A normalization procedure for pulse thermographic nondestructive evaluation

Author’s Accepted Manuscript A normalization procedure for pulse thermographic nondestructive evaluation Letchuman Sripragash, Mannur J. Sundaresan

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To appear in: NDT and E International Received date: 3 October 2015 Revised date: 23 March 2016 Accepted date: 24 March 2016 Cite this article as: Letchuman Sripragash and Mannur J. Sundaresan, A normalization procedure for pulse thermographic nondestructive evaluation, NDT and E International, http://dx.doi.org/10.1016/j.ndteint.2016.03.005 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

A Normalization Procedure for Pulse Thermographic Nondestructive Evaluation Letchuman Sripragash, Mannur J. Sundaresan∗ NC A & T,1601 E.Market Street, Greensboro, NC 27411, USA

Abstract Pulse thermographic nondestructive evaluation (TNDE) technique can be used to estimate defect dimensions, and in particular the depth at which the defect is located. Numerical models of this procedure can aid in the interpretation of experimental results. However, the thermophysical properties of the test object as well as the amount of energy absorbed during this process are not readily available for such models. This paper presents an extension of the thermographic signal reconstruction (TSR) procedure in which the temperature and the time scales are respectively normalized with equilibrium temperature and the break time. In the normalized form these profiles are independent of material properties and instrumentation settings. Thus in the normalized format, experimental results can be readily compared with numerically generated thermographic results. The defect depth can also be easily obtained as a fraction of plate thickness from this plot. Keywords: Pulse thermographic technique, Thermography, Nondestructive Evaluation, Flaw detection, Finite Element Analysis, TSR technique

1

1. Introduction

2

Thermographic nondestructive evaluation (TNDE) is one of the Nondestruc-

3

tive Evaluation (NDE) techniques capable of assessing large areas of structures ∗ +1

336 285 3750 Email address: [email protected] (Mannur J. Sundaresan)

Preprint submitted to NDT & E International

May 21, 2016

4

in a relatively short duration of time [1]. In general TNDE can be classified

5

into two main categories, namely active and passive thermographic techniques.

6

In active thermography heat is applied to the surface of the test object by an

7

external energy source while in passive thermography heat is generated within

8

the object.

9

A comprehensive review on different thermographic techniques used in NDE

10

and condition monitoring techniques are provided by Ibarra-Castanedo, et. al.

11

[2] and [3]. In addition to the pulsed thermography and lock-in thermography

12

techniques newer approaches of exciting the specimens and extracting damage

13

related information have been demonstrated by Gao et. al. [4, 5], and Ahmed

14

et. al. [6].

15

Pulse thermography falls under the category of active thermographic tech-

16

nique and it uses a pulse of heat energy applied to the surface of the test object,

17

usually by a flash lamp. Following the instantaneous rise in the temperature of

18

the surface, due to the applied heat, the rate of change of surface temperatures

19

as a function of time is monitored using an infrared camera. In a defect free

20

sample the heat diffuses through the thickness resulting in an asymptotic drop

21

in surface temperature. However, in areas where there are defects, this diffusion

22

of heat in the thickness direction is obstructed, and hence, the surface temper-

23

ature remains higher than that of the defect free areas. Defect free areas in a

24

plate are commonly termed as sound zone in TNDE literature. The variation of

25

temperature with time provides an indication of the depth at which the defect

26

is located.

27

In TNDE field tests there are multiple unknowns that are to be quanti-

28

fied, namely, thermal diffusivity of the material, lateral dimension and depth

29

of defects, thickness of the part being inspected, and amount of heat absorbed

30

by the part from the flash. All of these parameters determine thermal images

31

and their variation with time which are obtained from thermographic tests. As

32

with other NDE techniques reliable calibration specimens would facilitate the

33

characterization of defects. The existence of defects can be qualitatively seen

34

in raw thermographic images. Quantitative information can be obtained with 2

35

additional image processing techniques. There are two approaches in image

36

processing, namely pixel based and image based techniques [7]. Pixel based

37

technique is based on the temperature evolution of a single pixel or point on

38

the surface. Shepard et al. [8] introduced a pixel based technique termed Ther-

39

mographic Signal Reconstruction (TSR) technique. On the other hand, image

40

based technique is based on spatial variations of temperature seen in the images

41

at different instants of time. Both methods have their merits and it was noted

42

by Shepard et al. [7] that combining both methods would also be of beneficial

43

in quantitative characterization.

