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Use of the mark-tracking method for optical ber characterizationV. Chean, E. Robin, R. El Abdi n , J-C. Sangleboeuf, P. HouizotUniversite de Rennes1, Larmaur, ERL CNRS 6274, Campus de Beaulieu, 35042 Rennes Cedex, France

a r t i c l e i n f o

Article history:Received 7 December 2010Received in revised form15 February 2011

Accepted 2 March 2011Available online 25 March 2011

Keywords:Optical bersYoung’s modulusMark-traking method

a b s t r a c t

The mark-tracking method was used in the uniaxial tensile test to determine the elastic properties of optical bers. The mark-tracking method is based on the follow-up of two markers on the specimenwith the help of an image processing technique. It allows us to determine the true strain with respect tothe small strains assumption ( r 1%) or the nite strains ( 4 1%) without any impact of the rigid solidmovement or pulley ber sliding on the measured strain. Both coated optical ber and stripped berwere subjected to the uniaxial tensile test and the cantilever beam bending test. The Young’ modulusresults of the stripped ber were found to be very similar for both tests. Thus, the mark-trackingmethod is adaptable to the tensile test of optical bers and the elastic behaviors of both coated opticalber and stripped ber are found to be non-linear. Their Young’s moduli are 22 and 79 GPa,respectively. These results revealed that those coatings play a mechanical role in ber elongation.

& 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Besides signal transmission for telecommunications, bers areused in an increasing number of devices and the availability of silica bers enlarges the eld of possible applications.

A large group of applications encompasses optical ber sen-sors, remote chemical analysis, thermal measurements and ther-mal imaging, reectometry, optical instrumentation and also laserpower delivery [1,2]. Most medical applications of bers, withtheir specic requirements, are related to this group. Moreover,optical ber sensors are widely used in smart materials [3–5], forexample, in order to monitor civil engineering structures to assesstheir durability. In the framework of this study, compositematerial embedded optical bers were used in order to improvethe use in service of high technology bridges which are made upof composite materials. Therefore, elastic properties have been amajor consideration in the application of optical bers. In order tocharacterize the elastic properties of optical bers, both coated

ber and stripped ber (stripped polymer coating ber) weresubjected to mechanical tests. In this work, cantilever beambending test and uniaxial beam bending test and uniaxial tensiletest were performed to determine the Young’ modulus andmechanical behavior of silica optical ber.

The Young’ modulus of stripped ber is determined by acantilever beam test. Then, to validate this result some uniaxialtensile tests were performed. The uniaxial tensile test was usually

used to characterize the mechanical behavior of optical ber bymany studies [6 ,7]. In this paper, during the tensile testing, anoptical method (mark–tracking method) is used to measure berelongation instead of using the crosshead machine displacement.

2. Fiber structure, ber reliability and used ber

2.1. Fiber structure

An optical ber is a waveguide: a beam of light launched atone end of an optical ber travels down the ber with negligibleloss of input light. The optical ber is made of two transparentmaterials, most of the time glass for the core and the claddingaround this. The cross section of most optical bers is cylindrical,but other geometries (rectangular, ower-shaped, D-shaped,honeycomb, etc.) have been developed to address particularneeds.

2.2. Fiber reliability

As a general rule, the lifetime of the ber depends mainly onchemical durability and applied stress. Failure corresponds tobreaking, which is known to happen as crack propagation from asurface aw. Real bers have surface aws resulting from proces-sing. The initial intrinsic strength of a ber is related to chemicalcomposition, and ultimately to the energy of the chemical bond.Current values are 4 GPa for silica bers and less than 1 GPa foruoride and sulde bers. Initial strength decreases with respectto time when the ber is subjected to stress corrosion, or more

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journal homepage: www.elsevier.com/locate/optlastec

Optics & Laser Technology

0030-3992/$- see front matter & 2011 Elsevier Ltd. All rights reserved.

doi: 10.1016/j.optlastec.2011.03.004

n Corresponding author. IUT de Rennes, 3, Rue du Clos Courtel, B.P. 90422, 35704Rennes Cedex 7, France. Tel.: þ 33 2 23 23 41 12; fax: þ 33 2 23 23 41 12.

E-mail address: [email protected] (R. El Abdi) .

Optics & Laser Technology 43 (2011) 1172–1178

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simply, under a permanent stress in a humid environment. Thisphenomenon has been extensively studied in silica bers [8] .

