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doi:10.1016/j.op

�CorrespondiExactas, Ingenie

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Optics and Lasers in Engineering 46 (2008) 230–235

www.elsevier.com/locate/optlaseng

Feasibility study of a digital speckle pattern interferometry and bendingtest combined technique to investigate coating adhesion

Andres E. Dolinkoa, Guillermo H. Kaufmanna,b,�

aInstituto de Fısica Rosario (CONICET-UNR), Blvd. 27 de Febrero 210 bis, 2000EZP Rosario, ArgentinabDepartamento de Fısica, Facultad de Ciencias Exactas, Ingenierıa y Agrimensura, Universidad Nacional de Rosario, S2000BTP Rosario, Argentina

Received 6 June 2007; received in revised form 5 October 2007; accepted 9 October 2007

Available online 19 November 2007

Abstract

This paper presents a feasibility study to assess whether digital speckle pattern interferometry could be used as a possible technique to

investigate the adhesive performance of coatings. The approach is based on the measurement of the deflections produced by a pre-

notched coated specimen subjected to a four-point bending test. When the bending load is increased, a delamination between the coating

and the substrate is propagated with its length depending on the adhesion strength. Experiments carried out with specimens having

simulated delaminations confirm that digital speckle pattern interferometry can be used to estimate the delamination length.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: Adhesion; Digital speckle pattern interferometry; Delamination; Four-point bending test

1. Introduction

The development of novel coating techniques during thelast two decades has opened the application of coatedmaterials in different fields, such as machine tools,biomedical components, microelectronics and magneticrecording. Coatings are also used to protect mechanicalcomponents against high temperatures, radiation orcorrosion. Moreover, certain components put under highlocalised loads are reinforced with coatings of moreresistant materials to enhance its durability. Even thoughcoating failure in service can have many causes, usuallyadhesion is the most important one. For this reason, it isessential to have suitable test methods to guarantee theadhesion of a given coating–substrate system.

Although several test methods exist that can be appliedto evaluate the adhesion of a given coating–substratecombination, the characterisation of this property is not a

e front matter r 2007 Elsevier Ltd. All rights reserved.

tlaseng.2007.10.003

ng author. Departamento de Fısica, Facultad de Ciencias

rıa y Agrimensura, Universidad Nacional de Rosario, Blvd.

0 bis, S2000BTP Rosario, Argentina. Tel.: +543414853200,

x: +543414821772.

ess: guille@ifir.edu.ar (G.H. Kaufmann).

simple issue [1]. Many of these tests are qualitative or semi-quantitative and the adhesion is assessed from theappearance of the fracture surface, as in the tape peel test[2]. A quantitative test method to evaluate adhesion isthe four-point bending test [2], in which it is fairlystraightforward to convert load–displacement data takenfrom a coated specimen into fracture energy, results thatare directly relevant to the adhesion failure process tobe investigated [3]. This adhesion test is based on theintroduction of a notch over the coated surface of thespecimen. As the bending load is increased, a delaminationwill be propagated along the interface between the coatingand the substrate. For a given bending load, the extensionof the delamination will depend on the adhesive strength ofthe coating, so that its length will give a quantitativeestimation of the adhesion.The aim of this paper is to present a feasibility study to

assess if digital speckle pattern interferometry (DSPI) [4]could be used as a possible technique to estimate theadhesion of coatings. DSPI is a very attractive technique inoptical metrology not only for its non contacting naturebut also for its relative speed of inspection procedure,mainly due to the use of video detection and digital imageprocessing. The application of digital techniques in DSPI

ARTICLE IN PRESSA.E. Dolinko, G.H. Kaufmann / Optics and Lasers in Engineering 46 (2008) 230–235 231

allows the automation of the data analysis process, which isusually based on the extraction of the optical phasedistribution encoded by the generated correlation fringes.From these data, the displacement field can be measuredover the whole surface of any rough object without makingcontact with it.

Using specimens containing simulated delaminationsand being subjected to four-point bending, this paperdemonstrates that the DSPI measurement of the deflectionscan be used to estimate their delamination lengths.Therefore, in the case of real delaminations these datacould be used to estimate the coating adhesion.

