Zrhaiba et al. - 2019 - A SIMPLE METHOD FOR DETERMINING A THICKNESS OF MET

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.
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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.
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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
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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
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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
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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. Anal. 28 (2013) 275–288.
10. C. Ibarra-Castanedo and X. Maldague, Quant. Infrared Thermography J. 1 (2004) 47–70.
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