NON-DESTRUCTIVE ASSESSMENT OF REBAR CORROSION USING PEIZO-TRANSDUCERS USING EQUIVALENT STRUCTURAL PARAMETERS V. Talakokula1, S. Bhalla2, B. Bhattacharjee3 and A. Gupta4 ABSTRACT Occurrence of corrosion in rebars of reinforced concrete (RC) structures is a very common problem faced by the ageing infrastructure across the world. This paper presents a new approach for detecting and quantifying corrosion of steel bars via a piezoelectric ceramic (PZT) patch surface-bonded on the rebars using equivalent structural parameters extracted from PZT sensors via the electro-mechanical impedance (EMI) technique. The EMI technique utilizes the electro-mechanical coupling property of piezoelectric materials for damage diagnosis. Through tests on three steel rebars, empherical relations are derived to relate the corrosion induced mass and stiffness loss to the loss in the equivalent mass and stiffness identified by the PZT patch. The equivalent mass loss and stiffness loss correlates well with the actual mass loss and stiffness loss and provides an alternative corrosion assessment paradigm suitable for diagnosing corrosion in steel rebars.
Key words:
Electro mechanical impedance technique, PZT sensors, Reinforced
concrete, Steel. 1
Associate Professor, School of Civil Engineering, Galgotia’s University, Grater Noida, UP 201308 (INDIA),
Email:
[email protected], Tel:(91)9871857979. 2
(Corresponding author) Associate Professor, Department of Civil Engineering, Indian Institute of Technology Delhi, Hauz Khas,
New Delhi 110016 (INDIA), Email:
[email protected], Tel:(91)-11-2659-1040, Fax:(91)-11-2658-1117. 3, 4
Professor, Department of Civil Engineering, Indian Institute of Technology Delhi, Hauz Khas, New Delhi 110016 (INDIA).
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INTRODUCTION Corrosion is defined as the undesirable deterioration of a metal or an alloy caused by its interaction with the environment that adversely affects its properties which should otherwise be preserved. Interest of the scientific community in corrosion problem has been increasing for several years because of the wastage of precious metal due to corrosion, apart from endangering the structural performance and inducing failure. Corrosion of steel rebars has been identified as the most common cause of deterioration and premature failure of reinforced concrete (RC) structures1. Reinforcement corrosion induced structural failure does not necessarily imply structural collapse but in most cases manifests as the loss of structural serviceability, characterized by concrete spalling and the excessive deflection of the affected RC members2. Practical experience and experimental observations suggest that corrosion affected RC structures deteriorate at different rates as measured by strength and serviceability, with the latter deteriorating at a much faster rate. The reason for this is attributed to the fact that the corrosion products exert an expansive pressure on the concrete. Due to the low tensile strength of concrete, this expansive pressure leads to concrete cracking, spalling and de-bonding between the reinforcement and the surrounding concrete, all these effects soon become prominent once corrosion actively propagates in the structure. As a consequence, the stiffness of the structure reduces and the deflection increases3, 4. This paper presents a new approach for assesment of corrosion in steel rebars, using the electro-mechanical impedance (EMI) technique. The quantification of corrosion induced damage is based on the equivalent parameters identified by the surface
2
bonded piezoelectric ceramic (PZT) patch. The paper first presents a brief description of the EMI technique, followed by details of the specific experiments conducted on steel rebar specimens and the development of empirical equivalent models based on the measured electro-mechanical data.