2.3. Used ber

In this study, monomode silica optical bers were used and theber diameter is equal to 125 mm. Two acrylate polymer coatings(0.2 NA acrylate coupler bers) with a thickness of 62.5 mm wereused ( Fig. 1). The acrylate coating is the most used in standardoptical bers. It protects the ber but it is not perfectly water-tight. The internal layer is soft with a low glass transitiontemperature ( T g ) and is applied onto the glass ber surface. Itensures protection against micro-bending and damping of theexternal stresses. The external layer has a higher T g and protectsthe ber against physical aggression. To comply with processrequirements, UV-polymerization of the acrylate resins is rapidlyperformed, in line, and offers an excellent adhesion and a largerange of elasticity (Young’s modulus).

Usually, the tensile test is used to determine the Youngmodulus of a ber. During a dynamic tensile test, the ber issubjected to deformation under a constant velocity until rupture.The two ber ends are rolled up onto pulleys. The lower pulley isxed while the higher pulley is mobile and its displacementvelocity corresponds to the chosen deformation speed to carry outthe test. During the test, the deformation and the tensile load aremeasured using a dynamometric cell while the ber deformationis deduced from the displacement between the xed lower pulleyand the mobile higher plate. But in some cases, ber slippingduring the dynamic test cannot be prevented and the measuredparameters are not exact. In the following study, the marktracking method is used and leads to correct measurements.The mark tracking method is a non-contact technique is welladapted for the measurement of the optical ber strains. Thistechnique presents great interest: it is not inuenced by themotion of the sample, nor sensitive to variation in the sample

color and canbe used to analyze both large and small strains.

3. Experimental tests

3.1. Cantilever beam bending test

A cantilever is a beam that is supported only at one end asshown in Fig. 2a. This test, thanks to the strength of materialstheory, leads to the determination of the Young’ modulus of silicaber (stripped polymer coated ber) [9] . The gauge length L of thespecimen is 244 mm and stripped ber density r is 2.15 g/cm 3

(measured by helium pycnometry).The geometry of the bending ber and the coordinate system

that will be used are shown in Fig. 2b. Deection y along the beam

is given by

y ¼-Wx2

24 EI ð x2 À 4Lxþ 6L2 Þ ð1Þ

I ¼pd4

64 ð2Þ

W ¼ r g pd2

4 ð3Þ

E and I are, respectively, the Young’ modulus and the moment of inertia of the stripped ber,. W is the self-weight load (N/mm),d is the diameter of the stripped ber equal to 125 mm asmeasured by optical microscopy and also by SEM (ScanningElectronic Microscopy)and g is the gravity acceleration.

With deection measured at the free end of the beam, theYoung’ modulus of a stripped polymer coating ber is calculated as

E ¼À WL4

8 f N I ð4Þ

From Eq. (4), the elastic deection f N (in mm) at point N(Fig. 2b) can be obtained:

f N ¼À WL4

8IE ð5Þ

The diameter of the core (wave guide) is 8 7 1 mm andis positioned on the neutral axis of the beam so that theYoung’ modulus obtained is that of silica.

The maximum strength s in the bending section is given by

s ¼Md2I

ð6Þ

M is the bending moment at the end support.The maximum strain e in the bending section is given by

e ¼sE ð7Þ

In this study, eight specimens of different gauge lengths wereused in the cantilever bending test.

Fig. 3 gives the s =eevolution according to e of experimental

results and the theoretical Mallinder–Proctor model, which is

Fig. 1. Silica optical ber used.

W

y

L

f

NM x

Stripped fiber(clamped – free)

Fig. 2. Cantilever beam test: (a) cantilever beam test of stripped ber and (b)schema of cantilever.

0

20

40

60

80

100

120

0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006

S t r e s s

/ s t r a i n ( G P a

)

Experimental results

Model of Mallinder-Proctor 27 % of incertitude

17 % of incertitude

72

Strain

Smallgaugelength

Fig. 3. Comparison with the Mallinder–Proctor model.

V. Chean et al. / Optics & Laser Technology 43 (2011) 1172–1178 1173



written asse ¼ E 0 1 þ

a :e2 ð8Þ

For most silica optical bers, generally E 0 ¼ 72 GPa and a ¼ 6are the chosen values.

For samples with a small gauge length, this can result in alarge measurement incertitude (from 17% to 27%) as shownin Fig. 3.

Some experimental results cannot be represented by theMallinder–Proctor model, particularly when e 4 0.00049(Fig. 3). If only two experimental results ( e ¼ 0.00039 and e¼ 0.00047) approach those of the Mallinder–Proctor model(Fig. 3), it is not easy to draw a conclusion from the experimentalprotocol test employed for the bers used with respect to thestrain–stress relationship.

