Non-destructive detection of glue deficiency in laminated wood using thermography

L U L E Å I U N I V E R S I T Y . J k ^ , O F T E C H N O L O G Y

2003:02

DOCTORAL THESIS

Nondestructive Detection of

Glue Deficiency in Laminated Wood

Using Thermography

H E N R I K B E R G L I N D

S K E L L E F T E Å C A M P U S Division o f W o o d Technology

Nondestructive Detection of

Glue Deficiency in Laminated Wood

Using Thermography

Henrik Berglind

Trätek - Institutet för träteknisk forskning

Doktorand vid:

Avdelningen för träteknik, Institutionen i Skellefteå

Luleå tekniska universitet

Akademisk avhandling

som med vederbörligt tillstånd av Tekniska fakultetsnämnden vid

Luleå tekniska universitet för avläggande av teknologie

doktors-examen, offentligt kommer att försvaras på svenska i A-husets

Hörsal på SKERIA-området i Skellefteå, fredagen den 14:e

februari 2003, k l . 10.00

Ordförande: Professor Anders Grönlund

Luleå Tekniska Universitet

Fakultetsopponent: Professor Alexander Lauber

Högskolan i Kalmar

Doctoral Thesis 2003:02

ISSN: 1402-1544

Sammanfattning

Syftet med arbetet beskrivet i denna doktorsavhandling har varit att

studera potentialen hos termografi, vilken är en beröringsfri och

oförstörande provmetod, att detektera limbrist under ett tunt

laminerat träskikt. Tekniken är ämnad för användning inom t.ex.

fanerlimningsindustrier.

Resultaten har bekräftat att det är möjligt att detektera limbrist i

laminerade träprodukter med puls-, uppvärmnings- och

lock-in-termografi. När inspektionstid ej är en större begränsning, t.ex. vid

off-line-provning, bör lock-in-termografi användas för varje

defektdjup; den kan detektera defekter som är 4 gånger bredare än

defektdjupet hos åtminstone 2,0 rnm tjocka ytskikt. Under

förutsättning att signal-till-brus-förhållandet kan ökas är

puls-termografi lämpat för defektdjup på 0,5-1,0 mm i en

on-line-tillämpning där inspektionstid är en kritisk parameter och ligger

omkring några sekunder. Om signal-till-brus-förhållandet inte kan

ökas tillräckligt är uppvärmningstermografi ett alternativ som bör

användas för defektdjup mellan 0,5-1,4 mm. När den limmade

produkten är varm direkt efter limningen kan även

nedkylnings-termografi vara ett alternativ.

För luftkopplad ultraljud i transmissionsmod minskade varken

kontrast eller upplösning med defektdjupet ner till 2.0 mm, vilket

kvalitativt gör den till ett konkurrenskraftigt alternativ till

termografi. Inspektionstiden är dock proportionell mot den

skannade ytan och kan bli väldigt lång när det krävs en god

upplösning.

Limbristmönstret hos brottytorna överensstämde väldigt bra med

kontrastmönstret detekterat med termografi och luftkopplat

ultraljud. Kontrast detekterad med termografi och luftkopplat

ultraljud kan alltså anses indikera en hållfasthetsminskning av

limfogen.

Nyckelord: oförstörande provning; puls-, uppvärmnings och

lock-in-termografi; laminerat trä; faner; limfog; defekt; delaminering;

limbrist.

The scope o f the work described i n this doctoral thesis has been to study the potential o f thermography as a noncontact and nondestructive test ( N D T ) method to detect glue deficiency beneath a thin laminated layer o f wood. The w o o d lamination industry is clearly an appropriate sphere f o r the application o f the technology described here. The thesis is presented as a monograph mainly based on five appended papers.

The purpose o f the theoretical part, based on a survey o f the literature, was to understand how thermal phenomena coupled to thermography can be described theoretically, how different factors and thermographic methods affect the results o f a thermography measurement and to ascertain the status o f delamination detection w i t h thermography.

The principal purpose o f the experimental measurements was to determine penetration depth, resolution, inspection time and repeatability f o r pulse, heating-up, and lock-in thermography. Using image thresholding as a defect classification method, a method comparison has also been performed. Furthermore, the performance o f another N D T method, air-coupled ultrasound, was briefly investigated. Finally, the contrast detected by the two N D T methods has been validated with the crack test as a destructive reference test method.

The results have confirmed that it is possible to detect glue deficiency i n laminated wood products w i t h pulse, heating-up and lock-in thermography. Whenever time is not a restriction, lock-in thermography should be used f o r each defect depth; it is capable o f detecting defects which are 4 times wider than the defect depth w i t h at least a 2.0-mm-thick surface layer. Provided the signal to noise ratio (SNR) can be increased, pulse thermography is suitable for defect depths o f 0.5-1.0 m m i n an on-line application where inspection time is a critical parameter and lies around a few seconds. I f the SNR cannot be sufficiently increased for pulse thermography, heating-up thermography is an alternative that should be used f o r defect depths between 0.5-1.4 mm.

For air-coupled ultrasound in transmission mode, the contrast and resolution did not decrease with defect depth down to 2 m m , which qualitatively makes it a competitive alternative to thermography. However, its inspection time is proportional to the scanned surface and might be very long i f a good resolution is needed.

The glue deficiency pattern o f t h e fracture surfaces corresponded very w e l l to the contrast pattern detected by thermography and air-coupled ultrasound. Thus, contrast detected by thermography and air-coupled ultrasound can be regarded as capable o f indicating reduction o f the mechanical resistance o f the glue line.

Keywords: nondestructive testing; pulse, heating-up and lock-in thermography; laminated

Preface

This w o r k began i n the spring o f 1997 when I realised it was time to think o f what to work w i t h after m y master's degree i n materials science. I was interested i n nondestructive testing and wanted, i f possible, to connect it to materials science. As 1 liked to gain more practical and theoretical knowledge o f measurement technique, I was very happy when I later on became employed as an industrial thesis worker at Trätek, the Swedish Institute f o r W o o d Technology Research, w o r k i n g to solve a problem coupled both to materials science and to nondestructive testing. The industrial dimension o f m y employment has spurred me constantly during the course o f scientific investigation to take the requirements o f industry into account.

D u r i n g the work I have had the privilege o f being included in different networks: more exactly, the personnel at Trätek and Luleå University o f Technology at Skellefteå Campus, and also the board o f directors i n the Company Research School at Trätek, who at regular intervals have listened to me and given valuable advice. I am very happy to have had such a stimulating and pleasant w o r k i n g environment. Otherwise, as a thesis worker, it is easy to feel disengaged f r o m the rest o f humanity. I also want to express my gratitude to Casco Products, A B Gustaf K ä h r s and Tarkett-Sommer, who have given m y work a problem area and a financial raison d'etre. It is my hope that this w o r k w i l l lead to an added value i n their business. Further, the financial support f r o m KK-stiftelsen (Knowledge Foundation) N U T E K (Swedish National Board for Industrial and Technical Development), IRECO (Institute for Research and Competence Holding) and Svenskt Trä (the Swedish W o o d Association) is gratefully acknowledged.

Since the experimental phase o f the work, I owe above all nine persons a thousands thanks: Birger Marklund and Göran Forsberg, who helped me plane 0.5 m m thin wood samples; Helgo Heuer f o r helping me to keep m y deadlines; Pascal Henninot f o r helping me w i t h the tedious evaluation; Jan N y s t r ö m for sharing his knowledge i n spectral imaging; Gerhard Busse at the Institute for Polymer Testing and Polymer Science i n Stuttgart f o r his hospitality; Rainer Stößel at the same institute f o r performing air-coupled ultrasound measurements; and Alexander Dillenz, also at the same institute, f o r being the person he is and f o r sharing his Matlab software, without which every other word in the evaluation section would be o f the kind: "seems", "maybe", "probably", ... Many thanks also to Å k e Östlund for mathematical support; to Brian Reedy f o r clarifying comments regarding the English language and his computer calmness; and to Lars-Erik W i k s t r ö m for his thorough revision.

