Fully Coupled 3-D Modelling of Ferroelectric Polycrystalline Material Behavior
- PDF / 146,145 Bytes
- 6 Pages / 612 x 792 pts (letter) Page_size
- 103 Downloads / 250 Views
CC4.9.1
Fully coupled 3-D modelling of ferroelectric polycrystalline material behavior V. Mehling, Ch. Tsakmakis and D. Gross Institute of Mechanics, Technical University Darmstadt, Hochschulstrasse 1, 64289 Darmstadt, Germany ABSTRACT A thermodynamically consistent phenomenological model for the material behavior of polycrystalline ferroelectric ceramics is presented. The internal state of the material is described by two internal state variables. The first one is a second-order texture tensor, determining a simple orientation distribution function (ODF) for the axes of the crystal unit cells. The second is the vector of relative irreversible polarization. The irreversible strains are derived from the ODF by volume averaging. The polarization saturation states are calculated by summing up the possible contributions of all cells to the overall polarization. An invariant formulation of the piezoelectric law is applied. Analogous to the thermodynamical framework of rate-independent plasticity, driving forces and evolution laws for the internal state variables are established. Saturation and coupling of the switching behavior are governed by energy barrier functions introduced in the electric enthalpy function. Numerical examples illustrate the models capabilities. INTRODUCTION Piezoelectricity is used in a wide field of application for actuation and sensoring. Piezoelectric materials with the capability of repolarization under high electrical or mechanical fields are called ferroelectrics. The microscopic reason for repolarization is the switching of unit cells or of domains within the crystal from one polarization state to another. The uni-axial hysteresis loops have been reported by a large number of authors (e.g. [11, 4, 14]), but only few multi-axial experiments have been conducted [5]. Accordingly, although the number of publications addressing the simulation of uni-axial behavior of ferroelectric materials is large, the development of reliable three-dimensional models is still subject to intensive research. For an overview of the literature the reader is referred to the review articles by Kamlah [7] and Landis [10]. The model discussed in this paper is presented in detail in [12]. It partly relies upon previous works by Kamlah&Jiang [8] and Landis [9]. Analogous to the former we chose a set of internal state variables, which has a sound microscopical motivation. The irreversible strain tensor and polarization vector are then formulated as functions of these internal state variables. Similar to incremental plasticity theory, a convex switching surface, combined with an associated switching rule is used to determine the rates of change of internal state variables. Energy barrier functions are used to model the saturation of irreversible strain and polarization, the saturation states being defined by the boundaries of the admissible range of the internal state variables. Unlike most approaches, we do not assume the linear piezoelectric law to be isotropic in its elastic and dielectric parts. We adopt the coordinat
Data Loading...
