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infrared nondestructive testing
NDT&E International 61 (2014) 16–23
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NDT&E International journal homepage: www.elsevier.com/locate/ndteint
Noise-limited thermal/infrared nondestructive testing V. Vavilov n Tomsk Polytechnic University, Savinykh St. 7, 634028 Russia
art ic l e i nf o
a b s t r a c t
Article history: Received 22 January 2013 Received in revised form 5 September 2013 Accepted 9 September 2013 Available online 18 September 2013
In thermal/infrared nondestructive testing (T/I NDT), the presence of noise in the infrared signal is an inconvenience in the method. It is convenient to introduce two extreme types of T/I NDT noise: (1) this type is purely additive and is defined by background reflections and the IR detector and (2) this is purely multiplicative and is defined by the material's absorptivity/emissivity variations. Multiple T/I NDT tests performed on various materials have shown that none of materials reveal a ‘pure′ additive or multiplicative type of noise. However, in the case of optical heating, many composite and blackpainted materials exhibit multiplicative noise with a noise contrast of Cn ¼ 2 5%, and this determines the defect detection limits. The Cn concept has been applied to a graphite epoxy composite to demonstrate that the maximum depth of detected defects in a one-sided procedure is about 4 mm. Also, in 1–10 mmthick black-painted steel, the minimum detectable material loss is from 3% to 9%. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Defects Infrared thermography Noise Theoretical modeling
1. Introduction All nondestructive testing (NDT) techniques involve defect sensing, detection and characterization. A defect can be sensed if it produces a signal that exceeds the sensitivity of the test equipment. And the sensitivity is limited by the inherent noise of the sensor (detector) being used. Detection is considered to be completed when an operator or an automatic device characterizes a test object as being either nondefective, i.e. meeting approved standards (norms), or defective, i.e. containing specific flaws. At these two inspection stages, defect parameters are not quantitatively evaluated, and the decision making represents a typical statistical procedure. At the characterization stage, one mathematically evaluates or analyzes defect parameters and then determines the severity of the detected flaws. In some cases, the lifetime of the test object can be estimated. “Thermal/infrared NDT” (T/I NDT), also called “Infrared thermographic NDT”, means that hidden flaws are detected due to disturbances in the heat flux flowing through a test object under a particular thermal stimulation. These disturbances result in specific surface temperature patterns which are detected by monitoring the infrared patterns on the sample surface, usually as a function of time. This NDT technique operates remotely and applies to almost all materials. 2. Detection parameters in T/I NDT In T/I NDT, one monitors the surface temperature distribution Tðx; y; τÞ as the heat diffuses in space (x,y) and as it evolves in n
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time (τ). Respectively, the quality of the test object is evaluated by analyzing: 1) amplitude of the detected temperature anomalies, 2) anomalies of the temporal evolutions of temperature, and 3) morphology of temperature anomalies. The first two criteria are amenable to quantitative evaluation, by either an operator or an automatic device, while morphology analysis still depends on operator training. The so-called differential temperature signal ΔTðτÞ ¼ T d ðτÞ T nd ðτÞ serves as a natural amplitude detection parameter in T/I NDT (here T d ðτÞ and T nd ðτÞ are the temperatures in a defect and non-defect areas respectively). Due to the linear character of heat conduction, ΔT is linearly proportional to the absorbed thermal energy W. Some invariant parameters have been introduced, e.g. the running temperature contrast CðτÞ ¼ ΔTðτÞ=TðτÞ, where TðτÞis the sample excess temperature, also linearly proportional to W. Hence, by definition, C is independent of W (see the description of other T/I NDT invariants, such as the normalized and differentiated contrasts in [1,2]), In transient T/I NDT, the temporal evolutions of T; ΔT and C are of the most interest. The comparison between theoretical and experimental data is shown in Fig. 1 for the case of the inspection of graphite epoxy pipes used in nuclear engineering. A standard sample (thickness 5 mm, diameter 150 mm) contained three 0.15 mm-thick Teflon inserts (lateral sizes 60 20, 20 20 and 10 20 mm2) placed at a depth of 1.6 mm. The sample was uniformly heated for 30 s with two tubular 1 kW halogen lamps. The first step in modeling was the evaluation of the anisotropic thermal properties of the composite, and this was performed according to the procedure described in [3]. This resulted in the following property values: K x ¼0.58 W/(m K), K y ¼ 0.33 W/(m K), K z ¼0.65 W/(m K), C ¼780 J/(kg K) and ρ¼ 1570 kg/m3. 3D numerical modeling was performed using ThermoCalc-6L software [4].
V. Vavilov / NDT&E International 61 (2014) 16–23
ΔT m maximum differential temperature signal, 1C ΔT res temperature resolution of IR equipment, 1C W absorbed thermal energy, J/m2 Q heat power density, W/m2 CðτÞ ¼ ΔTðτÞ=TðτÞ running temperature contrast Cn noise running contrast K thermal conductivity, W/(m.K), C specific heat, J/(kg.K) ρ density, kg/m3 S signal-to-noise ratio sn noise standard deviation, oC sa additive noise standard deviation, oC sm multiplicative noise standard deviation, oC f IR thermogram acquisition rate, Hz
Nomenclature T/I NDT GFRP IR Tðx; y; τÞ T nd Td Ta T abs x; y; z L τ τm ΔTðτÞ
Thermal/Infrared Nondestructive Testing Glass Fiber Reinforced Plastic Infrared sample temperature (excess temperature), 1C sample temperature in non-defect area, 1C sample temperature in defect area, 1C sample initial (ambient) temperature, 1C sample absolute temperature, oC spatial coordinates, m sample thickness, m time, s optimum observation time, s differential temperature signal, 1C
Next, the theoretical and experimental evolutions of excess temperature (Fig. 1a) have been compared by equalizing the temperatures at the end of heating. In this way, the absorbed energy was estimated to be 3440 W/m2, and this value was used in subsequent calculations. The calculated evolution of ΔT (vs. time) was quite close to the experimental evolution in both amplitude and signal profile (Fig. 1b). Note that the maximum value of ΔT m 3 1C occurred at τm ðΔT m Þ ¼ 0.8 s after heating stopped. Another important observation is that, although the programmed defects were Teflon inserts, the modeling was performed for air-filled defects by assuming imperfect contact between the composite and the Teflon. If the Teflon were in perfect contact with the composite, the modeling would have yielded a smaller ΔT. The observed discrepancy between the theoretical and calculated values of the running contrast C can be explained by an increase in the noise that is a result of the division of the two noisy functions: ΔT and T. However, it is observed that the first maximum contrast appears within the heating period, and the second one appears immediately after the heating period, with both maximums being about 0.15 (dimensionless units), or 15% of full temperature increase. According to the classical theory of T/I NDT, the second maximum contrast appears at τm ðC m Þ ¼2.2 s after the heating stopped, i.e. later than ΔT m . A flaw can be reliably identified if, at any time during the observation, the temperature signal ΔT produced by the flaw exceeds the level of noise. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ΔT 4
N
2
∑ ΔT i n ;
ð1Þ
i¼1
17
where ΔT i n specifies the i-th source of noise. Eq. (1) assumes that all N sources of noise are independent, which is not absolutely true, and 2
that it is characterized by the dispersion ΔT i n . By introducing the qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 signal-to-noise ratio, S ¼ ΔT= ∑N i ¼ 1 ΔT i←- n , Eq. (1) becomes trivial,
as S 4 1. Note that, in order to make the flaw decision more reliable, the last equation is often expressed as S41 3 to provide the necessary confidence level for decision making. Using S allows the determination of an optimum observation time as a maximum of the SðτÞ function. The curve SðτÞ for the experimental example above reaches a maximum value of 5.3 (dimensionless units) at τm ðSm Þ¼ 2.6 s after the heating stopped (Fig. 1d), and this is close to τm ðC m Þ. The normal approach to the determination of T/I NDT limits is to compare ‘pure’ ΔT signals and noise characteristics. Values of ΔT are typically predicted by modeling particular test cases [1,2,4–7],
while the noise parameters of various materials and the test procedures are rarely studied [8,9].
