A Review of Trends for Corrosion Loss and Pit Depth in Longer-Term Exposures

corrosion and materials degradation

Review A Review of Trends for Corrosion Loss and Pit Depth in Longer-Term Exposures

Robert E. Melchers Centre for Infrastructure Performance and Reliability, The University of Newcastle, Newcastle, NSW 2308, Australia; [email protected] Received: 19 June 2018; Accepted: 17 July 2018; Published: 18 July 2018

Abstract: For infrastructure applications in marine environments, the eventual initiation of corrosion (and pitting) of steels (and other metals and alloys) often is assumed an inescapable fact, and practical interest then centres on the rate at which corrosion damage is likely to occur in the future. This demands models with a reasonable degree of accuracy, preferably anchored in corrosion theory and calibrated to actual observations under realistic exposure conditions. Recent developments in the understanding of the development of corrosion loss and of maximum pit depth in particular are reviewed in light of modern techniques that permit much closer examination of pitted and corroded surfaces. From these observations, and from sometimes forgotten or ignored observations in the literature, it is proposed that pitting (and crevice corrosion) plays an important role in the overall corrosion process, but that longer term pitting behaviour is considerably more complex than usually considered. In turn, this explains much of the, often high, variability in maximum depths of pits observed at any point in time. The practical implications are outlined.

Keywords: metal corrosion; uniform; pitting; anoxic; bi-modal; long term

1. Introduction Despite their proneness to corrosion, particularly if not well-protected, mild and low alloy structural steels remain important economic construction materials in marine offshore and marine coastal industrial environments. In part, this is because of their relative ease of use in construction in hostile environments, their high strength to weight ratio and also their relatively lower down-time costs for maintenance. Particularly in the offshore environment, for shipping, naval defence facilities and structures in coastal industrial environments, corrosion is an important aspect of overall facility management [1–3] and estimates of the likely rate or development of future corrosion of considerable practical interest [4]. For these applications, it is recognized that corrosion tests under laboratory conditions, such as short-term exposures in artiﬁcial seawaters, electrochemical tests or accelerated tests are of limited value, mainly because the results from such tests are difﬁcult to relate to longer term corrosion behaviour. Because of these practical demands, renewed efforts have been made in the last two decades to develop more realistic models for corrosion. For estimating the likely structural strength and structural reliability of structures, models for predicting the development of general corrosion loss are critical [5]. Pitting is of interest more for liquid retaining or exclusion systems such as pipelines, tanks and cofferdams or sheet piling, but for these, too, prediction of pit depth development is of much interest [3]. Careful examination of data and consideration of the corrosion mechanisms that may be involved have shown that for the general or ‘uniform’ corrosion, or corrosion as measured by mass loss as a function of exposure time, the bi-modal characteristic (Figure1) is more appropriate than earlier models [6]. This model has been shown to be suitable for the longer term exposure of steels, cast irons and aluminium and copper alloys to a wide variety of natural exposure environments, including

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including immersion (fresh and marine), tidal and various atmospheric exposure zones [7–9], as well immersionas for ferrous (fresh metals and in marine),soils [10]. tidal and various atmospheric exposure zones [7–9], as well as for ferrous metals in soils [10].

Figure 1. Schematic bi-modal model for long-term corrosion loss (from mass loss) showing the two Figure 1. Schematic bi‐modal model for long‐term corrosion loss (from mass loss) showing the two modes, the various phases and some of the model parameters. In the idealized case, the change modes, the various phases and some of the model parameters. In the idealized case, the change from from predominantly oxic Mode 1 to predominantly anoxic Mode 2 occurs at ta with a change of the predominantly oxic Mode 1 to predominantly anoxic Mode 2 occurs at ta with a change of the instantaneous corrosion rate from r to ra. instantaneous corrosion rate from rb bto ra.

WhileWhile thethe actual mass loss loss values values and and the the timing timing of of the the phases phases shown shown in Figure in Figure 1 depend1 depend very very muchmuch onon the metal or or alloy alloy and and on on the the environment, environment, the theoverall overall characteristic characteristic is pervasive. is pervasive. It is at It is atodds odds with with the the conventional conventional power power law law function function that that has has its roots its roots in the in theoriginal original derivation derivation by by TammannTammann inin 19231923 [[11]11] and refined refined and and examined examined by by many many authors authors [12–14]. [12–14 The]. The power power law lawhas has mathematicalmathematical deficienciesdeficiencies in meeting meeting the the conditions conditions for for the the corrosion corrosion process process at t at = t0,= as 0, well as well as other as other issuesissues [ [14],14], althoughalthough it could could be be taken taken as as an an approximation approximation to tothe the bi‐ bi-modalmodal model model for forthe theearly early period period of exposure, that is from Time 0–ta (Figure 1), during which time, the corrosion process is assumed to of exposure, that is from Time 0–ta (Figure1), during which time, the corrosion process is assumed to be predominantly under oxygen diffusion control. This is shown as Mode 1. Subsequently, in Mode be predominantly under oxygen diffusion control. This is shown as Mode 1. Subsequently, in Mode 2, 2, the corrosion processes according to the bi‐modal model are predominantly under anoxic the corrosion processes according to the bi-modal model are predominantly under anoxic conditions. conditions. In each of these two modes, the model has a number of different phases, each of which In each of these two modes, the model has a number of different phases, each of which idealize the idealize the dominant corrosion process at that time. The details have been given many times (e.g., dominant corrosion process at that time. The details have been given many times (e.g., [7]) and need [7]) and need not be rehearsed here. not be rehearsed here. The critical issue for an explanation of the bi‐modal behaviour is the change at ta from a very low t instantaneousThe critical corrosion issue for rate an explanationrb before ta is of reached the bi-modal to ra almost behaviour immediately is the change after it, at althougha from ain very lowpractice, instantaneous there is some corrosion short transition rate rb before period t(Figurea is reached 1). Given to r thata almost the bi immediately‐modal characteristic after it, is although seen infor practice, a range of there aluminium is some alloys short and transition for many period copper (Figure alloys1 ).(but Given not for that ‘pure’ the bi-modal copper in characteristic ‘pure’ water is seen[15]), for as a well range as offor aluminium many different alloys steels and including for many high copper chromium alloys (but steels, not it for follows ‘pure’ that copper it is in not ‘pure’ waterprimarily [15]), a asfunction well as of for the many type of different material. steels Moreover, including it has high been chromiumshown that steels,small changes it follows in steel that it is notcomposition primarily (including a function carbon of the typecontent) of material. have little Moreover, effect on it the has mass been losses shown or that on smallthe bi‐ changesmodal in steelcharacteristic composition [16,17]. (including Similarly, carbon the bi‐ content)modal characteristic have little effect is seen on for the the mass outer losses skin orof cast on the irons, bi-modal as characteristicwell as for machined [16,17]. cast Similarly, irons in thethe bi-modalsame environment characteristic [18]. In is this seen context, for the it outeris interesting skin of that cast for irons, assteels well (and as for cast machined irons) buried cast irons in soils, in the the same degree environment of compaction, [18]. Inand this by context,implication it is the interesting air‐void that forcontent steels next (and to cast the irons)metal surface, buried inhas soils, a major the degreeinfluence of on compaction, the amount and of corrosion, by implication but not the on air-void the contentgeneral nextform to (topology) the metal of surface, the bi‐modal has a characteristic major influence [10]. on the amount of corrosion, but not on the generalUsing form the (topology) limited data of the that bi-modal were available characteristic at the [10 time,]. it was proposed that the bi‐modal characteristicUsing the also limited applies data thatto longer were availableterm trends at the for time, maximum it was proposed and average that pit the depths bi-modal [19]. characteristic Some relationship between them might be expected particularly for metals that corrode mainly by pitting also applies to longer term trends for maximum and average pit depths [19]. Some relationship between since mass loss caused by pitting is included automatically and predominantly in the overall mass them might be expected particularly for metals that corrode mainly by pitting since mass loss caused by loss. In other cases, such as for steels, pit depth usually is corrected by increasing it by the corrosion pitting is included automatically and predominantly in the overall mass loss. In other cases, such as for loss equivalent to the mass loss, on the basis that the mass loss in pitting is very small compared to steels, pit depth usually is corrected by increasing it by the corrosion loss equivalent to the mass loss, on the overall mass loss [20]. However, more detailed observations, including extensive microscope basis that the mass loss in pitting is very small compared to overall mass loss [20]. However, more detailed observations, including extensive microscope observations of the surfaces of steel samples recovered from Corros. Mater. Degrad. 2018, 1 44 marine corrosion immersion environments, have suggested a more complex relationship between the bi-modal trend for corrosion loss and the pitting of the steel surfaces. This is explored in the present paper. Largely, it reinterprets data already in the literature to present a new view of the interaction between pitting corrosion and trends for mass loss or uniform corrosion. The next section reviews a selection of data for pitting to consider the relation between pitting corrosion and mass loss initially in an oxygen-rich environment, followed by such corrosion in the oxygen-poor environment created by the development of heavy rusts, including the presence of magnetite and possibly hematite. Based on detailed and extensive experimental observations for steels subject to extended exposures in a marine immersion environment, the following section provides a hypothesis for the processes involved in the progression of pitting through Mode 1 to the start of Mode 2 of the bi-modal model. It includes photographs of corroded surfaces after superficial rusts have been removed, carefully, so as not to destroy the patterns and features of the underlying metal as created by the interaction of the corroding steel surface and the overlying rusts. Some comments are then made about what could be expected to be observed in new experimental programs with careful observation. Practical implications are discussed briefly.

