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Transient response analysis of steel in concrete
Corrosion Science 45 (2003) 1895–1902 www.elsevier.com/locate/corsci
Letter
Transient response analysis of steel in concrete Nick Birbilis *, Kate M. Nairn, Maria Forsyth School of Physics and Materials Engineering, Monash University, Clayton, Victoria 3800, Australia Received 27 February 2003; accepted 18 March 2003
Abstract A new approach is presented for the analysis of galvanostatically induced transients allowing for the rapid evaluation of the corrosion activity of steel in concrete. This method of analysis is based on the iterative fitting of a non-exponential model based on a modified KWW (Kohlrausch–Williams–Watt) formalism. This analysis yields values for the parameters related to corrosion such as the concrete resistance, polarisation resistance, interfacial capacitance and b, the non-ideality exponent. Ó 2003 Elsevier Science Ltd. All rights reserved. Keywords: A. Steel reinforced concrete; B. Galvanostatic; Time constant; Transient; Corrosion rate measurement
1. Introduction A technique that can accurately monitor the corrosion status of steel in concrete is still elusive. Present electrochemical techniques, such as linear polarisation resistance (LPR) have been used to monitor steel in concrete for a number of decades [1]. Limitations of LPR have been reviewed by Gonzalez [2,3]. Alternative electrochemical techniques such as analysing the potential response to a galvanostatic pulse have also been investigated [1–8]. Galvanostatic pulse measurements used to date are straightforward, however present data analysis techniques are complicated by the fact that the steel in concrete system does not usually reach a steady-state of potential shift, regardless of the size of the applied pulse [7]. Analysis of galvanostatically induced transients necessitates the use of an equivalent circuit that can accurately model the transient response. However, a RandleÕs
*
Corresponding author. Tel.: +61-3-9905-3599; fax: +61-3-9905-4940. E-mail address: [email protected] (N. Birbilis).
0010-938X/03/$ - see front matter Ó 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0010-938X(03)00086-6
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N. Birbilis et al. / Corrosion Science 45 (2003) 1895–1902
circuit [9,10] is not appropriate given the lack of steady-state behaviour observed in real systems such as steel in concrete. Alternative approaches using larger Voigt type circuits consisting of various resistor–capacitor (RC) combinations [11] have also been considered for transient analysis. Although such circuits have provided a good fit to the measured data, the physical significance of the individual circuit elements is somewhat difficult to interpret. Ideally, any equivalent circuit to model the steel in concrete system must be capable of accounting for mass transport, since this is the likely reason for the failure to reach steady-state in response to a current pulse [5,7,8]. Such a circuit has been presented by Feliu [9,10] incorporating circuit elements commonly used in the interpretation of AC impedance spectra [5] in order to simulate the electrical response of real systems in the time domain. In contrast, in this work we are fitting data obtained in the time domain to a circuit comprising elements defined in the time domain. In the present work we propose an alternative circuit to model the transient response of steel in concrete, Fig. 1. The circuit element RD ðQÞ describes the resistance owing to diffusion (i.e. responsible for concentration overpotential). This element has a value dependant upon Q, the amount of charge passed, where Q is itself a function of current and time. The double layer capacitance of the system is CNI (non-ideal capacitance), a capacitor-like element that does not follow ideal exponential behaviour in the time domain. This non-ideality may be explained by the heterogeneous nature of concrete and the surface inhomogeneity of steel, especially actively corroding steel [5,8]. Non-exponential relaxations are often analysed in the time domain using the Kohlrausch–Williams–Watt (KWW) formalism (Eq. (1)) [12–15]. The KWW function includes an exponent b which characterises the non-ideality of the relaxation; where b ¼ 1 corresponds to exponential decay (i.e. ideal capacitance) and 0 < b < 1 corresponds to a ÔstretchedÕ exponential (i.e. non-ideal capacitance); t is time, j is the time constant of the relaxation. b
/ðtÞ ¼ exp½ðt=jÞ 0 < b 6 1
ð1Þ
1.1. Development of modified KWW function It has been shown elsewhere [8], when the applied current pulse is small enough (i.e. <100 lC/cm2 ) disturbance to the electrode is minimised, and significant resis-
RP RΩ
RD(Q) CNI
Fig. 1. Improved circuit used to interpret the response of reinforcement to an applied stimulus. RP represents the polarisation resistance, RX the electrolyte/concrete resistance, CNI the non-ideal capacitance and RD ðQÞ the resistance owing to diffusion.
