Electrochemical characterization of the corrosion resistance of aluminum-lithium alloys

Corrosion Science, Vot. 35, Nos 14, pp. 213-221, 1993

0010-938X/93 $6.00 + (h00 © 1993 Pergamon Press Ltd

Printed in Great Britain.

ELECTROCHEMICAL CHARACTERIZATION OF THE CORROSION RESISTANCE OF ALUMINUM-LITHIUM ALLOYS P. R. ROBERGE, E. HALLIOP, D. R. LENARD* and J. G. MOORES* Department of Chemistry and Chemical Engineering, Royal Military College, Kingston, Ontario, Canada K7K 5L0 *Materials Technology Section, Defence Research Establishment Pacific, FMO Victoria, B.C., Canada V0S 1B0 Abstract--The corrosion resistance of several promising new aluminum-lithium alloys has been characterized using electrochemical noise and impedance spectroscopy measurements. Corrosion of ALCAN 8090-T8 was compared with that of its conventional counterpart, aluminum alloy AA2024-T3. ALCAN and Kaiser 2090-T8 were compared with AA7075-T6. The samples were prepared so that they were exposed on only one surface for each of the three orthogonal planes that are related to the rolling direction of the sheet. The measurements were made for each of the alloys while exposed to a synthetic marine environment. An automatic statistical analysis performed on electrochemical spectroscopy (EIS) data permitted the establishment of the relationship between the measured polarization resistance and the corrosion resistance of aluminum alloys. Detection of any difference in intergranular corrosion (exfoliation) as a function of orientation has been accomplished by simultaneous analysis of the EIS data for the deviation from the semicircle of a Nyquist representation. The conclusions from the electrochemical noise and EIS data analyses were confirmed by optical and scanning electron microscopy examination and compared to results obtained during the exposure of the same alloys to seawater. INTRODUCTION

HISTORICALLY,improvements in mechanical properties gained by the formulation of new aluminum alloys have often been taxed by a parallel increase of the susceptibility to corrosion of these alloys. For example, the T6 temper of aluminum alloy (AA) 7075 was readily adopted by aircraft designers because of its high modulus and strength. It was subsequently discovered to be highly susceptible to stress corrosion and exfoliation in the marine environment, 1 at great cost to aircraft operators. As a result of this history and because elemental lithium is extremely reactive, there has been considerable interest in the corrosion susceptibility of aluminum-lithium alloys. A variety of accelerated corrosion tests 2 and standard electrochemical techniques3"4have been used to study the corrosion behavior of AI-Li. No consistent picture of the corrosion resistance of these alloys has yet emerged. Although there is general agreement that localized corrosion can occur in these alloys, there are differences of opinion about the relative susceptibilities between different AI-Li alloys, and with respect to conventional alloys. In order to acquire some first hand experience with the behavior of these alloys in the marine environment, the Defence Research Establishment Pacific (DREP) subjected panels made from AA2090 and 8090 sheet, along with 2024 and 7075 sheet, to several tests involving exposure to seawater fog and full or part immersion in seawater. The results of these tests were then compared with results obtained at the Royal Military College of Canada during the analysis of EIS and electrochemical noise measurements made with the same alloys exposed to simulated seawater. 213

P . R . ROBERGEet al.

214

NOISE ANALYSIS

The most common way to analyse noise data has been to transform time records in the frequency domain in order to obtain power spectra. Since noise signals can be produced by either deterministic or stochastic processes and often consist of a complex combination of these processes, the most universal analytical approach has been to correlate predominant frequencies and deconvolute unwanted signals in an iterative manner using well established mathematical functions. 5'6 Spectral density plots would thus be computed utilizing fast Fourier transforms (FFT) or other algorithms such as the maximum entropy method (MEM). 7'8 Although these techniques find a very appropriate use for the deconvolution of spectroscopic data sets which often contain millions of data points, they can yield disappointing results when applied to smaller sets of data points. The utilization of approximations as in the MEM technique to circumvent this limitation will itself be affected by the presence of non-stationary phenomena which can greatly complicate the final analysis. The approach taken here for the analysis of voltage fluctuations consisted of two levels of transformation of the original recordings. At the first level (Fig. 1) the voltage fluctuations were transformed into individual voltage peaks at basic events. This was accomplished relatively simply by sorting the consecutive voltage fluctuations as a function of the recorded voltage inflection points. Each directional change of the slope of the recorded voltage was used as a trigger and the resulting length-ofpeak compiled as a basic event in an histogram type distribution. The rise time of these singular peaks was also sorted in parallel with this first grid since the rise time (dV/dt) is an important characteristic of electrochemical systems. This first level of transformation of incoming signals, which was accomplished by a few lines of BASIC programming language, can yield drastically simplified results. The approach taken to perform the second level of transformation was imported from the field of statistics of event series such as practiced in reliability engineering. 9 Situations in which discrete events occur randomly in a continuum (e.g. time) and which are called stochastic point processes can normally be described by a Poisson probability distribution p(x; 2 t), as in equation (1), where x represents a random variable, t the specific time involved and 2 the mean number of events per unit time.