2. Trends in Pit Depth and Corrosion Loss It is sometime claimed that mild and structural steels do not ‘pit’, but rather that they suffer from ‘localized corrosion’, based on the notion that only a run-out of corrosion current i on an E-i plot as obtained in an electrochemical experiment denotes pitting. A little reflection will show that this type of electrochemical behaviour is observable only for metals with passive films, such as stainless steels and aluminium alloys, and is considered the direct result of breaching of the passive film, without which it is claimed pitting cannot occur [21]. On the other hand, the term pitting has been applied also to mild steels exposed to alkaline solutions, such as seawater, and has been so for many decades [13,22–24], despite the passive film on mild and low alloys steels being accepted as weak and unable to have any significant passivity effect [21]. This is consistent also with the Pourbaix [25] diagram for mild steel in chloride-rich waters. Herein, we follow the classic convention and apply the term pitting also for mild and low alloy steels in seawater. The detailed work of Butler et al. [23] showed that for (almost) pure iron and some other ferrous metals in alkaline solutions, pitting commenced very quickly (within days), showing circular or near-circular pits, usually exhibiting shiny bases, that extended only some way into the metal, that is the pits appeared to be limited in depth. Butler et al. [23] noted that usually, each pit was associated with a ring of corrosion product around and over the pit mouth and that this region was slightly alkaline. These observations are consistent with pitting theories such as that advanced by Wranglen [26]. Butler et al. [23] also observed that, after removal of the rusts, new or ‘daughter’ pits had formed at the peripheries of the corrosion product mounds, giving rise to small clusters of pits. This is in contrast to observations that pitting of stainless steels appears to show ‘minimum distances’ between pits, at least for shorter exposure periods [27]. For mild steels immersed for long periods (years) in seawater, pit depth development has been observed [28] to occur in what appear to be steps in pit depth, with early pitting producing plateaus, these plateaus then permitting new pitting. That new pitting then, in turn, produced new, lower corrosion plateaus that, in turn, allowed further, deeper pitting. Figure2 shows that pattern. It suggests immediately that the pitting corrosion process, for mild steels at least, is more complex than simple smooth, gradual, growth in pit depth with increased exposure time, as is the behaviour usually proposed or assumed in standard texts. Importantly, the pattern shown in Figure2 was observed only when the exposure period was sufficiently long in time, and there were observations sufficiently close in time to note the changing corrosion patterns. In this context, it has been shown recently that the pitting of cast iron surfaces buried in soils shows distinct cohorts of pit depths, all roughly of similar pit depth increments [29]. It is thus of interest whether a similar pattern can be seen for immersion corrosion in data that so far have not been considered. Corros. Mater. Degrad. 2018, 1 45 Corros. Mater. Degrad. 2018, 1, x FOR PEER REVIEW 4 of 17

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Figure 2. Rims of corrosion plateaus and pits at the base of the deepest plateau, as observed for mild Figure 2. Rims of corrosion plateaus and pits at the base of the deepest plateau, as observed for mild steelFigure exposed 2. Rims for of about corrosion 12 months plateaus in temperateand pits at seawater the base of(Jeffrey the deepest and Melchers plateau, [28]).as observed for mild steel exposed for about 12 months in temperate seawater (Jeffrey and Melchers [28]). steel exposed for about 12 months in temperate seawater (Jeffrey and Melchers [28]). Evidence for the stepped pattern of pit depth development can be discerned also in some literatureEvidenceEvidence data for for for the the the stepped corrosion stepped pattern patternand ofpitting pit of depth pit of depthsteels. development developmentThus, in can well be ‐can discernedcontrolled be discerned also and in well some also‐monitored literaturein some tests,dataliterature for Mercer the data corrosion and for Lumbard the and corrosion pitting [24] ofandnoted steels. pitting that Thus, pittingof steels. in well-controlled became Thus, inlimited well and‐ controlledin well-monitored depth veryand wellsoon tests,‐monitored after Mercer first exposure.andtests, Lumbard Mercer This [ 24limitedand] noted Lumbard development that pitting [24] noted became of pit that depth limited pitting was in observed depthbecame very limited for soon mild afterin steels depth ﬁrst in exposure. verya variety soon Thisof after exposure limited first environments,developmentexposure. This of including pitlimited depth development wastriply observed‐distilled of for pit water milddepth (TDW), steels was inobserved aTeddington variety for of mild exposure (hard) steels drinking environments, in a variety‐water, of exposure including brackish watertriply-distilledenvironments, and transported waterincluding (TDW), seawater. triply Teddington‐ distilledThey measured water (hard) (TDW), both drinking-water, mass Teddington loss and brackish (hard) pit depth drinking water and andalso‐water, counted transported brackish the numberseawater.water and of They pits transported per measured unit area.seawater. both Figure mass They 3 loss shows measured and data pit depth forboth mild mass and steel also loss in countedand TDW pit at depth the 70 °C number and and also under of pitscounted quite per unitlowthe ◦ oxygenarea.number Figure concentration of 3pits shows per unit data conditions. area. for mild Figure It steel is 3 acknowledged shows in TDW data at for 70 thatmildC in and steel these under in dataTDW quite and at 70 low the °C others oxygen and under to concentration follow, quite there low isconditions.oxygen a degree concentration of It uncertainty is acknowledged conditions. or variability that It is acknowledged in in thesethe reported data andthat pit in thedepth these others or data mass to and follow, loss. the In others theremany to is cases, follow, a degree there there ofis insufficientuncertaintyis a degree data orof uncertainty variability to ascertain in or the datavariability reported variability; in pit the depth however,reported or mass pitsome depth loss. estimates or In mass many have loss. cases, been In many there made cases, is in insufﬁcient specially there is conducteddatainsufficient to ascertain experiments, data data to ascertain variability; and such data however,variability variability; some (or however, scatter) estimates somein the have estimates data been was made haveshown been in to specially bemade small in conducted [30,31].specially experiments,conducted experiments, and such variability and such (or variability scatter) in(or the scatter) data wasin the shown data was to be shown small to [30 be,31 small]. [30,31].

