Czichos H., Saito T., Smith L.E. (Eds.) Handbook of Metrology and Testing

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938 Part D Materials Performance Testing

a) Intrinsic Fabry–Pérot interferometer (IFPI)

Optical

signal

Optical

signal

Fiber

Optical

signal

Fiber

Outer

alignment

tube

Bond or

fusion weld

Reflecting

fiber

In-fiber

reflective

splices

Extrinsic Fabry–Pérot interferometer (EFPI)b)

Fig. 16.86a,b Common types of ﬁber Fabry–Pérot inter-

ferometer (after [16.71])

FPI sensor systems are commercially available for

strain, temperature and pressure measurements. They

allow local measurements of strain in a range between

−5000 μm/m (shortening) and +5000 μm/m (elonga-

tion) with a resolution of up to 0.1 μm/m. Available

gauge lengths are in the range 1–20 mm. Because of

their excellent response time behavior of up to 2 MHz,

they can also be used for detection of mechanical

vibrations and acoustic waves. However, the interro-

gation unit used deﬁnes the dynamic behavior. With

regard to measuring performance and applicability, the

ﬁber Fabry–Pérot interferometer (FPI)sensoristhe

most often applied interferometric point sensor type for

structural health monitoring.

Fiber Bragg Grating Sensor

The discovery of the photosensitivity in germanium-

doped ﬁbers by Hill and coworkers in 1978 was the

basis for fabrication of in-ﬁber reﬂective Bragg grat-

ing ﬁlters with a narrow-band, back-reﬂected spectrum.

They discovered that the refractive index n of a ﬁber

increases when ultraviolet (UV) light is incident upon

such a ﬁber. Today ﬁber grating manufacturing is well

established at special wavelengths with a given periodi-

cally changing refractive index and spacing between the

individual grating planes (grating period or pitch Λ).

Fiber Bragg gratings (FBG) are usually 1–25 mm long

and act as typical point sensors.

The distance Λ between the grating planes can vary;

the common FBG satisﬁes the condition Λ<λwhere

Λ is less than 1 μm (in contrast to so-called long-period

gratings with Λ  λ, where Λ is 100–500 μm). Fiber

Bragg gratings for sensor applications are primarily re-

ferred to as uniform gratings: the grating along the ﬁber

has a constant pitch and the planes are positioned nor-

mally to the ﬁber axis (Fig. 16.87). The principle of

function is as follows: when a broadband light signal

passes through the ﬁber Bragg grating, only a nar-

row wavelength range λ

which satisﬁes the Bragg

condition

=2n

eff

Λ (16.34)

is reﬂected back due to interference between the grating

planes (n

eff

is the effective refractive index of the ﬁber

core and Λ is the grating period). The quantity of the

Bragg resonance wavelength λ

is determined by the

grating pitch Λ manufactured and corresponds to twice

the period of the refractive index modulation of the

grating. The grating periodicity is relatively small, typi-

cally less than 1 μm. From (16.34) it can be derived that

the Bragg resonance wavelength λ

will change when

eff

changes (for example by temperature variation)

or Λ changes (due to pitch changes by ﬁber-grating

deformation). That means that changes in strain or tem-

perature (or both together) will shift the reﬂected center

wavelength. In general, λ

increases when the ﬁber is

strained (Δε>0) and decreases when the ﬁber is com-

pressed (Δε<0). By means of a spectrum analyzer this

wavelength shift can be measured. In this way, one can

determine strain variations (for constant temperature) or

temperature variations (without any deformation of the

grating).

Assuming uniform axial strain changes in the grat-

ing area and the absence of lateral deformation of the

grating, the strain seen by a grating can be computed by

a simple linear equation

ε = K

Δλ

(ε

)

+ξΔT , (16.35)

where K has to be estimated by a calibration pro-

cedure [16.72]. The strain sensitivity depends on the

wavelength used (Table 16.8). With regard to ther-

Grating plane Δn

Light in λ

Light out λ

Transmitted

beam

Pitch

eff

≈ 1.46

Optical fiber Fiber core

Fig. 16.87 Fiber Bragg grating sensor

Part D 16.6

Performance Control 16.6 Structural Health Monitoring – Embedded Sensors 939

Table 16.8 Typical strain and temperature sensitivities

of FBGs

Wavelength Strain sensitivity Temperature

(pm/με) sensitivity (pm/K)

800 nm 0.63–0.64 5.3–5.5

1300 nm 1.0 8.67–10.0

1550 nm 1.15–1.22 10.0–13.7

mal sensitivity the Bragg resonance wavelength shift is

dominated by the temperature-induced change of the

refractive index. Only a very small thermal-induced

wavelength change comes from the thermal expansion

of the glass material (coefﬁcient of expansion of optical

ﬁber glass is 0.55 K

−1

Bragg grating sensors possess a number of advan-

tages that make them attractive compared with other

sensor arrangements.