p(x; 20

= (2t)----xe ~-x`) x!

x = 0, 1, 2 . . . .

(1)

The goodness-of-fit can be evaluated by comparing the ideal exponential distribution, corresponding to this mean value 2, to the experimental distributions observed and corresponding to individual 2t calculated with equation (2) and subsequently averaged to find 2. The goodness-of-fit itself would be an expression of the difference (equation 3) between 2 and 2 (equation 4). 2t = f ( t )

e-at

Difference ( % ) =

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Goodness-of-fit = 100 - INT (Difference).

(2)

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Corrosion resistance of A1-Li alloys

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ELECTROCHEMICAL IMPEDANCE SPECTROSCOPY In recent years, electrochemical impedance spectroscopy (EIS) has found increasing use in the investigation of the mechanisms and rates of corroding systems. The non-destructive nature of the test, the short time needed to attain reproducible results and the need for electrochemical monitoring of corrosion processes in situ have all contributed to the growing success of this method. EIS data can be obtained by applying a small sinusoidai current signal to a specimen and measuring the amplitude and phase shift of the resulting voltage. For many corroding interfaces, EIS measurements taken over a wide range of frequencies show a circular arc in the complex impedance plane when the real and

216

P. R. ROBERGEet al. TABLE 1.

NOMINAL COMPOSITION OF ALLOYS TESTED ( w t % )

Alloy

Li

Cu

Mg

Si

Fe

Mn

Zn

Zr

2024 2090 7075 8090*

-1.9-2.6 -2.35

3.8-4.9 2.4-3.0 1.2-2.0 1.23

1.2-1.8 0.25 2.1-2.9 0.67

0.5 0.1 0.4 0.02

0.5 0.12 0.5 0.03

0.3-0.9 0.05 0.3 0.001

0.25 0.1 5.1~.1 0.02

-0.08-0.15 -0.11

*Actual heat analysis for the specimens supplied by ALCAN.

i m a g i n a r y c o m p o n e n t s a r e p l o t t e d a g a i n s t e a c h o t h e r in a N y q u i s t p l o t . t°'11 B y e x a m i n i n g t h e i m p e d a n c e at a p p r o p r i a t e f r e q u e n c i e s , a c c u r a t e v a l u e s o f t h e p o l a r i z ation resistance can be determined. Using the Stern-Geary equation, corrosion rates can b e o b t a i n e d as a n i n v e r s e f u n c t i o n o f t h e p o l a r i z a t i o n r e s i s t a n c e . I T I n m a n y s y s t e m s o f p r a c t i c a l i n t e r e s t , a n a l y s i s o f E I S d a t a is c o m p l i c a t e d b y t h e fact t h a t t h e N y q u i s t p l o t s e x h i b i t d e p r e s s i o n b e l o w t h e r e a l axis a n d b y l o w c o r r o s i o n r a t e s w h i c h m a k e it difficult to o b t a i n r e p r o d u c i b l e r e s u l t s at all f r e q u e n c i e s . R o b e r g e a n d c o - w o r k e r s 13--15 h a v e r e c e n t l y d e v e l o p e d g e o m e t r i c a n a l y s i s a n d statistical t e c h n i q u e s t h a t h a v e o v e r c o m e t h e s e difficulties. T h e i r p r o c e d u r e y i e l d s r e l i a b l e v a l u e s for both the polarization resistance and the angle of depression. In a recent study of m i l d s t e e l s p e c i m e n s in i n h i b i t e d s o d i u m c h l o r i d e s o l u t i o n s , t h e y w e r e a b l e to o b t a i n o v e r a l l c o r r o s i o n r a t e s f r o m t h e p o l a r i z a t i o n r e s i s t a n c e a n d to s h o w a c o r r e l a t i o n b e t w e e n t h e a n g l e o f d e p r e s s i o n a n d t h e e x t e n t o f l o c a l i z e d c o r r o s i o n ( p i t t i n g ) . 16

