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Quantification of defects in composites and rubber materials using active thermography
Infrared Physics & Technology 55 (2012) 191–199
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Quantification of defects in composites and rubber materials using active thermography B.B. Lahiri a, S. Bagavathiappan a, P.R. Reshmi b, John Philip a,⇑, T. Jayakumar a, B. Raj a a b
Non Destructive Evaluation Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, India Department of Optoelectronics, University of Kerala, Trivandrum, India
a r t i c l e
i n f o
Article history: Received 5 September 2011 Available online 21 January 2012 Keywords: Lock-in thermography Pulsed thermography Composite materials Phase contrast Thermal contrast Defect depth quantification
a b s t r a c t Active (lock-in and pulsed) thermography technique is used to quantify defect features in specimens of glass fiber reinforced polymer, high density rubber, low density rubber and aluminum bonded low density rubber with artificially produced defects. The relationship between phase contrast and thermal contrast with defect features are examined. Using lock-in approach, the optimal frequencies for different specimens are determined experimentally. It is observed that with increasing defect depth, the phase contrast increases while the thermal contrast decreases. Defects with radius to depth ratio greater than 1.0 are found to be discernible. The phase difference between sound and defective region as a function of square root of excitation frequency for glass fiber reinforced polymer specimen is found to be in good agreement with the predictions of Bennet and Patty model [1]. Further, using pulsed thermography, the defects depth could be measured accurately for glass fiber reinforced polymer specimen from the thermal contrast using the analytical approach of Balageas et al. [2]. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction Infrared thermography (IRT) is extensively used in the field of nondestructive testing (NDT) for inspection, monitoring and basic research [3–6]. Apart from NDT, in recent years, thermography is being widely used in a wide range of areas, such as determination of thermophysical parameters [7,8], agriculture [4], medical [9– 12], biology [13] and even bird location [14]. Recently IRT is successfully used for indirect identification of sectors with high current density concentration in planar microwave devices [15]. The developments in the field of quantum detector technology enhanced the accuracy in temperature measurements within a few millikelvin. The advent of focal plane arrays has resulted in superior thermal imaging system with better spatial and temperature resolution [16]. In IRT, the infrared radiation (wavelength lies between 0.75 lm and 1000 lm) emitted by a body is detected using an infrared detector and the information about temperature is obtained from the acquired data using Stefan–Boltzmann’s law, which is expressed as follows [3].
q ¼ erT 4 A
ð1Þ
where q is the rate of energy emission (W), A is the area of emitting surface (m2), T is the absolute temperature (K) and r is the Stefan– ⇑ Corresponding author. Tel.: +91 044 27480232; fax: +91 044 27480356. E-mail address: [email protected] (J. Philip). 1350-4495/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.infrared.2012.01.001
Boltzmann’s constant (r = 5.676 108 W/m2 K4) and e is the emissivity of the material. Thermography can be broadly classified into two categories, viz. passive and active [3]. In passive thermography no external heating is required. Only the thermal radiation due to difference in temperature (caused by any other reasons apart from external stimuli) between the surrounding and specimen is monitored. The applications of passive thermography include monitoring of buildings and concrete structures [17–20], medical [9–12] and biological investigations [13]. On the other hand, in active thermography, an external heating is required and the evolution of surface temperature is monitored in the transient or stationary domain. Depending on the heating procedure, active thermography can be further subdivided into different categories such as pulsed, step heating, lock-in, vibrothermography and pulsed phase thermography [3,21]. In pulsed thermography, a short heating pulse is applied to the specimen and the cooling data is monitored in the transient domain. In step heating, the temperature rise is monitored in the transient domain where a long heating pulse is applied. Lock-in thermography is carried out in stationary domain, where a modulated heat wave is launched on the sample for heating which travels through the bulk by diffusion and reflects back from the defect sites. In vibrothermography, under the effect of external mechanical vibration, heat is generated at the defect locations due to friction. Pulsed phase thermography is a combination of both pulsed and lock-in thermography, where data is acquired in transient domain but phase image is generated by Fourier analysis of the acquired images.
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Pulsed thermography is being routinely used for quantitative evaluation of defect in both metallic and composite specimens [20,22,23]. Though there is a problem of determining optimum frequency, lock-in thermography, in recent years, has become an effective tool for non-contact defect detection. This method has been extensively used to find quantitative information of subsurface defects [24,25], corrosion protective paints [22], morphologies of defects (like circular, square-like, etc.) [26] and industrial processes [27]. Typical applications of vibrothermography and step heating thermography are detection of closed cracks, delaminations and coating thickness evaluation [3]. Vibrothermography suffers from the problems of mechanical and dynamical instability, difficulty in application of mechanical load and difficulty in determination of vibration frequencies [3]. Both pulsed phase thermography and step heating thermography are associated with overheating problems [28]. Among the various active thermography techniques, lock-in and pulsed thermography techniques, due to their ease of application, straight forwardness and capability of detection of versatile types of defects, have gained widespread popularity in the field of NDT [3]. Pulsed thermography is one of the most popular active thermography techniques, primarily due to its fast inspection time. Lock-in thermography, on the other hand, is a comparatively slower technique. But signal to noise ratio (SNR) is higher in lock-in thermography, as a single frequency thermal wave is used for defect detection. Phase image of lock-in thermography technique is independent of local disturbances, like nonuniform heating and emissivity variation [3,28]. In lock-in thermography, defect depths can be measured directly, without postprocessing of the acquired images, by varying the excitation frequencies [3,29]. Energy input is also considerably lower in lockin technique [28]. In pulsed thermography, defect detection is primarily due to the temperature difference (contrast) between the defect and defect-free region. Several types of contrasts are defined in literature, like thermal contrast, differential absolute contrast, etc. [23]. Though differential absolute contrast is independent of non-uniform heating, it requires time consuming post-processing of the acquired data [6]. Thermal contrast based techniques are comparatively fast, straight forward and hence more suitable for industrial adaptation. This was the motivation to use lock-in and pulsed thermography technique in our experiments. Reinforced polymers are light weight structural materials. In recent times, glass fiber reinforced polymer is used to improve the load carrying capacity of concrete deck slabs [30] and mesh type
Fig. 1. Schematic of the specimens (z is the defect depth and x is total thickness of the specimens).
