Measurement 188 (2022) 110546

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Measurement
journal homepage: www.elsevier.com/locate/measurement

Modeling and experimental validation of a quantitative bar-type corrosion

measuring probe using piezoelectric stack and electromechanical
impedance technique
Jianjun Wang a, Weijie Li b, *, Wei Luo c, Jianchao Wu d, Chengming Lan e
a
Department of Applied Mechanics, University of Science and Technology Beijing, Beijing 100083, China
b
School of Civil Engineering, Dalian University of Technology, Dalian 116024, China
c
School of Civil and Environmental Engineering, Harbin Institute of Technology, Shenzhen, Shenzhen 518055, China
d
Hubei Key Laboratory of Earthquake Early Warning, Institute of Seismology, China Earthquake Administration, Wuhan 430071, China
e
School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, China

A R T I C L E I N F O A B S T R A C T

Keywords: Corrosion coupon method has been widely used to estimate the corrosion rate in multiple industries. However, in
Corrosion measuring probe this method, the weights of the coupons are measured periodically, which limit the application for on-line
Quantitative measurement monitoring. In this paper, a novel type of quantitative bar-type corrosion measuring probe using piezoelectric
Piezoelectric stack
stack and electromechanical impedance (EMI) technique was proposed. The probe consists of a piezoelectric
Electromechanical impedance
stack and a metal bar. The multilayer models were used to derive the solution of the probe in longitudinal vi­
Longitudinal resonant frequency
bration mode. Five probe prototypes with designated probe length were fabricated to simulate uniform corrosion
induced mass loss and investigate the EMI response with probe length. The relationship between the corrosion
induced probe length loss and the first and second resonant and anti-resonant frequencies were analyzed. The
measured results agreed well with the theoretical predictions. In addition, the accelerated corrosion tests were
also performed to induce corrosion to the probe in a realistic setup and further validate the efficacy of the
proposed method. The present study proved the feasibility of using the proposed bar-type corrosion measuring
probe to quantitatively assess the corrosion amount by introducing the longitudinal vibration with piezoelectric
stack and EMI.

1. Introduction the SCC will leads to the variation in the EMI signatures. The results
showed that the SCC is able to assess the corrosion amount in a quan­
Corrosion of metals is the process of material loss by chemical or titative way, and has the on-line and remote monitoring capability.
electrochemical interactions with its environment. Corrosion coupon Subsequently, a new corrosion-measuring probe was investigated based
method has been widely used to estimate the corrosion rate to ensure the on a PZT patch and a metal rod for widespread applications in uniform
safety of the important facilities in the multiple industries, such as oil and non-uniform corrosion monitoring [4]. These preliminary in­
and gas, mechanical, mining, and civil engineering. In this method, the vestigations have proved the feasibility of using piezoelectric materials
corrosion coupons are installed in critical locations, and the weights of based on EMI technique to tackle the limitations of traditional corrosion
the coupons are periodically measure to obtain the weight loss to esti­ coupon method. However, these methods are at their early stage of
mate the corrosion rate [1,2]. The method is relatively simple yet it is development, and there are still some limitations. One is that the PZT
time consuming and requires intensive human labor involvement, which patches are usually used, which do not have the capability in designing
limits the applications in the on-line monitoring [3]. much larger-sized probe due to their lower power capacity. The other is
Recently, a novel smart corrosion coupon (SCC) was developed based that the corrosion induced the variation in the EMI signatures are usu­
on PZT patch and the electromechanical impedance (EMI) technique ally analyzed by the statistical metrics, which may suffer the following
[3]. The working principle is that the corrosion induced thickness loss of drawbacks. The effectiveness of the statistical metrics dependents on the

* Corresponding author.
E-mail address: liweijie@dlut.edu.cn (W. Li).

https://doi.org/10.1016/j.measurement.2021.110546
Received 8 September 2021; Received in revised form 10 November 2021; Accepted 29 November 2021
Available online 8 December 2021
0263-2241/© 2021 Elsevier Ltd. All rights reserved.
J. Wang et al. Measurement 188 (2022) 110546