EXPERIMENTAL

METHOD

Laboratory tests

The aluminum specimens, with nominal compositions presented in Table 1, were cut to appropriate sizes for mounting in epoxy according to metallographic techniques. The samples were mounted in a manner that would expose only one face of each of three orthogonal planes that were related to the rolling direction of the sheet. Henceforth, these faces will be called the rolled surface, the long transverse edge (with its long axis parallel and its short axis perpendicular to the rolling direction) and the short transverse edge (with both long and short axes perpendicular to the rolling direction), respectively. Prior to mounting, provisions were made for electrical connection to the unexposed back of the samples, and the unexposed edges were coated with an aluminum-vinyl anti corrosive paint to prevent crevice corrosion between the epoxy mount and the aluminum electrodes. After mounting, the specimens were polished (using 240,400 and finally 600 grit papers) and cleaned with dichloromethane and acetone. For each experiment, a pair of identical aluminum specimens (same alloy and same exposed face) were immersed in a 2-1 beaker containing a solution of 3% sodium chloride. Each cell was equipped with an air purge and a saturated calomel reference electrode brought into close proximity with one electrode by a Luggin probe. The mounted specimens were separated by 2.5 mm and kept in a stable parallel position with plastic holders. EIS measurements were performed with a commercial frequency response analyser (Solartron Model 1255) at the corrosion potential. A potentiostat was not used in these measurements. The alternating current was applied between the two aluminum electrodes and kept at a value which would not cause more than 10 mV difference (peak to peak) across the cell. The reference electrode served to measure the corrosion potential and its fluctuations which were monitored with a sensitive multimeter (HP model 3457) through a high pass filter (1 MI) resistor in parallel to a 1 pF capacitor) which served to increase the sensitivity even further by nulling the d.c. voltage component. A custom-made multiplexer controlled by a laboratory computer directed the inputs from each technique to a storage device. At the completion of these experiments, which lasted approximately 2 weeks, the specimens were

Corrosion resistance of AI-Li alloys

217

removed and examined with both optical and scanning electron microscopy to observe any differences in corrosion morphologies.

Seawater exposure The 76 x 76 mm panels used in the exposure tests were sheared from sheets made of AA 2024-T3, 2090-T8, 7075-T6 and 8090-T851. Both surfaces of each panel were sanded with 120 grit silicon carbide abrasive paper and each panel was then fitted with two ceramic multiple-crevice washers (designed according to ASTM G78) that were held in place with a #12 stainless steel nut and bolt assembly that passed through a 6.3 mm central hole. Each bolt was fitted through plastic tubing to prevent contact with the aluminum panel. Each washer provided twelve separate sites for initiation of crevice corrosion. Each panel was suspended by way of a plastic-coated wire that was passed through a 3 mm hole that had been drilled in one corner of the specimen. SF850 Corrosive fog exposure system. The exposure was conducted according to ASTM B 117 with the exception that natural seawater was used to generate the fog instead of the standard sodium chloride solution.

Partial and total immersion. The remaining specimens were suspended in seawater that was drawn from the Strait of Juan de Fuca and directed through a tank measuring 16 x 62 x 177 cm. The sea water flowed past any specimen immersed in it at a rate of 1 cm s-J and was then returned to the Strait 40 m from the intake. The water temperature in this location was within the range 7-11°C. One set was suspended in a single row perpendicular to the direction of flow so that one half of the specimen was under water. A second set was suspended in a single row 1 m downstream from the first so that the entire specimen was immersed. All specimens were removed after an exposure time of 4 months. After the specimens were dismantled, the aluminum panels were cleaned by immersion in concentrated nitric acid. They were then rinsed with distilled water and allowed to dry after a final rinse with ethanol. Sections were cut from the panels and set in epoxy according to standard metallographic techniques in an effort to determine the depth of corrosion that had been initiated at the edges of the specimens. EXPERIMENTAL