civil structures [31]. Rubber is an abrasion resistant material and low density (soft) rubber is used in many parts of vehicle tyres and conveyor belts. High density (hard) rubber finds application in hose pipes, pump housing, etc. Rubber is also used as insulators in many heavy electrical components. NDT of these materials is very important for the production of light weight, highly reliable industrial components. In this paper, lock-in thermography was used to study the defect detectability in four different specimens, viz. glass fiber reinforced polymer (GFRP), high density rubber (HDR), low density rubber (LDR) and low density rubber with aluminum bonding (LDRAl) with defects of different depths and diameters. It was observed that the ratio of radius (r) to depth (z) of a particular defect sets a limit on the detectability. The critical ratio of r/z is determined for each type of specimen. Defect depths were quantified using pulsed thermography in case of GFRP specimen using an analytical approach. Similar thermal contrast based technique was earlier applied for defect depth quantification in carbon fiber reinforced polymer (CFRP) specimen [2,3,23]. However, to the best of our knowledge, there is no published report on GFRP specimen using the above experimental approach. 2. Materials and experimental methods 2.1. Specimen details Square shaped (10 cm 10 cm) specimens of the four materials, viz. GFRP, HDR, LDR and LDRAl were used in our experiment. In each of these specimens, artificial defects (flat bottom holes) of different depths and diameters were created. The schematics of these specimens with defect locations are shown in Fig. 1. Detailed geometrical descriptions of the defects in each of the specimens are provided in Table 1. 2.2. Experimental details For generation of sine waves of a single frequency, a programmable function generator (model: HM 8131-2, Hameg) was used and for detection of thermal waves FLIR SC5000 infrared camera was used. This camera has indium antimonide (InSb) detector with an array of 320 256 elements with a thermal sensitivity better than 25 mK. The detector elements are cooled using Stirling cycle. The spectral range of the camera is 2.0–5.1 lm. The sample was heated with a sinusoidally modulated heat wave from two 1 kW halogen lamps (connected to the output of function generator) kept at 50–55 cm away from the specimen. The camera was kept at a distance of 70 cm from the specimen in such a way that the axis of the camera coincides with the axis of the sample. The photograph of experimental setup is shown in Fig. 2. In thermography, temperature is interpreted from the radiation emitted from the surface under investigation. If the emissivity of the surface is very low, then the radiation emitted from this surface is very weak, which leads to the formation of an image with low SNR. It has been reported that thermographic measurement is not possible for surfaces having emissivity value lower than 20% of blackbody emissivity [3]. Low emissivity surfaces also suffer from the problem of secondary reflection, due to the presence of surrounding bodies. The most common methodology to overcome the above mentioned emissivity problems is by applying a uniform black paint of high emissivity value, which not only increases the surface emissivity value but also reduces the secondary reflections, besides providing a uniformly emissive surface [3]. Hence, the surface of the specimens facing the camera was black painted using a high emissivity (e 0.98) black paint. Similar methodology was also adopted by other research groups [3,24,32]. Reflection method
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B.B. Lahiri et al. / Infrared Physics & Technology 55 (2012) 191–199 Table 1 Geometrical description of the flat bottom holes in the four specimens. Hole number
A1 A2 A3 A4 B1 B2 B3 B4 C1 C2 C3 C4 D1 D2 D3 D4
Glass fiber reinforced polymer
High density rubber
Low density rubber
Low density rubber with aluminum bonding
Diameter (mm)
Depth (mm)
Diameter (mm)
Depth (mm)
Diameter (mm)
Depth (mm)
Diameter (mm)
Depth (mm)
10 10 10 10 7 7 7 7 5 5 5 5 2 2 2 2
1.5 2.5 3 4 1.5 2.5 3 4 1.5 2.5 3 4 1.5 2.5 3 4
5 5 5 5 12 12 12 12 9 9 9 9 7 7 7 7
1 3 4 6 1 3 4 6 1 3 4 6 1 3 4 6
10 10 10 10 8 8 8 8 5 5 5 5 4 4 4 4
2 3 4 5 2 3 4 5 2 3 4 5 2 3 4 5
10 10 10 10 8 8 8 8 5 5 5 5 4 4 4 4
2 3 4 5 2 3 4 5 2 3 4 5 2 3 4 5
Fig. 2. Photograph of experimental set-up (A = specimen, B = camera, C = halogen lamps, D = function generator).
was adopted, i.e., images were acquired from the same surface that was heated periodically. In case of LDRAl specimen, the rubber surface was inspected. Lock-in images were acquired by using ALTAIR LI software. Several excitation frequencies were used to determine the optimum frequency for each specimen. Five millisecond pulses from one of the 1 kW halogen lamps were used for pulsed thermography purpose.
the thermal wave in the bulk of the sample depends on a and also on the excitation frequency (f = x/2p) [21]. Thermal wavelength is defined as k = 2pl [3,21]. From the argument of the cosine term in Eq. (2), we get the phase difference U (degree), which is related to the defect depth z as
/ðzÞ ¼
z
ð4Þ
l
3. Theory 3.1. Theory of thermal waves For a planar semi-infinite specimen heated by a sinusoidal heat source of fixed amplitude and frequency, treating the problem as one-dimensional [3,21], the temperature T (°C) can be expressed as a function of defect depth z (mm), time t (s) and angular frequency x (Hz) as
z 2p z Tðz; tÞ ¼ T 0 el cos xt k
ð2Þ
where T0 is initial temperature (°C), k is thermal wavelength (m) and l is thermal diffusion length (m) which is given by
l¼
Eq. (4) indicates that phase difference increases with defect depth and the value of thermal diffusion length can be obtained from the slope. It is also evident from Eq. (2) that, for deeper defects the signal is highly attenuated. Therefore, the defect features (like depth and size) limits the detectability. Strictly speaking, Eqs. (2) and (4) are valid for semi-infinite specimen devoid of any defects. Bennett and Patty model [1] calculates the summation of all of the reflections from the interfaces (both defect and surface) and predicts the actual phase difference at the surface. According to
rffiffiffiffiffiffi 2a
ð3Þ
x 2
1
where a is thermal diffusivity of the material (m s ). Eq. (2) indicates that the temperature is attenuated exponentially with l in the bulk of the specimen and that the damping of
Table 2 Optimum frequencies of the four specimens. Serial no.
