Specified value based defect depth prediction using pulsed thermographyZhi Zeng, Ning Tao, Lichun Feng, and Cunlin Zhang Citation: Journal of Applied Physics 112, 023112 (2012); doi: 10.1063/1.4737784 View online: http://dx.doi.org/10.1063/1.4737784 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/112/2?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Prediction of blind frequency in lock-in thermography using electro-thermal model based numerical simulation J. Appl. Phys. 114, 174905 (2013); 10.1063/1.4828480 PHASE ANGLE THERMOGRAPHY FOR DEPTH RESOLVED DEFECT CHARACTERIZATION AIP Conf. Proc. 1096, 526 (2009); 10.1063/1.3114300 Pulsed thermography modeling AIP Conf. Proc. 615, 564 (2002); 10.1063/1.1472848 Method-of-images formulation of the inverse problem of depth profiling the thermal reflection coefficient in animpulse heated solid AIP Conf. Proc. 509, 595 (2000); 10.1063/1.1306103 Temporal treatment of a thermal response for defect depth estimation AIP Conf. Proc. 509, 587 (2000); 10.1063/1.1306102

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

128.123.44.23 On: Fri, 19 Dec 2014 03:02:34

Specified value based defect depth prediction using pulsed thermography

Zhi Zeng,1 Ning Tao,2,a) Lichun Feng,2 and Cunlin Zhang2

1Institute of Physics and Electronic Engineering, Chongqing Normal University, 400047 China2Beijing Key Laboratory for Terahertz Spectroscopy and Imaging, Key Laboratory of TerahertzOptoelectronics, Ministry of Education, Department of Physics, Capital Normal University,Beijing 100048 China

(Received 14 November 2011; accepted 27 June 2012; published online 24 July 2012)

Several methods have been reported in the literature using pulsed thermography for quantitative

measurement of defect depth or sample thickness. In this paper, based on the analysis of a

theoretical one-dimensional solution of pulsed thermography, a new method was proposed to first

multiply the original temperature decay with square root of the corresponding time to obtain a

monotonically increasing function f. A specific time was obtained by setting f equals to a

predefined value, the theoretical model shows that the obtained specific time has linear relation

with square of defect depth, which was verified with the experimental results of one aluminum and

one glass fiber reinforced polymer specimen machined with six flat-bottom wedges as simulated

defects. This linearity can be used for defect depth prediction in pulsed thermography. VC 2012American Institute of Physics. [http://dx.doi.org/10.1063/1.4737784]

I. INTRODUCTION

Pulsed thermography is a nondestructive evaluation

method, which has been qualitatively and quantitatively

applied for different classes of materials to detect variety of

defects, such as corrosions and delaminations in composite,

metal, etc.1 Quantitative characterization in order to extract

defect depth, size, and thermal properties has been proven

effective in pulsed thermography.2–5 Active pulsed thermogra-

phy includes reflection and transmission modes. The reflection

mode heats and inspects the sample from the same side, and it

is normally adopted because only one side of sample is

required. With transmission mode, the tested sample is heated

from one side and inspected from the other side. In the situa-

tion when both sides of sample are accessible, the transmission

mode is a better choice for some applications because it is not

so affected by 3D heat diffusion compared with reflection

mode.

Quantitative prediction of defect depth has been an im-

portant research topic in the past twenty years, and the

research is mainly conducted with reflection mode. Many

methods have been proposed for depth prediction, most of

them constructed the relation between defect depth with a

characteristic time. The characteristic time is normally cho-

sen as the peak time in the 1st derivative or 2nd derivative

forms of the original temperature decay which was pre-

treated in some forms. Among these methods, most work

was based on the thermal contrast, in which a reference

curve from the sound area is required. Peak contrast time

(PCT) is corresponding to the peak time of maximal ther-

mal contrast, it is proportional to the square of the defect

depth, and the proportionality coefficient depends on the

size of the defect.5–8 Peak slope time (PST) is correspond-

ing to the peak time of the 1st derivative of thermal con-

trast, it was found that PST is also proportional to the

square of the defect depth, and the proportionality coeffi-

cient does not depend on defect size.9–11 The deviation time

of defect signal from sound signal in the natural logarithmic

plots is a function of the depth of the interface, so that it is

possible to measure the depth or thickness by measuring

this thermal transit time.12,13 Those methods are all based

on temporal domain processing, Maldague14–16 proposed to

calculate defect depth in frequency domain that the zero

crossing frequency has certain relation with defect depth.