44

This study uses pixel based approach for developing the normalization pro-

45

cedure. In these discussions, the variation of temperature with time recorded at

46

an individual pixel is termed as the thermographic profile for that point. Nor-

47

malization is widely used in presenting solutions to heat conduction problems.

48

Fourier number is a fundamental parameter that characterizes transient heat

49

conduction. Different reference values of temperature and time have been used

50

in the past for normalizing thermographic profiles. Ringermacher et al. [9] used

51

the time of occurrence of the maximum slope in the temperature versus time

52

plot, the inflection time, as the reference parameter for normalization. The pur-

53

pose of normalization in their study was to eliminate the influence of lateral heat

54

flow when comparing thermographic profiles of different defects. Krishnapillai

55

et al. [10] numerically generated thermographic profiles of defects in composite

56

laminates and these results were validated through suitable experiments. They

57

used the inflection time to find a calibration value for diffusivity to correlate ex-

58

perimental and numerical results. Ramirez-Granados, et al. [11] carried out a

59

normalization procedure in which the time and temperature difference were nor-

60

malized with respect to the maximum values, in order to validate their approach

61

and to aid better comparisons of the results for a variety of specimens. Balageas

62

[12] provided a detailed assessment of different approaches for extracting quan-

63

titative information from thermographic nondestructive tests, and pointed out

64

a few of the current deficiencies. He also introduced a normalization procedure

65

for minimizing variations in intensity of images within a defect free zone that 3

66

are caused by variations in the absorption of incident radiation. He used the

67

temperature of a pixel at a time immediately following the flash, such as 0.1

68

second after the flash, to normalize the temperature.

69

The objective of this research is to provide a better means of comparing and

70

correlating thermographic results from numerical and experimental analyses.

71

There are some challenges in quantitative matching of experimental results with

72

results from numerical simulations. The first difficulty arises from the fact that

73

accurate thermo-mechanical properties of the specimen under investigation are

74

not generally available prior to the test. The second difficulty arises from the

75

fact that the temperature values obtained in the experiments cannot be readily

76

related to those in the numerical simulations, because of the arbitrary, but

77

linear scale variation of signal received from the thermographic camera. A

78

new normalization scheme is introduced in this research that eliminates both

79

of these difficulties. Further, as a result of this normalization, it is feasible to

80

directly obtain estimation of defect depth as a fraction of plate thickness. As

81

shown in later sections, results from a validated numerical simulation can be

82

used to generate thermographic profiles corresponding to a range of materials

83

and flash intensities as long as the defect geometry remains the same. Once

84

the numerical simulations are validated, it becomes readily feasible to create a

85

database of thermographic profiles that can help in the interpretation of results

86

obtained in the field.

87

2. Theoretical Background

88

The variation of surface temperature of a semi-infinite solid as a function of

89

time, after the surface is subjected to an instantaneous rise in temperature such

90

as in flash heating, is given by [13], q0 ∆T = √ ε πt

(1)

91

where ∆T = T − T0 , which is the difference between the temperature T at any

92

time t after the flash and the initial temperature T0 of the surface before the

4

93

flash, q0 is the heat supplied at the boundary as a flash and ε is the effusivity

94

given by, ε=

√ κρc.

(2)

95

In equation (2), κ, ρ, and c are thermal conductivity, density, and heat capacity

96

of the material respectively. . In a semi-infinite body, following the flash, the

97

surface temperature instantaneously raises and subsequently decreases accord-

98

ing to the relationship given in equation (1). However, for a slab with a finite

99

thickness of L, the evolution of ∆T can be derived from the equations given in

100

[13] and is given as, q0 ∆T = Lρc

101

( 1+2

∞ X

) e

(−π2 i2 Lαt2 )

(3)

i=1

where α is the diffusivity of the material given by, α=

κ . ρc

(4)

102

The equilibrium temperature or saturation temperature difference, when the

103

temperature of the plate (slab) becomes uniform throughout its thickness, is

104

given by, ∆T ∗ =

q0 Lρc

(5)

105

Using equations (1) and (5), the corresponding time at which saturation occurs,

106

commonly referred to as break time, t∗ , is given by, t∗ =

L2 πα

(6)