Sample code
Excitation frequencies employed (Hz)
Optimum frequency (Hz)
1 2 3 4
GFRP HDR LDR LDRAl
0.001–0.8 0.0003–0.05 0.0001–0.05 0.0001–0.05
0.002 0.003 0.007 0.009
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this model the phase difference is calculated by the following equation.
D/ ¼ tan1
Rb ð1 þ Rg Þ expð2as zÞ sin 2as z 1 Rg ðRb expð2as zÞÞ2 þ Rb ð1 Rg Þ cos 2as z
! ð5Þ
where D/ is the phase difference (degree) between the sound and defective region and as is the thermal wave number (m1), which is given by the following equation:
pffiffiffi f as ¼ pffiffiffiffiffiffiffi 2 pa
ð6Þ
Rb and Rg are thermal wave reflection coefficients at back (i.e. defect) and front (i.e. specimen) interfaces respectively. For the present case, as both the interfaces were air-material in nature the values of Rb and Rg are same, as indicated below
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qa ca ka Rb ¼ Rg ¼ qm c m km
ð7Þ
where qa, qm, ca, cm, ka, km are densities, specific heats and thermal conductivities of air and specimen material respectively.
Fig. 3. Typical amplitude (left) and phase (right) images of (a) GFRP, (b) LDR and (c) HDR specimens at optimal frequencies.
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3.2. Theory of lock-in thermography
Phase image contains information about the propagation time and average image is the conventional thermography image [3].
In lock-in thermography, after externally heating the specimen sinusoidally (with fixed amplitude and frequency), the resultant temperature distribution on the surface is observed in the stationary regime and the corresponding data is recorded real time. Using four point method, it is possible to determine the amplitude and phase from these data [3,33]. At least four equidistant temperature data points are required in one modulation cycle to get the correct phase and amplitude. For example, if P1, P2, P3 and P4 are four equidistant temperature data points in a complete period then the phase (U) and amplitude (A) are given by
P P3 U ¼ tan1 1 P2 P4 Aðx; yÞ ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðP1 P3 Þ2 þ ðP2 P 4 Þ2
ð8Þ
ð9Þ
The average (M) is the simple average of the four data points as given below
M¼
P1 þ P2 þ P3 þ P4 4
195
ð10Þ
3.3. Pulsed thermography, thermal contrast and depth quantification For a homogenous, semi-infinite specimen after absorption of a Dirac heat pulse at time t = 0, the temperature decay follows the following pattern [23,34].
Q DT ¼ pffiffiffiffiffiffi e pt
ð11Þ
where DT is the temperature change of the surface (°C), Q is the quantity of energy absorbed per unit area (W m2), t is the elapsed time (s) and e is the thermal effusivity of the material (Ws1/2 K1 m2), which is given as
e¼
qffiffiffiffiffiffiffiffi kqc
ð12Þ
where k, q and c are the thermal conductivity, density and specific heat of the material respectively. Thermal contrast (°C) over a defect region is defined as
CðtÞ ¼ T def ðtÞ T sound ðtÞ
ð13Þ
Fig. 4. Typical surface plots of phase images of (a) GFRP and (b) LDR specimens.
Fig. 5. (a) Original HDR amplitude image, binary image corresponding to threshold levels of (b) 0.65, (c) 0.698, (d) 0.73, (e) Original GFRP phase image, binary image corresponding to threshold levels of (f) 0.21, (g) 0.25, (h) 0.30.
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where Tdef and Tsound are the temperatures of defect and sound regions respectively. An analytical expression for defect depth quantification in case of carbon–epoxy composites using pulsed thermography is derived by Balageas et al. [2].
pffiffiffiffiffiffiffiffiffi zdef ¼ m tmax ðC max Þn
ð14Þ
where zdef is the defect depth, Cmax is the maximum contrast observed, tmax is the time when contrast is maximum, m and n are numerical constants. This approach has been successfully used for defect quantification in CFRP specimen and plexiglas [23]. The values of m and n are 0.6722 and 0.258 for CFRP [3,23]. Rearranging
the terms and on performing logarithm on both sides of Eq. (14) the following equation of a straight line is obtained [3].
zdef log10 pffiffiffiffiffiffiffiffiffi ¼ log10 m þ nlog10 ðC max Þ tmax
ð15Þ
From the slope and intercept of this straight line the values of the constants n and m can be found respectively. 4. Results and discussion In lock-in thermography, defects are visible only when the thermal diffusion length is of the order of defect depths [3]. Hence Eq.
Fig. 6. Plot of difference in digital level between sound and defective regions (DDL) as a function of defect depth at different excitation frequencies for (a) GFRP, (b) HDR, (c) LDRAl and (d) LDR.
Fig. 7. Plot of phase difference between sound and defective regions as a function of (r/z) at different excitation frequencies for (a) GFRP, (b) HDR, (c) LDRAl and (d) LDR.
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(3) indicates that defects of a particular depth could be detected with maximum contrast by a thermal wave of a particular frequency. So a range of frequencies were used for detecting defects of various depths in all the four specimens. The upper limits are chosen such that thermal diffusion length is around 0.2 mm in all the specimens, whereas the lower limits are chosen in such way that the thermal diffusion lengths match with the deepest defects in the corresponding specimens. Though the phase contrast (phase difference between defective and sound region) is maximum at a single frequency, defect of a particular depth is visible over a wide band of frequency. An overlapping band of frequencies, where maximum number of defects is visible, not necessarily with maximum contrast, is identified and the average frequency of this band was considered as the optimum frequency for that specimen. The range of frequencies and the optimum frequencies for each of the specimen is presented in Table 2. This procedure makes the process of defect identification comparatively fast and hence suitable for industrial applications [32]. A few typical amplitude and phase images of different specimens are shown in Fig. 3. It must be noted that the defects C1 and C2 (encircled in the Fig. 3a) in case of GFRP specimen were actually through – holes. It is evident from the images that phase images provide better clarity in terms of defect location and contrast, compared to the amplitude images. This is because; phase image is independent
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of the local problems such as non-uniform heating and emissivity variation [3,28]. Defects B1 and B2 are absent in the phase image of LDR specimen (Fig. 3b) whereas there is a faint signature of B2 in the corresponding amplitude image. The blurring of the images is attributed to the infrared fog created by the afterglow of the halogen lamps. Image processing, nowadays, is considered as a fundamental tool to enhance readability of an image [35–37]. Segmentation is one of the basic image processing techniques [35]. Others are like surface plots of 2-D images where slight variations in gray level are magnified and represented pictorially with a pseudo color scale. In Fig. 4, we have shown the surface plots of the phase images of GFRP and LDR specimens. It can be seen that these surface plots (after suitable enhancement) help us to visualize the surface phase contrast clearly that enables faster and easier identification of defects from sound regions. Image segmentation was done using binary image processing with a global threshold value. Binary images are digital images, where only two (0 and 1) gray level values are allowed for each pixel. Visual representations of such images correspond to binary shading where 0 is shaded as black and 1 as white. While converting an image to its binary equivalent, we can set a threshold gray level value for the original image, below which all gray level values will be set to zero. Thresholds can be of two types, viz. global and local [38]. In the case of global threshold we set a single
Fig. 8. Plot of Phase difference between sound and defect regions as a function of square root of excitation frequencies in GFRP specimen for defects of depths (a) 1.5 mm and (b) 3 mm.