ELECTRO-MECHANICAL IMPEDANCE (EMI) TECHNIQUE The word ‘piezo’ is derived from a Greek word meaning pressure. The phenomenon of piezoelectricity was discovered in 1880 by Pierre and Paul-Jacques Curie. It occurs in non-centro symmetric crystals, such as quartz (SiO2), Lithium Niobate (LiNbO3), and lead zirconate titanate [PZT, Pb(Zr1-xTix)O3], in which electric dipoles (surface charges) are generated when the crystal is subjected to mechanical stress. The same crystals also exhibit the converse effect, that is, they undergo mechanical deformations when subjected to electric fields. The direct and the converse effects are illustrated in Figure.1. and can be mathematically expressed as5 T D3 = ε 33 E3 + d 31T1
S1 =
T1 + D31 E3 YE
(1)
(2)
where axis ‘3’ points along the thickness of the patch and axes ‘1’ and ‘2’ lie in the plane of patch, as shown in the Figure. 26. Further, S1 is the strain along axis’1’, D3 the electric displacement over the surface of PZT patch, d31 the piezoelectric strain coefficient and T1 the axial stress in the patch along the axis ‘1’. �𝑌��𝐸� = 𝑌 𝐸 (1 + 𝜂𝑗)
represents the complex Young’s modulus of elasticity of the patch at constant electric
𝑇 𝑇 field and 𝜀���� 33 = 𝜀33 (1 − 𝛿𝑗) its complex electric permittivity at constant stress, with η
and δ respectively denoting the mechanical and dielectric loss factors of the patch. 3
The EMI technique is a relatively new technique for structural health monitoring (SHM). The technique was invented by Liang et al7 and then further developed by several research groups such as Guirgiutiu and coworkers8-10, Park et al11, 12, Bhalla and Soh6,
13, 14
. The EMI technique has been experimentally found to be a very
powerful in detecting localized incipient damage in a variety of structures15-21. In this technique, a PZT patch is surface bonded to the monitored structure as shown in Figure.2 and electrically excited by means of an impedance analyzer/LCR meter. Under external field excitation, the bonded patch induces deformations in the host structure, whose response is transferred back to the patch in the form of admittance function, consisting of conductance and susceptance. This admittance signature acquired over a high frequency range (30-400 kHz), forms the bench mark for assessing the structural health. At any future point of time, when it is desired to assess the health of the structure, the signature is acquired again and compared to the baseline signature, any deviation of which provides an indication of damage. The electrical admittance of the piezo-transducer can be expressed as a function of the mechanical impedance of the transducer and the drive point mechanical impedance of the host structure by means of a coupled equation derived by Liang et al7, who first proposed the impedance approach to model PZT-structure electromechanical interaction in 1D structures. Bhalla and Soh16 extended the impedance formulations to 2D by introducing the concept of “effective impedance” and derived a modified expression
for
the
complex
electro-mechanical
I l 2 T 2d 312 Y E 2d 312 Y E Y = = G + Bj = 4ωj ε 33 − + (1 − υ ) (1 − υ ) h V
4
Z a ,eff Z s ,eff + Z a ,eff
admittance
tan kl kl
𝑌�
as
(3)
where h is the thickness of the patch, ν the Poisson’s ratio, Z a ,eff the short- circuited effective mechanical impedance of PZT patch, Z s ,eff the mechanical impedance of host structure and ω the angular frequency. Mechanical impedance of the host structure depends on its mass, stiffness and damping properties. Damage in the structure alters these structural properties and hence the mechanical impedance, which is reflected in the electrical admittance of the piezo-transducer. The subsequent sections cover a description of the rebar experimental specimens, their testing under accelerated corrosion in laboratory, monitoring the process using the EMI technique, extracting equivalent parameters from the admittance signature and developing a equivalent mass model based on measured data.
ASSESMENT OF CORROSION IN STEEL REBARS USING EMI TECHNIQUE Steel rebars are principally used as reinforcement in concrete. Concrete ordinarily provides an almost ideal environment for protecting steel from corrosion; due to its high alkalinity which facilitates the formation of a thin invisible protective passive film around the steel. It can be safely assumed that the corrosion of steel would not occur till the embedded steel is protected from this alkaline film. This assumption however, is not fully satisfied in practice as is evident from the unusually high prevalence of damage in RC structures due to corrosion of rebars. Therefore, the assessment of corrosion and timely remedial action on the corrosion affected portion can permit the optimum utilization of the structure and imparts longevity to it.
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Corrosion is monitored basically using electro chemical techniques; a detailed review of the corrosion monitoring techniques along with their applications is covered by Rothwell22. The most commonly used electrochemical technique for corrosion assessment is open circuit potential measurement (half cell potential) technique. The half-cell potential, which is the measure of the electrode potential, equals the potential difference between the steel and the adjacent concrete electrolyte, and hence is a property of steel/concrete interface. Thus, in a given concrete environment, it may serve as an indicator of rebar corrosion initiation since the threshold of depassivation depends mainly on the electrode potential compared to other factors23. This technique detects the likelihood of corrosion of steel at a given location and time but cannot indicate the rate of corrosion24. Also while interpreting the half-cell potential data; one must consider factors such as oxygen and chloride concentrations and concrete electrical resistance, all of which have a significant influence on the readings25. Hence there is a need of a sensing technique which can remotely operate and assess the condition of the structure. It is now recognized that in the total management of structures, which involves both whole life economics and life cycle estimations, integrated monitoring systems and procedures have an important role to play. For this purpose, effective corrosion sensor technology is critical for ensuring safety of RC structures during life time. The newest generation of autonomous SHM systems with active sensors can possibly extract more information of the current and future performance of the structure. Extensive analytical and experimental works have been devoted to the detection of corrosion in concrete structures using fiber optic sensors26-31. However, only limited studies have been reported for corrosion detection using PZT patches. Proof of concept experiments to detect corrosion using PZT patch in metallic structures have 6
been reported32-35. The authors’ previous studies36,37 presented the corrosion assessment in RC structures using surface bonded as well as embedded sensors. The present paper, on the other hand, aims at developing dimensionless parameters for bare steel bars, that is, when the piezo sensor surface bonded to the rebar is unconfined. In previous studies, the rebar was embedded inside concrete. The results of the study shall be of significant relevance to structural steel constructions. In addition, during construction, bare rebars lie at the site for prolonged periods before final casting, attracting corrosion. The technique will facilitate fitness of rebars in such scenarios. EXPERIMENTAL DETAILS Three high yield deformed (HYD) steel rebars of 300 mm long and 16 mm diameter were surface bonded with square PZT patches of size 10x10x0.3 mm of grade PIC15138. All the rebars were machined in the central portion so as to achieve a smooth surface to bond the patch (as shown in Figure 3a). A thin layer of two part Araldite epoxy adhesive was applied on the machined surface and the PZT patch was placed on it. Light pressure was applied over the assembly using small weight. The set up was left undisturbed in this condition at room temperature for 24 hours to enable full curing of the adhesive. The electrodes were then soldered to the PZT patch and attached to Agilent E4980A LCR meter39 as shown in Figure 3b. In this manner, the electro mechanical admittance signature, consisting of the real part (conductance G) and the imaginary part (susceptance B) was acquired in a frequency range of 100300 kHz for all the three rebars. A frequency interval of 100 Hz was used for each admittance measurement. All the tests were performed under controlled laboratory conditions so that the temperature fluctuations could be ruled out.