107

This equation is often used to find the thermal diffusivity of materials using

108

flash thermographic technique [14]. Taking natural logarithm of equation (1)

109

results in the following equation,  ln(∆T ) = −0.5 ln(t) + ln

q √0 ε π

 (7)

110

For the semi-infinite body, the slope of the plot of ln ∆T versus ln(t) has a value

111

of -0.5. However, for a finite thickness plate, as indicated in equation (3), the 5

112

temperature difference will eventually levels off to a value of ∆T ∗ . The variation

113

of ∆T as a function of time in logarithmic domain is shown in Figure 1 for both

114

the semi-infinite body as well as a finite thickness plate. It has been found that

115

the plots of first and second derivatives of the ln(∆T ) with respect to ln(t) are

116

quite informative as demonstrated by Shepard et al. [8]. These are referred to

117

as the first derivative and second derivative, or 1d and 2d by Shepard and they

118

are given by, d[ln(∆T )] d[ln(t)]

(8)

2d =

d2 [ln(∆T )] d[ln(t)]2

(9)

and

ln(∆T )

119

1d =

eq. (3) ∆T* t* eq. (1)

ln(t) Figure 1: Schematic variation of ln(∆T ) with ln(t) 120

Typical variation of temperature and its derivatives as a function of time,

121

in logarithmic scale are given in Figure 1. For the 2d plot shown in Figure 3c,

122

the time of occurrence td , of the first peak corresponding to the defect provides

123

an estimate to the defect depth, and that of sound zone pixel tbw provides an

124

estimate to the specimen thickness [14] and [15]. The time td is related to the

125

defect depth Ld by, td =

126

L2d πα

(10)

3. Normalization

127

The characteristic time, t∗ , and the saturation temperature difference, ∆T ∗ ,

128

are the two parameters selected for the new normalization procedure. Equation 6

P

Q

P

Q

Figure 2: A flat plate with flat bottom hole

129

(1) can be normalized by dividing both sides with ∆T ∗ as, q0 1 ∆T = √ ∗ ∆T ∗ ∆T ε πt

(11)

130

By substituting equation (5) in (11) and using equation (6) the following rela-

131

tionship is obtained ∆T = ∆T ∗

132

∆T ∆T ∗

παt t = 2 t∗ L

(14)

(15)

The normalized time also can be given in terms of Fourier number, F o as, tn = πF o

136

(13)

equation (12) can be re-written as, 1 ∆Tn = √ tn

135

(12)

and normalized time as, tn =

134

t∗ t

Denoting the normalized temperature difference as, ∆Tn =

133

r

(16)

F o, can be found in Carslaw and Jaeger [13], and is defined as, Fo = 7

αt L2

(17)

a ln(∆T )

16 15 14 13

4

6

8

10

8

10

ln(t)

b

1d

0 -0.2 -0.4 -0.6

4

6

ln(t)

c 0.2

Defect-free zone (Q) Defected zone (P)

2d

0.1 0

tbw

td

-0.1 -0.2

4

6

8

10

ln(t) Figure 3: A schematic representation of the variation of temperature and its derivatives with time

8

137

equation (15) can be written in natural logarithmic domain as, ln(∆Tn ) = −0.5 ln(tn )

(18)

138

An analytical solution for normalized temperature evolution is given by Balageas

139

et. al. [16] as, ∆Tn = 1 + 2

∞ X

2 2 αt e(−π i L2 )

(19)

i=1 140

Using the normalized time given in equation (14), equation (19) can be re-

141

written as, ∆Tn = 1 + 2

∞ X

2 e(−πi tn )

(20)

i=1 142

Balageas [17] normalized equation (19) in terms of Fourier number, F o , and

143

used this normalized form to illustrate the significance of 1d and 2d plots. The

144

normalization used in this paper, in terms of break time, t∗ , relates the defect

145

depth directly to the plate thickness. It should be noted that normalization can

146

also be performed in terms of the Fourier number F o. In this paper, break time

147

(t∗ ) and the equilibrium temperature (∆T ∗ ) from the ln(∆T ) vs. ln(t) plot,

148

were chosen as the normalizing parameters. The first and second derivatives, in

149

the normalized domain are given by equations (21) and (22).