Fig. 1. Schematic model for bar-type corrosion measuring probe.

selected frequency range [5,6], and if the selected frequency range is along with the coupled modes corresponding to the resonant peaks in
inadequate, the statistical metrics may not work well [4,7]. In addition, the EMI signature can be activated, which induce the mode identifica­
some resonant peaks in the EMI signatures lack the corresponding tion difficulties. Compared with other forms, the bar-shaped corrosion
physical meanings, which may also induce the identification difficulties sensor has the advantage of easily identified longitudinal vibration
[3]. mode.
In the last two decades, the piezoelectric materials and EMI tech­ Based on the above analysis and the previous work about the
nique have been successfully used in the field structural health moni­ corrosion-measuring probe [4], a kind of quantitatively bar-type
toring [8–14]. For example, the piezoelectric transducers have been corrosion measuring probe was proposed by combining the advan­
improved from the previous piezoelectric patches [15–19] to other tages of the piezoelectric stack and the metal bar. The capability in the
piezoelectric elements, such as the macro fiber composite (MFC) quantitative assessment of the corrosion amount was verified theoreti­
[20–22], the prism-shaped Smart Probe [23], the steel wire combined cally and experimentally by inducing the longitudinal vibration of the
piezoelectric transducer [24,25], the dual piezo configuration [26–28], probe. The rest of the paper is organized as follows. In Section 2, the
the spherical smart aggregate transducer [29], the piezoelectric rings schematic representation of quantitatively bar-type corrosion measuring
[30,31], to meet the different application requirements. These improved probe was introduced, and the theoretical solution based on the previ­
piezoelectric elements greatly enrich the application of the piezoelectric ously published work about piezoelectric stack actuator was derived
materials based on EMI technique and promote the developments. [43]. In Section 3, five probe prototypes with different probe length
Compared to these improved piezoelectric elements, the piezoelectric were fabricated to manually construct the uniform corrosion amount,
stacks show higher power characteristics [32–34], which are suitable to and the accelerated corrosion tests were perform to simulate the
develop the larger-sized probe. In addition, different design re­ corrosion process in a more realistic setting. Both the theoretical and
quirements in the real applications can be satisfied by selecting the experimental results were analyzed and discussed in Section 4. Con­
proper number of layers. Although the piezoelectric stacks have been clusions were drawn in Section 5.
widely used as the actuators [35–38] and energy harvesters [39–41], to
the authors best knowledge, the application of EMI technique in the 2. Theoretical modeling
piezoelectric stacks are rarely reported. The piezoelectric stacks have
not explored in designing the EMI based corrosion measuring probe. The The model for bar-type corrosion measuring probe is formed by a
benefits achieved by using the piezoelectric stacks are higher actuating variable cross-section metal bar with a piezoelectric stack attached on
power thus higher sensitivity and accuracy. top, as shown in Fig. 1. The piezoelectric stack consists of N piezoelectric
In addition to the improvement of the piezoelectric transducers, the layers, N + 1 electrode layers and 2 common ceramic layers, which are
shape and form of the corrosion coupon should be also properly selected. represented by P#, E#, C#1 and C#2, respectively. The corresponding
In our previous works, four shapes are investigated, including the rect­ thicknesses are denoted as h2i− 1 − h2i− 2 , h2i − h2i− 1 , H0 and H1 , respec­
angular plate [42], the circular plate [7], the beam-type SCC [3] and the tively. All the layers have the same area, which is denoted as S. Here, the
circular rod [4]. The results showed that for the rectangular plate, the common ceramic layers mean that the ceramic layers contain no elec­
circular plate, and the beam-type SCC, the multiple vibration modes trodes and are unpolarized, which are positioned at the two ends of the

