The electromechanical conditions inside stress corrosion and corrosion fatigue cracks

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ter verkrijging van de graad van doctor in de technische wetenschappen

aan de Technische Hogeschool Delft, op gezag van de

Rector Magnificus, prof.dr. J . M . Dirken,

in het openbaar te verdedigen ten overstaan van het College van

Dekanen op donderdag 11 maart 1986 om 14.00 uur

door

ROBERT ARTHUR HENRY EDWARDS B.Sc, D.I.C.

geboren te Bristol, England

Bachelor of science (honours), Diploma of Imperial College

TR diss

1474

Dit proefschrift is goedgekeurd door de promotoren

prof.dr. J.H.W. de Wit

prof.dr.ir. W.A. Schultze

SUMMARY

in situ measurements of crack tip electrode potential and pH were made during stress corrosion cracking (SCC) of aluminium alloy 7075 in halide solutions and corrosion fatigue (CF) of pipeline steel in seawater. They show chat absorbed hydrogen is probably responsible for the CF effect. A simple relation was discovered between the crack tip potential and SCC growth rate in Al-7075, but this does not reveal the mechanism of crack growth. The effecL of the straining at the crack tip on the internal electrode potential was i ndetec table: the cracks behaved like crevices, They are so narrow that the walls lie close to the rest potential in the local solution. Theory shows that the local solution composition is an explicit function of the potential drop in the crack regardless of geometry. Thus for each potential drop the internal potential can be found by measuring the rest potential in the appropriate solution. The corresponding external (applied) potential can be found by adding on the potential drop. The theory agrees with experiments after correcting for changes in activity coefficient (Al) and for ion association ( F e ) .

The way in which the rest potential changes with increasing concentrations of soluble corrosion product determines the existance and extent of acidification in cracks and crevices: for Al-7075 in chloride solution the theory predic ts a critical minimum potential for crevice corrosion. The theory could be applied to wide crevices and pits using electrode k:netic data from tests which simulated the local chemistry. Pitting potentials for Al-7075 were accurately predicted.

NEDERLANDSE SAMENVATTING

In situ metingen van scheurtip-elektrodepotentiaal en -pH zijn uit­ gevoerd tijdens spanningskorrosiescheurgroei van aluminium 7075 in hal ide oplossingen en korrosievermoeing van pijpIeidingstaal in zeewater. Deze tonen aan dat geabsorbeerde waterstof waarschijnlijk verantwoordelijk is voor het korrosievermoeingseffeet. Een eenvoudige relati e tussen scheurtip-elektrodepotentiaal en spanningskorrosiescheurgroeisnelheid is gevonden, maar dit legt het scheurgroeimechanisme niet vast. De Invloed van het vervormen van de scheurtip was niet waar te nemen; de scheuren gedroegen zich als spleten. Ze zijn zo smal dat de potentiaal van de wanden altijd dichtbij de rustpotentiaal in de plaatselijke oplossing ligt. De theorie toont aan dat de locale samenstelling van de oplossing een expliciete funktie is van de potentiaalval in de scheur, ongeacht de geometrie. Dus, voor elke potentiaalval kan de inwendige potentiaal gevonden worden door het meten van de rustpotentiaal in de geschikte oplossing. De uitwendige (opgelegde) potentiaal is te bepalen door de potentiaalval hierbij op te tellen. De theorie wordt bevestigd door het experiment als rekening gehouden wordt met ion associatie (Fe) en veranderingen in aktiviteits-koefficienten ( A l ) .

Het verloop van de rustpoteential als functie van de koncentratie van oplosbaar korrosieproduct regelt of en in hoeverre lokale verzuring optreedt. Voor A1-7075 in chloride oplossing wordt een kritische spleetkorrosiepotentiaal voorspeld. De theorie voldoet ook voor brede spleten en putten, onder gebruikmaking van elektrodekinetische gegevens gemeten in proeven waarbij de lokale oplossing gesimuleerd wordt. Putkorrosiepotentialen van Al-7075 zijn nauwkeurig voorspeld.

ACKNOWLEDGEMENTS

Thankyou to everyone who helped with this work. Peter Schuitemaker, Jan Rademaker, Tine Baerentsen and Derek Riehm carried out experiments Technical work was cheerfully undertaken by Fred Onneweer, Chris v Beekuji and the people in the Werkplaats Metaalkunde. Anneke van Veen did the typing without complaining about the frequent text changes. Jan Pehleman and Geert van Slingerland did the nice diagrams. Prof, de Wit, Prof. Schultze and ir. Bakker made helpful suggestions.

HOW TO READ THIS THESIS

If you are already familiar with the field of stress corrosion, corrosion fatigue and localized corrosion in general you need not read the introduction - go straight to chapter 2. Others should read the introduction first.

Chanter 2 is the core of the thesis and serves as an "executive summary" of the rest. The remaining chanters should be read as appendices, givina more detail for those interested in specific aspects of the work.

Chapters 3, 5 and 6 give more discussion and details of the experimental techniaues, whereas chapters 4 , 7 , 8 and 9 give details of narts of the theory in chanter 2.

Each chanter is followed by ibs own list of references.

CONTENTS

Chapter 1 Introduction

Chapter 2 Electrochemical conditions inside stress corrosion cracks, corrosion fatigue cracks and pits.

{Based on a paper delivered at "Predictive capabilities in environment sensitive cracking", Miami, Florida, Nov. 1985).

Chapter 3 Determination of crack tip pH and electrode potential during corrosion fatigue of steel.

(Paner deliverd at "Solution chemistry within pits, crevices and cracks", M.P.L. Teddington, England, October 1 9 8 4 ) .

Chapter 4 Conversion of potential vs. depth scans inside cracks into plots of current density on the walls.

(Technical note to be published in "Corrosion"-NACE).

Chapter 5 Improved in situ technigues for corrosion fatigue of steels in seawater.

(UDdate of chapter 3 ) .

Chapter 6 Potential drops and concentration changes in stress corrosion cracks in 7075 alloy in halide solutions.

(Paper deliverd to "Control and exploitation of the corrosion of aluminium alloys", Cranfield, England, April 1983).

Chapter 7 Licruid junction notentials.

A semi-empirical estimate of individual ion activity coefficient ratios in concentrated chloride solutions.

Program listing for calculating crack tip composition in alumini alloys in NaCl solution.

Chapter 1 Introduction

STRESS CORROSION AND CORROSION FATIGUE

The in situ measurements in this report were carried out on growing stress corrosion and corrosion fatigue cracks. Stress corrosion cracking (SCC) and corrosion fatigue (CF) can be regarded as forms of localized corrosion in which the reaction at the crack tip is stimulated by the local mechanical stresses and strains. The maanitude of the local stresses and strains around the crack tip is described by the stress intensity factor, K, which takes into account the applied load, the specimen geometry and the crack length. In the case of SCC, the presence of the environment makes cracks grow even though the stress intensity at the crack tip is below the critical value, K , needed to propagate the crack in an inert environment. In the case of commercial alloys based on the Al-Zn-Mg system (1000-series a l l o y s ) , the rate of SCC crack growth rises rapidly as the stress intensity increases above a threshold value (K ) out as K is approached, the crack growth rate reaches a limiting value. This is alternatively referred to as the "plateau" or "stress-independent" or "region II" crack growth rate. Host work on environ­ mental effects in SCC have been carried out in this region of stress intensities.

