Corrosion researchers have developed many approaches to predicting the occurrence of different corrosion modes. Four types of predictive analytics can be identified: data-centric correlative analysis, theory-based semi-empirical models, expert-knowledge-based models, and theory-based, multi-scale models. However, most new corrosion failures have been serendipitous discoveries, rather than anticipated through a systematic process. This paper reviews stress corrosion cracking (SCC) of carbon steel in non-aqueous electrolytes and in aqueous solutions of oxyanions, to understand whether using the appropriate predictive analytic strategy may have helped anticipate the failures. In all of these cases of SCC, some information was available in related environments prior to field failures, but a framework was lacking to identify the connections and anticipate failures. Data-centric predictive analytics would not have helped anticipate the failures because of the low frequency of the phenomena and the lack of prior failure data. A better predictive analytic strategy will need methods to integrate diverse sources of knowledge into a theoretical framework. Predictive analytics also must have a probabilistic component because both the knowledge and data are uncertain. The paper provides a conceptual approach to developing such a predictive analytics framework.
Analytics is a term that is being used increasingly in the context of discerning patterns in underlying data to improve business decisions. The term “predictive analytics” implies that these data patterns are used to build models to predict the future behavior of a system. One author1 defined predictive analytics as the process of deriving models solely from the data through automated computational methods (machine learning), without recourse to assumptions (or theory) made by an analyst. Machine learning models are flexible and can change dynamically with data. The advent of widely accessible information via the worldwide web, sensors to collect ever more information, and increased computer processing power has made data-centric predictions highly sought after. Unlike the case of data-centric predictive analytics mentioned above, many of the life prediction approaches in the materials and corrosion field use knowledge/theory gained from materials research.2-8 If the parameters in the theoretical models can be derived from even more fundamental models at the molecular or atomic level, extrapolation beyond the environments in which the tests were conducted becomes possible.
Thus, the realm of predictive analytics can be viewed in terms of the spectrum of data types and predictive model types (Figure 1). The type of predictive approach ranging from purely data-centric to purely knowledge-based is charted on the horizontal axis. On the vertical axis is the type of data ranging from the aggregated to the fundamental.
In the lower right quadrant, the combination of aggregated data and knowledge-based models result in expert-based approaches that rely on judgment or rules of thumb developed by subject matter experts using aggregated data such as alloy composition, corrosion rate, mechanical properties, or crack growth rate.9-11 These types of models may also be used when a failure mode does not lend itself to physical models (e.g., human interactions). Because aggregated data and expert knowledge based on past experiences are used in these models, they are useful mainly to anticipate known failure modes in systems where significant experience exists. These knowledge-based approaches are incorporated in various industry standards and guidance documents.
In the lower left quadrant, the use of aggregated data and various statistical/machine learning tools leads to correlative models12-16 or pattern recognition tools. The correlative models, such as artificial neural networks (ANN), simply relate different input factors (e.g., pH) to a desired metric (e.g., corrosion rate) and do not rely on other fundamental assumptions about the process in an explicit manner. The correlative models are useful when predicting known failures of a known system, where there are data for a similar system. Unlike the expert-based models in the lower right quadrant, the correlative models may yield quantitative predictions and may be used as control algorithms.
In the upper left quadrant, the use of fundamental data and data-centric prediction leads to empirical predictive models. These models combine theoretical framework with fundamental data. Examples abound in modeling localized corrosion,17-20 flow-induced corrosion,5,21 and stress corrosion cracking (SCC) in high-purity water systems.22-23 These types of models are useful when predicting known failure modes as new conditions arise within a system. Unlike the correlative models, these models can be extrapolated beyond the data from which they were derived, but the assumption is that the mechanism does not change. Statistical models also fall into this category because they essentially help to extrapolate known conditions to different size scales.24-27 However, statistical models, by themselves, do not carry any time information. The time evolution of corrosion or cracking in statistical models must be derived either empirically or using a theoretical model.
The upper right hand quadrant combines fundamental data with mechanistic models, especially across multiple length scales. For example, SCC may occur as a result of a combination of plastic deformation enhanced destabilization of passive films and therefore the many different combinations of microstructures and environmental conditions leading to such local destabilization of passive films may be evaluated.28-29 If a wide range of fundamental data is available, then they can be combined in different ways through the known laws representing them to predict new phenomena. If assembled properly, these types of models have the potential to predict new failure modes that could arise in new systems or as systems age. The upper right quadrant predictive analytics is very much in the spirit of Frank Newman Speller, who tried to find commonalities among corrosion phenomena.30
Can We Anticipate Unknown Failure Modes?