2
J. Wang et al. Measurement 188 (2022) 110546

stack to play a protective and insulating role. The metal bar consists of N
̃ Substituting equations (1), (2), (4) and (5) into equations (7) to (9),
metal layers, which are represented by M#. ̃ The thickness and area of and combining the results of the piezoelectric stack in the Appendix 1
from our previously published work [43], the coefficients of the variable
each layer are defined as ̃ hn − ̃
hn− 1 and Sn , respectively. A harmonic
cross-section metal bar part à and B̃ can be obtained, as follows.
voltage V(t) = V0 ejωt is applied to the piezoelectric stack using an Mn Mn

impedance analyzer to activate the whole structure in longitudinal vi­ {

à = δ3n AE1 + λ3n V0
√̅̅̅̅̅̅̅
bration mode. Here, symbols V0 , ω (ω = 2πf), f, t, and j = − 1 repre­
Mn
(10)
B̃ = δ4n AE1 + λ4n V0
sent voltage amplitude, angular frequency, frequency, time, and Mn

imaginary unit in the harmonic voltage, respectively.

where
Based on the structural form, the solution can be divided into two
parts. For the piezoelectric stack, its exact analytical solution under the AE1 = L10 V0 (11)
harmonic voltage has been derived in our previously published work
⎧
[43]. In order to avoid repetition here, the solution given in the Ap­ ⎪
⎪
⎪ δ31 = L1 A30 + L2 A40
pendix 1 from our previously published work [43] will be directly used ⎪
⎪
⎨ δ4 = L A3 + L A4
in this work. For the variable cross-section metal bar, its theoretical 1 3 0 4 0
(12)
⎪ 3 5 3 6 4
solution can be derived by combining the continuous conditions at the ⎪ δn+1 = Ln δn + Ln δn
⎪
⎪
⎪
⎩ δ4n+1 = L7n δ3n + L8n δ4n
interface z = ̃
h0 and the solution of piezoelectric stack.
Based on our previously published work [43], the displacement ũ
Mn ⎧
and stress σ ̃ of the n-th metal layer in harmonic motion can be written ⎪
⎪ λ31 = L1 B30 + L2 B40
zMn ⎪
⎪
as ⎪
⎨ λ4 = L B3 + L B4
(13)
1 3 0 4 0

ũ = [Ã f15 (z) + B̃ f16 (z)]ejωt (1) ⎪ λ3n+1 = L5n λ3n + L6n λ4n
⎪
⎪
Mn Mn Mn ⎪
⎪
⎩ λ4n+1 = L7n λ3n + L8n λ4n
σ zM̃n = [AM̃n f17 (z) + BM̃n f18 (z)]ejωt (2)

where k̃ = ω/V ̃ , V 2 = Ẽ /ρ̃ , p̃ = Ẽ k̃ ; the functions f15 (z) ,

M M ̃
M M M M M M ⎧
f16 (z) , f17 (z) , and f18 (z) are defined as follows.
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
L0 = f15 (̃ h0 )f18 (̃h0 )S1 − f16 (̃h0 )f17 (̃h0 )S1
⎪
L1 = [f11 (̃h0 )f18 (̃h0 )S1 − f13 (̃h0 )f16 (̃
⎪
⎪
⎪
⎪
⎪ h0 )S]/L0
f15 (z) = sink̃ z, f16 (z) = cosk̃ z, f17 (z) = p̃ cosk̃ z, f18 (z) = − p̃ sink̃ z ⎪
(14)
⎨
M M M M M M L2 = [f12 (̃h0 )f18 (̃h0 )S1 − f14 (̃h0 )f16 (̃h0 )S]/L0
(3)
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪ L3 = − [f (̃
h )f
11 0 17 0 1 (̃
h )S − f (̃ ̃
13 h0 )f15 (h0 )S]/L0
⎪
⎪
⎪
In addition, to establish the continuous equations at the interface z = ̃ ̃ ̃ ̃
⎪
⎪
⎪
⎪
⎩ L4 = − [f12 (h 0 )f17 (h 0 )S1 − f14 (h 0 )f15 (h0 )S]/L0
h0 , the displacement uC2 and stress σzC2 of the C#2 layer are also
̃
addressed here, as follows [43].

uC2 = [AC2 f11 (z) + BC2 f12 (z)]ejωt (4)