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Under normal environmental conditions, corrosion of a rebar is a relatively slow process, often taking several years to progress significantly. In order to obtain data in a reasonable time frame for a laboratory-based study, the corrosion was accelerated using impressed current through anodic method28-31. After the baseline admittance signatures were acquired, the specimens were placed in a beaker containing “brine” solution (of salinity 35 parts per thousand). An electrical loop was set up with the steel rebar specimens forming the anode and the negative terminal was connected to a copper bar dipped in the solution acting as cathode, as shown in Figure 4. To accelerate the corrosion process, a constant current of 150 µA/cm2 was applied to the specimen using fixed power supply device, model ST 407640 for a period of eight hours. The admittance signatures were acquired for each specimen at regular intervals after each hour of accelerated corrosion exposure. Before any signature acquisition, the rebars were taken out of the brine solution, wiped clean of water, and dried in running fan. It was ensured that the PZT patch was always above the top layer of the brine solution i.e. the PZT patch was never submerged in the solution (as shown in Figure 4). Figure 5 shows the condition of one the rebar before and after the exposure to accelerated corrosion. As clearly visible in the figure, substantial corrosion has occurred in the bar after eight hours of the application of the constant current where as when the same rebar was embedded inside concrete36,
37
, it took 120 days for
substantial corrosion to occur. The distance of the affected region from the patch is within its zone of influence of the PZT patch, which typically extends to about 1m in such 1D structures11. The conductance signatures obtained from the sensor are shown in Figure 6. The variation of G (the real part of admittance) of the PZT patches, bonded to the rebar specimens is considerable and the signature can be observed to 8
change substantially with corrosion for all the three specimens. The conductance signatures vary from specimen to specimen, as they depending on number of factors such as bonding conditions of the patch, local surface and the variability of the PZT parameters. Further the overall effect of exposure may have small variation from specimen to specimen. From the marked difference in the signature of corroded state from the pristine state of each specimen, it can be concluded that the mechanical impedance has changed due to corrosion. This happens because the corrosion changes the mass, stiffness, and/or damping properties of the bar, which in turn causes the conductance signature to change in accordance with Eq. (3).
DAMAGE QUANTIFICATION Several damage metrics can be used to mathematically quantify the damage while reducing the admittance data to single scalar value. For preliminary investigations, the root mean square deviation (RMSD) metric was used because it is an established statistical metric to quantify damage41, 42. The RMSD metric is defined as
∑ (Gi − Gi0 ) N
RMSD =
1
2
∑ (G N 1
)
0 2 i
× 100
(4)
where Gi is the conductance of the PZT patch at any stage during the test and Gi0 is the baseline value (in pristine condition), i representing the frequency index (100 to 300 kHz). Figure 7, shows the variation of the RMSD indices of the three specimens as a function of the duration of accelerated corrosion exposure. For specimen 1, the RMSD index appears to follow a crudely linear trend (Figure 7a). For specimen 2, the RMSD increases abruptly after the first hour and then exhibits a weakly linearly
9
increasing trend (Figure 7b). However, for Specimen 3 (Figure 7c), essentially a scatter of values can be observed. Although all the three bars were identically affected, since the specimen as well as the exposure conditions were identical, the overall magnitude of the RMSD index differs significantly from specimen to specimen. Hence, it has not able to provide damage related information regarding the corrosion severity consistently. This is not unexpected since RMSD is a statistical quantifier43. The raw conductance signatures as well as RMSD index are not very dependable as they provide qualitative information about the damage43, to get further insight into the phenomenon structural parameters were extracted from the impedance spectrum. The next section performs detailed analysis to extract inherent system parameters and identify the one showing consistent variation with advancement of corrosion.
