On the evolution of the linear material properties of PZT during loading history—an experimental study

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Abstract

Ferroelectrics exhibit material behavior which is strongly affected by its loading history. Among other phenomena, the coefficients describing the linear material behavior are known to change when the state of polarization is altered. There are several approaches to modeling ferroelectric/ferroelastic behavior. However, with all models, assumptions have to be made on how the linear coefficients depend on the state of polarization. Often the elastic and dielectric coefficients are defined to be constant for the sake of simplicity. Alternatively, their evolution and that of the piezoelectric constants are described rather intuitively, while systematic experimental data are sparse. The present study explores the impact of large signal mechanical and electrical loading on the low frequency linear response of a soft PZT ceramic. This is accomplished via cyclic tests with progressively increasing maximum electrical or mechanical load. Upon load reversal, the quasi-linear response is measured. Remanent polarization and remanent strain are used as internal variables to describe the material behavior as a function of loading history. While the dielectric permittivity κ33 is shown to exhibit only minor variation, Young’s modulus and the piezoelectric coefficient d33 change significantly in the course of loading.

Introduction

Lead zirconate titanate (PZT) ceramics are popular materials for actuator and sensor applications. These ferroelectric materials combine several beneficial properties such as high piezoelectric coefficients, a relatively high Curie-Temperature and relatively low sintering temperatures. Furthermore, PZT ceramics form solid solutions with many different constituents, which allows for a wide range of achievable properties (Haertling, 1999).

Predictions on the performance or reliability of devices are desirable when PZT ceramics are used in actuator or sensor applications. For this purpose finite element simulations will be needed in most cases. Therefore, there is significant interest in modeling the nonlinear material behavior of ferroelectric ceramics. Consequently, there are a variety of modeling approaches and we can differentiate between micromechanical (Hwang et al., 1998, Chen and Lynch, 1998) and phenomenological (McMeeking and Landis, 2002, Kamlah and Jiang, 1999) approaches. Regardless of the nature of the modeling approach, comprehensive knowledge of the material behavior for a variety of loading conditions is needed for a mathematical description of the large signal behavior.

The extent of experimental large signal investigations of the ferroelectric properties of PZT is limited but increasing (Cao and Evans, 1993, Schaeufele and Haerdtl, 1996, Lynch, 1996). Dielectric and piezoelectric parameters are usually derived from small signal measurements. The small signal behavior has been studied extensively, it has even been used to quantify the contributions of domain wall processes to the dielectric and piezoelectric properties of PZT ceramics (Zhang et al., 1994). It was shown that the piezoelectric response depends on the degree of loading even in the small signal range (Damjanovic and Demartin, 1997). Furthermore, it is well known that ferroelectrics exhibit a strongly frequency dependent material behavior (Jaffe et al., 1971). A pronounced effect of loading frequency has been reported elsewhere for small signal (Damjanovic, 1997) as well as for large signal (Lente and Eiras, 2001) testing conditions. Consequently, small signal parameters are not suitable for describing the material behavior of ferroelectrics under loading conditions relevant to typical actuator and sensor applications, since there the amount of loading is significantly higher compared to small signal conditions. Additionally, the loading frequency is generally several orders of magnitude lower than measurement frequencies in small signal testing.

This is the motivation for presenting this study of the history dependence of linear material properties on the basis of large signal investigations. This history dependence is of great relevance to modeling the low frequency material behavior because models for ferroelectric/ferroelastic ceramics ought to account for this effect to enable realistic predictions of the material behavior for a variety of possible loading profiles. In this study we present results of mechanical and electrical loading tests on PZT. These are discussed in regard to the impact of loading on the coefficients describing linear material behavior.

Section snippets

General remarks

In the experiments presented in this paper we use a cold isostatically pressed, multiple doped lead zirconate titanate (PZT) ceramic with a composition close to the morphotropic phase boundary. The composition of the ceramic used is proprietary, so we provide a plot of remanent polarization versus electric field instead (see Fig. 1). The remanent polarization is determined as will be described later in the discussion. It can be seen from Fig. 1 that the material can be classified as a soft

Electrical loading experiments

The specimens for electrical loading tests are provided with electrodes for electrical connection. These are applied on two opposite sample surfaces by physical vapor deposition (PVD). The electrodes consist of a 750 nm gold layer with a 30 nm tungsten–titanium alloy as an adhesive layer between the gold and the PZT. The electric field necessary for the PVD-process (approximately 5 kV/m) has no measurable impact on the polarization state of the material, which has a coercive field of 1.14 MV/m.

Mechanical loading experiments

For the compressive mechanical tests, cubic samples with an edge length of 8 mm are employed. Additional experiments have shown, that the cubic geometry does not lead to a reduction of measurement accuracy by a possible inhomogeneous stress state. The PZT-cubes are compressed between steel platens as above, but with the servo-hydraulic testing machine now used to generate mechanical loads up to 200 MPa in magnitude. Due to the setup, a small stress of −1 MPa is needed in these tests to locate the

Results

First we show results from an electrical loading experiment. Subsequently, results for the material behavior under mechanical loading are presented. In each case the data shown here are derived from one experiment. Similar experiments have been carried out to ensure reproducibility. Fig. 2 shows the evolution of the electric displacement D in a unipolar electrical loading test with dwell times at zero field. The corresponding strain data are plotted versus the electric field in Fig. 3.

As can be

Discussion

Fig. 4 shows the permittivity κ33 as a function of the prior maximum electric field. Note that due to the previously described method of their determination, these values are not true small signal parameters in the sense of IEEE standards. As already mentioned in the introduction, measuring small signal parameters in the classical meaning is not the objective of this study, since these quantify the high frequency material behavior measured for small load amplitudes. The effect of the amount of

Conclusions

The experimental findings on the low frequency properties of PZT presented above show a significant change of Young’s modulus and piezoelectric coefficient during loading history. Since these variations contribute to the overall behavior of the material, this effect should be implemented in models which aim to predict ferroelectric/ferroelastic behavior. This can be done conveniently via relationships between the coefficients and internal variables such as remanent strain or remanent

Acknowledgment

The authors would like to thank Mr. Martin Streeb for his experimental assistance in the experiments. Financial support by the DAAD is gratefully acknowledged.

References (21)

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