**4. Results and discussion**

We first consider the PZT stack actuators under DC electric fields. Figure 7 shows the predicted normal strain ε*zz* versus temperature *T* at x = 0 mm, *y* = *Wp*/2 + *he* = 3.1 mm and *z* = 0 mm of the PZT stack actuators for mole fraction X = 0.44 and 0.56 with *a* = *Wp* = 5.2 mm (full electrodes) under DC electric field *E*0 = *V*0/*hp* = 0.1 MV/m (*f* = 0 Hz). Also shown are the measured data (average of four values) for X = 0.44. The electric field induced stain of the PZT stack actuator for X = 0.44 decreases with decreasing temperature due to a shift in the MPB. We see that the trend is sufficiently similar between the prediction and measurement. On the other hand, the electric field induced stain of the PZT stack actuator for X = 0.56 tends to increase with decreasing temperature reaching a peak at about *T* = 20 K and then decrease in magnitude. Figure 8 shows the predicted normal strain ε*zz* versus DC electric field *E*0 at x = 0 mm, *y* = 3.1 mm and *z* = 0 mm (strain measurement location) of the PZT stack actuators for X = 0.56 with *a* = 5.0 mm (partial electrodes) and *a* = *Wp* = 5.2 (full electrodes) at liquid hydrogen temperature (20 K). Strain versus electric field curves show nonlinear behavior due to the polarization switching under high negative DC electric fields. Small difference is observed in the DC electric field induced strains for *a* = 5.0 and 5.2 mm. Figure 9 shows the polarization switching zones near the electrode tip (*x* = 2.4 mm) at *y* = 0 mm plane of the PZT layer for X = 0.56 with *a* = 5.0 mm (partial electrodes) at 20 K. The coercive electric field at 20 K is about 1.65 MV/m. As the negative DC electric field increases, the area of the switched region grows.

We next consider the PZT stack actuators under AC electric fields. Figure 10 shows the normal strain ε*zz* versus electric field amplitude *E*0 at *x* = 0 mm, *y* = 3.1 mm and *z* = 0 mm of the PZT stack actuators for X = 0.44 and 0.56 at frequency *f* = 400 Hz and *T* = 20 K. The dashed line represents the strain computed by the FEA without domain wall motion effect, and the solid line represents the strain after the domain wall motion effect has been applied. The open circle denotes the experimental data. As AC electric field increases, the strain increases gradually away from the linear curve. This is due to the domain wall motion under the influence of AC electric fields. It can be seen that agreement between analysis with domain wall motion effect and experiment is fair. Figure 11 shows the distribution of the normal component of stress σ*zz* as a function of *x* at *y* = 0 mm and *z* = 0.025 mm of the PZT stack actuators for X = 0.44 and 0.56 with *a* = 5.0 mm (partial electrodes) and *a* = *Wp* = 5.2 mm (full electrodes) under *E*0 = 1.65 MV/m at *f* = 400 Hz and 20 K. The coercive electric field at 20 K is about 1.65 MV/m. In the case of the PZT stack actuator with full electrodes, small difference is observed for X = 0.44 and 0.56. For the PZT stack actuators with partial electrodes, a high normal stress occurs near the electrode tip (*x* = 2.4 mm) as is expected. Figure 12 shows the electric field distribution *Ez* as a function of *x* at *y* = 0 mm and *z* = 0.025 mm for the PZT stack actuators with *a* = 5.0 mm (partial electrodes) and *a* = 5.2 mm (full electrodes) under *E*0 = 1.65 MV/m at *f* = 400 Hz and 20 K. For the PZT stack actuators with partial electrodes, a high electric field is observed near the electrode tip.

650 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

specimens are experimented, and four strain values are obtained.

decrease in magnitude. Figure 8 shows the predicted normal strain

0.214 and 1100 kg/m3, respectively.

**4. Results and discussion** 

of the switched region grows.