The above mentioned methods requiring reference normally

choose the reference from sound area manually; there are

several reports that tried to obtain a reference automati-

cally. The method developed by Ringermacher et al. used

the averaged temperature from the entire surface as the ref-

erence temperature,11 Pilla et al. used the first several

frames to automatically simulate the reference tempera-

ture.17 However, the experimentally chosen reference may

introduce extra error.

There are some methods which do not need a reference.

Shepard et al.18 identified a method that the second deriva-

tive of the surface temperature in the logarithmic scale con-

tains a peak that can be used to determine the defect depth

(PSDT). The authors proposed to use absolute PST (APST)

for depth prediction, which also does not need a reference

and only need 1st derivative in temporal domain.19 All of

the methods described above are based on finding a charac-

teristic time to correlate with defect depth. Sun20 is based

on least-squares fitting of a theoretical model to the temper-

ature decay curve for a direct determination of depth, and

developed the theoretical model and discussed the experi-

mental errors for PCT, PST, and PSDT methods.5

In some situations, when both sides of tested sample are

accessible, transmission mode can also be applied for depth

prediction. All above mentioned methods are normally

adopted in reflection mode, however, some of them are appli-

cable to transmission mode, such as PST method. In

a)Author to whom correspondence should be addressed. Electronic mail:

ninatao1021@hotmail.com.

0021-8979/2012/112(2)/023112/7/$30.00 VC 2012 American Institute of Physics112, 023112-1

JOURNAL OF APPLIED PHYSICS 112, 023112 (2012)

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

128.123.44.23 On: Fri, 19 Dec 2014 03:02:34

transmission mode, half maximal time (HMT) method is sim-

ple and can obtain very accurate result,21 whose characteristic

time is the time when its temperature is half of the maximal

temperature. However, HMT method does not applicable to

reflection mode.

In this paper, a new method using reflective pulsed ther-

mography was proposed for thickness or defect depth mea-

surement, which does not need a reference and does not need

derivative process. The anode oxidation treated aluminum

(Al) sample and the glass fiber reinforced polymer (GFRP)

sample with 6 flat-bottom wedges were used to test the pro-

posed method, the result indicates that it is a viable method

for depth prediction.

II. METHOD

The principle of reflective pulsed thermography is

shown in Fig. 1, the front surface of the detected sample is

heated with a short pulse of light, and the generated heat at

front surface propagates to the interior of the sample because

of heat conduction, and leads to a continuous decrease of the

surface temperature.1,12 An infrared camera controlled by a

PC captures the time dependent response of the sample sur-

face temperature to the thermal excitation. In areas of the

sample surface above a thermal discontinuity, the transient

flow of heat from the surface into the sample bulk is wholly

or partially obstructed, thus, causing a temperature deviation

from sound areas. In such a situation, the decay of the sur-

face temperature T with time t is expressed as1,3

DTðtÞ ¼ Q

effiffiffiffiffiptp 1þ 2

X1n¼1

exp�n2d2

at

� �" #; (1)

where Q is the heat deposited on the surface, e is the thermal

effusivity, d is the defect depth, and a is the thermal diffusiv-

ity. The temperature-time curves of six different depths simu-

lated with Eq. (1) are shown in Fig. 2, the temperature

decreases with time and it decreases faster for deeper depth.

For the theoretical simulations in this study, the term Q=effiffiffipp

was set to 1 for a relative comparison among different depths.