•

Linear response. The Bragg wavelength shift is

a simple linear response to the sensor defor-

mation as shown in (16.34). In contrast to FPI

sensors the sensor signal has no ambiguity for

strain/compression changes.

•

Absolute measurement. The strain or temperature

information obtained from a measurement system is

inherently encoded in the wavelength (strain and/or

temperature, index changes due to cladding affec-

tion); an interruption in the power supply does not

lead to a lost of measurement information.

•

Line neutrality. The measured data can be isolated

from noisy sources, e.g. bending loss in the leading

ﬁber or intensity ﬂuctuations of the light source.

•

Separation of the interrogation unit from sensor.

Removal of the reading unit or exchange of leading

Table 16.9 Commercially available interrogation units for FBG sensors

Parameter si 720

Micron Optics

I-MON 400E

Ibsen

Spectraleye SE600

FOS&S

Wavelength range 1510–1590 nm 1520–1585 nm 1527–1565 nm

Resolution 0.25 pm wavelength at 0.5Hz 0.5pm 1pm

Uncertainty in wavelength

scanning

1pm 5pm ±10 pm

Maximum scan frequency 5Hz 970 Hz 1Hz

Number of channels 2 (8 optional) > 50 FBGs 1

Weight 15.5kg 0.6kg 1.3kg

Specialty Fabry–Pérot sensors,

long-period gratings

Vibration analysis, distributed

strain measurements

90 min battery operation

Preferred use;

operating temperature

Laboratory,

◦

Cto+50

◦

Small system with USB

interface for ﬁeld applications,

◦

Cto+50

◦

Handheld system for ﬁeld

applications,

◦

Cto+40

◦

cable using special connectors with polished angled

end-faces do not inﬂuence the signal response.

•

Potential for quasi-distributed measurement with

multiplexed sensing elements. Because a number of

gratings (sensor array) can be written along the ﬁber

and be multiplexed, a quasi-distributed sensing of

strain and temperature is possible by serial interro-

gation of a limited number of gratings. The distance

between the gratings can be designed according to

the requirements.

There are different techniques to read the grating re-

sponse under the inﬂuence of a measurand. The basic

operation principles of ﬁber-grating-based Bragg grat-

ing sensors are monitoring either the shift in the wave-

length or change in intensity of the return signal due

to measurand-induced changes. To get high-precision

monitoring of wavelength shift, laboratory-grade instru-

mentation based on highly resolving monochromators

or optical spectrum analyzers (OSA)havetobeused.

For applications that do not have high requirements on

strain resolution in the submicron or micron range low-

cost portable reading units are commercially available

(Table 16.9). These interrogation units ﬁt laboratory as

well as on-site requirements. When choosing a reading

unit for on-site applications, a set of requirements has to

be considered, e.g. scan frequency, number of gratings

to be read simultaneously, long-term reproducibility of

wavelength shift, immunity to optical power ﬂuctua-

tions, low sensitivity to temperature and vibrations, easy

handling and a reasonable price.

To exploit the multiplexing capability of FBG sen-

sor, two different methods can principally be used.

Because of the wavelength-encoded nature of grating,

each sensor in the ﬁber can be designed to have its own

Part D 16.6

940 Part D Materials Performance Testing

2004 Sep 10 12:01

3.0 dB/D

–40.6

(dBm)

–46.6

–52.6

–58.6

–64.6

0.3

FBG

(%)

0.2

0.15

0.1

0.05

0.25

06:3706:3606:36

FBG1 FBG2 FBG3

06:3506:34 06:38

Time

985983981979977975973971969967 987

(nm)

RES: 0.1 nm SENS: NORM HLD AVG: 10 SMPL: AUTO

A:Write /DSP

B:Fix /BLK

C:Fix /BLK

∇ :

