Introduction
Chapter 1: Introduction
1.3 Piezoelectric fiber composites
The monolithic piezoelectric sensors and actuators are immensely utilized in the development of smart structures as it is observed from the review of literature in
the previous section. The piezoelectric ceramics are easily available at low cost, and this may be a reason for its wide utilization in the development of smart structures.
However, in the structural applications, the piezoelectric sensors and actuators are usually used in the form of the patch or the layer. The piezoelectric patch or layer is attached to the surface of the host structure or embedded in the domain of the host structure. For this kind of integration of the piezoelectric sensors/actuators with the host structure, they need to possess sufficient flexibility and conformability.
The flexibility is also an important property of a piezoelectric sensor/actuator for its utilization under the circumstance of the moderate or large amplitude of vibration of a smart structure, while the conformable actuators are required for a host structure with curved boundary surfaces or complex geometry. Apart from these properties, a piezoelectric actuator is expected to be capable of providing sufficient control force as well as directional actuation. With reference to these required properties of a piezoelectric actuator, the monolithic piezoelectric actuators have several disadvantages like high stiffness, low strain energy density, insufficient flexibility and poor conformability. These actuators are also incapable of providing directional actuation. In view of these discrepancies, the piezoelectric actuators are made in the form of polymer-based composites with the inclusions of piezoelectric ceramics. The polymer constituent provides sufficient flexibility and conformability of the actuator, while the piezoelectric properties of the composite arise due to the inclusions of piezoelectric ceramics. The piezoelectric inclusions may be of different forms like particles, long fibers, short fibers, flakes etc., while most of the available piezoelectric composites are comprised of long/short piezoelectric fibers. In this section, a review of literature on the development of short/continuous (long) piezoelectric fiber-reinforced composites (PFCs) is presented.
1.3.1 Design of piezoelectric fiber composites (PFCs)
The first PFC appeared due to Chan and Unsworth (1989). Subsequently, Smith and Auld (1991) proposed a vertically reinforced 1-3 PFC that is capable of providing thickness mode actuation for an externally applied transverse electric field. Later, an exhaustive research has been carried out by many researchers and various PFCs have been developed. Bent (1999) and Bent and Hagood (1997) proposed Active Fibre Composite (AFC). In AFC, the unidirectional piezoelectric fibres are aligned in the plane of the PFC lamina. But the poling direction of the
Chapter 1: Introduction
fibres is their longitudinal direction so that this PFC produces the in-plane actuation force when the external electric field is applied along the longitudinal direction through a unique arrangement of electrodes (Interdigitated Electrodes (IDEs)). After the proposition of the AFC, a similar PFC was developed at NASA using the piezoelectric fibres of rectangular cross-section (High and Wilkie, 2003) instead of the fibres of circular cross-section (Bent, 1999). This PFC (High and Wilkie, 2003) is known as Macro-Fibre Composite (MFC). As a novel contribution, Raja and Ikeda (2008) designed a shear actuated fiber composite (SAFC), and estimated its effective electromechanical behaviour for the shear mode of actuation.
1.3.2 Analytical and FE evaluation of effective properties of PFCs
Wang (1992) derived the analytical relations between the overall properties of the 0- 3 PFC and the properties of its constituents. Bing et al. (1997b) and Jiang et al.
(1999) derived the closed-form solutions for effective electro-elastic moduli of the piezoelectric composites comprised of ellipsoidal inclusions. Poizat and Sester (1999) estimated the effective piezoelectric constants as the functions of the fiber- volume fraction (FVF) and the fiber-aspect ratio for 1-3 and 0-3 PFCs. Pettermann and Suresh (2000) predicted all the moduli of a 1-3 PFC comprised of a dielectric matrix and piezoelectric fibers. Bowen et al. (2001) and Bowen and Kara (2002) studied the effects of FVF and elastic modulus of the polymer phase on the hydrostatic piezoelectric voltage constant and hydrostatic strain constant of 3-3 PFCs. Kari et al. (2007) investigated the effects of diameter and arrangement of fibers on the effective properties of unidirectional PFCs.
Berger et al. (2005a, 2005b, 2005c, 2006) proposed an FE procedure for estimation of effective properties of unidirectional and uniaxial periodic 1-3 PFCs.
