Through a combination of mechanical stresses and corrosive environments, a material’s performance may be hindered by the complex evolution of damage due to stress corrosion cracking (SCC) or corrosion fatigue (CF). Understanding the contribution of the localized corrosion features, loading state, crack-formation features, local microstructure, and environment remains a critical issue when predicting crack initiation and propagation leading to potential metal failure. As such, the lifetimes of many exposed alloys are greatly reduced by the presence of corrosion damage and the prediction of this deleterious influence via standard fracture mechanics methods is nontrivial. Current knowledge is insufficient to fully address governing features and mechanism of the pit-to-crack transition, a common initiation mode of SCC and CF. This review examines current research of pit-to-crack transitions for various alloys and loading conditions and highlights critical areas of research necessary for informing the mechanism related to a material’s lifetime in a stressed corrosive environment.

Informing a material’s performance under stress (residual or applied) in a corrosive environment, requires a detailed understanding of localized corrosion processes, loading state, crack-formation features, local microstructure, and environment.1-5  Environmentally assisted cracking (EAC) is a cracking mode induced by the presence of a stress and a corrosive environment, and has been a topic of interest since as early as the 1940s.6-7  Failures due to this phenomena are well-documented in metals across many industries and infrastructures, particularly in pipelines,8  bridges,9  aircraft,10  and the nuclear power industry.11-13  Localized corrosion features, such as pits or intergranular corrosion, have been shown to promote the initiation of stable EAC modes such as stress corrosion cracking (SCC; propagation of a crack under a constant load or stress intensity in a corrosive environment), corrosion fatigue (CF; the propagation of a crack in a material due to cyclic loading and a corrosive environment), and hydrogen embrittlement (HE; hydrogen-assisted crack growth due to the loss of local ductility through absorbed hydrogen),1,14-27  as these localized corrosion features can act to concentrate stress and strain which in turn promotes crack nucleation and growth.28-34  Thus, a decrease in total exposure lifetime for metals and alloys, including steel, stainless steel (SS), and aluminum alloys (AA), has been observed when localized corrosion features are present.26,35-37  To prevent catastrophic failure due to SCC, interval inspections are performed in applications where crack initiation is anticipated, crack growth is relatively slow, and the material of interest is accessible. However, in applications where inspection is not feasible, or the crack growth rate is rapid, the emphasis is on ensuring that crack initiation or growth has ceased38  or the conditions necessary for initiation are not present. There has been substantial research applicable to the transition from a pit to a crack, particularly regarding the lifetime of a part,26,35-37  but identification of governing features and mechanisms still remains elusive.

Within this review, the pit-to-crack transition will be considered the nucleation of a stable, propagating crack from a corrosion feature (actively growing, stifled, or passivated) under SCC, CF, or HE modes of EAC. While various mechanisms exist for these modes of EAC, complete details of all mechanisms are outside of the scope of this paper. For stable crack growth, the crack growth rate is considered to be sufficiently faster than that of a growing pit (either continuous or re-initiated growth), such that the pit will not overcome the crack. This creates two scenarios: (i) under actively corroding scenarios, an aggressive environment (i.e., low pH and high chloride concentration) is present in the pit; and (ii) under passivated conditions, a passive layer and potential corrosion products (and elevated chloride concentration) can exist on the surface of the pit. In either case, the pit-to-crack transition relies on the fact that in the presence of a stress (either applied or residual), the pit acts as a stress concentrator.14,39  Additionally, in both cases, pit characteristics (i.e., morphology, size, etc.) affect the pit-to-crack transition while in the case of an actively corroding pit, pit growth kinetics and crack growth rate also influence transitions. Furthermore, the environment (i.e., chloride concentration, composition, etc.) influences pit shape40  and crack growth rate,41  and may play a role in governing the transition. Additionally, metallurgical features (i.e., grain phase/orientation, constituent particles, etc.) influence localized corrosion formation as well as crack initiation1,22,25,42-46  presenting further complicating features in the pit-to-crack transition. All of these phenomena can increase the complexity of a pit, as presented in Figure 1, highlighting the detailed nature of the pit-to-crack transition. Early research exploited the growth rate of an idealized active pit (such as an ellipsoid in Figure 1[a]) and the competing growth rate of a crack to predict critical localized corrosion feature sizes at which a transition to stable cracking will occur.
FIGURE 1.