Fatigue is another form of "subcritical crack growth" in which cracks grow at stress intensities below K when they are subject to a varying stress. For a regular loading cycle, the growth rate depends on the range of stress intensity, AK. Corrosion fatigue seems to show two forms: "stress corrosion fatigue" occurs when Darts of the stress intensity cycle exceed K, . However,

J

-

x

* iscc

the CF system investigated in this work; piDeline steel in seawater; hardly disDlays SCC at all. The behaviour is more like the second tyne of CF known as "true corrosion fatigue": the environment increases the crack growth rate by an approximately constant factor over a wide range of AK,

1.2

CRACK GROWTH MECHANISMS AND CRACK TIP CHEMISTRY

The presence of the word "corrosion" in SCC and CF merely indicates that the phenomenon is caused by a corrosive environment acting toaether with the stress: crack advance need not be caused directly by dissolution of the metal. Several other mechanisms have been proposed: for example, the adsorption of molecules from the environment on the metal surface at the crack tip could either helo or prevent dislocation emergence. The result could be localized weakening or embrittlement. This might account for the difference in crack growth rate between tests in air and vacuum, but it is difficult to see why, according to this theory, crack growth rate should be faster in specific corrosive environments than in air or in a passivating solution. Another proposal is that the formation of corrosion product on the fresh surfaces of a CF crack tip prevents the crack re-welding itself during the compressive part of a load cycle. Again, this explains the difference between air and vacuum, but there is the objection that any sort of oxidation should suffice, so it is difficult to explain why, for example, corrosive environments generally give faster CF crack growth rates than passivating ones.

The mechanisms which offer the most convincing explanations are ones in which crack advance is caused either directly by dissolution or indirectly by hydrogen embrittlement. Hydrogen is known to enter metals when the cathodic reaction of hydrogen ion reduction occurs on the surface. For a dissolution theory to be tenable, there must be some reason why the dissolution should be most rapid in the direction of crack propagation, and of course the electro­ chemical conditions at the tin should be conducive to rapid dissolution. For a hydrogen embrittlement theory, the metal must suffer a loss in strength as a result of hydrogen absorption, and the electrochemical conditions must be such that hydrogen is produced at the crack tip, and is allowed to enter the metal before it is all evolved as bubbles.

In order to test whether the appropriate condi tions are fulfilled, investigators carry out crack tip simulation tests on metal surfaces in open solution, for accessibility. For example, the repassivation behaviour of the tip, which is crucial to the slip-dissolution model of SCC, has been extensively investigated, often by scratching the passivated surface of an electrode and recording the resulting current transient. Another example: hydrogen input during corrosion of an alloy sheet has been monitored by detecting the hydrogen which emerges from the other side, and the effect of corrosion-induced hydrogen on mechanical properties is found bv exposing small specimens to corrosion before polishing away the surface and measuring their elongation-to-fracture.

1.3

There are many theories which attempt to account Quantitatively for crack growth rates, and the most realistic ones are drawn up on the basis of such simulation tests. Yet almost all these tests are carried out in the solutions which are used as external solutions in SCC or CF tests, although it is well known that the solution in contact with the crack tip may be quite different. This means that the results of the simulation tests can hardly ever be applied with confidence in the crack growth rate models.

The reason for the lack of testing in realistic solutions is that there was only a Qualitative idea of how the solution composition changed inside a crack. Acidification in SCC cracks was first measured by B.F. Brown and co-workers around 1968, although it was well-known to exist in other forms of localized corrosion well before then. Some investigators subsequently acidified the solutions in simulation tests in an attempt to come closer to the situation at the crack tip. However, it will be seen in the light of this report that adding, say, HCl to a salt solution will not give the same solution composition as exists at a crack tip, where acidification is caused by formation of soluble corrosion product. Besides the point was sometimes missed that the pH at the crack tip depends on the applied potential.

The results and theory presented in this report can be used to make U P solutions which really correspond to those in crack tips. Thus in the future we may hope that simulation tests may form a more reliable basis for ouantitativ models for predicting crack growth rates.

More directly, the results of the in situ measurements of electrode potent­ ial and pH during SCC and CF can be used to make deductions about the mechanisms of SCC and CF, even before any simulation tests are carried out. The deductions are summarized in chapter 2 and more details are given in chapters 3 and 6.

EXISTING THEORIES OF CHEMISTRY IN SCC AND CF CRACKS

Turnbull (1) has recently reviewed this field. He cites several theories which are concerned with calculating a dissolution-rate limited SCC crack growth rate. Several assume that the anodic dissolution reactions is confined to the crack tip and the complementary cathodic reaction to the crack walls, or outside the crack. The in situ measurements in this report show that such assumptions are not valid for the systems investigated here; in fact the whole of the crack walls appear to lie close to the rest potential in the adjacent solution, so that at all points the rate of cathodic and anodic reactions is nearly equal. None of the theories were tested with in situ measurements.

Turnbull himself (2) has developed an elaborate numerical model for a oarallel-sided crack in salt water (SCC and CF cracks actually approximate much better to wedge shaped cracks - see chapter 4 ) . The rates of the anodic and cathodic reactions were determined from the electrode potential and the calculated solution pH on the basis of polarization curves measured in salt solutions with HC1 or NaOH added to change the pH. Such solutions probably show different anodic behaviour to that inside a crack, where the pH is de­ termined by the concentration of soluble corrosion of soluble product (e.g. F e C l2 or N a F e O H . ) . Furthermore, only diffusive transport of the reaction products was considered, which limits the applicability to small changes in solution composition. The theory provided some useful predictions, especially about cathodic protection, but it is numerical and specific to steel and a one-dimensional geometry, so cannot be very generally applied.

Beck (3) has produced a sophisticated dissolution model which predicts SCC crack growth rates in titanium alloy. Almost uniquely, some care was taken to make sure the solution used in the simulation tests was something like what might exist at a crack tip. This makes the model more convincing than most from the electrochemical point of view; the biggest conundrum is why plastic flow around the crack tip should concentrate dissolution to a reaion much narrower than the radius of the crack tip. However, whatever its merits as theory of crack growth, all the action takes place within a milli­ meter of the crack tiD, so the model cannot be used to calculate concentration gradients in the rest of the crack.

No one apnears to have attempted a theory for concentration changes inside a CF crack, nrobably because very little is known about the effects of solution pumping. Hartt (4) predicted that solution pumping would suddenly become more effective as the loading frequency is increased above a critical value.

At low frecmencies laminar flov; means that the solution drawn into the crack during crack opening tends to be the same as has just been expelled during crack closure, but at higher frequencies turbulence causes mixing with the external solution. Previous work at Delft (5) indicated that for the corrosion

fatigue conditions in this work, the critical frequency lies in the region of 2 to 10 Hz for a stress ratio (R = Kmin/Kmax) of 0.1. The tests in chapters 2 and 4 were carried out below the critical frequency at 1 H z . Furthermore, the stress ratio was 0.7, for which one would expect even less mixing. For these conditions, solution pumping does not seem to affect the solution composition inside the crack, because when the fatigue was stopped the conditions at the crack tip did not change. This is why it is possible in chapter 2 to use essent­ ially the same theory to predict CF as was used for SCC. The theory is also valid for narrow crevices. Of course, this also means that it might be possible to apply a theory of crevice corrosion from the literature to explain how the solution composition inside a crack should vary with applied potential.

1.6

CREVICE CORROSION AND PITTING THEORIES

In crevice corrosion there is no mechanical crack opening; the crevice is formed by the gap between two components or by corrosion under a damaged coating. Preferential corrosion inside the crevice is a result of the solution composition changes which take place inside the "occluded cell" formed by the crevice.