N. Birbilis et al. / Corrosion Science 45 (2003) 1895–1902
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tance owing to diffusion can be avoided. These rapid tests may eliminate the need for the RD ðQÞ element in the analysis of the circuit of Fig. 1. Although the KWW theory is intended for damping/relaxations as opposed to charging, the KWW function presented in Eq. (1) may be modified to give Eq. (2). This equation represents the potential response during the charging cycle of the system represented by Fig. 1 in the absence of diffusion effects. b
DEðtÞ ¼ DI RX þ DI RP ð1 expððt=CNI RP Þ Þ 0 < b 6 1
ð2Þ
where DEðtÞ is the potential shift with time, DI the applied current, RX the electrolyte/ concrete resistance, RP the polarisation resistance, t the time, CNI the non-ideal capacitance, and b is the non-ideality exponent. Given that the ohmic component, DIRX , of the potential response may be subtracted [6,8,16], Eq. (2) may be modified for investigation of the charging due to an applied current, to yield, n o DEðtÞcharge ¼ P 1 P 1ðexp½ðt=P 2Þb Þ 0 < b61 ð3Þ where P 1 ¼ ðDI RP Þ and P 2 ¼ ðRP CNI Þ. Iterative curve fitting of Eq. (3) yields values for P 1, P 2 and b. Eq. (2) may be further modified to obtain an equation for the discharging of the system following a short galvanostatic pulse, given by: b
DEðtÞdischarge ¼ P 1 exp½ððt þ -Þ=P 2Þ
0 < b61
ð4Þ
where P 1, P 2 and b have been previously defined, - and is a time shift parameter (as defined in Fig. 2), which accounts for the system being only partially charged. This term is required, so that calculations do not perceive the potential immediately following the pulse as the maximum potential shift. Transient data obtained from short galvanostatic pulses will be fitted using Eqs. (3) and (4) and presented below.
ϖ Fig. 2. Schematic representation of fitting procedure for Eq. (4).
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N. Birbilis et al. / Corrosion Science 45 (2003) 1895–1902
2. Experimental Reinforced mortar prisms were specifically designed at 4:2:1 (sand:OPC:water) for laboratory testing such that the entire surface area of steel (100 cm2 ) exposed within the concrete could be polarised. An Ag/AgCl Sat. reference electrode and a mixed metal oxide coated titanium counter electrode were embedded in each prism. The prisms were exposed to various environments within the laboratory in order to stimulate different degrees of corrosion in each block. A variable current generator connected in series with a current interrupter was used to produce the galvanostatic pulses. Current was passed between the counter and working electrodes such that the steel was polarised cathodically. The potential response of the rebar was monitored via the reference electrode, with readings logged digitally using a Maclab (ADI Instruments). Curve fitting was carried out using a commercial program.