ANALYSIS OF STRUCTURAL MECHANICAL IMPEDANCE EXTRACTED FROM ADMITTANCE SIGNATURE The electromechanical admittance (given by Eq. 3) can be decomposed into active and passive parts as 2
2
����
2
���� 2
𝑙 ���� 2𝑑31 𝑌 𝐸 8𝜔𝑑31 𝑌 𝐸 𝑙 𝑇 � 𝑌 = 4𝜔𝑗 �𝜀33 − (1−𝜈) � + (1−𝜈) � ℎ
Passive Part
𝑍𝑎,𝑒𝑓𝑓
𝑍𝑠,𝑒𝑓𝑓 +𝑍𝑎,𝑒𝑓𝑓
� 𝑇�𝑗
(5)
Active Part
or 𝑌 = 𝑌𝑃 + 𝑌𝐴
10
(6)
The passive part solely depends upon the parameters of the PZT patch and is independent of the host structure. The host structure’s parameters appear in the active part only, in the form of the structural impedance, 𝑍𝑠,𝑒𝑓𝑓 . Using the computational
procedure outlined by Bhalla and Soh43, the real and the imaginary components (x and y, respectively) of the structural impedance i.e. 𝑍𝑠,𝑒𝑓𝑓 can be determined as 𝑍𝑠,𝑒𝑓𝑓 = 𝑥 + 𝑦𝑗
Where
𝑥=
𝑀(𝑥𝑎 𝑅−𝑦𝑎 𝑆)+𝑁(𝑥𝑎 𝑆+𝑦𝑎 𝑅) 𝑀2 +𝑁2
𝑦=
− 𝑥𝑎
𝑀(𝑥𝑎 𝑅+𝑦𝑎 𝑆)−𝑁(𝑥𝑎 𝑆−𝑦𝑎 𝑅) 𝑀2 +𝑁2
𝐵 ℎ
− 𝑦𝑎
𝐺 ℎ
𝐴 𝐴 𝑀 = 4𝜔𝐾𝑙 2 and 𝑁 = − 4𝜔𝐾𝑙 2
(7)
(8)
(9)
(10)
and
𝑅 = 𝑟 − 𝜂𝑡, 𝑆 = 𝑡 + 𝜂𝑟, 𝐾 =
2 ���� 2𝑑31 𝑌𝐸 (1−𝜈)
(11)
𝐺𝐴 and 𝐵𝐴 are the real and the imaginary components of the active admittance, computed from
𝑌�𝐴 = 𝑌� − 𝑌�𝑃
(12)
and 𝑍𝑎,𝑒𝑓𝑓 = 𝑥𝑎 + 𝑦𝑎 𝑗 is the effective mechanical impedance of the PZT patch. This
procedure enables the determination of the drive point mechanical impedance of the structure, 𝑍𝑠,𝑒𝑓𝑓 , at a particular angular frequency 𝜔 from the measured data, without
demanding any a priori information governing the phenomenological nature of the structure. Depending upon the variation of ‘x’ and ‘y’ with the frequency and the
11
associated values, the inherent elements (stiffness k, mass m and Damping c) making the host structural system can be identified. The experimental signature of the PZT patches bonded to the three specimens consists of G and B over 100-300 kHz range. Using Eqs. (3), (7) and (8), the mechanical impedance of the host structure (here steel rebars) was obtained at each frequency using the already established computational procedure43. The extracted mechanical impedance 𝑍𝑠,𝑒𝑓𝑓 consists of the real and imaginary components x and y respectively.
A close examination of the extracted impedance components in the frequency range 100-110 kHz of the healthy state revealed that the system behavior is similar to that of a Kelvin-Voigt system i.e. a parallel arrangement of a spring element (k) with a damper (c), shown in Figure 8(a) for which the real and imaginary components are given by Hixon44 as
𝑥 = 𝑐 and y = −
k
ω
𝑘
𝑦=𝜔
(13)
Within the frequency range 100-110 kHz, x was found to possess more or less a constant positive value and y a negative value with magnitude decreasing with frequency, similar to the characteristic of the Kelvin-Voigt system as shown in Figure 8 (b), (c) and (d) for all the three specimens. For Kelvin-Voigt system, the value of ‘k’ (stiffness) is basically equal to the slope of plot of y with ω-1 (Eq. 6) which should be a straight line. This is confirmed in Figure 9 (a), (b) and (c), which show the plot of y Vs ω-1 for specimens 1, 2 and 3 corresponding to different level of corrosion. A very consistent observation for all the three specimens is that with the advancement of corrosion, the slope of the curve decreases consistently, this is much more consistent than the trend of the RMSD indices shown in Figure 7. Using Eq. (13), the values of k and c were determined for all specimens after each hour of 12
exposure to accelerated corrosion. Figures 10 (a, b and c) display the effect of corrosion severity (in terms of number of hours of application of constant current) on the identified equivalent structural parameters (c and k). With corrosion progression, the damping can be observed to increase by about 41%, 38% and 30% and the identified stiffness can be observed to reduce by about 19%, 16% and 29% for the specimens 1, 2 and 3 respectively for an exposure time of eight hours of accelerated corrosion. Compared to the variation of the RMSD index (see Figure 7), this observed variation in indentified parameters is much more agreeable. Among c and k, the relative decrease in the values of c is much more agreeable among the specimens. Although the Kelvin-Voigt system based analysis showed consistent results, the identified system (parallel spring-damper combination) does not include mass element, which is expected to play significant role due to loss of mass associated with corrosion process. So, a close observation of frequency range 250 to 300 kHz showed that the system behavior was similar to a series combination of spring, damper and mass such as the one shown in Figure 11(a). For this combination, the system parameters are related to x and y as44 .