Remarkably few theories have been formulated specifically for crevice corrosion. Hebert and filklre (6) formulated one to calculate the initiation time f or Al crevice corrosion in a particular geometry and Oldfield and Sutton pro­ duced a model with a similar aim, for stainless steel. Both models assumed that crevice corrosion would initiate when a critical pH was reached inside the crevice and showed satisfactory agreement with experiment. However, the choice of the critical pH is somewhat arbitary, since the oxide film does not suddenly break down at a precise D H . The models are for a specific geometry, for ooen circuit conditions and do not attempt to calculate a final concentration distribution, so they cannot be applied to calculating the concentration changes inside SCC and CF cracks for various applied potentials.

Vermilyea and Tedmon made a fairly simple theory for iron in NaCl-solution (7_) . They predicted the potential and solution composition at the bottom of a

crevice as a function of the current density, for a one-dimensional crevice with inert walls. The chloride ion concentration was made a function of potential drop, in the same way as in the "ideal" theory in chapter 2. They calculated the potential distribution using ohm's law, and an approximate solution conductivity deduced from the chloride ion concentration. There was good agreement with experiment. However, by trying to relate the crevice tip potential to the current density instead of the external potential, the authors were forced, in common with all the other models, to restrict it to a particular geometry which is not representative of a crack.

Mostly, crevice corrosion is considered to be vaguely related to pitting, and scientists have shown more interest in explaining pitting.

In pitting the occluded cell geometry does not pre-exist: the typical near-hemisDherical pit shape is the natural result of uniform dissolution start­ ing at a point on the surface. Pitting is a characteristic form of attack on metals which rely on a passive oxide film for corrosion protection. Aggressive anions must be present in the solution, and the most universal and effective of these are halide ions. As the potential of a passive metal in contact with such a solution is made more anodic a small "passive current" may be detected which merely replaces oxide which dissolves uniformly into the solution. For aluminium in neutral solution this current is negligable . But at and beyond a critical

1.7

potential there is a sudden increase in anodic current, due to the formation and growth of pits. This is called the pitting potential, and it depends on the type and concentration of the aggressive anion. The dissolution rate is many orders of magnitude higher inside the pit than on the surface. If a fixed anodic current is applied to an initially passive surface, the potential will rise beyond the pitting ootential at first, and pits will nucleate and grow until the total surface area of the pits reaches a certain value which is proportional to the overall current. The rate of nit growth then becomes equal to the rate of re-passivation of pits, and the potential falls to the critical pitting potential. A nit thus appears to need a certain minimum load current density to survive, and under galvanostatic conditions all pits end up on the borderline between growth and renassivation. If the solution is aerated, the cathodic reaction of dissolved oxygen reduction can support, under open circuit con­ ditions, an anodic current greater than the passive current, so that after a while one would expect the rest potential to equal the pitting potential.

However, measuring the pitting potential is not as straightforward as the previous paragraph suagests. Even on pure aluminium, a rise in the anodic current, starting about 50 mV below the pitting potential, is often observed. This is caused by crevice corrosion under the specimen bolder or the screening lacquer. In an alloy there is the additional problem of compositional inhomogene-ities in the microstructure. For example, intermetallic precipitates may pit at a lower potential than the matrix, but then become etched out. Grain boundaries, or precipitate-free zones either side of them, may be enhanced or depleted in solid-solution alloying elements, depending on the heat treatment. In some cases they remain unattacked, but in others intergranular corrosion ensues. This may start as a line of pits and develop into a form of crevice corrosion.

There have been some misfounded attempts to investigate pitting by examining the structure of the oxide film, on the basis that defects might be aggrevated by the adsorption of aggresive ions. But experiments have shown that below the pitting potential pits will not form, even if the oxide layer is damaged mechan­ ically. More evidence againt this viewpoint is the fact that the pitting potential of aluminium alloys is not changed by the presence of comparatively noble particles in the microstructure, which cause disruption of the oxide film.

The gradual change of pitting potential with increasing contents of solid solution alloying elements suggests that the pitting potential is related to the thermodynamics of the corrosion process inside the pit. Keasche combined this idea with the proposal that a thin salt layer is necessary for pit stability.

ï.a

If a metal chloride layer is formed in the pit instead of oxide, repassiv-ation would be prevented . He calculated from thermochemical data the revers­ ible electrode potential for the formation of AlCl , AlBr and M I , . Each value turned out to be about 350 mV more active than the equivalent pitting potential, so that some relationship seems to exist. Vermilyea came closer (10)

(within 100 mV) to the measured pitting potentials for a number of metals by estimating the potential at which the formation of a chloride layer become thermodynamically as favorable as oxide formation, assuming that the pit was saturated in metal chloride at the interface.

Kaesche (S) reasoned that if a salt layer existed at the interface, the rate of dissolution would be controlled by the rate at which the salt layer was dissolved away. He assumed this was controlled by simple diffusion of Al , and by solving the diffusion equation, estimated the minimum rate of dissolution which would maintain a saturated solution of AlCl at the base of the pit. The equivalent anodic current density aqreed reasonably with experiment. In fact one can only ignore migration and consider simply diffusion if the aluminium ion concentration is small compared with that of NaCl, which then acts as a supporting electrolyte. In the case of near-saturated AlCl- this is obviously not the case: the transport of Al is aided by migration in the electric field. If Kaesche had taken this into account, his estimate of the critical current density would have been higher by a factor of between 2 and 4. The agreement with experiment is still satisfactory, considering the errors involved in neglect ing changes in activity coefficients. Other workers have produced similar models, as discussed in chapter 2.

Galvele considered the initial stages of pitting, and considered a one-dimensional pit with passive walls. Again, only diffusion was considered, but in this case less concentrated AlCl solutions were dealt with» because he proposed that all that was necessary for pit stability was that the pH of the solution at the pit base should be lowered Dy hydrolysis to a point where more soluble corrosion products were formed than insoluble ones. This implies that a salt layer is not necessary for a stable p i t : a rapidly-dissolving oxide layer is sufficient. The conflict between "salt-layer" and "soluble oxide" theories is resolved at the end of chapter 2, where it is proposed that an aluminium hydroxychloride layer precipitates and prevents repassivation,at about the Al concentration which Galvele proposes is necessary to start form­ ing mostly soluble corrosion product. Cross out "aluminium chloride" in the salt-layer theories and replace it with "aluminium (hydr-)oxychloride" and most people should be happy. The new theory gives much more accurate predictions of pitting potentials than previous theories for pitting in aluminium, b u t this is partly because it uses empirical data from pit simulation tests to estimate the potential inside the pit.

As far as applying existing theories to predicting solution changes in cracks is concerned, the only theory which could be of much use is the recent one produced by Strehblcw (12) which starts off the same as the simple ideal theory in chapter 2. All the others are too much involved with pitting geometries, and make poor assumptions like neglecting migration,

1 .10

DEVELOPMENT OF THE PRESENT THEORY

The first aim of the theory was to explain the changes in crack tip pH which were measured. The first version of the theory f o m e d the final part of a paper delivered at a conference in 1903, which now forms chapter 6. However, it is not necessary to read chapter G first because the complete theory is expounded from scratch in chapter 2. It does not derive from any particular theory in the literature. Since no suitable theory seemed to be available "off the shelf", it was worked out from first principles. It turned out that by not aiming to calculate current densities (which were not measured in the tests) the theory gained the great advantage of not being tied to any particular geometry. This led to the possibility of extending the theory to predict crevice and even pitting corrosion.