(a) (b) (c) (a) (b) (c) Figure 3. Data and trends for immersion corrosion of mild steel rotating coupons exposed in Figure 3. Data and trends for immersion corrosion of mild steel rotating coupons exposed in laboratoryFigure 3. Data triply and‐distilled trends for water immersion at 70 °C corrosion and 0.4 of ppm mild O steel2: (a rotating) mass‐loss, coupons (b) depth exposed of inpits laboratory and (c) laboratory triply‐distilled ◦water at 70 °C and 0.4 ppm O2: (a) mass‐loss, (b) depth of pits and (c) numbertriply-distilled of pits waterper unit at 70areaC (data, and 0.4 but ppm not Othe2:( interpretationsa) mass-loss, (b or) depth trends, of from pits andMercer (c) number and Lumbard of pits number of pits per unit area (data, but not the interpretations or trends, from Mercer and Lumbard [24]).per unit area (data, but not the interpretations or trends, from Mercer and Lumbard [24]). [24]).

TheThe data data trends trends in in Figure Figure 3 3 have have been been addedadded andand werewere notnot provided by Mercer andand LumbardLumbard [24].[24]. These These authors authors made made little little comment comment aboutabout thethe datadata andand anyany trending,trending, including thethe possibilitypossibility

Corros. Mater. Degrad. 2018, 1 46

The data trends in Figure3 have been added and were not provided by Mercer and Lumbard [ 24]. These authors made little comment about the data and any trending, including the possibility that the Corros. Mater. Degrad. 2018, 1, x FOR PEER REVIEW 5 of 17 data for mass loss at least (Figure3a) can be readily interpreted as having an obvious bi-modal character Figurethat the3 bdata for for pit mass depth loss also at least appears (Figure to 3a) show can bi-modal be readily trending. interpreted It as also having shows an obvious that pit bi depth‐ reachedmodal a peak character value soon after ﬁrst exposure and that maximum pit depth increased relatively little for some timeFigure thereafter. 3b for pit Comparingdepth also appears with Figure to show3a shows bi‐modal that trending. mass-loss It also increased shows roughlythat pit depth in concert withreached the number a peak of value pits per soon unit after area. first Interestingly,exposure and that the upswingmaximum in pit the depth trend increased for pit relatively depth and little that for for some time thereafter. Comparing with Figure 3a shows that mass‐loss increased roughly in mass-loss occur at a very similar time: 25–30 days after ﬁrst exposure, shown as time ta on all three concert with the number of pits per unit area. Interestingly, the upswing in the trend for pit depth plots. Figure3c shows the number of pits as a function of time and that this number increases in the and that for mass‐loss occur at a very similar time: 25–30 days after first exposure, shown as time ta periodon immediately all three plots. after Figureta, i.e.,3c shows during the the number period of 30–40 pits as days. a function It is possible of time also and tothat read this into number Figure 3c that thereincreases is a in higher the period rate of immediately pit formation after in ta the, i.e., very during early the period, period i.e.,30–40 in days. the period It is possible 0–10 days. also to This is consistentread into with Figure the observations 3c that there byis a Butler higher et rate al. of [23 pit]. formation in the very early period, i.e., in the Further,period 0–10 Figure days.3 Thisshows is consistent the relationships with the observations between a majorby Butler increase et al. [23]. in pit depth, the number of pits and corrosionFurther, Figure loss as3 shows measured the relationships by mass loss. between In particular, a major increase the duration in pit depth, of Mode the number 1 (cf. Figure of 1) as measuredpits and corrosion by ta is essentially loss as measured the same by mass for loss. pit depth In particular, and for the mass duration loss, of being, Mode for 1 (cf. these Figure exposure 1) as measured by ta is essentially the same for pit depth and for mass loss, being, for these exposure conditions, around 27 days. The consistency between the change-over time ta from Mode 1 to Mode 2 conditions, around 27 days. The consistency between the change‐over time ta from Mode 1 to Mode was noted also for a number of other datasets, although for much longer times ta [32]. 2 was noted also for a number of other datasets, although for much longer times ta [32]. The data for pit depth (Figure3b) can be re-interpreted using the notion that pit depth The data for pit depth (Figure 3b) can be re‐interpreted using the notion that pit depth developmentdevelopment occurs occurs in stages, in stages, as as is implicitis implicit in in Figure Figure2 .2. Although Although thethe amount of of data data for for pit pit depths depths is limited,is limited, a possible a possible re-interpretation re‐interpretation of the of data the data in Figure in Figure3b is 3b given is given in Figure in Figure4, using 4, using also also the the notion that pitnotion depth that increments pit depth increments are likely are to likely be of to similar be of similar value. value.

FigureFigure 4. Pit 4. depthPit depth data data as as in in Figure Figure3 b3b interpreted interpreted asas stepped development development of ofthe the depth depth of pitting. of pitting.

Generally, similar observations have been made for field exposure of mild steels in seawater Generally,immersion over similar periods observations of up to 3–4 have years, been carried made out for ﬁeldat Taylors exposure Beach. of In mild one steelsof the inearlier seawater immersionprograms, over both periods mass ofloss up (general to 3–4 corrosion) years, carried and pit out depths at Taylors were recorded Beach. In and one reported. of the earlier Particularly programs, bothfor mass the losslatter, (general the maximum corrosion) pit depth, and as pit well depths as the were next recordedsix deepest and pits reported. were reported Particularly [23]. Figure for the latter,5 theshows maximum the results. pit It depth, is seen that as well the maximum as the next pit six depth deepest and the pits average were reportedpit depth are [23 reached]. Figure quite5 shows the results.early and It is then seen become that the almost maximum steady at pit about depth 0.25 and mm, the until average ta ≈ 1 year pit depth is reached, are reached at which quite time earlyboth and trends increase. The trend for the deepest pit increases some considerable amount, but the average then become almost steady at about 0.25 mm, until ta ≈ 1 year is reached, at which time both trends

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Corros. Mater. Degrad. 2018, 1, x FOR PEER REVIEW 6 of 17 increase.Corros. The Mater. trend Degrad. for 2018 the, 1, x deepestFOR PEER REVIEW pit increases some considerable amount, but the average6 of 17 trend for thetrend six for deepest the six pits deepest (i.e., includingpits (i.e., including the deepest the deepest pits) can pits) be can interpreted be interpreted as consisting as consisting of stepped of trend for the six deepest pits (i.e., including the deepest pits) can be interpreted as consisting of incrementsstepped in increments pit depth in of pit about depth 0.35 of about mm (Figure 0.35 mm6 ).(Figure 6). stepped increments in pit depth of about 0.35 mm (Figure 6).