3. Noise in T/IR NDT It is convenient to introduce two extreme types of T/I NDT noise: (1) purely additive noise, which is caused by background reflections and IR detector noise, or by the temperature resolution qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 of the IR equipment ΔT res ¼ ∑N i ¼ 1 ΔT i←- n , and (2) purely multiplicative noise, which is caused by material absorptivity/emissivity variations. The latter can be characterized by the noise running qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 contrast C n ðτÞ ¼ ∑N i ¼ 1 ΔT i n ðτÞ=T nd ðτÞ ¼ sn ðτÞ=T nd ðτÞ, where T nd ðτÞ
is the mean temperature in a non-defect area of interest, and sn is the noise standard deviation. 3.1. Additive noise
Conventional background noise can be easily eliminated by simply subtracting the pre-heating image from all subsequent images captured in a transient test. However, the additive noise created by a heater cannot be suppressed in this way, at least, within the heating period. This noise is low, if not zero, in the case of microwave, ultrasonic and laser stimulation but it can be significant if inductive or optical heating is used. In the case of laser heating, the wavelength of the laser should be outside the spectral band of the IR imager being used. Ultimately, the “white” additive noise of an IR detector determines the temperature resolution ΔT res of the IR camera being used. Therefore, defects cannot be detected thermographically if they produce temperature differences (ΔT) smaller than ΔT res E0.01–0.1 1C. In this case, the optimum observation time coincides with the maximum value of ΔTðτm Þ. Then the first, or basic, condition for the detection of defects is as follows: ΔTðτm Þ 4ΔT res
ð2Þ
3.2. Multiplicative noise In the ideal case of purely multiplicative noise, the running noise contrast С noise is time-independent if ΔT is linear with respect to the sample excess temperature. For example, this is the case if the noise is caused by variations in the surface emissivity/absorptivity. Then, the optimum detection takes place at the maximum contrast Cðτm Þ, and the second, or practical,
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V. Vavilov / NDT&E International 61 (2014) 16–23
(energy W). Eq. (3) is independent of Q (W) and is caused by material surface properties. The peculiarities of both additive and multiplicative noise determined in a certain area on a sample surface are graphically shown in Fig. 2. Here T is the mean sample excess temperature above the initial temperature Ta, sa and sm are respectively the temperature standard deviations specifying additive and multiplicative components of noise. Purely additive noise is constant as a function of time (see the plots on the left). Hence, the evolution of the corresponding noise contrast sa =T is inversely related to the evolution of T. Conversely, in the case of multiplicative noise, sm is proportional to T reaching a maximum at the end of heating, while the noise contrast sm =T remains constant.
25
Theory
20 15 10
Experiment
5 0
10
20
30
40
50
τ, s
3.3. Additional detection conditions 3.0
In practice, the absolute sample front-surface temperature at the end of heating must not exceed the destruction temperature T destr of a sample being tested. This is the third detection condition:
Theory
2.4 1.8
T abs ðτ ¼ τh Þ o T destr
Experiment
1.2 0.6 0
10
20
30
40
0.15
50
τ, s
Theory
f Z ð5 10Þ=τm
0.12 0.9
ð4Þ
Since the sample excess temperature is proportional to W ðQ Þ, the third condition also limits the absorbed energy. Overheating is most likely to occur during or after flash heating; therefore, each test requires a judicious choice of heat pulse power and duration. The fourth detection condition is imposed by the temporal resolution of the IR equipment, or the IR thermogram acquisition rate f, which must be fast enough to store a required number of images (5 to 10) prior to the optimum observation time τm . This condition can be written as follows: ð5Þ
Eqs. ((2)–(5)) involve the parameters of: (1) equipment (ΔT res and f), (2) material (Cn), (3) heatingðT abs Þ, and 4) defect (ΔT and C).
Experiment
0.6
4. Experimental results
0.3 0
10
20
30
40
50
4.1. Additive noise
τ, s
S 5 4 3 2 1 0
τm 10
20
30
40
50
τ, s
Fig. 1. Detection parameters in T/I NDT vs. time (uniform heating of 5 mm-thick graphite epoxy composite with 60 20 0.15 mm3 Teflon insert at a depth of 1.6 mm): (a) excess temperature; (b) differential temperature signal; (c) running temperature contrast; and (d) signal-to-noise ratio (experimental data).
The strong influence of optical reflected radiation on transient temperature profiles obtained in a two-sided procedure by using both flash and square-pulse heating is illustrated in Fig. 3. The heating pulse of a Xenon lamp can be resolved only with a high-speed IR camera, but very often the short spike caused by the radiation of the hot glass tube is clearly seen in the profile (Fig. 3a). By preventing multiple reflections from the ambient objects, e.g. by enclosing the radiation path using opaque foil, it is possible to obtain experimental results which are close to those that are theoretically predicted (Fig. 3b). When heating a sample with a halogen lamp for a long time, reflected radiation enters the IR camera and appears as an apparent temperature elevation at the initial stage of heating even if the sample surface temperature is low (Fig. 3c). Again, by carefully excluding or shuttering the reflected radiation, the “classically” predicted temperature response of the sample rear surface was obtained (Fig. 3d).
