temperature effect on PZT

7/28/2019 temperature effect on PZT

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Chapter 2

Removing Temperature Effects

2.1 Temperature Effects on Piezoelectric Materials

2.1.1 Theory

The electromechanical interaction of a PZT with its host structure is described by

Equation (1.3). The first term in the equation is the capacitive admittance of a free PZT which

appears as a gradual increase in an electrical admittance with frequency. The second term

includes the mechanical impedance of both the PZT and the host structure. When a PZT is

bonded onto a structure, its own mechanical impedance, Za , is basically fixed. Therefore, it is

the structures impedance, Zs , that uniquely determines the contribution of the second term to

the overall admittance. The contribution of the second term shows up in the admittance versus

frequency plot as sharp peaks above the baseline electrical admittance. Since these peaks

correspond to specific structural resonances, they constitute a unique description of the dynamic

behavior of the structure. Hence, changes in this impedance pattern can be attributed to damage

or some other physical change in the structure.

In the first term, the permittivity, 33T

, is known to vary significantly with temperature.

As shown in Equation (2.1), the permittivity is proportional to the relative dielectric constant, K.

Figure 2.1 shows the variation of the relative dielectric constant, K, of typical piezoelectric

materials with temperature change, and where 0 is the permittivity of free space.


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T K farad meter = = 0 012885 10( . / ) (2.1)

Figure 2.1: Influence of temperature on the relative dielectric constant, K [26]

Figure 2.2: Influence of temperature on the piezoelectric strain constant, dx3 [26]

Figure 2.2 shows the variation of the piezoelectric strain constant, dx3 , with temperature

change. These graphs are supplied by a manufacturer [26]. As can be seen in the figures, an

increase in temperature leads to an increase in both the relative dielectric constant and the

piezoelectric strain constant. The 5H shows significant increase in both of them. Although the

5A is less sensitive to temperature changes than the 5H, it still exhibits a significant temperature


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dependency. Also, the Youngs modulus of PZT is known to being slightly dependent on the

change in temperature.

Among the temperature dependent constants, the relative dielectric constant exhibits the

most significant effect on the electric impedance of PZT. It modifies the first term, the capacitive

admittance of free PZT, and causes a baseline shift in the electrical admittance. The piezoelectric

strain constant and the Youngs modulus also result in a baseline shift, however, the effect on the

overall admittance can be negligible compared with the relative dielectric constant.

2.1.2 Experimental Results

In this section, the temperature effects on a free PZT is investigated experimentally.

The experiment was conducted by suspending a PZT (5A) specimen (30 mm x 30 mm x 0.254

mm) inside an oven equipped with a temperature controller (Figure 2.3). Using the controller,

the temperature in the oven was varied from 80 to 160 F (26.7 to 71.1 C) in steps of 20 F. A

Hewlett-Packard electrical impedance analyzer (model HP4194A), which is shown in Figure 2.4,

was used to measure the PZTs electrical impedance. At each step, the impedance was measured

after the temperature had reached steady state. The measured impedance data was transferred

from the impedance analyzer to a PC through a GPIB bus for post processing. All the control,

communication and data acquisition were accomplished by a dedicated software program coded

by a former CIMSS researcher.

Figure 2.3: Oven with a temperature controller


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Figure 2.4: HP4194A electrical impedance analyzer and PC for data transfer

As can be seen in Figure 2.5, an increase in temperature leads to a decrease in the

impedance magnitude. This baseline shift is due to the temperature dependency of piezoelectric

constants as mentioned before. There were no structural resonances of the free PZT existed in

these frequency ranges. The resonant frequencies of the PZT were avoided so we can focus only

on the effect of piezoelectric properties.

80F120F160F

80F120F160F

25 30 35 4040

60

80

100

Frequency kHz

Magnitu

de

V/A

85 90 95 10040

60

80

100

Frequency kHz

Magnitude

V/A

Figure 2.5: Temperature effect on the electrical impedance of a free PZT


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2.2 Temperature Effects on Structure Being Monitored

2.2.1 Theory

In the previous section, it is shown that piezoelectric materials such as PZT have strong

temperature dependency, which causes significant variation of the electrical impedance with

temperature change. In this section, temperature effects on a structure being monitored are

investigated.