Complexity of various experimentally observed pit shapes and the comparison to modeling studies. The figures are reprinted with permission from the following references: (a) adapted from Kondo,36  (b) Horner, et al.,16  (c) Cerit,126  (d) Mai and Soghrati,80  (e) Weirich, et al.,47  (under the CC BY 4.0 license) (f) Street, et al.,67  (g) Co and Burns,23  and (h) Örnek, et al.206 

FIGURE 1.

Complexity of various experimentally observed pit shapes and the comparison to modeling studies. The figures are reprinted with permission from the following references: (a) adapted from Kondo,36  (b) Horner, et al.,16  (c) Cerit,126  (d) Mai and Soghrati,80  (e) Weirich, et al.,47  (under the CC BY 4.0 license) (f) Street, et al.,67  (g) Co and Burns,23  and (h) Örnek, et al.206 

Close modal

While hemispherical pits are observed in exposure testing such as Figure 1(e),47-48  more complex features are also observed, such as Figure 1(h), and simplified models fall short of describing the formation of these complex features and the ability to concentrate stress. Additionally, many experimental methods utilized precorroded surfaces eliminating the corrosive environment and potential electrochemical driving forces. Inherently, precorroded features do not account for the influence of the aggressive environment on localized corrosion passivation, repassivation, or dynamic strain redistribution.15  Another potential influence of the aggressive environment within the pit is the possibility of HE. The aggressive environment within the pit is typically high in chloride concentrations, undergoes hydrolysis rapidly, and high hydrogen concentrations (low pH) could facilitate HE through hydrogen uptake into the material.

Early models, therefore, are limited in their application to predict pit-to-crack transitions of these complex shapes (Figure 1) or cracking under various mechanisms in a meaningful manner limiting extrapolation of created models and mechanistic understanding.38,49  As such, further modeling and experimental investigations have been geared toward identifying governing features of the pit-to-crack transition and have attempted to accurately predict the transition from a pit to a crack.

This review summarizes both modeling and experimental efforts geared toward understanding the governing features and mechanisms of the pit-to-crack transition for SCC and CF. As previously stated, the pit-to-crack transition will also encompass the formation of stable cracks from both actively corroding and passivated features. Additionally, it presents pitting and crack growth research that has larger implications for the pit-to-crack transition and informs further development of higher fidelity models. This work recognizes previous reviews of Turnbull,28,38  Larrosa, et al.,50  Akid,51  and Hoeppner and Arriscorreta.52  While these reviews are helpful, existing reviews typically cover fatigue and CF scenarios,50-52  are limited in the scope of materials covered,28,38  or do not fully address localized corrosion phenomena related to the transition.28,38,50-52  Additionally, models have summarized the influence of the pit-to-crack transition on lifetime approaches in corrosive environments,50,52  however, this is not the focus of the current review, which instead will be focused on the scientific and mechanistic studies of the pit-to-crack transition.

In the current review, historical models and interpretations of the pit-to-crack transitions are first put forth and potential limitations are identified. Next, current models and experimental work are summarized with regard to the pit-to-crack transition. Additionally, important factors governing pit growth and resultant geometries are also outlined. After summarizing current research, experimental and modeling advances are identified to inform the mechanisms of the pit-to-crack transition and allow for the extrapolation of mechanistic-based models. The summary of existing work incorporates mechanical fatigue, CF, and SCC, pit-to-crack transitions from an active and nonactive corrosion feature, covers a wide range of materials, and relates the different aspects of pit nucleation and growth to crack initiation. All three loading scenarios are considered within this review due to the nature of mechanical or corrosion defects acting as stress and strain concentrators regardless of tensile loading mode. Pit-to-crack transition studies performed under mechanical fatigue and CF are often extended to SCC scenarios, however, it is unknown if the governing mechanisms are similar. For instance, it is often noted that chemical and electrochemical conditions vary between CF and SCC scenarios53  and could hinder the extension of governing principles. Further models for CF (such as the Kondo criterion36 ) are extended to static loading conditions without proper justification or exploration of the underlying assumptions. Additionally, governing aspects of the pit-to-crack transition from one materials system are often extended to others which may be further oversight. As many materials systems and exposure environments will be presented, it will be made clear what type of pit-to-crack transition is being reviewed. Overall, it will be noted that the mechanistic understanding of pit-to-crack transitions is still being developed and there is no single governing feature or metric that describes this transition. Future areas of research will be suggested and are geared toward a mechanistic understanding.

Early research regarding the transition from localized corrosion features to cracks focused on fatigue scenarios and the determination of overall structure lifetimes or safe operating spaces for a metallic structure.26,36-37,54-56  A brief review of seminal models accounting for fatigue crack transitions from defects and corrosion-related features will be presented in chronological order.