This paper proposed to first multiply both sides of Eq. (1)

withffiffitp

, and define a new time-dependent function f(t) as

f ðtÞ ¼ DTðtÞ �ffiffitp¼ Q

effiffiffipp 1þ 2

X1n¼1

exp�n2d2

at

� �" #; (2)

when t starts from zero, the exponential term in Eq. (2) is 0,

when t is infinity, the exponential term is 1. Thus, the magni-

tude of f(t) mainly depends on Q and e. Three Al and three

GFRP f curves of different depths simulated with Eq. (2) are

shown in Fig. 3, where n is set to 5, the original time-

dependent decreasing temperature curves change to time-

dependent increasing curves. As shown in Fig. 3, f increases

faster for thinner defect, and it saturates earlier for sample

with bigger thermal diffusivity. In Fig. 3, one horizontal line

is used to indicate that when f is set to the same value v0, the

corresponding time for different materials and depths is dif-

ferent. The magnitude of f mainly depends on Q and e, how-

ever, its changing character is decided by the parameters in

the exponential term. For a simplicity, suppose we set

w ¼ d2=at, then f can be expressed as

f ðwÞ ¼ Q

effiffiffipp 1þ 2

X1n¼1

exp �n2w� �" #

: (3)

The time, depth, and thermal diffusivity dependent f curve is

changed to a dimensionless curve, which only depends on a

new parameter w. The corresponding w dependent f curve is

shown in Fig. 4, it is clearly shown that f is a monotonically

decreasing curve. Suppose we set

FIG. 1. Sketch map of pulsed thermographic principle.

FIG. 2. The simulated temperature decay at six different depths for GFRP

sample.

FIG. 3. Simulated f curves for Al and GFRP materials with 2 mm-4 mm

depths.

023112-2 Zeng et al. J. Appl. Phys. 112, 023112 (2012)

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

128.123.44.23 On: Fri, 19 Dec 2014 03:02:34

f ðwÞ ¼ v0; (4)

where v0 is a predefined value, and w0 is supposed to be the

single solution of this equation as shown in Fig. 4. And

because of w ¼ d2=at, we have

t0 ¼d2

aw0

: (5)

Eq. (5) means that when it is to predict defect depth, the

obtained t0 corresponding to the time that satisfies Eq. (4),

which is indicated in Fig. 3, is linearly related with square

depth. This linear relation is very similar with other methods

based on a characteristic time, such as PCT, PST, and LPDT,

etc., except that the slope of linearity is different. The charac-

teristic time of other methods could be expressed as d2=ka,

where k is a constant for each method. However, the slope of

this linear relation is decided by w0, which has approximate

exponential relation with the chosen v0 as simulated in Fig. 4.

As discussed above, when adopting this method for

defect depth prediction, it is first to set a value v0, and then

extract the corresponding time t0. If the thermal diffusivity

and w0 are known, defect depth can be obtained with Eq. (5).

However, in practical applications, the thermal diffusivity of

measured sample may not be exactly known, and moreover,

it is very difficult to calculate w0 because v0 and w0 depend

on Q and e. Q may have very big difference for different

samples due to its surface condition, emissivity, etc. So if we

directly use Eq. (5) to predict the defect depth, the uncer-

tainty or the error of parameter w0 could not be neglected.

The better way is to use a standard sample to construct the

linearity between d2 and t0, and then the calibrated linearity

could be used for depth prediction. In Sec. III, we will dis-

cuss how to choose v0 and verify if it is linear relation

between d2 and t0.