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Fig. 9. Thermal contrast as a function of time for different defects in case of GFRP specimen.
Fig. 10. log10(zdef/sqrt(tmax)) vs. log10(Cmax) for different defects for GFRP specimen.
threshold value for the entire image, whereas, in the case of local threshold, the entire image is subdivided into smaller sub images and a threshold value is chosen for each sub image. Global threshold method was applied for the present case. Typical binary images are shown in Fig. 5. These binary images provide better insights into the defect locations and the relative contrast corresponding to different defects. As we can see from Fig. 5d that defects B1 and B2 have highest contrast as they are visible in the binary image even after the threshold is set to 0.73. Such binary images may help in the development of automatic defect recognition algorithms for thermal images. Fig. 6 shows the difference in digital level between the sound and the defective regions as a function of defect depth, which follows a similar trend in all the four specimens. Digital level is basically analogous to amplitude value. Hence a plot of DDL vs. defect depth is good enough to get an idea of thermal contrast variation.
We observe that, for lower frequencies, the values of DDL are higher. This is because lower frequency means longer heating period and hence the amount of heat deposited will be more. Moreover, DDL value increases as defect depth decreases because a defect of less depth results in sharp contrast in temperature which is manifested as a higher DDL value. It is seen that in all the graphs, DDL is a monotonically decreasing function of defect depth except for GFRP and HDR specimens, where there is a saturation tendency around 4.0 mm of defect depth. Fig. 7 shows the plot of phase difference (between the sound and defect regions) vs. r/z (where r is the radius of a defect and z is its depth). We have chosen the largest diameter defects for this plot. A similar trend for each of the four specimens is seen even in this case also. With increase in r/z value (i.e. with fixed r and decreasing z value) the phase difference also decreases. From Eq. (4), it is evident that the phase difference is directly proportional to the defect depth. This is expected from the theory of thermal waves as the phase difference is incorporated because of mixing of two waves originating from two regions, one at the depth of the defect and another on the surface (i.e. depth = 0). Further, we also observe that defects having r/z values less than 1.0 were not detected. This is also in accordance with the thumb-rule that ‘‘the radius of the smallest detectable defect should be at least one to two times larger than its depth under the surface’’ [3]. Busse also reported that phase difference increases with defect depth for polymer specimens [39]. The rate and extent of decrease of the phase difference is different for different materials, which shows that these quantities are dependent on material properties. The lower frequencies offer better detectability due to longer heating time. Fig. 8a and b shows the plots of phase difference between sound and defective region as a function of square root of excitation frequency for two different defects in GFRP specimen. Similar plots were also reported by Wallbrink et al. for defects of various depths in steel specimen [32]. It is observed that the experimental data points are in good agreement with the theoretical Bennett and Patty curve [1], i.e. Eq. (5). The deviations from theoretical curve are more prominent in case of 3 mm defect compared to 1.5 mm defect. This may be due to the greater depth of the former defect as the Bennett and Patty model is strictly one dimensional and hence may not be suitable for defects of larger sizes. Fig. 9 shows the thermal contrast as a function of time for five different defects in GFRP specimen. It can be seen from the graph that initially thermal contrast increases and after attaining a maximum value, it again decreases. It can also be seen that for the defects A1 (zdef = 1.5 mm), A2 (zdef = 2.5 mm) and A3 (zdef = 3.0 mm) the Cmax values decreased steadily, whereas tmax values increased. This is expected as defects of greater depth will show lesser contrast compared to defects of lesser depth. Time required for the thermal wave-front to travel from the defect site to the surface will also be more in case of deeper defects. Similar trend is also followed in case of the other two defects (B1 and B2) also. Fig. 10 shows the plot of log10(zdef/tmax) vs. log10(Cmax) for the five defects shown in Fig. 9. The values of the constants m and n were found from the intercept and slope of the straight line fit of the calibration data points using Eq. (15). For calibration purpose
Table 3 Depth quantification in GFRP specimen. Hole number
zdef (measured) (mm)
Cmax
tmax (s)
m
n
zdef (calculated) (mm)
A1 A2 A3 B1 B2
1.5 2.5 3 1.5 2.5
0.26 0.14 0.11 0.17 0.15
2.5 5.0 6.5 2.0 5.3
0.67502
0.25319
1.5011 2.4831 3.0094 1.4951 2.5122
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the measured values of zdef are used. On finding the values of the constants m and n, Eq. (14) was used to quantify the defect depths. The detailed values are presented in Table 3. From Table 3 it can be seen that the calculated values of the defect depths are in excellent agreement with the corresponding measured values. It was also observed that the values of the constants m and n are similar to the earlier reported values in case of CFRP [3,23].
5. Conclusions Our studies on the defect detection using lock-in thermography reveal that the phase contrast increases with defect depth, while thermal contrast decreases with defect depth. Defects with radius to depth ratio greater than 1.0 are detectable using lock-in thermography. It is observed that surface plots and binary images along with the amplitude and phase thermography images could provide better visualization of the defects. The variation of phase difference with the excitation frequency in GFRP specimen is in good agreement with theoretical values. With Pulsed thermography, defects depths in GFRP specimen are successfully estimated from the thermal contrast using the analytical approach of Balageas et al.