The first version only attempted to explain the relation between the crack tip pH and the potential drops in cracks during SCC of aluminium alloy*. Although the theory was qualitatively successful, it became clear that changes in activity coefficient were of great importance in this system, and these could not be quantitatively considered in this simple model. The full treatment, shown in chapter 2 (1985), rectifies this shortcoming, but then goes a lot further:

1. It corrects for changes in individual ion activity coefficients.

2. It adapts the theory f or the iron/saltwater system, which reauires a different deviation from ideal behaviour to be corrected: namely ion association. 3. The potential inside a crack is related to the solution composition using

empirical data. This means that the potential inside the crack can be related to the potential drop and thus to the potential outside the crack. This relation is compared with the experimental measurements.

4. The theory also applies to narrow crevices. The solution chemistry and potential inside crevices in iron and aluminium alloy can be calculated for various applied potentials. In the case of aluminium it is shown that there is a critical potential for crevice corrosion.

5. The theory is extended to predict pitting potentials in aluminium alloys, using more empirical data from tests which simulate the local chemistry. Accurate predictions of pitting potentials in aluminium alloy are obtained.

Since the metal is highly conductive, the potential drop in the solution in the crack must be equal and opposite to the difference between the electrode potentials measured at the crack mouth and tip.

1.11

REFERENCES

(1) Turnbull, A., Reviews on coatings and corrosion, 5.(1982), No 1-4, pp. 43-171. (2) Turnbull, A. and Thomas, J.G.N., MPL DMA report no All (1979).

(3) Beck, T.R., "The theory of SCC in alloys" (Ed. Scully) NATO-SAD, Brussels, 1971, p. 6 7 .

(4) Hartt, W.H., Tenant, J.S. and Hooper, W.C., "Corrosion Fatigue Technology", ASTH STP 6 4 2 , 1978, p. 5.

(5) Ewalds, H.L. and Edwards, R.A.H., "The effect of crack surface corrosion product on fatigue crack growth".

(6) Hebert, K. and Alkire, R. , J. Electrochem. Soc. 130, 5_(1983), p p . 1007-1014. (7) Vermilyea, D.E. and Tedmon, C.S., J. Electrochem. Soc. 117, 4 ( 1 9 7 0 ) , P . 437. (8) Nisancioqlu, K. and Holtan, H., Corrosion Science, 18(1978), pp. 835-844. (9) Kaesche, H., 2. Phys, Chemie N.F., 2 6 ( 1 9 6 0 ) , pp. 138-142.

(10) Vermilyea, D.E., J. Electrochem. Soc. 118, 4 ( 1 9 7 1 ) , pp. 529-531. (11) Galvele, J.R.,

Chapter 2

"ELECTROCHEMICAL CONDITIONS INSIDE STRESS CORROSION CRACKS, CORROSION FATIGUE CRACKS AND PITS"

by R.A.H. Edwards

Based on a paper presented at

"Predictive capabilities in Environment Sensitive Cracking", Miami, Florida, Nov. 1985, A.s.M.E.

ABSTRACT

In situ measurements of crack tip potential and pH are presented for SCC of an aluminium alloy in halide solutions and CF of pipeline steel in seawater. The evidence shows that absorbed hydrogen is probably responsible for the environment component of the CF. A simple relation was revealed between the crack tip potential and the SCC growth rate in aluminium alloys, but no conclusions about mechanisms were possible.

A simple analysis shows that where convection can be neglected, there is an explicit relation, independent of geometry, between the potential drop in a crack and the steady-state composition attained by the solution at the crack tip. Important modifications are necessary in concentrated solutions. In the case of aluminium in chloride solution there is a large effect due to changes in the activity coefficients of the ions. For iron, the effect of ion associ­ ation in iron chloride solutions is more important. Both effects tend to limit the concentration changes in the crack.

Often, a crevice or crack approximates to a "most occluded cavity", in which the internal and external electrode potentials correspond to the open circuit potentials of the metal in the respective solutions. Then it is possible, using simple measurements of open circuit potentials in various solutions, to extend the theory to predict the crack tip potential as a function of the ex­ ternally applied potential. By comparing the change in the open circuit potential produced by increasing concentrations of soluble corrosion product with the potential dron needed to sustain these concentrations at the crack tip, one can analyse the stability of localized corrosion.

NOMENCLATURE

a

C D E F h I J Ki activity concentration diffusion coefficient potential Faraday's constant hydration number Ionic strength (- Zen2] flux vector

first ion association constant

K2 n R S r T 0 V Y V

second ion association constant charge number of an ion qas constant

dependence of d» on I

f V

temperature absolute mobility

"qrad" (gradient vector operator) activity coefficient

oartial molar volume

*

limiting $ at infinite dilution

2.3

1. INTRODUCTION

This paper presents the results of some in situ measurements of crack tip potential and pH during environment sensitive cracking of steel and aluminium alloy, together with an outline of a simple theoretical approach to the problem of predicting the crack tip environment and electrode potent­ ial for given external conditions. The theory does not attempt to predict how long it takes for a given environment and potential to be established at the crack tip: it confines itself to predicting the final time-independent situation obtained under steady external conditions. Because the theory con­ centrates on the direct relation between potential drops and concentration changes it is applicable to any localized corrosion geometry, subject only to the condition that transport by convection may be neclected.

1.1. In situ measurements and crack growth rates

In environment sensitive cracking the environment to which cracking is sensitive is the one at the crack tip; therefore any theory which seeks to predict crack growth rates in solution must take into account any differences in composition and electrode ootential between the crack tip and the external solution. Taking these differences into account can revise our view of which mechanism is responsible for the cracking.

The classic example is the work of B.F. Brown and co-workers [1] who carried cut in situ pH measurements on stress corrosion cracks (SCC) in high strength

steel. In salt solution both anodic polarization and moderate to extreme cathodic polarization increases the SCC rate in these alloys. It was found that the pH change inside the crack compensated for the potential change as far as the over-potential for hydrogen evolution reaction was concerned; (see the -.-.- line in fig. I) with the result that there was always a thermodynamic driving force for hydrogen production inside the crack, whatever the applied potential. Their conclusion was that SCC at all potentials could be attributed to a hydrogen-assisted cracking mechanism.

Corrosion fatigue (CF) of structural and pipeline steels in seawater shows a similar response to changing potential. However, attempts to measure the pH inside growing CF cracks in ferritic steels [2,3] produced results which were consistent neither, with each other or with what one might expect from crevice measurements [4], so that the respective authors reached different conclusions regarding the growing mechanism.

2.4

Measurements by the present author [5] of crack tip pH and potential during CF of pipeline steel have, however, Droduced results which are more in line with recent measurements in crevices [4] (see fig. 2 ) . High currents flowing

from the crack walls at extreme polarization produced large iR drops, which restricted the range of variation of the crack tip potential to between -650 and -950 mv S.C.E. The acidification at the crack tip during anodic polariz­ ation was sufficient to cause a slight increase in the hydrogen reduction over-potential (represented by the distance below the hydrogen line in fig. 1 ) , so that a hydrogen-assisted fatigue mechanism may be postulated for all applied potentials in seawater.

A hydrogen-assisted cracking mechanism could also explain the potential deoendence of CF crack growth rates measured in a variety of buffer solutions: the growth rate only exceeded that in air when there was an overpotential for hydrogen evolution. The crack tip pH measurements showed that the buffer sol­ utions were effective in preventing pH changes inside the crack. Transient crack growth rate effects which were observed after a sudden change in crack tip potential were consistent with hydrogen transport into the plastic zone ahead of the crack tip.