Kar-Gupta and Venkatesh (2005, 2007a, 2007b) studied the effects of fiber distribution and poling direction on the electromechanical behaviour of a 1-3 PFC.
Ho et al. (2006) derived two new explicit formulae for prediction of effective piezoelectric coefficients of binary 0-3 piezoelectric composites. Ray (2006a) proposed an electrode arrangement for applying a uniform transverse electric field across the thickness of a 1-3 PFC, and derived the corresponding effective properties of the PFC. Deraemaeker et al. (2007) presented an FE procedure for estimation of effective properties of MFC actuator. The corresponding results are also compared with the similar results obtained using Uniform Fields Method
(UFM). Kar-Gupta and Venkatesh (2008) studied the effects of geometrical connectivity, volume fraction, grain size distribution and poling direction of piezoelectric inclusions on the electromechanical properties of five types of piezoelectric composites (particulate, short-fiber, long-fiber, laminate and networked composites). Using the mixing rules, Deraemaeker et al. (2009) estimated the effective piezoelectric coefficients of d33 and d31 MFCs. These estimated coefficients were also substantiated by the computation of the same coefficients using FE procedure. Deraemaeker and Nasser (2010) evaluated the properties of d33 and d31 MFCs using the FE procedure and compared the results with the similar analytical results.
Trindade and Benjeddou (2011) evaluated the effective material properties of a shear actuated d15 MFC using FE procedure and validated the results with the similar analytical results (Benjeddou and Al-Ajmi, 2011). Nasser et al. (2011) computed the effective electromechanical properties of MFC using UFM. Berger et al. (2010) presented the effective electromechanical behaviour of PFCs comprised of arbitrary fiber distributions. Li et al. (2011) studied the effects of geometric properties of piezoelectric phase on the electromechanical coupling coefficients of 1–
3 PFCs. Chambion et al. (2011) analyzed the importance of the filler arrangement to optimize the electromechanical response of 0-3 composites (piezoelectric particle composites). Brenner et al. (2012) analytically investigated the effective piezoelectric response of 2-1-2 piezoelectric composite. Sakthivel and Arockiarajan (2010) studied thermo-electro-mechanical behaviour of 1-3 PFCs and demonstrated the thermal effect on the overall properties of 1-3 PFCs. The same authors (Sakthivel and Arockiarajan (2011, 2012)) also presented the effects of poling of matrix and fiber orientation on the thermo-electro-mechanical behaviour of 1-3-2 piezoelectric composites where both fiber and matrix are piezoelectrically active. Kalamkarov and Savi (2012) presented analytical expressions of a smart composite structure that is reinforced with a periodic grid of generally orthotropic cylindrical reinforcements. Trindade and Benjeddou (2012) proposed a novel electrode design for d15 thickness-shear MFC (Trindade and Benjeddou, 2011). They also carried out parametric studies to investigate the effects of FVF, epoxy elastic modulus, electrode and active layer thicknesses on the effective material properties of the shear MFC. Prasath and Arockiarajan (2013) developed an analytical model to evaluate the effective electromechanical properties of d33 and d31 MFCs. Kranz et
Chapter 1: Introduction
al. (2013a, 2013b) presented FE analysis of the effective properties of d15 shear MFC based on the enthalpy-based homogenization method.
Iyer and Venkatesh (2014) presented an analytical model to estimate the effective properties of the 3–0 and 3–1 piezoelectric composites and validated the model by computing the properties using FE procedure. Fu et al. (2017) developed an efficient multi-scale FE procedure to investigate the nonlinear electromechanical responses of heterogeneous PFCs.
