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

Подождите немного. Документ загружается.

928 Part D Materials Performance Testing

Intensity (arb. units)

Rel. scattering angle

Critical

angle

PP fiber, 20 μm

Pt wires, 100 μm

Cu wires, 25 μm

Quartz fibers, 10μm

Refraction theory

0 0.80.60.40.2

Fig. 16.72 The normalized shape of the angular intensity

distribution of cylindrical objects; PP – polypropylene

if normalized to the critical angle θ

of total reﬂection

(Fig. 16.72) deﬁned by the refractive index θ

=2ε. The

intensity of the deﬂected x-rays becomes nearly zero at

the critical angle (Fig. 16.72), with a small contribution

from total reﬂection.

Applying a Kratky-type high-resolution small-angle

scattering camera with slit collimation a cross section of

−3

of the ﬁber diameter contributes to the detectable

intensity typically above 2 min of arc. Total reﬂection

of x-rays occurs as well but only 10

−6

of the cylin-

der diameter is involved and this is therefore negligible,

although planar surfaces may scatter all the primary in-

tensity if well aligned. Based on Snell’s Law the angular

intensity distribution of cylinders has been modeled and

X-ray

Slits

Scanning

Absorption

detector

Scattering

foil

Refraction

detector

Sample

source

Fig. 16.73 Schematic of a SAXS instrumentation with a collimated

x-ray beam, sample manipulator, refraction detector for refracted

intensity, I

with sample or I

without sample, and an absorp-

tion detector for the attenuation intensity, I

or I

of the primary

beam

ﬁtted to measurements on most different ﬁbers, as il-

lustrated by Fig. 16.72. The refracted intensity I

∗

a cylinder (without absorption effects) can be expressed

by [16.51]

∗

(2θ



) =

sin



arctan





∼

2Rε

(16.31)

is the irradiation density of the incident x-rays, R is

the cylinder radius and 2θ



=θ is the scattering angle.

In the case of spherical particles or pores I

∗

becomes

∗

(2θ



)

∼

2Rε

. (16.32)

The conventional understanding of continuous small-

angle x-ray scattering (SAXS) is governed by the

interpretation of diffraction effects. Both the well-

known Guinier’s theory [16.53] for separated particles

and Porod’s theory [16.54] of densely packed col-

loids are based on diffraction of Rayleigh scattering.

Nevertheless Porod approximates the same angular in-

tensity decay as in (16.32). However both diffraction

approaches are about scattering objects two orders of

magnitude smaller.

16.5.2 Refraction Techniques Applying

X-ray Tubes

The SAXS instrumentation with an x-ray ﬁne-structure

tube and a Kratky camera is relatively straightforward.

The camera needs an additional scattering foil for the

primary-beam attenuation measurement and a micro-

manipulation device for the sample (Fig. 16.73). For

practical measurements the refraction detector remains

at a ﬁxed scattering angle 2θ



, so that the relative surface

density C of the specimen can be measured according

to [16.52]

C =



−1



, (16.33)

where I

and I

are measured by the refraction detec-

tor with and without sample, respectively, I

and I

are measured by the absorption detector, and where d

the wall thickness of a sample. Apart from the choice of

materials the relative surface density C depends solely

on the scattering angle and the radiation wavelength.

The absolute inner surface density (speciﬁc surface, sur-

face per unit volume) is determined by comparison with

Part D 16.5

Performance Control 16.5 Computed Tomography – Application to Composites and Microstructures 929

a known calibration standard at retained boundary con-

ditions (wavelength and scattering angle).

As well as the inner surface of pores and particles,

interfaces and cracks such as ﬁber debonding in com-

posites can also be determined. A model composite

has been made to demonstrate the refraction behavior

of a bonded and a debonded 140 μm sapphire ﬁber in

a polymer matrix (Fig. 16.74, left). Figure 16.74 (mid-

dle) shows the resulting intensity distribution of a two-

dimensional refraction scan of the model composite.

