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Modeling of piezoelectric composite transducers

Contact : André Preumont

Piezoelectric actuators and sensors have been widely used in active vibration control applications. PZT ceramics are commonly used due to their good actuation capability and very wide bandwidth. The major drawbacks of these ceramics are their brittle nature, and the fact that they cannot be easily attached to curved structures. In order to overcome these drawbacks, two techniques have been developed: (i) thick film deposition of PZT which requires that the part be heated at 900 °C for sintering, and (ii) using packaged PZT composites which can be glued on curved structures. This research topic focuses on the second alternative.

A typical piezocomposite transducer is made of an active layer sandwiched between two soft thin encapsulating layers (Fig.1). The packaging plays two different roles: (i) applying prestress to the active layer in order to avoid cracks, and (ii) bringing the electric field to the active layer through the use of a specific surface electrode pattern. The active layer can be made of bulk PZT or a combination of PZT fibers and an epoxy matrix, and the fibers can take different shapes (round or rectangular)

Fig. 1 : Overview of flat piezocomposite transducers with surface electrodes

A major issue with this kind of transducer comes from the very large difference in the dielectric permittivities of the piezoelectric fiber (εr =1850) and the epoxy matrix (εr=4). This results in a drastic reduction of the electric field applied to the active fiber if a small layer of epoxy is trapped between the electrodes and the fibers (Fig. 2).

Fig. 2 : Electric field in the round PZT fiber as a function of the thickness of the epoxy layer between the electrodes and the fibers.

Macro Fiber Composites (MFC, Fig. 3) first developed at NASA and currently sold by the company Smart Material do not suffer from this problem too much because of the rectangular shape of the fibers which allows to bring the electrodes in direct contact with the fibers.

Fig. 3 : MFC transducer

The modeling of such transducers attached to thin structures is however not straightforward. The analysis of multi-layer shells including piezoelectric layers can be performed using finite element formulations. MFCs are made of several layers (electrode layer, glue layer, active layer), some of which may consists of different materials. For an accurate modeling of these devices, a detailed description of the layer sequence and thicknesses, as well as equivalent, homogeneous mechanical, piezoelectric and dielectric properties of each layer is needed. Unfortunately, the manufacturer only provides global information about the transducers, such as the total thickness, the free strain in the fiber direction, the blocking force, the capacitance, etc. This information is not sufficient to build accurate numerical models of structures with embedded piezocomposites.

This is the motivation for the development of analytical mixing rules for MFCs which give the homogenized properties of the active layer, based on the material properties from the constituents (epoxy and PZT) and the volume fraction of fibers.

Mixing rules for Macro Fiber Composites

We have developed analytical mixing rules for the active layer of MFCs using the Uniform Field Method (UFM) under the plane stress hypothesis. The expressions found are in good accordance with the classical results of layered composite materials: (i) for the mechanical properties, (ii) for the piezoelectric properties (considering the thermal analogy), and (iii) for the dielectric properties (capacitors). As an example, we give here below the mixing rules for the piezoelectric properties of d31 MFCs (Mixing rules have also been developed for d33 MFCs, ρ is the volume fraction of fibers).

These analytical mixing rules have been validated using finite element homogenization.