Active infrared thermography: frequency-modulated thermal wave imaging for sub surface fault recognition Chinmayee Jena*, Alok Kumar Singh** *(Electronics & Communication Dept., ABES Engineering College, Ghaziabad) Email: chinujena55@gmail.com) ** (Electronics & Communication Dept., ABES Engineering College, Ghaziabad) Email: eraloksingh@ahes.ac.in) ABSTRACT Active thermography has been modeled in terms of electrical equivalent circuit by using the correspondence between the fundamental laws of heat transfer and electricity. 1D, 2D and 3D electrothermal models have been given for finding direct solutions of active thermography problems. A Thermal nondestructive testing (TNDT) method ensuring the determination of characteristics of tested objects from an analysis of their temperature fields including the heat engineering characteristics has been presented. Thermal non-destructive testing is a whole field and non-contact technique for defect detection. The current work describes a variation of TNDT for subsurface defect detection based on frequency modulated thermal wave imaging (FMTWI). The apply has been made for the frequency dependence of thermal diffusion length, to achieve entire depth scanning of a sample in one run. This novel technique overcomes some of the drawbacks associated with traditional pulse and Lock-in thermography. Experimental results are presented in sustain. Keywords - Active thermography,thermal nondestructive testing (TNDT), frequency modulated thermal wave imaging (FMTWI),thermal diffusion length, pulse thermography,lock-in thermography I. INTRODUCTION Direct solutions of active thermography problems are important for understanding the mechanism of formation and investigation of temperature fields, created by various types of defects and thermal stimulations. They are also useful in establishing the effect of various parameters on these temperature fields. TNDT stands for a new method in NDT which uses thermal wave for sub-surface defect detection. This is also a whole field technique. Here the sample under test produces unequal surface heating on external heat stimulus which, in turn, carries the signature of hidden defects inside the sample. Since all solids conduct heat, this technique can therefore be widely used for defect detection in a variety of materials such as metals, composites and ceramics [5.6]. With time many different ideas were proposed to carry out NDT using thermal techniques. This leads to two broad ways of TNDT, viz. Passive thermography and Active thermography. In the passive technique, a defect shows up if its inherent temperature is different from its surroundings. However, detection of defects below the surface of the test sample, especially if they are deep, is difficult with passive techniques, and active thermograph is preferred [7,8]. In active thermography an external stimulus is applied to view the deeper defects with higher contrast. Traditionally, two different approaches are possible: pulse thermography (PT) and lock-in (sinusoidal modulated) thermography (LT) [2]. In PT, a short-duration energy pulse (optical, eddy current,
ultrasonic pulse, etc.) is applied and the thermal response is recorded. The resultant sequence of infrared images indicates defects in the material at different depths. In practice, the method requires highpower heat sources and has the additional drawback of being sensitive to surface in-homogeneities. In contrast, lock-in thermography uses mono-frequency sinusoidal thermal excitation. From the recorded images, information about the phase and magnitude of the reflected thermal wave is derived. The phase angle has the advantage of being insensitive to local variations of illumination or of surface emissivity. However, the mono-frequency excitation in LT limits the depth resolution [2, 3]. The time taken, therefore, to take measurements over a span of frequencies, and hence depths, can be very large. In an attempt to address some of the drawbacks of PT and LT, the present work focuses on the use of frequency-modulated thermal waves. In this technique, being named Frequency-Modulated Thermal Wave Imaging (FMTWI), the surface heating is not at a single frequency (as in LT), or at all frequencies (as in PT), but in a predetermined, limited range of frequencies. The frequency range is decided by the sample characteristics, for example thermal diffusivity, thickness of the sample, thermal conductivity and defect depth. A similar approach to the one presented here has been reported recently, but which utilized elastic wave ultrasonic excitation [3]. II. THEROY Consider the case of LT of a test sample (diffusivity α) on to the surface of which a uniform heat source periodically deposits heat at a modulating angular frequency w. Then, neglecting convection and radiation losses, the variation of temperature T, as a function of depth z (within the sample), and time t 0 is given in (1) : T (z, t 0 ) =T a + T 0 exp (-z*sqrt (π/α*t 0 )) cos (2πz/λt 0 )... (1) Where T a is the ambient temperature, T 0 is the amplitude of the oscillating temperature, z is the distance from the sample surface, and t 0 is thermal wavelength. In a given material, the depth of penetration of the thermal waves characterized by the thermal diffusion length µ, dependent on the thermal diffusivity α and is given in (1,2) : µ= [2α/w] ½...