∇ 001 :

∇ 002 :

∇ 003 :

∇–∇ n:

Fig. 16.88 (a) Distributed strain measurement in a composite struc-

ture of a rotor blade for a windmill by three FBG; (b) FBG signals

after 10 Mio. cycles of dynamic loading during reliability testing

wavelength within the available source spectrum. Then,

using wavelength multiplexing, a quasi-distributed

sensing of strain, temperature or other measurands

associated with spatial location of the measurand is

possible. The number of sensors depends on the band-

width of the source (typically about 70 nm), on the

Bragg reﬂection bandwidth (typically 0.4nm) and on

the wavelength range needed for pulse shifting due to

measurand changes (sometimes up to ±3.5nm). Us-

ing this method, up to 20 sensors can be interrogated

in series (Fig. 16.88).

Low-Coherence Interferometry

An integrating or long-gauge-length sensor can be re-

alized by the concept of low-coherence interferometry.

It is based on a double Michelson interferometer and

a low-coherence source (e.g. a LED or a thermal light

source) (Fig. 16.89). A sensing interferometer uses two

ﬁber arms – a measurement ﬁber that is in mechanical

contact with the structure, and a reference arm, which

compensates for the temperature dependence of the

measuring ﬁber. The reference ﬁber must not be strained

and needs to be installed loose near the ﬁrst ﬁber. When

the measurement ﬁber is contracted or elongated, defor-

mation of the structure results in a change of the length

difference between the two ﬁbers. By the second inter-

ferometer, which is placed in the portable reading unit,

the path-length difference of the measurement interfer-

ometer can be evaluated. This procedure can be repeated

at arbitrary times and, because the displacement infor-

mation is encoded in the coherence properties of the

light (coherence length of a typical LED: 10–100 μm)

and does not affect its intensity. Due to its physical prin-

cipal and easy set up, not only the precision but also

the repeatability of measurements is high for this sen-

sor type. The measurement system can be switched off

between two measurement events or components such

as connectors or cable can be exchanged without zero-

point data loss.

Typical parameters of commercially available long-

gauge-length sensor are

•

measuring length: 50 cm to several 10 m

•

measuring range: 0.5% in shortening, 1.0% in elon-

gation

•

precision in measurement: 2 μm (error of measure-

ment: Δε =±1.25 × 10

−5

)

•

proportionality factor between the measured delay

and the applied deformation: (128±1) μm/ps.

Such sensors can be provided as tube sensors

or as ﬂat tape sensors. Tape sensors allow its in-

tegration into composites or into interface zone of

multilayer materials. Several sensors can be interro-

gated by multiplexing.

Optical Time-Domain Reﬂectometry

A quasi-distributed sensor system within a material or

construction can realized by ﬁber-optic techniques in

the following way. By measurement of the time of ﬂight

of a ultrashort light pulse transmitted into the ﬁber and

backscattered on markers (splices, photoinduced reﬂec-

tors, or squeezing points) at the end of these sections,

Part D 16.6

Performance Control 16.6 Structural Health Monitoring – Embedded Sensors 941

the measurand can be determined at deﬁnite locations

along the ﬁber (Fig. 16.90). An elongation (compression

or contraction) of a measuring section, determined by

two reﬂector sites on the ﬁber, changes the time of ﬂight

of the pulse: Δε ∼Δt

[(c/2L

)n], where c is the speed

of light and n the index of refraction. Based on this rela-

tionship, the changes in the average strain of a chain of

marked sections along the ﬁber can be interrogated by

an OTDR device.

This method allows the evaluation of strain proﬁles

in large components without using sensor ﬁbers con-

taining discrete sensor points along the ﬁber. The OTDR

device used determines the strain resolution achievable.

A high-resolution picosecond OTDR device enables the

resolution of elongation to 0.2 mm, assuming the mini-

mum distance between two reﬂectors in the measuring

section is not less than 100 mm [16.74]. Using this

method, a reﬂector shift of 0.35 mm can be resolved,

however only long-term reproducibility of reﬂector

shifts of 0.85 mm can be achieved. This value is sufﬁ-

cient to recognized dangerous changes in the material or

loss of bonding integrity. Automatic scanning run takes

between one and some ten seconds depending on the

wanted precision. The sensor sections are interrogated

one after another. Ofﬂine measurements are preferred

because the rather expensive OTDR devices should al-

ternatively be used for other measurement tasks, too.