4.2. Multiplicative noise condition for the detection of defects is: Cðτm Þ 4 C noise
ð3Þ
Note that the maximum temperature contrasts appear after short (Dirac) heating. A principal difference between the two conditions above is that Eq. (2) can be met by increasing the heat power density Q
The flaw detection theory described above has been applied to four tests of one-sided T/I NDT: (1) flash optical stimulation of a 2 mm-thick graphite/epoxy sample with 25 Teflon inserts (sizes 3 3, 5 5, 7 7, 10 10 and 15 15 mm2) at depths from 0.2 to 1.0 mm (experimental data courtesy of W. Świderski), (2) convective heating of a 6 mm-thick steel sample with 9 flat bottomed holes simulating rear-surface corrosion (16%, 50% and 66% material
V. Vavilov / NDT&E International 61 (2014) 16–23
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Fig. 2. Comparison between purely additive and multiplicative noise components.
T, oC
T, oC Heating pulse Weak residual heating
Time
T, oC
Time
T, oC Reflected radiation
Time
Time
Fig. 3. Influence of reflected radiation on rear-surface temperature profiles: (a) – 1.6 kJ Xenon flash tube, 1.8 mm-thick aluminum sample, painted black, reflected radiation present; (b) same as (a), reflected radiation suppressed; (c) 1 kW halogen lamp, heating 4.1 mm-thick graphite epoxy composite for 5 s, reflected radiation present; and (d) same as (c), reflected radiation suppressed.
loss and 5, 10 and 20 mm defect diameter); (3) ultrasonic stimulation of a 10 mm-thick honeycomb sample (0.8 mm-thick graphite/ epoxy skin, with Nomex honeycomb reinforcement); (4) optical
heating of a graphite/epoxy composite cylindrical sample using six tubular halogen lamps. Sample photographs and examples of IR thermograms are shown in Fig. 4.
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V. Vavilov / NDT&E International 61 (2014) 16–23
Fig. 4. Experimental samples: (a) graphite epoxy composite (2 mm-thick, 25 Teflon inserts); (d) steel (2 mm-thick, 5 bottom holes); (g) composite honeycomb (10 mm-thick, graphite epoxy skin, Nomex cells); (l) 5 mm-thick graphite/epoxy composite cylinder; (b), (e), (h), (m) optimum source IR thermograms; (c), (f), (k), (n) PCA images.
In each case, experimental image sequences were captured in the corresponding one-sided T/I NDT test (the number of images in the sequences varied from 50 to 250). ThermoFit Pro software was used to process the image sequences by applying several algorithms developed in pulsed T/I NDT. These were: 1D Fourier transform (pulse phase thermography), polynomial fitting, principal component analysis (PCA), wavelet transform, correlation technique and dynamic thermal tomography (see [2,4] for details). Each processing technique resulted
in a “best” image characterized by a maximum signal-to-noise ratio which was determined for both defect and non-defect areas. In many test cases, images of principle components provided the highest S values, as shown in Fig. 4.1
1 Advanced processing results obtained on these samples were presented at the ASNT Fall conference, Palm Springs, USA, 2011.
V. Vavilov / NDT&E International 61 (2014) 16–23
An area of interest of about 10 10 mm2 was used in the analysis of each sample, as this is frequently the detection limit in many practical cases. Using this, evolutions of both sn and Cn as a function of time have been obtained (Fig. 5), so they could be compared to the ideal ones shown in Fig. 2. The results in Fig. 5 show that none of the tested materials reveals ‘pure’ additive or multiplicative noise behavior. However, in the flash heating of a graphite/epoxy composite (Curve 1), the noise is close to multiplicative since its standard deviation varies with excess temperature and the running contrast remains nearly constant. The noise associated with “square-pulse” heating of composite (curve 2) and black-painted steel (curve 3) behaves in a similar way. In all three cases, the test materials can be characterized by the following values of Cn: 1 3% (graphite/epoxy composite plane sample), 5% (graphite/epoxy composite cylindrical sample) and 2 3% (black-painted steel). Ultrasonic stimulation represents a special case where the concept of noise running contrast becomes meaningless because of zero excess temperature. In this case, the detection limit is governed by Eq. (2), i.e. the higher the injected energy, the smaller the minimum detectable defect size will be.
21
Table 1 Material noise characteristics in T/I NDT.a Material (surface condition)
Cn, %b
Graphite epoxy composite Manufacturer 1 (flat sample) Manufacturer 2 (cylindrical sample) Manufacturer 3 (flat sample) Manufacturer 4 (cylindrical sample, air heating)
1–3 5 2–3 2–4
Glass fiber reinforced plastic (flat samples) Manufacturer 1 Manufacturer 2
2-2,5 2–3
Steel (plane samples) St 45 (black-painted) St 45 (yellow-painted, shiny, convection heating) St 45 (yellow-painted, mat, convection heating) AISI 1010 M76T (inductive stimulation) M76T (inductive stimulation, welding area) Aluminum (flat sample, black-painted) Turbine blade thermal protection coating
2–3 2.5 2.5 12 50 5-28c 3-9
a
Optical stimulation, if not stated otherwise. Cn values depend on the type of heating, time and area of interest (are given as examples). c Cn values depend on paint thickness. b
Another interesting fact is that a higher energy input can make noise more “multiplicative” due to the decreasing contribution of additive IR detector noise, which is independent of the energy input. Vice versa, after flash heating of metals, temperature quickly returns to the ambient level and Cn values increase significantly. The concept of Cn has been applied to several test cases, resulting in the estimates shown in Table 1. Examples of choosing areas of interest are shown in Fig. 6. Since Cn values depend on the type of heating, the time and area of interest, sample values are shown in Table 1. However, these reveal some stable T/I NDT features, thus making the Cn parameter useful in the determination of T/I NDT detection limits. For example, graphite/epoxy composite can be regarded as a very convenient material for T/I NDT not only because of its medium conductivity, but also due to its low surface clutter close to that of “black” coatings. The level of the surface-related multiplicative noise depends weakly on the manufacturer of the composite and whether convective or optical heating is used. Glass fiber reinforced plastic (GFRP) is similar to graphite/epoxy composite and is also regarded as a very convenient material for T/I NDT. Emissivity-enhancing coatings (dye, lacquer etc.) provide rather low multiplicative noise (less than 2% in terms of running contrast) independent of color. Some coatings are semitransparent to both heating radiation and sample thermal emission, and in the case of reflective surfaces, such as aluminum, this phenomenon may contribute to noise, as shown in Fig. 6a and Table 1. Natural metallic surfaces are characterized not only by high reflectivity that makes optical heating inefficient, but may produce false indications, particularly, in the areas of welding (see Fig. 6b), rust, etc.
