Developments in Ceramic Materials Research

Progress in Porous Piezoceramics 219
polymer composite (1821x10 -15 Pa -1 ). This improvement is more pronounced in the case of
the 20% PZT-air composite, which has a value of 15095x10 -15 Pa -1 .
3. EFFECTIVE MATERIAL PARAMETERS
Consider a 3-3 piezocomposite made up of porous piezoceramic and polymer
components. The material coefficients of the piezoelectric resonators can be accurately
determined from the measured electrical impedance spectrum [35]. Different sets of
coefficients are determined from different shapes of the piezoelectric resonators and exciting
them in specific modes, viz., thickness-mode of thin plates, radial-mode of discs, axial-mode
of thin rods, lateral-mode of bars and so on. However, it is sometimes difficult to prepare
piezocomposite specimens in all shapes. Approximate material properties of composites can
be easily determined using rule of mixtures. Effective material parameters of piezocomposites
can be determined from the material parameters of the constituent phases, viz. piezoceramic
and polymer [6, 11].
3.1. Constitutive Relations
The effective material parameters of a composite are strong functions of the amount of
ceramic and polymer components present in it. Some parameters obey simple linear relations
and others do not. Several material parameters can be determined from the constitutive
relations described in this section.
The density of the composite is given by,
c
ρ = ρ v + ρ v
c
p
p
where ρ and v are the density and volume fraction of the ceramic and polymer phases marked
by the superscripts c and p, respectively. The bar over the character represents the effective
materials parameters of the composite.
The acoustic impedance is given by,
D
Z aco = c33
ρ
The stiffness coefficient at constant electric field is given by,
c
E
33
= v
c
⎡
⎢c
⎢
⎣
E
33
−
v
c
p E 2
2v
( c13
− c12
)
p E E
( c + c ) + v ( c + c )
11
12
11
12
⎤
⎥ + v
⎥
⎦
The dielectric permittivity at constant strain is given by,
p
c
(1)
(2)
(3)