In situ measurements bv the author of crack tip potential and pH during SCC Of 7075 aluminium alloy in h a H d e solutions [6] did not lead to definite conclusions about mechanisms. However, they shed new light on the apparently complex response of the crack growth rate to changes in the external electro­ chemical conditions. Fig. 3 shows the effects of changina external potential on the region II (stress-independent) crack growth rate in 7075-T651 alloy in aqueous solutions of NaCl, KI and H I . Above the pitting potential in KI and NaCl solution, and in HI solution, the crack growth rate was independent of the applied potential. The in situ measurements of crack tiD potential shown in fig. 4 explain why this should be so: in these cases the crack tip potential also does not change. In fact, correcting the results in fig. 3 for the potent­ ial drop in the crack results in a single line of crack growth rate against crack tio potential, as shown in fig. 5. Fig. 4 shows a levelling-off of the dependence of crack tip potential on externally applied potential in the extreem cathodic range, as well as at anodic potentials. If, as suggested by fig. 5, the crack growth rate is a simple function of the crack tiD potential, then one would expect to see a constant minimum crack growth rate approached at extreme cathodic applied potentials. Such an effect has indeed been reported for high purity Al-Zn-Mg alloy [7], but in 7075 alloy the crack growth rates are so slow at these cathodic potentials that they can hardly be measured.

1) The pH values were measured using the microelectrode technicrue in chapter 5. 2) Further experimental details in chapter 3.

2.5

The simple monotonie increase in crack growth rate as the crack tip potential is made more anodic immediately suggests a dissolution mechanism of SCC. Un­ fortunately, such a straightforward deduction cannot b e m a d e , because hydrogen permeation into 7075 alloy has been reported to increase with anodic as well as extreme cathodic polarization [ 8 ] . In fact the most cathodic potential re­ corded at the crack tip approximately eguals the potential of minimum hydrogen permeation, so that the increase in crack growth rate for less cathodic potent­ ials could well be caused by an increase in hydrogen permeation rate. Thus either a hydrogen-assisted cracking mechanism or a dissolution mechanism could explain the results.

The potential drop changed sign with the current delivered by the potentio-stat, so that the crack tip potential was closer to the open circuit potential than the crack mouth potential. This observation is at odds with some SCC theories (e.g. ref. 9} which reouire that the crack tip remains at an almost constant, active, potential (corresponding to the mixed potential of bare metal) for all external potentials.

In the anodic region the crack tip potential remained constant for all applied potentials above the pitting potential whereas in the cathodic region the rate of change of tip potential with apiplied potential gradually decreased at increasingly cathodic potentials. Thus the crack tip can only be polarized within a certain range of electrode potentials.

The crack tip could be polarized to more positive values in the iodide solution because of the more positive value of the pitting potential. The potential drop arises from the passage, through the electrolyte resistance in the crack, of currents drawn from or to the crack walls and the crack tip. Under open circuit conditions the average potential at the crack tip was found to be of the order of 10-50 mV more negative than at the crack mouth (precise measurements were difficult because of the drift of both potentials with t i m e ) . This potential difference could be due to differential aeration, as well as a dissolution current from the crack tip. Under impressed potentials, the current arising from crack tip dissolution has a negligible effect on the potential drop compared to the currents flowing from the crack walls. The rapid increase in anodic current density in the crack walls nearest the mouth caused by pitting is obviously responsible for the flattening of the tip potential curve at anodic potentials. The applied potential above which no further change in the crack tip potential occurs was also the potential at which a discontinuous increase in current was recorded. This discontinuous increase in current is usually taken to mark the pittlnq potential, although in 7075 alloy there is a considerable anodic current before this potential is attained. In fact, the discontinuous

increase in current means that it is impossible to polarize even the outside of the specimen beyond the pitting potential. Setting on the potentiostat a ootential which is more anodic than the pitting potential merely produces ohmic potential drop in the solution, which results in a difference in potent­ ial between the mouth of the Luggin tube and the specimen surface - without significantly changing the electrode potential at the surface itself.

200

--600

-■ " - .CP H , =

',»

\

4* ^

-■400

-600

1000

PH

Fig. 1. Relation between crack tip potential and crack tip p H , superimposed on simplified Pourbaix diagram (non-hydrated corrosion product, C = 10--1 M) .

Bold curve shows, for various FeClo solutions in the presence of iron powder, the O.C. potential of iron against pH of the solution [21]; -.-. Measured crack tip conditions for high strength

steels in 0.6 M NaCl [l]J

+ In-situ measurements by the author during corrosion fatigue of pipeline steel in ASTM seawater; • Similar, but for stationary CF crack shaded area Measurements in an simulated corrosion cell of

mild steel in 0.001 M NaCl [21], pH 12.

tig. 2. Crack tip potential as a function of externally applied potential: Artificial crevice in structural steel, 0.6 H NaCl i; + Measurements by the author during corrosion fatigue of

pipeline steel in ASTM seawater;

0 Similar, but without fatigue;

- Bold line shows calculated potential drop for "completely occluded crevice", using Fe-Cl association constants K, = 6

da dt fm/s)

7075-T651

TL direction. K= 16-18 M P d \ / m results from Speidel o»

Nguyen et-al. ♦ present work D

— Ee x t e r n a (l m V S C E'

Fig. 3. Region II (stress-independent) crack growth rates in 7075-T65I as a function of applied potential.

E tip [mVSCEJ 1 -6Q0 -acn ■1000

_

5M 707S-T651 25c TL direction K=l crack length 13-t\ t p H = O l -n ptatC 3-21 MPal/m 8 mm from no

sS

ch

S

v

'/

(PH 6 L # ^ OC pottnr.tial Eo c

/

/

/

, ' / ^

-_

-Ep i t " Ee . t e m a l| r n V S C E'

Fig. 4a. Crack tip electrode potential measured as a function of externally applied potential in 8M KI solution and in 5M HI solution.

Etip t

(mVSCE) 0 6 M N a C l

hour between measure

day between measurements

--"°"

o< ■ — measurements /

/

/

/

/,

/

/ +_ + o - o - o . nents ' '

r

a plastic film method

lOdays between measurements o open method lOdays betv^?en

measurement

-600 Ee x tl m V S C E )

Fig. 4b. Crack tip electrode potential measured as a function of externally applied potential in 0.6 M NaCl solution. For comparison the broken line shows E on the E . scale.

ext tip dt

[m/s

I d

3

i n '

i n

5

10

6 107

i n

8

i n

9 7 0 7 5 - T 6 5 1 TL direc " points

-I M N a C -I 0 /

o

lion

com

. K» 16-21 MPaVrS

Speidel o o Nguyen et al O present w o r k D

re

J /"5MKJ

/o

r

Q f

□

'

5. Region II (stress-independent) crack growth rates in 7075-T651 as a function of the crack tip potential (estimated from figs. 3 and 4 ) , for chloride and iodide solutions.

2.10

2. THE RELATION BETWEEN POTENTIAL DROPS AND CRACK TIP ACIDIFICATION

Turnbull [10] has reviewed theories for modelling electrochemical con­ ditions in pits, crevices and cracks. The object of most theories is to pre­ dict dissolution rates, so they concentrate on calculating current density as a function of position and time. Almost all the theories neglect the effect of convection, ion-ion interaction effects on migration and activity coeffic­ ients. Additional simplifications, such as neglect of migration or diffusion often have to be made to produce analytical solutions. The theory below is analytical, but it remains simple because it does not attempt to calculate the current density distribution, but concentrates on a direct relation between potential drops and concentration changes, which, under the conditions imposed, turns out to be independent of geometry. The theory has been foreshadowed by the direct relation between potential and anion concentration used by Vermilyea and Tedmon in their "simple crevice corrosion theory" [11]• However, they re­ stricted the applicability of their theory to cases where the crevice walls were completely inert and parallel sided, whereas the relations below apply to any geometry. The oresent theory deals with aluminium dissolving in NaCl sol­ ution, but the same basic arguments could be applied to many systems.