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Infrared Physics & Technology journal homepage: www.elsevier.com/locate/infrared
Quantification of defects in composites and rubber materials using active thermography B.B. Lahiri a, S. Bagavathiappan a, P.R. Reshmi b, John Philip a,⇑, T. Jayakumar a, B. Raj a a b
Non Destructive Evaluation Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, India Department of Optoelectronics, University of Kerala, Trivandrum, India
a r t i c l e
i n f o
Article history: Received 5 September 2011 Available online 21 January 2012 Keywords: Lock-in thermography Pulsed thermography Composite materials Phase contrast Thermal contrast Defect depth quantification
a b s t r a c t Active (lock-in and pulsed) thermography technique is used to quantify defect features in specimens of glass fiber reinforced polymer, high density rubber, low density rubber and aluminum bonded low density rubber with artificially produced defects. The relationship between phase contrast and thermal contrast with defect features are examined. Using lock-in approach, the optimal frequencies for different specimens are determined experimentally. It is observed that with increasing defect depth, the phase contrast increases while the thermal contrast decreases. Defects with radius to depth ratio greater than 1.0 are found to be discernible. The phase difference between sound and defective region as a function of square root of excitation frequency for glass fiber reinforced polymer specimen is found to be in good agreement with the predictions of Bennet and Patty model [1]. Further, using pulsed thermography, the defects depth could be measured accurately for glass fiber reinforced polymer specimen from the thermal contrast using the analytical approach of Balageas et al. [2]. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction Infrared thermography (IRT) is extensively used in the field of nondestructive testing (NDT) for inspection, monitoring and basic research [3–6]. Apart from NDT, in recent years, thermography is being widely used in a wide range of areas, such as determination of thermophysical parameters [7,8], agriculture [4], medical [9– 12], biology [13] and even bird location [14]. Recently IRT is successfully used for indirect identification of sectors with high current density concentration in planar microwave devices [15]. The developments in the field of quantum detector technology enhanced the accuracy in temperature measurements within a few millikelvin. The advent of focal plane arrays has resulted in superior thermal imaging system with better spatial and temperature resolution [16]. In IRT, the infrared radiation (wavelength lies between 0.75 lm and 1000 lm) emitted by a body is detected using an infrared detector and the information about temperature is obtained from the acquired data using Stefan–Boltzmann’s law, which is expressed as follows [3].
q ¼ erT 4 A
ð1Þ
where q is the rate of energy emission (W), A is the area of emitting surface (m2), T is the absolute temperature (K) and r is the Stefan– ⇑ Corresponding author. Tel.: +91 044 27480232; fax: +91 044 27480356. E-mail address: [email protected] (J. Philip). 1350-4495/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.infrared.2012.01.001
Boltzmann’s constant (r = 5.676 108 W/m2 K4) and e is the emissivity of the material. Thermography can be broadly classified into two categories, viz. passive and active [3]. In passive thermography no external heating is required. Only the thermal radiation due to difference in temperature (caused by any other reasons apart from external stimuli) between the surrounding and specimen is monitored. The applications of passive thermography include monitoring of buildings and concrete structures [17–20], medical [9–12] and biological investigations [13]. On the other hand, in active thermography, an external heating is required and the evolution of surface temperature is monitored in the transient or stationary domain. Depending on the heating procedure, active thermography can be further subdivided into different categories such as pulsed, step heating, lock-in, vibrothermography and pulsed phase thermography [3,21]. In pulsed thermography, a short heating pulse is applied to the specimen and the cooling data is monitored in the transient domain. In step heating, the temperature rise is monitored in the transient domain where a long heating pulse is applied. Lock-in thermography is carried out in stationary domain, where a modulated heat wave is launched on the sample for heating which travels through the bulk by diffusion and reflects back from the defect sites. In vibrothermography, under the effect of external mechanical vibration, heat is generated at the defect locations due to friction. Pulsed phase thermography is a combination of both pulsed and lock-in thermography, where data is acquired in transient domain but phase image is generated by Fourier analysis of the acquired images.
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Pulsed thermography is being routinely used for quantitative evaluation of defect in both metallic and composite specimens [20,22,23]. Though there is a problem of determining optimum frequency, lock-in thermography, in recent years, has become an effective tool for non-contact defect detection. This method has been extensively used to find quantitative information of subsurface defects [24,25], corrosion protective paints [22], morphologies of defects (like circular, square-like, etc.) [26] and industrial processes [27]. Typical applications of vibrothermography and step heating thermography are detection of closed cracks, delaminations and coating thickness evaluation [3]. Vibrothermography suffers from the problems of mechanical and dynamical instability, difficulty in application of mechanical load and difficulty in determination of vibration frequencies [3]. Both pulsed phase thermography and step heating thermography are associated with overheating problems [28]. Among the various active thermography techniques, lock-in and pulsed thermography techniques, due to their ease of application, straight forwardness and capability of detection of versatile types of defects, have gained widespread popularity in the field of NDT [3]. Pulsed thermography is one of the most popular active thermography techniques, primarily due to its fast inspection time. Lock-in thermography, on the other hand, is a comparatively slower technique. But signal to noise ratio (SNR) is higher in lock-in thermography, as a single frequency thermal wave is used for defect detection. Phase image of lock-in thermography technique is independent of local disturbances, like nonuniform heating and emissivity variation [3,28]. In lock-in thermography, defect depths can be measured directly, without postprocessing of the acquired images, by varying the excitation frequencies [3,29]. Energy input is also considerably lower in lockin technique [28]. In pulsed thermography, defect detection is primarily due to the temperature difference (contrast) between the defect and defect-free region. Several types of contrasts are defined in literature, like thermal contrast, differential absolute contrast, etc. [23]. Though differential absolute contrast is independent of non-uniform heating, it requires time consuming post-processing of the acquired data [6]. Thermal contrast based techniques are comparatively fast, straight forward and hence more suitable for industrial adaptation. This was the motivation to use lock-in and pulsed thermography technique in our experiments. Reinforced polymers are light weight structural materials. In recent times, glass fiber reinforced polymer is used to improve the load carrying capacity of concrete deck slabs [30] and mesh type
Fig. 1. Schematic of the specimens (z is the defect depth and x is total thickness of the specimens).