σ zC2 = [AC2 f13 (z) + BC2 f14 (z)]ejωt (5) ⎧

⎪
⎪
⎪
⎪
⎪
⎪
⎪ Ln9 = f15 (̃
hn )f18 (̃
hn )Sn+1 − f16 (̃
hn )f17 (̃
hn )Sn+1
where kC = ω/VC , VC2 = EC /ρC , pC = EC kC ; the functions f11 (z) , f12 (z) ,
⎪
⎪
⎪
⎪
⎪
Ln = [f15 (hn )f18 (hn )Sn+1 − f16 (hn )f17 (̃
̃ ̃ ̃
⎪ 5
⎪
⎪ hn )Sn ]/Ln9
f13 (z) , and f14 (z) are as follows.
⎪
⎪
⎪
⎪
⎪
(15)
⎨
⎪
⎪
L6n = [f16 (̃
hn )f18 (̃
hn )Sn+1 − f16 (̃
hn )f18 (̃
hn )Sn ]/Ln9
⎪
f11 (z) = sinkC z, f12 (z) = coskC z, f13 (z) = pC coskC z, f14 (z) = − pC sinkC z ⎪
⎪
⎪
⎪
⎪
⎪ L7 = − [f15 (̃hn )f17 (̃
hn )Sn+1 − f15 (̃
hn )f17 (̃
hn )Sn ]/Ln9
(6)
⎪
⎪ n
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
8 ̃ ̃ ̃ ̃
L = − [f16 (hn )f17 (hn )Sn+1 − f15 (hn )f18 (hn )Sn ]/Ln9
⎪ n
For the part of variable cross-section metal bar in Fig. 1, the
⎩

continuous conditions and mechanical boundary conditions are given as

follows.
⎧ ⃒
⎪
⎪ ⃒ 4
⎨ uC2 |z=̃h0 = uM ̃1 z=⃒̃h0 λ̃3 f17 (̃
h̃) + λ̃ f18 (̃
h̃)
⃒ (7) L10 = − N N N
4
N
(16)
⎪ ⃒ ̃ ̃
⎩ Sσ zC2 |z=̃h0 = S1 σzM
3
⎪ ̃1 ⃒z=̃h0 δ̃f17 (h̃) + δ̃ f18 (h̃)
N N N N

⎧ Further, combining the results of the piezoelectric stack [43], the

⎪
⎪ ⃒ ⃒
⃒ electrical impendence Z can be expressed as
⎨ ũ ⃒ ̃ = u ̃ ⃒ h
M (n+1) z=̃
M n z=hn
⃒ n ⃒
⃒
̃ − 1)
(n = 1, 2, 3, ⋯, N (8) 1
⎪
⎩ Sn σzM
⎪ ⃒
̃n z=̃hn = Sn+1 σ zM
̃ (n + 1)⃒z=̃hn Z= − ∑ (17)
jωSe33 Ni=1 ci
⃒
S̃σ ⃒̃̃ ̃ = 0 (9) in which,
N zM N z=h
̃N

3
J. Wang et al. Measurement 188 (2022) 110546

Fig. 2. The fabricated bar-type corrosion measuring probe.

Fig. 4. The experimental setup.