If transDort by convection can be ignored, then the movement of an ion under the combined influence of an electric field and a concentration gradient can be described by the general form of the Nernst-Planck equation [12];

J = - — . C . (RTV In a + nF VE) (1) RT

The first term in the bracket represents the free energy gradient caused by the changing activity of the species; the second term represents the energy gradient due to the changinq of electrical potential.

The use of a constant for D implies neglect of the drag which results from short-range interactions with other moving ion species. This simplific­ ation is commonly adopted in theories of localized corrosion; the effect of ion-ion interactions in concentrated solutions will be discussed later.

Since sodium ions and chloride ions are not created or consumed during the corrosion process, their steady-state fluxes must be zero. Provided these ions are completely dissociated and do not indulge in any homogeneous reactions we can write simply:

V(ln a) = — VE (for N a+, Cl~) (2)

Now, the gradient vector V(ln a) is a scalar multiple of V E , so the two vectors must lie in the same direction. Therefore there is a simple relation between the rate of change of activity and the rate of change of potential, moving along any line in the solution.

This equation can be integrated between two points at potentials E and E o 1 give :

(5)

If '■{ and Y , are the activity coefticients of the species at activities a

o i - 0

and a respectively, then:

E )1 (for Na , Cl ) '1 '

If we take C and E to be the concentration of NaCl and the potential in the bulk solution respectively, and E, - E is the potential droD, A E , in the

1 o -crack, the C. represents the concentration of Na or Cl at the tip. Note that the relation is independent of geometry: geometrical factors only affect the current density reauired to sustain a certain AE. According to this equation, the chloride ion concentration should rise towards an anode, and the sodium ion concentration should fall.

For a pH of less than 3, most of the dissolved aluminium is oresent as Al . The hydrogen and hydroxyl ion concentrations will be controlled by either hydrolysis or the hydroxide precipitation eauilibrium and will in either case be much smaller than the Al concentration. So to preserve charge neutrality we can say to a good approximation:

[Al3 +] = l/3([Cl"] - [Na+])

3+ Co Y 'C l^ Y 'N a +

The potential droD, AE, in this equation is one and the same thing as the ohmic drop in the crack; the current in the crack can be found by adding the ion fluxes given by equation 1 (multiplied by the respective charge number of each i o n ) , and this would correspond to the value found using the overall solution conductivity. It is misleading to call AE a diffusion potential, because this suggests that it arises only when there is an unequal mobility of anions and cations, which is not true. It is true that diffusion potentials

(or, more generally, liouid junction potentials) can cause errors when one attemots to measure AE. In many experimental set-ups there will be an ohmic drop between the reference electrode in the bulk solution and the mouth of the crack. This ohmic drop contributes little to the acidification because convect-ive mixing tends to keep the solution homogeneous outside the crack.

If all the activity coefficients were equal to one, as almost all localized corrosion theories assume, than equation 7 would reduce to:

aAj3+ = [Al3 + ] = 2/3 CQs i n h (^ AE) (ideal) (6) Note that, for a given potential drop in the crack, the crack tip aluminium

ion concentration is proportional to the external salt concentration and in­ dependent of halide ion type. Pig. 6 shows how the concentration of sodium, chloride and aluminium ions should vary with potential drop, according to eauation 8. For an external NaCl concentration of 0.6 M, the dashed line on fig. 6 shows an ideal calculation of the pH corresponding to the Al con­ centration found usinq eauation 8. Following the ideas of Sedricks et al. [ 1 3 ] , this calculation assumes that the hydroxyl ion concentration in the crack is determined by the solubility product of freshly precipitated aluminium hydro­ xide corrosion nroduct [13] This ideal calculation appears to explain why most workers have reported pH values between 3 and 3.5 in actively corroding aluminium oits and crevices: a potential drop of only a few millivolts is sufficient to give a pH of about 3.5, but larger potential drops do not apparently make m u c h difference to the pH. On the basis of such considerations it seems quite reason­ able to suppose that the crack tip might be saturated in AlCl and have a pH of about 3, as has been proposed in the past [7,14]. However, this illusion is shattered if one actually measures the pH values of AlCl., solutions. Fig. 7 shows the pH as a function of concentration before and after adding aluminium powder. Before adding the aluminium, t h e p H i s fixed by the hydrolysis equilibrium:

A l3 + + 2H 0 * A l ( O H )2 + + H+

with [H+] = [Al(OH) ] . Line 1 in fig. 7 is the pH predicted from the data-book hydrolysis constant (1 . 4x10 ) assuming unit activity coefficients.

The remarkable deviation towards lower pH values at higher concentrations can be attributed to a very high activity coefficients for Al"1 ions. As the aluminium powder corrodes, hydrogen ions are consumed by the cathodic reaction. Only when Al(OH) starts to precipitate should the neutralization process cease [13]. Even after this partial neutralization, the D H of satur­ ated aluminium chloride is about 0.6 - very much lower than the ideal calcul­ ation based on the Al(OH) solubility product (illustrated by line 2 in fig. 7 ) .

The cause of the large activity coefficients for Al is a decrease in the free energy change of solvation due to a loss of free water to the hydration shells around the aluminium ions. The "lost water effect" will increase the activity coefficients of the Ma and Cl ions, and this should be taken into account if we wish to quantify the relation between the crack tip pH (or Al concentration) and the potential drop expressed by eauation 7.

The single ion activity coefficients for Cl and Ha in mixed solutions of NaCl and A l C l , were calculated theoretically from the mean activity coefficient data for NaCl and A1C1_, . The values obtained depend strongly on how many water molecules are assumed to surround the Cl iuns. To get the best Possible estimate the procedure in appendix 1 was developed. This improves on Bates and Robinson's approach to estimating individual ion activities, which assumes that chloride ions are not hvdrated at all [15].

The procedure in the appendix was first used to obtain the single ion act­ ivity coefficients, y + and "('-,-, in the external solution. Then equation 7 could be used to find the activity of Na and Cl in the crack tip solution for a given value of AE. The concentrations of NaCl and AlCl could not be evaluated directly, because the procedure in the appendix can only be used to evaluate Y„,- and Y + as a function of these concentrations, and not visa

Cl Na

versa. Therefore the concentrations of NaCl and AlCl which would give the re­ quired activities were found by the following interactive technioue:

~Y0

As a first approximation, it was assumed that in equation 6, — = 1 for

+ + Yl

Na . Then, using this ideal estimate for the Na (=NaCl) concentration, the procedure in the appendix was used to calculate a ._ in mixtures containing different AlCl- concentrations, until the required activity of Cl" was arrived at by successive approximation. The A l C l , concentration was then held constant and the NaCl concentration was changed until the correct a + was computed for the

Na

mixture. This improved estimate of the NaCl concentration was used to find a better estimate of the A1C1-; concentration, and so on.

* For pendants who do not think single ion activity coefficients are meaningful, there is the point that eauation 7 only actually uses ratios of activity coefficients.

In practice it was never necessary to repeat the iteration more than three times before successive estimates agreed to better than 1%. The computer program is shown in chapter 3.

Fig. 8a shows, as a function of the potential difference, the computed concentrations of A l3 +, Na and C l " ions as a function of AE, for CQ = 0.6 H.