ε

normal strain

ε

predicted normal strain

actuator is coated with epoxy layer of thickness *he* = 0.5 mm. The total dimensions of the specimen are width of 6.2 mm and length of 40.5 mm. Table 1 lists the material properties of N-10. The coercive electric field of N-10 at room temperature is approximately *Ec* = 0.36 MV/m. Young's modulus, Poisson's ratio and mass density of epoxy layer are 3.35 GPa,

The actuator is bonded to the test rig of a SUS304 stainless steel plate using epoxy bond, and DC voltage (0 Hz) and AC voltage (400 Hz) are applied using a power supply. Two strain gages are attached at the center of the *y* = ± 3.1 mm planes, and the magnitude of strain is measured. To control the temperature of the actuator, an automated helium refill system (TRG-300, Taiyo Toyo Sanso Co. Ltd., Japan) is used. For the reliability of the test, two

We first consider the PZT stack actuators under DC electric fields. Figure 7 shows the

0 mm of the PZT stack actuators for mole fraction X = 0.44 and 0.56 with *a* = *Wp* = 5.2 mm (full electrodes) under DC electric field *E*0 = *V*0/*hp* = 0.1 MV/m (*f* = 0 Hz). Also shown are the measured data (average of four values) for X = 0.44. The electric field induced stain of the PZT stack actuator for X = 0.44 decreases with decreasing temperature due to a shift in the MPB. We see that the trend is sufficiently similar between the prediction and measurement. On the other hand, the electric field induced stain of the PZT stack actuator for X = 0.56 tends to increase with decreasing temperature reaching a peak at about *T* = 20 K and then

field *E*0 at x = 0 mm, *y* = 3.1 mm and *z* = 0 mm (strain measurement location) of the PZT stack actuators for X = 0.56 with *a* = 5.0 mm (partial electrodes) and *a* = *Wp* = 5.2 (full electrodes) at liquid hydrogen temperature (20 K). Strain versus electric field curves show nonlinear behavior due to the polarization switching under high negative DC electric fields. Small difference is observed in the DC electric field induced strains for *a* = 5.0 and 5.2 mm. Figure 9 shows the polarization switching zones near the electrode tip (*x* = 2.4 mm) at *y* = 0 mm plane of the PZT layer for X = 0.56 with *a* = 5.0 mm (partial electrodes) at 20 K. The coercive electric field at 20 K is about 1.65 MV/m. As the negative DC electric field increases, the area

We next consider the PZT stack actuators under AC electric fields. Figure 10 shows the

the PZT stack actuators for X = 0.44 and 0.56 at frequency *f* = 400 Hz and *T* = 20 K. The dashed line represents the strain computed by the FEA without domain wall motion effect, and the solid line represents the strain after the domain wall motion effect has been applied. The open circle denotes the experimental data. As AC electric field increases, the strain increases gradually away from the linear curve. This is due to the domain wall motion under the influence of AC electric fields. It can be seen that agreement between analysis

*zz* versus electric field amplitude *E*0 at *x* = 0 mm, *y* = 3.1 mm and *z* = 0 mm of

*zz* versus temperature *T* at x = 0 mm, *y* = *Wp*/2 + *he* = 3.1 mm and *z* =

ε

*zz* versus DC electric

**Figure 7.** Strain vs temperature of PZT stack actuators for X = 0.44 and 0.56 under DC electric field *E*0 = 0.1 MV/m.

**Figure 8.** Strain vs DC electric field of PZT stack actuators for X = 0.56 at 20 K.

**Figure 9.** Polarization switching zones at *y* = 0 mm plane of PZT layer for *X* = 0.56 at 20 K, induced by DC electric field (a) *E*0 = -1.5 MV/m, (b) *E*0 = -1.64 MV/m and (c) *E*0 = -1.72 MV/m.