2. Experimental technique

The four-point bending technique used to evaluate theadhesion of a coating consists of two steps. The first step isthe application of a bending load to generate a delamina-tion parallel to the substrate–coating interface from thenotch introduced over the coated surface of the specimen.In the second step, the surface fracture energy that isdirectly relevant to the adhesion failure process is evaluated

Fig. 1. The experimental setup: beam splitter (BS), piezoelectric transdu-

cer (PZT), piezoelectric driver (PD), mirror (M), camera lens (CL),

microscope objective (L), specimen (S), support plate (SP), observing hole

(OH), loading screw (LS), load cell (LC) and display (D).

Fig. 2. (a) Cross section of the loading device showing the specimen with bot

(SR), applied load (L), steel plate (P), bronze sheets (Sh), glued region (G), dista

(b) front view of the specimen showing the imaging region.

using fracture mechanics-based models. As previouslymentioned, the aim of this work is to investigate whetherDSPI can be used to identify delaminations havingdifferent lengths.A diagram of the experimental setup used to measure the

deflections of a specimen (S) subjected to a four-pointbending test is shown in Fig. 1. Basically, this is aconventional DSPI interferometer with an out-of-planedisplacement sensitivity. The light from a He–Ne laser witha wavelength l ¼ 632.8 nm is divided into the object andreference beams by the beam splitter (BS). The referencebeam is directed to a mirror (M) that is linked to apiezoelectric transducer (PZT) used to introduce the phaseshifts and whose movement is driven by a control unit(PD). This beam is expanded by the microscope objective(L) and is directed to the CCD camera (Pulnix TM-620)through a BS where it is recombined with the specklepattern scattered by the specimen. The camera output is fedto a frame grabber (Matrox Pulsar) located inside thepersonal computer, which digitises the images in grey levelswith a resolution of 512� 512 pixels� 8 bits. The videocamera has a zoom lens (CL) which allows to image a smallregion of the specimen of approximately 14mm� 14mmin size.In order to load the specimen, a specially designed

loading device was built. It basically consists of a steelsupport plate (SP) in which the specimen was verticallypositioned. A conical hole (OH) was introduced in thesupport plate to allow the illumination and observation ofthe specimen. The bending load was manually controlledby means of a loading screw (LS) and was measuredusing a load cell (LC). Its value was displayed in a digitaldisplay (D).Fig. 2(a) shows a cross-section of the specimen contain-

ing the simulated delaminations when it was located in theloading device. The specimens to be tested were steel plates(P), each one with a dimension of 50mm� 15mm�1.5mm. In each specimen, two bronze sheets (Sh) with athickness of 0.25mm were glued over the specimen using

h simulated delaminations of length a: support plate (SP), supporting rod

nce between the loading rods (DL), distance between the support rods (DS);

ARTICLE IN PRESSA.E. Dolinko, G.H. Kaufmann / Optics and Lasers in Engineering 46 (2008) 230–235232

an epoxy resin. Both bronze sheets were positioned with aseparation of 0.3mm between them in order to simulate thenotch used to drive the delamination during the four-pointbending test. The simulated delaminations were producedby leaving a region without glue. To accurately controlthe shape and dimensions of the delaminated region, aTeflon tape with a thickness of 50 mm was laid over thesteel plate in the region where no adherence was required.The glued region (G) is shown in grey in Fig. 2(a). As aresult, each specimen contained two simulated delamina-tions of length a, symmetrically located with respect tothe notch.

The specimen was laid over two supporting rods (SR)made of steel and separated by a distance DS ¼ 36mm,which were in contact with its coated surface and werelocated near the specimen edges. The SP was thick enoughto prevent deformations due to the bending load. The load(L) was applied through two loading rods separated fromeach other by a distance DL ¼ 16mm. These rods werepositioned at the backside of the specimen and locatedsymmetrically from the notch. Fig. 2(b) shows a front viewof the specimen with the imaging region and the coordinatesystem used to analyse the experimental data.