The upper ray crosses the bonded ﬁber–matrix interface,

causing a small amount of deﬂected intensity. At the

debonded ﬁber and at the matrix surfaces (lower ray)

many more x-rays are deﬂected, due to the larger dif-

ference of the refractive index against air. The polymer

channel is clearly separated from the ﬁber surface. For

comparison a mapping of I

yields the transmission to-

pograph containing only the absorption information of

the projected densities, like in conventional radiography

(Fig. 16.74, right). In the case of a real composite mater-

ial the much thinner ﬁbers are not spatially resolved, but

the higher refraction signal of debonded ﬁbers reveals

quantitatively the percentage of debonded ﬁbers.

Beyond the capabilities for two-dimensional to-

pographs the set up of Fig. 16.73 can be employed for

conducting computed tomography of a transversal sec-

tion. This requires vertical linear scans and rotation of

the sample to gain multiple projections for the parallel-

beam reconstruction procedure. A section of a C/C

ceramic matrix composite (CMC) for high-temperature

applications is investigated to image the different crack

patterns developing during manufacture by pyrolysis.

The three samples (Fig. 16.75, left) are based on dif-

ferent phenolic resin carbon-ﬁber-reinforced polymer

(CFRP) green bodies of good, intermediate and bad

ﬁber/matrix bonding.

The absorption signals are reconstructed according

to the rules for parallel-beam ﬁltered back-projection as

shownbyFig.16.75, center. The resulting transversal

sections reveal major cracks and homogeneous do-

mains.

The refraction and the absorption intensities per-

mit the reconstruction of the relative inner surface

density according to (16.33)(Fig.16.75, right) which

shows a signiﬁcantly higher number and ﬁner cracks.

Additionally the average intensity levels reveal the

quantitative crack density without resoling individual

cracks. These ﬁndings have proved for the ﬁrst time

that the degree of ﬁber debonding is retained during

processing from the green state to high-temperature

treatment [16.55].

Refraction topograph Transmission topograph

Fig. 16.74 x-ray scanning topography; left: model composite of

polymer matrix and embedded bonded (top) and debonded (bottom)

140-μm sapphire ﬁber; middle: x-ray refraction topograph of C-

values resolving debonding spatially: an interface image, free from

absorption effects; right: absorption projection

Samples:

C/C-ceramic

matrix composite

1mm

bonding of

carbon-fibers

good

medium

bad

Fig. 16.75 x-ray computed tomography (CT) of carbon/carbon ce-

ramic matrix composite (C/C-CMC); left: sample arrangement,

middle: crack pattern by conventional (x-ray absorption) CT, right:

highly contrasted cracks by refraction computed tomography

16.5.3 3-D Synchrotron Refraction

Computed Tomography

2-D refraction CT by conventional x-ray tubes has dis-

advantages. It is limited to low x-ray energies from

characteristic Cu and Mo radiation and thus restricted

to low-density materials. The thickness of the investi-

gated layer is as large as 1 mm and the measurements

require over 10 h. To overcome these limitations 3-D

synchrotron refraction CT is employed. At the BAMline

at BESSY, Berlin the available monochromatic energy

ranges from 5 keV up to 60 keV. Further advantages

are the high photon ﬂux, the selectable energy and the

highly parallel photon ﬂux.

The experimental set up is sketched in Fig. 16.76

[16.56]. A parallel monochromatic beam (up to 60 keV)

at about 2% bandwidth is delivered by a double mul-

tilayer monochromator (DMM). At the experimental

stage a beam of several 10 mm

is reﬂected sequentially

by two Si(111) single crystals at their Bragg condition

for the chosen energy. An x-ray-sensitive CCD cam-

era of about 5 × 5 μm

resolution is placed behind the

Part D 16.5

930 Part D Materials Performance Testing

OCD-

camera

2nd crystal

Specimen

Refraction Absorption

1 st crystal

Rocking curve Si(111)

Intensity (arb. units)

100

4.8372 4.838

Bragg angle (°)