III. EXPERIMENTAL RESULTS

A. Sample

In this study, one anodic oxidated aluminum sample and

one GFRP sample with 300 mm� 200 mm� 15 mm size

were machined with six flat-bottom wedges whose depth

ranges from 2 mm to 7 mm to simulate defect with an air

interface. GFRP specimen was machined by maintaining

their geometric axis parallel and normal to the fibre direc-

tions for longitudinal (0) and transverse (90), off-axis orien-

tation of the specimen makes an angle 45 with its geometric

axis, and its thermal diffusivity is 4.68� 10�7 (measured

with TCiTM Thermal Conductivity Analyzer made by C

Therm Technologies, Ltd.). The schematic illustration of the

detected sample with machined flat-bottom wedges is dis-

played in Fig. 5, the depth of each wedge is also shown in

the figure. There is a small circle in each wedge, the distance

from circle to horizontal edge is 20 mm, and the following

temperature curves are extracted from those circle positions

in experimental thermographic sequence.

The experimental temperature data were obtained by

using a reflective flash pulsed thermographic system, as illus-

trated in Fig. 1. During the test, flash lamps were triggered at

t¼ 0 to deposit a nearly instantaneous thermal impulse on

the sample’s surface. The surface temperature variation was

monitored by an infrared camera, which takes a series of

thermal images that are stored in a PC for data processing. A

fast and high precision infrared camera was set at a 60 Hz

sampling frequency for Al sample and 20 Hz for GFRP sam-

ple to capture the temperature evolution.

B. Thermographic data analysis

The experimental temperature amplitude is affected by

inhomogeneities of optical surface heating and absorption,

and infrared emission for different materials, such as the color

and the surface condition. Therefore, the experimental tem-

perature data was first normalized (such as with the second

frame for Al sample and the eighteenth frame for GFRP sam-

ple, which are the same as in theoretical simulations) to

reduce the influence of those factors. The experimental tem-

perature decay curves of GFRP sample are displayed in Fig.

6. Those curves are very similar with the theoretical simula-

tions as shown in Fig. 2, except that it is polluted with random

noise. The corresponding f curves are displayed in Fig. 7,

which is polynomial curve fitted, it is also coincided with the-

oretical simulations shown in Fig. 3. The experimental fcurves of Al sample are displayed in Fig. 8, those curves are

different with the theoretical simulations in later times, which

FIG. 4. Simulated w dependent f curve.FIG. 5. Schematic illustration of Al sample with machined flat-bottom

wedges.

023112-3 Zeng et al. J. Appl. Phys. 112, 023112 (2012)

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

128.123.44.23 On: Fri, 19 Dec 2014 03:02:34

are caused by 3D heat diffusion because Al has a big value of

thermal diffusivity. The difference between the experimental

and theoretical simulations of Al sample is that the curves

with different depths merge very early and do not saturate.

However, if we are only interested in the early times, such as

the values before 0.5 s, those values are well fitted with theo-

retical simulations. The magnitude of some experimental fcurves shown in Figs. 7 and 8 may be different with the theo-

retical simulations as shown in Fig. 3 because the experimen-

tal flash pulse duration is several milliseconds, not a pulse as

considered in theoretical simulations.

C. The selection of v0

Because the magnitude of different materials may have

very big difference even though all temperature data were

normalized, thus, the selection of v0 for experimental data

may have to be reconsidered for different materials. The fcurves of materials with big thermal diffusivity, such as Al

sample, change very fast and saturate very early, and its

magnitude is easily affected by 3D heat diffusion as shown

in Fig. 8. Therefore, the selection of v0 should be limited in a

relatively small range at early times, and the experimental

sampling frequency for this kind of fast materials should be

as high as possible to obtain enough data. For slower materi-

als, such as GFRP shown in Fig. 7, f curves saturate very late

and are not so easily affected by 3D heat diffusion which

allows a relatively big range of v0 to be chosen.

From the theoretical simulations and experimental data

comparison, we can find that it is difficult to construct a sin-

gle standard for the selection of v0. However, v0 should not

be too big or too small. When the chosen v0 is big, the slope

of the linearity between t0 and square depth is also big,

which is easier to obtain more accurate result because the

same level of noise has smaller effect for a bigger slope.