5. Determining defect detection limits
Fig. 5. Noise parameters vs. time (1-graphite/epoxy composite, flash heating, cooling stage, 2-graphite/epoxy composite, optical heating, cooling stage): 3-steel, convective heating, cooling stage, 4-composite honeycomb structure, ultrasonic heating, heating stage): (a) temperature standard deviation; (b) noise running contrast.
For each T/I NDT procedure, a curve of temperature vs. time can be calculated for each defect size and depth. An example of such a curve is shown in Fig. 7a for the one-sided inspection of a 5 mmthick cylindrical graphite/epoxy composite sample (3D numerical modeling performed with ThermoCalc-6L).
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V. Vavilov / NDT&E International 61 (2014) 16–23
Fatigue crack
Areas of interest
Welding seam Fig. 6. IR thermograms in transient T/I NDT: (a) 2 mm-thick aluminum, black-painted; (b) M76T steel (moving rail under inductive stimulation, no coating).
5–10 s heat pulse, the maximum detection depth will be from 3.9 to 3.2 mm. Another example relates to the detection of corrosion in steel. The calculated curves are shown in Fig. 7b and they demonstrate how the running temperature contrast C depends on the rearsurface material loss δ ¼ ΔL=L in 1 and 10 mm-thick steel samples with the following thermal properties: thermal diffusivity α¼7.3 10 6 m2/s and thermal conductivity K ¼ 32 W/(mK). The curves can be approximated with the polynomials C ¼ 0:0197 δ 0:00108 δ2 þ 0:0000218 δ3 for L ¼ 1 mm C ¼ 0:00905 δ 0:000482 δ2 þ 0:0000107 δ3 for L ¼ 10 mm;
ð6Þ
where δ is expressed in %, and L is the sample thickness. Eq. (6) can be easily solved for δ. If Cn ¼5%, the minimal material loss that can be detected in 1 mm thick steel reaches 3%, while in 10 mm-thick steel the detection limit will be about 9%. Note that these limits are theoretical and are lower than achieved by actual tests.
6. Conclusions
Several decision making parameters, in both time and ampli-
Fig. 7. Determining detection limits (3D numerical modeling with ThermoCalc6 L): (a) running contrast vs. defect depth (air-filled defects in 5 mm-thick graphite/ epoxy composite, square-pulse heating); (b) running contrast vs. material loss (corrosion sites in steel, flash heating).
The following assumptions are made:
detection efficiency is limited by the noise running contrast Cn, defects larger than 10 10 mm2 can be regarded as one
dimensional and they do not influence the temperature signals; therefore, the data is calculated for 10 10 mm2 defects only, the T/I NDT parameters that vary are heating time and defect thickness; this results in a limit on the depth at which a defect may be detected, when assuming Cn ¼5%, the differential temperature signal ΛTserves as an additional detection parameter which is calculated for a heat power density of Q¼10 kW/m2; other Q values will change ΛT in direct proportion.
The 5% detection threshold determines the defect depth at which a particular defect can be detected. For example, when detecting defects with a thickness of 0.2–0.1 mm by applying
tude domains, have been suggested in T/I NDT, but the most appropriate ones are excess temperature T, differential temperature signal ΔT, running temperature contrast C ¼ ΔT=T, and their time evolution functions. Maximum values of ΔT and C appear at different times depending on whether they are observed within or after a heat pulse. However, optimum observation time should correspond to the maximum signalto-noise ratio. In T/I NDT, the presence of complex noise is a sort of “payment” for the universal character of this method. It is convenient to introduce two extreme types of T/I NDT noise: (1) additive noise, which is defined by background reflections and IR detector noise, or by the temperature resolution of the IR equipment, and (2) multiplicative noise, which is defined by material absorptivity/emissivity variations. In the case of optical stimulation, the reflected radiation from the heat source strongly affects the transient temperature profiles. To make the actual temperature response agree more closely with the theoretical prediction during the cooling stage, the heater should be shuttered as soon as the heat source is turned off. Multiple tests conducted on various materials have shown that no real material exhibits either a “pure” additive or multiplicative noise behavior. However, in flash and square-pulse optical heating of many composite and black-painted materials, the noise is close to multiplicative, being characterized by the
V. Vavilov / NDT&E International 61 (2014) 16–23
noise contrast Cn 2 5%, and this determines the defect detection limits. The Cn concept has been applied to graphite epoxy composites to demonstrate that, in the one-sided procedure, the maximum depth at which defects can be detected is about 4 mm; this has been confirmed by other research. Respectively, in 1–10 mm thick black-painted steel, the minimum detectable material loss is from 3% to 9%. Emissivity enhancing coatings (dye, lacquer etc.) provide rather low surface-related multiplicative noise (up to 2% in terms of running contrast) independent of color. Some coatings are semi-transparent to both heating radiation and sample thermal emission, and in the case of reflective surfaces such as aluminum, this phenomenon may contribute to noise. Natural (uncoated) metallic surfaces are characterized by high reflectivity, which makes optical heating inefficient and may also produce false indications, particularly in the areas of welding, rust, etc. Ultrasonic stimulation represents a special case where higher injected energy allows the detection of smaller detected flaws.
Acknowledgment This research was supported by the grant of the Russian Fund for Fundamental Research No. 13-08-00190.
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References [1] Maldague X. Theory and practice of infrared technology for nondestructive testing. Wiley Series in Microwave and Optical Engineering. New York. U.S.A: John Wiley & Sons; 682. [2] Vavilov V. Thermal/Infrared Testing-NDT Handbook. Moscow: Spektr Publishing House; 475. [3] Lahiri J, Kuchipudi S, Siddiqui A, Vavilov V. IR thermographic inspection of filament wound CFRP shell samples. Proceedings of SPIE 2007;6541. [4] Vavilov V. Pulsed thermal NDT of materials: back to the basics. NDT and E International 2007;22:177–97. [5] Balageas DL, Krapez J-C, Cielo P. Pulsed photo-thermal modeling of layered materials. Journal of Applied Physics 1986;59(2):348–57. [6] Vavilov V, Maldague X, Dufort B, Robitaille F, Picard J. Thermal nondestructive testing of carbon epoxy composites: detailed analysis and data processing. NDT and E International 1993;26(2):85–95. [7] Maierhofer Ch. Brink A, Röllig M, Wiggenhauser H. Quantitative impulsethermography as non-destructive testing method in civil engineering – experimental results and numerical simulations. Construction and Building Materials 2005;19:731–7. [8] Infrared methodology and technology. Nondestructive testing monographs and tracts, 7. U.S.A: Gordon and Breach Science Publishers; 526. [9] Vavilov V., Bison P.G., Bressan C., Grinzato E., Marinetti S. Informative parameters and noise in transient thermal NDT. In: Maldague X, editors. Advances in signal processing for non destructive evaluation of materials. NATO ASI Series. Series E: Applied Sciences. Kluwer Academic Publishers, vol. 262. p.193– 208.
