Experimental Investigation of Rate-Dependent Inner Hysteresis Loops in PZT
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Experimental Investigation of Rate-Dependent Inner Hysteresis Loops in PZT Alexander York and Stefan Seelecke Dept. Mech. & Aero. Eng., North Carolina State Univ., Raleigh, NC 27695 ABSTRACT The rate-dependence of piezoelectric materials resulting from the kinetics of domain switching is an important factor that needs to be included in realistic modeling attempts. This paper provides a systematic study of the rate-dependent hysteresis behavior of a commercially available PZT stack actuator. Experiments covering full as well as minor loops are conducted at different loading rates with polarization and strain recorded. In addition, the creep behavior at different constant levels of the electric field is observed. This provides evidence of kinetics being characterized by strongly varying relaxation times that can be associated with different switching mechanisms. Keywords: PZT, hysteresis, rate dependence, experimental data, piezoelectrics INTRODUCTION Modeling efforts for piezoceramic material are challenging due to characteristics such as nonlinearity, hysteresis, rate dependence, temperature dependence, and creep. Many mathematical models of PZT behavior have been suggested to describe the nonlinearity and hysteresis. The most well known model is the Preisach model [6]. Many improvements and additions to Preisach’s model have been used as well [8] ,[7], [10]. A problem with Preisach-based models is that they are based on a mathematical concept without clear physical background, and as such do not account for ratedependence or creep behavior without the addition of highly specified operators [10] that only work for limited cases. The non-linear rate-dependent behavior of the material is known to be due to domain switching processes in the material which has been studied in, e.g., [5], [11], [15]. However, most of these domain switching modeling efforts confine attention to the rate-independent limit of the material behavior. Only recently, Smith et al. [13], [12], [14], have proposed a free energy model based on the theory of thermal activation, which is capable of describing rate effects in a natural way. In order to obtain the parameters for such a model, a systematic experimental study of the material is needed. A literature survey revealed that most of the experimental work in the field has either been devoted to extremely high loading rates in the acoustic region [10] where no domain switching occurs, or focuses on full-loop behavior only [2], [4], [11], [15], [16]. As this is a good starting point, it is not sufficient for the description of, e.g., actuators, which mostly follow paths in the interior of the hysteresis. To the best of our knowledge, this paper presents the first systematic study of the ratedependent inner loop behavior including creep phenomena. First, the full-loop behavior of polarization and strain vs. electric field is studied. Subsequently, the creep, behavior is documented followed by inner-loop at various stages of the switching process. Hysteresis curves are shown to behave in a
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