Applied corrosion research is almost always associated with failure modes that are already known. Typically, a corrosion failure happens in the field and, provided it is of sufficient concern to an organization, significant resources are devoted to understanding the causative factors and taking preventive measures (the two quadrants on the left side in Figure 1). If the organization is enlightened or the funding body is public, the results are published so others can learn from them, enabling the use of the bottom right-hand quadrant approach of Figure 1. However, proactive management of failures (identifying potential failure modes before they happen) is rare. The first formal attempt at proactively addressing failure modes in nuclear power reactors was made by a group of experts assembled by the U.S. Nuclear Regulatory Commission.4 In another activity, the late Staehle explored proactive assessment through the organization of a series of conferences focused on the integration of knowledge of processes leading to SCC in high-purity water at multiple length scales.31-34
The ultimate questions raised in this paper are: Can new failure modes be predicted with the data and knowledge existing prior to the time the failures occurred? And, if not, what approaches could be used for improved foresight? Such a foresight must be probabilistic because both the data and knowledge are uncertain. To illustrate the issues involved, a few failures from the literature are cited along with the research that was conducted by the author and others to generate a knowledge base. This paper focuses on the environment side of the corrosion process, although the materials side of predictive analytics is equally important.
STRESS CORROSION CRACKING IN NON-AQUEOUS SOLVENTS
Farina and Grassini35 were among the earliest investigators to view the SCC of steel in various non-aqueous environments as a related set of information. They reported that SCC was found in methanol (CH3OH), ethanol (CH3CH2OH), dimethylformamide ((CH3)2CNH), and acetonitrile (CH3CN), all containing 10−4 M lithium chloride (LiCl) and acidified by 10−4 M sulfuric acid (H2SO4), but not in 2-propanol ((CH3)2CH2OH). They examined the SCC tendency in terms of the dielectric properties and dipole moments of these solvents. Newman36 examined the SCC of carbon steel in alcohols and compared that to the SCC in NH3. However, he was focused on similarities of the mechanisms of cracking and not on the electrolyte properties that could assist in predicting future SCC in other non-aqueous electrolytes. Since then, significantly more data have been generated in methanol and ethanol. Exploration of other non-aqueous environments, such as liquid H2S, has also been done. Models for mixed solvent electrolytes are available.37-39 The following sections provide a re-examination of this information and then revisit the correlations that were originally attempted by Farina and Grassini.35
SCC of carbon steel in anhydrous liquid NH3 was first observed in the early 1950s in agricultural operations in distribution facilities, transportation tanks (also called nurse tanks), and in field storage tanks. About 3% of the agricultural NH3 tanks exhibited SCC. At that time, no failure of NH3 tanks in chemical process and refrigeration industries were reported. Loginow and Phelps40 conducted constant deflection tests in anhydrous NH3 cylinders. They showed that dissolved oxygen exacerbated SCC, whereas addition of 0.2% or more water inhibited SCC. Tanks that were stress relieved after welding did not show any SCC. Cracks were predominantly intergranular, but mixed transgranular–intergranular cracking was also observed. After this research, the composition of agricultural grade of NH3 included approximately 2,000 ppm water. Deegan and Wilde41 examined the effect of applied potential in addition to water and oxygen on the SCC of carbon steels in anhydrous, metallurgical grade NH3 using slow strain rate tests (SSRT). They found that approximately 0.1% by weight water inhibited SCC in NH3 exposed to ambient air. Furthermore, applied anodic currents increased SCC susceptibility in aerated NH3, whereas cathodic polarization inhibited cracking. In the presence of 0.2% H2O, no SCC was observed at any potential. Deegan, et al.,42 showed that both O2 and N2 were needed for cracking and their roles were not reproduced by the application of anodic potentials alone. In NH3 containing 9 ppm O2 plus 3 ppm N2, cathodic reduction charge densities for various anodically polarized specimens suggested the presence of a reducible surface film, hypothesized by the authors to be an oxide. On the other hand, the survey of industry in the 1950s did not indicate any incidence of SCC in NH3 used for chemical and refrigeration purposes. In the 1960s through the 1980s, about 50% of the NH3 storage spheres inspected worldwide exhibited SCC.43 This led to a systematic research43 that showed that SCC can occur in liquid NH3 with dissolved oxygen concentration down to 0.5 ppm and water inhibited SCC, depending on the dissolved O2 concentration (Figure 2). Lunde and Nyborg43 used air to control O2 content, thereby including nitrogen in the solution. Despite the long history of research in this area, failures have been reported recently.44-45
The effect of methanol on the corrosion and cracking behavior of titanium and zirconium alloys was first reported by Mori, et al., in 196646 and has since been studied extensively, for example, see refences.47-50 In all of these cases, the role of halides in increasing the SCC susceptibility of these alloys was well documented. The role of water was more complex. At low concentrations (below about 0.1 vol%) water exacerbated SCC, whereas at higher concentrations it inhibited SCC.48 Anodic potentials exacerbated SCC, whereas cathodic potentials inhibited SCC in these alloys. SCC of carbon steels in methanol was first reported in 1978 by Matsukura and Sato,51 who found that C-Mn steel of yield strength 255 MPa (37 ksi) showed SCC in methanol containing 0.01% formic acid and less than 0.2% water. No SCC was found in methanol containing 1% water.