The Youngs modulus varies slightly with temperature and the thermal expansion of the

material changes structural dimensions in free structures and induces stresses in constrained

structures. However, to a large extent precise and detailed material property data at slight

temperature variations is lacking. Most of the previous work is concerned with very large

magnitudes of temperature variations at extremely high temperatures, as usually encountered in

the aerospace field, where this structural health monitoring technique may not yet be applicable.

As well, in complex structures, the analytical modeling of the temperature effects would be a

tremendous task. According to the published literature [27], [28], it is obvious that changes in

temperature have a distinct effect on the dynamic properties of structures, which is dependent on

boundary conditions, temperature distribution and structure materials. However, the exact nature

of these relationships in the frequency ranges we test could not be established from previously

developed models.

A simple steel beam with free-free boundary condition is used for the analytical study of

the variations in structural response caused by temperature changes. Only the shifts in resonant

frequencies are discussed here. Experimental investigations have shown that the Youngs

modulus of carbon steel varies linearly with temperature [29]. Thus, the Youngs modulus can

be written as functions of temperature based on its rates of change around reference temperature,


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E T EE

TT T E T ( ) ( )= + = +0 0 0

(2.2)

where E is the Youngs modulus at the measuring temperature, E0 is the Youngs modulus at

the reference temperature, T is the measuring temperature, T0 is the reference temperature, and

is the linear change in Youngs modulus with respect to temperature.

It is also shown experimentally that the coefficient of linear thermal expansion of steel

is approximately constant over the small temperature range. Therefore, the structural dimensions

can be written as functions of temperature,

w w T= +0 1( ) (2.3a)

l l T= +0 1( ) (2.3b)

t t T= +0 1( ) (2.3c)

where w is the width of the beam, w0 is the reference width of the beam, l is the length of the

beam, l0

is the reference length of the beam, t is the thickness of the beam, t0

is the reference

thickness of the beam, and is the mean coefficient of linear thermal expansion.

Due to the thermal expansion, the beam density per unit volume also varies with

temperature. Since the mass of the beam remains the same regardless of temperature and the

beam is assumed isotropic, we can write

= = + = + = +

M

V

M

w l t T

M

V T T0 0 03

0

3

0

31 1 1( ) ( ) ( ) (2.4)

where M is the mass of the beam, is the mass density of the beam, 0 is the mass density of

the beam at the reference temperature, V is the volume of the beam, and V0 is the volume of the


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beam at the reference temperature.

The natural frequencies of the free-free beam in bending has well-known solutions for

the first several modes, which is:

fEI

Ar

r=

2

2(2.5)

where fr is the natural frequency in Hz of the rth bending mode,

ris the weight for the rth

bending mode, I is the area moment of inertia of the beam, and A is the area of the cross

section of the beam.

For a beam with a constant rectangular cross section, I wt= 3 12 and A wt= . Then,

Equation (2.5) can be rewritten to account for the temperature dependency of the material

properties by incorporating Equations (2.2) - (2.4) as follows:

fl t

l

E T Tr

r=+ +( ) ( )( )

2

0

0

2

0

04

1

3

(2.6)

and, since the natural frequency at the reference temperature can be expressed as,

fl t

l

Er

r

0

2

0

0

2

0

04 3=

( )

(2.7)

then the ratio of the natural frequency shifting with temperature can be defined as follows:

f

f

E T T

E

r

r0

0

0

1=

+ +( )( ) (2.8)


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The following values are used for material properties of steel.

E0 = 2.1 x 1011 N/m2, = 6.0 x 10-6, = -3.7 x 107 N/m2

Therefore, the term ( )E T0 + in this equation is dominant for changes in temperature.

Figure 2.6 shows the ratio of the natural frequency of steel beam to the natural frequency at the

reference temperature, f fr r0 , as a function of temperature. The reference temperature is 75 F.