The length of the ﬁbers evaluated by conventional

OTDR technique is limited by the permissible power

loss along the ﬁber (quality of the markers), and can

reach up to several hundreds meters, or tens of sensing

sections. This method has a serious advantage: determi-

nation of the position of all reﬂectors can be referred

to one stable position (reference reﬂector). Therefore,

there is no propagation of error due to propagating from

one reﬂector to the next one.

The examples considered above were focused on

strain or deformation measurement in direction of the

ﬁber axis. However in composites, transversely ap-

plied pressure, arising forces or beginning delamination

might be of interest. For such purposes, single-mode

birefringent ﬁbers can be embedded. Internal birefrin-

gence can be induced by using a noncircular core

geometry of the ﬁber or by the introduction of stress

anisotropy around the core such as done in panda or

bow-tie ﬁbers. The refractive-index difference of the

two orthogonal polarization modes produces a differ-

ential propagation velocity. Any damage or parameter

change in the composite or material structure will per-

turb the birefringence parameters in the sensor ﬁber.

Using the time-delay measurement technique, the in-

Measuring and reference fiber Optical

multiplexer

Low-coherence light source and

optomechanical reading unit

Processing and

control unit

RS-232

Fig. 16.89 Fiber-optic low-coherence interferometry sensor system

(after [16.73])

tensity and position of the perturbation can be located

with an uncertainty of about 10 cm [16.75]. However,

a reproducible correlation between affecting external

events and optical effects in the ﬁber is quite difﬁcult

because the interface zone of the sensing ﬁber strongly

inﬂuences the response of the sensor. Nowadays, ﬁber

Bragg gratings will be written into birefringence ﬁbers

to make multiple parameter sensing with the capability

to discriminate between them [16.76].

Brillouin Scattering

In optical ﬁbers Brillouin scattering arises due to the

interaction of light with phonons. Phonons are quan-

tized acoustic waves. In essence, the light is scattered

from variations in the index of refraction associated

with acoustic waves. Light which is scattered off these

phonons is frequency shifted by an amount of deter-

mined by the acoustic velocity of the phonons. The

Measuring sections Reflectors

Δε

Δε~Δt

Pulse input Pulse output

Fig. 16.90 Quasi-distributed ﬁber-optic sensor based on backscat-

tering signal evaluation

Part D 16.6

942 Part D Materials Performance Testing

Anchor head

Free

length

anchor

Fixed

length

anchor

From

measurement

device

Sensor fiber

Steel strands

Measuring segment

Fixed

anchor

=10m

R10

R11

R10

R11

Year

200320022001 20042000

–5

Length change (mm)

R1–R11:

Reflectors in the

fixed anchor length

+245.00 NN

+240.00 NN

Anchor head

Bridge

Newly built gallery with

load distribution beam

104 permanent anchors (System STUMP)

Working load: 4500 kN

Stilling

basin

+200.00 NN

+177.00 NN

+167.00 NN

Greywacke

and claystone

Anchor

Transverse gallery

Longitudinal gallery

Borehole

inclination:

3.2°

Anchor and sensors:

SUSPA

Spannbeton

STUMP

Spezialtiefbau

Fig. 16.91 Monitoring of the bonding behavior along the ﬁxed anchor length by quasi-distributed ﬁber-optic sensors

(Eder Gravity Dam Germany) (after [16.77])

acoustic velocity is in turn dependent on the density of

glass and thus the material temperature. The Brillouin

frequency shift is given by

=2n

, (16.36)

where V

is the velocity of sound in glass and is

afunctionof(T,ε), n is the effective index of refrac-

tion, and λ is the free-space wavelength of operation.

The frequency shift is linearly dependent on both

the temperature and strain in the ﬁber [16.78, 79].

Part D 16.6

Performance Control 16.6 Structural Health Monitoring – Embedded Sensors 943

The sensitivity of the frequency shift is of the order

4.6×10

−6

με

−1

for strain and 9.4×10

−5

◦

Cfortem-

perature.