150

1dn =

d[ln(∆Tn )] d[ln(tn )]

(21)

2dn =

d2 [ln(∆Tn )] d[ln(tn )]2

(22)

and

151

The time derivatives of temperature shown in Figure 3 are reproduced after

152

normalization in Figure 4. Time tbw shown along the time axis in Figure 3c cor-

153

respond to the instant when surface temperature approaches the steady state

154

value, indicating the thickness of the of the plate, L. The corresponding normal-

155

ized time for tbw in Figure 4c would be tnbw and because of the normalization,

156

the numerical value of tnbw is unity. As stated before, the value of time td shown

157

in Figure 3c is indicative of the depth of the defect Ld [10]. In the normalized

158

plot shown in Figure 4c, time tnd corresponds to the defect depth ratio. It can 9

159

be seen that the defect depth ratio can be obtained directly from equation (10)

160

and (6) as, √ Ld = tnd L

(23)

161

The steps used for normalization of the ln(∆T ) vs. ln(t) graphs of all the

162

pixels in the data set are shown in Figure 5. The data in thermographic images

163

were pre-processed and the ln(∆T ) vs. ln(t) corresponding to each pixel was

164

fitted with a smooth curve following a procedure such as the one described by

165

Shepard et al. [8]. Based on profiles of all the pixels in the field of view, a pixel

166

within the sound zone was selected and its ln(∆T ) vs. ln(t) graph was used to

167

determine equilibrium temperature,∆T ∗ and break time, t∗ , as shown in Figure

168

6 [7]. The ln(∆T ) vs. ln(t) graphs corresponding to each pixel in the field of

169

view were normalized using ∆T ∗ and t∗ to obtain the graphs of ln(∆Tn ) vs.

170

ln(tn ), according to equations (13) and (14).

171

4. Numerical Analysis

172

Calibration specimens with flat bottom holes are widely used in thermo-

173

graphic analysis [9]. In this study, axisymmetric finite element analysis was

174

used to simulate the flash thermographic testing of specimens with flat bottom

175

holes. Flat bottom holes with different depths were modeled. The dimensions

176

of one such model are shown in Figure 7. This model includes the important

177

aspects of the TNDE procedure including the initial flash as well as subsequent

178

diffusion of heat from the surface into the volume of the specimen until the entire

179

volume reaches thermal equilibrium. Since the variation of surface temperature

180

during the TNDE procedure is primarily determined by thermal diffusion within

181

the volume of the specimen, the heat losses due to convection and radiation are

182

neglected. Variation of temperature for different radial locations on the surface

183

was recorded as a function of time. The objectives of this section are to illus-

184

trate the advantages offered by the normalization procedure and to validate the

185

numerical results using the experimental results. Numerical models for several

186

different material properties and defect depths were examined for this purpose. 10

a ln(∆Tn )

3 2 1 0 -4

-2

0

2

0

2

ln(tn )

b

1dn

0 -0.2 -0.4 -0.6

-4

-2

ln(tn )

c 0.2

Defect-free zone (Q) Defected zone (P)

2dn

0.1 0

tnbw

tnd

-0.1 -0.2

-4

-2

0

2

ln(tn ) Figure 4: Evolution of a - temperature, b - 1d and c - 2d in normalized parameters

11

Raw thermal images

Pre-process and smoothen the data

Smoothened data of ∆T Selction of sound zone pixel Find t∗ and ∆T ∗ Normalize the data obtained (∆Tn and tn )

Normalized Data Figure 5: The Normalizing Procedure

187

This section provides the results corresponding to four different cases all having

188

the same defect geometry, but different material properties to illustrate that it is

189

possible to eliminate the influence of material properties on the thermographic

190

profile. The dimensions of numerical models used in the analysis are L = 12.5

191

mm, r = 12.5 mm, and Ld = 5 mm. Materials considered in this study are

192

listed in Table 1. In TNDE practice, the total duration and the frequency of

193

data acquisition are two of the important parameters to be selected before the

194

beginning the test. According to ASTM E2582 – 07 [18], the data is usually

195

recorded for a duration, tf , that is about two times the break time, t∗ , tf > 2t∗

(24)

196

Sufficiently high frame rate should be used to record the surface temperature in

197

order to preserve important defect related information. Ensuring the adequacy

198

of sampling frequency is particularly important for defects located close to the

199

surface. The frame rate and the number of frames that were successful in

12

6 t*

ln(∆T)

