Composite Materials Research Progress

Eletromechanical Field Concentrations and Polarization Switching... 263
element in a material. The electric potential φ is applied, and the electromechanical fields
of each element are computed from the finite element analysis (FEA). The switching criterion
of Eq. (19) or (26) is checked for every element to see if switching will occur. After
all possible polarization switches have occurred, the piezoelectric tensor of each element
is rotated to the new polarization direction. The electroelastic fields are re-calculated, and
the process is repeated until the solution converges. The macroscopic response of the material
is determined by the finite element model, which is an aggregate of elements. The
spontaneous polarization P s and strain γ s are assigned representative values of 0.3 C/m 2
and 0.004, respectively. Our previous experiments [8] verified the accuracy of the above
scheme, and showed that the results obtained are of general applicability.
3.2. Experiments
The actuator discussed in this section was fabricated using a soft lead zirconate titanate
(PZT) C-91 [9]. The material properties are listed in Table 1, and the corcive electric field
is approximately Ec = 0.35 MV/m. The dimensions of the specimen are L = 30 mm, W =
10 mm, and 4h = 20 mm. The electrode length is a = 20 mm. The specimen was placed
on the rigid floor.
The high-voltage amplifier was limited to 1.25 kV so that a 0.25 MV/m field corresponded
to a layer thickness of 5.0 mm. Strain gauges were placed around the electrode tip
region. The sensors have an active length of 0.2 mm.
Table 1. Material properties of C-91.
Elastic stiffnesses Piezoelectric coefficients Dielectric permittivities
(×1010N/m2 ) (C/m2 ) (×10−10C/Vm) c11 c12 c13 c33 c44 e31 e33 e15 ɛ11 ɛ33
C-91 12.0 7.7 7.7 11.4 2.4 −17.3 21.2 20.2 226 235
3.3. Results and Discussion
We first present analytical and experimental results for L = 30 mm, W = 10 mm, and
4h =20mm. The electrode length is a = 20 mm. Fig. 2 shows the finite element analysis
results for the strain εzz versus electric field E0 = V0/h at the face of the actuator (at
y =5mm plane) for x = 5 mm and z = 0.8 mm. For the polarization switching effect, the
predictions based on work (Eq. (19)) and energy density (Eq. (26)) are shown. Also plotted
are the experimental data in the range approximately ± 0.18 MV/m. Calculation results
show that a monotonically increasing negative electric field causes polarization reversal.
Polarization switching in a local region leads to a significant increase of compressive strain
within the actuator when compared to the linear case. After the electric field reaches about
−0.20 (0.24) MV/m, local polarization switching, based on work (energy density), can
cause an unexpected decrease in compressive strain near the electrode tip during switching.