by placing them on a sponge. The measured impedance spectra in the

frequency range from 10 kHz to 40 kHz with a frequency step of 10 Hz
are shown in Fig. 5. In the spectra, the two groups of valley and peak
frequencies correspond to the first two resonance and anti-resonance
frequencies of the probe in longitudinal vibration mode, respectively.
These frequencies will be used to quantitatively analyze the corrosion of
the probe in the longitudinal direction.
The accelerated corrosion tests were performed for probes NO.1,
No.2, and NO.3, to validate the results in a more realistic scenario. The
circumferential surface of the third part of the probes was waterproofed
using silicone gel, while the end surface of the third part was directly
exposed to corrosive environment and subjected corrosion loss. The
Fig. 3. The detailed sizes of the five variable cross-section metal bars. accelerated corrosion test setup is shown in Fig. 6. The probe was used as
anode and connected to the positive pole of the DC power supply, while
ci = a1i [a4i (λ1i + δ1i L10 ) + b4i (λ2i + δ2i L10 ) + Vi2 ] the copper plate was used as cathode and connected to the negative pole
(18) of the power supply. The third part of the probe and the copper plate
+b1i [a5i (λ1i + δ1i L10 ) + b5i (λ2i + δ2i L10 ) + Vi3 ] + Vi1
were immersed in the 3.5% NaCl solution. A constant current of 80 mA
Finally, the resonance frequency fr and the anti-resonance frequency was impressed to accelerate the corrosion process. By Faraday’s law
fa can be obtained by solving equations |Z| = 0 and |Z| = ∞ , respec­ Δm = MIt/zF (where Δm (g) is the mass loss, M (g) is the atomic weight
tively. These obtained theoretical frequencies will be used to quantita­ of metal (56 g for Fe), I (A) is the applied current, z = 2 is the ionic
tively access the corrosion of the probe in the longitudinal direction. charge, F = 96500 (A/s) is the Faraday’s constant and t is the duration),
the expected daily mass loss will be 2 g. In the ideal even corrosion
3. Experimental study condition, a mass loss of 2 g corresponds to an even thickness loss of 1
mm at the end of the probe. The impedance spectra were measured
Five prototypes of corrosion measuring probe were fabricated, which every day and the mass loss was also measured. The tests lasted for nine
are numbered as NO.1, NO.2, NO.3, NO.4, and NO.5, as shown in Fig. 2.
The piezoelectric stack with 10 piezoelectric layers (N = 10) was used,
whose detailed material properties can be found in our previous work
[43]. Five variable cross-section metal bars were designed, and each one
includes three parts (N
̃ = 3) in the length direction, as shown in Fig. 3.
The first part has a length of 40 mm and a diameter of 18 mm, which is
directly connected the piezoelectric stack. The second part has a length
of 40 mm and a diameter of 28 mm, which is designed to characterize
the variable cross-section properties in the theoretical modeling. The
third part has a diameter of 18 mm and different length is designed to
artificially describe the uniform corrosion amount. As can be seen, the
length of the third part of the probe is reduced from 80 mm to 40 mm
with a step of 10 mm. The metal material is taken as grade 45 steel in
Chinese standard, which is equivalent to the 1045 steel in US ASTM
standard. The Young’s modulus and Density are Ẽ = 210GPa and ρ̃ =
M M
7850kg/m3 , respectively.
The impedance spectra were measured using the impedance analyzer
PV520A (Bandera Electronics Co., Ltd., Beijing), as shown in Fig. 4. The
excitation voltage is 1 V and the measurement speed is 200 data points
per second. The free stress state of the specimens can be approximated Fig. 5. The measured impedance spectra showing first and second resonance
and anti-resonance frequencies.

4
J. Wang et al. Measurement 188 (2022) 110546

assess the corrosion amount of the probe.