On the other hand, using Eq. (5), Fig. 4 gives the evolution of the theoretical deection f N for different gauge lengths. Even fora large Young modulus (80 GPa), the experimental results(for gauge lengths greater than 240 mm) cannot be representedby the strength material theory.

We can conclude that the deection method is not easy to

adapt for the optical ber behavior evaluation and the mechanicalber behavior cannot be represented by Eq. (5) or by the tradi-tional model of Mallinder–Proctor.

Therefore, a uniaxial tensile test with the attachment of marktracking method was chosen to develop a new behavior model.

3.2. Uniaxial tensile test with mark–tracking method

3.2.1. Mark-tracking methodThe mark-tracking method is an optical technique that enables

local strain computation [10] .The principle of this method consists of tracking marks with

the help of image processing. The marks are applied on the berspecimen with a pencil. During the test, numerical ber imagesare stored (the frame rate is 1 image per second).

A digital image is considered as a matrix where each pixel isdened by its position and its intensity. A CCD sensor coded on8 bits is used and the grey level evolves between 0 and 255. So analgorithm coded in C þþ is developed and allows tracking of themarker positions s.

The tracking process is divided into three steps:

First stepA zone of interest (ZOI) position is dened. This zone leads todelimiting the image process area of each mark ( Fig. 5).Second stepIn this step, a calculation area A (in the ZOI) is dened bythe operator who chooses a ’’mask’’ (a selected zone),

where the barycentre calculation will be made. The barycentre

coordinates are given by [11]

x g ¼ Pi xiðI iÀ I sÞ

PiðI iÀ I sÞ

y g ¼ Pi yiðI iÀ I sÞ

PiðI iÀ I sÞ

8>>><>>>:ð9Þ

I i is the grey level of the pixels belonging to A, whosecoordinates are xi , yið Þ and I s is the threshold value thatdistinguishes the pixels of markers . Fig. 6 gives a tridimen-sional representation of the lower limit of the light intensity I s.I s is directly linked to the illumination conditions during the

threshold process. One can note ( Fig. 6) the inuence of I s onthe A calculation area. On the other hand, there must be onlyone calculation area in the ZOI (due to the process using abarycenter calculation) and the geometrical form of A must notbe changed for each acquired image.As the conditions of the illumination evolve during the test, wecannot use the same value of I s for each image. An algorithmwas developed and allows to recalculation of the optimal I svalue in order to attenuate the illumination variation and tokeep the same geometrical form of area A. Indeed, from theoptimal value of I s previously dened by the operator for therst image, the software determines the ratio of 9Max- I s9to9Min- I s 9. Max and Min represent the grey level optimal valuesof the image. This ratio helps to recalculate I s from the

optimum grey levels of the next image.

D e

f l e c

t i o n

( m m

)

Gauge length (mm)-250

-200

-150

-100

-50

00 50 100 150 200 250 300

Deflection for E =72 GPaDeflection for E =80 GPaExperimental results

N

Fig. 4. Deection versus gauge length for different Young modul.

Fiber

specimen

ZOI

Mark

Fig. 5. Zone of interest position (ZOI).

Not acceptablethreshold

A obtainedwhen Is = 174

ZOI

ZOI

ZOI

Grey level

P i x e

l

Pixel

A obtainedwhen Is =140

A obtainedwhen Is = 68

Not acceptablethreshold

Acceptablethreshold

Fig. 6. Evolution of the threshold intensity value.

V. Chean et al. / Optics & Laser Technology 43 (2011) 1172–11781174



Third stepFrom ZOI position and the I s value dened by the operator atthe rst image, the software tracks automatically the marks(the software can simultaneously track four marks) andcalculates the mark positions for the next image. Thus, theoptimal I s value is automatically computed for each image andif the barycenter position of mark gets too close to ZOI border,the ZOI position is automatically redened.

Two markers are gently and carefully deposited in order toavoid incidental surface cracks on the ber surface, as is the casewhen permanent marker pen is used. Strain determination wascarried out using the principle of measurement.

The calculation of mark position is performed with only onecamera and the out of plan ber position cannot be estimated.The out of plan displacement is prejudicial for the methodaccuracy, since this phenomenon induces geometrical distortion.