In similarity to Ti and Zr alloys, SCC was exacerbated by anodic potentials and inhibited by cathodic potentials.51 Around the same time, Farina, et al.,52 studied the electrochemical behavior of Armco iron and a C-Mn steel in methanol containing 0.1 M lithium perchlorate (LiClO4), added as a supporting electrolyte with various concentrations of water, acid, and chloride ions. In all of their tests, the solutions were deaerated with nitrogen. The role of oxygen was studied only on the cathodic polarization. They found that water increased the passivity of steel, while acidity and chloride increased active dissolution. Bellucci, et al.,53 conducted SCC tests on Armco iron and a low-C steel in methanol that contained 0.0 M LiClO4 with 10−4 M to 10−3 M LiCl and 10−4 H2SO4. They found that both the acid and chloride were needed for SCC in the presence of oxygen, and that water above about 1.0% inhibited SCC.
More recently, SCC has been observed in a pipeline transporting liquid hydrocarbon in northern Canada.54-55 Because of the cold climate, methanol was added to the pipeline during the commissioning pneumatic test and as a test medium for valve testing. Laboratory testing in methanol showed that the steel was susceptible to SCC in methanol, provided there was sufficient concentration of formic acid (a natural contaminant resulting from the degradation of methanol in the presence of oxygen) and oxygen. Water inhibited SCC. The results on the effect of oxygen and water on the SCC of carbon steel in methanol are combined from different investigators53-55 and shown in Figure 3.
Fractography showed that as the chloride concentration increased from 0 ppm to 5 ppm, cracking shifted from an intergranular to a transgranular mode.
A report of SCC of carbon steel in fuel grade ethanol (FGE) was first published in 2005 as a result of leakage observed in ethanol storage tanks, primarily in the west coast of the United States.56-57 The initial survey conducted as a part of that work found 20 incidents of SCC, mostly in tanks and associated piping in end-user storage and blending facilities. At that time, no failures of transportation pipelines and tankers (trucks, rail cars, or barges) were reported. Since then, additional failures have been observed in terminal equipment as well as pipelines. These failures led to an extensive research program to identify the factors that cause the SCC and provide engineering solutions.58-75 The early studies using a factorial test design based on simulated fuel grade ethanol (SFGE) showed that the factors most influential for SCC in ethanol were dissolved oxygen and galvanic coupling to a steel coupon that had corrosion products.72 The effect of oxygen is dependent on the ethanol-gasoline blend ratio, as shown in Figure 4.
Furthermore, the lowest concentration of dissolved oxygen for SCC is observed for 50 vol% ethanol in gasoline (E-50), indicating that this is the most severe blend for SCC. Subsequent controlled crack growth rate studies quantified the effect of blend ratio and also showed that the effect of dissolved oxygen on crack growth rate is reversible,59 where the crack growth rate is reduced or increased by lowering or raising the oxygen concentration of the sparging gas.
As in the case with anhydrous NH3 and methanol, water has been found to inhibit SCC of carbon steel in FGE (Figure 5).
At least 4.5 wt% water is required to inhibit SCC in FGE and SFGE. This is consistent with the findings of Lou, et al.,75 who showed that an increase in water content promoted pitting rather than SCC. Fuel ethanol in Brazil that is not blended with gasoline contains about 7 wt% water. This may be the reason for lack of SCC observations in ethanol transportation and storage systems in Brazil.
As in the case of methanol, early investigations showed that the addition of chloride changed the cracking mode from intergranular (observed in the field) to transgranular.72 Later studies showed that even small additions of chloride (5 ppm) increased cracking significantly. Beavers, et al.,58 showed that, at the lowest chloride concentrations found in high-purity ethanol, only minor cracking was found in smooth bar SSRT; whereas, even the addition of 5 ppm chloride resulted in significant SCC. A similar result was found by Lou, et al., using N-SSRT.75 The significant increase in SCC susceptibility in SFGE versus FGE may be attributed to the higher chloride concentration in the former.
