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2ndReading June 15, 2019 3:56:37pm WSPC/149-SRL 1930003 ISSN: 0218-625X Surface Review and Letters, 1930003 (5 pages) c World Scienti¯c Publishing Company ° DOI: 10.1142/S0218625X1930003X A SIMPLE METHOD FOR DETERMINING A THICKNESS OF METAL BASED ON LOCK-IN THERMOGRAPHY A. ZRHAIBA*,§, A. BALOUKI*,¶ , A. ELHASSNAOUI*, S. YADIR†,‡, H. HALLOUA† and S. SAHNOUN† *Industrial Engineering Laboratory, Faculty of Science and Technology, BP: 523, Beni Mellal, Morocco †Laboratory of Electronics, Instrumentation and Energetic, Faculty of Sciences, B.P 20. 24000 El Jadida, Morocco ‡Laboratory of Materials, Processes, Environment and Quality, National School of Applied Sciences, Cadi Ayyad University, Sa¯, Morocco § [email protected] ¶[email protected] Received 23 May 2018 Revised 18 November 2018 Accepted 1 May 2019 Published The use of coatings is an important tool in the industry. It allows protecting against oxidation, corrosion and various types of fatigue. The coating thickness is an important characteristic that in°uences the quality and the performance of materials. In this paper, we develop a simple method of infrared lock-in thermography (LIT) to determine galvanizing coating thickness measurement, by using a sample multiple zinc layer with thickness ranging from 0.25 mm to 1.5 mm. The method has the particularity of taking a sinusoidal excitation heat °ux which contributes with a heat exchange coe±cient ¯xed at 10 w/m2k and a surface emissivity of about 0.1. The ¯nite element method (FEM) is used to model and analyze the thermal response of studied structure. The metal substrate used in this study is a structural steel, covered with six zinc layers. The ¯nite elements analysis allows us to determine the temperature evolution at di®erent points on the specimen. The Fourier transform method is used on the Matlab software to determine the phase angle of the data found. A correlation between the coating thickness and the equivalent phase angle is de¯ned, and the results deduced show that the estimated values are close to the actual coating thicknesses with a precision ranging from 0.029 mm to 0.011 mm. Keywords: Lock-in thermography; Fourier transform; galvanization; thermal response; phase angle. 1. Introduction Galvanizing is an industrial process that consists of covering the metal with a zinc layer and represents an e®ective way of preventing corrosion. The galvanized sheets and sections ¯nd their use in the chemical industry, in airplanes, and boats, because of their ability to resist oxidation. The evaluation of the zinc coating thickness takes a primordial interest for the §Corresponding author. 1930003-1 2ndReading June 15, 2019 3:56:37pm WSPC/149-SRL 1930003 ISSN: 0218-625X A. Zrhaiba et al. use and the industrial function. Modulated thermography is proposed as an e®ective and modern method to determine the coatings' thickness. It consists of applying a sinusoidal heat °ux at speci¯c zinc coating layers deposited with various thicknesses on steel substrate. The temperature evolution within the material follows the sinusoidal excitation and a transient regime before entering a steady state.1,2 Several methods are used in the evaluation of the coating thickness as the method of ultrasound, the method of eddy current, but they are limited.3 Pulsed thermography is widely used in inspection, but the measurement accuracy is low.4 The method applied has the advantage that the heating excitation is average, and the resistance to the surface re°ection interference is high.5 Lock-in thermography (LIT) proves its e®ectiveness in evaluating the coating thickness, the thermal response varies according to material properties such as thermal conductivity, density and speci¯c heat capacity, and depends on the thickness of this material.6 In this work, the ¯nite element method (FEM) allows to determine the variation of the temperature, to evaluate the zinc layer thickness deposited on the structural steel substrate. The sample structure is de¯ned with a set of zinc layers whose thickness takes the values from 0.25 to 1.5 mm. The thermal excitation frequency is varied from 0.01 Hz to 0.2 Hz, the phase angle of the thermal response is extracted by Fourier transform using software MATLAB, then the correlation is explored to establish the relationship between phase angle and coating thickness. Fig. 1. (Color online) Schematic of experience LIT. The generator of thermal excitation produces a periodic heat °ux. 2.2. Theory of the Lock-in thermography The LIT consists of applying the sinusoidal heat °ux as the external excitation. The thermal excitation form is QðtÞ ¼ Am ð1 cosð2 pi fe tÞÞ: ð1Þ QðtÞ is the sinusoidal heat °ux, Am is the amplitude of the heat source and fe is