Since this technique was ﬁrst published, several

developments and technical innovations have led to

dramatic advances in the capabilities of the Brillouin

approach. Today, several devises based on Brillouin

optical-ﬁber time-domain analysis (BOTDA) are com-

mercially available. One typical example is an arrange-

ment where the sensing ﬁber follows a double path in

the structure to be monitored. One path is attached to the

structure or embedded in the material and is thus sub-

jected to both temperature and strain. The return path is

loosely installed, measuring only the temperature pro-

ﬁle. By such an arrangement a temperature resolution of

Brillouin frequency shift (GHz)

12.88

12.86

12.82

12.8

12.78

0 2000 10 000 12 000

Location (m)

3 MHz

4000 6000 8000

4000 4200 5000 5200

Location (m)

4400 4600 4800

12.84

12.88

12.86

12.82

12.8

12.78

12.84

Fig. 16.92 Zones of shifted Brillouin frequencies within an

11-km-long optical ﬁber (upper). A closer look at these

zones demonstrates that the resolution of 3 MHz represents

a temperature resolution of 2.6

◦

C or a strain resolution of

0.006% (after [16.80])

◦

C and a strain sensitivity of 25 με with a spatial reso-

lution of approximately 1 m have been achieved [16.81].

Figure 16.92 shows zones of shifted Brillouin fre-

quencies with an 11-km-long optical ﬁber [16.80].

A closer look on these zones demonstrates the temper-

ature and strain resolution of such a set up. The peak

difference of both indications is in the order of 3 MHz,

which represents a temperature resolution of 2.6

◦

Cor

a strain resolution of 0.006%.

An alternative approach is named Brillouin optical-

ﬁber frequency-domain analysis (BOFDA) [16.82].

The BOFDA operates with sinusoidally amplitude-

modulated light and is based on the measurement of

a baseband transfer function in frequency domain by

a network analyzer. A signal processor calculates the

inverse fast Fourier transform (IFFT) of the baseband

transfer function. In a linear system this IFFT is a good

approximation of the pulse response of the sensor and

resembles the strain and temperature distribution along

the ﬁber (Fig. 16.93a). The frequency-domain method

offers some advantages compared to the BOTDA

concept. One important aspect is the possibility of

a narrow-bandwidth operation in the case of BOFDA.

In a BOTDA system broadband measurements are nec-

essary to record very short pulses, but in a BOFDA

system the baseband transfer function is determined

point-wise for each modulation frequency, so only one

frequency component has to be measured by a network

analyser with a narrow resolution bandwidth. The use

of a narrow bandwidth operation (detectors) improves

the signal-to-noise ratio and the dynamic range com-

pared to those of a BOTDA sensor without increasing

the measurement time. Another important advantage

of a BOFDA sensor is that no fast sampling and data

acquisition techniques are used. This reduces costs. Par-

ticularly, the low-cost-potential of BOFDA sensors is

very attractive for industrial applications.

For stabilization and reinforcement of geotechni-

cal structures like dikes, dams, railway track ballasts,

embankments, landﬁlls and slopes geotextiles are com-

monly used. The incorporation of optical ﬁbers in

geotextiles leads to additional functionalities of the

textiles, e.g. monitoring of mechanical deformation,

strain, temperature, humidity, pore pressure, detec-

tion of chemicals, measurement of the structural

integrity and the condition of the geotechnical struc-

ture (structural health monitoring). Especially solutions

for distributed measurement of mechanical deforma-

tions over extended areas of some hundred meters

up to some kilometers are urgently needed. Textile-

integrated distributed ﬁber optic sensors can provide

Part D 16.6

944 Part D Materials Performance Testing

for any position of extended geotechnical structures

information about critical soil displacement or slope

slides via distributed strain measurement along the ﬁber

with a high spatial resolution of less than 1 m [16.83].

So an early detection of failures and damages in

geotechnical structures of high risk potential can be en-

sured.

Figure 16.93c shows the result of a validation test

at a test dike at the University of Hannover. A sensor-

based geotextile was installed on top of the dike and was

covered with a thin soil layer. To simulate a mechanical

deformation/soil displacement, a lifting bag was em-

bedded into the soil and was inﬂated by air pressure.