3. Data analysis

As was previously mentioned, the deflection w(x,y)generated by each specimen was determined from theevaluation of the phase difference f(x,y) coded by theDSPI fringes produced after a variation of the bendingload. In the case of an out-of-plane interferometer withnormal illumination, the relationship between these mag-nitudes is given by [4]

wðx; yÞ ¼l4p

fðx; yÞ. (1)

The wrapped phase distribution was evaluated using theCarre phase-shifting technique [4], which is based on theprocessing of two sets of four phase-shifted speckleinterferograms recorded before and after introducing avariation of the bending load. This technique is based onthe evaluation of the difference in phase and gives asignificant improvement in the quality of the reconstructedphase maps when it is compared with the phase ofdifferences method (or the phase coded by the DSPIfringes) [5]. A local smoothing using a kernel of 3� 3 pixelswas also performed to improve the signal-to-noise ratio ofpixels having very low-intensity modulation.

The wrapped phase maps generated with DSPI usuallypresent a severe data contamination by noise and speckledecorrelation. In order to avoid the influence of incon-sistent pixels due to noise and erroneous discontinuities,the continuous phase distribution was calculated using aniterative and robust unwrapping algorithm based on theminimum L0-norm solution [6]. This phase-unwrappingalgorithm uses a weighting matrix to mask inconsistentpixels. In contrast to least-squares unwrapping methods for

which weights must be provided, the L0-norm algorithmestimates its own weights from the input phase data.

4. Removal of rigid body displacements

Undesirable small rigid body displacements, which quitefrequently are introduced during the loading process andare mainly due to alignment problems, make the compar-ison of the phase maps more difficult to be produced, byspecimens having different delamination lengths. More-over, these spurious displacements can only be detectedafter the acquisition procedure is completed and thespeckle interferograms are processed.In order to remove the rigid body displacements, a least-

squares method similar to the one used in Ref. [7] wasimplemented in this work. The rigid body motion isdisplayed in the displacement map as an inclination addedto the deflections produced in the bending test. In general,the removal method consists of evaluating a plane that fitsthe inclination of the rigid body displacement field by usinga set of pixels that depends on the phase map produced bythe tested specimen. In this case we used the pixelscontained along two lines parallel to the y-axis with awidth of 2 pixels. These lines were located on both sides ofthe notch and at a distance h ¼ 250 pixels from the y-axis.As it is described in detail in Ref. [7], the least-squares

method used to remove the rigid body displacementsconsists in writing the estimated phase f free of rigidmotion as

f ¼ f0 � d, (2)

where f0 is the measured phase containing rigid bodydisplacements and d is a corrective factor expressed by

d ¼MxþNyþO, (3)

the coefficients M, N and O being corrective parametersdue to rigid translations and rotations.These parameters were calculated by means of the

following least-squares fitting:

x1 y1 1

x2 y2 1

..

. ... ..

.

xs ys 1

2666664

3777775

M

N

O

264

375 ¼

f01ðx1; y1Þ

f02ðx2; y2Þ

..

.

f0sðxs; ysÞ

2666664

3777775, (4)

where xi, yi with i ¼ 1,y, S are the rectangular coordinatesof the S pixels of the phase map used in the fitting process.In order to evaluate the error produced by the removal

method, the out-of-plane displacement field w generated bythe four-point bending test was simulated according to thefollowing analytical expression [8]:

w ¼1

2EIðLD3

A � LD2ADL þ LDADLx� LDAx2Þ, (5)

where E is the Young modulus of the specimen, I is itsmoment of inertia, DA is the distance between the loadingrod and the supporting rod along the x-axis, and DL is the

ARTICLE IN PRESSA.E. Dolinko, G.H. Kaufmann / Optics and Lasers in Engineering 46 (2008) 230–235 233

distance between the loading rods and L the applied force.Eq. (5), which is valid in the region between the loadingrods, was used to calculate the displacement fieldscorresponding to both loading states, the initial state witha pre-bending load of 120N and the final state with abending load of 125N. For each of these displacementfields, a set of four speckle interferograms with a phase shiftof 901 between successive frames was computer-generatedusing a simulation method similar to the one proposed inRef. [9]. Following the procedure described in Section 3,each set of four computer-simulated speckle interferogramswas used to determine the unwrapped phase map f, whichrepresents the displacement field generated by the variationof the bending load between the initial and final states.