FigureFigure 5. Data 5. Data and and trends trends for for natural natural seawater seawater immersion immersion corrosion corrosion asas a function of of exposure exposure time time for Figure 5. Data and trends for natural seawater immersion corrosion as a function of exposure time for mild steel exposed at Taylors Beach: (Figure 5) mass loss and (Figure 6) maximum pit depth, as mild steelfor mild exposed steel exposed at Taylors at Taylors Beach: Beach: (Figure (Figure5) mass 5) lossmass and loss (Figure and (Figure6) maximum 6) maximum pit depth, pit depth, as well as as well as the best‐fit trends through the data sets. the best-ﬁtwell as trends the best through‐fit trends the through data sets. the data sets.

Figure 6. Same data as in Figure 5, but interpreted as stepped increments in the maximum depth of Figure 6. Same data as in Figure 5, but interpreted as stepped increments in the maximum depth of Figurepits. 6. TheSame data data suggest as in all Figure increments5, but are interpreted about 0.35 as mm. stepped increments in the maximum depth of pits. The data suggest all increments are about 0.35 mm. pits. The data suggest all increments are about 0.35 mm.

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A similar comparison between the trends for maximum pit depth can be seen for a variety of steelsA immersion similar comparison exposed in between the North the Sea trends for for7.2 maximum years [33]. pit Just depth three can examples be seen of for the a varietymatching of steelsdatasets immersion for maximum exposed pit indepth the Northare shown Sea forin Figure 7.2 years 7 together [33]. Just with three added examples trends. of In the these matching cases, datasetsthe increment for maximum in pit depth pit is depth around are 1.0 shown mm. inAlmost Figure certainly,7 together this with can added be attributed trends. to In the these high cases, level theof nutrient increment pollution in pit depth in the is North around Sea 1.0 [34] mm. contributing Almost certainly, to microbiologically this can be attributed‐influenced to corrosion the high level and ofcausing nutrient more pollution severe in and the Northmuch Seadeeper [34] pitting contributing [35]. The to microbiologically-inﬂuenced severe pitting caused by high corrosion levels and of causingnutrient more pollution severe has and been much observed deeper pittingalso off [ 35the]. Thecoast severe of Nigeria pitting in caused oil exploration by high levels areas of [36]. nutrient The pollutionimportant has point been here observed is the stepped, also off the progressive, coast of Nigeria development in oil exploration of pit depth. areas Quantification [36]. The important of the pointeffect hereof isnutrient the stepped, pollution progressive, on such development pit depth of incrementation pit depth. Quantiﬁcation remains ofa thematter effect for of nutrientfurther pollutioninvestigation. on such pit depth incrementation remains a matter for further investigation.

Figure 7.7. Data andand trends trends for for the the maximum maximum pit pit depth depth of of three three low low alloy alloy steels steels exposed exposed to the to Norththe North Sea, showingSea, showing interpreted interpreted step-wise step‐wise trending trending for pit for depth pit depth development development (data (data from Blekkenhorstfrom Blekkenhorst et al. [ et33 al.]). [33]). A further example can be seen in the experimental results for the 6–8 deepest pits measured in A further example can be seen in the experimental results for the 6–8 deepest pits measured in the heat-affected zone of the longitudinal fusion weld of a steel pipeline [37]. The results are shown in the heat‐affected zone of the longitudinal fusion weld of a steel pipeline [37]. The results are shown Figure8, again with interpreted trends added. It shows the same kind of progressive increase in pit in Figure 8, again with interpreted trends added. It shows the same kind of progressive increase in depth as before. pit depth as before.

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FigureFigure 8. 8. DataData forfor pitpit depthdepth inin thethe heat-affectedheat‐affected zonezone ofof thethe pipepipe weldweld regionregion withwith addedadded interpretedinterpreted step-wisestep‐wise trending trending (data (data from from [ 37[37]).]). Figure 8. Data for pit depth in the heat‐affected zone of the pipe weld region with added interpreted step‐wise trending (data from [37]). AsAs a a further further example, example, consider consider Figure Figure9 for 9 for the the mass mass loss loss of a of 99% a 99% (wt) (wt) pure pure aluminium aluminium alloy [alloy38]. In[38]. the In case theAs of acase aluminium further of example,aluminium alloys, consider general alloys, Figure or general uniform 9 for orthe corrosion uniform mass loss is corrosion almostof a 99% negligible, (wt)is almost pure andaluminium negligible, the predominant alloy and the corrosionpredominant[38]. In mechanism the corrosion case of isaluminium mechanism by pitting alloys, [ 39is ].by Itgeneral pitting might or[39]. thus uniform It be might expected corrosion thus be that is expected almost average negligible, that mass average loss and at massthe any oneloss timeat anypredominant represents, one time inrepresents, corrosion some way, mechanism in the some average way,is by pitting depththe average [39]. of pitting, It mightdepth and thus of thispitting, be expected can beand expected thatthis averagecan tobe be expectedmass similar loss overto be asimilar surfaceat any over for one a time givensurface represents, period for a given of in exposure.some period way, the Thisof exposure.average is not depth to This say of thatis pitting, not there to and say will this that not can there bebe expected some will pitsnot to be thatbe some are similar over a surface for a given period of exposure. This is not to say that there will not be some deeper,pits that but are the deeper, majority but the of pittingmajority is of likely pitting to beis likely similar to (cf.be similar Figure 2(cf.). FigureFigure9 2). shows Figure the 9 shows data for the datapits for that mass are loss deeper, and but the the step majority‐wise ofinterpreted pitting is likely trend. to beAlso similar added, (cf. Figure entirely 2). Figureschematically, 9 shows the is what massdata loss for and mass the loss step-wise and the interpreted step‐wise interpreted trend. Also trend. added, Also entirely added, schematically, entirely schematically, is what mightis what be the might be the expected step‐wise, or episodic, development of pit depth. Clearly, this is not definitive, expectedmight step-wise, be the expected or episodic, step‐wise, development or episodic, development of pit depth. of Clearly, pit depth. this Clearly, is not this deﬁnitive, is not definitive, but suggests but suggests it as a topic for further investigation. it as abut topic suggests for further it as a topic investigation. for further investigation.