This induced a break of the inner slope of the dike and

a soil displacement. The soil displacement was clearly

02010 30 40 50 7060 80

Time (days)

Total length change of POF (cm)

17.11.2008

22.10.2008

06.10.2008

30.09.2008

22.09.2008

02.09.2008

208 250 212 214 216 220218 222

12.77

12.78

12.79

12.8

12.81

12.82

12.83

12.84

z (m)

Brillouin frequency shift (GHz)

6 bar

3 bar

Strain value: 1.1‰

200 250 300 350 400 450

1000

2000

3000

4000

5000

6000

z (m)

Strain (με)

Applied strain

Measured strain

Fig. 16.93 (a) Distributed strain proﬁle measured on a single-mode silica ﬁber using BOFDA (after [16.83]); (b) Geotextile

with embedded glass ﬁber cables manufactured by STFI, Germany;

dike using a BOFDA system (after [16.83]); (d) Creep behaviour of a slope at a coal pit measured with a POF sensor-equipped

geogrid (after [16.84])

detected and localized by the BOFDA system. The dis-

tribution of the mechanical deformation (strain) in the

dike measured by the BOFDA system at two different

air pressure values is shown in Fig. 16.93c.

However, the excellent measurement technique

based on Brillouin scattering in silica ﬁbers reaches

its limits when strong mechanical deformations, i.e.

strain of more than 1% occurs. In such a case sensors

based on silica ﬁbers cannot be reliably used. Further-

more, silica ﬁbers are very fragile when installing on

construction sites and, therefore, special robust and ex-

pensive glass ﬁber cables have to be used. For that

reason, the integration of polymer optical ﬁbers (POF)

as a sensor into geotextiles has become very attractive

because of the high elasticity, high breakdown strain

Part D 16.6

Performance Control 16.6 Structural Health Monitoring – Embedded Sensors 945

and the capability of POF of measuring strain of more

than 40%. Especially the monitoring of relative small

areas with an expected high mechanical deformation

such as endangered slopes takes advantage of the out-

standing mechanical properties of POF. The monitoring

of slopes is a very important task in the geotechni-

cal engineering for prevention of landslide disasters.

To overcome the limit of glass-ﬁber-based geotextiles

novel distributed ﬁber optic sensors based on low-priced

standard POF and using OTDR (optical time-domain

reﬂectometry) were developed and embedded into geo-

textiles [16.85].

Figure 16.93d shows the result of a ﬁeld applica-

tion of a POF sensor-equipped geogrid at a coal pit.

The 10 m long geogrid was installed directly on top

of a creeping slope. It was covered with a 10 cm thick

sand layer. The textile is installed with the POF sensor

bridging the cleft perpendicular to the opening. Mea-

surements were conducted before and after installation.

Figure 16.93d shows a relative linear increase of the

POF length with time. The measurements indicate that

the creep velocity of the slope was constant during the

time of observation with an average rate of about 2 mm

per day [16.84].

16.6.3 Piezoelectric Sensing Techniques

Basics

The origin of the piezoelectric effect is related to an

asymmetry in the unit cell of the crystal and the re-

sultant generation of electric dipoles due to mechanical

distortion. However, it was not until 1946 that scien-

tists discovered that barium titanate (BaTiO

) ceramics

could be made piezoelectric by application of an electric

ﬁeld. The polycrystalline ceramic materials have several

advantages over single crystals, such as higher sensi-

tivity and ease of fabrication into a variety of shapes

and sizes. In contrast, single crystals must be cut along

certain crystallographic directions, limiting the possible

number of geometrical shapes. After the BaTiO

ceram-

ics, scientists discovered a number of piezoceramics and

in particularly the lead zirconate titanate (PZT) class

in 1956. With its increased sensitivity and higher op-

erating temperature, PZTs soon replaced BaTiO

and

are still the most widely used piezoceramics. In the

sixties, new varieties of piezoelectrics were developed

based on both ceramics and polymers. Piezoelectrics

are available in different forms, such as ﬁlm, powder,

paint, multilayered or single ﬁber. They are available in

several types, such as polyvinylidene ﬂuoride (PVDF)

lanthanide-modiﬁed piezoceramic (PLZT) or the popu-

lar class of lead zirconate titanate piezoceramics. This

list is not complete, because the composition of the

piezoelectric materials allows a large variety of piezo-

electrics, and new piezoelectric classes are expected

to be developed in the near future [16.86]. The prop-

erties of piezoceramics have attracted a large group

of industries such as the aerospace and automotive

industries.

The piezoceramics offer a large selection of mater-

ials with different electromechanical properties [16.87].