In order to simulate a phase map produced by a specimensubjected to a four-point bending test and also affected byrigid body motion, a plane deflection map was added to thedisplacement field produced in the final loading state. Thenew set of four phase-shifted speckle interferograms wassimulated and afterwards a second unwrapped phase mapf0 produced by a four-point bending test contaminated withrigid body motion was evaluated.

Finally, the removal method was applied to the phasemap f0 and the estimated phase map f was compared withthe phase map f produced by a specimen subjected to afour-point bending test but without rigid body displace-ments. This comparison was carried out by evaluating therms phase error s defined as

s ¼1

ðN � 1ÞN

XG�1x;y¼0

fðx; yÞ � fðx; yÞ��� ���� Dfðx; yÞ

� �h i2

( )1=2

,

(6)

with

Dfðx; yÞ� �

¼1

N

XG�1x;y¼0

fðx; yÞ � fðx; yÞ��� ���, (7)

Fig. 3. Computer-simulated wrapped phase map: (a) produced by a plate su

method to remove the rigid body motion was applied.

where N ¼ G�G is the total number of pixels, being G thewidth and height of the image in pixels.Several displacement fields having different magnitudes

of rigid body motion were used to evaluate the perfor-mance of the proposed removal method. As a typicalexample, Fig. 3(a) shows a computer-simulated wrappedphase map produced by a specimen subjected to a four-point bending test and contaminated with a rigid bodydisplacement that introduced four fringes across the x- andy-axis. Fig. 3(b) displays the wrapped phase map obtainedafter the removal method to cancel rigid body motion wasapplied. In this case an rms phase error of s ¼ 3.7� 10�4

was obtained, which is a quite low value. This typical resultis a clear indication that the estimated phase map fobtained after the rigid body displacement was removed bymeans of the proposed least-squares method agrees quitewell with the original phase f free of rigid motion.

5. Experimental results

Several specimens containing simulated delaminationswith different lengths were tested using the same loadingconditions in order to compare the deflections obtainedwith the DSPI technique. As mentioned previously, thespeckle interferograms corresponding to the reference stateof each specimen were recorded by pre-loading them with aload of 120N. The speckle interferograms correspondingto the deformed state were recorded after the bending forcewas increased to a value of 125N. In all specimens, theobtained phase maps were corrected with the removalmethod presented in the previous section. As a typicalexample, Fig. 4(a) shows the wrapped phase mapdetermined for a specimen having no delamination, thismeans a specimen with both bronze sheets perfectly gluedto the steel plate. In contrast, Fig. 4(b) shows the wrappedphase map produced by a specimen having a simulateddelamination with a length of 6.5mm. It is important to

bjected to bending and rigid body displacements; (b) evaluated after the

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Fig. 4. Wrapped phase map determined for a specimen containing: (a) no delamination; (b) a delamination with a length of 6.5mm.

y

x

w

y

x

w

Fig. 5. Deflection w evaluated for a specimen containing: (a) no delamination; (b) a delamination with a length of 6.5mm.

A.E. Dolinko, G.H. Kaufmann / Optics and Lasers in Engineering 46 (2008) 230–235234

mention that the wrapped phase maps shown in these lastfigures are those obtained previously to the application ofthe least-squares method used to remove rigid bodydisplacements.

It can be noticed that the fringe number is higher inFig. 4(b) than in Fig. 4(a), since the deflections are higherfor a specimen having a given delamination. However, thedifferences between the mechanical behaviour generated byboth specimens can be visualised more clearly by observingthe deflections determined after the application of thephase unwrapping algorithm. Figs. 5(a) and (b) show a 3Dplot of the deflections produced by a specimen having nodelamination and another one containing a simulateddelamination with a length of 6.5mm, respectively. Fromthese figures, it is clearly observed that the presence ofdelamination changes quite strongly the shape of themeasured defections. When the specimen does not containa delamination, the coating copies the deflection of thesubstrate. However, when a delamination is present at theinterface between the coating and the substrate, Fig. 5(b)

shows that the coating deforms similar to a cantileverbeam.Finally, Fig. 6 shows a comparison between the

deflections measured along the longitudinal directiony ¼ 0 for a specimen containing no delamination and threesimilar plates, each one containing a simulated delamina-tion with length a ¼ 2.5, 5 and 6.5mm. As previouslymentioned, the speckle interferograms generated by eachspecimen were recorded using the same load combination.The first observation to point from this figure is that thedeflection generated at the notch by each specimenincreases with the length of the delamination. It is alsoobserved that the curves evaluated for the differentspecimens follow the curve produced by the sample withno delamination (a ¼ 0mm), except for the portion wherethe debonding is present. Therefore, the delaminationlength of each specimen can be estimated by comparing thedeflections generated by a specimen with and without thedebond. From the results shown in Fig. 6 and also from thetests performed using other specimens, it can be concluded