Further, the relative error (Relative error=(Experiment–Theoy)/
Experiment) is defined to analyze the difference between the theoretical
and experiment results. Form Fig. 7 and Fig. 8, it can be found that the
maximum relative error for the first resonance frequency and the first
anti-resonance frequency is less than 13%, while the maximum relative
error for the second resonance frequency and the second anti-resonance
frequency is less than − 16%. The comparative results show that the
theoretical model is reliable.
In addition, the effects of the number of piezoelectric layers N on the
first two resonance and anti-resonance frequencies as well as the
impedance amplitude are analyzed theoretically. Here, it should be
noted that without damping, the impedance amplitude may become
singular at the resonance and anti-resonance frequencies. To exactly
simulate the actual working state in the calculation, the elastic modulus
EP is replaced by a complex form EP (1 + jQ) to describe the structural
damping of the device [44–46]. Q is the quality factor of the material
and is also a real number. For the piezoelectric material, Q is in the order
of 10-3 to 10-2. In the following calculations, Q = 10-2 is adopted. Fig. 9
Fig. 6. The illustration of the experimental setup for accelerated corro­ gives the theoretical impedance spectra showing first and second reso­
sion tests. nance and anti-resonance frequencies for different number of piezo­
electric layers. It can be found that with the decrease of the number of
days. The tests were conducted in a constant room temperature piezoelectric layers, the impedance amplitude apart from the resonance
environment. and anti-resonance frequencies will present an increasing trend with the
approximate linear relationship. For example, at 10 kHz, the theoretical
4. Results and discussion impedance values are 153.67 Ω for N = 10, 311.98 Ω for N = 5, 783.86 Ω
for N = 2, 1569.44 Ω for N = 1, respectively. A main reason is that with
The impedance spectra of five prototypes were shown in Fig. 5. The the decrease of the number of piezoelectric layers, the equivalent
length of third part corresponding to the probes NO.1, NO.2, NO.3, capacitance of the piezoelectric stack is decreased linearly. Besides, the
NO.4, NO.5 are 80 mm, 70 mm, 60 mm, 50 mm, 40 mm, respectively. impedance peaks at the first resonance and anti-resonance frequencies
The different length of third part corresponds to the artificial uniform are difficult to be observed. That may be caused by the relative smaller
corrosion amount. That is to say, with the length of third part decreases, proportion of piezoelectric part in the whole device. Therefore, selecting
the corrosion amount is increased. From Fig. 5, it can be observed that the proper number of piezoelectric layers is very helpful to clearly
with the increase of the corrosion amount, the first two resonance and identify the impedance peaks of the resonance and anti-resonance
anti-resonance frequencies are shifted from the smaller values to the frequencies.
larger ones. Further, these frequencies are addressed in Fig. 7 and Fig. 8. Further, Fig. 10 shows first and second resonance and anti-resonance
In addition, the theoretical results are also presented in these figures for frequencies as well as the corresponding impedance peaks versus
comparisons. From Fig. 7, it can be found that with the increase of the number of piezoelectric layers N. It can be found that with the decrease
corrosion amount, the first resonance and anti-resonance frequencies of the number of piezoelectric layers, the first second resonance and
present an increasing trend. Similarly, from Fig. 8, it also can be found anti-resonance frequencies are increasing and they tend to be the same
that the second resonance and anti-resonance frequencies also present values, respectively. The relative smaller proportion of piezoelectric part
an increasing trend when the corrosion amount is increased. In other in the whole device is also the main reason. But for the impedance peaks,
words, there is a corresponding relation between the corrosion amount such tendencies are not found. Therefore, adopting the resonance and
and the first two resonance and anti-resonance frequencies of the probe anti-resonance frequencies for the corrosion quantification is much
in longitudinal vibration mode, which can be used to quantitatively more effective than the impedance peaks.

Fig. 7. First resonance frequency (a) and first anti-resonance frequency (b) versus length of third part of the probe.

5
J. Wang et al. Measurement 188 (2022) 110546

Fig. 8. Second resonance frequency (a) and second anti-resonance frequency (b) versus length of third part of the probe.

from these probes are very similar, therefore only the representative
results of probe NO.1 were presented. The impedance spectra of probe
NO.1 under different corrosion duration are shown in Fig. 11. The first
group of the valleys and peaks correspond to the first resonance and

3
Day 0
10 Day 1
Day 2
Day 3
Day 4
Day 5
Day 6
|Z| ( )

2
10 Day 7
Day 8
Day 9

1
Fig. 9. The theoretical impedance spectra showing first and second resonance 10
and anti-resonance frequencies.
10 15 20 25 30 35 40
f (kHz)
In the experimental setup, three probes, that is NO.1, NO.2, and
NO.3, were subjected to accelerated corrosion tests to induce mass or Fig. 11. The impedance spectra of probe NO.1 under different corro­
thickness loss to the end of probe. The results and conclusions made sion duration.

Fig. 10. First (a) and second (b) resonance and anti-resonance frequencies as well as the corresponding impedance peaks versus number of piezoelectric layers N.