The common electromechanical properties are the cou-

pling factor, piezoelectric charge constant, piezoelectric

voltage constant, mechanical quality factor, dielectric

loss and relative dielectric constant. The coupling factor

is deﬁned as the ratio of the mechanical energy stored

to the electrical energy applied, at a given frequency

or frequency range. It could also be deﬁned as the ra-

tio of the electrical energy stored to the mechanical

energy applied. The coupling factor characterizes the

coupling between the electrical and mechanical prop-

erties of the piezoceramic. The piezoelectric constant d

also called the charge constant, is the ratio of the elec-

tric charge generated per unit area to an applied force. It

can also be deﬁned as the ratio of the strain developed

by the applied electric ﬁeld. Another piezoelectric con-

stant exists, called the voltage constant, which is derived

from the charge constant. The piezoelectric voltage con-

stant g is the ratio of the strain developed to the charge

applied or the electric ﬁeld developed to the mechanical

stress applied. The mechanical quality factor is the ratio

of the reactance to the resistance in the series equivalent

circuit (RS, CS) identifying a piezoelectric resonator.

The relative dielectric constant, also called the relative

permittivity, is deﬁned as the ratio of the material dielec-

tric constant ε to the free-space dielectric constant ε

The dielectric loss, also known as loss tangent in the

literature, is deﬁned as the ratio of the imaginary com-

ponent of the complex dielectric to its real component.

However, the most important electromechanical

properties are the coupling factor and the piezoelectric

constants. A high coupling factor gives a greater sensi-

tivity to the piezoceramic in converting the Lamb waves

into an electrical signal. A high piezoelectric charge

constant is desirable for materials intended to generate

ultrasonic waves such as Lamb waves, because for an

applied electric ﬁeld, or excitation signal, a large de-

veloped strain is necessary to propagate over a long

distance.

Other nonelectromechanical parameters also exist

and play a large role in the selection of the PZT;the

most important are the mechanical elastic constants, the

Part D 16.6

946 Part D Materials Performance Testing

Curie temperature and thermal coefﬁcients of expan-

sion. The value of the elastic constants needs to be as

low as possible to reduce the local stress inside the PZT

as well as in its vicinity. The Curie temperature is the

temperature at which the piezoceramic loses its piezo-

electric properties. The Curie temperature has to be as

high as possible to allow a large working-temperature

range and must be higher than the curing temperature of

the composite laminate to prevent the loss of piezoelec-

tric properties. Typically, the working temperature has

to be 100

◦

C lower than the Curie temperature. The ther-

mal coefﬁcients of expansion have to be similar to those

of the composite to reduce the stresses in the transducer

and the composite.

Four main piezoceramic materials are commercially

available; lead zirconate titanate, modiﬁed lead titanate,

lead metaniobate and bismuth titanate. For transducers

used in damage detection as well as sensitive detec-

tors and actuators, the class of PZT is considered to be

a suitable material because of its high coupling factor,

high charge constant, high Curie temperature, low me-

chanical quality factor and thermal coefﬁcients similar

to those of composites. The dimension of the embed-

ded piezoceramic element has a direct inﬂuence on the

way the PZT works, that is, the functioning character-

istics of the PZT.SomePZT coefﬁcients, such as the

coupling factor, the relative dielectric constant or the

mechanical quality factor, are dependent on the PZT di-

mensions. Moreover, the piezoceramic dimensions are

chosen by analytical methods based on the properties of

wave propagation in the composite.

Embedment Techniques

Two principle conﬁgurations with embedded piezoce-

ramic transducers are described in the literature. The

technique concerns how to embed the PZT transducer

in the composite. Some researchers have chosen to cut

the composite plies surrounding the embedded piezo-

ceramic transducer, as done by Elspass et al., Hagood

et al. [16.88, 89], Moulin et al. or Luis and Craw-

ley [16.90–92]. Other researchers directly embedded the

PZT transducers to avoid cutting the ﬁbers, as done by

Bourasseau et al., Neary et al. or Shen et al. [16.93–95].

Elspass et al. manufactured a piezoceramic trans-

ducer to be embedded in carbon-ﬁber-reinforced ther-

moplastic composites [16.90]. The material in the

interconnectors was the same as the composite. The two

interconnectors were placed on each side of the piezoce-

ramic element. The electrical insulation from the upper

and lower interconnectors was achieved by two glass-

ﬁber-reinforced thermoplastics, as shown in Fig. 16.94.