However, a bigger v0 means that it is at a later time that 3D

heat diffusion is significant, and the result would be easily

affected by defect size. The chosen v0 should not be very

small either, because the defect signal may have not deviated

from sound signal yet at an early time and noise may cause

very big error too. The better choice is that the standard sam-

ples with several known depths are used to experimentally

construct the optimal selection of v0 selection and the linear-

ity between t0 and square depth.

The chosen v0 value should be able to well separate dif-

ferent depths, and also the extracted time t0 should represent

depth too. Pulsed thermography is normally used for subsur-

face defect detection, thus, a medium chosen value of v0 nor-

mally can guarantee that defect signal already deviate from

sound signal and also is not at a very late time to be affected

by 3D heat diffusion. In this study, 6 different depths from

2 mm to 7 mm for two samples were used, those depth range

can cover most of applications of depth prediction in pulsed

thermography. The experimentally chosen v0 ranging from

0.25 to 0.35 and from 2.5 to 3.5 for Al sample and GFRP

sample respectively can represent the depth relation.

D. Results

In order to predict defect depth, the Al and GFRP sam-

ples with known depth defects were used for calibrating the

linearity between t0 and square depth as indicated in Eq. (5).

Figs. 7 and 8 display f curves of Al sample and GFRP sam-

ple, which can represent fast and slow diffusive samples.

When the proposed method directly using Eq. (5) is applied

for depth prediction, the exact value of a and w0 should be

known. The thermal diffusivities of the processed Al sample

FIG. 6. Experimental temperature curves of GFRP sample.

FIG. 7. Experimental f curves of GFRP sample.

FIG. 8. Experimental f curves of Al sample.

023112-4 Zeng et al. J. Appl. Phys. 112, 023112 (2012)

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

128.123.44.23 On: Fri, 19 Dec 2014 03:02:34

and GFRP sample are known values or they can be measured

with some technologies. The theoretical value of w0 can be

obtained because the term of Q=effiffiffipp

is set to 1, however, it

is difficult to obtain the exact value of experimental w0

because Q depends on lots of conditions as discussed above.

Thus, the linearity between t0 and square depth is a better

choice for depth prediction since we have standard samples.

For each chosen v0 value, the corresponding t0 for each

depth is extracted. Figs. 9 and 10 display three t0 versus

square depth curves for GFRP and Al samples, respectively,

and it is clearly shown that t0 has very good linearity with

square depth for both samples. Table I lists the slopes of t0versus square depth curves for Al and GFRP samples, and it

shows that the slope increases monotonically and approxi-

mately linearly with v0. Eq. (5) shows that t0 is inversely pro-

portional to a and w0, and the experimental results listed in

Table I show that the slope of GFRP is much bigger than Al

because the thermal diffusivity of Al is much bigger than

GFRP. Even though f is approximately exponentially

decreasing with w, it can be approximately taken as linearly

changing with w because the range of experimentally chosen

v0 is in a small range, and the experimental results of both

samples verified this relation that the slope approximately

linearly increases with v0.

The experimental results of both samples not only show

good linearity between t0 and square depth, and but also the

slope of this linearity fits quite well with theoretical predic-

tions. The experimental results also show that the linearity

for the chosen range of v0 is very good because the experi-

mental f curves were polynomial curve fitted to remove the

effect of random noise. Thus, the selection of v0 is not cru-

cial that it can be chosen in a relative big range as compared

in this study.

In the quantitative application of depth prediction using

pulsed thermography, the thermal diffusivity of measured

sample and some of experimental parameters are unknown,

thus, the linear relation between the characteristic time and

square depth was normally adopted for quantitative prediction

of defect depth. The good linearity experimentally obtained

with two samples indicates that the proposed method can be

used for quantitative prediction of defect depth.