Thus, a stereo system is used. A camera with a mirror (whichgives another visualization plan) was used ( Fig. 7). The out-of-plan displacement is carefully controlled by using a mirrorinclined at 45 1 with respect to the axis of CCD camera. This set-up allows determining the three-dimensional position of eachmark during the test. When and only when the image of a realspecimen and the one of the mirror-presented specimen weresuperimposed (out of plan compound was not detected), the testresults were analyzed. Once the marks are located, the lengthbetween the two markers l(t ) and the strain e(t ) are calculatedevery second following the principle of the deformationmeasurement.

3.2.2. Principle of deformation measurement In Fig. 8, the line segment M 1 M2, considered as the segment of

the two markers at the initial state (time t ¼ 0) in the reference(O, X

!, Y !

), changes into the segment M 3 M4 at time t (change ismeasured every second) once a load is applied.

The deformed length l(t ) and the initial length L are given by

lðt Þ ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið X 4 À X 3 Þ2 þð Y 4 À Y 3 Þ2q ð10 Þ

and

L¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið X 2 À X 1 Þ2 þð Y 2 À Y 1 Þ2q ð11 Þ

Strain calculations are performed with respect to the small

strains assumption (strain r 1%) or the nite strains (strain 4 1%).

For strains greater than 1%, the nite strain assumption isused. Thus, the Euler–Almansi nite strain tensor is given by:

eij ¼12

@u i

@ x jþ

@u j

@ xiÀ

@uk

@ xi

@uk

@ x j ð12 Þ

where u! ¼u i

u jrepresents the displacement vector.

The uniaxial deformation becomes

e ¼ e11 ¼12

½lðt Þ �2 À L2

½lðt Þ �2 !¼12

1ÀL

lðt Þ 2 !¼

12

1À1l 2 ð13 Þ

If the strains are lower than 1%, the following Equation (14) isused. The engineering normal strain or engineering extensionalstrain e of the ber axially loaded is expressed as a change in thelength DL per unit of the initial length L of the line element orber. The normal strain is given by

e ¼DlL ¼

lðt ÞÀLL ¼

lðt ÞL À1 ¼ l ðt ÞÀ1 ð14 Þ

l is a stretch ratio or extension ratio and is dened as the ratio of the nal length l(t )to the initial ber length L.

The parameters which must be determined are the coordinatesof M1 , M2 (initial state) and M 3 , M4 (deformed state). Then, onecalculates the axial strains of the ber, which can be small ( r 1%)or large ( 4 1%). The tensile strength of the optical ber s iscalculated as follows:

s ¼F A ð15 Þ

where: F is the measured force, A is the cross-sectional area of theoptical ber for polymer coated ber testing or cross-sectionalarea of the glass ber for stripped polymer coating ber.

3.2.3. Mark–tracking metrology performanceThe mark–tracking method performance is limited by several

sensibilities of parameters such as the light intensity during the

test. To study the method accuracy, repeatability tests were done.The tests consist in tracking a mark on a ber xed before loading.The change of the barycentre coordinates x g and y g is studiedand leads to computation of the standard deviation, which givesthe method accuracy ( Fig. 9). With a small strain assumption(Lb l(t )–L) and using Eq. (14), the accuracy formula is

Dee

¼Dlðt Þþ DL

lðt ÞÀLþ

DLL

%Dlðt Þþ DL

lðt ÞÀL) De ¼

Dlðt ÞL

þDLL

¼2Dlðt Þ

Lð16 Þ

The minimum value of L is equal to 150 pixels and themaximum accuracy value of Dl(t ) is equal to 0.1 pixel. So, thestrain accuracy is equal to:

De ¼ 7 2 Â 0:1=150 ¼ 7 13 Â 10À4

ð17 Þ

Realspecimenimage

Specimenimagepresented bymirror

Fiber specimen

CCD videoCamera G

a u g e

l e n g

t h

Mirror

Pulley

Fig. 7. (a) Data acquisition system devices and (b) Image analysis.

X

Y

Initial state (time t=0)

M1

M2

X1

Y1

X2

Y2

O

Y

XM3

M4

X3

Y3

X4

Y4

Deformed state (time t)

O

Fig. 8. Deformation of line segment.