6
J. Wang et al. Measurement 188 (2022) 110546

17.5
Day 0 Resonance
Day 1 Anti-resonance
Day 2 Anti-resonance
17
Day 3 y = 0.13x + 16.01
Day 4 R2 = 0.9983

Frequency (kHz)
Day 5
Day 6
|Z| ( )

16.5
2 Day 7
10
Day 8 Resonance
Day 9 y = 0.13x + 15.94
16 R2 = 0.9991

15.5
15.5 16 16.5 17 17.5 18 18.5 0 2 4 6 8 10
f (kHz) Corrosion Duration (Day)

(a) (b)
Fig. 12. (a) The detailed impedance spectra of first group, and (b) resonance and anti-resonance frequencies versus the corrosion duration.

26.5
3
Day 0 Resonance
10 Day 1 Anti-resonance
Day 2
26 Anti-resonance
Day 3
y = 0.08x + 25.38
Day 4 2
Frequency (kHz)
R = 0.9943
Day 5
Day 6
|Z| ( )

2
10 Day 7 25.5
Day 8
Resonance
Day 9
y = 0.08x + 25.02
25 2
R = 0.9952

1
10
24.5
24.5 25 25.5 26 26.5 27 27.5 0 2 4 6 8 10
f (kHz) Corrosion Duration (Day)

(a) (b)
Fig. 13. (a) The detailed impedance spectra of second group, and (b) resonance and anti-resonance frequencies versus the corrosion duration.

Fig. 14. Photos of the corroded probe NO.1 on day 1, day 5, and day 9.

anti-resonance frequencies. Similarly, the second group of the valleys duration or corrosion amount. The resonance and anti-resonance fre­
and peaks associate with the second resonance and anti-resonance fre­ quencies are increased with the increase of corrosion duration. The
quencies. The detailed view of the first group is shown in Fig. 12(a) and resonance and anti-resonance frequencies are also fitted with a linear
the resonance and anti-resonance frequencies versus the corrosion line to shown the trend. It can be found that the relationship between the
duration are shown in Fig. 12(b). As can be seen valleys and peaks in the resonance, anti-resonance frequencies and the corrosion amount show
impedance spectra are shifted to the right with the increase of corrosion excellent linearity, with coefficients of determination (R2) very close to

7
J. Wang et al. Measurement 188 (2022) 110546

vibration mode, which is more intuitive than the statistical quantifying

metrics [4]. In addition, the impedance spectra with the apparent valley
and peak frequencies can be easily measured using the impedance
measurement chip AD5933 from Analog Devices Inc., which has been
successfully used in structural health monitoring [15,47–49], to realize
the low cost and the high accuracy online real-time monitoring capa­
bility. Future effects will optimize the probe and explore its performance
in the real pipe corrosion monitoring situations.

5. Conclusions

In this paper, a kind of quantitative bar-type corrosion measuring

probe using piezoelectric stack and electromechanical impedance (EMI)
technique was proposed and its quantitative monitoring performance of
the corrosion amount were evaluated theoretically and experimentally.
The results showed that there is a corresponding relation between the
corrosion amount and the first two resonance and anti-resonance fre­
quencies of the probe in longitudinal vibration mode. When the corro­
sion amount increases, the first two resonance and anti-resonance
frequencies also present an increasing trend. In addition, the universal
multilayer model of the probe consisted of the piezoelectric stack with
the arbitrary layer numbers and the metal bar with the arbitrary variable
cross-section was developed and validated experimentally, which can be
used as the benchmark for designing this kind of probe. The proposed
probe is expected to combine with the impedance measurement chip
AD5933 to develop the low cost and high accuracy online real-time
monitoring technology for the real pipe corrosion monitoring.