The result indicates that an increase in temperature leads to a decrease in resonant frequencies.

This is due to the Youngs modulus effect because is a negative value. On the other hand, the

thermal expansion increases the resonant frequencies of beam, though the effect is very small.

0 50 100 150 200 250 3000.98

0.985

0.99

0.995

1

1.005

1.01

Temperature F

Ratio

ofNaturalFrequency(1at75F)

Figure 2.6: Predicted ratio of natural frequency of the steel beam shifting with temperature

(reference temperature = 75 F)

2.2.2 Experimental Results

The experiments were performed in the following manner. First, the effect of


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temperature on the resonant frequencies and peak resonant magnitude of the beam was

investigated at low frequency range. Next, the temperature effect on the interaction between a

PZT and its host structure was examined. A free-free steel beam (30 mm x 250 mm x 0.85 mm)

with a PZT bonded in the middle was used.

The beam was put into the oven mentioned before and the measurements were also

taken in the temperature range of 80 to 160 F. Figure 2.7 is a schematic of the experimental

setup. For the first experiment, the beam was excited by the PZT bonded in the middle. A

Kistler miniature accelerometer (model 8728A500) and a PCB signal conditioner (model

482A16) were used to measure the response acceleration of the beam and the frequency response

function (FRF) was obtained by a Tektronix FFT analyzer (model 2630). Secondly, the electrical

impedance of the PZT was measured by using a Hewlett-Packard electrical impedance analyzer

(model HP4194A). The measurements were taken at two frequency ranges, 3 to 5 kHz and 70 to

80 kHz. The first one is to compare with the FRF of the beam and the second one is the

frequency range at which the impedance-based structural health monitoring technique is normally

used.

FFT Analyzer

Computer (PC)

Excitation Voltage

Signal Conditioner

Accelerometer

Impedance Analyzer

Computer (PC)

PZT

Oven with Temperature Controller

PZT

Beam

Figure 2.7: Schematic of the experiment on temperature effects


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The FRF of the free-free steel beam is shown in Figure 2.8. The numerator of the FRF

is the output voltage from the accelerometer on the beam and the denominator is the input

voltage to the PZT. It is observed that an increase in temperature leads to shifting of resonant

frequencies and fluctuations in peak response magnitude. The shifting of the peak frequencies

indicates a variation in the structural stiffness, caused by changes in the material and structural

dimensional properties. Likewise, variations in the peak response magnitude suggest a damping-

related phenomenon. Hence, it can be said that a combination of both structural stiffness and

damping variations are involved in temperature change. Incidentally, the resonance near 3.6 kHz

is the 10th bending mode and 4.4 kHz is the 11th bending mode

80F120F160F

3 3.5 4 4.5 510

-2

10-1

100

Frequency kHz

Magnitude

V/V

Figure 2.8: FRF of the steel beam with temperature change

Figure 2.9 indicates the comparison of the analytical frequency shift with the

experimental. The solid line represents the analytically predicted value and the asterisks

represent the averaged experimental results of the first ten bending modes. Both demonstrate thesame characteristics, i.e., the natural frequencies decrease as temperature increases. The error

between the predicted and measured natural frequencies is less than 1 %.


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AnalyticalExperimental

50 100 150 2000.98

0.985

0.99

0.995

1

1.005

1.01

1.015

1.02

Temperature F

RatioofNaturalFrequency(1at80F)

Figure 2.9: Comparison of the analytical frequency shift with the experimental

Figure 2.10 shows the electrical impedance of the PZT on the beam. A real part, an

imaginary part and a magnitude are demonstrated. All these plots indicate that the change in

temperature leads to a horizontal shift and the peak frequencies of these plots match with those of

the FRF plot. This verifies that the electrical impedance of PZT constitutes a unique signature of

the dynamic behavior of the structure. In the imaginary part and the magnitude plots, a drift,

which is caused by the capacitive property of PZT, can be found. Since the drift makes resonant

peaks unclear sometimes, we usually focus on the real part to assess damage in the impedance-

based structural health monitoring technique. The experiments conducted during the various

case studies at CIMSS have also shown that the real part is more sensitive to changes in

structural integrity.