3. Results and discussion Figs. 3 and 4 show the typical potential responses of an active and passive block exposed to a galvanostatic pulse. The timescale for potential discharge of the passive block is significantly longer than that of the active block, in spite of a much smaller applied current density being used. In order to carry out transient analysis, this pulse data was corrected for the ohmic contribution, and is presented as Ôpotential shift vs. timeÕ for the charging and discharging cycles in Figs. 3 and 4 respectively. The experimentally obtained data points () are shown together with the fit determined by modified KWW functions (––) and presented on the same figures. It is apparent that the modified KWW type equations provide a good fit to the experimentally obtained data under these circumstances. It is interesting to note that the parameters obtained for the charging period are also obtained in the discharging period. These parameters are listed in Table 1, where it is obvious that the technique can distinguish between the characteristics of active and passive samples. The active sample yields a RP value that is several orders of magnitude smaller than the passive sample. Also the CNI value for the active sample is significantly higher than that obtained for passive sample, possibly owing to greater inhomogeneity of the steel– concrete interface as corrosion of the metal surface proceeds. The transient obtained for the active sample gave a b parameter further from 1, indicating significantly greater non-ideality than in the passive sample. The b values are an indication of the interfacial properties of the system [16,17] and may serve to distinguish between active and passive reinforcements, with the more passive steel yielding b values close to 1. It is also seen that the ohmic resistance (RX ) is significantly lower in the active sample (Table 1). This is attributed to the presence of chlorides from the brine used to accelerate corrosion in the active specimen. The time constant of the system, denoted in Table 1 as j can also be useful as previously noted in [6,8] for its ability to serve as an indicator to the corrosion status
N. Birbilis et al. / Corrosion Science 45 (2003) 1895–1902
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Fig. 3. (a) Response of an active block to a galvanostatic pulse of 1 s duration and a current density of 100 lA/cm2 . (b) Potential shift upon charging corrected for ohmic contribution () and calculated fit (––) according to Eq. (3) for data shown in (a). (c) Potential shift upon discharging corrected for ohmic contribution () and calculated fit (––) according to Eq. (3) for data shown in (a).
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N. Birbilis et al. / Corrosion Science 45 (2003) 1895–1902
Fig. 4. (a) Response of a passive block to a galvanostatic pulse of 0.5 s duration and a current density of 1 lA/cm2 . (b) Potential shift upon charging corrected for ohmic contribution () and calculated fit (––) according to Eq. (4) for data shown in (a). (c) Potential shift upon discharging corrected for ohmic contribution () and calculated fit (––) according to Eq. (4) for data shown in (a).
N. Birbilis et al. / Corrosion Science 45 (2003) 1895–1902
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Table 1 Values obtained by analysis of data presented in Figs. 3 and 4 using KWW functions Block condition Active Passive
Data presented Fig. 3 Fig. 4
RX (X cm2 ) 180 4000
RP (X cm2 ) 3
4.9 10 2100 103
CNI (lF/cm2 )
b
j (s)
240 31
0.514 0.861
1.17 65
of steel in concrete. Since the j value is independent of area, it may serve to indicate corrosion activity in cases where confinement of the electrical signal may not be feasible, such as in difficult reinforcement geometries encountered on-site. However, to determine RP values for on-site applications, some method for confinement of the electrical signal would be required. The results presented within this paper indicate that in cases where galvanostatic pulse length is short and significant concentration gradients are avoided, Eqs. (3) and (4) provide a good fit to the real behaviour of a steel–concrete system. In cases where galvanostatic pulse size is increased (not shown here), then the modified KWW functions presented cannot provide a close fit to the data, most likely due to the influence of diffusion effects. This is further exemplified by the poor correspondence between the charging and discharging cycles, and by the fact that j becomes dependant on pulse size. This effect can also allow for the identification of situations where mass transport becomes significant and the use of smaller pulses is required. As previously discussed, an ideal analysis of the transient response of steel in concrete would account for diffusion, given that in some situations significant concentration gradients are present prior to monitoring, such as in partially submerged structures. Consequently future work will allow for this by incorporating additional terms in the KWW model. In the majority of cases however, the use of short galvanostatic pulses and analysis via modified KWW equations should provide satisfactory measurement of the corrosion status of steel in concrete. Furthermore, it may be possible to analyse only the charging transient since the information in the charging cycle can be collected in timescales of a few seconds, whereas there are lengthy delays in the discharging cycle, especially in passive cases.
4. Conclusions 1. A novel analysis method to assess the potential response of steel in concrete following a short galvanostatic pulse has been obtained using modified KWW expressions. 2. Potential transients for steel in concrete in response to a galvanostatic signal are non-exponential in their form, and can be analysed using KWW formalisms. 3. It has been shown that the use of short pulses avoids significant concentration gradients in many cases, and the analysis technique presented allows for accurate evaluation of RP , CNI , b and j.