With specimen

FWHM: 1.8''

Without specimen

FWHM: 1.4''

4.8376

Fig. 16.76 Experimental setup for 3-D refraction CT at the synchrotron BAMline; left and top: goniometer and beam

components, right: rocking curve of the second Si(111) crystal (symmetric) with specimen (squares) and without

specimen (circles)

second crystal. A small inclination of the second crys-

tal varies the reﬂected intensity. The resulting rocking

curve widthis4×10

−4◦

full width at half-maximum

(FWHM)(Fig.16.76, circles). In contrast to the set up

for phase-contrast CT, the sample is positioned between

the two crystals. Thus the most-parallel beam traverses

the specimen and is attenuated according to the mass

distribution. Additionally, the beam is deﬂected due to

the refraction effect at all interfaces (Fig. 16.76,top

right). This leads to a broadening of the rocking curve

(Fig. 16.76, squares).

The presented investigation is performed on cylin-

drical tensile test samples of metal matrix composites

(MMCs, MTU Aero Engines, München). The most

advanced new material for aero engine compressor

components with high tensile strength at low spe-

ciﬁc weight is based on a Ti matrix embedding SiC

ﬁbers. Their mechanical properties depend on the

ﬁber/matrix bonding and their high crack resistance

under high loads. Both characteristics require nonde-

structive characterization.

First a conventional 3-D CT investigation is car-

ried out employing a ﬁne-focus x-ray tube. Figure 16.77

shows the density reconstruction of one out of 300

planes at 100-kV tube voltage and 5 × 5 × 5 μm

voxel resolution (720 projections, rotation about cylin-

der axes, Fourier-ﬁltered back-projection). It shows

a transversal section of a low cycle fatigue (LCF)sam-

ple. Higher density appears brighter. The reinforcing

SiC ﬁbers appear as dark discs with a slightly darker

(carbon) core. Solely in the selected plane of Fig. 16.77,

bottom, a dark shaded crack area appears due to reduced

absorption.

Synchrotron refraction computed tomography of

the same sample is performed at the BAMline with

the described set up at 50-keV radiation and 5 ×

5×5μm

detector voxel resolution (360 projections,

Fourier-ﬁltered parallel-beam back-projection). The re-

construction of Fig. 16.78 images the same cross section

of the MMC LCF sample, but now the crack area

appears bright (color enhanced) and is much more de-

tailed. Also some debonded ﬁbers can be identiﬁed by

Part D 16.5

Performance Control 16.5 Computed Tomography – Application to Composites and Microstructures 931

1mm

Fig. 16.77 Conventional CT reconstruction of the absorp-

tion measurement on Ti-SiC MMC sample after fatigue;

ﬁne-focus tube, 100-kV single-slice 3-D measurement

bright surrounding rings. In contrast to conventional

absorptive CT measurements the refraction contrast

provides crack indications in about 20% of the 300 re-

constructed slices of the sample [16.56].

The high inverse contrast (compared to Fig. 16.77)

originates from the rejection of deﬂected x-rays by the

second Si crystal in front of the CCD detector due to

refraction and total reﬂection interaction at the crack

boundaries. The refraction contrast is nearly indepen-

dent of the width of the cracks as it is a surface effect.

However, the contrast depends strongly on the angle of

the incident beam, which is only effective at (0±1)

◦

(plane crack). In the given set up, with both Si crystals

set to the top of their rocking curves, the image infor-

mation from absorption and refraction effects are both

present. If desired they can be separated by different

operation of the Si crystals.