Especially thanks to my guides: m y industrial tutor Hans B r ä n n s t r ö m f o r giving the industrial perspective; m y examiner f r o m L u l e å Technical University, Anders G r ö n l u n d , for his pertinent remarks; and my tutor at Trätek, Owe Lindgren, for his support and everlasting trust. Finally, a big hug to my w i f e Catarina and the rest o f my family, who f i l l my existence w i t h life and j o y .

S k e l l e f t e å , January 2003

A B S T R A C T I P R E F A C E H T A B L E O F C O N T E N T S I l l L I S T O F PAP E R S / A P P E N D I X V 1 I N T R O D U C T I O N 1 1.1 B A C K G R O U N D 1 1.2 T H E R M O G R A P H Y 1 1.3 E A R L I E R WORK 2 1.4 S C O P E , PURPOSE A N D L I M I T A T I O N S 2 2 T H E R M O G R A P H Y T H E O R Y 4 2.1 P A S S I V E T H E R M O G R A P H Y 4 2.2 P U L S E T H E R M O G R A P H Y 4 2.2.1 Principle 4 2.2.2 History 5 2.2.3 Energy1 source 5 2.2.4 Photothermal effect 5 2.2.5 Heat transport 9 2.2.6 Penetration depth 14 2.2.7 Reflection 14 2.2.8 Scattering of a thermal wave 16

2.2.9 Contrast and inspection time 17

2.2.10 Resolution 19 2.2.11 Defect size determination 22

2.2.12 Defect depth determination 24

2.3 H E A T I N G - U P T H E R M O G R A P H Y 2 4

2.3.1 Principle 24 2.3.2 Energy source 25 2.3.3 Photothermal effect and heal transport 25

2.3.4 Penetration depth 26 2.3.5 Scattering of a thermal wave 27

2.3.6 Defect depth determination 27

2.4 C O O L I N G - D O W N T H E R M O G R A P H Y 2 8 2.5 L O C K - I N T H E R M O G R A P H Y 2 8 '

2.5.1 Principle 28 2.5.2 Energy source 29 2.5.3 Photothermal effect and heal transport 29

2.5.4 Penetration depth 31 2.5.5 Phase velocity 32 2.5.6 Reflection and interference 32

2.5.7 Scattering of a thermal wave 34 2.5.8 Defect depth determination 36

2.6 C O M P A R I S O N O F T H E R M O G R A P H I C METHODS 3 6 3 T H E R M O G R A P H Y E X P E R I M E N T S 38

3 . 1 M A T E R I A L S A N D METHODS 3 9

3.1.1 Test pieces

3.1.2 Experimental setup 41 3.1.3 Experiments 4 2 3.1.4 Contrast evaluation method 43

3 . 2 R E S U L T S A N D DISCUSSIONS 4 4 3.2.1 Surface temperature 44 3.2.2 Contrast 45 3.2.3 Penetration depth 47 3.2.4 Resolution 48 3.2.5 Inspection time 50 3.2.6 Repeatability 51 3.3 Q U A L I T Y C L A S S I F I C A T I O N T H R O U G H T H R E S H O L D I N G 5 1 3.3.1 Penetration depth -52 3.3.2 Resolution 52 3.3.3 Inspection time 53 3.3.4 Summary '4 3 . 4 I N F L U E N C E O F WOOD S P E C I E S ON C O N T R A S T 5 4 3.5 I N F L U E N C E O F V A R I O U S P A R A M E T E R S ON C O N T R A S T 5 5 4 A I R - C O U P L E D U L T R A S O U N D E X P E R I M E N T S 57 4 . 1 M A T E R I A L A N D METHODS 5 7 4.1.1 Test pieces 57 4.1.2 Experimental setup 57 4.1.3 Experiments 5$ 4 . 2 R E S U L T S A N D DISCUSSIONS 5 8 5 N D T V A L I D A T I O N W I T H A D E S T R U C T I V E R E F E R E N C E M E T H O D 60 5 . 1 M A T E R I A L S A N D M E T H O D S 6 0 5.1.1 Test pieces 00 5.1.2 Digital colour camera 60

5.1.3 Crack test 5.1.4 Flatbed scanner 61 5.1.5 Spectral imaging 61 5 . 2 R E S U L T S A N D DISCUSSIONS 6 3 5.2.1 Crack lest 65 5.2.2 Spectral imaging 63 5.2.3 Validation 65 6 C O N C L U S I O N S 67 6.1 T H E R M O G R A P H Y P E R F O R M A N C E 6 7 6 . 2 Q U A L I T Y C L A S S I F I C A T I O N T H R O U G H T H R E S H O L D I N G 6 8 6.3 A I R - C O U P L E D U L T R A S O U N D 6 8 6 . 4 N D T V A L I D A T I O N W I T H A D E S T R U C T I V E T E S T METHOD 6 8 7 R E C O M M E N D A T I O N S AND F U T U R E W O R K 69 8 R E F E R E N C E S 70

This thesis is essentially based on work reported i n the f o l l o w i n g five appended papers:

I Berglind H (2000) Classification o f cracked glue lines w i t h the aid o f an image spectrometer. In: Kline DA, Abbott AL (Eds) Proceedings of the 4th International conference on Image Processing and Scanning of Wood Mountain Lake, Virginia, U S A

21-23 August 2000, pp 177-185

I I Berglind H , Dillenz A (2000) Detection o f glue deficiency i n laminated w o o d w i t h thermography. In: Divos F (Ed) Proceedings of the 12th International symposium on

Nondestructive Testing of Wood Sopron, Hungary 13-15 September 2000, pp 413-420

I I I Berglind H , Dillenz A (2002) Detection o f glue deficiency i n laminated w o o d w i t h pulse thermography. Accepted for publication in J Wood Sei (Springer Verlag)

I V Berglind H , Dillenz A (2002) Detection o f glue deficiency i n laminated w o o d w i t h lock-i n thermography. Submlock-itted to Holz Roh- Werkstoff (Sprlock-inger Verlag)

V Berglind H , Dillenz A (2002) Detecting glue deficiency i n laminated wood - a thermography method comparison. Accepted for publication in NDT E Int (Elsevier

Science)

V I Thermal data

Introduction

1 Introduction

During the past decades, production has been assisted by quality assurance systems i n many parts o f the industry i n order to achieve reliable production processes and high quality products. W i t h i n this area, nondestructive control o f the production process, as w e l l as nondestructive testing ( N D T ) o f the products, plays an increasingly important role. This development has become feasible due to the rapid development o f sensor and processor technology and easy-to-use computer software.

1.1 Background

Adhesion problems occasionally occur during w o o d lamination.1 Products w i t h defects that are

detected i n the visual quality inspection are discarded, which is a direct production loss, and the defects not detected may lead to an expensive customer compensation claim.

One source o f adhesion problems is that the amount o f glue that is satisfactory in normal cases may, due to varying w o o d layer thickness, not be sufficient and may leave an air-gap after the gluing operation without mechanical resistance between surface layer and glue. Glue deficiency can also arise f r o m dosage equipment problems.

Principally, the first step is then to control the input parameters in the gluing process. When this is no longer cost effective, a worthwhile strategy might be to detect all faulty products w i t h an on-line N D T method and sort them out i n order to avoid compensation claims. Such a method does not exist today.