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N. Birbilis et al. / Corrosion Science 45 (2003) 1895–1902
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]
G.K. Glass, C.L. Page, N.R. Short, S.W. Yu, Corros. Sci. 35 (5–8) (1993) 1585. J.A. Gonz alez, A. Molina, M.L. Escudero, C. Andrade, Corros. Sci. 25 (10) (1985) 917. J.A. Gonz alez, A. Molina, M.L. Escudero, C. Andrade, Corros. Sci. 25 (7) (1985) 519. C.J. Newton, J.M. Sykes, Corros. Sci. 28 (11) (1988) 1051. V. Feliu, A. Cobo, J.A. Gonzalez, S. Feliu, Corrosion 58 (1) (2002) 72. J.A. Gonz alez, A. Cobo, M.N. Gonzalez, S. Feliu, Corros. Sci. 43 (2001) 611. N. Birbilis, B.W. Cherry, M. Forsyth, K.M. Nairn, in: Proceedings Corrosion and Prevention, Paper no. 85, Newcastle, Australia, 2001. N. Birbilis, K.M. Nairn, M. Forsyth, in: Proceedings Corrosion and Prevention, Paper no. 21, Adelaide, Australia, 2002. V. Feliu, J.A. Gonzalez, C. Andrade, S. Feliu, Corros. Sci. 40 (6) (1998) 975. V. Feliu, J.A. Gonzalez, C. Andrade, S. Feliu, Corros. Sci. 40 (6) (1998) 995. D.W. Law, S.G. Millard, J.H. Bungey, Brit. Corros. J. 36 (2001) 75. R. Kohlrausch, Ann. Phys. 72 (1847) 393. P.M. Sathyanarayana, G. Shariff, M.C. Thimmegowda, M.B. Ashalatha, R. Ramani, C. Ranganathaiah, Polym. Int. 51 (2002) 765. V. Pena, A. Rivera, C. Leon, J. Santamaria, E. Garcia-Gonzalez, J.M. Gonzalez-Calbet, Chem. Mater. 14 (2002) 1606. M.D. Ediger, C.A. Angell, S.R. Nagel, J. Phys. Chem. 100 (1996) 13200. E.M.A. Martini, I.L. Muller, Corros. Sci. 42 (2000) 443. E. McCafferty, Corros. Sci. 39 (2) (1997) 243.
Letter
Transient response analysis of steel in concrete Nick Birbilis *, Kate M. Nairn, Maria Forsyth School of Physics and Materials Engineering, Monash University, Clayton, Victoria 3800, Australia Received 27 February 2003; accepted 18 March 2003
Abstract A new approach is presented for the analysis of galvanostatically induced transients allowing for the rapid evaluation of the corrosion activity of steel in concrete. This method of analysis is based on the iterative fitting of a non-exponential model based on a modified KWW (Kohlrausch–Williams–Watt) formalism. This analysis yields values for the parameters related to corrosion such as the concrete resistance, polarisation resistance, interfacial capacitance and b, the non-ideality exponent. Ó 2003 Elsevier Science Ltd. All rights reserved. Keywords: A. Steel reinforced concrete; B. Galvanostatic; Time constant; Transient; Corrosion rate measurement
1. Introduction A technique that can accurately monitor the corrosion status of steel in concrete is still elusive. Present electrochemical techniques, such as linear polarisation resistance (LPR) have been used to monitor steel in concrete for a number of decades [1]. Limitations of LPR have been reviewed by Gonzalez [2,3]. Alternative electrochemical techniques such as analysing the potential response to a galvanostatic pulse have also been investigated [1–8]. Galvanostatic pulse measurements used to date are straightforward, however present data analysis techniques are complicated by the fact that the steel in concrete system does not usually reach a steady-state of potential shift, regardless of the size of the applied pulse [7]. Analysis of galvanostatically induced transients necessitates the use of an equivalent circuit that can accurately model the transient response. However, a RandleÕs
*
Corresponding author. Tel.: +61-3-9905-3599; fax: +61-3-9905-4940. E-mail address: [email protected] (N. Birbilis).