1.3.3 Effective behavior of PFCs using Micromechanical Approaches
Dunn and Taya (1993) presented the electro-elastic behaviour of PFCs by computing the effective electro-elastic moduli through the extension of dilute, self- consistent, Mori-Tanaka and differential micromechanics theories. Tungyang (1994) and Chen (1996) derived the expressions for the effective thermo-electro-elastic moduli of a PFC employing self-consistent and Mori-Tanaka methods. Benveniste and Dvorak (1992) and Benveniste (1993, 1994) derived the exact solutions for effective constants of binary and multiphase composites with arbitrary phase geometry. Huang and Kuo (1996), Kuo and Huang (1997) and Fakri et al. (2003) developed micromechanical models of PFCs consisting of spatially oriented inclusions and reported the effective electro-elastic behaviour of the PFCs. Aboudi (1998) presented micromechanical generalized method of cells model to predict the thermo-electro-elastic behavior of multiphase piezoelectric composites. . Yu (1999) developed a micromechanical model for analytic estimates of the effective electro- elastic properties of two-phase PFCs. Jiang et al. (2001) developed a generalized self-consistent micromechanical model and obtained the closed-form expressions of the effective electro-elastic coefficients of PFCs under anti-plane shear. Tan and Tong (2001a, 2001b) proposed rectangle and rectangle-cylinder micromechanical models to investigate the linear and nonlinear electro-elastic behaviour of PFCs.
Ruan et al. (2002) developed a three-dimensional micromechanics model to investigate the effects of fiber orientation and matrix properties on the effective piezoelectric properties of a PFC comprised of unidirectional piezoelectric fiber yarn in a polymer matrix. Glushanin and Topolov (2003) proposed a micromechanics model to analyze the electromechanical behaviour of the 1-2 ferroelectric piezoactive ceramic (FEPC) composite comprised of ferroelectric ceramic inclusions in a polymer matrix.
Mallik and Ray (2003) proposed a unidirectional PFC comprised of transversely poled piezoelectric fibers embedded in the epoxy matrix, and derived the effective properties of the PFC using method of cells. Qin (2005) developed a micromechanics model of piezoelectric composites based on boundary element method (BEM), and presented their effective electro-elastic properties for the piezoelectric inclusions of various shapes. Della and Shu (2007, 2008) presented a micromechanics model based on the Mori-Tanaka method for analyzing the electromechanical behavior of 1-3 PFCs comprised of a porous matrix. Challagulla and Venkatesh (2009) developed a micromechanical model based on the AHM for investigating the electro-elastic behaviour of 2-2 PFCs where the constituents were elastically anisotropic and piezoelectrically active. Sabina et al. (2001) derived the closed-form expressions for the effective electro-elastic properties of PFCs employing the Asymptotic Homogenization Method (AHM). Kar-Gupta and Venkatesh (2013) developed an analytical micromechanical model to characterize the effects of phase volume fractions and orientation of the poling direction of piezoelectric inclusions on the effective properties of 2-2 PFCs. Lin and Muliana (2013, 2014) analyzed the nonlinear electromechanical responses of 0-3 and 1-3 PFCs utilizing Mori-Tanaka (MT), Self-Consistent (SC) and Unit-Cell (UC) methods.
Eynbeygui and Aghdam (2015) developed a generalized plane strain (GPS) micromechanics model using the element free Galerkin method to study the electro-elastic behaviour of PFCs.
1.3.4 Experimental studies on the effective behavior of PFCs
Shindo et al. (2010) presented the experimental results for the nonlinear electromechanical responses of a 1-3 PFC consisting of the square or circular piezoelectric rods in an epoxy matrix. Lu et al. (2016) presented experimental results for the effects of voltage amplitude, operating frequency and FVF on the free strain of d33 PFC. Yuan et al. (2017) designed and fabricated a novel d15 shear PFC, and reported its good actuation capability in control of cantilever beams. Zhen et al.
(2008) experimentally determined the electromechanical properties of 1-3 PFC with 10-35% volume fraction of a piezoelectric constituent. Zhou et al. (2012) fabricated and determined the electromechanical properties of a 1-3-2 piezoelectric composite.
Jayendiran and Arockiarajan (2013) experimentally studied the nonlinear electromechanical behaviour of 1-3 PFC for its different FVFs and bulk piezoelectric
Chapter 1: Introduction
ceramics. Dongyu et al. (2015) designed 1-3 PFCs for different distributions of piezoelectric ceramic and matrix phases, and determined their (1-3 PFCs) effective electromechanical properties. Dongyu et al. (2016) designed three types of 1-3 PFCs and addressed great improvements in the electromechanical and acoustic properties of the composites. Trindade and Benjeddou (2016) presented the dependence of the effective properties of d31 MFC on the electric field. Recently, Mi et al. (2017) presented a 1-1-3 piezoelectric composite along with its electromechanical behaviour.