civil structures [31]. Rubber is an abrasion resistant material and low density (soft) rubber is used in many parts of vehicle tyres and conveyor belts. High density (hard) rubber finds application in hose pipes, pump housing, etc. Rubber is also used as insulators in many heavy electrical components. NDT of these materials is very important for the production of light weight, highly reliable industrial components. In this paper, lock-in thermography was used to study the defect detectability in four different specimens, viz. glass fiber reinforced polymer (GFRP), high density rubber (HDR), low density rubber (LDR) and low density rubber with aluminum bonding (LDRAl) with defects of different depths and diameters. It was observed that the ratio of radius (r) to depth (z) of a particular defect sets a limit on the detectability. The critical ratio of r/z is determined for each type of specimen. Defect depths were quantified using pulsed thermography in case of GFRP specimen using an analytical approach. Similar thermal contrast based technique was earlier applied for defect depth quantification in carbon fiber reinforced polymer (CFRP) specimen [2,3,23]. However, to the best of our knowledge, there is no published report on GFRP specimen using the above experimental approach. 2. Materials and experimental methods 2.1. Specimen details Square shaped (10 cm 10 cm) specimens of the four materials, viz. GFRP, HDR, LDR and LDRAl were used in our experiment. In each of these specimens, artificial defects (flat bottom holes) of different depths and diameters were created. The schematics of these specimens with defect locations are shown in Fig. 1. Detailed geometrical descriptions of the defects in each of the specimens are provided in Table 1. 2.2. Experimental details For generation of sine waves of a single frequency, a programmable function generator (model: HM 8131-2, Hameg) was used and for detection of thermal waves FLIR SC5000 infrared camera was used. This camera has indium antimonide (InSb) detector with an array of 320 256 elements with a thermal sensitivity better than 25 mK. The detector elements are cooled using Stirling cycle. The spectral range of the camera is 2.0–5.1 lm. The sample was heated with a sinusoidally modulated heat wave from two 1 kW halogen lamps (connected to the output of function generator) kept at 50–55 cm away from the specimen. The camera was kept at a distance of 70 cm from the specimen in such a way that the axis of the camera coincides with the axis of the sample. The photograph of experimental setup is shown in Fig. 2. In thermography, temperature is interpreted from the radiation emitted from the surface under investigation. If the emissivity of the surface is very low, then the radiation emitted from this surface is very weak, which leads to the formation of an image with low SNR. It has been reported that thermographic measurement is not possible for surfaces having emissivity value lower than 20% of blackbody emissivity [3]. Low emissivity surfaces also suffer from the problem of secondary reflection, due to the presence of surrounding bodies. The most common methodology to overcome the above mentioned emissivity problems is by applying a uniform black paint of high emissivity value, which not only increases the surface emissivity value but also reduces the secondary reflections, besides providing a uniformly emissive surface [3]. Hence, the surface of the specimens facing the camera was black painted using a high emissivity (e 0.98) black paint. Similar methodology was also adopted by other research groups [3,24,32]. Reflection method
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B.B. Lahiri et al. / Infrared Physics & Technology 55 (2012) 191–199 Table 1 Geometrical description of the flat bottom holes in the four specimens. Hole number
A1 A2 A3 A4 B1 B2 B3 B4 C1 C2 C3 C4 D1 D2 D3 D4
Glass fiber reinforced polymer
High density rubber
Low density rubber
Low density rubber with aluminum bonding
Diameter (mm)
Depth (mm)
Diameter (mm)
Depth (mm)
Diameter (mm)
Depth (mm)
Diameter (mm)
Depth (mm)
10 10 10 10 7 7 7 7 5 5 5 5 2 2 2 2
1.5 2.5 3 4 1.5 2.5 3 4 1.5 2.5 3 4 1.5 2.5 3 4
5 5 5 5 12 12 12 12 9 9 9 9 7 7 7 7
1 3 4 6 1 3 4 6 1 3 4 6 1 3 4 6
10 10 10 10 8 8 8 8 5 5 5 5 4 4 4 4
2 3 4 5 2 3 4 5 2 3 4 5 2 3 4 5
10 10 10 10 8 8 8 8 5 5 5 5 4 4 4 4
2 3 4 5 2 3 4 5 2 3 4 5 2 3 4 5
Fig. 2. Photograph of experimental set-up (A = specimen, B = camera, C = halogen lamps, D = function generator).
was adopted, i.e., images were acquired from the same surface that was heated periodically. In case of LDRAl specimen, the rubber surface was inspected. Lock-in images were acquired by using ALTAIR LI software. Several excitation frequencies were used to determine the optimum frequency for each specimen. Five millisecond pulses from one of the 1 kW halogen lamps were used for pulsed thermography purpose.
the thermal wave in the bulk of the sample depends on a and also on the excitation frequency (f = x/2p) [21]. Thermal wavelength is defined as k = 2pl [3,21]. From the argument of the cosine term in Eq. (2), we get the phase difference U (degree), which is related to the defect depth z as
/ðzÞ ¼
z
ð4Þ
l
3. Theory 3.1. Theory of thermal waves For a planar semi-infinite specimen heated by a sinusoidal heat source of fixed amplitude and frequency, treating the problem as one-dimensional [3,21], the temperature T (°C) can be expressed as a function of defect depth z (mm), time t (s) and angular frequency x (Hz) as
z 2p z Tðz; tÞ ¼ T 0 el cos xt k
ð2Þ
where T0 is initial temperature (°C), k is thermal wavelength (m) and l is thermal diffusion length (m) which is given by
l¼
Eq. (4) indicates that phase difference increases with defect depth and the value of thermal diffusion length can be obtained from the slope. It is also evident from Eq. (2) that, for deeper defects the signal is highly attenuated. Therefore, the defect features (like depth and size) limits the detectability. Strictly speaking, Eqs. (2) and (4) are valid for semi-infinite specimen devoid of any defects. Bennett and Patty model [1] calculates the summation of all of the reflections from the interfaces (both defect and surface) and predicts the actual phase difference at the surface. According to
rffiffiffiffiffiffi 2a
ð3Þ
x 2
1
where a is thermal diffusivity of the material (m s ). Eq. (2) indicates that the temperature is attenuated exponentially with l in the bulk of the specimen and that the damping of
Table 2 Optimum frequencies of the four specimens. Serial no.