0010-938X/03/$ - see front matter Ó 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0010-938X(03)00086-6
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N. Birbilis et al. / Corrosion Science 45 (2003) 1895–1902
circuit [9,10] is not appropriate given the lack of steady-state behaviour observed in real systems such as steel in concrete. Alternative approaches using larger Voigt type circuits consisting of various resistor–capacitor (RC) combinations [11] have also been considered for transient analysis. Although such circuits have provided a good fit to the measured data, the physical significance of the individual circuit elements is somewhat difficult to interpret. Ideally, any equivalent circuit to model the steel in concrete system must be capable of accounting for mass transport, since this is the likely reason for the failure to reach steady-state in response to a current pulse [5,7,8]. Such a circuit has been presented by Feliu [9,10] incorporating circuit elements commonly used in the interpretation of AC impedance spectra [5] in order to simulate the electrical response of real systems in the time domain. In contrast, in this work we are fitting data obtained in the time domain to a circuit comprising elements defined in the time domain. In the present work we propose an alternative circuit to model the transient response of steel in concrete, Fig. 1. The circuit element RD ðQÞ describes the resistance owing to diffusion (i.e. responsible for concentration overpotential). This element has a value dependant upon Q, the amount of charge passed, where Q is itself a function of current and time. The double layer capacitance of the system is CNI (non-ideal capacitance), a capacitor-like element that does not follow ideal exponential behaviour in the time domain. This non-ideality may be explained by the heterogeneous nature of concrete and the surface inhomogeneity of steel, especially actively corroding steel [5,8]. Non-exponential relaxations are often analysed in the time domain using the Kohlrausch–Williams–Watt (KWW) formalism (Eq. (1)) [12–15]. The KWW function includes an exponent b which characterises the non-ideality of the relaxation; where b ¼ 1 corresponds to exponential decay (i.e. ideal capacitance) and 0 < b < 1 corresponds to a ÔstretchedÕ exponential (i.e. non-ideal capacitance); t is time, j is the time constant of the relaxation. b
/ðtÞ ¼ exp½ðt=jÞ 0 < b 6 1
ð1Þ
1.1. Development of modified KWW function It has been shown elsewhere [8], when the applied current pulse is small enough (i.e. <100 lC/cm2 ) disturbance to the electrode is minimised, and significant resis-
RP RΩ
RD(Q) CNI
Fig. 1. Improved circuit used to interpret the response of reinforcement to an applied stimulus. RP represents the polarisation resistance, RX the electrolyte/concrete resistance, CNI the non-ideal capacitance and RD ðQÞ the resistance owing to diffusion.
N. Birbilis et al. / Corrosion Science 45 (2003) 1895–1902
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tance owing to diffusion can be avoided. These rapid tests may eliminate the need for the RD ðQÞ element in the analysis of the circuit of Fig. 1. Although the KWW theory is intended for damping/relaxations as opposed to charging, the KWW function presented in Eq. (1) may be modified to give Eq. (2). This equation represents the potential response during the charging cycle of the system represented by Fig. 1 in the absence of diffusion effects. b
DEðtÞ ¼ DI RX þ DI RP ð1 expððt=CNI RP Þ Þ 0 < b 6 1
ð2Þ
where DEðtÞ is the potential shift with time, DI the applied current, RX the electrolyte/ concrete resistance, RP the polarisation resistance, t the time, CNI the non-ideal capacitance, and b is the non-ideality exponent. Given that the ohmic component, DIRX , of the potential response may be subtracted [6,8,16], Eq. (2) may be modified for investigation of the charging due to an applied current, to yield, n o DEðtÞcharge ¼ P 1 P 1ðexp½ðt=P 2Þb Þ 0 < b61 ð3Þ where P 1 ¼ ðDI RP Þ and P 2 ¼ ðRP CNI Þ. Iterative curve fitting of Eq. (3) yields values for P 1, P 2 and b. Eq. (2) may be further modified to obtain an equation for the discharging of the system following a short galvanostatic pulse, given by: b
DEðtÞdischarge ¼ P 1 exp½ððt þ -Þ=P 2Þ
0 < b61
ð4Þ
where P 1, P 2 and b have been previously defined, - and is a time shift parameter (as defined in Fig. 2), which accounts for the system being only partially charged. This term is required, so that calculations do not perceive the potential immediately following the pulse as the maximum potential shift. Transient data obtained from short galvanostatic pulses will be fitted using Eqs. (3) and (4) and presented below.