Contents lists available at ScienceDirect
NDT&E International journal homepage: www.elsevier.com/locate/ndteint
Noise-limited thermal/infrared nondestructive testing V. Vavilov n Tomsk Polytechnic University, Savinykh St. 7, 634028 Russia
art ic l e i nf o
a b s t r a c t
Article history: Received 22 January 2013 Received in revised form 5 September 2013 Accepted 9 September 2013 Available online 18 September 2013
In thermal/infrared nondestructive testing (T/I NDT), the presence of noise in the infrared signal is an inconvenience in the method. It is convenient to introduce two extreme types of T/I NDT noise: (1) this type is purely additive and is defined by background reflections and the IR detector and (2) this is purely multiplicative and is defined by the material's absorptivity/emissivity variations. Multiple T/I NDT tests performed on various materials have shown that none of materials reveal a ‘pure′ additive or multiplicative type of noise. However, in the case of optical heating, many composite and blackpainted materials exhibit multiplicative noise with a noise contrast of Cn ¼ 2 5%, and this determines the defect detection limits. The Cn concept has been applied to a graphite epoxy composite to demonstrate that the maximum depth of detected defects in a one-sided procedure is about 4 mm. Also, in 1–10 mmthick black-painted steel, the minimum detectable material loss is from 3% to 9%. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Defects Infrared thermography Noise Theoretical modeling
1. Introduction All nondestructive testing (NDT) techniques involve defect sensing, detection and characterization. A defect can be sensed if it produces a signal that exceeds the sensitivity of the test equipment. And the sensitivity is limited by the inherent noise of the sensor (detector) being used. Detection is considered to be completed when an operator or an automatic device characterizes a test object as being either nondefective, i.e. meeting approved standards (norms), or defective, i.e. containing specific flaws. At these two inspection stages, defect parameters are not quantitatively evaluated, and the decision making represents a typical statistical procedure. At the characterization stage, one mathematically evaluates or analyzes defect parameters and then determines the severity of the detected flaws. In some cases, the lifetime of the test object can be estimated. “Thermal/infrared NDT” (T/I NDT), also called “Infrared thermographic NDT”, means that hidden flaws are detected due to disturbances in the heat flux flowing through a test object under a particular thermal stimulation. These disturbances result in specific surface temperature patterns which are detected by monitoring the infrared patterns on the sample surface, usually as a function of time. This NDT technique operates remotely and applies to almost all materials. 2. Detection parameters in T/I NDT In T/I NDT, one monitors the surface temperature distribution Tðx; y; τÞ as the heat diffuses in space (x,y) and as it evolves in n
Tel.: þ 7 913 821 9749; fax: þ 7 3822 417281. E-mail address: [email protected]
0963-8695/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ndteint.2013.09.002
time (τ). Respectively, the quality of the test object is evaluated by analyzing: 1) amplitude of the detected temperature anomalies, 2) anomalies of the temporal evolutions of temperature, and 3) morphology of temperature anomalies. The first two criteria are amenable to quantitative evaluation, by either an operator or an automatic device, while morphology analysis still depends on operator training. The so-called differential temperature signal ΔTðτÞ ¼ T d ðτÞ T nd ðτÞ serves as a natural amplitude detection parameter in T/I NDT (here T d ðτÞ and T nd ðτÞ are the temperatures in a defect and non-defect areas respectively). Due to the linear character of heat conduction, ΔT is linearly proportional to the absorbed thermal energy W. Some invariant parameters have been introduced, e.g. the running temperature contrast CðτÞ ¼ ΔTðτÞ=TðτÞ, where TðτÞis the sample excess temperature, also linearly proportional to W. Hence, by definition, C is independent of W (see the description of other T/I NDT invariants, such as the normalized and differentiated contrasts in [1,2]), In transient T/I NDT, the temporal evolutions of T; ΔT and C are of the most interest. The comparison between theoretical and experimental data is shown in Fig. 1 for the case of the inspection of graphite epoxy pipes used in nuclear engineering. A standard sample (thickness 5 mm, diameter 150 mm) contained three 0.15 mm-thick Teflon inserts (lateral sizes 60 20, 20 20 and 10 20 mm2) placed at a depth of 1.6 mm. The sample was uniformly heated for 30 s with two tubular 1 kW halogen lamps. The first step in modeling was the evaluation of the anisotropic thermal properties of the composite, and this was performed according to the procedure described in [3]. This resulted in the following property values: K x ¼0.58 W/(m K), K y ¼ 0.33 W/(m K), K z ¼0.65 W/(m K), C ¼780 J/(kg K) and ρ¼ 1570 kg/m3. 3D numerical modeling was performed using ThermoCalc-6L software [4].
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ΔT m maximum differential temperature signal, 1C ΔT res temperature resolution of IR equipment, 1C W absorbed thermal energy, J/m2 Q heat power density, W/m2 CðτÞ ¼ ΔTðτÞ=TðτÞ running temperature contrast Cn noise running contrast K thermal conductivity, W/(m.K), C specific heat, J/(kg.K) ρ density, kg/m3 S signal-to-noise ratio sn noise standard deviation, oC sa additive noise standard deviation, oC sm multiplicative noise standard deviation, oC f IR thermogram acquisition rate, Hz
Nomenclature T/I NDT GFRP IR Tðx; y; τÞ T nd Td Ta T abs x; y; z L τ τm ΔTðτÞ
Thermal/Infrared Nondestructive Testing Glass Fiber Reinforced Plastic Infrared sample temperature (excess temperature), 1C sample temperature in non-defect area, 1C sample temperature in defect area, 1C sample initial (ambient) temperature, 1C sample absolute temperature, oC spatial coordinates, m sample thickness, m time, s optimum observation time, s differential temperature signal, 1C
Next, the theoretical and experimental evolutions of excess temperature (Fig. 1a) have been compared by equalizing the temperatures at the end of heating. In this way, the absorbed energy was estimated to be 3440 W/m2, and this value was used in subsequent calculations. The calculated evolution of ΔT (vs. time) was quite close to the experimental evolution in both amplitude and signal profile (Fig. 1b). Note that the maximum value of ΔT m 3 1C occurred at τm ðΔT m Þ ¼ 0.8 s after heating stopped. Another important observation is that, although the programmed defects were Teflon inserts, the modeling was performed for air-filled defects by assuming imperfect contact between the composite and the Teflon. If the Teflon were in perfect contact with the composite, the modeling would have yielded a smaller ΔT. The observed discrepancy between the theoretical and calculated values of the running contrast C can be explained by an increase in the noise that is a result of the division of the two noisy functions: ΔT and T. However, it is observed that the first maximum contrast appears within the heating period, and the second one appears immediately after the heating period, with both maximums being about 0.15 (dimensionless units), or 15% of full temperature increase. According to the classical theory of T/I NDT, the second maximum contrast appears at τm ðC m Þ ¼2.2 s after the heating stopped, i.e. later than ΔT m . A flaw can be reliably identified if, at any time during the observation, the temperature signal ΔT produced by the flaw exceeds the level of noise. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ΔT 4
N
2
∑ ΔT i n ;
ð1Þ
i¼1
17
where ΔT i n specifies the i-th source of noise. Eq. (1) assumes that all N sources of noise are independent, which is not absolutely true, and 2
that it is characterized by the dispersion ΔT i n . By introducing the qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 signal-to-noise ratio, S ¼ ΔT= ∑N i ¼ 1 ΔT i←- n , Eq. (1) becomes trivial,
as S 4 1. Note that, in order to make the flaw decision more reliable, the last equation is often expressed as S41 3 to provide the necessary confidence level for decision making. Using S allows the determination of an optimum observation time as a maximum of the SðτÞ function. The curve SðτÞ for the experimental example above reaches a maximum value of 5.3 (dimensionless units) at τm ðSm Þ¼ 2.6 s after the heating stopped (Fig. 1d), and this is close to τm ðC m Þ. The normal approach to the determination of T/I NDT limits is to compare ‘pure’ ΔT signals and noise characteristics. Values of ΔT are typically predicted by modeling particular test cases [1,2,4–7],
while the noise parameters of various materials and the test procedures are rarely studied [8,9].