The low conductivity of ethanol initially hampered electrochemical characterization. A significant advance in our understanding of the SCC mechanism in ethanol was made through the use of microelectrodes and the identification of specific supporting electrolyte that did not affect the electrochemical behavior of steel in ethanol.65 Gui, et al., showed that addition of water to deaerated SFGE shifted the anodic polarization to higher current densities and also lowered the pitting repassivation potential.66 They also found that increasing the chloride concentration from 5 ppm to 50 ppm in SFGE decreased the repassivation potential and increased the anodic current density significantly. The dissolved oxygen had a complex effect. Increasing dissolved oxygen increased the passivity of steel as reflected by the increase in repassivation potential (Figure 6) in addition to increasing the open-circuit potential (OCP).66
Cao, et al.,60 developed a supporting electrolyte consisting of 0.01 M Tetrabutylammonium tetrafluoborate (TBA-TFB) that enabled SCC tests to be conducted at applied potentials without the presence of oxygen. They showed that TBA-TFB did not significantly alter the polarization behavior and SCC of steel in ethanol. Utilizing this approach, they were able to show that there was a lower and an upper critical potential for SCC of steel in deaerated SFGE and that high dissolution rates during deformation were observed in this potential range (Figure 7).61
Cyclic loading introduces active plastic deformation at the crack tip that exacerbates SCC. The need for active plastic deformation is the reason why statically loaded specimens (U-bends, C-rings) take a long time to exhibit SCC, if at all. SSRT provides active plastic deformation through a monotonic increase in tensile strain until failure occurs. However, the SSRT does not simulate actual field conditions. Cyclic loading at high R-ratios (high-minimum to maximum load ratios) and low frequencies representative of pipeline loading frequencies have been shown to cause SCC in FGE.59,62,64,70 Fatigue-type loading under ΔK control, with much lower R-ratios (R = 0.1), at frequency of 0.1 Hz have been shown to increase crack growth rates in comparison to fatigue in air under the same conditions.71 The crack growth rate per cycle also increased as the frequency decreased below about 0.5 Hz, suggesting a significant environmental component. For these fatigue types of loading, the fracture mode was exclusively transgranular at all ΔK levels; whereas, cracking was intergranular at higher R ratios and lower frequencies. Based on the fatigue tests at different frequencies, Sowards, et al.,70 estimated a critical crack tip strain rate of about 10−7 s−1.
Dense phase H2S is encountered in highly sour oil and gas production and transportation systems. Yu, et al.,76 examined the effect of moisture on cracking of API X60 pipe steel in this environment under low frequency, cyclic loading. Tests were conducted in a mixture of 1,440 psi H2S + 500 psi CO2 + 500 psi CH4 (9.93 MPa H2S + 3.45 MPa CO2 + 3.45 MPa CH4) with moisture contents ranging from essentially 0 ppm to 450 ppm. All of these environments were deaerated using nitrogen. The contribution of the environment to cracking was characterized by the ratio of crack growth rate in the environment to that in air. The results from the authors are replotted in Figure 8 for 95°C. It is noteworthy that the inhibitive effort of water is found at this level in similarity to other non-aqueous environments. It is well known that hydrogen embrittlement is the mechanism of cracking aqueous H2S solutions, but this data, limited as they are, are indicative of the similarity of cracking mechanism in dense phase H2S to other non-aqueous fluids, i.e., plastic deformation assisted crack-tip dissolution. It must be noted that although oxygen was excluded in this environment, perhaps the presence of CO2 is sufficient to passivate the steel in dense phase liquids leading to cracking in the presence of an aggressive agent. It is interesting that in these tests, the samples did not exhibit significant general corrosion despite the high acidity of the environment.
Water has many interesting properties77 above its critical point of 374.1°C and 22.1 MPa (3.21 ksi). For example, under supercritical conditions, the equilibrium product of water can be several orders of magnitude higher than the typical 10−14 that one associates with water at near ambient conditions, rendering water much more acidic. The dielectric constant at the critical point is approximately 6 and at higher temperatures and pressures in the supercritical regime is 10 to 25, thus making supercritical water similar to some alcohols. The dipole moment above the critical point can range from 1.6 debyes to 3.6 debyes. Thus, water under supercritical conditions behaves similarly to a polar organic solvent, such as acetonitrile and methanol. The solubility of oxidizing gases, such as oxygen, also increases dramatically in supercritical water.78 The corrosion and SCC behavior of a variety of Ni-Fe-Cr-Mo alloys have been reviewed79-80 and cases of localized corrosion and SCC have been described in the presence of several dissolved anionic species. Intergranular SCC has been observed in austenitic alloys in supercritical water with activation energies for crack growth ranging from 84 kJ/mol to 105 kJ/mol.80
Other Non-Aqueous Environments
In the case of isobutanol, limited SCC studies have indicated that carbon steel was not susceptible to SCC in isobutanol ((CH3)2CHCH2OH)-gasoline blends ranging from 100% isobutanol to 12.5 vol% isobutanol in gasoline without any impurities.81 In the case of the 12.5% isobutanol solution, addition of 50 ppm chloride did not cause SCC in a smooth bar SSRT. In the case of a 92.8% isobutanol with 0.5% methanol, 1% water, 1.96% gasoline, 40 ppm chloride, SCC was observed in a notched SSRT,65 but based on the mechanical parameters, the SCC was considered borderline. Therefore, the information to date suggests that the SCC susceptibility of steel in isobutanol is less than that in ethanol and methanol, but further studies are needed to establish clear comparison between the three alcohols.
Procter, et al.,82 and Newman, et al.,83 reported severe SCC of carbon steel in a methanol—18 wt% NH3 mixture at ambient temperature when the mixture was exposed to a gas mixture of N2, O2, and CO2. The addition of 3,000 ppm H2O to the mixture completely inhibited cracking. Based on applied potential testing, they argued that the role of oxygen was only to raise the potential and was not affecting passive film formation. Because the addition of N2 caused significant increase in SCC, they argued that nitrogen assisted in the formation of nitride film, which then let to a cleavage-type mechanism.