ϖ Fig. 2. Schematic representation of fitting procedure for Eq. (4).
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N. Birbilis et al. / Corrosion Science 45 (2003) 1895–1902
2. Experimental Reinforced mortar prisms were specifically designed at 4:2:1 (sand:OPC:water) for laboratory testing such that the entire surface area of steel (100 cm2 ) exposed within the concrete could be polarised. An Ag/AgCl Sat. reference electrode and a mixed metal oxide coated titanium counter electrode were embedded in each prism. The prisms were exposed to various environments within the laboratory in order to stimulate different degrees of corrosion in each block. A variable current generator connected in series with a current interrupter was used to produce the galvanostatic pulses. Current was passed between the counter and working electrodes such that the steel was polarised cathodically. The potential response of the rebar was monitored via the reference electrode, with readings logged digitally using a Maclab (ADI Instruments). Curve fitting was carried out using a commercial program.
3. Results and discussion Figs. 3 and 4 show the typical potential responses of an active and passive block exposed to a galvanostatic pulse. The timescale for potential discharge of the passive block is significantly longer than that of the active block, in spite of a much smaller applied current density being used. In order to carry out transient analysis, this pulse data was corrected for the ohmic contribution, and is presented as Ôpotential shift vs. timeÕ for the charging and discharging cycles in Figs. 3 and 4 respectively. The experimentally obtained data points () are shown together with the fit determined by modified KWW functions (––) and presented on the same figures. It is apparent that the modified KWW type equations provide a good fit to the experimentally obtained data under these circumstances. It is interesting to note that the parameters obtained for the charging period are also obtained in the discharging period. These parameters are listed in Table 1, where it is obvious that the technique can distinguish between the characteristics of active and passive samples. The active sample yields a RP value that is several orders of magnitude smaller than the passive sample. Also the CNI value for the active sample is significantly higher than that obtained for passive sample, possibly owing to greater inhomogeneity of the steel– concrete interface as corrosion of the metal surface proceeds. The transient obtained for the active sample gave a b parameter further from 1, indicating significantly greater non-ideality than in the passive sample. The b values are an indication of the interfacial properties of the system [16,17] and may serve to distinguish between active and passive reinforcements, with the more passive steel yielding b values close to 1. It is also seen that the ohmic resistance (RX ) is significantly lower in the active sample (Table 1). This is attributed to the presence of chlorides from the brine used to accelerate corrosion in the active specimen. The time constant of the system, denoted in Table 1 as j can also be useful as previously noted in [6,8] for its ability to serve as an indicator to the corrosion status
N. Birbilis et al. / Corrosion Science 45 (2003) 1895–1902
1899
Fig. 3. (a) Response of an active block to a galvanostatic pulse of 1 s duration and a current density of 100 lA/cm2 . (b) Potential shift upon charging corrected for ohmic contribution () and calculated fit (––) according to Eq. (3) for data shown in (a). (c) Potential shift upon discharging corrected for ohmic contribution () and calculated fit (––) according to Eq. (3) for data shown in (a).
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N. Birbilis et al. / Corrosion Science 45 (2003) 1895–1902
Fig. 4. (a) Response of a passive block to a galvanostatic pulse of 0.5 s duration and a current density of 1 lA/cm2 . (b) Potential shift upon charging corrected for ohmic contribution () and calculated fit (––) according to Eq. (4) for data shown in (a). (c) Potential shift upon discharging corrected for ohmic contribution () and calculated fit (––) according to Eq. (4) for data shown in (a).