5 ∆ T*

4

-0.5 gradient tangent to the early portion of the data

3 2

5

6

7

8

9

10

ln(t)

Figure 6: Determination of break time

P

Ld

Q L

r R

Figure 7: Dimensions of axisymmetric model

200

the experiments were used to guide the selection of these parameters in the

201

numerical analysis. The experimental results used for validating the numerical

202

simulations were obtained using a 12.7 mm thick steel plate with a thermal

203

diffusivity of 12.5 mm2 /s. For this specimen, the break time, t∗ , was found to

204

be 4.1 seconds and a data acquisition for a period, tf , of 15 seconds at a frame

205

rate of 60 Hz was found satisfactory. In the numerical simulations for different

206

materials listed in Table 1, the same ratio of

tf t∗

and the number of frames to

Table 1: Materials and their properties to cover wide range of diffusivities

Specific heat

Thermal

Capacity

Conductivity

Density

Diffusivity

(J/Kg)

(W/m/K)

(kg/m3 )

(mm2 /s)

Delrin

1470

0.37

1420

0.18

Steel

500

45.00

7200

12.50

Silver

235

425.00

10490

172.40

Hypothetical

800

2.00

2500

1.00

Material

13

207

reach t∗ were maintained. A commercial finite element software was used for

208

the numerical simulation. An axisymmetric finite element model with a uniform

209

element size of approximately 0.06 mm × 0.06 mm was used.

210

First, the results for the four materials obtained from numerical simulations

211

are compared. From the temperature versus time record for locations P and

212

Q (refer Figure 7), plots of first and second derivatives were generated. The

213

plots were generated for each of the four materials considered. These graphs

214

are presented in both regular form as well as normalized form in Figure 8.

215

The geometry of the defect and the heat applied are identical for the four

216

cases shown in Figure 8 (a), (c), and (e). The position of the individual graphs

217

are determined by their respective material properties. When these graphs are

218

plotted in terms of the normalized coordinates, the four sets of graphs collapse

219

to a single set of graphs, eliminating the dependence on material properties.

220

Results corresponding to variations in energy inputs during the flash were also

221

examined and found to have no influence on the normalized plots. Hence, the

222

normalized plots provides a convenient means of comparing results from numer-

223

ical simulations and experiments, when accurate material properties of the test

224

piece and absolute temperatures measured by the instrument are not available.

225

5. Validation of Numerically Obtained Results

226

In this section the results of numerical simulations are validated using the

227

results from experiments, taking advantage of the normalization procedure de-

228

scribed in the previous sections. The three defect configurations C1, C2, and

229

C3 considered were 25.4 mm diameter flat bottom holes in a 12.7 mm thick

230

low carbon steel plate. The main difference among the three configurations

231

were their depth location, which respectively, were 2.16, 3.81, and 5.46 mm

232

from the top surface. The thermal diffusivity for this material was found to

233

be 12.5 mm2 /s. Results corresponding to each of the defect configurations C1,

234

C2, and C3 are respectively shown in Figures 9, 10, and 11. The temperature

235

profiles corresponding to the center of the defect as well as a far field location

14

a

b 5

ln(∆Tn )

ln(∆T )

2 4 3 2 0

1.5 1 0.5 0

5

10

15

-6

-4

ln(t)

0

2

0

2

0

2

d 0.2

0.2

0

0

1dn

1d

c

-0.2 -0.4 -0.6 0

-0.2 -0.4

5

10

-0.6 -6

15

-4

ln(t)

-2

ln(tn )

e

f 0.2

0.2

0.1

0.1

2dn

2d

-2

ln(tn )

0

-0.1

-0.1 -0.2 0

0

5

10

-0.2 -6

15

ln(t)

Delrin sound Delrin defect Steel sound Steel defect Silver sound Silver defect Synthetic sound Synthetic defect

-4

-2

ln(tn )

Figure 8: Thermographic signal evolution of a defect with four different materials given in Table 1. Broken lines refer to a sample defect region point (P) and the solid lines refer to the point on the sound region (Q). a, c and e are before normalization and b, d, and f are after normalization. Legends are given in f

15

236

were experimentally determined, using commercial pulse thermographic equip-

237

ment, Thermoscope II, comprising of FLIR SC5000 IR camera, two optical flash

238

lamps for the application of pulse heat energy, and proprietary software. The

239

experimental data from the steel specimen are collected at a frame rate of 60

240

Hz with an image resolution of 320 by 256 pixels. These profiles are shown as

241

continuous lines in figures 7 to 9. Results from numerical simulations for these

242

geometries and material properties with arbitrary energy input during the initial

243

pulse heating were obtained and were plotted as dashed lines in these figures.