Figure 2.11 is the impedance versus frequency plot with change in temperature at high

frequency range. As expected, the horizontal shifts of impedance peaks are significant comparedwith low frequency range. Some changes in the peak level also can be found.


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80F120F160F

80F120F160F

80F120F160F

3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5-1500

-1000

-500

Imag

V/A

3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5500

1000

1500

Frequency kHz

Magnitude

V/A

3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 50

200

400

600

RealV/A

Figure 2.10: Electrical impedance of the PZT bonded on the steel beam with temperature change

80F100F120F

140F160F

70 72 74 76 78 800

5

10

15

20

25

30

35

40

45

Frequency kHz

RealV/A

Figure 2.11: Electrical impedance of the PZT bonded on the steel beam at high frequency range

with temperature change


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2.3 Compensation Technique

As seen in the previous sections, the dynamic response of both PZTs and structures is

dependent on temperature. The impedance variation associated with temperature change is

similar to that produced by the presence of damage, and thus could lead to a wrong conclusion

regarding the integrity of the structure in question. Therefore, a temperature compensation

technique is necessary to minimize the effects of ambient or structural temperature changes in the

impedance-based structural health monitoring.

A couple of temperature compensation techniques were proposed at CIMSS, however,

they are not practical. The method presented by Sun et al. [30], which uses cross correlation to

correct the horizontal shift in the signature pattern, does not work if the signature has even a

small distortion. The method presented by Krishnamurthy et al. [31] requires some preliminary

impedance measurements of free PZTs and does not consider the temperature effects on the

structure being monitored.

Therefore, we have developed a new compensation technique [32] to minimize the

effects of ambient or structural temperature changes. The temperature compensation technique

should account for the temperature effects on the structure being monitored as well as the PZT

sensor-actuators. Nevertheless, in complex real world structures, a compensation technique

based on an analytical modeling of the temperature effects may not be practical due to the

complex constitutive thermo-electrical-mechanical model of piezoelectric materials and the

requirement of the complicated modeling of structures. Thus, an empirical approach is used to

minimize the temperature effects in the impedance-based structural health monitoring technique.

Fortunately, the vertical and horizontal shifts of impedance or admittance pattern can be

considered as uniform in a narrow frequency range as seen in the previous section; that is, the

entire signature pattern essentially translates vertically and horizontally. On the other hand, the


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impedance or admittance variation due to structural damage is somewhat local and irregular.

This feature allows us to remove the temperature effect from the impedance-based technique.

The following is the procedure of the temperature compensation. At first, the vertical

shift is simply corrected by the difference in overall average value of the original and the

interrogated impedance patterns as shown below:

v

i

i

n

i

i

n

Z

n

Z

n= = =

Re( ) Re( ), ,21

1

1 (2.9)

where v is the vertical shift, Zi ,1 is the original impedance at frequency interval i (baseline

measurement), Zi ,2 interrogated impedance at frequency interval i (subsequent measurement),

and n is the number of data points.

Next, the data are interpolated to increase the frequency resolution if necessary. The

number of data points or frequency lines, n , increases to N. Finally, the horizontal shift is

searched by the iteration to minimize the damage metric, which is defined as follows:

{ }[ ]M Z Zi i vi

N

h= +

=

Re( ) Re( ), ,1 22

1

(2.10)

where M is the damage metric (squared difference) and h is the horizontal shift (data point

shift). The damage metric is constructed to give some indication of the level of damage

compared with the baseline impedance measurement.

Thus, the optimal v and h which minimize the effects of temperature variation are

found and the measured impedance is compensated by vertical and horizontal translations.


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The temperature compensation technique is applied to the data of the beam experiment.

Figure 2.12 demonstrates the result. The solid 80 F line shows the baseline impedance

measurement. Compared with Figure 2.11, it can be said that the temperature compensation

technique successfully minimizes the temperature effects.