3.2.4. Tensile testsThe monitor is used to control the ber deformation during the

test. Recording of marker positions is carried out using a CCDvideo camera sensor and a data acquisition card. Then all datainformation is stored in a computer for strain calculations, withcorresponding tensile force data for stress calculations. Opticalbers are wound around the pulleys to perform the tensile test as

shown in Fig. 7.The gauge length is 0.2 m and the tests are performed at roomtemperature (19 7 1 1C, 40–50% RH). The cross-head speeds are8 and 4 mm/min for polymer coated ber and stripped polymercoating ber, respectively. In order to avoid the bers slipping anddamaging the contact area, a double sided tap is applied on theside surface of each pulley on which three windings of the berspecimen are carried out. For the stripped polymer coating berspecimen, the stripped length is 2–3 cm in the middle part of thespecimen (polymer coated ber).

4. Experimental results

4.1. Discussion

The main purposes of these tensile tests are to nd out Young’smodulus of used polymer coated ber (PCF) and stripped ber(SF), and to analyze the mechanical ber behavior.

Results from the mirror ( Fig. 7b) show that during the tensiletests, no out-of-plane angle is noticed (the real specimen imageand the image presented by the mirror are parallel and themarked points are at the same level) and the strain curves of the real specimen and of the mirror-presented specimen aresuperimposed ( Fig. 10). As a result, the mark–tracking methodis available.

Tables 1 and 2 reveal that Young modul of the polymer coatedber (PCF) and the stripped ber (SF) are found to be 22 and82 GPa with (at rst sight) an elastic linear behavior in terms of 5–6% and 3%, deformation respectively as shown in Fig. 11 .

In our studies, Young’s modulus of silica bers are found to bearound 82 GPa, which is different from the results mentioned inprevious studies ( E ¼ 72 GPa) and with a linear stress–strainrelationship as shown in Fig. 11. Moreover, the stress–strainrelationship of optical bers was rst examined by Mallinderand Proctor [12] and later by Glaesemann et al. [13] . They foundthat the relation between stress and strain of an optical ber isnonlinear. Then, the nonlinear behavior was used in the strengthmeasurement of optical bers in many studies [ 14–16 ]. Hence,there are two aspects to be considered and to be discussed.

The rst aspect refers to strain calculation. One would com-pare the nite strain assumption in our case, with the small

assumption strain e. As the strain results varied from 3% to 6%, the

strains calculated by the small assumption, e (Eq.(14)), and thenite ones ( e) (Eqs. (12) and (13)) are very similar.

For the ve tested samples (SF), the same behavior was seen.Fig. 12 gives for sample No 4 (SF4), the experimental values of s / e(s is calculated using Eq. (15)) according to e as well as theMallinder–Proctor theoretical model, which is written as

s

e¼ E 0 1 þ

a :e

2 ð18 Þ

-0.2-0.15

-0.1-0.05

00.05

0.10.15

0.2

0 50 100 150 200 250Time (s)

XgYg

X g a n

d Y g

( P i x e

l s )

Fig. 9. Evolution of barycentre coordinates during the repeatability test.

0

500

1000

1500

2000

2500

0 0.005 0.01 0.015 0.02 0.025

Strain ( )

S t r e s s

( ) ( M P a

)

Mirror Real

Fig. 10. Results from mirror and real measurements.

Table 1Mechanical property of polymer coated ber (PCF).

Samplenumber

DiameterÂ 10 À 3 (mm)

Failurestrain (%)

Young’smodulus (GPa)

1 245 5.4 21.962 245 5.3 23.133 245 5.3 22.114 245 5.0 22.02

Average 22.30Standard deviation 0.55

Table 2Mechanical property of stripped ber (SF).

Samplenumber

DiameterÂ 10 À 3 (mm)

Failurestrain (%)

Young’smodulus (GPa)

1 125 2.3 81.922 125 2.5 81.123 125 2.7 81.91

4 125 2.2 83.385 125 3.0 83.42

Average 82.35Standard deviation 1.01

SF1 SF2 SF3SF4 SF5 PCF1PCF2 PCF3 PCF4

PCF

SF

Strain0

0500

1000

1500

2000

2500

3000

S t r e s s ( M P a )

0.01 0.02 0.03 0.04 0.05 0.06

Fig. 11. Stress–strain curve of polymer coated ber (PCF) and stripped ber (SF).




Non-linear ber behavior actually exists; the experimentalvalues approach the Mallinder–Proctor curve. A small dispersionof the experimental values is to be noted for low deformations (atthe beginning of the test; eo 0.005). This may be due to thesetting up of the ber at the beginning of the test and to thecomplex material behavior for small strain eo 0.005; Fig. 12 ).