1 ω − − k ωm y= 2 1 ω −2 c + − k ωm 2
x=
c −1 1 ω c −2 + − k ωm
2
and
(14)
The angular frequency at which 𝑦 = 0 is denoted by ω0. Using Eq. (7), the system parameters can be determined, by algebraic manipulations, a
m=
k
(15)
ω02
k=− 13
(
x 2 + y 2 ω 2 − ω00 ωy
)
(16)
and
c=
x2 + y2 x
(17)
The analytical plots of ‘x’ and ‘y’ obtained by equivalent parameters match well with their experimental counter parts, for specimen 1 as shown in Figure 11(b) and (c). Specimen 2 also followed a similar trend in the frequency range 250-300 kHz. However, specimen 3 was exception and was therefore not considered for analysis using this model. The system parameters i.e. equivalent spring constant, equivalent mass and equivalent damping constant were determined for specimens 1 and 2 using the Eqs. (15) to (17) after each hour of corrosion exposure. The identified equivalent damping increased by 25% and 23%, equivalent stiffness was found to reduce by 27% and 20% and the equivalent mass reduced by 20% and 25% for specimen 1 and 2 respectively after eight hours of exposure. The variation of the system parameters with increasing corrosion exposure for this system is shown in Figure 12. For this model, the relative reduction in the equivalent mass is agreeable between the two specimens. During the experiment the actual mass of the specimen is also measured to correlate with the PZT identified equivalent mass. Figure 13 shows a plot of the relative mass loss for the specimens (measured directly by removing the specimens from the accelerated corrosion exposure after each hour) with progression of corrosion. For purpose of quantification, mass loss can be expressed in non-dimensional form as ∆𝑚 =
𝛿𝑚 𝑚0
(18)
where m0 is the original mass of the specimen and 𝛿𝑚 is the loss of mass. Here, both
the actual and the PZT identified mass (using Eq. 15) can be substituted. This index defines the severity of corrosion in the present scenario.
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Although the values of m so determined by the PZT patches differed from the actual mass of the specimen (comparing Figures 12 (c) and 13), however the loss of the PZT 𝛿𝑚
identified 𝑚 reasonably correlates with the loss of the actual 0
𝛿𝑚 𝑚0
of the specimens, as
shown in Figure 14. Hence, the PZT identified mass can provide a reasonable estimation of the actual mass loss of the specimen. For the purpose of correlating both, the two are related by a non-dimensional mass model as 𝛿𝑚
�𝑚�
𝑎𝑐𝑡𝑢𝑎𝑙
𝛿𝑚
= 𝜆�𝑚�
𝑃𝑍𝑇
(19)
Based on the data averaged over the two patches spanning over the two specimens, the value of λ is found to be equal to 4.974. This model can be directly used, with no requirement of determining the absolute mass of the specimen as it gives the loss of mass directly. The experimental results were also verified using conventional half cell potential (using ACM field machine).When the PZT identified mass loss changed from 0.15 Kg to 0.21 Kg, the potential reading changed from -501mv to -394mv for specimen 1 which confirmed that corrosion has occurred. This model based approach is more reliable as compared to the conventional half-cell potential values because the value of the half cell potential difference will depend on various factors such as type of electrode used, concrete porosity etc. In addition, for real-life structures, the half cell potential of steel rebar embedded in concrete cannot be measured directly at the interface of concrete/ rebar due to the presence of concrete cover. Further, the half-cell potential measurements do not provide quantitative information on the actual corrosion rate of rebars. They need to be interpreted in the context of complementary data from the concrete structures by specialists or skilled 15
engineers45. The approach presented in this paper, however is more practical, direct and consistent.