80F100F120F140F160F

70 72 74 76 78 800

5

10

15

20

25

30

35

40

45

Frequency kHz

RealV/A

Figure 2.12: Compensated electrical impedance of the PZT bonded on the steel beam with

temperature change

2.4 Experimental Results

A proof of concept experiment on a bolted pipe joint model, which is shown in Figure

2.13, was carried out. There are two reasons why this kind of model was used: i) it is complex

enough to validate the temperature compensation technique; and ii) temperature variation in

pipeline systems are quite significant in the real world. The model consists of two 50 mm

diameter, 150 mm long steel pipes and two flanges jointed by four 7/16 in. bolts. A PZT (Piezo

Systems PSI-5A, 12.7 mm x 12.7 mm x 0.254 mm) was bonded on the flange and the same oven

and impedance analyzer as the previous experiments were used. The impedance measurements


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were taken over the selected frequency range (70 - 80 kHz) at five temperature levels; 80, 100,

120, 140 and 160 F. Damage was simulated by loosening a bolt (1/6 turn) located across the

PZT sensor-actuator at 120 F. All the impedance measurements were compensated by the

technique presented in the previous section and were compared to the baseline measurement

taken at 80 F.

PZT

Figure 2.13: Bolted pipe joint model in the oven

Figure 2.14 shows the real part of the electrical impedance of the PZT bonded on the

flange without temperature compensation. The impedance variation due to temperature changein this case is more complicated than that in the beam case and the amount of the variation is

almost as same as due to damage. It is very hard to distinguish the impedance variation due to

damage from that due to temperature change. However, this result may be closely describing the

real world application.

Figure 2.15 shows the compensated result. Even though the compensated curves are not

perfectly matched up with the baseline measurement at 80 F, we can clearly observe the

difference between the temperature change and the damage by the temperature compensation

technique.


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80F100F120F140F160FDamage

71 72 73 74 75 76 77 78 798

9

10

11

12

13

14

Frequency kHz

RealV/A

Figure 2.14: Uncompensated electrical impedance of the PZT bonded on the flange with

temperature change and damage

80F100F120F140F160FDamage

71 72 73 74 75 76 77 78 798

9

10

11

12

13

14

Frequency kHz

RealV

/A

Figure 2.15: Compensated electrical impedance of the PZT bonded on the flange with

temperature change and damage

The damage metric chart (Figure 2.16) demonstrates the results more clearly. In the

uncompensated case, temperature change may lead to an incorrect conclusion regarding the


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integrity of the structure because the damage metric of 160 F is larger than that of damage. The

presence of damage cannot be detected accurately in this temperature range without

compensation. However, in the compensated case, the damage metric of damage is much larger

than others and we can easily distinguish it. The temperature compensation technique minimizes

the effects of temperature change to a great extent and is able to provide a definite signal to

indicate the presence of damage.

0

200

400

600

800

1000

100 F 120 F 140 F 160 F Damage

Different Tests

DamageMetric

Uncompensated

Compensated

Figure 2.16: Damage metric of uncompensated and compensated impedance (reference 80 F)

2.5 Conclusions

The effects of temperature change on the impedance-based structural health monitoring

was investigated theoretically and experimentally, and it was found that the temperature change

significantly influenced both on the PZT sensor-actuators and the structure being monitored.


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Basically, the temperature change causes vertical and horizontal shifts of the signature pattern in

the impedance or admittance versus frequency plot, while damage causes somewhat irregular

changes.

An empirical temperature compensation technique was developed to remove the

temperature effects from the impedance-based structural health monitoring. The advantages of

the empirical approach include: i) it can be applied to complex real world structures since it does

not require any model; and ii) it does not need temperature measurements. The compensation

technique is a software correction based on vertical and horizontal translation of the signature

pattern in the impedance or admittance plot.

The experiment on a bolted pipe joint proved that the empirical temperature

compensation technique could minimize the temperature effects. By this compensation

procedure, we demonstrated the impedance-based structural health monitoring technique was

now able to detect incipient-type damage such as loosening a bolt by 1/6 turn, even with some

temperature variation.

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temperature effect on PZT