3. Noise in T/IR NDT It is convenient to introduce two extreme types of T/I NDT noise: (1) purely additive noise, which is caused by background reflections and IR detector noise, or by the temperature resolution qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 of the IR equipment ΔT res ¼ ∑N i ¼ 1 ΔT i←- n , and (2) purely multiplicative noise, which is caused by material absorptivity/emissivity variations. The latter can be characterized by the noise running qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 contrast C n ðτÞ ¼ ∑N i ¼ 1 ΔT i n ðτÞ=T nd ðτÞ ¼ sn ðτÞ=T nd ðτÞ, where T nd ðτÞ
is the mean temperature in a non-defect area of interest, and sn is the noise standard deviation. 3.1. Additive noise
Conventional background noise can be easily eliminated by simply subtracting the pre-heating image from all subsequent images captured in a transient test. However, the additive noise created by a heater cannot be suppressed in this way, at least, within the heating period. This noise is low, if not zero, in the case of microwave, ultrasonic and laser stimulation but it can be significant if inductive or optical heating is used. In the case of laser heating, the wavelength of the laser should be outside the spectral band of the IR imager being used. Ultimately, the “white” additive noise of an IR detector determines the temperature resolution ΔT res of the IR camera being used. Therefore, defects cannot be detected thermographically if they produce temperature differences (ΔT) smaller than ΔT res E0.01–0.1 1C. In this case, the optimum observation time coincides with the maximum value of ΔTðτm Þ. Then the first, or basic, condition for the detection of defects is as follows: ΔTðτm Þ 4ΔT res
ð2Þ
3.2. Multiplicative noise In the ideal case of purely multiplicative noise, the running noise contrast С noise is time-independent if ΔT is linear with respect to the sample excess temperature. For example, this is the case if the noise is caused by variations in the surface emissivity/absorptivity. Then, the optimum detection takes place at the maximum contrast Cðτm Þ, and the second, or practical,
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(energy W). Eq. (3) is independent of Q (W) and is caused by material surface properties. The peculiarities of both additive and multiplicative noise determined in a certain area on a sample surface are graphically shown in Fig. 2. Here T is the mean sample excess temperature above the initial temperature Ta, sa and sm are respectively the temperature standard deviations specifying additive and multiplicative components of noise. Purely additive noise is constant as a function of time (see the plots on the left). Hence, the evolution of the corresponding noise contrast sa =T is inversely related to the evolution of T. Conversely, in the case of multiplicative noise, sm is proportional to T reaching a maximum at the end of heating, while the noise contrast sm =T remains constant.
25
Theory
20 15 10
Experiment
5 0
10
20
30
40
50
τ, s
3.3. Additional detection conditions 3.0
In practice, the absolute sample front-surface temperature at the end of heating must not exceed the destruction temperature T destr of a sample being tested. This is the third detection condition:
Theory
2.4 1.8
T abs ðτ ¼ τh Þ o T destr
Experiment
1.2 0.6 0
10
20
30
40
0.15
50
τ, s
Theory
f Z ð5 10Þ=τm
0.12 0.9
ð4Þ
Since the sample excess temperature is proportional to W ðQ Þ, the third condition also limits the absorbed energy. Overheating is most likely to occur during or after flash heating; therefore, each test requires a judicious choice of heat pulse power and duration. The fourth detection condition is imposed by the temporal resolution of the IR equipment, or the IR thermogram acquisition rate f, which must be fast enough to store a required number of images (5 to 10) prior to the optimum observation time τm . This condition can be written as follows: ð5Þ
Eqs. ((2)–(5)) involve the parameters of: (1) equipment (ΔT res and f), (2) material (Cn), (3) heatingðT abs Þ, and 4) defect (ΔT and C).
Experiment
0.6
4. Experimental results
0.3 0
10
20
30
40
50
4.1. Additive noise
τ, s
S 5 4 3 2 1 0
τm 10
20
30
40
50
τ, s
Fig. 1. Detection parameters in T/I NDT vs. time (uniform heating of 5 mm-thick graphite epoxy composite with 60 20 0.15 mm3 Teflon insert at a depth of 1.6 mm): (a) excess temperature; (b) differential temperature signal; (c) running temperature contrast; and (d) signal-to-noise ratio (experimental data).
The strong influence of optical reflected radiation on transient temperature profiles obtained in a two-sided procedure by using both flash and square-pulse heating is illustrated in Fig. 3. The heating pulse of a Xenon lamp can be resolved only with a high-speed IR camera, but very often the short spike caused by the radiation of the hot glass tube is clearly seen in the profile (Fig. 3a). By preventing multiple reflections from the ambient objects, e.g. by enclosing the radiation path using opaque foil, it is possible to obtain experimental results which are close to those that are theoretically predicted (Fig. 3b). When heating a sample with a halogen lamp for a long time, reflected radiation enters the IR camera and appears as an apparent temperature elevation at the initial stage of heating even if the sample surface temperature is low (Fig. 3c). Again, by carefully excluding or shuttering the reflected radiation, the “classically” predicted temperature response of the sample rear surface was obtained (Fig. 3d).