I f defects appear not just statistically, but i n a pattern, a spin-off effect o f on-line detection is that an error search o f the production process is triggered automatically. Thus, a particular problem can quickly be solved without producing needlessly many faulty products.

A n on-line N D T method assuring the glue line quality should not disturb the production f l o w and should be positioned i n the production line as soon as possible after the gluing operation.

1.2 Thermography

Thermography is a noncontact and nondestructive test method that uses an infrared (IR) camera, capable o f providing information about the structure to a limited depth beneath the surface o f a test object. Compared to many other nondestructive test methods, thermography is fast and manages to examine large areas w i t h relatively high speed. This makes thermography suitable f o r industrial quality inspection purposes.

In thermography tests, a heat f l o w inside the test piece is often externally generated. When the heat f l o w reaches a thermal irregularity, there w i l l be a perturbation o f the heat f l o w . I f the perturbation is high enough, the I R camera w i l l detect a contrast in the surface temperature o f the

test object. The information is then processed with appropriate computer software. The main thermography methods are called pulse,2 heating-up3, cooling-down and lock-in thermography.4

The principal differences between these methods are different ways o f heating the test piece and evaluating the signals measured f r o m the I R camera.

1.3 Earlier work

Considerable work has been done using thermography to detect defects i n the boundary layer between different materials. Principally, materials connected to the aircraft industry like carbon fibre reinforced polymers,5 thermal sprayed coatings6 and laminated a l u m i n i u m7 have been

investigated.

There have also been measurements performed on wood. Sembach et a l .8 detected 19-mm-wide

air-channels 4-5 m m beneath the surface o f medium density fibreboards and chipboards using lock-in thermography. W u et a l .9 also used lock-in thermography and detected holes w i t h a

diameter o f 4 m m , differences i n w o o d species o f the substrate and knots i n the substrate beneath a 2-mm-thick laminated veneer. Furthermore, W u et a l .1 0 detected glue threads under a

1-mm-thick veneer and delaminated areas under a 2-mm-1-mm-thick veneer as w e l l as under a 1-mm-1-mm-thick high-pressure laminated f i l m .

X u et a l . " used heating-up thermography, where 10 to 50-mm-large areas without glue was detected w i t h a contrast up to 0.7 ° C beneath 1.3 to 3-mm-thick surface layers o f white seraya. Danesi et a l .1 2 used cooling-down thermography and detected channels i n w o o d at a depth o f up

to 4 m m and a delamination i n a plastic coating. M e i n l s c h m i d t1 3 has detected delaminated

regions beneath a continuous pressure decorative laminate w i t h both pulse and cooling-down thermography.

1.4 Scope, purpose and limitations

The scope o f this w o r k has been to evaluate the applicability o f thermography to quality inspection o f laminated w o o d , more precisely, to determine which thermographic method is most suitable f o r the detection o f glue deficiency defects i n a product w i t h i n a reasonable period o f time.

The thesis is presented as a monograph. The purpose o f the theoretical section is to present an overview o f how thermal phenomena i n thermography can be described theoretically and how different factors affect measurement results. The theoretical section is based on a survey o f the literature. The greater part o f research and development w o r k described here has been directed towards pulse thermography and lock-in thermography. This is reflected i n the space distribution between the different thermographic methods i n this theory section.

The purpose o f the experimental laboratory measurements was to present a simultaneously performed experimental comparison o f the different thermographic methods as regards detection o f glue deficiency defects i n laminated wood. The purpose was further to determine penetration depth, resolution, inspection time and repeatability o f the thermographic methods, The

Introduction

experimental work has principally been directed towards pulse, heating-up and lock-in thermography. Cooling-down thermography has been used to a lesser extent.

Mainly merbau, but also oak, alder and pine were used as surface layers w i t h thicknesses ranging from 0.5 to 4.0 m m . They were essentially knotless. The substrates, made o f Scots Pine, were glued together w i t h the surface layers w i t h urea-formaldehyde glue. A reduced clamping pressure was used in order to avoid smearing the glue over the simulated glue deficiency areas. The test pieces were made i n six replicates each. It should be pointed out that this is too f e w replicates to reflect the whole variation range o f wood material properties.

As ultrasound is an alternative N D T method to thermography, a short experimental comparison has been performed.

Lastly, the contrast measured w i t h the N D T methods was compared w i t h the fracture surface o f the test pieces after performing a destructive crack test.

2

Thermography theory

Studies o f the interaction between electromagnetic energy, heat and materials using a number o f different methods did not really begin u n t i l the middle o f the 1970s.1 4 The introduction o f the I R

camera1 5 came at about the same time after the invention o f charged coupled devices and made

graphical visualisation o f thermal emissions f r o m an object possible. This is w h y the method is called thermography.

The advantage o f thermography over other N D T methods is that the testing process is noncontact and relatively quick, as w e l l as o f f e r i n g a simple ocular interpretation o f the results. The I R camera is also portable and quite robust.

I n thermography, the examined object is usually exposed to an external energy excitation i n order to produce a heat f l o w inside the object, whereafter the thermal emission f r o m the surface o f t h e object is observed w i t h an I R camera. When the heat f l o w reaches a thermal irregularity, there w i l l be a perturbation o f the heat f l o w . I f the perturbation is great enough, the I R camera w i l l detect a contrast i n the surface temperature o f t h e object. This can be used to detect and quantify defects.

There are some variants o f thermography. The energy source and IR camera can be placed on the same side (reflection mode) or on opposite sides (transmission mode) o f the test object. The heating can be i n the f o r m o f a pulse, a continuous or a periodical signal. Heating and detection can be done along a line across the test piece or over a large area. I n this chapter, f i v e thermographic methods in reflection mode w i l l be presented: passive thermography, pulse thermography, heating-up thermography, cooling-down thermography and lock-in thermography.

2.1 Passive thermography

Passive thermography is the simplest f o r m o f thermography and only requires an I R camera. The thermal emission f r o m a body is measured, and thermal bridges inside walls o f apartment houses can be investigated, for instance.

Areas on the surface o f the studied object that show a contrast compared to other areas have different structural and/or different thermal properties at the surface or somewhere inside the body.

2.2 Pulse thermography

2.2.1 Principle

When contrast i n passive thermography is too low or does not exist at all, an external stimulus is applied i n so-called active thermography. This is the case with pulse thermography. A test piece

Thermography theory

is exposed to a short heat pulse (see Figure 2.1a) and an IR camera measures the cooling-down process. The heat pulse is normally produced w i t h a p o w e r f u l flashbulb that irradiates a relatively large surface o f a test piece. A f t e r a certain time, contrasts in thermal emissions can arise on the test piece surface (see Figure 2.1c and d). This indicates the presence o f thermal irregularities, e.g. defects (see Figure 2.1b) that influence heat f l o w beneath the surface o f the test piece. The I R camera records an image after a predetermined inspection time, i.e. when the contrast is highest.

Material T e m p e r a t u r e c o n t r a s t

a b c d

Figure 2.1 Schematic description of pulse thermography: a) shape of the heat pulse, b) test piece with defect,

c) development of the surface temperature above a defect (point 4) and above a defect free area (point 3), d) development of the contrast between the surface temperature at points 4 and 3.

2.2.2 History

In the 1960s an early variant o f pulse thermography was used, i n which heating was done w i t h a laser pulse and signal detection was done w i t h one I R detector.1 7 I n 1984 Reynolds and Wells

used a flash f r o m a high-power lamp as heating method combined w i t h signal detection and storage o f data with a compatible IR camera and called the method pulsed

video-thermography.18 Thus, an opportunity to inspect large surfaces at an industrially acceptable speed

arose. Nowadays, a computer controls measurements, data processing, classification and storage of information.

