TL;DR: In this article, a model for studying the domain pattern of ferroelectric materials and its evolution is developed, and the electrostatic potential is made explicit, and consequently the model is able to predict the micro-structural evolution and the macro-scopic behavior of Ferroelectrics subjected to realistic electro-mechanical boundary conditions.
Abstract: A model for studying the domain pattern of ferroelectric materials and its evolution is developed. In a departure from prior work, the electrostatic potential is made explicit, and consequently the model is able to predict the microstructural evolution and the macroscopic behavior of ferroelectrics subjected to realistic electro-mechanical boundary conditions. Nucleation of domains and propagation of domain walls are investigated under combined electro-mechanical loading and compared to recent experiments. The correlation between the microstructural change and macroscopic response provides evidence that the recently observed large strain actuation of ferroelectric materials is due to 90° domain switching.
TL;DR: Theoretical analyses and experimental observations of the failure and fracture behaviors of piezoelectric materials are presented in this paper, where the theoretical analyses are based on the Stroh formalism.
Abstract: Theoretical analyses and experimental observations of the failure and fracture behaviors of piezoelectric materials are presented. The theoretical analyses are based on the Stroh formalism. A strip dielectric breakdown model is proposed to estimate the effect of electrical non-linearity on the piezoelectric fracture of electrically insulated cracks. The reviewed experiments include the indentation fracture test, the bending test on smooth samples, the fracture test on pre-notched or pre-cracked samples, the environment-assisted fracture test, etc. For electrically insulated cracks, the experimental results show a complicated fracture behavior under combined electrical and mechanical loading. Fracture data are greatly scattered when a static electric field is applied. For electrically conducting cracks, the experimental results demonstrate that static electric fields can fracture poled and depoled lead zirconate titanate (PZT) ceramics. A charge-free zone model is introduced to understand the failure behavior of conducting cracks in the depoled lead zirconate titanate ceramics under electrical and/or mechanical loading. These theoretical and experimental results indicate that fracture mechanics concepts are useful in the study of the failure behaviors of piezoelectric materials.
TL;DR: In this paper, the authors give a short overview and a critical discussion about the present state in the field of piezoelectric fracture mechanics, with emphasis on special features like anisotropy, mode mixture and electric properties of cracks.
Abstract: Piezoelectric and ferroelectric materials have gained extensive applications in electromechanical devices, microelectromechanical systems and smart composite materials. In order to assess the strength and durability of those materials and components, exhaustive theoretical and experimental investigations have been performed over the past three decades. The aim of the paper is to give a short overview and a critical discussion about the present state in the field of piezoelectric fracture mechanics. After an introduction, linear piezoelectric fracture theory is explained with emphasis to special features like anisotropy, mode mixture and electric properties of cracks. Next, suggested fracture criteria are presented and contrasted with experimental observations in fracture testing. Cracks under static, cyclic and dynamic loading by electrical and mechanical fields are taken into account. A great challenge is to tackle the non-linear phenomena and ferroelectric domain switching in the fracture process zone. Finally, conclusions are drawn with respect to open problems and desirable future research areas. To limit the scope of the paper, fracture behavior of interface cracks will not be addressed.
TL;DR: In this paper, the influence of preload stress on the ferroelectric hysteretic behavior of piezoelectric ceramics was investigated for soft lead zirconate titanate (PZT) material under various uniaxial compressive stress preloads.
Abstract: This paper deals with the influence of preload stress on the ferroelectric hysteretic behavior of piezoelectric ceramics. The polarization and strain versus electric field hysteresis loops were measured for soft lead zirconate titanate (PZT) piezoceramic material under various uniaxial compressive stress preloads of up to −400 MPa. The investigation revealed that the superimposed compression load reduced the remnant polarization, decreased the coercive field, and also had a significant impact on the dielectric and piezoelectric properties. With increasing mechanical load, dielectric hysteresis and butterfly hysteresis became less and less pronounced, as the compressive stress prevented full alignment of the domains and induced mechanical depolarization. The slopes of the polarization and strain curves at zero electric field were measured to evaluate the dependence of permittivity and piezoelectric coefficients on the prestress. The experimental results were interpreted in terms of the non-180° domain switching process under combined electromechanical loading.
TL;DR: In this article, a phenomenological constitutive law for ferroelectric switching due to multi-axial mechanical and electrical loading of a polycrystalline material is developed, which is based on kinematic hardening plasticity theory and has a switching surface in the space of mechanical stress and electric field.
Abstract: A phenomenological constitutive law for ferroelectric switching due to multi-axial mechanical and electrical loading of a polycrystalline material is developed. The framework of the law is based on kinematic hardening plasticity theory and has a switching surface in the space of mechanical stress and electric field that determines when non-linear response is possible. The size and shape of the switching surface in a modified electric field space remains fixed during non-linear behavior but its center moves around and thus is controlled by a kinematical hardening process. In general, the remanent polarization and the remanent strain are used as the internal variables that control how the center of the switching surface moves. However, the form presented in this paper has a one-to-one relationship between the remanent strain and the remanent polarization, simplifying the constitutive law and allowing remanent polarization to be used as the only internal variable controlling the kinematic effects. The constitutive law successfully reproduces hysteresis and butterfly loops for ferroelectric ceramics. The hysteresis and butterfly loops respond appropriately to the application of a fixed compressive stress parallel to the electric field. In addition, the law successfully handles remanent polarization rotation due to the application of electric field at an angle to the polarization direction.