FigureFigure 9. Data 9. Data and and trend trend for for mass mass loss loss of of 99% 99% (wt) (wt) pure pure aluminiumaluminium exposed exposed to to a amarine marine atmosphere atmosphere at at Bilbao, together with schematic trend for deepest pits and for maximum pit depth (data from [38]). Bilbao, together with schematic trend for deepest pits and for maximum pit depth (data from [38]). Figure 9. Data and trend for mass loss of 99% (wt) pure aluminium exposed to a marine atmosphere at Bilbao, together with schematic trend for deepest pits and for maximum pit depth (data from [38]).

Corros. Mater. Degrad. 2018, 1 50 Corros. Mater. Degrad. 2018, 1, x FOR PEER REVIEW 9 of 17 Corros. Mater. Degrad. 2018, 1, x FOR PEER REVIEW 9 of 17 3. Mechanism3. Mechanism for thefor the Development Development of of Pitting Pitting CorrosionCorrosion 3. Mechanism for the Development of Pitting Corrosion It is useful to review some basic notions for the development of pitting corrosion, particularly in It is usefulIt is useful to review to review some some basic basic notions notions forfor the the development development of pitting of pitting corrosion, corrosion, particularly particularly in seawater conditions. For the present purposes, the possible distinction between pitting on passive in seawaterseawater conditions. conditions. For For the the present present purposes,purposes, the the possible possible distinction distinction between between pitting pitting on passive on passive film metals and localized corrosion on others is not considered crucial for the discussion to follow, ﬁlm metalsfilm metals and localizedand localized corrosion corrosion on on others others is is not not consideredconsidered crucial crucial for for the the discussion discussion to follow, to follow, and the term pitting is used throughout. Most of the theories for the initiation and development of and theand term the termpitting pitting is used is used throughout. throughout. Most Most of the the theories theories for for the the initiation initiation and development and development of pitting focus on the way a pit can initiate on what is close to a perfect surface, with material of pittingpitting focus focus on on the the way way a a pit pit can can initiateinitiate on what is is close close to to a aperfect perfect surface, surface, with with material material imperfections, inclusions and local alloy constituents producing only very small differences in local imperfections, inclusions and local alloy constituents producing only very small differences in local imperfections,potential to inclusions drive dissolution and local that alloy can constituents lead to pit initiation producing [22,40,41]. only very Initial small pitting differences usually inis local potential to drive dissolution that can lead to pit initiation [22,40,41]. Initial pitting usually is potentialconsidered to drive to dissolution initiate at multiple that can sites lead on to the pit surface initiation of a [metal.22,40 ,Only41]. Initial some become pitting stable usually pits is able considered to considered to initiate at multiple sites on the surface of a metal. Only some become stable pits able to to initiatepropagate at multiple with time. sites The on following the surface discussion of a metal. is focussed Only entirely some become on the propagation stable pits of able pits to beyond propagate propagate with time. The following discussion is focussed entirely on the propagation of pits beyond the period in which pits become stable. Figure 10 gives a schematic representation of the process. with time.the period The following in which pits discussion become stable. is focussed Figure entirely 10 gives ona schematic the propagation representation of pits of beyond the process. the period in which pits become stable. Figure 10 gives a schematic representation of the process.

Figure 10. Schematic representation of the sequence in pit depth development. FigureFigure 10. Schematic 10. Schematic representation representation of of the the sequence sequence in pit pit depth depth development. development. Usually, it is considered that soon after a pit enters into a stable growth mode, it is necessary for Usually,Usually, it is considered it is considered that that soon soon after after a pita pit enters enters into into a stable growth growth mode, mode, it is it necessary is necessary for for the pit mouth to have a degree of cover so as to prevent the contents of the pit from interacting with the pitthe mouth pit mouth to have to have a degree a degree of coverof cover so so as as to to prevent prevent thethe contents of of the the pit pit from from interacting interacting with with the environment and thereby rendering the pit passive [40–42]. For mild steels, this occurs relatively the environment and thereby rendering the pit passive [40–42]. For mild steels, this occurs relatively the environmentquickly, and already and thereby soon after rendering becoming the stable, pit passive the pits [40 show–42]. localized For mild corrosion steels, this product occurs around relatively quickly, and already soon after becoming stable, the pits show localized corrosion product around quickly,and and over already the pit mouth soon after [23]; becomingthis soon develops stable, theinto pits widespread show localized cover by corrosion corrosion products product around(Figure and and over the pit mouth [23]; this soon develops into widespread cover by corrosion products (Figure over the11). pit mouth [23]; this soon develops into widespread cover by corrosion products (Figure 11). 11).

Figure 11. Mild steel showing corrosion product (rust) and its local rupture over pit mouths, after 12 FigureFigure 11. Mild 11. steelMild showingsteel showing corrosion corrosion product product (rust) (rust) and itsand local its local rupture rupture over over pit mouths, pit mouths, after after 12 months 12 months of exposure at Taylors Beach (bar = 20 microns). of exposuremonths at of Taylors exposure Beach at Taylors (bar = Beach 20 microns). (bar = 20 microns).

As is well established, as each pit develops in size, the interior becomes sufficiently far removed from the pit mouth to render oxygen diffusion into the pit more difficult. Furthermore, the corrosion Corros. Mater. Degrad. 2018, 1 51 products, particularly the magnetite layer (Figure 10c), retard diffusion processes. The net effect is that anoxic conditions can develop inside the pits. In turn, these permit conditions suitable for autocatalytic reactions to commence [26]. This occurs with dissociation of water and hydrogen ions replacing oxygen as the electron acceptor within the pit, with hydrogen gas evolving from the inside surfaces of the pit. The resulting pressure then usually causes the rupture of the covering corrosion product, allowing gas effusion through the pit mouth [40]. An example of a ruptured corrosion product over pit mouths is shown in Figure 11. As corrosion progresses, the magnitude of the exterior corrosion product will increase, and overall diffusion into and out of the pit will become more difficult. The mechanisms involved have been considered in detail by Wranglen [26], who noted the low pH inside the pits and the likelihood of autocatalytic reactions. Although secondary expositions of his work always refer to chlorides as essential for the process, this was not part of Wranglen’s exposition. He simply required a potential to drive the process (although he did attribute much of this to manganese sulphide inclusions). More generally, the potential driving pitting can be the result of any imperfections [40]. However, it should be clear that as pit depth increases, the net potential for further pit depth development becomes, slowly, exhausted, and growth in pit depth stops. Overall, these steps are shown in Figure 10a. It might be noted that for shorter term exposures, such as typical in laboratory observations of pitting corrosion, the notion of a limited pit depth caused much discussion in the corrosion literature, as summarized, for example, by Frankel [41]. The limited depth to which pits can propagate has been identified with the IR (I = current, R = resistance) or potential V (volts) drop through the depth of the pit and the rust layers, that is between the cathodic region around the pit mouth and the anodic base of the pit [43]. It does not depend directly on the external environment other than that a cathode can exist somewhere outside the pit. Galvele [42] considered the sharp transition between the alkaline region immediately around a pit mouth and the acidic pit interior and concluded that diffusion of species into and out of the pit was an important part in explaining experimental observations. This and similar work provided a basis for numerical simulation of the pitting process and the progression of pit depth. Using an idealized pit geometry and models of the electrochemical reactions and the diffusion processes involved, Sharland and Tasker [44], Turnbull [45] and others showed that the limited depth concept existed and could be simulated. It also could be calibrated (indirectly) to electrochemical experimental results [46]. However, physical evidence such as shown in Figure2 was not presented. An important finding from the numerical simulation work was that after the potential drop is reached and pits stop growing in depth, they can continue to grow laterally, as the wall regions are still within the potential range. Simple analysis shows that this implies a partly hemispherical region at the deeper end of a pit (Figure 10c). As the rusts become more robust, they provide a more robust barrier between the internal and external environments, allowing a greater part of the pit volume to be at lower pH, thus increasing the radius of aggressive attack from being mainly at the base of the pit to progressively moving upward toward the pit mouth. As a result, the pit radius increases, and this allows neighbouring pits to coalesce (Figure 10d). In practical descriptions of corrosion morphology, the resulting depressions have been described as ‘broad pits’ (e.g., Phull et al. [47]). Further lateral growth allows coalescence (Figure 10d) and the eventual development of plateaus formed by multiple, neighbouring pits. Indeed, this is as observed (Figure2). On the basis of the mechanism just described, it would be expected that the floors of plateaus should reflect the rounded ends of the pits that formed the plateaus (Figure 10e). During the development of the plateaus, it can be expected that the magnetite layer will have transformed towards the plateaus, eventually reaching it, as all intervening metal has been lost by dissolution and all electrolyte inside the pits has diffused away (Figure 10e). This process is likely to be faster in chloride-rich environments, as the formation of low pH FeCl2 in the pit bases is likely [26]. Ferrous chloride is highly soluble and thus able to leach out easily. It oxidizes rapidly once exposed to an oxic environment. The precise mechanisms by which these processes occur, slowly, as the pits coalesce and metal is lost through the lateral corrosion process, remains for further investigation. Corros. Mater. Degrad. 2018, 1 52