244

While the ln(∆T ) vs ln(t) plots in Figures 9 to 11 from the numerical simula-

245

tions were different from the experimentally obtained plots, the 1d and 2d plots

246

were identical since the material properties used in the numerical simulations

247

were quite accurate. However, inaccuracies in material properties can introduce

248

difference in the horizontal location of numerically obtained 1d and 2d plots

249

from the experimentally obtained ones, which can be easily eliminated through

250

normalization. This is demonstrated using numerical results corresponding to

251

the same three geometries, but for a hypothetical material having a significantly

252

different thermal diffusivity of 1 mm2 /s shown as dotted line in Figures 9 to 11.

253

Hence, the normalization scheme enables such a direct comparison even in the

254

presence of uncertainties regarding material properties and when the absolute

255

temperatures corresponding to the experimental results are unknown.

256

The normalized plots of experimental data corresponding to the three defect

257

configurations are combined in Figure 12 to indicate that it is possible to obtain

258

the depth of the defect directly from the normalized TSR 2d plot. The nor-

259

malized time corresponding to the defect’s first peak in the 2d plot, indicated

260

in Figure 12 (c), along with equation (23) provides a close approximation of

261

the defect’s depth. Alternatively, this graph can be replotted in terms of plate

262

thickness, in a linear scale, as shown in Figure 12 (d) for a direct indication

263

of defect depth. Table 2 lists the error magnitudes in the estimation of defect

264

depths for the three configurations.

265

The scope of the paper is to present a normalization procedure that enables

266

direct comparison of experimental results with results from numerical simula16

a

b 8

ln(∆Tn )

ln(∆T )

2 6 4

1 0

2 4

6

8

10

12

14

-6

-4

ln(t)

-2

0

2

0

2

0

2

ln(tn )

c

d 0.5

0

0

1d

1dn

0.5

-0.5 -1 4

-0.5

6

8

10

12

-1 -6

14

-4

ln(t)

-2

ln(tn )

e

f 0.2

0

0

2d

2dn

0.2

-0.2

-0.2 -0.4 4

6

8

10

12

-0.4 -6

14

ln(t)

exp. sound exp. defect num. Steel sound num. Steel defect num. synthetic sound num. synthetic defect

-4

-2

ln(tn )

Figure 9: Experimental and numerical results comparison for a defect configuration C1. a, c and e are before normalization and b, d, and f are after normalization. Legends are given in f

267

tions when precise material properties and pulse energy input are not available.

268

It should be noted that the normalization procedure is applicable to contrast

269

based methods as well. The direct estimation of depth presented here is an

270

extension of TSR method made possible by the normalization procedure.

271

6. Conclusion

272

One of the difficulties in the development of numerical models of pulsed

273

thermographic technique is that accurate thermophysical properties of the test

274

object as well as the exact amount of energy in the pulse are not available. 17

a

b 8

ln(∆Tn )

ln(∆T )

2 6 4

1 0

2 4

6

8

10

12

14

-6

-4

ln(t)

0

2

0

2

0

2

d 0.2

0.2

0

0

1dn

1d

c

-0.2 -0.4 -0.6 4

-0.2 -0.4

6

8

10

12

-0.6 -6

14

-4

ln(t)

-2

ln(tn )

e

f 0.2

0.2

0.1

0.1

2dn

2d

-2

ln(tn )

0

-0.1

-0.1 -0.2 4

0

6

8

10

12

-0.2 -6

14

ln(t)

exp. sound exp. defect num. Steel sound num. Steel defect num. synthetic sound num. synthetic defect

-4

-2

ln(tn )

Figure 10: Experimental and numerical results comparison for a defect configuration C2. a, c and e are before normalization and b, d, and f are after normalization. Legends are given in f

18

a

b 2.5

8

ln(∆Tn )

ln(∆T )

2 6 4 2 4

1.5 1 0.5 0

6

8

10

12

14

-6

-4

ln(t)

c

0

2

0

2

0

2

d 0.2

0.2

0

0

1dn

1d

-2

ln(tn )