Much higher spatial resolution can be achieved,

when the second crystal (Fig. 16.76) is replaced

by an asymmetric-cut crystal (Fankuchen cut). In

this the crystal surface is inclined against the re-

Fig. 16.79 3-D nano-refraction CT; reconstructed plane of

steel micro-drill from 19-keV projections; dark tubular

pores below 1 μm diameter; refraction contrast at outer

edges and around pores; magniﬁcation by Fankuchen-cut

single-crystal Si (at the center of the rocking curve)



Fig. 16.78 Synchrotron refraction CT of same slice

(Fig. 16.76); monochromatic 50-keV radiation, sample be-

tween two crystals at maximum reﬂection (after [16.56])

ﬂecting lattice plane, resulting in a broadened exit

beam of up to 100× magniﬁcation. An example

of such nanometer-resolution refraction CT is given

by Fig. 16.79, which presents the reconstruction of

a horizontal section of a standing steel micro-

drill (100 μm diameter) using 19-keV radiation. Dark

tubular pores below 1 μm diameter, and refraction

1µm

100 µm

Part D 16.5

932 Part D Materials Performance Testing

contrast at the outer edges and around pores are

visible.

16.5.4 Conclusion

The presented ﬁndings demonstrate the high perfor-

mance of refraction CT for inner surfaces and inter-

faces, including microcracks. Even beyond the spatial

resolution of the reconstruction average crack densities

are determined. The techniques are expected to close

an essential gap in the spectrum of nondestructive tech-

niques for a better understanding of microstructures of

materials down to the nanometer scale and their behav-

ior under thermal and mechanical loads.

16.6 Structural Health Monitoring – Embedded Sensors

The ﬁnal decade of the 20th century brought many

technological achievements, not only in regard to

the development of innovative and high-performance

materials but also in regard to advanced sensing tech-

niques. The embedment of sensors into materials or

structures opens up new possibilities to detect, e.g., the

presence of cracks or the onset of failure, to estimate

the extent of degradation, and to locate damaged zones.

This is the basic idea of structural health monitoring,

which has gained more importance within the last years.

This is an emerging technology that deals with the de-

velopment of techniques and systems for the continuous

monitoring, inspection and damage detection of struc-

tures. Today structural health monitoring can be found

in a wide area of industrial applications: starting from

A for aircraft and ending at Z for Zeppelin. Innova-

tive bridge design, higher safety requirements, extended

operation time, reduction of maintenance and inspec-

tion costs (e.g. less or no visual and NDT inspection)

are the driving forces for the usage of structural health

monitoring systems. The ultimate goal is to eliminate

current schedule-based inspection and replace it with

condition-based maintenance or repair.

Sensor array

Mechanical structure

Actuator array

Control and drive network

Signal processing and data reduction

Display

Fig. 16.80 Conceptual diagram of a smart structure (after [16.57])

This chapter introduces the concept of structural

health monitoring, gives an overview of state-of-the-art

sensing techniques used for performance control and

condition monitoring, and reviews topical applications

from different industrial areas. Further detailed descrip-

tions of a wide range of practical applications can be

found e.g. in [16.58–63].

16.6.1 Basics

of Structural Health Monitoring

The basic idea of structural health monitoring (SHM)

can simply be described as the integration of a type

of sensing system that provides information on demand

about any signiﬁcant change or damage occurring in an

aerospace, civil and mechanical engineering infrastruc-

ture [16.64]. The structural health monitoring process

involves the observation of a structure over time using

periodically sampled dynamic response measurements

from an array of sensors. The extraction of damage-

sensitive features from these measurements and the

statistical analysis of these features is then used to deter-

mine the current state of structural health. For long-term

structural health monitoring, the output of this process

is periodically updated information regarding the abil-

ity of the structure to perform its intended function in

light of the inevitable aging and degradation resulting

from operational environments. After extreme events,

such as earthquakes or blast loading, structural health

monitoring is used for rapid condition screening and

aims to provide, in near real time, reliable information

regarding the integrity of the structure [16.65]. During

operational use structural health monitoring attempts to

measure the inputs to and responses of a structure before

damage so that regression analysis can be used to pre-

dict the onset of damage and deterioration in structural

condition.

By combining the information of structural health

monitoring, current environmental and operational con-

Part D 16.6

Performance Control 16.6 Structural Health Monitoring – Embedded Sensors 933

ditions, previous component testing, nondestructive

testing, and numerical modeling, a prognosis is possi-

ble to estimate the remaining useful life of the structure.

