High-strain piezoelectric materials are often ceramics with a complicated constitution. In particular, PZT is used with compositions near to a so-called morphotropic phase boundary, where not only different variants of the same phase (domains), but different phases may coexist. Micro-mechanical models for ferroelectric ceramics would be much more realistic, if these effects could be incorporated.
In this paper, we consider the conditions of mechanical and electrical compatibility of ferroelectric domain structures. We are able to address the question of coexistence of different crystallographic phases within the very same crystallite. In general, the spontaneous strain and spontaneous polarization of different phases are not compatible.
The numerical analysis of the derived relationships are susceptible to the crystallographic description of the phases in question. In this presentation, a simple analysis and analytical, composition dependent fit of strain and polarization of PZT at room temperature for available data are used. The outlined approach can be used to model the overall behavior of multi-variant and multi-phase crystallites with certain, simplified geometrical arrangements of the constituents.
The degradation of ferroelectric properties (polarization and remnant strain) during cycling of piezoelectric ceramics limits the reliability and applicability of such materials. This ferroelectric fatigue is believed to be caused by domain wall pinning and grain boundary microcracking. In this paper we concentrate on the domain wall pinning effect. The analysis is based on a self-consistent non-linear micro-mechanical model. The particular domain model applies to loading situations according to quasistatic unipolar cycling. Internal fields on the grain level and stored internal energy can be calculated using the solution of the piezoelectric inclusion problem. Nonlinear material response and hysteresis is caused by rearrangement of ferroelectric domain walls which leads to relaxation of internal fields. According to a thermodynamic criterion, domain wall motion takes place if the energy release rate is equal to a critical value. The proposed model assumes that the critical energy release rate is coupled with a microscopic, history dependent internal variable. Thus the evolution of the internal variable determines the fatigue process. Decreasing relaxation of internal fields causes increase of stored energy which could be discussed in relation to the onset of additional fatigue mechanisms like microcracking.
A constitutive model for the nonlinear effective behavior of ferroelectric ceramics is presented. The model is developed on the basis of the effective medium approximation which describes the interaction of the crystallites in a statistical way. Additionally, a particular simplified domain configuration within the crystallites and the possibility of domain wall motion are taken into account. In connection with a thermodynamic criterion for the domain wall displacement the volume fractions of domains can be calculated dependent on the crystallite orientation and the applied load in a self-consistent manner. This mechanism leads to an extrinsic contribution to the effective behavior. If the domain wall displacement is associated with energy dissipation the macroscopic behavior is nonlinear and hysteretic.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.