-0.2 -0.4 -0.6 4

-0.2 -0.4

6

8

10

12

-0.6 -6

14

-4

ln(t)

-2

ln(tn )

e

f 0.2

0.1

0.1

2d

2dn

0.2

0

0 -0.1 4

exp. sound exp. defect num. Steel sound num. Steel defect num. synthetic sound num. synthetic defect

6

8

10

12

-0.1 -6

14

ln(t)

-4

-2

ln(tn )

Figure 11: Experimental and numerical results comparison for a defect configuration C3. a, c and e are before normalization and b, d, and f are after normalization. Legends are given in f

19

a ln(∆Tn )

3 2 1 0

-4

-3

-2

-1

0

1

0

1

0

1

ln(tn )

b 0.5

1dn

0 -0.5 -1

-4

-3

-2

-1

ln(tn )

c 0.2

2dn

0 -0.2 -0.4

-4

-3

-2

-1

ln(tn )

d

2dn

0.1 Backwall

0 C2

-0.1 -0.2 -0.3 0

C3

C1

0.2

0.4

0.6

0.8

1

Defect depth ratio, ld

Figure 12: Experimental results of evolution of a - temperature, b - 1d, c - 2d in normalized parameters, and d - defect depth ratio

20

Table 2: Comparison of defect depth ratios

Deffect depth ratio Configuration

Actual Value

Estimated Value

Error (%)

C1

0.17

0.18

-6

C2

0.30

0.29

3

C3

0.43

0.40

7

275

This paper proposes a normalization procedure that eliminates the need for

276

this information. After the normalization, the variations of temperature as

277

well as its first and second time derivatives, become essentially independent

278

of thermal properties as well as the energy absorbed by the specimen from

279

the flash and hence experimentally obtained thermograhic data can be readily

280

correlated with those obtained from numerical simulations. The procedure is

281

also effective in direct comparison of results for geometrically similar defects in

282

different materials. Experimental results for flat bottom holes in steel specimens

283

along with results of numerical simulations, in the normalized form, are shown

284

to have excellent correlation for several defect geometries. Hence, numerical

285

simulations can potentially complement calibration specimens. Using the results

286

from one numerical simulation, it is feasible to generate the temperature versus

287

time profile corresponding to a range of material properties and instrumentation

288

settings, as long as the geometry remains same.

289

Acknowledgements

290

The authors would like to thank NASA Grant # NNX09AV08A for the

291

financial support, Mr. Larry Hudson of NASA Armstrong for his encourage-

292

ment, and Dr. Kassahun Asamene, North Carolina A &T State University, for

293

his assistance.

21

294

References

295

[1] X. P. Maldague, Partrick O. Moore (Eds.), Nondestructive Testing Hand-

296

book; Volume 3, 3rd Edition, American Society for Nondestructive Testing,

297

2001.

298

[2] C. Ibarra-Castanedo, J. R. Tarpani, X. P. V. Maldague, Nondestructive

299

testing with thermography, European Journal of Physics 34 (2013)

300

S91–S109. doi:10.1088/0143-0807/34/6/S91.

301

URL http://stacks.iop.org/0143-0807/34/i=6/a=S91?key=crossref.d3a423e71c1502152038e20f63

302

[3] S. Bagavathiappan, B. Lahiri, T. Saravanan, J. Philip, T. Jayakumar,

303

Infrared thermography for condition monitoring – A review, Infrared

304

Physics & Technology 60 (2013) 35–55. doi:10.1016/j.infrared.2013.03.006.

305

URL http://linkinghub.elsevier.com/retrieve/pii/S1350449513000327

306

[4] B. Gao, L. Bai, W. L. Woo, S. Member, G. Y. Tian, S. Member, Y. Cheng,

307

A. Eddy, Automatic Defect Identification of Eddy Current Pulsed Ther-

308

mography Using Single Channel Blind Source Separation 63 (4) (2014)

309

913–922.

310

[5] B. Gao, A. J. Yin, G. Y. Tian, W. L. Woo, Thermography spatial-

311

transient-stage mathematical tensor construction and material property

312

variation track, International Journal of Thermal Sciences 85 (2014) 112–

313

122. doi:DOI 10.1016/j.ijthermalsci.2014.06.018.