CONCLUSIONS This paper has presented a potentially new corrosion assessment approach based on the EMI technique which employs surface bonded PZT patches utilizing the extracted structural parameters from the impedance spectrum. Better response of the equivalent extracted parameters, ‘k’ and ‘m’, is observed as compared to the RMSD index as it makes use of real as well as imaginary components of admittance signature for extracting damage sensitive equivalent structural parameters. This model based approach using equivalent structural parameters is an improvement over the statistical indicators, such as RMSD, which fail to provide meaningful indication of the loss of stiffness and mass of the specimens. Further, the identified mass from the observed model (series combination of spring-damper and mass) follows a very consistent behavior with corrosion progress and the relative loss of the identified mass correlates well with the relative loss of actual mass of the specimens. The half-cell potential measurements obtained also strongly indicate the occurrence of corrosion. However, the EMI technique provides much greater information. The model based corrosion assessment presented can be utilized for real life steel structures.
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[27] Grattan, S. K. T, Basheer, P. A. M, Taylor, S. E, Zhao, W, Sun, T and Grattan, K. T. V. (2007) Fibre Bragg Grating Sensors for Reinforcement Corrosion Monitoring in Civil Engineering Structures. American Journal of Physics, 76, 12-18. [28] Grattan, S. K. T, Basheer, P. A. M, Taylor, S. E, Zhao, W, Sun, T and Grattan, K. T. V. (2009) Monitoring of Corrosion in Structural Reinforcing Bars: Performance Comparison Using In Situ Fiber-Optic and Electric Wire Strain Gauge Systems. IEEE Sensors Journal, 9, 1484-1502. [29] Zheng. Z. P, Sun, X. N and Lei Y. (2009) Monitoring Corrosion of Reinforcement in Concrete Structures via Fiber Grating Sensors. Frontiers in Mechanical Engineering China, 4, 316-319. [30] Zheng, Z, Sun, X, Lie, Y. (2010) Monitoring Corrosion of Reinforcement In Concrete Structures Via Fiber Bragg Grating Sensors. ASCE, 4, 2422-2430. [31] Gao, J, Wu, J, Li, J and Zhao, X. (2011) Monitoring of Corrosion in Reinforced Concrete Structure using Bragg Grating Sensing. NDT &E International, 44, 202-205. [32] Park, S and Park, S. K. (2010) Quantitative Corrosion Monitoring Using Wireless Electromechanical Impedance Measurements. Res Nondestruct Eval, 21, 184-192. [33] Park, S, Benjamin, L. G, Inman, J and Yun, C. B. (2007) MFC-Based Structural Health Monitoring Using a Miniaturized Impedance Measuring Chip for Corrosion Detection. Res Nondestruct Eval, 18, 139-150. [34] Simmers, G. E. (2005) Impedance-Based Structural Health Monitoring to Detect Corrosion. MS Thesis, Blacksburg, Virginia, [35] Rathod V. T, Mahapatra D. R. (2011) Ultrasonic Lamb wave based monitoring of corrosion type of damage in plate using a circular array of piezoelectric transducers. NDT &E International, 44, 628-636.
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[36] Talakokula. V, Bhalla. S and Gupta. A, (2014) “Corrosion Assessment of Reinforced Concrete Structures Based on Equivalent Parameters Using ElectroMechanical Impedance Technique”, Journal of Intelligent Material Systems and Structures, Volume 25 (4), pp 484-500. [37] Talakokula, V. and Bhalla, S. (2014) “Reinforcement Corrosion Assessment Capability of Surface Bonded and Embedded Piezo Sensors for RC Structures”, Journal of Intelligent Material Systems and Structures, accepted on 09 Sep 2014. [38] PI Ceramics. (2012) Product Information Catalogue. Lindenstrabe, Germany, www.piceramic.de. [39] Agilent Technologies. (2012) Test and Measurement Catalogue, USA. [40] Scientech Technology (2012), http:// www.scientech.bz. [41] Giurgiutiu, V and Rogers, C. A. (1998) Recent Advancements in the ElectroMechanical (E/M) Impedance Method for Structural Health Monitoring and NDE. Proceedings of SPIE Conference on Smart Structures and Integrated Systems, San Diego, California, March, 3329, 536-547. [42] Giurgiutiu, V, Reynolds, A and Rogers, C. A. (1999) Experimental Investigation of E/M Impedance Health Monitoring for Spot-Welded Structural Joints. Journal of Intelligent Materials Systems and Structures, 10, 802-812. [43] Bhalla, S, Vittal, A. P. R and Veljkovic, M. (2012) Piezo-Impedance Transducers for residual Fatigue Life Assessment of Bolted Steel Joints, Journal of Structural Health Monitoring, 11(6), 733-750. [44] Hixon, E. L. (1988) Mechanical Impedance, Shock and Vibration Handbook. edited by C. M. Harris, Mc Graw Hill Book Co, New York, 10.1-10.46.