2.2.3 Energy source

The heat f l o w i n the test piece is often generated w i t h a lamp. Flashbulbs can emit 1.5-3 kJ o f electrical energy w i t h i n 5-10 m s .1 9

2.2.4 Photothermal effect

I f the energy emitted f r o m the lamp is to be useful, the test piece must absorb at least some o f the energy. Conversion o f electromagnetic radiation into heat inside the test piece is called

photothermal effect.

Radiant energy that hits a body is partly reflected f r o m the surface o f the test piece and partly transmitted into the body (see Figure 2.2). Due to absorption, the intensity o f the transmitted electromagnetic radiation decreases exponentially w i t h depth.

(Metal)

Figure 2.2 Schematic drawing of a test piece showing reflection, transmission and absorption of incident

electromagnetic radiation (E: intensity, i: incident, r: reflected, t: transmitted, k: absorption coefficient, z: test piece depth).2"

The incoming photons are reflected due to Compton scattering. The amount o f light reflected is described by the optical reflectance o f the test piece, R<,. In Figure 2.3, the optical reflectance w i t h i n the visible wave length interval is shown for earlywood and latewood, as w e l l as for some wood defects.2 1 Reflectance increases towards infrared wavelengths and averages w i t h i n the

visible area around 50 %.

- i i 1 1

400 500 600 700 Wavelength (nm)

Figure 2.3 Reflectance within the visible wavelength interval for earlywood and latewood of spruce andfor different

defects.2'

From reflectance, which depends on equipment and measurement method, the material parameter reflectivity, r, can be determined. Figure 2.4 a and b shows calculated reflectivity as a function o f wavelength for some metals and semiconductors.

Thermography theory'

Wavelenglh/jim

a

Waveiength/jirr b

Figure 2.4 Reflectivity- 'for a) metals (Al - aluminum, An - gold, Fe - iron, W - tungsten) and for b) semiconductors

(Ge - germanium, Si - silicon) .

A l u m i n i u m has a high reflectivity f o r ultraviolet light, visible light and infrared light*. Gold has a higher reflectivity for infrared and visible light than to ultraviolet light, while the contrary is true for silicon. Reflectivity also depends on colour. For example, a blackbody has low reflectivity.

Free electrons, atoms and molecules absorb the radiation energy that is transmitted into the body. They reach an excited state when they absorb radiation and then return to the normal state by emitting heat energy. For a material w i t h high optical absorption, the main part o f radiation is absorbed in a thin layer beneath the surface. For metallic materials the optical penetration depth,

Uo, is a f e w tenths o f a n m , f o r semiconductors it can extend to p m and f o r insulators like w o o d , a

few m m .2 0

A f t e r absorption o f a flash, containing a finite amount o f heat, Qo, the area between the surface and the optical penetration depth w i l l rise in temperature. As the energy is absorbed during a short time, the surface temperature can rise to high values that might be destructive f o r the test piece. For a flash w i t h a triangular shape (see Figure 2.5), the maximum temperature can be calculated w i t h the f o l l o w i n g equation:2 2

AT - 8Q »

m a s 3ßV2rcÄt"

(2.1)

Svmbol Quantity t nit AT™ maximum surface temperature °C Q. absorbed heat J/m:

ß effusivity Ws' :/ m:° C

At pulse length s

where effusivity, ß , is calculated f r o m the thermal properties o f the material:

(2.2)

* The wavelength interval o f the ultraviolet part o f the electromagnetic spectrum is 30 to 390 nm and 760 nm to 300 um for the infrared part.

Symbol Quantity Unit ß effusivity W sl :/ m2 oC

k thermal conductivity W / n f C P density kg/m'

cn specific heat capacity J/kg°C

A material w i t h high effusivity, like aluminium, shows a low rise in temperature. This can be explained by a high thermal conductivity, which implies that energy can be rapidly evacuated f r o m the surface. Another explanation is that w i t h a high heat storage capacity, i.e. the product o f density and heat capacity, a lot o f energy is needed for each degree o f temperature increase.

At

Figure 2.5 Schematic description of the power evolution, P, of a flash. At describes the length of the triangular

pulse.

I n appendix 6, an overview o f thermal properties for different materials is shown. Figure 2.6 shows which maximum temperature rise can be reached in different materials after absorption o f a flash.

Polystyrene Oak Brick Marble Aluminium

Figure 2.6 Comparison of maximum surface temperature rise between different materials after absorption of a

Thermography theory

2.2.5 Heat transport

The energy absorbed w i l l be partly emitted f r o m the surface o f the test piece through radiation and convection and partly be conducted into the test piece. According to signal processing theory, a flash can be idealised as a Dirac pulse, which is infinitely short and has an infinitely high intensity. Other properties o f a Dirac pulse are that infinitely many frequencies are needed in order to describe its spike-shape and that the energy in the pulse is regularly distributed over all frequencies. I n the case o f a flash, heat transport f r o m the surface can be seen as a propagation o f an infinite number o f thermal waves w i t h different frequencies. When t = 0 s at the surface, all the thermal waves are i n phase. The temperature i n the test piece after absorption o f the heat pulse is obtained through superposition o f all these waves.

W i t h the assumption that convection and radiation processes are negligible and that the test piece has a high optical absorption coefficient the one-dimensional solution o f the heat d i f f u s i o n equation:

82T 1 5T _

5 z2 a 5t

(2.3)

Symbol Quantity Unit

T temperature °C z distance below the surface in

a diffusivity m2/s

t time s

has the f o l l o w i n g solution:

AT(z, t ) = Q o

ßVTlt

(2.4)

Svmbol Quantity Unit

AT temperature change °C z distance below the surface m t time s Qo absorbed energy J/m2

a diffusivity m~/s

P effusivity Wsl / 2/m2 oC

The d i f f u s i v i t y , a, is analogous to the e f f u s i v i t y calculated f r o m the thermal properties o f a material, or more precisely as the ratio between its conductivity and its heat storage capacity: '

(2.5)

Svmbol Quantity Unit

a diffusivity TTT7S k thermal conductivity W/m°C P density kg/m3

D i f f u s i v i t y is a measure o f how high quantities o f energy can be conducted into a material and how fast this process is. Temperature at the surface (z = 0) is according to equation 2.4 proportional to the absorbed heat and inversely proportional to effusivity and the square root o f time. I n Figure 2.7, the cooling-down behaviour o f the surface o f the test piece is shown after absorption o f a flash for different materials. The temperature change is relative to f o r example the room temperature. The decline i n temperature is very fast at first, but then slows.

Time (s)

Figure 2.7 The cooling down behaviour of the surface of the test piece after absorption of a flash for different

materials. It is supposed that all materials have absorbed an equally high quantity of energy, i.e. Q0 = 2 kJ/nr.

Calculated from equation 2.4.

In Figure 2.8, the temperature change i n a test piece o f oak is shown as a function o f depth at three different time intervals after the flash.

Figure 2.8 Temperature distribution inside a test piece of oak as a function of depth at different times (0.1; 0.5; 3.0

Thermography theory

In the beginning, the second derivative o f the temperature w i t h reference to the depth, i.e. the curvature o f the curves i n Figure 2.8, is high close to the surface o f t h e test piece. This results, according to the heat diffusion equation, equation 2.3, i n a quick decrease i n temperature. Through thermal equalisation, heat is conducted into the body and the curvature decreases. The rate o f change in temperature is then successively slowed down.