Sample code
Excitation frequencies employed (Hz)
Optimum frequency (Hz)
1 2 3 4
GFRP HDR LDR LDRAl
0.001–0.8 0.0003–0.05 0.0001–0.05 0.0001–0.05
0.002 0.003 0.007 0.009
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this model the phase difference is calculated by the following equation.
D/ ¼ tan1
Rb ð1 þ Rg Þ expð2as zÞ sin 2as z 1 Rg ðRb expð2as zÞÞ2 þ Rb ð1 Rg Þ cos 2as z
! ð5Þ
where D/ is the phase difference (degree) between the sound and defective region and as is the thermal wave number (m1), which is given by the following equation:
pffiffiffi f as ¼ pffiffiffiffiffiffiffi 2 pa
ð6Þ
Rb and Rg are thermal wave reflection coefficients at back (i.e. defect) and front (i.e. specimen) interfaces respectively. For the present case, as both the interfaces were air-material in nature the values of Rb and Rg are same, as indicated below
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qa ca ka Rb ¼ Rg ¼ qm c m km
ð7Þ
where qa, qm, ca, cm, ka, km are densities, specific heats and thermal conductivities of air and specimen material respectively.
Fig. 3. Typical amplitude (left) and phase (right) images of (a) GFRP, (b) LDR and (c) HDR specimens at optimal frequencies.
B.B. Lahiri et al. / Infrared Physics & Technology 55 (2012) 191–199
3.2. Theory of lock-in thermography
Phase image contains information about the propagation time and average image is the conventional thermography image [3].
In lock-in thermography, after externally heating the specimen sinusoidally (with fixed amplitude and frequency), the resultant temperature distribution on the surface is observed in the stationary regime and the corresponding data is recorded real time. Using four point method, it is possible to determine the amplitude and phase from these data [3,33]. At least four equidistant temperature data points are required in one modulation cycle to get the correct phase and amplitude. For example, if P1, P2, P3 and P4 are four equidistant temperature data points in a complete period then the phase (U) and amplitude (A) are given by
P P3 U ¼ tan1 1 P2 P4 Aðx; yÞ ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðP1 P3 Þ2 þ ðP2 P 4 Þ2
ð8Þ
ð9Þ
The average (M) is the simple average of the four data points as given below
M¼
P1 þ P2 þ P3 þ P4 4
195
ð10Þ
3.3. Pulsed thermography, thermal contrast and depth quantification For a homogenous, semi-infinite specimen after absorption of a Dirac heat pulse at time t = 0, the temperature decay follows the following pattern [23,34].
Q DT ¼ pffiffiffiffiffiffi e pt
ð11Þ
where DT is the temperature change of the surface (°C), Q is the quantity of energy absorbed per unit area (W m2), t is the elapsed time (s) and e is the thermal effusivity of the material (Ws1/2 K1 m2), which is given as
e¼
qffiffiffiffiffiffiffiffi kqc
ð12Þ
where k, q and c are the thermal conductivity, density and specific heat of the material respectively. Thermal contrast (°C) over a defect region is defined as
CðtÞ ¼ T def ðtÞ T sound ðtÞ
ð13Þ
Fig. 4. Typical surface plots of phase images of (a) GFRP and (b) LDR specimens.
Fig. 5. (a) Original HDR amplitude image, binary image corresponding to threshold levels of (b) 0.65, (c) 0.698, (d) 0.73, (e) Original GFRP phase image, binary image corresponding to threshold levels of (f) 0.21, (g) 0.25, (h) 0.30.
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where Tdef and Tsound are the temperatures of defect and sound regions respectively. An analytical expression for defect depth quantification in case of carbon–epoxy composites using pulsed thermography is derived by Balageas et al. [2].
pffiffiffiffiffiffiffiffiffi zdef ¼ m tmax ðC max Þn
ð14Þ
where zdef is the defect depth, Cmax is the maximum contrast observed, tmax is the time when contrast is maximum, m and n are numerical constants. This approach has been successfully used for defect quantification in CFRP specimen and plexiglas [23]. The values of m and n are 0.6722 and 0.258 for CFRP [3,23]. Rearranging
the terms and on performing logarithm on both sides of Eq. (14) the following equation of a straight line is obtained [3].
zdef log10 pffiffiffiffiffiffiffiffiffi ¼ log10 m þ nlog10 ðC max Þ tmax
ð15Þ
From the slope and intercept of this straight line the values of the constants n and m can be found respectively. 4. Results and discussion In lock-in thermography, defects are visible only when the thermal diffusion length is of the order of defect depths [3]. Hence Eq.
Fig. 6. Plot of difference in digital level between sound and defective regions (DDL) as a function of defect depth at different excitation frequencies for (a) GFRP, (b) HDR, (c) LDRAl and (d) LDR.
Fig. 7. Plot of phase difference between sound and defective regions as a function of (r/z) at different excitation frequencies for (a) GFRP, (b) HDR, (c) LDRAl and (d) LDR.
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(3) indicates that defects of a particular depth could be detected with maximum contrast by a thermal wave of a particular frequency. So a range of frequencies were used for detecting defects of various depths in all the four specimens. The upper limits are chosen such that thermal diffusion length is around 0.2 mm in all the specimens, whereas the lower limits are chosen in such way that the thermal diffusion lengths match with the deepest defects in the corresponding specimens. Though the phase contrast (phase difference between defective and sound region) is maximum at a single frequency, defect of a particular depth is visible over a wide band of frequency. An overlapping band of frequencies, where maximum number of defects is visible, not necessarily with maximum contrast, is identified and the average frequency of this band was considered as the optimum frequency for that specimen. The range of frequencies and the optimum frequencies for each of the specimen is presented in Table 2. This procedure makes the process of defect identification comparatively fast and hence suitable for industrial applications [32]. A few typical amplitude and phase images of different specimens are shown in Fig. 3. It must be noted that the defects C1 and C2 (encircled in the Fig. 3a) in case of GFRP specimen were actually through – holes. It is evident from the images that phase images provide better clarity in terms of defect location and contrast, compared to the amplitude images. This is because; phase image is independent
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of the local problems such as non-uniform heating and emissivity variation [3,28]. Defects B1 and B2 are absent in the phase image of LDR specimen (Fig. 3b) whereas there is a faint signature of B2 in the corresponding amplitude image. The blurring of the images is attributed to the infrared fog created by the afterglow of the halogen lamps. Image processing, nowadays, is considered as a fundamental tool to enhance readability of an image [35–37]. Segmentation is one of the basic image processing techniques [35]. Others are like surface plots of 2-D images where slight variations in gray level are magnified and represented pictorially with a pseudo color scale. In Fig. 4, we have shown the surface plots of the phase images of GFRP and LDR specimens. It can be seen that these surface plots (after suitable enhancement) help us to visualize the surface phase contrast clearly that enables faster and easier identification of defects from sound regions. Image segmentation was done using binary image processing with a global threshold value. Binary images are digital images, where only two (0 and 1) gray level values are allowed for each pixel. Visual representations of such images correspond to binary shading where 0 is shaded as black and 1 as white. While converting an image to its binary equivalent, we can set a threshold gray level value for the original image, below which all gray level values will be set to zero. Thresholds can be of two types, viz. global and local [38]. In the case of global threshold we set a single
Fig. 8. Plot of Phase difference between sound and defect regions as a function of square root of excitation frequencies in GFRP specimen for defects of depths (a) 1.5 mm and (b) 3 mm.