(2) Thermal wave depth of penetration in the above equation depends not only on the thermal diffusivity but also on the excitation angular frequency, w. Therefore, if we modulate the frequency of the heat source with time (frequency modulation wave as shown in (Figure 2(a)), and then the depth of penetration would also vary with time. This permits scanning the entire material thickness in one (frequency modulated) cycle, leading to detection of defects at different depths in comparatively much less time than in LT. Therefore, in a given time, much better depth resolution is also achievable by FMTWI [4]. III.BASIC CONCEPTS OF THERMAL IMAGING SYSTEM A. Stefan s Law of Radiation We know from our daily experience that all bodies at finite temperature radiate heat. This was quantitatively explained by the Austrian physicist Joseph Stefan (1853-93). He proposed a law, known as Stefan s law of radiation, which states A body at temperature T radiates heat per unit area per unit time proportional to the fourth power of its absolute temperature. Where H: Heat radiated per unit area per unit time and σ: proportionality constant, known as Stefan s constant =5.67 x 10-8Wm -2 K -4. The body which follows the aforesaid law is termed as Black body. But, for any real object the law never
holds true. So, another parameter was introduced to quantitatively specify the resemblance of an object to a black body. This parameter is known as Emissivity and written as is defined as the ratio of the heat radiated by the real object (H o ) at some finite temperature to that radiated by an ideal black body (H B ) at the same temperature. H 0 H B Thus, = 1 signifies that the body is a perfect black body. Materials like lamp black are having 0.95 and are considered to be a black body in all practical purposes. B. Wien s Displacement Law So far, the radiated energy was referred to as heat. But strictly speaking the energy is released in the form of electro-magnetic wave. Light is an electro-magnetic wave that our eyes respond to. The typical wavelength of visible light varies from 4000A to 8000A where 1A = 10-10 m. The red light is having the longest wavelength and is least energetic while the violet is having the shortest wavelength and is most energetic. But there is a whole lot of electro-magnetic wave lying beyond the range of visible light. They cannot be seen with the naked eye. Waves having wavelength longer than that of the red are known infra-red and are primarily emitted by a hot body. The intensity vs. wavelength plot for a hot body is shown in figure 1 below. Fig 1 Intensity vs. wavelength plot for a hot body at different temperatures In above intensity vs. wavelength plot the emitted radiation peak shifts toward the shorter wave length side with the increase in temperature. This is known as Wien s displacement law. Additionally, the total amount of radiated energy, which is a function of the area under the curve, also increases with temperature as suggested by Stefan s law. C. Atmospheric Transparency for IR Although a hot body emits all possible wavelengths in the IR region, air does not act as transparent medium for all wavelengths of IR. Most of them gets absorbed by the air molecules, While only a few photons with 2 5μm and 10 12μm wavelength passes through air. So, unfortunately, remote IR imaging systems have to rely only on these two IR spectral windows. D. Psedo-coluring of an Image The IR image, being gray-scale in nature, is difficult to read. To ease out the process, deferent colors are mapped to deferent intensity levels of the gray-scale image generating a beautiful color image of the 2D surface temperature profile. Generally, hot portions are represented with red and cold with blue or black. This mapping can be changed according to user s choice. A typical color mapped infrared image is show in figure 2 below.
Fm (t) = (1/2π) dθ/dt... (4) The chirp rate represents the rate of change of instantaneous frequency, and is defined by: Fig 2 A typical colour mapped IR Image. IV. TIME VARYING SINUSOIDS Most signals encountered in engineering applications are inherently non-stationary: i.e. having time-varying frequency and/or amplitude. The present work focuses on using linear frequency-modulated thermal excitation of the sample surface to overcome the problems associated with lock-in thermography (long measurement time) and pulse thermography (high peak powers). It is well-known that spread energy methods offer almost the only solutions for such combined (resolution-peak power-depth of penetration) problems.figure 3(a) shows a schematic of a linear frequency modulated(chirp) signal and its corresponding frequency spectra, figure 3(b). The advantage of using a chirp is that it provides good accuracy for time-of-flight measurements, as it only correlates well at a single well-defined instant of time of arrival (5, 6). Additionally, the received chirp signal can be detected even when its level is well below the noise floor [9]. A frequency modulated signal can be represented in time of (Figure 2(a)), by: X (t) = a(t) sin(θ(t)), 0 t t D...(3) Where a(t) is the envelope of the chirp signal which is zero outside the time interval t D, and t is the phase of the chirp signal. The instantaneous frequency F m (t), of the chirp signal can be obtained as follows: Fig 3(a) A linear frequency -modulated chirp signal x(t), and (b) its frequency spectrum X(f) The waveform is said to be an up-chirp if t and a down-chirp if t For a linear chirp is constant and hence f m (t) is a linear function of time. (a) (b) V. FMTWI: EXPERIMENTS AND RESULTS FMTWI experiments were carried out on a mild-steel sample (figure 4.), using a CEDIP IR system (3-5 µm). A frequency modulated signal of 500 sec duration and linear frequency variation from 0.01 Hz to 0.04 Hz, generated from a signal source is used to