the excitation frequency. When the heat °ux reaches the surface of the sample, part of the energy will propagate into the material, the propagation depends on the property of the material and the excitation frequency. At the edge of the thickness, the change in the nature of the propagation material causes the thermal wave re°ection. Figure 2 shows a theoretical approach to 2. The Principle of the Lock-in Thermography for Evaluating the Coating Thickness of Material 2.1. Principle of the lock-in thermography LIT is a method of non-destructive control, which consists of analyzing the thermal response of a sample by an infrared camera, the sample is excited by a sinusoidal heat °ux with a speci¯ed frequency. Figure 1 shows the experimental schema for (LIT), as shown in the ¯gure, the infrared camera and the thermal excitation are placed in front of the sample, after the thermal excitation, a heat °ux is generated on the surface, a part of the energy is absorbed and the radiation process is thus established. Fig. 2. (Color online) The theoretical approach of modulated thermography for the evaluation of coating thickness. 1930003-2 2ndReading June 15, 2019 3:56:39pm WSPC/149-SRL 1930003 ISSN: 0218-625X A Simple Method for Determining a Thickness of Metal Based on LIT modulated thermography, the response to sinusoidal excitation is also sinusoidal whose amplitude and phase change with thermal properties and coating thickness. Heat propagates through the materials by conduction, the temperature distribution is obtained by Fourier law of heat conduction7: d 2 T ðz; tÞ K dT ðz; tÞ : ¼ dz 2 c dt ð2Þ T ðz; tÞ is the temperature, k is the thermal conductivity, c is the speci¯c heat, is the density and z the coordinate of the space. The heat °ux consists of two parts, the constant heat °ux which produces the increase of the temperature, and the harmonic heat °ux which produces the sinusoidal variation.8 The solution T ðz; tÞ can be expressed by Eq. (3)9: T ðz; tÞ ¼ AðzÞ cos½wt þ ðzÞ; 2.3. Fourier transform method The Fourier transform method consists of transforming the thermal response data acquired in the time domain to a frequency spectrum which makes it possible to highlight all the harmonics. The Ft used in this work permits to determine the phase angle of the thermal results. The Ft is expressed by Eq. (4)10: N 1 X k¼0 T ðKT Þ exp j2Kn ¼ Ren þ Imn ; N Table 1. coating. Mechanical property of the substrate steel and ð3Þ where AðzÞ is the amplitude, ðzÞ is the phase and w [rad/s] is the modulation frequency. Fn ¼ T Fig. 3. (Color online) Geometrical description of the sample. ð4Þ where T is the sampling interval, n is the frequency increment (n ¼ 0; 1 . . . ; N), Ren and Imn are, respectively, the real and imaginary parts of the transform, j is the imaginary number (j 2 ¼ 1). The phase angle is calculated from the real and imaginary part and expressed by Eq. (5): Imn n ¼ tan 1 : ð5Þ Ren Structural steel Zinc Conductivity (W/m k) Heat capacity (J/kg k) Density (Kg/m 3 ) 44.5 116 475 390 7850 7140 di®erent point. The structure of the sample was developed as shown in Fig. 3. The base metal dimensions are: 240 mm (length) 240 mm (width) 6 mm (height) and the layers coating thickness varied from 0.25 mm to 1.5 mm, this variation serves to illustrate the e®ects of the thickness on the thermal response. A normal mesh is adopted to determine the temperature variation. The mechanical properties of the substrate steel and the coating, are classi¯ed in Table 1, the intensity of heat °ux is 2000 w/m2, and the di®erent value of the excitation frequency is 0.01, 0.02, 0.05, 0.1 and 0.2 Hz. The initial temperature is the ambient temperature set at 298.15 K, the value of the heat transfer coe±cient is 10 W/m2.k, the surface radiation is " ¼ 0:1. There is no internal heat source during the inspection. 3. Results and Discussion 2.4. Modeling and simulation by ¯nite element method Finite Element Modeling (FEM) is used in infrared LIT to analyze the thermal wave propagation in materials, the temperature evolution is determined at The results of the thermal response of the layers coating at t ¼ 300 s are shown in Fig. 4, the thin coating attained the maximum temperature than the thick coating. The temperature changes from transient to steady state, with the periodical pattern. It depends on the 1930003-3 2ndReading June 15, 2019 3:56:40pm WSPC/149-SRL 1930003 ISSN: 0218-625X A. Zrhaiba et al. Table 2. Phase angle calculated for each thickness at fe ¼ 0:05 Hz. Fig. 4. Value of the thickness (mm) Phase angle (Rad) 0.25 0.50 0.75 1.00 1.25 1.50 1.7235 1.7192 1.7163 1.7138 1.7109 1.7074 Thermal response of the layers coating. Fig. 6. The variation of the coating thickness and phase angle as a function of the excitation frequencies. Fig. 