RESULTS AND DISCUSSION

T h e i m p e d a n c e d a t a a n a l y s i s t e c h n i q u e m e n t i o n e d e a r l i e r t3-15 w a s u s e d to c a l c u l a t e 1/Rp v a l u e s f o r e a c h i m p e d a n c e p l o t g a t h e r e d . T h e s e v a l u e s w e r e t h e n c o n v e r r t e d i n t o c o r r o s i o n c u r r e n t s b y m u l t i p l y i n g t h e m ( e q u a t i o n 5) w i t h a p r o p o r t i o n a l i t y c o n s t a n t ( B ) , 17 t y p i c a l f o r a l u m i n u m e x p o s e d t o a s a l i n e e n v i r o n m e n t , a c c o r d i n g to t h e T a f e l e x t r a p o l a t i o n t e c h n i q u e f o r m e a s u r e m e n t o f c o r r o s i o n k i n e t i c p a r a m e t e r s i n t r o d u c e d b y S t e r n 18 a n d S t e r n a n d G e a r y : 19 icorr = B / R p

(5)

w h e r e icor~ is t h e c o r r o s i o n c u r r e n t ~ A c m - 2 ) ; B is a p r o p o r t i o n a l i t y c o n s t a n t f o r a l u m i n u m in c h l o r i d e s ( 2 4 m V ) ; 17 Rp is t h e r e s i s t a n c e c a l c u l a t e d f r o m E I S l o w f r e q u e n c y m e a s u r e m e n t s ( k D cm2). F a r a d a y ' s law ( e q u a t i o n 6) w a s u s e d to c o n v e r t t h e c o r r o s i o n c u r r e n t e s t i m a t e d from the EIS measurements into penetration corrosion rates. Corrosion rate - 3.3icorrEW d

(6)

w h e r e c o r r o s i o n r a t e is i n / ~ m y - ~ ; E W is t h e e q u i v a l e n t w e i g h t (9 g) o f t h e e l e m e n t b e i n g o x i d i z e d ( g / e q u i v . ) a n d d is t h e d e n s i t y (2.7 g c m - 3 ) o f t h e e l e m e n t b e i n g o x i d i z e d (g c m - 3 ) . A c c o r d i n g to t h e E I S p o l a r i z a t i o n r e s i s t a n c e d a t a , w h i c h a r e s u m m a r i z e d in

218

P.R. ROBERGEet al. TABLE2. ANALYSEDEIS RESULTSOBTAINEDWITHALUMINUMALLOYS Alloy

Thickness (mm)

Face

Corrosion rate (pm y-a)

Pitting rate*

2024-T3

1.0

Rolled Long Short Average

56 160 200 140

medium high high

2090-T3

1.2

Rolled Long Short Average

55 84 85 75

low medium medium

7075-T6

1.0

Rolled Long Short Average

140 110 105 118

medium very high very high

8090-T8

1.5

Rolled Long Short Average

45 38 25 36

very low low medium

*Pitting rate established by ranking the calculated depression angles and attributing them relative values (10° = low, 35° = very high).

Table 2, the 8090 alloy showed roughly equal corrosion rates for all three faces. Except for the rolled faces, the corrosion rate of the 8090 alloy was substantially lower than the corresponding face of the 2024 alloy. A n o t h e r interesting characteristic of interfacial behavior was revealed during the analysis of EIS m e a s u r e m e n t s and used to rank the alloys susceptibility to pitting corrosion. The depression angle from the real axis in a Nyquist representation of EIS results is an omnipresent character of EIS measurements. It has often been introduced by some authors 11'12'2° in their mathematical fitting procedures as an empirical factor which would appear as an exponent (a or fl, with values between 0 and 1) added to the imaginary term of an R C circuit model. Others 21-23 have demonstrated experimentally that the constantphase angle element, which has to be added to the classical R C circuit to produce such a depression angle, originates from the microscopic roughness of the interface. During a recent study of carbon steel resistance to corrosion, 16 a practical correlation was established between pit depth measurements and the cumulative depression angle calculated from EIS data. With the assumption that the angle of depression increases in some m a n n e r with increased pitting, the EIS data indicated that the rolled surface of the 8090 had the lowest susceptibility to pitting, followed by the long transverse edge and the short transverse edge, which had the highest rate (Table 2). Examination of these surfaces with optical and scanning electron microscopy suggested that the correlation between angle of depression and pitting rate involved the n u m b e r of pits formed in any given area (pit density) rather than the pit depth. For the 2024 alloy, the EIS data indicated that the rolled surface had the lowest pitting rate, while the long transverse and short transverse edges had higher rates. The higher rates for these edges reached

219

Corrosion resistance of AI-Li alloys TABLE 3.