However, it is clear that the sharp transition region around a pit mouth from the alkaline pit exterior to the acidic pit interior, so critical in Galvele’s [42] studies, must disappear in the region where two adjacent pits merge, leaving a longer transition region encompassing the new, merged pits and remnant ofCorros. metal Mater. between Degrad. 2018, them1, x FOR thatPEER REVIEW is subject to highly acidic conditions and therefore11 of 17 subject to rapid dissolution. The translationcoalesce and ofmetal the is magnetite lost through layer the lateral from corrosion being over process, the remains original for pitfurther mouths investigation. and then slowly However, it is clear that the sharp transition region around a pit mouth from the alkaline pit exterior moving towardto the acidic the floor pit interior, of the so plateau critical in created Galvele’s by [42] the studies, coalesced must disappear pits could in the be region the result where oftwo the process proposed byadjacent Evans pits and merge, Taylor leaving [48 ].a Inlonger their transition proposal, region the encompassing gradual movement the new, merged of the magnetitepits and layer is consideredremnant the result of metal of it between building them up that on is the subject inside to (i.e.,highly the acidic oxygen-poor conditions and side therefore adjacent subject to the to pits) and being oxidizedrapid dissolution. on the outer side, that is the side closest to the (oxygen-rich) environment, consistent The translation of the magnetite layer from being over the original pit mouths and then slowly with observationsmoving toward by Stratmann the floor of the and plateau Muller created [49 by]. the The coalesced Evans pits and could Taylor be the [result48] model of the process was proposed originallyproposed for atmospheric by Evans and corrosion Taylor [48]. to attempt In their proposal, to explain the gradual the presence movement of theof the magnetite magnetite layer layer adjacent to the corrosionis considered interface, the result noting of it building that this up on is the also inside the (i.e., zone the with oxygen the‐poor lowest side adjacent degree to of the oxygen pits) access, consistentand with being magnetite oxidized ason the the corrosionouter side, productthat is the forming side closest in oxygen-poorto the (oxygen‐rich) environments environment, [ 50]. Some consistent with observations by Stratmann and Muller [49]. The Evans and Taylor [48] model was observationalproposed evidence originally supporting for atmospheric these corrosion propositions to attempt is given to explain in the the nextpresence section. of the magnetite layer adjacent to the corrosion interface, noting that this is also the zone with the lowest degree of 4. Field Observationsoxygen access, consistent with magnetite as the corrosion product forming in oxygen‐poor environments [50]. Some observational evidence supporting these propositions is given in the next A number of observations made over a number of years of the corrosion products and their section. relation to the underlying steel, not previously reported, can be given meaning when viewed in terms of the propositions4. Field Observations given above. For example, vertical steel strips exposed to immersion and tidal corrosion [51]A showed number of overall observations corrosion made products,over a number but of when years of sharply the corrosion struck products mechanically, and their revealed concentrated,relation localized to the underlying areas of steel, bright not previously steel showing reported, a dimpledcan be given pattern meaning consistent when viewed with in terms the rounded bottoms ofof groups the propositions of pits (Figuregiven above. 10d). For These example, areas vertical were steel roughly strips exposed circular to immersion and occupied and tidal only a small corrosion [51] showed overall corrosion products, but when sharply struck mechanically, revealed proportionconcentrated, of the total localized metal areas surface, of bright most steel of showing which a was dimpled covered pattern with consistent very with adherent the rounded rusts. In some cases (e.g.,bottoms Figure of 12 groups), part of ofpits the (Figure area 10d). from These which areas the were rusts roughly had circular been removedand occupied by only mechanical a small impact also showedproportion a black of area,the total which metal surface, when closelymost of which examined, was covered was with very very thin adherent and followed rusts. In some the dimpled surface underneath.cases (e.g., Figure The 12), whole part of the area area oxidized from which within the rusts 1–2 had been h of removed exposure, by mechanical an insufficient impact time to also showed a black area, which when closely examined, was very thin and followed the dimpled obtain thesurface composition underneath. using The whole techniques area oxidized such within as X-ray 1–2 h of diffraction exposure, an (XRD) insufficient or Ramantime to obtain spectroscopy. There wasthe no composition evidence using of hydrogen techniques such sulphide as X‐ray odour diffraction immediately (XRD) or Raman after spectroscopy. uncovering There the was bright steel area, supportingno evidence the notionof hydrogen that sulphide the black odour material immediately was not after FeS uncovering or a similar the bright product steel from area, corrosion involvingsupporting microbiologically-influenced the notion that the black corrosion material was through not FeS sulphate-reducing or a similar product bacteria from corrosion [52]. involving microbiologically‐influenced corrosion through sulphate‐reducing bacteria [52].