By adding an actuator network and a related control

and drive system, the structure can be improved to

a so-called smart material or smart structure.Itisable

to monitor itself and/or its environment to respond to

changes in its conditions (Fig. 16.80) [16.57].

As mentioned before the detection and prediction

of onset of damage is the main target of structural

health monitoring. Damage in engineering structures is

deﬁned as intentional or unintentional changes to the

material and/or functional or geometric properties of

these structures, including changes to the boundary con-

ditions and system connectivity, which adversely affect

the current or future performance of that structure. All

damage begins at the material level and, under appro-

priate loading scenarios, progresses to component- and

structure-level failure at various rates. Materials degra-

dation and failure can occur in different ways.

•

Gradually (e.g. fatigue, creep, corrosion, wear,

biodegradation, chemical degradation);

•

Suddenly and unpredictably (e.g. fracture, ﬁber

breakage, matrix cracking, ﬁber splitting, delamina-

tion, debonding).

All material degradation and failure precedes a change

of mechanical and/or chemico-physical characteristics

of the material. In this context mechanical character-

istics (e.g. elasticity, strength) and chemico-physical

characteristics (e.g. thermal expansion, temperature dis-

100 μm

Fig. 16.81 Cross section of a ﬁber-optic sensor embedded

into concrete (after [16.66])

tribution, humidity, oxidation or corrosion status) have

special meaning. These characteristics and/or associ-

ated auxiliary variables (such as, e.g., strain) must

be detected by means of physical sensor effects or

measurable quantities and converted into a useful out-

put signal. In all cases the sensing system must be

able to resolve the parameter of interest as a func-

tion of both position and time throughout the structure.

The spatial and temporal bandwidths that are required

to address these detection needs must be adapted to

the special requirements of the structure being moni-

tored.

Sensing capabilities can be given to materials or

structures by externally attaching sensors or incorpo-

rating them within the material or structure during

manufacturing. In the ﬁrst place the incorporation of

the sensing system must be in compatibility with the

material structure. This means that the functional char-

acteristics and performance of the material may not be

impaired by the sensor integration. The embedding of

piezoelectric sensors into ﬁber-reinforced composites or

of ﬁber-optic sensors into concrete are typical exam-

ples for such a way of integration (Fig. 16.81). On the

other hand the sensor must be robust enough to survive

the manufacturing process (e.g. high temperatures dur-

ing curing process), withstand chemical attacks from

F (N)

1.5

0.5

2.5

du(26)iaaka.009

14.10.2004

Probe G

Ind. ca 95 μm

Thickness ca. 220 μm

du(26)iaaka.010

du(26)iaaka.011

du(26)iaaka.012

du(26)iaaka.023

du(26)iaaka.026

8070605040302010090

x (μm)

–10

Fig. 16.82 Strain transfer of a two-layer coated ﬁber measured by

indentation testing (after [16.67])

Part D 16.6

934 Part D Materials Performance Testing

F (N)

max

0.75

0.5

0.25

1.25

1.5

1.75

du(26)iaaka.027

14.10.2004

Probe C

Ind. ca 95 μm

Thickness ca. 220 μm

du(26)iaaka.028

du(26)iaaka.029

du(26)iaaka.030

50403020100

x (μm)

–10

Fig. 16.83 Strain transfer of a polyimide-coated ﬁber measured by

indentation testing (after [16.67])

the material (e.g. very high pH environment in con-

crete), and withstand extreme mechanical loads (e.g.

highly elastic behavior of plastics) (Figs.16.82 and

16.83).

A wide range of physical sensor effects can be

used to detect changes of mechanical and/or chemico-

physical characteristics of a material. Preferably elec-

trical (e.g. piezoelectric materials) or optical sensing

effects (e.g. optical ﬁbers) are used. Table 16.6 gives an

overview about common sensor effects, which are used

today for smart materials or structures.