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List of Figures Fig. 1
Direct and converse effect of piezoelectric materials
Fig. 2
Modelling PZT-structure interaction using effective impedance approach Experimental set up (a) Rebar specimen prepared for bonding PZT (b) Experimental set up
Fig. 3
Fig. 4
Accelerating corrosion set up
Fig. 5
Condition of specimens (a) Pristine specimen (b) Corroded specimen
Fig. 6
Variation of the conductance signature due to accelerated corrosion Exposure. (a) Specimen 1 (b) Specimen 2 (c) Specimen 3
Fig. 7
Variation of RMSD (a) Specimen 1 (b) Specimen 2 (c) Specimen 3
Fig. 8
Equivalent system parameters a) Kelvin-Voigt system b) Comparison of experimental plots of x and y with those of identified system for Specimen 1 c) Comparison of experimental plots of x and y with those of identified system for Specimen 2 d) Comparison of experimental plots of x and y with those of identified system for Specimen 3
Fig. 9
Variation of ‘y’ with ω1 (a) Specimen 1 (b) Specimen 2 (c) Specimen 3
Fig. 10
Variation of extracted system parameters (stiffness and damping) (a) Specimen 1 (b) Specimen 2 (c) Specimen 3
Fig. 11
Equivalent System parameters (a) Equivalent system (series combination of spring-damper and mass) (b) x vs f of specimen1 (c) y vs f of specimen 1
Fig. 12
Variation of extracted system parameters (a) Equivalent damping of specimen 1 and 2 (b) Equivalent stiffness of specimen 1and 2 (c) Equivalent mass of specimen 1 and 2
Fig. 13
Variation of actual mass loss with accelerated corrosion exposure (a) Specimen 1 (b) Specimen 2
Fig. 14
Correlation between loss of actual mass with PZT identified mass loss (a) Specimen 1 (b) Specimen 2
23
Piezoelectric Materials (a) Direct effect (Sensor) Mechanical stress
Electric field
++++++++++++++++++++++++++++++++++++++
T
T Surface charge
(a) Converse effect (Actuator) E
Electric field
Mechanical strain
+ PZT patch
Elongation
Figure 1 Direct and converse effect of piezoelectric materials
24
Figure 2 Modelling PZT-structure interaction using effective impedance approach6
25
LCR meter
Machined surface Rebar
Computer (a)
(b)
Figure 3 Experimental set up (a) Rebar specimen prepared for bonding the PZT (b) Experimental set up
26
Copper rod (Cathode) -
PZT patch
Brine solution Brine solution
Figure 4 Accelerating corrosion set up
27
+
+
PZT Patch
Severe corrosion area
PZT patch
(a)
(b)
Figure 5 Condition of specimens (a) Pristine specimen (b) Corroded specimen
28
0.0024
Conductance (S)
0.0022
Pristine State
0.002 0.0018 0.0016 0.0014 0.0012
Corroded State
0.001 200
210
220
230
240
250
Frequency (kHz)
(a) 0.0024
Pristine State
Conductance (S)
0.0022 0.002 0.0018 0.0016 0.0014 0.0012
Corroded State
0.001 200
210
220
230
240
250
240
250
Frequency (kHz)
(b) 0.024
Pristine State
0.021
Conductance (S)
0.018 0.015
Corroded State
0.012 0.009 0.006 0.003 0 200
210
220
230
Frequency (kHz)
(c) Figure 6 Variation of the conductance signature due to accelerated corrosion exposure (a) Specimen 1 (b) Specimen 2 (c) Specimen 3
29
16 15
RMSD (%)
14 13 12 11 10 0
1
2
3
4
5
6
7
8
Duration of exposure (hr)
(a) 80 70
RMSD (%)
60 50 40 30 20 10 0
1
2
3
4
5
6
7
8
Duration of exposure (hr)
(b)
27
RMSD (%)
26 25 24 23 22 0
1
2
3
4
5
6
7
8
Duration of exposure (hr)
(c) Figure 7 Variation of RMSD (a) Specimen 1 (b) Specimen 2 (c) Specimen 3
30
140
-62
120
Experimental
80
y (Ns/m)
x (Ns/m)
100
Equivalent system
60 40 0
-68 -71 -74
-80 100
102
104
106
108
110
100
102
(a)
Frequency (kHz) 140
104
106
108
110
Frequency (kHz)
-62
120
Experimental
-65
Figure 3.7 Kelvin-Voigt system
Experimental
100
Equivalent system
80
-68
y (Ns/m)
x (Ns/m)