Figure 12. Broad pit revealed after removal of loose rusts by mechanical impact. Dimpled bright steel at the ﬂoor of the plateau partly covered with (dark/black) magnetite. The whole area oxidized within 1–2 h after exposure. Corros. Mater. Degrad. 2018, 1 53

Closer examination of the sample in Figure 12 shows that the black layer extends under the brown rusts at the left edge of the bright steel zone. This is consistent with the notion that (oxygen-poor) magnetite underlies rusts that are more oxygenated and that magnetite lies immediately adjacent to the metal where there is no pitting (Figure 10e). However, this would not have been the case over the bright metal where it would be expected, on the basis of Figure 10c,d, that the magnetite is separated from the pit bases by electrolyte. Since this is a fluid with no structural strength, the magnetite will not be adherent to the steel and instead would have come away with the overlying rusts removed by the mechanical impact. Indeed, examination of the fragments of the removed rusts indicated that this was the case. A number of other examples, generally similar to Figure 12, were obtained in the same experiment for different steel strips and for different elevations in the water column (Jeffrey and Melchers, 2009). Similar results were obtained, for example, for steel coupons recovered after four years of exposure in a tropical marine atmospheric environment. In these cases, too, bright dimpled metallic surface areas were revealed, surrounded by areas covered with adherent rusts. Often, there are also some areas with a green tinge, dimpled, adjacent to the bright steel, probably the so-called ‘green rusts’, known to be a transitory rust product [50]. From this, it appears likely that Figure 12 is not specific to one particular exposure condition. Much less information is available for other metals, but there are some observations of pits having formed inside plateaus for aluminium exposed for up to 20 years in seawater environments [53] and also for shorter term exposures (two years) for aluminium alloy in natural seawater [54]. There also are similar observations for pitting of aluminium alloys under artificially-accelerated saline corrosion conditions [55].

5. Discussion The observations of the corrosion and the rusts shown in Figure 12 and elsewhere are considered to be entirely consistent with the mechanism of the development of the corrosion process through pitting shown, schematically, in Figure 10. They indicate that pits can coalesce, as has been shown earlier [28], but now with a plausible mechanism for this to occur and consistent with the observation of bright steel at the bottom of plateaus being the merging of the bottoms of clusters of adjacent pits (Figure 12). Such bright steel can be associated only with low pH conditions, recognized as characteristic of the bottoms of pits in pitting corrosion [22,26,40,41]. The regular pattern of the dimpled ﬂoors of the plateaus adds support to the notion of groups of pits amalgamating to form plateaus. As outlined in Figure 10, this requires lateral growth of pits, and this is consistent with the results and implications of theoretical modelling [44]. Overall, Figures 10 and 12 add support for the development of plateaus from the amalgamation of individual, adjacent pits under essentially anoxic conditions. Once a plateau has been established, it is possible, still under anoxic conditions, for new pitting to occur since, at the local level, the corrosion processes are unable to distinguish between a virgin surface and a pre-corroded one; the only matter of importance are the conditions for the initiation and development of the pitting process. Gathering these strands together means that a continuous progression or cyclic pattern of repeated pitting can occur, within plateaus that then accommodate new pitting and that eventually combine to form a newer, deeper plateau than before. The basic component of this repeated cycle of pitting is shown schematically in Figure 13. It shows that pit depth increases by ∆d over a time increment ∆t. During the whole of the time increment ∆t, new pits are being formed, increasing the overall mass loss, but by and large, not signiﬁcantly changing the maximum depth of pitting. This depth is constrained by the potential limitation (i.e., by ∆V). Corros. Mater. Degrad. 2018, 1 54 Corros. Mater. Degrad. 2018, 1, x FOR PEER REVIEW 13 of 17

Figure 13. One cycle of pitting under internally anoxic conditions showing pit depth increment ∆d Figure 13. One cycle of pitting under internally anoxic conditions showing pit depth increment Δd for time increment ∆t. Furthermore, ∆V is the electrochemical potential driving the depth of the for time increment Δt. Furthermore, ΔV is the electrochemical potential driving the depth of the pit pit increment. increment.

ItIt follows follows from from Figure Figure 13 13 that that the the development development of of pitting pitting corrosion corrosion over over extended extended exposure exposure periodsperiods is is governed governed both both by by Δ∆VV andand by by Δ∆t.t .For For a a given given exposure exposure scenario, scenario, Δ∆VV cancan be be expected expected to to remainremain relatively relatively constant, andand thus, thus, the the development development of pittingof pitting and and corrosion corrosion loss isloss governed is governed largely largelyby ∆t. by It Δ dependst. It depends on the on total the total amount amount of ferrous of ferrous material material that that needs needs to be to removedbe removed to createto create the theplateaus plateaus and and also also on theon ratethe rate at which at which the metal the metal is removed is removed under under the given the given potential. potential. These These factors factorslargely largely are controlled are controlled by the rateby the of diffusionrate of diffusion of species of species operating operating under cathodic under cathodic control. control. It has been It hasproposed been proposed earlier that earlier these that are these oxygen are oxygen for Mode for 1 Mode and hydrogen 1 and hydrogen for Mode for 2 Mode and that 2 and the that rates the of ratesdiffusion of diffusion depend depend on the thicknesson the thickness of the corrosion of the corrosion products, products, in particular in particular that of magnetite that of magnetite [56]. [56]. In this context, it is noted that the process of cycling of pitting corrosion occurring under anoxic conditionsIn this context, differs in it important is noted that ways the from process the initialof cycling cycle of of pitting pitting corrosion from first occurring exposure, under that is anoxic Mode 1 conditionsin Figure1 differs. In this in mode, important the processways from usually the initial starts cycle ab-initio of pitting from from oxygen-rich first exposure, conditions, that is with Mode the 1rate in Figure limiting 1. In condition this mode, being the the process rate of usually oxygen starts arrival ab‐ atinitio the corrodingfrom oxygen surface,‐rich conditions, limited by the with rate the of ratediffusion limiting of condition oxygen through being the rate layers of ofoxygen corrosion arrival products, at the corroding reducing as surface, these build-up, limited by including the rate of the diffusionformation of of oxygen the magnetite through layer. the layers For much of corrosion of Mode products, 1, the instantaneous reducing as rate these of corrosion build‐up, is including controlled theprimarily formation by theof the rate magnetite of inward diffusionlayer. For of much oxygen of throughMode 1, thethe rust instantaneous layer that builds rate of up corrosion as corrosion is controlledprogresses primarily [6,56]. Since by the a build-up rate of inward of corrosion diffusion products of oxygen is required, through the the time rust required layer that for builds the pitting up asprocesses corrosion to progresses achieve a pit[6,56]. plateau Since will a build take‐ considerablyup of corrosion longer products in Mode is required, 1 than for the the time earlier required cycles forin the Mode pitting 2 when processes hydrogen to achieve is involved. a pit plateau This time will difference take considerably gives rise longer to the in bi-modal Mode 1 characteristic. than for the earlierThe rust cycles layer in that Mode develops 2 when during hydrogen corrosion is involved. in Mode This 1 is time known difference to become gives non-homogeneous rise to the bi‐modal with characteristic.depth and to beThe denser rust andlayer less that permeable develops closer during to thecorrosion metal surface. in Mode Magnetite 1 is known invariably to become is the non inner‐ homogeneouslayer of rusts with [48]. depth When and the ruststo be havedenser developed and less permeable sufficiently, closer the magnetite to the metal layer surface. will be Magnetite the main invariablybarrier to is oxygen the inner transportation layer of rusts inwards, [48]. When that the is up rusts to time havet adeveloped. It also will sufficiently, be the main the barrier magnetite in the layerearly will part be of the Mode main 2, butbarrier now to for oxygen the corrosion transportation rate controlled inwards, by that outward is up to hydrogen time ta. It transportation. also will be theThe main latter barrier is consistent in the early with part experimental of Mode 2, observations but now for (e.g., the corrosion [57]). A mechanism rate controlled for thisby outward has been hydrogenproposed transportation. [56]. The latter is consistent with experimental observations (e.g., [57]). A mechanismThe severity for this of has pitting, been proposed and thus [56]. also corrosion loss, in a given time period depends much on ∆V The(Figure severity 13). Oneof pitting, factor and to affect thus ∆alsoV is corrosion that of microbiological loss, in a given corrosion time period effects. depends Laboratory-based much on ΔV (Figureexperimental 13). One work factor using to affect artificially ΔV is high that nutrient of microbiological loadings and corrosion mainly pureeffects. bacterial Laboratory cultures‐based has experimentalshown that severework using corrosion, artificially particularly high nutrient pitting loadings corrosion, and can mainly result pure from bacterial these conditions cultures has [52 ]. shownAs part that of severe that process, corrosion, the bacteriaparticularly are consideredpitting corrosion, to provide can result the abiotic from these metabolites conditions that [52]. increase As partthe of corrosion that process, potential the bacteria [56]. Further, are considered it has been to demonstrated,provide the abiotic empirically, metabolites that that elevated increase nutrient the corrosionconcentrations, potential causing [56]. increasedFurther, it corrosion has been of demonstrated, steels in seawater, empirically, have their that main elevated effect during nutrient the concentrations,early part of Mode causing 2 (Phase increased 3) and corrosion also that theyof steels increase in seawater, the long-term have corrosiontheir main in effect Phase during 4 (Figure the1), earlyat least part for of up Mode to about 2 (Phase 15–20 3) years and also [35]. that In terms they increase of the mechanisms the long‐term outlined corrosion herein, in itPhase can be 4 (Figure inferred 1),that, at least as a result for up of to microbiological about 15–20 years activity, [35]. the In increment terms of inthe pit mechanisms depth ∆p in outlined Figure 12 herein, will be it increased, can be inferred that, as a result of microbiological activity, the increment in pit depth Δp in Figure 12 will be increased, as a consequence of the increase in the electrochemical potential ΔV set up by metabolites.