To monitor a complete structure or a part of mater-

ial, different architectures of sensor arrangement can be

used. Basically the following variations are of practical

interest [16.57].

•

A point sensor is one that monitors a particular pa-

rameter at a closely conﬁned point deﬁned by the

effective cross-sectional area of the sensor element.

In principle, the point sensor only sees a sample of

the measurand at one particular point.

•

An integrating sensor is one that takes an aver-

age value of a particular measurand over an area

or length that is comparable to the area or length

of the structure being monitored. Integrating sensors

are sometimes spatially weighted (e.g. by variation

of sensitivity) to ensure that they are sensitized to

particular spatial distributions and not others.

•

A distributed sensor is capable of evaluating the

parameter of interest as a function of position

throughout the geometry of the sensor element. The

ability to perform distributed measurements is par-

ticularly important in structural health monitoring

since it enables the derivation of the measurand at

a large number of points throughout the structure

using a single interrogation port and thereby elimi-

nates the need for complex wiring harnesses.

•

A multiplexed sensor system is one that combines

a number of point, integrating, or distributed sensors

into a complex system. It could go through an elec-

tronic interface and use techniques derived from the

ﬁeld. It can also be implemented at the sensor tech-

nology level. Here the multiplexing may be effected

on the measurand subcarrier.

•

A quasi-distributed sensor system combines a num-

ber of integrating sensors into a single system that

is multiplexed in the measurand carrier domain.

Finally the role of signal processing in structural

health monitoring should not be understated. Signal-

processing procedures can be divided into basic and

advanced methods [16.65]. A typical basic procedure is

data normalization. Data normalization is a procedure

to normalize data sets so that signal changes caused by

operational and environmental variations of the struc-

ture can be separated from structural changes of interest,

such as structural or material deterioration or degrada-

tion.

The purpose of data fusion is to integrate data from

a multitude of sensors with the objective of making

a more robust and conﬁdent decision than is possible

with any one sensor alone. In many cases, data fusion

is performed in an unsophisticated manner, as when

one examines relative information between various sen-

sors. At other times, such as those provided by artiﬁcial

neural networks, complex analyses of information from

sensor arrays are used in the data-fusion process.

Data cleansing is the process of selectively choos-

ing data to accept for, or reject from, the feature

selection process. The data-cleansing process is usu-

ally based on knowledge gained by individuals directly

involved with the data acquisition.

Feature extraction is the process of identifying

damage-sensitive properties, derived from the meas-

ured vibration response, which allows one to distinguish

between the undamaged and damaged structure. The

Part D 16.6

Performance Control 16.6 Structural Health Monitoring – Embedded Sensors 935

Table 16.6 Typical sensor effects to detect material degradation and failure

Material characteristics/ Sensor effects

measurand Electrical signals Optical signals

Mechanical:

• Strain

• Displacement

• Vibration

• Acceleration

• Force

• Pressure

• Piezoelectric effect

• Piezoresistive effect

• Change of resistance

• Change of

- Transmission

- Wavelength

-Phase

-Timeofﬂight

- Brillouin scattering

Chemico-physical:

• Temperature

• Humidity

• pH value

• O

concentration

• Heat ﬂow

• Thermo resistance

• Thermoelectric effect

• Chemical resistance

• Conductivity

• Fluorescence

• Change of

− Transmission

− Wavelength

− Phase

− Raman scattering

− Brillouin scattering

best features for damage detection are typically appli-

cation speciﬁc. Numerous features are often identiﬁed

for a structure and assembled into a feature vector. In

general, a low-dimensional feature vector is desirable.

It is also desirable to obtain many samples of the fea-

ture vectors. There are no restrictions on the types or

combinations of data contained in the feature vector.