In Figure 2.9 the temperature inside the test piece is shown as a function o f time f o r different depths.

Time (s)

Figure 2.9 Evolution of the temperature change inside a test piece of oak as a function of time after a heat pulse at

different depths (0.1; 0.5; 1.5 mm). Calculated from equation 2.4 with an absorbed energy Qn~ 2 kJ/m'.

As expected, it takes longer for areas deeper inside the body to increase i n temperature. The increase is also not as high deep in the test piece as it is on the surface due to absorption o f the heat f l o w .

Parker et a l .2 2 have formed the f o l l o w i n g equation f o r the length o f time it takes at a position

within the test piece to reach half o f its maximum rise i n temperature after absorption o f a flash:

t , / 2 =

-1.38z2

(2.6)

Svmbol Quantity Unit

11a time in order to reach half T-increase s z distance below the surface m a diffusivity m'/s

- * - Polystyrene - e - O a k

- a- Brick - x - Marble

Aluminium

Figure 2.10 The time for a position within the test piece to reach half of its maximum temperature rise after

absorption of a flash plotted as a function of depth for different materials. Calculated from equation 2.6.

As seen i n Figure 2.10, after 3.6 seconds the temperature has reached h a l f o f its maximum rise at a depth o f 2.0 m m i n oak.

A f t e r derivation o f temperature w i t h respect to depth i n equation 2.4, the heat f l o w is obtained w i t h Fourier's law:

dT

dz (2.7)

Symbol Quantity Unit

q heat flow W/m-k thermal conductivity W/m°C T temperature oC

2 distance below the surface m

Then the f o l l o w i n g one-dimensional expression for heat f l o w after absorption o f a flash is obtained:

2 V Teat

( 2 .

Symbol Quantity Unit

q heat flow W/nr Qo absorbed energy J/W a diffusivity m2/s

t time s z distance below the surface m

Thermography theory

Figure 2.11 illustrates heat f l o w i n a test piece o f oak as a function o f depth at three different time intervals after a flash. A s the heat penetrates into the body, the signal is heavily damped through heat absorption. Simultaneously, the signal becomes wider. This can be explained by the fact that thermal waves w i t h high frequencies propagate faster than waves w i t h lower frequencies (see section 2.5.5). 1400 1200 — 1000 800 £ S C 600 400 200 -0,1 s -0,5 s -3,0 s 0,0 0.5 1.0 Depth (mm)

Figure 2.11 Heat flow in a test piece oak as a function of depth at different times (0.1; 0.5; 3.0 s) after absorption of

a heat pulse. Calculated from equation 2.8 with an absorbed energy Q0- 2 kj/m".

Figure 2.12 shows heat f l o w as a function o f time for different depths. The maximum f l o w passes the depth 1.5 m m at 2.5 s, for example. The further inside the body, the slower the increase and decline o f heat f l o w .

1400

Figure 2.12 Heat flow in a test piece oak as a function of time after absorption of a heat pulse for different depths

; 0.5: 1.5 mm). Calculatedfrom equation 2.8 with an absorbed energy: Qa = 2 kj/nr.

2.2.6 Penetration depth

Since heat is absorbed when propagating into a material, there is a "maximum" depth to which a signal can reach. I n pulse thermography, thermal d i f f u s i o n length, p.,, is a measure o f penetration depth f o r transient thermal waves, where the temperature is the fractional part 1/e » 37 % o f the surface temperature (see also the exponent in equation 2 . 4 ) :2 4

m = 2 v a t (2.9)

Symbol Quantity Unit

thermal diffusion length for transient waves m a diffusivity nr/s t time s

The short time behaviour is dominated by the fastest propagating high frequency components o f the pulse and the longer time behaviour by the slower l o w frequency components. Figure 2.13 shows how the penetration depth varies over time i n different materials.

1E-01

1E-04 1 1

0 2 4 6 8 10 T i m e (s)

Figure 2.13 Penetration depth, fi,, for transient thermal waves as a function of time for different materials.

Calculated from equation 2.9.

Pulse thermography can be used to a depth o f 1 cm to 1 dm f o r aluminium and to a couple o f m m for marble, brick, oak and polystyrene.

2.2.7 Reflection

For a perfectly homogeneous material, the heat f l o w passes calmly and smoothly through the material. When a thermal wave hits a new medium w i t h different effusivity, e.g. a defect, both a reflection and a transmission o f the energy o f the heat pulse appear. The proportion between reflection and transmission is calculated f r o m the reflection coefficient and the transmission coefficient.

Thermography theory

For a perpendicularly incident thermal wave interacting w i t h a new medium, the thermal reflection coefficient and transmission coefficient are calculated w i t h the f o l l o w i n g equations:2 0

(2.10 a and b)

T =

—=-1 + b

Symbol Quantity Unit

R reflection coefficient

-T transmission coefficient

-where b stands f o r the ratio between the effusivities o f the two media:

(2.11)

Symbol Qu an tin I Dit

b ratio of the effusivities of the media

Pi effusivity ofthe area close to the surface Ws1 :/ m:° C

& effusivity of the defect Ws1 -/m2 oC

When heat propagates in a m e d i u m w i t h high effusivity, e.g. aluminium, and hits a material w i t h low e f f u s i v i t y , e.g. air, a high reflection (R * 1.0) o f thermal energy occurs. A n air-gap or delamination thus functions as a heat barrier. The reflection coefficient between oak and air is 0.98.

In section 2.5.6 interference f o r periodic waves is described and concludes that the reflection coefficient for a thin air-gap decreases with decreasing modulation or thermal wave frequency. Thus, the reflection coefficient is high i n the beginning o f a pulse thermography experiment, but decreases when these high frequency thermal waves are absorbed and only low frequency waves are left.

The reflection coefficient is limited to situations with distinct layers. When two media don't have direct contact, e.g. when rough surfaces are i n connection w i t h each other, it is more suitable to adopt a " j u m p i n temperature" instead o f a continuous change o f temperature at the boundary layer. This is why a thermal contact resistance is introduced:"3

(2.12)

Svmbol Quantity Unit

Rc thermal contact resistance CC . W

dd defect thickness m

2.2.8 Scattering of a thermal wave

The reflection o f heat f l o w gradually affects surface temperature i n f o r m o f a slower cooling above a defect than above defect free areas. The temperature change at the surface o f a test piece above a defect is described by the f o l l o w i n g one-dimensional equation:"

AT(z

=

0,t)

l + 2 £ R ° e " (2.13)

Symbol Quantity S Unit

AT temperature change °C z distance below the surface m t time s Qo absorbed energy J/m" R reflection coefficient -n number of echos -L defect depth m a diffusivity m:/s ß effusivitv Ws1 :/ n r ° C

The first term is known f r o m equation 2.4 and expresses decrease i n temperature inversely proportional to the square root o f time for a homogeneous material. The second term describes the deviation f r o m a homogeneous material. The sum sign accounts f o r the total effect f r o m a number o f echoes, n, reflected between a defect and the surface o f the test piece. Figure 2.14 shows how the reflection f r o m a defect affects the cooling o f the surface o f the test piece for different defect depths.

Time (s)

Figure 2.14 Cw-ves with the calculated surface temperature above a defect for different defect depths: 1, 2, 3, 4 and

Thermography theoiy

2.2.9 Contrast and inspection time

There are three different ways to define contrast.2 6 The most common is to use the temperature

difference or the absolute contrast, Ca, between areas with and without defects:

Ca( t ) = Td( t ) - Td f( t ) (2.14)

Svmhol Quantify Unit

C absolute contrast °C t time s Td surface temperature above area with defect °C T,„ surface temperature above defect free area ° c

The disadvantage w i t h this definition is that Ca varies linearly w i t h the absorbed energy. The

running contrast, Cr, is less influenced by the appearance and duration o f the heat pulse.