Corros. Mater. Degrad. 2018, 1 55 as a consequence of the increase in the electrochemical potential ∆V set up by metabolites. Further verification and quantification of this effect would be desirable, but the principles appear to be clear. Somewhat similar comments are likely to apply for the effect of chloride ion concentration. Natural chloride concentrations are very similar for most seawaters, but for these and for freshwaters, increasing the chloride concentration would be expected to increase the severity of pitting corrosion. The principles for this are well established [58]. Even in natural waters, the effect can be seen by comparing the data for pit depths observed on steels exposed in the Panama Canal Zone to seawater as compare with those exposed to fresh water [20]. The observations given above do call into question the applicability of electrochemical techniques in the study of longer term pitting and in particular the use of applied potentials to speed up the corrosion process. Since the depth of pitting, such as in the natural environments considered herein, is constrained by the potential drop through the pit, potential applied to increase the rate of corrosion also will increase the potential for pitting and thus lead to deeper pits, deeper than would be expected under natural conditions. In the limit, the plateauing effect would be bypassed and the cyclic nature of pitting lost. The imitations of electrochemical techniques in this regard are well known [59] and have been demonstrated by comparing field studies with electrochemical observations [60]. Particularly for longer term observations with observation points at intervals of several years, any observation of the depths of the pits at a particular time point constitutes very much a ‘snap-shot’ of the development of pit depths to that point in time. Unlike the idealized behaviour shown in Figure6, in most scenarios, it would be expected that pit depths would be at various stages in the cycle of pitting (Figure 13). In addition, in practice, there will be small variations in ∆V and in ∆t, but likely to be far more important is the accumulated effect of such variations over the exposure period. The latter is likely to produce a corrosion pattern in which the developments of pits over the surface are not in sequence, in part owing to delayed commencement of pit initiation and in part due to slightly different rates of pit growth. The net effect is the apparent randomness often associated with pit depths, particularly at longer exposure times. Because of these factors, it is permissible, in the limit (i.e., asymptotically), to consider pit depths as statistically independent variable ‘realizations’ [61]. Such independence is an important theoretical requirement for the proper application of extreme value theory, including to pit depth data [62]. In turn, this is necessary for maximum pit depth predictions and associated probabilities of occurrence to have both fundamental and empirical validity for practical applications. Finally, a proposition can be offered for the overall development of pit depth with time, and the observations that it tends to follow a pattern similar to general corrosion as derived from mass loss, even for mild and low alloy steels (Figure5). As noted, for the early part of the process (Mode 1, Figure1), oxygen-rich conditions exist, and the rate of pitting is controlled by the rate of inwards oxygen diffusion that slows as the rust layers build-up. In the early part of Mode 2 (Phase 3, Figure1), the potential for pitting will be adjusted slightly to match the change from oxygen to hydrogen in the cathodic reaction, theoretically [56] and also observed in pit depth data [63]. However, the change from the rate of the cathodic reaction being governed by oxygen diffusion to hydrogen diffusion means the time increment ∆t becomes much shorter, leading to a considerable increase in the rate at which pit depth develops. Eventually, however, the further build-up of corrosion products also will reduce the rate of outward hydrogen diffusion [56], lengthening the time increments ∆t and slowing the rate at which pit depth develops, on average. This proposition appears plausible. It can be used as a basis for further investigations to ascertain its validity.

6. Concluding Remarks Collecting together various observations from diverse parts of the literature, it is possible to give explanations for the development of pitting corrosion in the slightly alkaline seawater marine environment. The principal features of such development are: Corros. Mater. Degrad. 2018, 1 56

1. After initiation and reaching stable growth, pits will continue to grow in depth until the potential driving the growth in pit depth becomes exhausted as pit depth increases. However, this still permits lateral growth of the pits, and eventually, this may result in pit coalescence with neighbouring pits to form plateaus of relatively uniform depth. These are sometimes known as broad pits. 2. Observational data indicate that new pits form on the ﬂoors of the broad pits, particularly in low pH anoxic conditions such as under the magnetite corrosion product layer. In turn, this can lead to a new cycle of pit coalescence and the formation of deeper broad pits. The result is that the pitting growth behaviour can be considered episodic rather than a continued smooth growth in depth, as commonly assumed. 3. Since not all points on a surface where anodic dissolution occurs are subject to exactly the same potential differences, pit development will vary from point to point on the surface and can be considered, asymptotically, to have pit depths that are statically independent. This allows valid application of extreme value analysis to the depth of pitting, as has been done for many years, but on an empirical basis. 4. The model for pit depth development proposed herein also allows rational explanations for the effects of chlorides and of microbiological inﬂuences on pit depth. It also provides a basis for relating pit depth development to overall general corrosion loss development, even for mild and low alloys steels.

Funding: This research received funding from the Australian Research Council under grant DP140103388. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References

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