Common Factors for Stress Corrosion Cracking in Non-Aqueous Environments
As mentioned in previous sections, SCC of carbon steel in all of the non-aqueous fluids is exacerbated by dissolved oxygen and inhibited by water. A list of non-aqueous liquids and the history of observed SCC are shown in Table 1. Although the electrolytic properties of these liquids can be characterized in many ways, their dielectric constants and polarity are of interest. Dielectric constant is a global property that determines the degree of dissociation of ionic species in a solvent. The strength of the electrostatic attraction between ions is inversely proportional to the dielectric constant of the medium resulting in greater ionic dissociation in a higher dielectric constant medium. On the other hand, the polarity (dipole moment) reflects the charge separation in the solvent molecule and is a measure of the local interaction of solute and solvent molecules. The greater the polarity, the greater the solubility of inorganic species and lesser the solubility of organic species. The dielectric constant is related to the dipole moment by Kirkwood relationship:84
where ε is the static dielectric constant, NA is the Avogadro number, ϑ is the molar volume, μ is the dipole moment of the solvent molecule, g is a correlation factor that pertains to the relative orientation of the neighboring molecules, k is the Boltzmann’s constant, and T is the temperature in K. Non-polar solvents, with μ = 0, have a low dielectric constant. The solvents that have a low dipole moment do not exhibit SCC (Figure 9), whereas solvents that have a high dipole moment show SCC, even if their dielectric constant is quite low (liquid H2S). Butanol appears to be an outlier, in that the SCC that was observed was considered borderline, even if its dielectric constant and dipole moment fall in line with other solvents that show significant SCC. However, the data in butanol are rather sparse compared to the other solvents.
Table 1 shows environments where SCC has not been studied on carbon steel. For example, supercritical water with a relatively low dielectric constant, but high dipole moment has been shown to cause SCC of Ni-based alloys, but carbon steel has not been studied. Although these two solvent properties appear to be important in determining the ability to cause SCC, they are not complete determinants of SCC. Liquid water with high dielectric constant and moderately high polarity does not always cause SCC of steel. Other factors, such as the formation and breakdown of passive films, the presence of aggressive species, and applied potential, are also important. However, the solvent sets the stage for ionic species to interact.
The dielectric constants in mixed solvents can be estimated at different temperatures and pressures from that of pure solvents and ambient temperatures and pressures.37 The calculated dielectric constant as a function of ethanol volume percent in gasoline is shown in Figure 10 using the mixed solvent electrolyte model.38-39 Also shown is the calculated dissolved oxygen concentration in equilibrium with ambient air.
The dielectric constant decreases with an increase in gasoline concentration. The decrease in the dielectric constant with the addition of gasoline to ethanol would be expected to lead to a decrease in susceptibility of steel to SCC. However, the dissolved oxygen concentration is a maximum in intermediate gasoline content. The increase in dissolved oxygen can increase the susceptibility of SCC as mentioned previously. The combination of these two factors can be expected to lead to a maximum in SCC susceptibility in intermediate ethanol-gasoline blends as shown in Figure 4.
STRESS CORROSION CRACKING OF STEEL IN AQUEOUS SOLUTIONS OF OXYANIONS
SCC of carbon steel has been observed in aqueous environments containing various oxyanions, such as nitrate, carbonate, phosphate, molybdate, sulfate, and acetate.85 Congleton, et al., mapped these SCC phenomena on a Pourbaix diagram and suggested that SCC was confined close to the Fe3O4−Fe2O3 boundary.86 However, Pourbaix diagram is not valid for some of the highly concentrated solutions because it does not consider the effect of ion-ion, ion-molecule interactions, as well as the effect of counter ions. Furthermore, SCC has since been observed over a wider range of pH, temperature, concentration, and potential than originally thought. As an example, a more in-depth examination of carbon steel SCC in nitrate environments is provided in the following sections.
Stress Corrosion Cracking and Localized Corrosion in Nitrate
In the 1940s through the 1960s, the focus was on higher temperatures (80°C to 120°C) and lower pH values (less than 7), related to coke oven gas and ammonium nitrate production. Since the 1970s, focus has been on radioactive waste storage tanks containing high concentrations of mostly Na-based nitrate wastes.103-104 The temperatures were initially high, but since about 2000, lower temperatures (30°C to 50°C) and higher pH values (higher than 10) are of greater interest. Nitrate is the main aggressive agent for the SCC and localized corrosion of carbon steel, while nitrite and hydroxide provide inhibition. The effects of nitrite and nitrate on localized corrosion are shown in Figure 12.
The repassivation potential increases dramatically above a nitrite/nitrate molar ratio of approximately 0.5. Fuentes105 conducted statistically designed experiments and showed that the critical nitrite/nitrate ratio was independent of pH between 10 and 12, and decreased above a pH of 13. For a given ratio of nitrite/nitrate, the pH required to inhibit pitting increased as the chloride concentration increased from 0.1 M to 0.2 M.