C,

T«(t)

(2.15)

Svmbol Quantity Unit

C: running contrast

-t time s C absolute contrast K T„, surface temperature above defect free area K

The normalised contrast, C„, is another way to describe contrast.

Td( t ) Td f( t )

C„

j max ^ max j --pmax |^max j

Symbol Quantity Unit

C„ normalised contrast

t time s

t " " time at maximum surface temperature s Td surface temperature above area with defect "C Td, surface temperature above defect free area °C T dn" maximum surface temperature above area with defect °C

T " maximum surface temperature above defect free area ° c

From this point i n this thesis, only absolute contrast w i l l be used and w i l l be referred to as

contrast. Contrast is directly measured w i t h the IR camera, but can also be calculated f r o m the

second term in equation 2.13:

C(z = 0 , t ) = f ^ j R " e

ßVTrt

Symbol Quantity Unit C contrast °C z distance below the surface m t time s Q» absorbed energy J/m: R reflection coefficient -n number of echoes -L defect depth m a diffusivity nr/s effusivity W si :/ n rDC

In Figure 2.15, contrast is shown as a function o f time for defects 1-5 m m beneath the surface. M a x i m u m contrast decreases inversely proportionally with the cube o f defect depth" and inspection time, i.e. the time needed to reach maximum contrast, increases w i t h the square o f defect depth.5

T i m o ( s )

T i m e ( s )

Figure 2.15 Calculated contrast as a function of time for defects located on five different depths, 1, 2, 3, 4 and 5 mm

in steel2. Q„= 10kJ/m2, R = 0.9.

M a x i m u m contrast also increases w i t h the reflection coefficient (see Figure 2.16). Inspection time is also influenced to a certain extent by the reflection coefficient. According to A h m e d6 and

Thermography theory

1 . 6

T i m e ( s )

Figure 2.16 Calculated contrast as a function of time for defects with different reflection coefficients in steet. Q0=

10 kJ/nr, 1. I mm.

I f the heat f l o w contains enough energy, it can be reflected one or more times between the defect and the surface o f the test piece before the heat f l o w is effectively absorbed. Figure 2.17 shows that such reflections increase maximum contrast, as w e l l as inspection time.

T i m e ( s J

Figure 2.17 Calculated contrast as a function of time for different numbers of echoes between the defect and the

surface ofthe test piece in steel2. Q0= 10 kJ/m2, R = 0.9, L - 0.7 mm.

2.2.10 Resolution

The ability o f a method to visualise small objects is described by its spatial resolution. I n order to describe which influence a finite extension o f the defects i n the plane has on the surface

temperature, the f o l l o w i n g three-dimensional model can be used, where a stands f o r defect radius:2

A T ( Z = 0 , I ) =

ßVrrt

e — e (2.18)

Symbol Quantity Unit

AT temperature change °C z distance below tbe surface m t time s Qo absorbed energy J/m2

a defect radius m a diffusivity m/s

effusivity Ws1 / 2/m2 oC

Figure 2.18 shows that maximum contrast decreases w i t h defect size and occurs somewhat earlier for smaller defects. Furthermore, contrast decreases faster f o r smaller defects.

0 . 8 f , — • ,

0 . 3 0 . 6 0 . 9 1.2 T i m e (s I

Figure 2.18 Contrast as a function of time for defects with different diameters (0.5-10 mm) in steel2. Calculated

from equation 2.18 with Qo = 10 kJ/nr, L = 0.7 mm. The curve on top has been calculated with the one-dimensional equation 2.13. n = 1, R = J.

The measurements shown in Figure 2.19 confirm the effect illustrated i n Figure 2.18 and i n equation 2.18.

Thermography theory

10

0 1.5 T i m e ( s )

Figure 2.19 Measured contrast as a function of time for different defect sizes (1)2 mm, (2) 2.8 mm, (J) 4 mm, (4) 5.7

mm, (5) 10 mm for air-gaps in diffusion bonded steel'.

In order to describe the ability o f a thermographic method to detect a defect, taking both the defect depth and the defect size into account, the notion thermal defect size, öx, is used:

6t= £ (2.19)

Svmbol Quantity Unit

8, thermal defect size -d true defect size m L detect depth m

Wyss et a l .2 9 have determined the relation between contrast and thermal defect size f o r laminates

o f isotropic PVC (see Figure 2.20). Defects i n f o r m o f air filled holes were detectable f r o m a thermal defect size o f 3. Contrast does not clearly depend on thermal defect size, as contrast develops differently depending on whether defect size or defect depth varies.

Above a thermal defect size o f 10 units, it seems as i f the curve levels o f f . This is expected according to Seidel et a l .3 0 as the edge effects w i t h heat f l o w around the defect edges become

deltaT max. [°C] PVC/PVC

Ratio defect diameter to the defect's depth (D/x)

Figure 2.20 Contrast plotted over thermal defect size for laminates of isotropic PVC"1.

As a rule o f thumb, V a v i l o v3 1 states that the resolution l i m i t is around 2-3 thermal defect size

units. I f the test piece is anisotropic, a correction factor is introduced whereby the thermal defect size is calculated according to the f o l l o w i n g equation3 2:

(2.20)

Symbol Quant itv Lnil 5, thermal detect size

d true diameter m L defect depth m diffusivity in the plane nv/s Oz diffusivity in the depth direction nr/s

2.2.11 Defect size determination

In pulse thermography, finite defects near the surface o f the test piece show up as a locally warmer area at the surface o f the test piece. I n order to estimate the real size o f the defect, it is often assumed that the boundaries o f the defect are situated where the measured thermal contrast intersects at half the m a x i m u m contrast^ ( F W H M : F u l l Width at H a l f Maximum, see Figure 2.21). Another way to estimate the real size o f the defect is to assess the edges o f the defect to the highest spatial contrast gradient.1 9 j 2

Thermography theory

C o n t r a s t

D e f e c t

-P o s i t i o n

T e s t o b j e c t

Figure 2.21 Schematic description ofthe FWHM method.

I f the defect size is estimated w i t h the F W H M - m e t h o d , an underestimation o f the defect diameter by 0.54p.t' occurs due to a heat f l o w conducted f r o m the warm topside, around the edges to the cold underside o f the defect.3"5 This means that the measured defect size w i l l decrease w i t h time, as thermal waves with low frequencies become dominant, according to the f o l l o w i n g equation:

= d - 1 . 0 8 v a t (2.21)

Symbol Quantity Unit measured diameter m d true diameter m a diffusivity rir/s t time s

A n air-gap inside oak ( a = 0.15 x 10"6 m2/s) w i t h a diameter of, f o r example, 10 m m , w i l l after a cooling o f 10 s according to equation 2.21 be underestimated by 13 % . Figure 2.22 shows how size measured, using the F W H M method, varies w i t h time and corresponds to finite difference modelling for different defect sizes.

12 11 10 _ 9 1 8 c 7 Z 1 0 I - J U L . Simulation • -J •, ". m~ j -Simulation Jl * » • — ""' S i m u l a t i o n -r • * -0 »0 ( -:f e j & f * •• Simuteflon :r " Simulation 3 4 5 Ttrrn^aoconris) * l O r e m » 6mm o Sa

Figure 2.22 Measured defect size compared to finite difference modelled size for 2, 3, 5. 8 and 10 mm wide

back-drilled flat bottomed holes beneath 0.5 mm Bakelite14.