**Figure 10.** Strain vs AC electric field of PZT stack actuators for X = 0.44 and 0.56 at 20 K.

FEA

**Figure 8.** Strain vs DC electric field of PZT stack actuators for X = 0.56 at 20 K.

*x* = 0 mm *y* = 3.1 mm *z* = 0 mm

*f* = 0 Hz

(a)

2.4 mm

(b)

(c)

DC electric field (a) *E*0 = -1.5 MV/m, (b) *E*0 = -1.64 MV/m and (c) *E*0 = -1.72 MV/m.

**Figure 9.** Polarization switching zones at *y* = 0 mm plane of PZT layer for *X* = 0.56 at 20 K, induced by

Poling


*E*0 (MV/m)

*T* = 20 K

*E*0 = -1.5 MV/m

*T* = 20 K

*X* = 0.56

*a* = 5.2 mm = 5.0 mm

= -1.64 MV/m

= -1.72 MV/m

*f* = 0 Hz

*x*

0.1 mm

*z*

*X* = 0.56

*a* = 5.0 mm


ε*zz* (10-6)

0

1000

O

*y* = 0 mm plane

**Figure 11.** Variation of normal stress *σzz* as a function of *x* at *y* = 0 mm and *z* = 0.025 mm for PZT stack actuators under AC electric field *E*0 = 1.65 MV/m at *T* = 20 K.

**Figure 12.** Variation of electric field *Ez* as a function of *x* at *y* = 0 mm and *z* = 0.025 mm for PZT stack actuators under *E*0 = 1.65 MV/m at *T* = 20 K.

#### **5. Conclusions**

Numerical and experimental examination on the electromechanical response of PZT stack actuators at cryogenic temperatures is reported. It is found that the electric field induced strain decreases or increases with decreasing temperature depending on the mole fraction. That is, in the case of high performance PZTs for X = 0.44, the electric field induced strain is very high at room temperature, whereas in the case of PZTs for X = 0.56, the electric field induced strain at cryogenic temperatures will seem to be higher than at room temperature. It is also shown that the stress and electric field in the PZT layers are very high near the electrode tip for the PZT stack actuators with partial electrodes, although the electric field induced strains at the center of the surface for the partially and fully electroded PZT stack actuators have the same level. This study may be useful in designing high performance hydrogen fuel injectors.

#### **Author details**

Yasuhide Shindo and Fumio Narita *Tohoku University, Japan* 

#### **6. References**

654 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

*E*0 = 1.65 MV/m

*T* = 20 K

*f* = 400 Hz

*y* = 0 mm *z* = 0.025 mm

**Figure 12.** Variation of electric field *Ez* as a function of *x* at *y* = 0 mm and *z* = 0.025 mm for PZT stack

FEA with domain wall motion effect

*a* = 5.2 mm = 5.0 mm

*X* = 0.44

*X* = 0.56

2.2 2.3 2.4 2.5 2.6

*x*(mm)

Numerical and experimental examination on the electromechanical response of PZT stack actuators at cryogenic temperatures is reported. It is found that the electric field induced strain decreases or increases with decreasing temperature depending on the mole fraction. That is, in the case of high performance PZTs for X = 0.44, the electric field induced strain is very high at room temperature, whereas in the case of PZTs for X = 0.56, the electric field induced strain at cryogenic temperatures will seem to be higher than at room temperature. It is also shown that the stress and electric field in the PZT layers are very high near the electrode tip for the PZT stack actuators with partial electrodes, although the electric field induced strains at the center of the surface for the partially and fully electroded PZT stack actuators have the same level. This study may be useful in designing high performance

actuators under *E*0 = 1.65 MV/m at *T* = 20 K.

0

1

*Ez*

(MV/m)

2

**5. Conclusions** 

hydrogen fuel injectors.

*Tohoku University, Japan* 

Yasuhide Shindo and Fumio Narita

**Author details** 

	- Shindo, Y., Sasakura, T. & Narita, F. (2012). Dynamic electromechanical response of multilayered piezoelectric composites from room to cryogenic temperatures for fuel injector applications, *ASME Journal of Engineering Materials and Technology*, in press.