In 1976, Kitagawa and Takahashi observed fatigue crack growth rates in air of small cracks emanating from hemispherical surface notches in HT-80 steel representative of a repassivated pit.26  The authors determined the stress regime in which an alloy could safely operate by plotting threshold fatigue stress ratio (Δσth) against crack length, as shown in Figure 2. Above 0.5 mm in crack length, it was noticed that a constant slope was present and is indicative of a constant threshold stress intensity for fatigue (ΔKth) regardless of crack length. Below 0.5 mm, the threshold stress plateaued and is indicative of the fatigue limit of unnotched specimens.26  Their formulae presented a safe life approach diagram that gives the Δσth (and ΔKth) range in which a material can safely operate. When the crack length and stress exceed the operating range, the material has the propensity to undergo failure. While initially performed on smooth hemispheres from a machined notch,26  the formulism has since been extended to corrosion scenarios containing a corrosive environment.57,-58 
FIGURE 2.

Effect of crack length on the threshold stress range for fatigue crack growth. Figure recreated from Kitagawa and Takahashi.26 

FIGURE 2.

Effect of crack length on the threshold stress range for fatigue crack growth. Figure recreated from Kitagawa and Takahashi.26 

Close modal
One of the initial models of note to consider both pitting and fatigue crack growth was presented by Hoeppner in which the total number of fatigue cycles possible in service were determined for 7075-T6 aluminum undergoing pitting and CF failure.37  Hoeppner detailed the failure process chronologically as follows: (i) initiation of corrosion pits, (ii) propagation of pits, (iii) initiation of a crack at a corrosion pit site, (iv) propagation of the crack, (v) initiation of fracture instability, and (vi) unstable crack propagation. The model utilized a power law formulism for pit growth, assuming pit growth to be
formula
where d is the pit depth, C is a parameter related to the material exposed to a specific environment, and t is the exposure time. During pit growth, the stress intensity range (ΔK) was calculated assuming a surface flaw geometry. By comparing ΔK of the pit to ΔKth, it was theorized that once ΔK ≥ ΔKth, cracking began. The total life was determined by adding the cycles present in each stage to complete failure.37 

At a similar time, a statistical approach to fracture from a generic defect (representative of a passivated pit) exposed to fatigue cycling was taken by McCartney.55,-56  The theory was based on the cumulative failure probability of a nonhomogeneous stressed structure. The model was applied to materials containing a distribution of randomly oriented cracks and accounted for a material having defect nucleation in service.55,-56  Similar to Kitagawa and Takahashi,26  the formulism was not directed toward pitting corrosion, but many of the underlying concepts from McCartney55,-56  which were later extended to pitting scenarios in collaboration with Turnbull utilizing the Kondo criterion.54 

Next, in 1989, Kondo utilized the competing rates of pitting and CF crack growth to calculate the critical K for pit-to-crack transition and the size of the defect at the K.36  The criteria exploited a power law formalism for rate of pit growth (Equation [1]) and a ΔK based on Newman-Raju's formula for semielliptical cracks.59  By combining the power law pit growth and assumptions regarding the pit growth in a cyclic loading condition with the ΔK definition for semielliptical cracks, a pitting growth rate as a function of ΔK was obtained. The pitting growth rate was then compared to the fatigue crack growth rate of short cracks (due to an increase in crack growth or decrease in threshold stress intensity, ΔKth, for short cracks in comparison to long cracks38,60-61 ) for material in the same exposure environment; however, initiation of pitting corrosion was ignored. When the fatigue crack growth rate exceeded the growth rate of a pit, a crack emanates from a pit. Although pit growth does not necessarily cease at this point, the crack grows faster than the pit (due to a higher mechanical driving force), and the feature of concern becomes the crack. A schematic for Kondo’s approach is presented in Figure 3. The intersection of the pit growth rate and the fatigue crack growth rate yields the critical fatigue stress intensity (ΔKP) for a pit to transition to a crack, as presented schematically in Figure 3. Following this logic, a critical pit size, which will nucleate a fatigue crack growing faster than a pit, can also be calculated.36  The Kondo approach of pit-to-crack transitions became the basis for many models today32,54,62  and, of particular note, Wei62  and Chen, et al.,32  continued the discussion of the rate competition theory between pit growth and fatigue crack growth.
FIGURE 3.

Model for Kondo criterion for the transition from a pit to a crack. Image adapted from Kondo with permission.36 

FIGURE 3.