The environmental control limits in terms of hydroxide, temperature, nitrite, and nitrate have been established for localized corrosion and SCC of carbon steel.106 Stock, et al.,100 used 440 SCC data points collected over several decades in tank waste simulants by many investigators to derive control limits on waste temperature (less than 50°C), nitrate (less than 6 M), hydroxide (less than 6 M), pH (greater than 11), nitrite (greater than 0.01 M), and nitrite/nitrate molar ratio (greater than 0.15). Since the 2011 publication of their report, significantly more data on the effects of chemistry, testing conditions, and potential have been obtained.101-102,107-109 This is presented in Figure 13 along with the control limits for SCC. In this figure, the chemistries in terms of pH and nitrite/nitrate ratio that lie within the rectangular box are considered to be safe from SCC and those that lie outside the box are considered to be susceptible. Although most of the SCC occurrences lie outside the limits (filled points), there are some within the limits. Additionally, there is a sizeable population of specimens showing no SCC that lie outside the control limits. This suggests that, in addition to the inherent variability in the test results, other accelerating and inhibiting factors in these environments exist. The inhibiting species for SCC not considered in the control limits in Figure 13 include total organic carbon110 and phosphate.108 However, carbonate (total inorganic carbon) was not found to be an inhibitor of SCC.109
An important accelerating factor of the SCC of carbon steel in nitrate solutions is the applied potential.97,111-112 The nitrite/nitrate ratio required for inhibition of SCC in nitrate solution increases with potentials (Figure 14). This figure combines data from Parkins,85 Beavers, et al.,111 and Chawla, et al.113 Although the critical potential for SCC was significantly above the OCP of steel in these environments, recent results have indicated that the OCP shifts to more positive values with time.87,114 The positive shift in OCP is dependent on pH, with alkaline pH values showing less positive shift.113 The comparison of the long-term OCP with critical potentials for localized corrosion and SCC suggests that for environments with pH less than about 11.5, there is a probability for SCC to occur even when the chemistry limits (the box in Figure 12) are satisfied. Investigation of the passive film evolution with time has indicated that the defect density in the passive film increases with time and the semi-conductive nature of the passive film changes.114 These results suggest that to predict the long-term performance of tank steel in these wastes, a better understanding of the evolution of the passive film over long time periods is needed.
Data-Based Analytics of Nitrate Cracking and Localized Corrosion
Ondrejcin115 was the first to pursue a data-based analytics approach to assess the effect of various factors on SCC of steel using a fractional factorial test design with the independent variables being temperature, nitrate, nitrite, and hydroxide, and SSRT. More recent studies using a similar approach have established a statistical correlation between various factors to localized corrosion.105 In statistically designed experiments, one must determine a priori what the important factors are (e.g., Ondrejcin115 assumed that phosphate, sulfate, and carbonate were to be held constant). Some of the factors can be determined through screening tests, but the use of a “mental model” or “expert judgment” cannot be completely avoided. For example, factorial design can be developed by assuming that certain factors have interactive effects and others have non-linear effects, but these design decisions are not completely model agnostic. Leifer, et al.,12 used logistic regression and ANN models to predict pitting from 222 to 331 archival data points. For the lower number of data points, the logistic regression model predicted correctly 53% of the cases where the presence of pitting was observed and 66% of the cases where the absence of pitting was observed. For the logistic regression of the 331 data sets, the prediction accuracy was better: 77.4% of pitting and 77.3% of no pitting. The 222 data sets were also trained using ANN model and predicted 69% of pitting and 69% of no pitting correctly. The percentage of cases where the model predictions were incorrect was significant. The authors realized that their data set was relatively small for ANN model. In both the logistic regression and ANN approach, the model is essentially a black box—there are no discernible physical laws operating between the factors.
Model-Based Analytics of Nitrate Stress Corrosion Cracking and Localized Corrosion
Despite the almost 100 y of experience in nitrate SCC of carbon steel (the first reported incidence of SCC in nitrate was in 1921), our mechanistic understanding, especially in terms of environmental chemistry effects, is still evolving. In the early years of SCC studies, the mechanism of nitrate cracking rested on intergranular corrosion caused by nitrate and the effect of plastic deformation in enhancing the dissolution.92-93,116-119 Parkins85 established a correlation between maximum current density during fast anodic scan to crack velocity in SSRT in a variety of oxyanions. His kinetic correlation is reproduced in Figure 15. This mechanistic view did not attempt to explain why different oxyanions produced different anodic dissolution rate.
As mentioned previously, an alternative view of SCC is a thermodynamic view as proposed by Congleton, et al.,86 that suggested that SCC occurred at the boundary of stability of Fe3O4 and Fe2O3. However, these boundaries are dependent on: (1) solute concentrations, (2) temperature, and (3) surface effects. Bulk thermodynamics based on infinitely dilute solutions are ill-equipped to develop a coherent model of SCC in these environments.
