Thermo-Electro-Mechanical Behavior of Ferroelectric Materials Part I: A Computational Micromechanical Model Versus Experimental Results

Abstract

A micro-electro-mechanical model of the behavior of piezoelectric ceramics including thermal effects is presented and compared to experimental data. Results include analytical and numerical investigations of the behavior of piezoelectric ceramics. The model is based on physical mechanisms and includes elastic, dielectric, and piezoelectric anisotropy. Moreover, the model is based on an internal energy approach so that work-energy relations may be directly applied. Results from the model give insight into material behavior.

A finite element formulation for piezoelectric shell structures considering geometrical and material non‐linearities

“…According to Reference [26], we choose the macroscopic material parameter for soft PZT polychristals as given in Figure 16. We compare the numerical results of the present formulation with the experimental data and the micromechanical model in [36]. Figure 17 presents the dielectric hysteresis and the butterfly hysteresis for a temperature of 28 25 • C. Figure 17(a) shows that the dielectric hysteresis curve at 25 • C can be described very well.…”

“…In [36], experimental results are given for the polarization and the expansion behavior under an electric field tested at the temperatures 25 • C (298K) and 100 • C (373K). Besides experimental results also a micro-mechanical model is introduced in [36]. The formulation is based on the principles of energy conservation and models the nonlinear behavior of polycrystal ferroelectric materials with a switching criterion that accounts for temperature effects.…”

“…This test specimen was introduced by Mauck and Lynch [36], to depict the dielectric and the butterfly hysteresis for different temperatures. In [36], experimental results are given for the polarization and the expansion behavior under an electric field tested at the temperatures 25 • C (298K) and 100 • C (373K). Besides experimental results also a micro-mechanical model is introduced in [36].…”

“…The formulation is based on the principles of energy conservation and models the nonlinear behavior of polycrystal ferroelectric materials with a switching criterion that accounts for temperature effects. For the micro-mechanical calculation, the material paramters in [36] are derived from the single crystal parameters of barium titanate and are modified via a correction parameter to get the material parameter of soft PZT single crystal. According to Reference [26], we choose the macroscopic material parameter for soft PZT polychristals as given in Figure 16.…”

“…proposed by Reference [34]. The influence of the temperature on piezoelectric material behavior has been studied experimentally in References [36,37,38,39]. [39] shows that the ferroelectric hysteresis curves become smaller with increasing temperature.…”