A variety of methods is employed to identify features

for damage detection. Past experience with measured

data from a structure, particularly if damaging events

have been previously observed for that structure, is

often the basis for feature selection. Numerical simu-

lation of the damaged structure’s response to postulated

inputs is another means of identifying features. The ap-

plication of artiﬁcial ﬂaws, similar to those expected

in actual operating conditions, to laboratory specimens

can identify parameters that are sensitive to the ex-

pected damage. Damage-accumulation testing, during

which structural components of the system under study

are subjected to a realistic loading, can also be used

to identify appropriate features. Fitting linear or non-

linear, physical-based, or non-physical-based models of

the structural response to measured data can also help

identify damage-sensitive features.

Statistical model development is concerned with the

implementation of the algorithms that operate on the

extracted features to quantify the damage state of the

structure. The algorithms used in statistical-model de-

velopment usually fall into three categories. When data

are available from both the undamaged and damaged

structure, the statistical pattern-recognition algorithms

fall into the general classiﬁcation referred to as su-

pervised learning. Group classiﬁcation and regression

analysis are supervised learning algorithms. Unsuper-

vised learning refers to the class of algorithms that are

applied to data not containing examples from the dam-

aged structure.

The damage state of a structure can be described

as a ﬁve-step process [16.68]. The damage state is de-

scribed by answering the following questions.

1. Is there damage in the structure (existence)?

2. Where is the damage in the structure (location)?

3. What kind of damage is present (type)?

4. How severe is the damage (extent)?

5. How much useful life remains (prognosis)?

Answers to these questions in the order presented rep-

resent increasing knowledge of the damage state. The

statistical models are used to answer these questions in

an unambiguous and quantiﬁable manner.

16.6.2 Fiber-Optic Sensing Techniques

Basics

Basic element of a ﬁber-optic sensor is a thin optical

ﬁber made of a highly transparent glass or plastic (poly-

meric) material. The optical ﬁber consists of a core

having a refractive index n

core

and a surrounding

cladding having a refractive index n

cladd

.Insuchaﬁber

the propagation of light can be explained by different

models. The models are based on some fundamental

postulations and have certain limits of application. Ray

optics explains the kinematics of propagation. Wave op-

tics explains diffraction and interference phenomena.

Electromagnetic optics makes possible an exact anal-

ysis of the phenomena of classic optics, including the

effect of energy at the interfaces. Finally quantum optics

Part D 16.6

936 Part D Materials Performance Testing

Table 16.7 Overview of most common types of silica optical ﬁbers used for sensors

Fiber type Multimode step index Multimode graded index Single-mode step index

Refractive-index proﬁle

1 n

Light propagation (schematic)

Beam is reflected

Beam is refracted

Beam is guided

Geometry

Core (n

)

Cladding

)

Protective coating

Typical diameter Core: 50 μm

Cladding: 125 μm

Coating: 140 μm

to 250 μm

Core: 50 μm

Cladding: 125 μm

Coating: 140 μm

to 250 μm

Core: 6 μm (870 nm)

9 μm (1300 nm)

Cladding: 125 μm

Coating: 140–250 μm

explains all the known optical phenomena, including

interaction of light with matter. In this section the ex-

planations are limited to ray and wave optics, because

they allow a simple and practical understanding of ﬁber

optic sensing techniques. A comprehensive and detailed

introduction to all models (including Maxwell’s equa-

tions) can be found in [16.69,70].

Based on ray optics, light propagation in an opti-

cal ﬁber can be understood as follows. When light is

launched into one end of the ﬁber and n

core

> n

cladd

is true, it propagates along the ﬁber to the other end

corresponding to the physical effect of total internal re-

ﬂection. Only light that is launched for 0 <Θ<Θ

max

can be guided along the ﬁber (assuming that Θ

max

the maximum value of the range of the accepted an-

gles Θ)(Fig.16.84). It is continuously reﬂected at the

interface between the core and the cladding; the criti-

cal angle α

max

must not be exceeded. Light that strike

the end face of the ﬁber at an angle greater than Θ

max

is no longer completely reﬂected at the core/cladding

Part D 16.6

Performance Control 16.6 Structural Health Monitoring – Embedded Sensors 937

boundary; instead it is partly refracted into the cladding

so that it is no longer completely available for further

propagation.