The purely anodic dissolution-based model must explain the inhibiting role of nitrite and hydroxide in nitrate SCC. The inhibiting effect of nitrite was rationalized,98,115 in terms of the back reaction of nitrate/nitrite reduction. The various equilibria involving nitrate reduction are shown in Figure 16, including nitrate/nitrite reaction at two molar ratios of nitrate/nitrite. Note that the measured long-term OCP values in nitrate solutions straddle the nitrate/nitrite reaction equilibrium lines, suggesting that this reaction cannot account for the measured OCP.
Furthermore, the increase in nitrite concentration would be expected to decrease the OCP if nitrite back reaction were the mechanism of inhibition. Recent long-term OCP measurements114 have indicated that the shift in OCP with nitrogen was the same as with air, suggesting some reaction other than oxygen reduction reaction controls the OCP. From Figure 16, one can also postulate that the nitrate to nitrogen or nitrate to nitrous oxide cathodic reactions could contribute to SCC. The addition of nitrite increases the OCP,87,120 suggesting that nitrite contribution to passivation is the likely explanation for inhibition. Asphahani and Uhlig97 first proposed that the adsorption of nitrate at defect sites and the resulting reduction in metal-metal bond was responsible for SCC of steel in nitrate solutions. However, they lacked detailed theoretical and experimental evidence for this hypothesis. It is likely that the mechanism of SCC in these environments involve a combination of surface adsorption and plasticity-assisted dissolution. Density functional theory (DFT) calculations of nitrate and nitrite interactions with oxide covered iron surfaces may provide some additional insights into the effect of nitrate and nitrite.
CAN WE ANTICIPATE FAILURES?
With the specific cases of carbon steel SCC as examples, one can speculate whether the failures could have been predicted using prior knowledge. The SCC of carbon steel non-aqueous environments suggests that although related experiences existed historically, those experiences were not used to anticipate SCC in ethanol or liquid H2S. In the latter case, the authors were surprised that SCC occurred despite the low water content because the frame of reference that was used was that of sulfide stress cracking in aqueous environments. The same can be said for nitrate SCC of steel—cracking in nitrate was known before carbon steel tanks were used to store nitrate wastes. This lack of anticipatory ability is not confined to a few cases. For example, the SCC of carbon steel in alkaline pH and near-neutral pH carbonate-bicarbonate environments were not anticipated before field failures occurred. This is illustrated in Figure 17.121 In 1965, a pipeline explosion occurred in Natchitoches, Louisiana resulting in 17 fatalities. Subsequent failure analysis resulted in the discovery of alkaline-pH SCC and significant research on the factors influencing that SCC.122 SCC of pipelines occurred again in 1986 in Canada, which was subsequently discovered to be a different form of SCC than that found in Louisiana.122
Similarly, Ni-based alloys, especially Alloy 600 (UNS N06600(1)), a Ni-Cr-Fe alloy, experienced significant SCC failures in high-purity water in steam generators of pressurized water reactors from about 1978.8 Laboratory data on SCC of Alloy 600 in high-purity water existed as early as 1959.123
Data-centric analytics (lower left quadrant of Figure 1) are unlikely to lead to success in anticipating failures. This is because failures such as SCC are relatively rare (see the number of failures in Figure 17 in comparison to the millions of kilometers of pipelines in North America). There are not sufficient failure data to detect patterns. For example, prior to the pipeline SCC failure in 1965, there was no published data on SCC of pipelines. Furthermore, in data-centric analytics, the act of selecting factors that may influence a failure biases the model. This was the case for high-purity water SCC. The data developed by Coriou in 1959 was ignored because the preponderance of data at that time in chloride-containing environments indicated that the high Ni alloys should be resistant to SCC.8,124 It was only after failures occurred in steam generators in the 1970s that subsequent research confirmed the validity of Coriou’s results125 for high-purity water.
A possible solution to the problem of failure anticipation, as mentioned at the beginning of this paper, is to link the fundamental understanding of physical processes at multiple scales to predict failures. From this perspective, new failures occur because the fundamental processes, such as passive dissolution, defect movement, hydrogen effects on metal bonding, etc., combine in new ways determined by materials and environmental factors. The laws and the mathematical relationships governing the fundamental processes themselves do not change, but they can be modified and linked in new ways to perform “what if” scenario analyses. This was the basis for the “Quantitative Micro Nano (QMN)” approach by Staehle.31-34 However, there are many practical and conceptual difficulties with this approach: (1) linking detailed mathematical models at multiple size and time scales is difficult because the interfaces between different models are difficult to identify and execute; (2) the computational requirements to run these enormous models may be prohibitive; (3) there may be multiple theoretical models for the same phenomenon; and (4) there may be considerable uncertainties in the model parameters and no easy way to obtain some of the data. The “cure” in this case may be worse than the “disease.”