314

URL ://WOS:000209035500012

315

[6] T. J. Ahmed, G. F. Nino, H. E. N. Bersee, A. Beukers, Heat emitting

316

layers for enhancing NDE of composite structures, Composites Part a-

317

Applied Science and Manufacturing 39 (6) (2008) 1025–1036. doi:DOI

318

10.1016/j.compositesa.2008.02.017.

319

URL ://000257014700014

320

[7] S. M. Shepard, J. R. Lhota, Flash thermography modeling based on IR

321

camera noise characteristics, Nondestructive Testing and Evaluation 22 (2 22

322

- 3) (2007) 113 – 126. doi:10.1063/1.2902704.

323

URL http://dx.doi.org/10.1063/1.2902704

324

[8] S. M. Shepard, J. R. Lhota, B. A. Rubadeux, D. Wang, T. Ahmed, Re-

325

construction and enhancement of active thermographic image sequences,

326

Optical Engineering 42 (5) (2003) 1337–1342. doi:10.1117/1.1566969.

327

URL http://dx.doi.org/10.1117/1.1566969

328

[9] H. Ringermacher, D. Mayton, D. R. Howard, B. Cassenti, Towards a flat

329

bottom hole standard for thermal imaging, Review of Progress in Quan-

330

titative Nondestructive Evaluation 17 (1998) 425–429. doi:10.1007/978-1-

331

4615-5339-7 54.

332

URL http://dx.doi.org/10.1007/978-1-4615-5339-7 54

333

[10] M. Krishnapillai, R. Jones, I. H. Marshall, M. Bannister, N. Ra-

334

jic, NDTE using pulse thermography:

Numerical modeling of com-

335

posite subsurface defects, Composite Structures 75 (2006) 241–249.

336

doi:10.1016/j.compstruct.2006.04.079.

337

URL http://dx.doi.org/10.1016/j.compstruct.2006.04.079

338

[11] J. C. Ramirez-Granados, G. Paez, M. Strojnik, Reconstruction and analysis

339

of pulsed thermographic sequences for nondestructive testing of layered ma-

340

terials., Applied optics 49 (9) (2010) 1494–1502. doi:10.1364/AO.49.001494.

341

URL http://dx.doi.org/10.1364/AO.49.001494

342

[12] D. L. Balageas, Defense and illustration of time-resolved pulsed thermog-

343

raphy for NDE, Quantitative InfraRed Thermography Journal 9 (1) (2012)

344

3–32. doi:10.1080/17686733.2012.676902.

345

URL http://dx.doi.org/10.1080/17686733.2012.676902

346

[13] H. S. Carslow, J. C. Jaeger, J. E. Morral, Conduction of Heat in Solids,

347

Second Edition, Vol. 108, Clarendon Press, 1986. doi:10.1115/1.3225900.

348

URL http://books.google.com/books/about/Conduction of Heat in Solids.html?id=y20sAAAAYAAJ

23

349

[14] S. M. Shepard, Y. Hou, T. Ahmed, J. R. Lhota, Reference-free inter-

350

pretation of flash thermography data, Insight 48 (5) (2006) 298–302.

351

doi:10.1117/12.669396.

352

URL http://dx.doi.org/10.1117/12.669396

353

[15] J. G. Sun, Analysis of Pulsed Thermography Methods for Defect

354

Depth Prediction, Journal of Heat Transfer 128 (4) (2006) 329 – 338.

355

doi:10.1115/1.2165211.

356

URL http://dx.doi.org/10.1115/1.2165211

357

[16] D. L. Balageas, J. C. Krapez, P. Cielo, Pulsed photothermal modeling

358

of layered materials, Journal of Applied Physics 59 (2) (1986) 348 – 357.

359

doi:10.1063/1.336690.

360

URL http://dx.doi.org/10.1063/1.336690

361

[17] D. L. Balageas, Thickness or diffusivity measurements from front-face

362

flash experiments using the TSR (thermographic signal reconstruction)

363

approach, in: Quantitative InfraRed Thermography, 2010, pp. 873 – 880.

364

URL

365

2010-011.pdf

http://qirt.gel.ulaval.ca/archives/qirt2010/papers/QIRT

366

[18] ASTM E2582-07, Standard Practice for Infrared Flash Thermography of

367

Composite Panels and Repair Patches Used in Aerospace Applications 1,

368

Tech. rep. (2007). doi:10.1520/E2582-07.1.7.

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