E. Effect of uneven heating and surface emissivityvariations

Due to the manufacturing process, the surface of GFRP

sample may have different color or roughness at different

locations. In order to have different surface emissivity condi-

tions for the same location, the surface of GFRP sample is

processed with different paintings, however, all of them are

with very thin black paint. The experiment is conducted on

GFRP sample under different surface conditions with com-

mercial EchoTherm system manufactured in 2003 by Ther-

mal wave imaging, Inc., which may have uneven heating. In

order to simulate uneven heating, a lower power level (about

90%) is also used as a comparison. Under approximately the

same experimental condition, due to the variations of surface

emissivity and uneven heating, the temperatures increase of

the first frame for the above extracted pixels may vary about

4 �C, which is about 30% of temperature increase. For the

same pixels among different experimental results, the tem-

peratures of different surface condition results also vary

about 4 �C.

For above conditions, the experimental results are proc-

essed with the same procedure, the characteristic time and

square depth extracted from the same experimental result

FIG. 9. t0 versus square depth for GFRP sample.

FIG. 10. t0 versus square depth for Al sample.

TABLE I. Slopes at different v0 for Al and GFRP samples.

Al GFRP

v0 Slope (10�3) v0 Slope

0.25 1.7701 1.5 0.171

0.26 2.3584 1.6 0.2628

0.27 2.9822 1.7 0.3478

0.28 3.6293 1.8 0.4271

0.29 4.3137 1.9 0.5023

0.3 5.0419 2 0.5755

0.31 5.8016 2.1 0.6483

0.32 6.615 2.2 0.7225

0.33 7.4648 2.3 0.8

0.34 8.3775 2.4 0.8834

0.35 9.3284 2.5 0.9767

023112-5 Zeng et al. J. Appl. Phys. 112, 023112 (2012)

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

128.123.44.23 On: Fri, 19 Dec 2014 03:02:34

shows good linear relationship. Among different experimen-

tal results, the errors are normally within 10%.

F. The depth detectability

Due to 3D heat diffusion, the temperature decay has no

difference after the defect depth is deeper than a specific

value, therefore, pulsed thermography is difficult to detect

very deep defect. In Figs. 7 and 8, f curves of 15 mm depth

are also shown, typically in pulsed thermography, 15 mm

depth positions are chosen as sound area which is normally

not used for depth prediction. Fig. 7 shows that 15 mm curve

is very close to 7 mm curve which means that the deepest

depth could be measured is close to this depth (about

7.5 mm) for GFRP sample. However, for Al sample as

shown in Fig. 8, 15mm curve still shows depth information

with other six curves. The values from 2 mm to 7 mm were

linearly fitted, Fig. 11 shows the original and the fitted t0 ver-

sus square depth including 15 mm depth. The extracted t0 for

15 mm depth was used in this linearity to obtain that its pre-

dicted depth is 13.2942 mm, 13.325 mm, and 12.1524 mm,

respectively, for three v0: 0.25, 0.3, and 0.35. Therefore, for

Al sample, the detectable deepest depth is about 13mm, and

the selected v0 should not be very big to reduce the effect of

3D heat diffusion. This ability to detect 13 mm depth for Al

sample may be better than other methods, which are not nor-

mally used for so deep depth prediction.

There is no derivative involved, and the characteristic

time is determined by magnitude. In order to detect deeper

defect, its corresponding temperature curve must show dif-

ference in magnitude, therefore, it is better to have stronger

signal level, which could be obtained by adopting higher

energy heating source, bigger thermal emissivity, etc. Once

the temperature curves of different depths can be well sepa-

rated with each other, the precision is mainly dependent on

the normalization procedure, therefore, bigger SNR is also

preferred especially when it is to detect deeper defects.

G. Comparison with other methods

The characteristic time of HMT method is corresponding

to the time when its temperature is half of the maximal tem-

perature, HMT method can only be used with transmission

mode of pulsed thermography, and it can be easily obtained

because the temperature curve saturates. HMT is one of the

special cases of the proposed method that v0 is set to be half

of the maximum, and it could obtain very accurate result

because less 3D heat diffusion is involved in transmission

mode. However, both sides of the detected sample are not

always accessible in practical applications, therefore, reflec-

tion mode is more often used. In reflection mode, f curve may

not saturate because of 3D heat diffusion, therefore, v0 has to

be experimentally chosen based on the standard sample.