An alternative approach to directly linking detailed mechanistic models is a Bayesian network (BN) model. The approach is sometimes called Bayesian belief networks, reflecting the idea that Bayesian probabilities denote the strength of our belief in the likelihood of an event rather than a frequency based on repeated, controlled experiments. The philosophical and mathematical underpinnings of the Bayesian probabilistic approach are given in several books.126-128 The BN approach relies on the Bayes theorem (Equation ):
where is the probability of an event, Ai, given the observation, B; P(Ai) is the prior probability of the event, Ai, before the observation, B; and is called the likelihood function and is the probability of the observation, B, given that event, Ai, occurred (this considers the probability of B being mistaken for the cause/observation related to Ai). The denominator in Equation (2) is called the probability of observation and is the sum of all the conditional probabilities of B given events, Aj, multiplied by the probabilities of Aj. Essentially, the conditional probabilities in Equation (2) refer to the strength of the connection between events Ai and B. The Bayes theorem considers only probability distributions. Uncertainties in data are readily accommodated. A wide variety of probability distributions are used in BN models depending on the type and availability of data. The conditional probabilities can be derived by running detailed models or from frequencies based on repeated testing outside of the BN, thus obviating the need for tightly linking diverse models. More than one model can be used for any given event, allowing for model uncertainties. Thus, BN provides a flexible framework for the top right quadrant approach in Figure 1. The details of application of BN in corrosion are provided in the literature.10-11,129-130
An illustration of the BN model is shown in Figure 18. In this figure, the various factors (or events) leading to either localized corrosion or SCC are linked through conditional probability relationships. The overall BN is divided into environmental, materials, and loading related factors, corresponding to the Venn diagram that is frequently used in the corrosion literature to illustrate the causes of SCC. The linkages represent the strength of the connections between the factors through conditional probability tables.
An example of the conditional probability table for deformation mode is shown in Table 2. Although this example is simplistic, it shows how a conditional probability table can be constructed based on fundamental knowledge (or expert opinions). As shown in Table 2, it is known that the deformation mode (assumed here simplistically to be either planar or cross slip) is dependent on certain precipitation hardening elements as well as matrix alloying. The deformation mode is also dependent on heat treatment that results in the formation of coherent precipitates. The conditional probability table reflects this knowledge. If the content of precipitation hardening elements (Al, Ti, and Nb) is high and there is a precipitation hardening heat treatment, the probability of planar deformation mode is 1 (100%). At intermediate levels, there is a lesser probability (0.8% or 80%), whereas at low alloying levels the probability decreases further. The couching of the knowledge in terms of probabilities allows for uncertainties in data as well as models. There are several models available for deformation mode as a function of alloying elements.131-135 These models may be used to develop conditional probabilities of deformation mode as a function of alloying. Similarly, conditional probabilities can be developed between environmental parameters, such as dielectric constant and dissolved oxygen, and SCC through models and correlations discussed previously.
If such conditional probability tables, as illustrated in Table 2, can be developed through integration of our collective knowledge and improved through further acquisition of data, new failure modes can be predicted by evaluating different linkages of the factors. This is indicated in Figure 18 through the thick solid and dashed lines. In the case of non-aqueous environments, the dielectric constant (and the related dipole moment) affects the active-passive behavior and, along with strain rate, governs SCC. Other factors, such as oxygen, can also be integrated into this framework. As new environments or new materials are produced, the BN helps us evaluate the probability that SCC will occur. It is obvious that the BN is not a static model, but is capable of being modified as new knowledge is acquired.
Although much of the predictive analytics and machine learning approaches today emphasize the discovery of patterns in data, these are inadequate in anticipating new failures. The history of corrosion is replete with failures that were not anticipated, even though related knowledge existed prior to these failures. Some examples were given in this paper. Our need to predict new failure modes has become particularly important as our engineered systems age and are challenged to operate well beyond their original design lives. The availability of vast quantities of information via the internet and the proliferation of outlets through which they are being published are placing further strains on our ability to integrate knowledge from the past with that from ongoing research. Different attempts have been made to assemble our collective knowledge using thermodynamic diagrams, kinetic models, and statistically-based treatments. They are necessary tools in our repertoire of predictive approaches, but are not sufficient. An approach based on Bayesian Network models promises to provide an integration framework for our knowledge through probabilistic treatment of models and data. However, BN models face significant challenge in terms of open availability of data and models. Such open sharing of knowledge, despite various organizational and legal constraints, is essential for predictive analytics of corrosion.
UNS numbers are listed in Metals and Alloys in the Unified Numbering System, published by the Society of Automotive Engineers (SAE International) and cosponsored by ASTM International.
The author wishes to acknowledge the NACE Speller Award committee for the privilege of presenting his ideas in this forum. These ideas were developed through interactions with numerous collaborators (too numerous to name individually) over his career and the many organizations that supported the research.
Presented as the Frank Newman Speller Award Lecture at CORROSION 2017, March 2017, New Orleans, LA.