CRediT authorship contribution statement

Fig. 15. Schematic of using multilayer structure to replace the whole
Jianjun Wang: Conceptualization, Methodology, Supervision,
conical bar.
Writing – original draft. Weijie Li: Conceptualization, Methodology,
Writing – review & editing. Wei Luo: Investigation. Jianchao Wu:
1. The detailed view of the second group is shown in Fig. 13(a) and the
Visualization. Chengming Lan: Validation.
resonance and anti-resonance frequencies versus the corrosion duration
are shown in Fig. 13(b). Same conclusions can also be drawn as those of
the first group.
Declaration of Competing Interest
The photos of the corroded probe NO.1 on day 1, day 5, and day 9 are
shown in Fig. 14. In an ideal situation, the material or thickness is lost
The authors declare that they have no known competing financial
evenly at the end of the probe. However, in the accelerated corrosion
interests or personal relationships that could have appeared to influence
tests, the metal material is lost in a way that the probe tends to be
the work reported in this paper.
sharpened. Nonetheless, the results further validate the application of
the proposed corrosion measuring probe in uneven corrosion situation.
In general, this study proved the feasibility of using the bar-type Acknowledgments
corrosion measuring probe to quantitatively access the corrosion
amount by introducing the longitudinal vibration to the probe using This work is supported in part by the National Natural Science
piezoelectric stack and EMI technique. Compared with the previous Foundation of China (51808170, 51878044), in part by the Funda­
researches [4], the proposed method has the following improvements mental Research Funds for the Central Universities (FRF-TP-20-014A3,
and advantages. Firstly, the piezoelectric stack is adopted, which can be DUT21RC(3)053).
used to design much larger-sized probe duo to their high power char­
acteristics [32–34]. In addition, the universal multilayer model of Appendix A. The reliability assessment of the measurements
piezoelectric stack actuator has also been developed in our previous
work [43], which can be used as guidance for choosing the proper In the experiment, three tests are performed to assess the reliability
piezoelectric layer to meet the real requirements. Secondly, the multi­ of the measurements, as shown in Fig. A.1. In the first test, the frequency
layer model of the metal bar is also established, which can be used to range is from 10 kHz to 25 kHz with a frequency step of 10 Hz. In the
described the arbitrary variable cross-section bar by dividing the bar second test, the frequency range is from 10 kHz to 40 kHz with a fre­
into the multiple elements in the longitudinal direction. For example, as quency step of 10 Hz. In the third test, the frequency range is from 10
shown in Fig. 15, the whole conical bar can be replaced by the multi­ kHz to 60 kHz with a frequency step of 10 Hz. From Fig. A1, it can
layer structure. In the schematic, the whole conical bar is divided into observed that the measured impedance spectra are very stable and
seven layers. Each layer can be approximated as a thin cylinder, which repeatable for the frequency range from 10 kHz to 40 kHz, which cover
can be solved directly using the multilayer model. Here, it should be the first two resonance and anti-resonance frequencies of the probe in
pointed out that if more layer number is divided, better accuracy can be longitudinal vibration mode. Further, comparisons of the experimental
obtained. Thirdly, the proposed method can quantitatively reflect the fr and fa for three tests are presented in Table A.1. The values of three
relationship between the corrosion amount of the probe and the reso­ tests are almost the same. Therefore, we finally select the results of
nance and anti-resonance frequencies of the probe in longitudinal second test as shown in Fig. 5 for the further analysis.

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J. Wang et al. Measurement 188 (2022) 110546

Fig. A1. The measured impedance spectra of three tests: (a) probe NO.1, (b) probe NO.2, (c) probe NO.3, (d) probe NO.4, and (e) probe NO.5.

Table A1
Comparisons of the experimental fr and fa for three tests.
Probe number First test (kHz) Second test (kHz) Third test (kHz)

fr1 fa1 fr1 fa1 fr2 fa2 fr1 fa1 fr2 fa2

NO.1 15.95 15.99 15.96 15.99 25.01 25.36 15.96 15.99 25.02 25.37
NO.2 17.19 17.25 17.19 17.25 25.96 26.34 17.19 17.25 25.96 26.34
NO.3 18.54 18.63 18.54 18.63 27.26 27.62 18.54 18.63 27.25 27.62
NO.4 19.69 19.85 19.69 19.85 28.93 29.32 19.69 19.85 28.92 29.32
NO.5 20.87 21.08 20.87 21.09 32.41 32.81 20.87 21.08 32.41 32.81

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J. Wang et al. Measurement 188 (2022) 110546

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