Measured and calculated values are quite i n accordance w i t h each other.

2.2.12 Defect depth determination

When the presence and the size o f a defect is determined, it is sometimes desirable to determine the defect depth. W i t h i n acoustics, distances are detected by time o f flight measurements, i.e. the time between the emitted signal and the arrival o f the echo.

Using the same approach in thermography, it seems natural to calculate defect depth f r o m the time to maximum contrast. This is not satisfactory i n this case, as the m a x i m u m contrast depends on the reflection coefficient, the defect size and the number o f echoes between the defect and the surface o f the test piece.

However, the slope o f the increase i n contrast immediately after a flash decreases w i t h defect depth independently o f defect size (see Figure 2.23).

; £ —

Simulation Simulation deDth 0.5 mm depth 1.2 mm

0 2 4 S 8 10 :2 Timetseconas)

i • 12 mm Daom • 0 5 nwn üaotn A : 7 Daom |

Figure 2.23 Contrast from defect images compared with simulations for different defect depths. The hole had a

diameter of 10 mm and was hack-drilled in bakelite. 3'1

The time between flash and the first sign o f a deviation f r o m f ° '5- c o o l i n g (see Figure 2.14), might

also be used f o r coating thickness measurements.2 4

2.3 Heating-up thermography

2.3.1 Principle

In heating-up thermography, the test piece is suddenly illuminated w i t h a lamp at constant intensity, after which the rise i n temperature is registered by the IR camera (see Figure 2.24). Above defects such as air-gaps, w a r m spots similar to those detected w i t h pulse thermography w i l l appear.

Thermography theory

I f

T

A

Figure 2.24 Schematic charts of how the emitted intensity, I, from a lamp affects the surface temperature, T, of a

test piece.

2.3.2 Energy source

Quartz lamps w i t h electric effects f r o m 500-2000 W w a r m up the test piece.1 9 The Fourier

spectrum o f a step pulse consists o f many frequencies, but the lower frequencies have a higher energy content than higher frequencies.

2.3.3 Photothermal effect and heat transport

With the assumption that electromagnetic energy is absorbed only at the surface o f the test piece, the temperature change inside the test piece is, relative to room temperature, as described by the f o l l o w i n g equation after a step change i n surface heat f l o w :3 5

A T ( z , t ) = ^ L I a t I 4M I z . [ z

—e erfc — f = (2.22)

Svmbol Quantity Unit

AT temperature change °C z distance below the surface m t time s (Jo absorbed heat flow W/nr k thermal conductivity W/m°C a diffusivity nr/s

where erfc (z) = 1 - erf (z). erf (z) stands for the Gauss error function:

9 Z

e r f ( z ) = -r= f e ^ d ; (2.23)

Svmbol Quantity Unit

z distance below the surface m C integration variable m

A t the surface, the temperature change is described by the f o l l o w i n g equation:

AT(z = 0,t) = - ^ V t ßV7t

(2.24)

Symbol Quantin Unit

AT temperature change ° c z distance below the surface m t time s qe absorbed heat flow W/nr ß effusivity Ws" 2/nr°C

Figure 2.25 shows how temperature increases as a function o f heating time for different materials. The temperature o f polystyrene increases quickly due to its l o w effusivity, while aluminium hardly increase i n temperature at all due to its high effusivity.

- a - Polystyrene - e - O a k

~b- Brick -*-Marble

••«-Aluminium

Figure 2.25 The rise in surface temperature of a test piece as a function of heating time for different materials. All

materials are assumed to absorb equal quantities of energy, i.e. qo = 1.3 kW/nr. Calculatedfrom equation 2.24.

2.3.4 Penetration depth

I n heating-up thermography, the thermal diffusion length or the penetration depth, u.t, i n

heating-up thermography is the same as for pulse thermography.

-24ÖX

Svmbol Quantity Unit

Pi thermal diffusion length for transient waves m a diffusivity nr/s t time s

Thermography theoiy

2.3.5 Scattering of a thermal wave

Heat f l o w reflection f r o m a defect affects the surface temperature as a faster heating above the defect than above defect-free areas. The surface temperature o f the test piece above a defect can be described by the f o l l o w i n g one-dimensional equation:2 3

AT(z = 0, t ) = ^ V t f 4 = + 2 ] T r " i e r f c nL (2.26)

Symbol Quantity Unit

AT temperature change °C z distance below the surface m t time s q« absorbed heat flow W/m:

r complex reflection coefficient

-n number of echoes

-L defect depth m a diffusivity nr/s P effusivity W sr :/ m2 cC

where ierfc(z) = ——e 2 - z ( l - e r f ( z )

Y7r

(2.27)

The first term i n equation 2.26 is similar to that i n equation 2.24 and shows that for a homogeneous material, temperature increases proportionally to the square root o f time. The second term describes the deviation f r o m homogeneous materials. The sum sign describes the total effect f r o m a number o f echoes, n, that are reflected between the defect and the surface o f the test piece.

2.3.6 Defect depth determination

Figure 2.26 shows how the reflection f r o m a substrate w i t h high effusivity affects the surface temperature o f the test piece for different coating thicknesses.

1.0 t

fe

/

Figure 2.26 Heating curves with the calculated surface temperature for opaque yttrium stabilised zirkonia with

W i t h i n half a second, the substrate has influenced the surface temperature o f the test piece for all coating thicknesses. The thicker the surface layers, the longer time it takes before the thermal properties o f the substrate become dominant.

2.4 Cooling-down thermography

Cooling-down thermography reminds o f heating-up thermography i n the respect that the test object is subject to a step change. I n cooling-down thermography, radiation, convection, conduction or a combination o f those suddenly cools the test object. The heat f l o w w i l l travel in the opposite direction i n comparison to heating-up thermography, i.e. f r o m the inside o f the test object towards the surface. Areas above defects like air-gaps w i l l then be cooler than surrounding defect free areas.

Cooling down thermography is particularly suitable when the products to inspect are already warm f r o m the production process.

2.5 Lock-in thermography

2.5.1 Principle

I n lock-in thermography, the surface o f the test piece is illuminated by a lamp whose intensity, I , varies periodically as a sine wave (see Figure 2.27). As a consequence o f the pulsating illumination, the measured surface temperature, A , varies w i t h the same rhythm. Thermal waves w i t h the same frequency as the modulation frequency o f the lamp are generated and propagate into the test piece.

input

output

<j>,

I-input signal

s ~ \ / " ^ \ time

0

output signal

/

\ time

0

Pi

de

y

ias

Lay

,e

•

Figure 2.27 The principle of lock-in thermography:" The illumination from the lamp with intensity I can be

regarded as an input signal. The amplitude of the measured IR signal, A, and its phase delay in comparison with the input signal, cp, can be seen as an output signal. The input and the output signal have the same angular modulation frequency, w.. Amplitude or phase delay is used for image presentation.

Thermography theory

Sine wave signals are often used i n different measurement techniques. B y making the assumption that the output signal varies as a sine wave, a considerable amount o f noise is eliminated resulting in a signal to noise ratio improvement. Furthermore, it is often more accurate to measure phase i n comparison to amplitude.

The measured amplitude, A , o f the sine wave and its phase, cp, are calculated according to equation 2.28 a and b for each p i x e l .4 j 7 The I R signals Si, S2, S3 and S4 have been sampled w i t h

a time difference o f a quarter o f a period when the temperature variation o f the test piece surface has reached a "stationary" state (see Figure 3.6c). Both amplitude and phase signals are used f o r image presentation.