RESULTSOF SEAWATEREXPOSURE Immersion

Fog Alloy 2024-T3 2090-T3 7075-T6 8090-T8

Partial

General pitting few deep pits pitting minor

Crevice 6 sites none 1 site 1 site

General

Interface

severe pitting "poultice" "poultice" minor

severe pitting severe severe few deep pits

Total severe pitting scattered pits scattered pits minor

similar and essentially constant values after 200 h. The angle of depression for every 8090 face was smaller than for the corresponding 2024 face. On the basis of the EIS data the conclusion would be reached that the 8090-T8 alloy had a lower overall corrosion rate and was less prone to pitting than the 2024-T3 alloy. This conclusion is consistent with visual observation of the rolled surfaces of the long term exposure panels 24 (Table 3). On the edges of these panels, the 8090 sheet had substantial areas where no visible corrosion occurred. This could be consistent with the lower overall corrosion rate and lower pitting density suggested by EIS in comparison with 2024. However, the depth of attack within each pit was as large or larger than a corresponding pit on 2024. Thus the rate of corrosion within a pit was at least as severe for 8090 as for 2024. The polarization resistance data for the 7075-T6 alloy showed a more pronounced difference in overall corrosion rate between its rolled surface and its edges, with the edges having consistently higher rates. After about 50 h, a similar trend was observed for the angle of depression. The results are consistent with observations made on the long term exposure panels (Table 3), which were characterized by a higher density of localized corrosion sites on the edges. According to the EIS data, the rolled surfaces of the 2090 alloys had roughly half the overall corrosion rates of the alloys they would replace (7075-T6). Similarly, both + R i s i n g Time (uV/s)

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~

750

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850

900

950

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FIG. 2. Positive rising time calculated for each of 134 noise records gathered during the laboratory testing of 8090-T8 sheet material as a function of the corrosion potential.

220

P.R. ROaERGEet al. Fraction of slow transients (%) lOOi 9o

2024T3

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the long and short transverse edges of 2090 showed lower overall corrosion rates and angles of depression than their 7075 counterparts. The resulting conclusion that 2090 had a lower pit density on its edges than 7075 was supported by the appearance of these edges on the EIS specimens at the conclusion of those experiments. In an effort to correlate the parameters calculated by the exponential decay model, 610 records of 20-min data gathered during the laboratory testing of the aluminum sheet material were compared to the results obtained on the same specimens with EIS or during the long term exposure to seawater. While the agreement between the noise patterns and the model seemed to be excellent [average goodness-of-fit = 97.2% (equation 4)], no simple correlation could be found between any of the calculated parameters and the general corrosion rates evaluated with EIS. Such a conclusion would confirm what others 25'26 had found previously, i.e. the degree of potential fluctuations at the corrosion potential is a relatively insensitive indication of general corrosion rates. Figure 2 illustrates the global behavior of the average rising time measured on all three faces of 8090-T8 sheet material for each of the noise data record gathered during the experiments, when plotted as a function of corrosion potential. These two parameters were chosen for this global representation of the results because they were thought to reflect the fundamental behavior of the equilibria being established during the continuous corrosion of aluminum specimens. It was observed that the four alloys tested behave quite differently during these 2-week experiments. The predominance of the high rising time values in the anodic fraction of these plots seems to be related to the good performance of an alloy and is probably associated with the control of the corrosion processes by passivation (anodic potentials). An electrical analogy would be an open circuit situation with fast unbuffered switching of the potential. The relative fraction of slow transients was quantified (everything that is not in the left uppermost corner of Fig. 2) and these fractions were compared (Fig. 3) to the average corrosion rates measured with EIS (Table 2). While the correlation coefficient between the two variables presented in Fig. 3 seems to be excellent (r = 0.99) the relation itself has to be interpreted with some caution since the time of exposure, which is not represented in these comparisons, would have a strong influence on the absolute values estimated for the predominance

