significant, where only a 25% increase was seen for the same cases. Likewise, the Young's modulus and the tensile strength of the AFCs decreased as temperature increases, and the Ultimate Strain increased. This observed change in properties is most likely caused by the viscoelastic behavior of the epoxy matrix and the Kapton tape used to protect the electrodes. Electrical and electromechanical experiments were conducted to obtain the effective properties; the results show that the AFCs exhibit a nonlinear electromechanical behavior. The AFC model we are proposing is uniquely addressing a gap of knowledge in the literature by considering both non-uniformity of applied electric field and nonlinear response of PZT fibers at high applied fields. The model considers several fibers as part of the RVE in order to investigate the electric potential and stress fields between fibers; furthermore, to investigate the effect of opposite fiber poling from one electrode gap to another, the model examines a few interdigitated electrodes. The model is built in ABAQUS, and the partition method is used to determine regions with different materials properties and different boundary conditions. Finally, a user subroutine is developed to address the nonlinear behavior of PZT. We conduct parametric studies to assess impact of the nature of polymer matrix, electrode width and gap distance, and fiber size to name a few. The results will be validated with experimental data on actuation and mechanical properties. This new model will inform improvements in manufacturing and design of future AFCs.