A = V /( S3- S , )2+ ( S4- S2)2

§ _ S (2.28 a and b) cp = arctan —

-S4- S2

Svmbol Quantity Unit

A amplitude a.u. S infrared signal a.u. © phase

-I f the thermal waves have interacted w i t h a new medium, e.g. a defect, the measured amplitude and phase are influenced and a contrast might show up in the I R image.

2.5.2 Energy source

The test piece is illuminated w i t h quartz lamps w i t h electric effects between 500-2000 W1 9 and

they are controlled w i t h a lock-in module. The radiation f r o m the lamp is described by the f o l l o w i n g equation:

(2.29)

Svmbol Quantity Unit

I intensity W/nr Io maximum lamp intensity W/nr to angular modulation frequency Hz t time s

In this type o f signal, all energy is concentrated to a single thermal wave frequency, i.e. the modulation frequency.

2.5.3 Photothermal effect and heat transport

The energy emitted f r o m the lamp is absorbed by the test piece according to the photothermal effect (see section 2.2.4).

For an isotropic homogeneous half-infinite medium w i t h the surface exposed to plane harmonious illumination according to equation 2.29, the one-dimensional temperature change

can, after a solution o f the heat d i f f u s i o n equation, be expressed by the f o l l o w i n g equation:2 0

CD II

A T (z >t ) = - 2 a _ e(-D'z + j u')= - % = - e1 U a ] U a 4 j (2.30) ' 2ka, 2 ß v r o

Symbol Quantity Unit

AT temperature change °C z distance below the surface m t time s q» absorbed heat flow W/nr k thermal conductivity W/m°C

CT, complex thermal absorption coefficient l/m ß effusivity WsI / 2/m2 oC

CO angular modulation frequency 1/s a diffusivity nr/s

The temperature change is relative to an average temperature o f the test piece where the input energy f r o m the lamps on average is equal to the output energy in the f o r m o f radiation. The first t w o factors on the right side i n equation 2.30 describe the signal amplitude, and the third factor describes the phase. According to the first factor, the amplitude o f the surface temperature is determined by the absorbed energy f r o m the illumination source, the effusivity o f the test piece material and the modulation frequency.

The second factor expresses the exponential damping o f the signal due to absorption as a function o f depth. Illumination w i t h a high modulation frequency and a test piece o f a material w i t h low d i f f u s i v i t y results i n high damping. The third factor describes how the signal is changed with time and depth o f t h e test piece. Figure 2.28 shows how temperature varies as a function o f depth at different times.

3

.3 J J

Depth (mm)

Figure 2.28 Temperature change as a function of depth in oak at different times. Calculated from equation 2.30 with

t = 2,7 and 12 s.;f= 0.05 Hz, q„ = 1.3 W/nr.

A t the surface, the phase o f the signal is shifted -45 ° i n relation to the phase o f the illumination source (see Figure 2.29). O n top o f that, the phase decreases linearly w i t h depth. The higher the

Thermography theory

modulation frequency and the lower the d i f f u s i v i t y o f the test piece material, the steeper is the phase decrease w i t h depth.

Figure 2.29 Phase as a function of depth in oak for different modulation frequencies. Calculated from equation 2.30

with t = 0 s, q„ = 1.3 W/m2.

2.5.4 Penetration depth

Thermal waves generated w i t h periodical illumination show, like ordinary propagating waves, an oscillating space dependency o f the f o r m e"kz. The wave vector, k, is given b y :2 4

(2.31)

Svmbol Quantity Unit

k wave vector 1/m Mr thermal diffusion length for periodic waves m

a. complex thermal absorption coefficient 1/m CO angular modulation frequency 1 s

a diffusivity m"/s

where the parameter p.p is the thermal diffusion length or the penetration depth for periodical

waves. The penetration depth is higher in a material w i t h high d i f f u s i v i t y tested w i t h a low modulation frequency. I n other words, there are only thermal waves w i t h lower frequencies that can give information f r o m deep inside the test piece. This is because according to equation 2.30 lower frequencies are less damped than higher frequencies.

Phase signals are reported to have twice as high penetration depth, i.e. two thermal d i f f u s i o n lengths, than amplitude signals.3 8

materials. 1E-01 'S 1E-02 3 I t 0>

X

X

\ X

n N x

\ X

< x

x

Figure 2.30 Curves showing thermal diffusion length for periodic waves as a function of modulation frequency for

different materials. Calculatedfrom equation 2.31.

I n order to be able to detect air-gaps beneath a 1-mm-thick surface layer o f oak frequencies below 0.1 Hz should be used. This equals a period o f at least 10 seconds.

2.5.5 Phase velocity

Thermal waves are dispersive. This means that waves w i t h different frequencies propagate w i t h different velocities i n the material. For pulsating illumination the phase velocity o f the waves, v, is defined as:2 0

v = cou = V2" aco (2.32)

Svmbol Quantity Unit

V wave velocity m/s Hp thennal diffusion length for periodic waves m a> angular modulation frequency 1/s a diffusivity m7s

Thus thermal waves propagate faster i n a material w i t h high d i f f u s i v i t y and under testing w i t h a higher modulation frequency.

2.5.6 Reflection and interference

A reflection that takes place when a thermal wave interferes w i t h a thermal irregularity is described i n the same w a y for lock-in thermography as f o r pulse thermography (see section 2.2.7). When a wave propagates into a " t h i n " medium like coatings or air-gaps, interference might occur, which is a superposition o f waves that are repeatedly reflected against the boundaries o f the thin medium (see Figure 2.31).

Thermography theory Transmitted thermal waves

t ff t f

\

1

i il 1

I I

Figure 2.31 Thermal wave components in a layer, which illustrates occurrence of interference.""

The major portion o f interference effects occurs when the layer thickness is less than the thermal diffusion length. For interference to occur, the reflection coefficient must not equal zero. Higher absolute value o f the reflection coefficient leads to a higher interference effect.

The interference effect results i n a modulation frequency dependence o f the reflection coefficient. In Figure 2.32, the predicted reflection coefficient f o r an air-gap i n stainless steel is plotted as a function o f air-gap thickness f o r different frequencies.

Air-gap Thickness /pm

Figure 2.32 Calculated reflection coefficient for a thermal wave as a function of the thickness of an air-gap in

stainless steel for the modulation frequencies: 1, 25 and 100 Hz.2'1

A reflection coefficient equal to one corresponds here to a reflection without interference effects. When the thickness o f the air-gap decreases, the reflection coefficient w i l l decrease. Increasing frequency w i l l decrease the thermal wavelength, whereby the reflected intensity f r o m the air-gap w i l l increase.

Depending on the material o f the test piece, the size o f the reflection coefficient f o r the air-gap w i l l change as described i n section 2.2.7. I n Figure 2.33, the reflection coefficient for an air-gap in different materials w i t h high and l o w effusivity is shown as a function o f air-gap thickness.

Air-gap Thickness /pm

Figure 2.33 The variation of the calculated reflection coefficient for a thermal wave as a function of the air-gap

thickness in 1) aluminium, 2) stainless steel and 3) Bakelite for the modulation frequency 25 Hz.20

In a high effusivity material, such as aluminium, it is easier to detect an air-gap than i n a material with low effusivity, like Bakelite.

2.5.7 Scattering of a thermal wave

Defects are finite in extent, and to obtain an accurate contrast model, scattering theory might be used when the defect is comparable to thermal wave wavelengths instead o f making the assumption o f semi-infinite boundaries between media. Consider a thermal wave shaped like a plane periodical wave w i t h an angular frequency co generated at the test piece surface. The thermal wave propagates into the test piece until it is perturbed b y a defect. The defect is disc-like w i t h a radius a at a depth z below the surface o f the test piece (see Figure 2.34).