Corrosion resistance of AI-Li alloys

221

of fast transients which were always more prevalent during the first few days of each experiment and tapered off as exposure time progressed. CONCLUSION The results obtained during the electrochemical testing of various faces of aluminum sheet material indicated that short term EIS measurements can help to predict relatively accurately the general and localized corrosion behavior of this material when exposed to sea water. A systematic analysis of 610 20-rain noise records with the exponential decay analysis technique has demonstrated that the exponential decay model describes almost perfectly the potential fluctuations observed during these experiments, thereby confirming the chaotic nature of the corrosion processes in progress. The parameters revealed during the noise analysis could additionally be globally related to the features calculated from EIS measurements or observed after long term exposure of the same alloys in a flowing sea water tank. REFERENCES 1. S.J. KETCHAMand J. J. DE LUCCIA,Aircraft Corrosion, A G A R D Conf. Proc., No. 315 (1981). 2. C . J . E . SMITH,J. A. GRAY,L. SCHRAand J. A. M. BOOGERS,New Light Alloys, A G A R D Conf. Proc., No. 444, Mierlo, Netherlands (3-5 October 1988), 3. R. G. BUCHHEITJR, J. P. MORANand G. E. STONER, Corrosion 46,610 (1990). 4. R. I. SLIFE, Corrosion 88, Paper NO. 385, National Association of Corrosion Engineers, Houston, TX (1988). 5. J. S. BENDAT and A. G. PIERSOL, Engineering Applications of Correlation and Spectral Analysis. Wiley, New York (1980). 6. J. S. BENDATand A. G. PIERSOL, Random Data: Analysis and Measurement Procedures, 2nd Edn. Wiley, New York (1986). 7. N. ANDERSEN,Modern Spectrum Analysis. IEEE, New York (1978). 8. N. ANDERSEN,Geophysics 39, 69 (1974). 9. P. D. T. O'CONNOR, Practical Reliability Engineering, 2nd Edn. Wiley, New York (1989). 10. K. HLADKY,L. M. CALLOWand J. L. DAWSON,Br. Corros. J. 15, 20 (1980). l I. M. W. KENDIG, E. M. MEYER, G. L1NDBERGand F. MANSFELO,Corros. Sci. 23, 1007 (1983). 12. D. C. SILVERMANand J. E. CARRICO,Corrosion 45,280 (1988). 13. P. R. ROBERGEand R. BEAUDOIN,J. appl. Electrochem. 18, 38 (1988). 14. P. R. ROBERGEand R. BEAUDOIN,J. appl. Electrochem. 18,601 (1988). 15. P. R. ROBERGE,E. HALLIOP,M. ASPLUNOand S. V. SASTR1,J. appl. Electroehem. 20, 1004 (1990). 16. P. R. ROBERGE,V. S. SASTRIand E. HALLIOP,Corrosion 48,333 (1992). 17. R. GRAUER,P. J. MORELANDand G. PINI, A Literature Review of Polarisation Resistance Constant (B) Values for the Measurement of Corrosion Rate, National Association of Corrosion Engineers, Houston, TX (1982). 18. M. STERN, Corrosion 14,440 (1958). 19. M. STERNand A. L. GEARY,J. electrochem. Soc. 104, 56 (1957). 20. I. EPELBOINand M. KEDDAM,J. electrochem. Soc. 117, 1082 (1970). 21. R. DE LEVIE, Electrochim. Acta 10, 113 (1965). 22. P. H. BOT'rELBERGHSand G. H. J. BROERS,J. Electroanal. Chem. 72,257 (1976). 23. J. B. BATES,J. C. WANG and Y. T. Cnv, Solid State lonics 18 & 19, 1045 (1986). 24. D. R. LENARD, J. G. MOORES, P. R. ROSERGEand E. HALLIOP, Marine Corrosion of AluminumLithium Aloy Sheet. TTCP-P-TP1 Report, Defence Research Establishment Pacific, Victoria, Canada (1991). 25. J. B. LUMSDEN, M. W. KENDIG and S. JEANJAQUET, Corrosion 92, Paper No. 224, National Association of Corrosion Engineers, Houston, TX (1992). 26. D. A. EDEN, K. HLADKVand D. G. JOHN, Corrosion 86, Paper No. 274, National Association of Corrosion Engineers, Houston, TX (1986).