CFRP strip

Terminal (+)

Terminal (–)

Cutout

Piezoceramic

Section A–A

CFRP ply

CFRP strip

GFRP plies

Fig. 16.94 Piezoceramic element embedded in a carbon-

ﬁber-reinforced thermoplastic composite

Cutouts in the glass- and carbon-ﬁber-reinforced ther-

moplastic were performed to allow electrical contact

between the terminals and the embedded piezoce-

ramic element. The manufacture of such a lay out was

complex.

Hagood et al., similar to Elspass et al., used a cut-out

technique to embed piezoceramic transducers in glass-

ﬁber-reinforced polymer (GFRP) laminates. A cut-out

window had about the same dimension as the PZT ele-

ment. Slits were also cut in the plies directly above and

below the piezoceramic element to allow the connectors

to be drawn out to the edges, as shown in Fig. 16.95. The

connectors were wires that were soldered to the faces

of the piezoceramic element. Hagood also embedded

the piezoceramic element in conducting material, such

as carbon-ﬁber-reinforced polymer (CFRP). To elec-

trically insulate the piezoceramic transducer from the

surrounding material, a polyamide layer was often used

to encapsulate both the piezoceramic element and the

connectors, as shown in Fig. 16.96.

A research group of Stanford University developed

a commercial transducer called the Stanford multi-

actuator receiver transduction layer (SMART Layer).

The SMART Layer was similar to the transducers used

by Mall and Hsu [16.96]. The transducer SMART Layer

could be customized in a variety of sizes, shapes and

complexity, allowing its embedment in many compos-

ite structures, such as pressure vessels, pipes or wings,

asshowninFig.16.97. The PZT elements were PKI-

Part D 16.6

Performance Control 16.6 Structural Health Monitoring – Embedded Sensors 947

Fiber

direction

Composite

ply

Wire

Slot for wire

Piezoceramic

Fig. 16.95 Piezoceramic element embedded in a glass/

epoxy laminate

400, with a thickness of 254 μm. The connector was

made of a copper layer bonded on a polyamide ﬁlm.

The connector was shaped to provide a perfect ﬁt to be

embedded in the composite. The conductive adhesive

linking the PZT element to the connector was probably

a silver/epoxy compound. The transducer could with-

stand over 200

◦

C, required for embedment in aerospace

composite structures.

Damage Detection Using Lamb Wave Response

Lamb waves are sensitive to damage in the composite,

resulting in changes in the Lamb wave response. The in-

teraction between damage and Lamb waves is complex

and difﬁcult to predict. Two different approaches to re-

search on Lamb waves for damage detection have been

seen in the literature. There are research groups that

try to simplify Lamb wave generation, and others that

directly postprocess the Lamb wave response without

simpliﬁcation in the Lamb wave generation. To gener-

ate simple Lamb waves, researchers use wedged PZT

to create an incidence angle between the PZT and the

composite plate, which allows the generation of spe-

ciﬁc Lamb wave modes. In the case of this thesis, the

piezoceramic transducers were embedded in the com-

posites, which excluded the use of wedges with the

transducers. Nevertheless, it is still possible to improve

the generation of Lamb waves by means of PZT size

optimization or simplify them by using arrays of em-

bedded transducer. The latter has so far only been done

on surface-bonded PZT transducers. This section deals

then with postprocessing techniques that are used to

track damage information in the Lamb wave response.

In 1885, the English scientist Lord Rayleigh demon-

strated theoretically that waves can be propagated along

Polyimide tape

Polyimide

tape

Wire

Solder dot

Section A–A

Polyimide

film

Epoxy Piezoceramic

Fig. 16.96 Insulation of a piezoceramic transducer

Fig. 16.97 Piezoceramic transducer network for embed-

ment in composite plates (left) and pressure vessels (right)

Globe deformation

of the laminate

Decomposition

Symmetrical mode

Antisymmetrical

mode

Fig. 16.98 Decomposition in symmetric and antisymmet-

ric modes

the boundary of an elastic half-space and vacuum or

sufﬁcient rareﬁed medium (for example air). It was

only in 1914 that Stoneley generalized the propagation

of waves in two different solids. In 1917, Lamb in-

Part D 16.6