5. Temperature variation of 0.25 mm thin coating at fe ¼ 0:05 Hz. excitation frequency, the temperature variation of 0.25 mm thin coating at the excitation frequency of 0.05 Hz is shown in Fig. 5. The thermal response is studied for di®erent excitation frequencies, 0.01, 0.02, 0.05, 0.1 and 0.2 Hz. The recorded results are exported to Matlab to perform the fast Fourier transform (FFT), so the phase and the amplitude are determined by FFT, Table 2 shows the results found for excitation frequency fe ¼ 0:05 Hz, as can be seen from the table, the phase angle decreases with increasing coating thickness. Figure 6 shows the change of the phase angle as a function of the thickness for di®erent excitation frequencies. Some frequencies do not display a large phase di®erence between the sample thicknesses. The relationship between the coating thickness and the phase angle under di®erent excitation frequencies is consistent, however, the large frequencies can give much better results for thin coatings.6 A correlation is applied to the curves plotted for the phase as a function of the frequency, for each curve the correlation coe±cient (R 2 ) is determined and classi¯ed in Table 3. The percentage error is 1930003-4 Table 3. The correlation coe±cient (R 2 ) for the di®erent frequency. Frequency (Hz) Correlation coe±cient (R 2 ) 0.01 0.02 0.05 0.1 0.2 0.9925 0.9941 0.9936 0.9966 0.9988 2ndReading June 15, 2019 3:56:47pm WSPC/149-SRL 1930003 ISSN: 0218-625X A Simple Method for Determining a Thickness of Metal Based on LIT Table 4. error. Predicted coating thickness and the percentage Actual thickness (mm) Calculated (rad) Predictive (mm) Error (%) 0.25 0.5 0.75 1 1.25 1.5 1.607 1.603 1.5987 1.5947 1.5906 1.5873 0.2425 0.4927 0.7617 1.0119 1.2684 1.4748 2.99 1.45 1.56 1.19 1.47 1.67 4. Conclusion Table 5. Percentage error for di®erent coating thickness as a function of modulation frequency. Percentage error for di®erent coating thickness Thickness T (mm) Frequency (Hz) 0.25 0.5 0.75 1 1.25 1.5 0.01 0.02 0.05 0.1 0.2 14.52 16.12 17.12 4.36 2.99 12.02 9.92 10.74 2.96 1.45 5.18 4.56 4.98 1.86 1.56 1.93 1.48 1.12 2.37 1.19 2.74 2.41 2.2 2.12 1.47 1.25 0.47 0.37 2.9 1.67 calculated for the di®erent excitation frequencies. Table 5 shows the found values of the percentage error. The value of the appropriate frequency is fe ¼ 0:2 Hz with R 2 ¼ 0:9988 and maximum percentage error with 2.99%. The correlation between the coating thickness and the phase angle is performed as shown in Fig. 7, the relationship can be expressed as Eq. (6) T ¼ 62:556 þ 100:77: Fig. 7. The estimated values of the error for the di®erent thicknesses and di®erent frequency is calculated and arranged in Table 4. ð6Þ Correlation between coating thickness and phase angle. In this study, the method of LIT is applied to a galvanized sample composed of multiple layers with various thicknesses ranging from 0.25 to 1.25 mm. The excitation contains a sinusoidal heat °ux contributing with a convective °ux whose thermal exchange coef¯cient is 10 w/m2.k, the emissivity of the de¯ned surface has the value of 0.1. The FEM determines the temperature evolution as a function of time. Several values of the excitation frequency ranging from 0.01 to 0.2 Hz are used to evaluate the accuracy of the results. The phase angle obtained by the Fourier transform characterizes the value of the coating thickness. The advantage of the method used is the linear correlation found between the phase and the thickness, the frequency which gives the good results is fe ¼ 0:2 Hz. A simple relation between the coating thickness and the phase angle is determined and the value of the estimated thickness is very close to the actual value with an accuracy of 0.011 to 0.029 mm. LIT proves its e±ciency in the calculation of the coating thickness. References 1. O. Breitenstein, W. Warta and M. Langenkamp, Lockin Thermography: Basics and Use for Evaluating Electronic Devices and Materials, seconded., (Springer Science & Business Media, New York, 2010). 2. A. C. Karaoglanli, K. M. Doleker and Y. Ozgurluk, State of the Art Thermal Barrier Coating (TBC) Materials and TBC Failure Mechanisms, Properties and Characterization of Modern Materials, (Springer, 2017), pp. 441–452. 3. C. Li, Non-destruct. Test. 27 (2005) 454–456. 4. Ptaszek, P. Cawley, D. Almond et al., NDTE Int. 45 (2012) 71–78. 5. G. U. O. Xing-wang and D. I. N. G. Meng-meng, Acta Aeronaut. Astronaut. Sin. 31 (2010) 198–203. 6. Y. Zhang, X. Meng and Y. Ma, Infrared Phys. Technol. 76 (2016) 655–660. 7. J. P. Holman, Heat transfer, Chinese machine press, 2005 J. Mater. Chem. 21 (2011) 5011–5020. 8. J. Liu, J. Dai and W. Yang, Infrared Phys. Technol. 53 (2010) 348–357. 9. D. Peng and R. Jones, Eng. Fail. 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