4.2. Multiplicative noise condition for the detection of defects is: Cðτm Þ 4 C noise
ð3Þ
Note that the maximum temperature contrasts appear after short (Dirac) heating. A principal difference between the two conditions above is that Eq. (2) can be met by increasing the heat power density Q
The flaw detection theory described above has been applied to four tests of one-sided T/I NDT: (1) flash optical stimulation of a 2 mm-thick graphite/epoxy sample with 25 Teflon inserts (sizes 3 3, 5 5, 7 7, 10 10 and 15 15 mm2) at depths from 0.2 to 1.0 mm (experimental data courtesy of W. Świderski), (2) convective heating of a 6 mm-thick steel sample with 9 flat bottomed holes simulating rear-surface corrosion (16%, 50% and 66% material
V. Vavilov / NDT&E International 61 (2014) 16–23
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Fig. 2. Comparison between purely additive and multiplicative noise components.
T, oC
T, oC Heating pulse Weak residual heating
Time
T, oC
Time
T, oC Reflected radiation
Time
Time
Fig. 3. Influence of reflected radiation on rear-surface temperature profiles: (a) – 1.6 kJ Xenon flash tube, 1.8 mm-thick aluminum sample, painted black, reflected radiation present; (b) same as (a), reflected radiation suppressed; (c) 1 kW halogen lamp, heating 4.1 mm-thick graphite epoxy composite for 5 s, reflected radiation present; and (d) same as (c), reflected radiation suppressed.
loss and 5, 10 and 20 mm defect diameter); (3) ultrasonic stimulation of a 10 mm-thick honeycomb sample (0.8 mm-thick graphite/ epoxy skin, with Nomex honeycomb reinforcement); (4) optical
heating of a graphite/epoxy composite cylindrical sample using six tubular halogen lamps. Sample photographs and examples of IR thermograms are shown in Fig. 4.
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Fig. 4. Experimental samples: (a) graphite epoxy composite (2 mm-thick, 25 Teflon inserts); (d) steel (2 mm-thick, 5 bottom holes); (g) composite honeycomb (10 mm-thick, graphite epoxy skin, Nomex cells); (l) 5 mm-thick graphite/epoxy composite cylinder; (b), (e), (h), (m) optimum source IR thermograms; (c), (f), (k), (n) PCA images.
In each case, experimental image sequences were captured in the corresponding one-sided T/I NDT test (the number of images in the sequences varied from 50 to 250). ThermoFit Pro software was used to process the image sequences by applying several algorithms developed in pulsed T/I NDT. These were: 1D Fourier transform (pulse phase thermography), polynomial fitting, principal component analysis (PCA), wavelet transform, correlation technique and dynamic thermal tomography (see [2,4] for details). Each processing technique resulted
in a “best” image characterized by a maximum signal-to-noise ratio which was determined for both defect and non-defect areas. In many test cases, images of principle components provided the highest S values, as shown in Fig. 4.1
1 Advanced processing results obtained on these samples were presented at the ASNT Fall conference, Palm Springs, USA, 2011.
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An area of interest of about 10 10 mm2 was used in the analysis of each sample, as this is frequently the detection limit in many practical cases. Using this, evolutions of both sn and Cn as a function of time have been obtained (Fig. 5), so they could be compared to the ideal ones shown in Fig. 2. The results in Fig. 5 show that none of the tested materials reveals ‘pure’ additive or multiplicative noise behavior. However, in the flash heating of a graphite/epoxy composite (Curve 1), the noise is close to multiplicative since its standard deviation varies with excess temperature and the running contrast remains nearly constant. The noise associated with “square-pulse” heating of composite (curve 2) and black-painted steel (curve 3) behaves in a similar way. In all three cases, the test materials can be characterized by the following values of Cn: 1 3% (graphite/epoxy composite plane sample), 5% (graphite/epoxy composite cylindrical sample) and 2 3% (black-painted steel). Ultrasonic stimulation represents a special case where the concept of noise running contrast becomes meaningless because of zero excess temperature. In this case, the detection limit is governed by Eq. (2), i.e. the higher the injected energy, the smaller the minimum detectable defect size will be.
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Table 1 Material noise characteristics in T/I NDT.a Material (surface condition)
Cn, %b
Graphite epoxy composite Manufacturer 1 (flat sample) Manufacturer 2 (cylindrical sample) Manufacturer 3 (flat sample) Manufacturer 4 (cylindrical sample, air heating)
1–3 5 2–3 2–4
Glass fiber reinforced plastic (flat samples) Manufacturer 1 Manufacturer 2
2-2,5 2–3
Steel (plane samples) St 45 (black-painted) St 45 (yellow-painted, shiny, convection heating) St 45 (yellow-painted, mat, convection heating) AISI 1010 M76T (inductive stimulation) M76T (inductive stimulation, welding area) Aluminum (flat sample, black-painted) Turbine blade thermal protection coating
2–3 2.5 2.5 12 50 5-28c 3-9
a
Optical stimulation, if not stated otherwise. Cn values depend on the type of heating, time and area of interest (are given as examples). c Cn values depend on paint thickness. b
Another interesting fact is that a higher energy input can make noise more “multiplicative” due to the decreasing contribution of additive IR detector noise, which is independent of the energy input. Vice versa, after flash heating of metals, temperature quickly returns to the ambient level and Cn values increase significantly. The concept of Cn has been applied to several test cases, resulting in the estimates shown in Table 1. Examples of choosing areas of interest are shown in Fig. 6. Since Cn values depend on the type of heating, the time and area of interest, sample values are shown in Table 1. However, these reveal some stable T/I NDT features, thus making the Cn parameter useful in the determination of T/I NDT detection limits. For example, graphite/epoxy composite can be regarded as a very convenient material for T/I NDT not only because of its medium conductivity, but also due to its low surface clutter close to that of “black” coatings. The level of the surface-related multiplicative noise depends weakly on the manufacturer of the composite and whether convective or optical heating is used. Glass fiber reinforced plastic (GFRP) is similar to graphite/epoxy composite and is also regarded as a very convenient material for T/I NDT. Emissivity-enhancing coatings (dye, lacquer etc.) provide rather low multiplicative noise (less than 2% in terms of running contrast) independent of color. Some coatings are semitransparent to both heating radiation and sample thermal emission, and in the case of reflective surfaces, such as aluminum, this phenomenon may contribute to noise, as shown in Fig. 6a and Table 1. Natural metallic surfaces are characterized not only by high reflectivity that makes optical heating inefficient, but may produce false indications, particularly, in the areas of welding (see Fig. 6b), rust, etc.
