Anisotropic piezoelectric properties of 1–3 ceramic / polymer composites comprising rods with elliptic cross section

Abstract

This paper is concerned with the study of effective piezoelectric properties of 1–3 ferroelectric ceramic / polymer composites. The aim of this paper is to show the role of a combination of the electromechanical properties of components and microgeometry of the 1–3 composite in determining its anisotropic piezoelectric response. The system of ceramic rods in the form of elliptic cylinders is an important microgeometric factor that influences the piezoelectric coefficients and their anisotropy. Examples of the piezoelectric response and anisotropy are analysed for the 1–3 composites based on either “soft” or “hard” ceramic and having either piezo-active or piezo-passive matrix. Combinations of the ceramic and polymer components are found that provide different volume-fraction dependences of the piezoelectric coefficients d3j*d3jand g3j*g3j: both monotonic, both non-monotonic, monotonic d3j*d3jand non-monotonic g3j*g3j, and vice versa. Examples of volume-fraction dependences of electromechanical coupling factors k3j*k3jare also considered. A comparison of the effective piezoelectric coefficients calculated by the effective field method and the finite element method is carried out for different compositions in wide ranges of the ratio of semiaxes of the ellipse and of volume fractions of the components. Good agreement between data calculated by means of the aforementioned methods is obtained for the 1–3 structure comprising the elliptic cylinders

Analytical and semi-analytical modeling of effective moduli bounds: Application to transversely isotropic piezoelectric materials

“…Calculations, done by Topolov and Bisegna (2010) and by Topolov et al (2011), are used for comparison of the incremental DS and US bounds developed in this article. Room-temperature electroelastic moduli of the constituents, used in our predictions, are given in Table 2.…”

“…These values are obtained from the books by Dantsiger et al (1994) and Levassort et al (1997). The comparison given in Table 3 shows the predictions obtained by the developed analytical bound relationships as well as with the incremental DS and US bounds ( n = 50) with those obtained by the element-free method (EFM) and the finite element method (FEM) of Topolov and Bisegna (2010). These predictions are carried out for the piezoelectric coefficients d 31 , d 32 , d 33 , and d h of composites with 0.01 ≤ η = b / a ≤ 1 and show very good agreements for a wide range fiber sections and volume fractions.…”

“… Predictions are obtained based on the element-free method (EFM) and the finite element method (FEM; Topolov and Bisegna, 2010) and on the downstream (DS), the upstream (US), and the analytical expressions of Hashin–Shtrikman lower (HSL) and Hashin–Shtrikman upper (HSU) bounds developed here. US and DS predictions are obtained by n = 50 steps. a see Topolov and Bisegna (2010). …”

1‐3‐Type Composites Based on Ferroelectrics: Electromechanical Coupling, Figures of Merit, and Piezotechnical Energy‐Harvesting Applications

“…In Figure , C1 is the main (FE) component with a high piezoelectric activity and C2 is the matrix component that can be either piezoelectric or piezopassive. The cross‐section of the FE ceramic rod in the ( X 1 OX 2 ) plane (Figure , insets 1 and 2) can be in the form of a circle, triangle, square, ellipse, etc . In the 1‐3 composite based on FE SCs, the system of crystal rods that are poled along a specific crystallographic direction is often surrounded by a polymer matrix .…”

“…The effective properties calculated using the effective field method are compared to the effective properties calculated by means of the matrix method and finite element method . Based on the full set of electromechanical constants (i.e., elements of ∥ C *∥ from Equations (1) or (4)) and conventional formulae for the piezoelectric medium, we calculate the following effective parameters of the composite:…”