The properties of light guidance through a ﬁber are

governed largely by the proﬁle of the refractive index

of the core and cladding. In a step-index-proﬁle ﬁber

the refractive index is constant across the entire cross

section of the core and cladding (Table 16.7) while the

light rays propagate along straight lines in the core and

are completely reﬂected at the core/cladding bound-

ary. The individual light rays cover different distances,

so that there are considerable differences in their re-

spective transit times. This is called a multimode ﬁber.

Very small core diameters (< 10 μm) allow only one

mode to travel through the ﬁber (called single-mode

ﬁbers). Fibers with a graded-index proﬁle are made up

of a core having a radius-dependent refractive index and

a cladding with a constant refractive index. Those rays

converging in the center travel a shorter distance, but

because of the higher refractive index there, they travel

at a lower speed. On the other hand, the smaller refrac-

tive index near the cladding causes the rays traveling

there to have a higher velocity, but they have a longer

distance to travel. By choosing a suitable proﬁle expo-

nent it is possible to compensate for these differences in

transit time.

An optoelectronic unit, which contains a light

source and a detector, and a processing unit for data

acquisition, data processing and instrument control

complete the ﬁber-optic sensing system (Fig. 16.85).

Depending on the sensor type, semiconductor laser

diodes (LD), vertical-cavity surface-emitting lasers

(VCSEL), or light emitting diodes (LED) are used

preferably. As detectors photo diode with p-i-n semi-

conductor structure (PIN diode), avalanche photodiodes

(APD), or miniaturized spectrometers are mostly inte-

grated into the optoelectronic unit. A comprehensive

and detailed explanation of common light sources and

detectors for ﬁber-optic sensing techniques can be

found in [16.69,70]. For special or high-resolution mea-

surements more complex measuring equipment like an

optical time-domain reﬂectometer (OTDR) or a high-

resolution optical spectrum analyzer are used.

Fiber Fabry–Pérot Interferometer

A ﬁber Fabry–Pérot interferometer sensor consists of

a cavity deﬁned by two mirrors that are parallel to each

other and perpendicular to the axis of the optical ﬁber.

There are two arrangements of Fabry–Pérot interfer-

ometer (FPI) sensors: ﬁrst, the (intrinsic) in-ﬁber FPI

sensor, where the cavity is formed by two mirrors at lo-

cladd

Refractive index n

Cladding

Core

core

max

Fig. 16.84 Light propagation in a multimode ﬁber

Light source

Coupler

Optical fiber or

fiber bundle

Sensor or sensitive

area in the fiber

Read-out unit

Fig. 16.85 Principle setup of a complete ﬁber optic sensor

system

cations in the length of the ﬁber. The maximum distance

of the mirrors (cavity length) can reach some mm and

deﬁnes the gauge length. The second type is the extrin-

sic FPI sensor (EFPI). The optical cavity is formed by

the air gap (usually about 10–100 μm) between to un-

coated ﬁber faces (Fig. 16.86). The most widely used

design is to ﬁx into position the two ﬁber ends in a hol-

low tube. The ﬁber end-faces act as mirrors and produce

the interference fringes.

The functional principle of an FPI sensor is as

follows. The incoming light reﬂects twice: at the inter-

face glass/air at the front of the air gap (the reference

(Fresnel) reﬂection) and at the air/glass interface at the

far end of the air gap (sensing reﬂection). Both re-

ﬂections interfere in the input/output ﬁber. The sensor

effect is induced by force-induced or temperature-

induced axial deformation of the hollow tube. This

leads to a shift of the ﬁber end-faces inside the tube

(because they are only ﬁxed at the ends of the tube),

which results in changes on the air gap length (gap

width s). From this follows a phase change between the

reference reﬂection and the sensing reﬂection that is de-

tected as an intensity change in the output interference

signal.

Part D 16.6