Model for Kondo criterion for the transition from a pit to a crack. Image adapted from Kondo with permission.36 

Close modal

While a majority of the initial work on pit-to-crack transitions was centered around fatigue crack nucleation, there have been notable advances that transfer CF interpretations to SCC. First, empirical methods have been introduced to predict failures in water reactor materials;63  however, empirical methods require significant datasets and are difficult to extrapolate to other environments or materials as they often lack an understanding of the underlying fundamentals. Next, Engelhardt and Macdonald created a statistical damage function analysis framework that led itself to various localized corrosion scenarios (i.e., pitting, SCC, and CF).64-65  Their framework,64  similar to that of McCartney55-56  with a transition criteria from Chen, et al.,32  was later applied to steam turbine blades in dilute chloride-containing environments (≤1.5 ppm Cl) under fatigue cycling, providing limited validation.65  Third, Turnbull, et al., created a similar model for SCC failure, in which the criteria for the transition from pit-to-crack was adopted from Kondo, and the growth rate of both the pits and cracks was assumed to be statistically distributed. Turnbull’s model was also applied to turbine blades and again showed good agreement for this combination of material (3NiCrMoV disk steel) and environment (dilute chlorides).54  Thus, studies show similarities exist between CF and SCC, however, the extent of possible limitations has not been fully explored including the potential differences of the electrochemical conditions in a stable CF as compared to SCC.53 

While early models introduced conceptual understandings of the pit-to-crack transition, there are several aspects of the models that limit the application. Most importantly, these early models do not determine the governing feature of the pit for the pit-to-crack transitions. Potential limitations include:

  1. It can be inappropriate to extrapolate a competing rate theory36  when corrosion damage laws, especially those obtained through accelerated conditions, are not determined over sufficient, realistic time periods. Further, having power law functions for pit growth associated with time indicates infinite pit growth (i.e., not considering repassivation or environmental effects, etc.) and eventually all pits would corrode through the entire metal and/or reach a critical size for transition. Assuming a constant growth prefactor (such as C in Equation [1]) rate neglects limitations such as availability of reactant (e.g., mass transport of chloride, etc.), availability of electrochemical driving force due to a limitation of available cathodic current, difficulties of maintaining the critical pit chemistry/ability to restrict mass transport out of the pit when it gets big, changing or dynamic environment, etc. There is often strong experimental evidence against this logic for many alloys.47-48,66-73 

  2. The underlying principles of competing rate theory are representative of a scenario where localized corrosion growth has created an aggressive environment in that feature. However, many validation studies are performed in artificially created defects1,21,23,28,74-76  that do not contain an aggressive environment replicating a scenario where mechanical and not electrochemical processes are occurring nor are the implications of this discussed.

  3. The pit geometry is going to be a function of many parameters—while in some cases hemispherical pits have been observed to form, in many environments the microstructure and electrochemistry result in more complex geometries. There are many features of a pit (such as fissures or microstructural attack)47-48,67,-68,77-78  that could exhibit a higher corrosion rate and influence the transition period creating a nonuniform corrosion rate.

  4. ΔKth for localized corrosion features is often based on ΔKth for long cracks (ΔKth,long) which could cause an overestimation due to the fact that ΔKth,short ≤ ΔKth,long,50  where ΔKth,short represents the ΔKth for short cracks. While the disparity of ΔKth,short and ΔKth,long and subsequent crack growth rates for short and long cracks is not the focus of this review, it is important to mention and highlight significant research60,-61  and reviews79  of this subject. Further, it is unknown whether the short crack growth rate measured in fracture mechanics testing bears a close relationship to the actual growth rate of the small cracks developing from the pit at the pit-to-crack transition. These small cracks would be of the scale of the microstructure which has implications not only for growth rate but also for assigning the stress intensity (K) for such cracks.38 

  5. K and ΔK represent the magnitude of the stress singularity at the tip of an atomically sharp crack in a linear elastic material. Pits are not geometrically sharp cracks and should be treated as stress concentrators. Thus, K is not appropriate for pits80-81  nor for small cracks due to strain localization-induced plasticity, which causes a breakdown of linear elastic fracture mechanics (LEFM) conditions, hence the applicability of using LEFM for addressing crack initiation and growth is at least questionable.50  Additionally, pits are often not smooth and would therefore contain multiple features that could act as a stress concentrator. Finally, K and ΔK are elastic parameters that may be inappropriate when considering the microplasticity generated by the pit and will be subsequently discussed.38 

  6. Many models and interpretations assume a single set of static conditions (either material or environmental) and are not readily able to incorporate or account for dynamic situations such as changes in electrochemical phenomena.