On the other hand, if the experimental values are interpolatedwhen e varies between 0.005 and 0.023 (0.005 o eo 0.023), theycan be represented by a non-linear function in the form ( Fig. 12 )

se ¼ 79 :3 1 þ

5:e2 ð19 Þ

Thus, a non-linear behavior exists for the ber, although thisbehavior is slightly non-linear for the Verrillon bers used(Fig. 12 ). The silica Young modulus E 0 for these bers approaches79 GPa, which is different from the Young modulus obtained forfailure strains between 0.02 and 0.03 ( Table 1 ). The nonlinearitycoefcient a for these bers is close to 5 (instead of the medianvalue for pure silica proposed by Mallinder ( a ¼ 6)).

The second aspect refers to the Young’s modulus aspect. Wefound that the Young’ modulus E 0 of the stripped ber is

approximately equal to 79 GPa, which seems to be a high valuecompared to that of fused silica ber, which is usually about72 GPa. Optical bers used for this study are commercial Verrillonsingle mode silica bers [17] .

Glass ber (core and cladding) is a composite material. Afterbeing drawn at a high temperature (around 1800 1C), the core andthe cladding are cooled and thereafter solidied. Core and clad-ding have different dilation coefcients; the core dilation coef-cient is larger than that of the cladding. When the core cools, itcannot contract because the cladding is opposed to this contrac-tion. A strained core and a compressed cladding are obtained.During the tensile test, it is necessary to overcome the residualcompressive stresses to which the cladding is subjected beforesubmitting the ber to a positive tensile stress.

Thus the Young modulus of ber is higher than that of puresilica, which is a homogeneous material.

4.2. SEM observations

We can note that under tensile stress, the ber breaks atultimate failure load and several small length ber pieces,identical to needles, are scattered. When the polymer coatedber is submitted to the tensile test, the glass ber sustains moststress because the polymer coating is much softer than the glassber. The glass ber is pulled out from the polymer coating asshown in Fig.1. It can be seen ( Fig.1) that the glass ber brokewith an angle of 45 1, which is the typical brittle fracturemorphology. The fracture initiation of the polymer coating

occurred at the right hand side.

The polymer coating and the glass ber do not have the sametensile resistance and the polymer coating can stretch more thanthe glass ber. On the other hand, the critical glass ber aw isnot at the same cross section as the critical polymer aw. Thus,the glass ber is pulled out from the polymer coating when theglass micro-crack reaches a critical value.

5. Conclusion

The cantilever beam bending test is an effective test thatenables rapid measurement of the Young’ modulus of a ber,but it is not effective for the determination of stress–strainrelationship. However, the tensile test provides not only theYoung’ modulus, but also its linearity presented by the stress–strain curves. With the attachment of the mark-tracking methodin the tensile test, we proved that the Young’ modul of both thecoated and the stripped bers are different, respectively, about 22and 79 GPa, with a slightly nonlinear behavior in terms of 5–6%and 3% deformation respectively, which emphasizes the smallestnonlinear effect of the studied optical bers. The Young’ modulusof the stripped ber is similar when using either the cantileverbeam bending test or uniaxial tensile test.

These results highlight the fact that those coatings play amechanical role in ber elongation. It is not easy to characterizeoptical bers using a traditional tensile test, during which therecan be slips and measurement errors. The mark-tracking methodpresents high simplicity, is fast to use leads to the obtaining of agood strain evaluation with accuracy close to 7 10 À 3 and isnally the potential and available technique for optical bermechanical properties measurements.

On the other hand, the mark-tracking method can be easilytransferred for an industrial application to obtain local small orlarge strain measurements. One can use all samples where thedistance between two marks is higher than 1 mm.

Acknowledgment

The authors express their gratitude to Verrillon, Inc.(North Grafton, MA) for technical assistance and for materialsupport.

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0

20

40

60

80

100

120

140

160

0 0.005 0.01 0.015 0.02 0.025

SF4

Model of Mallinder-Proctor

Slightly nonlinear

S t r e s

s / s t r a i n

( G P a

)

72

Strain

= 79.3 + 196.539 = 79.3[1+(1/2).5 . ] (GPa)

Model of Mallinder-Proctor = E 0 [1+(1/2). . ]

E 0 = 72 GPa; =6

Fig. 12. Nonlinear behavior of used glass ber.




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[14] Grifoen W. Effect of nonlinear elasticity on measured fatigue data andlifetime estimation of optical bers. Journal of the American Ceramic Society1992;75(10):2692–7.

[15] Matthewson MJ. Optical ber testing techniques. In: Proceedings of the Society of Photo-Optical Instrumentation Engineers, Critical Review Series, vol. CR50, 1994,p. 31–59.

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