5. Determining defect detection limits
Fig. 5. Noise parameters vs. time (1-graphite/epoxy composite, flash heating, cooling stage, 2-graphite/epoxy composite, optical heating, cooling stage): 3-steel, convective heating, cooling stage, 4-composite honeycomb structure, ultrasonic heating, heating stage): (a) temperature standard deviation; (b) noise running contrast.
For each T/I NDT procedure, a curve of temperature vs. time can be calculated for each defect size and depth. An example of such a curve is shown in Fig. 7a for the one-sided inspection of a 5 mmthick cylindrical graphite/epoxy composite sample (3D numerical modeling performed with ThermoCalc-6L).
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Fatigue crack
Areas of interest
Welding seam Fig. 6. IR thermograms in transient T/I NDT: (a) 2 mm-thick aluminum, black-painted; (b) M76T steel (moving rail under inductive stimulation, no coating).
5–10 s heat pulse, the maximum detection depth will be from 3.9 to 3.2 mm. Another example relates to the detection of corrosion in steel. The calculated curves are shown in Fig. 7b and they demonstrate how the running temperature contrast C depends on the rearsurface material loss δ ¼ ΔL=L in 1 and 10 mm-thick steel samples with the following thermal properties: thermal diffusivity α¼7.3 10 6 m2/s and thermal conductivity K ¼ 32 W/(mK). The curves can be approximated with the polynomials C ¼ 0:0197 δ 0:00108 δ2 þ 0:0000218 δ3 for L ¼ 1 mm C ¼ 0:00905 δ 0:000482 δ2 þ 0:0000107 δ3 for L ¼ 10 mm;
ð6Þ
where δ is expressed in %, and L is the sample thickness. Eq. (6) can be easily solved for δ. If Cn ¼5%, the minimal material loss that can be detected in 1 mm thick steel reaches 3%, while in 10 mm-thick steel the detection limit will be about 9%. Note that these limits are theoretical and are lower than achieved by actual tests.
6. Conclusions
Several decision making parameters, in both time and ampli-
Fig. 7. Determining detection limits (3D numerical modeling with ThermoCalc6 L): (a) running contrast vs. defect depth (air-filled defects in 5 mm-thick graphite/ epoxy composite, square-pulse heating); (b) running contrast vs. material loss (corrosion sites in steel, flash heating).
The following assumptions are made:
detection efficiency is limited by the noise running contrast Cn, defects larger than 10 10 mm2 can be regarded as one
dimensional and they do not influence the temperature signals; therefore, the data is calculated for 10 10 mm2 defects only, the T/I NDT parameters that vary are heating time and defect thickness; this results in a limit on the depth at which a defect may be detected, when assuming Cn ¼5%, the differential temperature signal ΛTserves as an additional detection parameter which is calculated for a heat power density of Q¼10 kW/m2; other Q values will change ΛT in direct proportion.
The 5% detection threshold determines the defect depth at which a particular defect can be detected. For example, when detecting defects with a thickness of 0.2–0.1 mm by applying
tude domains, have been suggested in T/I NDT, but the most appropriate ones are excess temperature T, differential temperature signal ΔT, running temperature contrast C ¼ ΔT=T, and their time evolution functions. Maximum values of ΔT and C appear at different times depending on whether they are observed within or after a heat pulse. However, optimum observation time should correspond to the maximum signalto-noise ratio. In T/I NDT, the presence of complex noise is a sort of “payment” for the universal character of this method. It is convenient to introduce two extreme types of T/I NDT noise: (1) additive noise, which is defined by background reflections and IR detector noise, or by the temperature resolution of the IR equipment, and (2) multiplicative noise, which is defined by material absorptivity/emissivity variations. In the case of optical stimulation, the reflected radiation from the heat source strongly affects the transient temperature profiles. To make the actual temperature response agree more closely with the theoretical prediction during the cooling stage, the heater should be shuttered as soon as the heat source is turned off. Multiple tests conducted on various materials have shown that no real material exhibits either a “pure” additive or multiplicative noise behavior. However, in flash and square-pulse optical heating of many composite and black-painted materials, the noise is close to multiplicative, being characterized by the
V. Vavilov / NDT&E International 61 (2014) 16–23
noise contrast Cn 2 5%, and this determines the defect detection limits. The Cn concept has been applied to graphite epoxy composites to demonstrate that, in the one-sided procedure, the maximum depth at which defects can be detected is about 4 mm; this has been confirmed by other research. Respectively, in 1–10 mm thick black-painted steel, the minimum detectable material loss is from 3% to 9%. Emissivity enhancing coatings (dye, lacquer etc.) provide rather low surface-related multiplicative noise (up to 2% in terms of running contrast) independent of color. Some coatings are semi-transparent to both heating radiation and sample thermal emission, and in the case of reflective surfaces such as aluminum, this phenomenon may contribute to noise. Natural (uncoated) metallic surfaces are characterized by high reflectivity, which makes optical heating inefficient and may also produce false indications, particularly in the areas of welding, rust, etc. Ultrasonic stimulation represents a special case where higher injected energy allows the detection of smaller detected flaws.
Acknowledgment This research was supported by the grant of the Russian Fund for Fundamental Research No. 13-08-00190.
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References [1] Maldague X. Theory and practice of infrared technology for nondestructive testing. Wiley Series in Microwave and Optical Engineering. New York. U.S.A: John Wiley & Sons; 682. [2] Vavilov V. Thermal/Infrared Testing-NDT Handbook. Moscow: Spektr Publishing House; 475. [3] Lahiri J, Kuchipudi S, Siddiqui A, Vavilov V. IR thermographic inspection of filament wound CFRP shell samples. Proceedings of SPIE 2007;6541. [4] Vavilov V. Pulsed thermal NDT of materials: back to the basics. NDT and E International 2007;22:177–97. [5] Balageas DL, Krapez J-C, Cielo P. Pulsed photo-thermal modeling of layered materials. Journal of Applied Physics 1986;59(2):348–57. [6] Vavilov V, Maldague X, Dufort B, Robitaille F, Picard J. Thermal nondestructive testing of carbon epoxy composites: detailed analysis and data processing. NDT and E International 1993;26(2):85–95. [7] Maierhofer Ch. Brink A, Röllig M, Wiggenhauser H. Quantitative impulsethermography as non-destructive testing method in civil engineering – experimental results and numerical simulations. Construction and Building Materials 2005;19:731–7. [8] Infrared methodology and technology. Nondestructive testing monographs and tracts, 7. U.S.A: Gordon and Breach Science Publishers; 526. [9] Vavilov V., Bison P.G., Bressan C., Grinzato E., Marinetti S. Informative parameters and noise in transient thermal NDT. In: Maldague X, editors. Advances in signal processing for non destructive evaluation of materials. NATO ASI Series. Series E: Applied Sciences. Kluwer Academic Publishers, vol. 262. p.193– 208.