The logarithmic deviation time method can also be taken

as a special case of this method, it takes the time when defect

signal deviates from sound signal in the logarithmic form as

the characteristic time. Here, the sound signal in the logarith-

mic form is normally thought as a line with the slope of �1/2,

so the deviation time is the time when defect signal deviates

from �1/2 line. GFRP sample has much slower thermal diffu-

sivity than Al sample, it can show better depth information

than a faster material in logarithmic form, and the theoretical

simulation of f curves in logarithmic form of GFRP sample is

displayed in Fig. 12. The starting �1/2 line of the original

temperature decay changes to the horizontal line for f curves

in logarithmic form, the deviation method is simplified by set-

ting v0 to be a small value after the original temperature trans-

forms to f values. However, the experimental logarithmic fvalues are not as perfect as shown in Fig. 13 that the starting

line is not horizontal, the slope of the linear section for the

early frames is positive for experimental results, this differ-

ence is caused by the pulse duration. v0 should be set as a

very small value to obtain the deviation time, however, the fcurves of deeper depth may not deviate from sound signal yet

at such a case due to pulse duration problem. So the deviation

method applied on f values when using typical flash lamp as

heat source has the same problem as the original method that

it is difficult to obtain the actual deviation time. However, if

the duration of heat source can be controlled to be very small,

such as using laser, the deviation method applied on f values

may be experimentally applicable. The advantage of deviation

method is that it is not so easily to be affected by 3D heat dif-

fusion because its characteristic time is the earliest, and its

disadvantage is that it is easily affected by noise because a

small specific value is chosen.

FIG. 11. t0 versus square depth of experimental and fitted values for Al

sample.

FIG. 12. Simulated logarithmic lnf curves of GFRP sample for 2 mm to

7 mm depths.

023112-6 Zeng et al. J. Appl. Phys. 112, 023112 (2012)

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

128.123.44.23 On: Fri, 19 Dec 2014 03:02:34

The proposed method is very similar with APST method

except that APST method takes the peak time of the 1st de-

rivative of f values as the characteristic time, and both meth-

ods are easy to implement. The advantage of APST, PST,

and the first peak of PSDT is that they are not affected by

defect size, however, their disadvantage is that the peak time

is sensitive to noise when it is processed with the derivations.

The advantage of the proposed method is that it is not sensi-

tive to noise because no derivation is required, however, it is

affected by defect size as PCT method.

IV. CONCLUSIONS

In this study, a new method for depth prediction is pro-

posed to first multiply the temperature decay with the square

root of time to obtain a new time sequence f, and then extract

the time that f equals to a predefined value. The extracted

time of theoretical model and the experimental results of Al

and GFRP samples has linear relation with square depth, if

the standard sample with known defect depth is available,

the constructed linearity which can also be expressed as an

equation can be used to measure defect depth with the same

material. The proposed method is simple to implement, it

does not need a reference or any derivative, and it can obtain

accurate result theoretically.

ACKNOWLEDGMENTS

This work is supported in part by National Science

Foundation of China Nos. 10804078, 51107156, and

61079020, in part by the Project Foundation of Chongqing

Municipal Education Committee (No. KJ100605), in part by

ChongQing Normal University No. 06LB012.

1X. Maldague, Nondestructive Evaluation of Materials by Infrared Ther-mography (Springer, New York, 1993).

2S. M. Shepard, “Flash thermography of aerospace composites,” in IV Con-ferencia Panamericana de END Buenos Aires, Octubre 2007.

3D. P. Almond and S. K. Lau, “Defect sizing by transient thermography. I.