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0 1 2 3 4 5 6

0.3

0.6

0.9

1.2

x [mm]

w [

µm]

a

a

a

a

= 0 mm

= 2.5 mm

= 5 mm

= 6.5 mm

data5

Fig. 6. Deflection w measured at one side of the notch and along the line

y ¼ 0 for specimens having delaminations with different lengths.

A.E. Dolinko, G.H. Kaufmann / Optics and Lasers in Engineering 46 (2008) 230–235 235

that the proposed technique is able to estimate thedelamination lengths with a relative error of not morethan 5%.

In case of a real test in which the adherence of thecoating is not known, the length of the delaminated regioncould be estimated by comparing the measured deflectionswith the curve obtained from a finite element analysis of asimilar specimen, subjected to the same bending load buthaving no debond. As for a given bending load, thedelamination length will depend on the adhesive strengthof the coating; by measuring the deflections of thedebonded region, it would be possible to obtain aquantitative estimation of its adhesion.

6. Conclusions

This paper presents a feasibility study to assess whetherDSPI could be used as a possible technique to investigatethe adhesive performance of coatings. It is experimentallydemonstrated here that DSPI allows the measurement oftiny differences between the deflections produced by quitesmall delaminations introduced in a pre-notched coatedspecimen subjected to a four-point bending test. Thesedelaminations are propagated from the notch and along

both sides of the coating–substrate interface as the bendingload is increased, with its length depending on the adhesionstrength. Results obtained using specimens containingsimulated delaminations confirm that DSPI can be usedto detect defects having different sizes and also to estimatetheir lengths.Additional investigations are necessary to develop a

practical approach, which could be used as a tool toestimate the adhesion of a coating–substrate system. Thiswork will involve the development of an appropriate modelto calculate the adhesion strength from the measurement ofthe deflections using inverse analysis and a fracturemechanics approach. These investigations will be the objectof future work.

Acknowledgements

The authors would like to thank the financial supportprovided by the Agencia Nacional de Promocion Cientıficay Tecnologica of Argentina.

References

[1] Lacombe R. Adhesion measurement methods. Boca Raton: Taylor &

Francis; 2006.

[2] Ollendorf H, Schneider D. A comparative study of adhesion test

methods for hard coatings. Surf Coat Technol 1999;113:86–102.

[3] Broek D. Elementary engineering fracture mechanics. 3rd ed. Boston:

Martinus Nijhoff Publishers; 1984.

[4] Rastogi PK. Measurement of static surface displacements, derivatives

of displacements and three-dimensional surface shape. Examples of

applications to non-destructive testing. In: Rastogi PK, editor. Digital

speckle pattern interferometry and related techniques. Chichester:

Wiley; 2001. p. 142–224.

[5] Huntley JM. Automated analysis of speckle interferograms. In:

Rastogi PK, editor. Digital speckle pattern interferometry and related

techniques. Chichester, New York: Wiley; 2001. p. 59–139.

[6] Ruiz PD, Kaufmann GH, Galizzi GE. Unwrapping of digital speckle-

pattern interferometry phase maps by use of a minimum L0-norm

algorithm. Appl Opt 1998;37:7632–44.

[7] Dolinko AE, Kaufmann GH. A least-squares method to cancel rigid

body displacements in a hole drilling and DSPI system for measuring

residual stresses. Opt Lasers Eng 2006;44:1336–47.

[8] Nash WA. Strength of materials (Schaum Outline Series). 2nd ed.

New York: McGraw-Hill; 1977.

[9] Kaufmann GH, Davila A, Kerr D. Digital processing of ESPI addition

fringes. Appl Opt 1994;33:5964–9.