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Fig. 9. Thermal contrast as a function of time for different defects in case of GFRP specimen.
Fig. 10. log10(zdef/sqrt(tmax)) vs. log10(Cmax) for different defects for GFRP specimen.
threshold value for the entire image, whereas, in the case of local threshold, the entire image is subdivided into smaller sub images and a threshold value is chosen for each sub image. Global threshold method was applied for the present case. Typical binary images are shown in Fig. 5. These binary images provide better insights into the defect locations and the relative contrast corresponding to different defects. As we can see from Fig. 5d that defects B1 and B2 have highest contrast as they are visible in the binary image even after the threshold is set to 0.73. Such binary images may help in the development of automatic defect recognition algorithms for thermal images. Fig. 6 shows the difference in digital level between the sound and the defective regions as a function of defect depth, which follows a similar trend in all the four specimens. Digital level is basically analogous to amplitude value. Hence a plot of DDL vs. defect depth is good enough to get an idea of thermal contrast variation.
We observe that, for lower frequencies, the values of DDL are higher. This is because lower frequency means longer heating period and hence the amount of heat deposited will be more. Moreover, DDL value increases as defect depth decreases because a defect of less depth results in sharp contrast in temperature which is manifested as a higher DDL value. It is seen that in all the graphs, DDL is a monotonically decreasing function of defect depth except for GFRP and HDR specimens, where there is a saturation tendency around 4.0 mm of defect depth. Fig. 7 shows the plot of phase difference (between the sound and defect regions) vs. r/z (where r is the radius of a defect and z is its depth). We have chosen the largest diameter defects for this plot. A similar trend for each of the four specimens is seen even in this case also. With increase in r/z value (i.e. with fixed r and decreasing z value) the phase difference also decreases. From Eq. (4), it is evident that the phase difference is directly proportional to the defect depth. This is expected from the theory of thermal waves as the phase difference is incorporated because of mixing of two waves originating from two regions, one at the depth of the defect and another on the surface (i.e. depth = 0). Further, we also observe that defects having r/z values less than 1.0 were not detected. This is also in accordance with the thumb-rule that ‘‘the radius of the smallest detectable defect should be at least one to two times larger than its depth under the surface’’ [3]. Busse also reported that phase difference increases with defect depth for polymer specimens [39]. The rate and extent of decrease of the phase difference is different for different materials, which shows that these quantities are dependent on material properties. The lower frequencies offer better detectability due to longer heating time. Fig. 8a and b shows the plots of phase difference between sound and defective region as a function of square root of excitation frequency for two different defects in GFRP specimen. Similar plots were also reported by Wallbrink et al. for defects of various depths in steel specimen [32]. It is observed that the experimental data points are in good agreement with the theoretical Bennett and Patty curve [1], i.e. Eq. (5). The deviations from theoretical curve are more prominent in case of 3 mm defect compared to 1.5 mm defect. This may be due to the greater depth of the former defect as the Bennett and Patty model is strictly one dimensional and hence may not be suitable for defects of larger sizes. Fig. 9 shows the thermal contrast as a function of time for five different defects in GFRP specimen. It can be seen from the graph that initially thermal contrast increases and after attaining a maximum value, it again decreases. It can also be seen that for the defects A1 (zdef = 1.5 mm), A2 (zdef = 2.5 mm) and A3 (zdef = 3.0 mm) the Cmax values decreased steadily, whereas tmax values increased. This is expected as defects of greater depth will show lesser contrast compared to defects of lesser depth. Time required for the thermal wave-front to travel from the defect site to the surface will also be more in case of deeper defects. Similar trend is also followed in case of the other two defects (B1 and B2) also. Fig. 10 shows the plot of log10(zdef/tmax) vs. log10(Cmax) for the five defects shown in Fig. 9. The values of the constants m and n were found from the intercept and slope of the straight line fit of the calibration data points using Eq. (15). For calibration purpose
Table 3 Depth quantification in GFRP specimen. Hole number
zdef (measured) (mm)
Cmax
tmax (s)
m
n
zdef (calculated) (mm)
A1 A2 A3 B1 B2
1.5 2.5 3 1.5 2.5
0.26 0.14 0.11 0.17 0.15
2.5 5.0 6.5 2.0 5.3
0.67502
0.25319
1.5011 2.4831 3.0094 1.4951 2.5122
B.B. Lahiri et al. / Infrared Physics & Technology 55 (2012) 191–199
the measured values of zdef are used. On finding the values of the constants m and n, Eq. (14) was used to quantify the defect depths. The detailed values are presented in Table 3. From Table 3 it can be seen that the calculated values of the defect depths are in excellent agreement with the corresponding measured values. It was also observed that the values of the constants m and n are similar to the earlier reported values in case of CFRP [3,23].
5. Conclusions Our studies on the defect detection using lock-in thermography reveal that the phase contrast increases with defect depth, while thermal contrast decreases with defect depth. Defects with radius to depth ratio greater than 1.0 are detectable using lock-in thermography. It is observed that surface plots and binary images along with the amplitude and phase thermography images could provide better visualization of the defects. The variation of phase difference with the excitation frequency in GFRP specimen is in good agreement with theoretical values. With Pulsed thermography, defects depths in GFRP specimen are successfully estimated from the thermal contrast using the analytical approach of Balageas et al.
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