N. Birbilis et al. / Corrosion Science 45 (2003) 1895–1902
1901
Table 1 Values obtained by analysis of data presented in Figs. 3 and 4 using KWW functions Block condition Active Passive
Data presented Fig. 3 Fig. 4
RX (X cm2 ) 180 4000
RP (X cm2 ) 3
4.9 10 2100 103
CNI (lF/cm2 )
b
j (s)
240 31
0.514 0.861
1.17 65
of steel in concrete. Since the j value is independent of area, it may serve to indicate corrosion activity in cases where confinement of the electrical signal may not be feasible, such as in difficult reinforcement geometries encountered on-site. However, to determine RP values for on-site applications, some method for confinement of the electrical signal would be required. The results presented within this paper indicate that in cases where galvanostatic pulse length is short and significant concentration gradients are avoided, Eqs. (3) and (4) provide a good fit to the real behaviour of a steel–concrete system. In cases where galvanostatic pulse size is increased (not shown here), then the modified KWW functions presented cannot provide a close fit to the data, most likely due to the influence of diffusion effects. This is further exemplified by the poor correspondence between the charging and discharging cycles, and by the fact that j becomes dependant on pulse size. This effect can also allow for the identification of situations where mass transport becomes significant and the use of smaller pulses is required. As previously discussed, an ideal analysis of the transient response of steel in concrete would account for diffusion, given that in some situations significant concentration gradients are present prior to monitoring, such as in partially submerged structures. Consequently future work will allow for this by incorporating additional terms in the KWW model. In the majority of cases however, the use of short galvanostatic pulses and analysis via modified KWW equations should provide satisfactory measurement of the corrosion status of steel in concrete. Furthermore, it may be possible to analyse only the charging transient since the information in the charging cycle can be collected in timescales of a few seconds, whereas there are lengthy delays in the discharging cycle, especially in passive cases.
4. Conclusions 1. A novel analysis method to assess the potential response of steel in concrete following a short galvanostatic pulse has been obtained using modified KWW expressions. 2. Potential transients for steel in concrete in response to a galvanostatic signal are non-exponential in their form, and can be analysed using KWW formalisms. 3. It has been shown that the use of short pulses avoids significant concentration gradients in many cases, and the analysis technique presented allows for accurate evaluation of RP , CNI , b and j.
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N. Birbilis et al. / Corrosion Science 45 (2003) 1895–1902
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17]
G.K. Glass, C.L. Page, N.R. Short, S.W. Yu, Corros. Sci. 35 (5–8) (1993) 1585. J.A. Gonz alez, A. Molina, M.L. Escudero, C. Andrade, Corros. Sci. 25 (10) (1985) 917. J.A. Gonz alez, A. Molina, M.L. Escudero, C. Andrade, Corros. Sci. 25 (7) (1985) 519. C.J. Newton, J.M. Sykes, Corros. Sci. 28 (11) (1988) 1051. V. Feliu, A. Cobo, J.A. Gonzalez, S. Feliu, Corrosion 58 (1) (2002) 72. J.A. Gonz alez, A. Cobo, M.N. Gonzalez, S. Feliu, Corros. Sci. 43 (2001) 611. N. Birbilis, B.W. Cherry, M. Forsyth, K.M. Nairn, in: Proceedings Corrosion and Prevention, Paper no. 85, Newcastle, Australia, 2001. N. Birbilis, K.M. Nairn, M. Forsyth, in: Proceedings Corrosion and Prevention, Paper no. 21, Adelaide, Australia, 2002. V. Feliu, J.A. Gonzalez, C. Andrade, S. Feliu, Corros. Sci. 40 (6) (1998) 975. V. Feliu, J.A. Gonzalez, C. Andrade, S. Feliu, Corros. Sci. 40 (6) (1998) 995. D.W. Law, S.G. Millard, J.H. Bungey, Brit. Corros. J. 36 (2001) 75. R. Kohlrausch, Ann. Phys. 72 (1847) 393. P.M. Sathyanarayana, G. Shariff, M.C. Thimmegowda, M.B. Ashalatha, R. Ramani, C. Ranganathaiah, Polym. Int. 51 (2002) 765. V. Pena, A. Rivera, C. Leon, J. Santamaria, E. Garcia-Gonzalez, J.M. Gonzalez-Calbet, Chem. Mater. 14 (2002) 1606. M.D. Ediger, C.A. Angell, S.R. Nagel, J. Phys. Chem. 100 (1996) 13200. E.M.A. Martini, I.L. Muller, Corros. Sci. 42 (2000) 443. E. McCafferty, Corros. Sci. 39 (2) (1997) 243.