Equivalent system
-77
20
60 40
-71 -74
Equivalent system
-77
20 0
-80
100
102
104
106
108
110
100
102
(b)
Frequency (kHz) 5
104
106
108
110
Frequency (kHz)
0 -10
Experimental
4 3
Equivalent system
y (Ns/m)
x (Ns/m)
Experimental
-65
2
-20 -30
Experimental
-40
1
Equivalent system
-50
0 100
102
104
106
108
110
-60
(c)
Frequency (kHz)
100
102
104 106 Frequency (kHz)
108
Figure 8 Comparison of experimental plots x and y with those of identified system a) Specimen 1 (b) Specimen 2 (c) Specimen 3 31
110
-40 -45
Increasing duration of applied current
y (Ns/m)
-50 -55
Corroded state Pristine state
-60 -65 -70 -75 0.007
0.0072 0.0074 0.0076 0.0078
0.008
0.0082 0.0084
ω-1 (s)
(a)
-40
Increasing duration of applied current Corroded state
y (Ns/m)
-50 -60
(a)
-70 -80
Pristine state
-90 -100 0.007
0.0075
0.0085
0.008
0.009
0.0095
ω-1 (s)
(a)
(b)
-60
Increasing duration of applied current
y (Ns/m)
-80
Corroded state
-100 -120 -140
Pristine state -160 0.007
0.0075
0.008
0.0085
0.009
0.0095
ω-1 (s)
A very consistent observation for all the three specimens is that with the advancement (c) Figure 9 variation of ‘y’ with ω1 (a) Specimen 1 (b) Specimen 2 (c) Specimen 3
32
(a)
80
42.5
75
40
70
k (kN/m)
c (Ns/m)
45
37.5 35
60 55
32.5
50
30 0
2
4
6
0
8
4
6
8
(a) 60
12
55
k (kN/m)
13.5
10.5
c (Ns/m)
2
Duration of exposure (hr)
Duration of exposure (hr)
9 7.5
50 45 40 35
6 2
0
4
6
30
8
0
Duration of exposure (hr)
45
80
40
75
35
70
30 25
2
4
6
8
Duration of exposure (hr)
(b)
k (kN/m)
C (Ns/m)
65
65 60
20
55
15 0
1
2
3
4
5
Duration of exposure (hr)
6
7
50
8
0
(c)
2
4
6
8
Duration of exposure (hr)
Figure 10 Variation of extracted system parameters (stiffness and damping) (a) Specimen 1 (b) Specimen 2 (c) Specimen 3
33
(a) 600
x (Ns/m)
500 400
Experimental
Equivalent system
300 200 100 0 250
260
270
280
290
300
Frequency (kHz)
(b) 0 -50
Equivalent system
y (Ns/m)
-100 -150 -200
Experimental
-250 -300 -350 250
260
270
280
290
300
Frequency (kHz)
(c) Figure 11 Equivalent System parameters (a) Equivalent system (series combination of springdamper and mass) (b) x vs f of specimen1 (c) y vs f of specimen 1
34
220
700
Specimen 1
600 550 500
400 0
1
2
3
4
5
6
7
190
170
8
0
Duration of exposure (hr)
1
2
3
4
5
6
7
8
7
8
7
8
Duration of exposure (hr)
(a)
210
195 185
Specimen 2
190
Specimen 1 k (kN/m)
175
k (kN/m)
200
180
450
165 155
170 150 130
145 135
110
0
1
2
3
4
5
6
7
8
Duration of exposure (hr)
0
1
2
3
4
5
6
Duration of exposure (hr)
(b)
0.3
0.22
0.29
Specimen 2
0.21
Specimen 1
0.28
0.2
m (kg)
0.27
m (kg)
Specimen 2
210
c (Ns/m)
c (Ns/m)
650
0.26
0.19 0.18
0.25
0.17 0.24
0.16
0.23
0.15
0.22 0
1
2
3
4
5
6
7
0
8
1
2
3
4
5
6
Duration of exposure (hr)
Duration of exposure (hr)
(c)
Figure 12 Variation of extracted system parameters (a) Equivalent damping of specimen 1 and 2 (b) Equivalent stiffness of specimen 1and 2 (c) Equivalent mass of specimen 1 and 2
35
Actual mass loss m (kg)
0.02 0.018
y = 0.0019x
0.016 0.014 0.012 0.01 0.008 0.006 0.004 0.002 0 0
2
6
4
8
10
Duration of exposure (hr) (a) 0.035 y = 0.0032x
Actual mass loss m (kg)
0.03 0.025 0.02 0.015 0.01 0.005 0 0
1
2
3
4
5
6
7
8
9
10
Duration of exposure (hr) (b)
Figure 13 Variation of actual mass loss with accelerated corrosion exposure (a) Specimen1 (b) Specimen 2
36
δ͙m/m (Based on actual mass)
0.35 y = 6.9138x
0.3 0.25 0.2 0.15 0.1 0.05 0 0
0.01
0.02 0.03 0.04 δ͙m/m (Identified by PZT patch)
0.05
(a) δ͙m/m (Based on actual mass)
0.25 y = 3.0361x
0.2 0.15 0.1 0.05 0 0
0.01
0.02 0.03 0.04 0.05 δ͙m/m (Identified by PZT patch)
0.06
0.07
(b) Figure 14 Correlation between loss of actual mass with PZT identified mass loss (a) Specimen1 (b) Specimen 2
37