An analytical treatment,” J. Phys. D: Appl. Phys. 27(5), 1063–1069

(1994).4D. W. Tang, G. H. He, and B. L. Zhou, “Effects of finite absorption depth

and infrared detector non-linearity on thermal diffusivity measurement of

thin films using the flash method,” Rev. Sci. Instrum. 66, 4249–4253

(1995).5J. G. Sun, “Analysis of pulsed thermography methods for defect depth pre-

diction,” J. Heat Transfer 128(4), 329 (2006).6V. Vavilov, T. Ahmed, J. Jin, R. L. Thomas, and L. D. Favro,

“Experimental thermal tomography of solids by using the flash one-side

heating,” Sov. J. NDT 12, 60–66 (1990).7L. D. Favro, H. J. Jin, Y. X. Wang, T. Ahmed, and X. Wang, “IR thermal

wave tomographic studies of structural composites, review of progress in

quantitative nondestructive evaluation,” in Proceedings of the 18th Annual

Review, Brunswick, ME, 28 July–2 Aug 1991 (A93-18576 05-38), Vol.

11A, pp. 447–451.8L. D. Favro, X. Han, Y. Wang, P. K. Kuo, and R. L. Thomas, “Pulse-echo

thermal wave imaging,” Rev. Prog. Quant. Nondestr. Eval. 14, 425–429

(1995).9L. D. Favro, X. Han, P. K. Kuo, and R. L. Thomas, “Imaging the early

time behavior of reflected thermal wave pulses,” Proc. SPIE 2473,

162–166 (1995).10X. Han, L. D. Favro, P. K. Kuo, and R. L. Thomas, “Early-time pulse-

echo thermal wave imaging,” Rev. Prog. Quant. Nondestr. Eval. 15,

519–524 (1996).11H. I. Ringermacher, R. J. Archacki, Jr., and W. A. Veronesi,

“Nondestructive testing: Transient depth thermography,” U.S. patent

5,711,603 (1998).12X. Han, L. D. Favro, and R. L. Thomas, “Thermal wave NDI of disbonds

and corrosion in aircraft,” in The Second Joint NASA/FAA/DOD Confer-

ence on Aging Aircraft, NASA/CP-1999-208982, Part 1, 1998, pp.

265–274.13X. Han, L. D. Favro, and R. L. Thomas, “Quantitative defect depth meas-

urements for NDE of composites,” in Proceedings of the American Society

for Composites (Technomic Publishing Co. INC, 1998), pp. 1077–1081.14X. P. Maldague and S. Marinetti, “Pulse phase infrared thermography,” J.

Appl. Phys. 79(5), 2694–2698 (1996).15C. I. Castanedo, “Quantitative subsurface defect evaluation by pulsed

phase thermography: Depth retrieval with the phase,” Ph.D. dissertation

(University of Laval, 2005).16C. I. Castanedo and X. Maldague, “Defect depth retrieval from pulsed

phase thermographic data on plexiglas and aluminum samples,” Proc.

SPIE 5405, 348–355 (2004).17M. Pilla, M. Klein, X. Maldague, and A. Salerno, “New absolute contrast

for pulsed thermography,” in QIRT, edited by D. Balageas, G. M. Busse,

and G. Carlomagno (2002), pp. 53–58.18S. M. Shepard, J. R. Lhota, B. A. Rubadeux, D. Wang, and T. Ahmed,

“Reconstruction and enhancement of active thermographic image

sequences,” Opt. Eng. 42,1337–1342 (2003).19Z. Zeng, J. Zhou, N. Tao, L. Feng, and C. Zhang, “Absolute peak slope

time based thickness measurement using pulsed thermography,” Infrared

Phys. Technol. 55(2–3), 200–204 (2012).20J. G. Sun, “Method for determining defect depth using thermal imaging,”

U.S. patent 6,542,849 (2003).21Z. Zeng, “Thickness measurement using thermal wave imaging and

enhance the detectability of SonicIR,” Ph.D. dissertation (Wayne state

University, 2006).

FIG. 13. Experimental lnf curves of GFRP sample for 2 mm to 7 mm

depths.

023112-7 Zeng et al. J. Appl. Phys. 112, 023112 (2012)

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:

128.123.44.23 On: Fri, 19 Dec 2014 03:02:34