drive the heat sources via a source control unit, as shown in Figure 5. The resultant temperature change over the sample surface was temporally captured in ALTAIR software. Various frequency components in the FMTWI are extracted using the Fourier transform (Fn) on each pixel of the thermogram sequence containing N images. Let T(k) be the temperature at a particular location of the kth thermogram in the image sequence(0<k<n). Then: = Re n + iim n...(6) length changes with time depending on the appropriate frequency modulated surface heating. The frequency dependent thermal diffusion length determines spatial resolution of LT. For a fixed test frequency (LT) the thermal diffusion length gets fixed and limits the depth resolution of the test. However in FMTWI the frequency varies with time causing variable depth probing. In this regard it can be compared to Pulse Phase thermography [1], in which a comparatively much wider range of frequencies are probed, simultaneously. Further as compared to PT, considerably less peak power is required from the heat sources. An = Re 2 n+im 2 n...(7) n = tan -1 (Im n / Re n )...(8) Here, Re and Im are the real and imaginary parts of the Fourier transform. The amplitude (An) and phase ( n) images are formed by repeating this process for all pixels in the frame/field of view. 3 4 4 4 4 3 5 1 7 2 9 1 All dimensions are in mm 2 5 1 Fig 5 Experiments arrangement for Frequency Modulated Thermal Wave Imaging (FMTWI) Fig 4 Dimensional layout of the mild steel sample with flatbottom 2 holes as 2defects 2 2 2 The phase and magnitude images of captured image sequence are obtained by the ALTAIR LI software. Figure 6. shows the phase image of FMTWI, at the modulation frequency of 0.068 Hz. However measurements were made over only one frequencymodulated cycle for FMTWI (0.01 to 4 Hz in 500 s). It can be seen that FMTWI can scan the entire sample thickness by utilizing thermal waves whose diffusion
VII. REFERENCES [1] F. Amon and C. Pearson, 'Thermal imaging in firefighting and thermographyapplications', Experimental Methods in the Physical Sciences, 43, pp 279-331,2010. Fig 6 Phase image obtained at 0.068 Hz frequency after applying Fourier transform throughout the captured image sequence in Frequency Modulated Thermal Wave Imaging (FMTWI) VI. CONCLUSION The aim of this paper was to focus attention on the aid provided by frequency modulated thermal wave imaging for their nondestructive evaluation. The article describes results of the frequency modulated thermal wave imaging Experiments has been carried out for justification and demonstration of the capability to detect defects with much less peak power (compared to PT), and in much less time (compared to LT).This paper also reflects some world trends in the TNDT theory. Furthermore, the capability of FMTWI is yet not completely exploited since it is believed that it could be employed in many other applications. In some cases, results are equivalent from the qualitative point of view. However, some techniques are best suited than others in quantification stages. More sensitive and fast IR cameras together with more powerful computers are making possible to manage even more complex and efficient outcome. [2] A. Levy, A. Dayan, M. Ben-David, and I. Gannot, 'A new thermography based early detection of cancer approach based on magnetic nanoparticles Theory simulation and in vitro validation (in press)', Nanomedicine: Nanotechnology, Biology andmedicine, doi:10.1016/j.nano.2010.06.007, 2010. [3] Louaayou, N. Naït-Saïd, and F.Z. Louai, '2D finite element method study ofthe stimulation induction heating in synchronic thermography NDT', NDT&E International, 41(8), pp 577-581, 2008. [4] P. Chaudhuri, P. Santra, S. Yoele, A. Prakash, D.C. Reddy, L.T. Lachhvani, J.Govindarajan, and Y.C. Saxena. 'Non-destructive evaluation of brazed joints between cooling tube and heat sink by IR thermography and its verification using FE analysis', NDT&E International, 39(2), pp 88-95, 2006. [5] C. Ibarra-Castanedo and X. Maldague. Pulsed Phase Thermography Reviewed, QIRT J., 1(1):47-70, 2004. [6] C. Ibarra-Castanedo, N. P. Avdelidis and X. Maldague. Quantitative assessment of steel plates using pulsed phase thermography, Materials Evaluation, 63(11): 1128-1133, November 2005. [7] Maldague X P V: Theory and Practice of Infrared Thermography for Non- destructive Testing, John Wiley & Sons Inc., 2001.
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