Fiq. 8b shows the same graph calculated without the correction for activity coefficients (i.e. usinp eauation 8 ) . According to both calculations the sodium ion concentration rapidly falls to a negligible value, so that the solution in the crack becomes virtually pure AlCl,.

To see the effect of the correction in practice we can compare the predict­ ions of the corrected and ideal theory for the acidification of the crack tip under anodic polarization. As stated above, the crack mouth can never be polar­ ized beyond the pitting potential. In this case "pitting potential" means the potential at which the current from the specimen shows such a steep rise that an iR drop appears between specimen and reference electrode. This potential decreases with time as the area of pits increases. The initial potential would b e about -720 raV, corresponding to the potential at which a steep rise current takes place in a potentiokinetic test at 3 mV/min [23]. This would be maintained until the pits become large enough to bring the potential down to the pitting potential of the matrix. At this point some pits are repassivating to all others to keep growing whilst maintaining a constant area. Pits located in susceptible areas of the microstructure, such as the solite-supersaturated precipitate-free zones around the grain boundaries, survive at the expanse of those in the matrix As a result, the pits come to occupy more electonegative areas of the micro-structure, and the pitting potential falls. The final rest potential lies at around -800 mV in aerated 0.6 M NaCl solution.

Whilst the potential at the mouth falls from -720 to -800 mV the potential at the tip, according tc the measurement in fiq. 4b, falls from -800 mV to about -850 mV SCE. Thus the potential drop in the crack falls from about 80 mV to about 50 mV.

For these potential drops the ideal theory predicts A l C l3 concentrations of 3.1 M (saturated) and 1.4 M, corresponding to pH values (in eouilibrium with Al powder, fig. 7) of 0.6 and 2.7. The corrected theory gives concentrations of 1-8 M (little more than half-saturated) and 0.96 M. The corresponding pH values are 2.2 and 3.2.

Although there is a lot of scatter in the experimental determinations of the crack tip pH, it is possible to see that the ideal theory overestimates the aluminium chloride concentration and underestimates the crack tip. pH.

The author's own measurements [6] during anodic polarization in 0.6 M NaCl gave pH values about 3, but Nguyen et al. [16] have reported pH values of 1.8 and 2.4 at the crack tip. for specimens at ootentiostat settings more positive than the pitting potential in their 1 M NaCl test solution. These workers did not attempt to measure the potential drop in the crack tiD, but one may suppose it was slightly smaller than the 30 raV measured in 0.6 H NaCl. The predicted pH would not be much different. Curiously, Nguyen et al. measured Al concen­

trations of 0.4 and 0.3 M at the crack tin, which would not give the same D H values as they measured, if one assumes that the aluminium chloride solution in the crack tip has had plenty of time to react with the crack walls and partially neutralize itself as described above.

The presence of significant Quantities of Hg and Zn in the crack tip solution should cause a slight increase in oH: they help to make up the differ­ ence between the Cl and Ha ion concentrations to preserve charae neutrality, but they are not hydrolysed strongly enough to contribute to acidification.

Fig. 6.

POTENTIAL DROP (mV)

An ideal prediction of concentration changes in a localized corrosion cavity in aluminium, as a function of potential drop (eq. 8 ) . Dashed line shows corresponding ideal pH prediction (see text) for C = 0.6 M

* ( « ]

Aluminium po pH m.asurtd

1

;der added to AICI3 solutions alter + 0 hrs O t hrs o 2C hrs □ max pH OOi 006 008 01 yci3] (r Dis dm3]

ss,'

Measured pH values for aluminium chloride solutions of various concentrations, and rise of pH with time following addition of aluminium powder. Line 1: pH predicted from hydrolysis equilibrium; Line 2: pH predicted from solubility product of

A l ( 0 H )3 (see text).

x: final pH of solution in conti th 7075 block (section 6 ) .

A E I V I

Calculated concentration changes inside an aluminium localized corrosion cavity in 0.6 M NaCl solution, taking into account changes in activity coefficients.

As fig. 8 a . but not taking activity coefficient changes into account.

3. APPLYING THE THEORY TO CRACKS IN IROM: ION ASSOCIATION

T u m b u l l [17] has shown that the dissolved oxygen concentration in a corrosion fatigue crack falls rapidly to a negligible value, at least for loading frequencies of 10 Hz or less. So it should be a good assumption that the tins of narrow crevices and stress corrosion cracks are completely deaer-ated. In the absence of dissolved oxygen, and in the range of potentials which can practicably be applied to steel specimens in seawater, all dissolved iron will be in the Fe oxidation state.

It is reasonable to suppose that convection is unimportant compared to diffusion and migration in the case of SCC; but in corrosion fatigue solution pumping may be important. Obviously at very low loading frequency CF approaches the SCC situation, whereas at high frequency (and low mean stress] the solution in the crack is constantly refreshed by solution pumping, so that a potential droo can be maintained with minimal changes in the local solution composition. Not only is the solution expelled from the crack less often at lower frequency, b u t , because laminar flow is maintained, the same solution tends to be drawn in again during the next half-cycle. At high frequencies the solution is ejected faster, and turbulence causes more mixing with the external solution [18].

The theory will consider oure NaCl solution as the external solution; there is little difference between in situ measurements carried out under similar conditions in seawater and in 0.6 M NaCl solution [ 4 ] . An attempt was made to use a similar theorv to explain acidification in iron crevices as was used for aluminium above. As before, the first stage of the activity coefficient calcul­ ation in the appendix is to fit the constants in the eauation which describes the mean activity coefficients, using measured data. However, in the case of FeCl it proved not to be nossible to obtain a single value of the hydration number which would give an acceptable fit to the data.

Mccafferty [19] experienced a similar problem whilst estimating the value of V o-i. in saturated FeCl solution, using the Bates-Robinson approach [15].

F ez + 2

He adopted a variable hydration number, which had to be decreased substantially at high FeCl concentrations.

In theories for predicting individual ion activity coefficients, and in the relation between potential drop and concentration changes for aluminium it has been assumed that the ions are completely dissociated in solution. Now, in the case of aluminium chloride no ion association constants have been reported, but in F e C l0 solutions several authors have reported quite strong association in concentrated solutions [20]. FeCl or FeCl., complexes have less net charge than F e2 + ions, so the" are much less strongly hydrated. Therefore significant ion association should indeed lead to a fall in the apparent value of the hydration

number. However, to account properly for association when calculation activity coefficients, the partial molar volume of the complexes should also be taken into account.

For a given concentration of Fe at the crack tip, ion association will tend to increase the potential drop above the value calculated according to the theory presented above for completely dissociated ions. This is because the flux of dissolved iron from the tin tends to drag chloride ions out as well, so that the Fe concentration must also be lower, to preserve charne neutrality.

Let us see how association will modify the theory described above. The eauations are much simnler if we consider only F e ' and FeCl^ species; treating two FeCl complexes has having the same effect as one Fe and one FeCl, ion. This is because for FeCl complexes we need only consider diffusion and not migration.

.Since sodium ions do not take part in the completing, and their flux under steadv-state conditions is still zero, the Ma concentration is still a direct function of the potential drop and the external salt concentration:

[Na ]

The chloride ions are not created or destroyed in heterogeneous reactions so their total flux is still zero; but they may be free or comnlexed. The flux of free chloride ions,

is no longer zero, but under steady-state conditions must be enual and opposite to the flux of chloride ions in the FeCl complexes:

Ci "2 JF e d , = 2 DF e d [FeC12] 'l n aF , c l ,

linked by activity coefficients, association constants and charge neutrality conditions: all scalar relations. Therefore the" must lie in the same direction. So too, then must VE.

As in the completely dissociated theory, we can lose the geometrical depend­ ence and obtain a direct relation between potential drop and concentration changes

d l n ac i - | 2 DF e C l2^e C 1^ d l n a F eC l , F

dE D_.,- [Cl-] dE RT

The first term of the left-hand side is the same as in the theor1' for d i s ­ sociated ions. The second term represents the contribution of the associated ion flu:-:, and is proportional to 2 [FeCl ] / [Cl~ ] , the ratio of associated C l " to free- C l " .

So far we have included activity coefficient effects. However, although in principle it should be possible to estimate individual ion activity coefficients in associated solutions using the approach described in the appendix, there is little point at present because the association constants auoted in the literat­ ure do not take activity coefficients into account, and in any case they are approximate. The large size and weak electrical interaction of the FeCl complex means that its activity coefficient will be close to 1. The effect of ignoring the Cl~ ion activity coefficient will be estimated later.

F e C l2 [FeCl?

1 a[PeCl,] p

(13) dE Dc l_ [Cl"]

In order to s o l v e t h i s equation we should e x p r e s s [FeCl ] as a f u n c t i o n of Cl

and AE.

Sin

e f f e c t i v e c o n c e n t r a t i o n of FeCl i s g i v e

[ F e C l

2

]

e f f

- [ F e d ] / 2 + [ F e d , J

r e a l

(14)

where a c c o r d i n g t o t h e s t a n d a r d convection for a s s o c i a t i o n c o n s t a n t s :

fFcCl

+

l

r e a l

= K J F C

2 +

HC1"1 (15)

[ F e C l

2

]

e e a l

= K j F e C l

+

] [Cl"] (16)

The e f f e c t i v e c o n c e n t r a t i o n of f r e e F e ' ( i . e . TFe 1 + MFeCl 1 ) i s found

1 J L Jreal

from charge neutrality:

2[Fe2 +l = [Cl"] - [Na+] (17)

and [Na ] is an explicit function of AE, as given above. Thus we can express [FeCl2] as f (Cl-, E) .

Although it is possible to solve the resultinq differential equations anal­ ytically, it is simpler to take small steps of [Cl~] and numerically commute AE for each step. Then the rest of the Quantities follow from the relations above

Fig. 9 shows the results of such a computation for an external solution of 0.6 M NaCl, showing the sodium, free chloride and total dissolved iron and effective F e C l . concentrations. The ratio D /D„,- was taken to be 1 on the

2 FeCl2 Cl following basis:

The C l- ion has an absolute mobilitv, U = -—-, of 6.8 units at infinite RT

dilution and 18 C. N o values are available for FeCl-^ (= 126 g/mol) or any other uncharged complex, but one would expect U . to be slightly higher (because of the lack of electrical interaction) than for a single-charged ion of similar

and i

V c i A i - = '•

Following the most modern and authoritative determination the first associ­ ation constant, K , is 6.0. K^ was made equal to 1.1, the only value available in the literature [20].

The maximum effect of neglecting the change in the activity coefficient of the chloride ions can be estimated approximately using equation 12 and the measured mean activity coefficient of F e C ^ - Assuming the chloride ions were not hydrated, and ignoring their contribution to co-volume effects (the Bates-Robinson approximation: see ref. 1 5 ) , McCaffertv [19] obtained Y_,_ = 1.09 in saturated FeCl„. In practice the C l- ions are slightly hydrated, but less strong lv than Fe ions, and they have a larger partial molar volume (although the activity coefficient depends less strongly on this quantity). If the hvdration number and martial molar volume was the same as for Fe ions than 7 , would eaual the mean activity coefficient, which is 2.55 in saturated FeCl . The first term in equation 12 can be split:

d In a , » d In V , + d lnfcl-] C l " 'Cl- L J

Upon integrating, the increase in Y«i- will increase the value of AE by (Aln Yp l_ ) - RT/F. For saturated F e C l . this means by between 12 and 34 mV.

Comparison with experimental results will be made after the next section.

2.22

4. FROM POTENTIAL DROP TO EXTERNAL POTENTIAL (IRON)

The "most occluded" cell one can imagine is one in which the resistance of the path leading to the external solution is so high that the metal inside of the occluded cell lies at the open circuit potential of the metal in the solution which fills the cavity.

If the cavity is more open than this a localized cell curent flows under free corrosion conditions between the interior of the crevice and the surface. This pulls the internal electrode potential towards the external value (and vice v e r s a ) , reducing the potential droo. According to the theorv above, this would reduce the concentration of dissolved metal ions in the cavity. Therefore a completely occluded cavity exhibits the maximum possible change in local solution chemistry which is possible under open circuit conditions. How closely an environmentally induced crack approximates to this conditions depends on the current density on the walls, their polarisation resistance and the crack geometry

In some cases it is possible to deduce the current density on the crack walls by measuring the variation in electrode potential with depth into the crack [5]-In the case of a crack in a pipline steel specimen prorogating by corrosion fatigus in seawater at 1 H z , the author was able to show that the current density on the crack walls near the tin was always less than 1 uA c m- 2 even for the most extreme applied potentials. At lower freauencies one would expect lower current densities. At the most extreme anodic potentials, one would exnect the crack tip to become near saturated in FeCl2- According to the polarization curve for iron in saturated F e C l2 [21], 1 uA c m- 2 is about the value of the exchange current density, and current densities smaller than this snould not cause signif­ icant polarization. Therefore, even at the most extreme anodic polarization the crack tip potential should hardly differ from the open circuit notential in the crack tip solution.

This conclusion is likely to apply to systems undergoing active corrosion. When passive layers are formed, it may be possible to polarize the crack tio directly. However, commercial aluminium alloys are imperfectly passive in chloride solutions, and an analysis similar to that above shows that stress corrosion cracks in 7075 alloy should also approximate to "completely occluded" cells, at least where there is any measurable potential drop in the crack.

The theories described in the preceding sections link the crack tin solution composition to the potential drop in the crack. In order to extend the theory to link the potential drop to the internal potential (and therefore the internal to the external potential) we only need to know the open circuit notential of the alloy In various solutions reoresenting the possible compositions at the crack tip.

The open circuit potential of iron or carbon steel in oxygen-free NaCl-FeCl-j mixtures is the mixed potential at which the production rate of F e "+ ions equals the rate of the hydrogen evolution reaction. The former depends on the F e2 +

concentration, and the latter on the pH, which is also linked to the F e2 + con­ centration by the hydrolysis equilibrium. Thus the open circuit notential should depend on the F e C l0 concentration and not much on the NaCl concentrations, so that a graph of open circuit potential against F e C l2 concentration is all that is required. This information is provided in fig. 10, which is based on the data reported in ref. 21. The result of combining the total dissolved iron concentr­ ation shown in fig. 8a with the data in fig. 10 is the theoretical line of internal potential against external potential plotted in fig. 2 together with some measured noints.

According to the "most occluded" approximation, the pB at the crack tip as a function of crack tip potential should correspond to the measured open circuit potential of iron as a function of the solution D H for various concentrations of FeCl-, Such measurements have also been re rted in ref. 21, and these have been plotted along with the in situ measurements in fig. 1.

~- FeCI2(iotoii

-550r '

E

f

„ i

Fig, 10. Open circuit potential of iron plotted against F e C l2 concentration or potential drop from 0.6 M NaCI solution (linear axis) as given by fig. 9 .