The reviews available on the pit-to-crack transition largely do not address these concerns, nor do existing experimental work or models address all of these phenomena. This review attempts to summarize the progress geared toward understanding pit-to-crack transitions as well as to suggest future areas of research and methods to fully capture the true intricacies of this problem.

Corrosion pits have many unique features that can contribute to the pit-to-crack transition. Pits and other surface defects can act as stress and strain concentrators in the presence of a stress27,36,54,82-84  and the characteristics of these defects, such as size, shape, and aspect ratio (α), have been shown to influence the pit-to-crack transition. Advancements in microscopy techniques, both in situ and ex situ, have allowed for a more in-depth examination of both CF and SCC shortly after the initiation of a stable propagating crack. Atom probe tomography (APT), transmission electron microscopy (TEM) used in conjunction with an in situ corrosion cell, and other techniques have been applied to study corrosion and SCC.85-98  In addition, due to the ability to obtain three-dimensional (3D) information, x-ray microtomography has become a popular technique to examine SCC and pits.16-17,48,99-108  Models have begun to incorporate the knowledge gained through these advances in microscopy. Similarly, advancements in computational power and simulation techniques have also allowed the intricacies observed with these microscopy techniques to be included in computational simulations.80,109 

The review will be structured as followed. First, the characteristics of a pit, including depth, α, shape, and asperities, and their influences on the pit-to-crack transition will be explored. Second, the role of stress, both applied and residual, will be detailed. Third, material properties, such as grain orientation and HE susceptibility, and the potential influences on transitions will be discussed. Finally, as pit characteristics are instrumental in terms of describing the pit-to-crack transition, electrochemical, environmental, and metallurgical effects on pit formation will also be explored. This review illustrates that there is likely no single metric that directly correlates pitting with crack initiation but instead a combination of pitting characteristics might ultimately lead to cracking.

Pit Depth may not be the Sole Governing Factor for Pit-to-Crack Transition

It has been generally shown that as the depth of a pit increases in the presence of a stress, the stress concentration increases.110-111  Therefore, it is expected that deeper pits would be more likely to initiate cracking if stress is the only critical factor. Initially, for CF, ΔKth was applied to estimate a critical pit depth for passivated pits.112  Experimental evidence supported this idea, both for corrosion pits and artificially drilled pits, as Harmsworth reported that for prepitted aluminum under fatigue, deeper defects failed in fewer cycles.27  Kondo also reported a decrease in critical pit size as the applied stress cycle increased for NiCrMoV fatigued in oxygenated, 90°C water.36  More recent fatigue research on both AA and SS in chloride environments showed that as pit depth increases, the pit-to-crack transition occurred sooner75,113-118  with deeper pits requiring lower maximum stress values or fewer cycles to initiate a crack.

For a constant loading scenario, Turnbull and Zhou made additional observations that for prepitted and unpitted steel in chloride solution and aerated water, a pit of 50 µm was the minimum size necessary to generate cracks greater than 25 µm but pits smaller than 50 µm could nucleate cracks less than 25 µm.45  A further look at their data indicates that while a 50 µm pit was necessary to nucleate a crack, it does not necessarily indicate that a pit greater than 50 µm nucleates a crack, as pits even up to 400 µm in size did not have a crack. While this was ex situ analysis and it is possible that a pitting feature outgrew a nucleated crack, this is further evidence that the deepest pit does not necessarily nucleate a stable crack or that for a given material and environment that pit and crack growth rates are statistically distributed. In deaerated water, cracking was not observed and the necessary depth to form cracks was greater than 200 μm, suggesting that, if a critical pit depth exists, it is also dependent on the exposure environment.45  Despite the trend that deeper pits enhance stress concentrations110  and require lower stresses or fewer cycles to fail,23,117,119  the deepest pit may not always transition to a crack for the observed time period.45  It is noted that the pit-to-crack transition is a time-dependent phenomenon and the absence of a nucleated crack for a deep pit may reflect short-test duration or that a corrosion feature may have outgrown a nucleated crack.

Several groups have noted for AA or steel, that the deepest pits or corrosion-like features were not the most likely location for cracks.20,23-25,75,118-120  Sankaran found on prepitted AA (i.e., a passivated pit) that the fatigue life for different applied stresses at a single frequency and R-ratio (minimum to maximum stress) was accurately predicted by the average pit size, rather than the maximum pit size indicating the deepest pit may not be responsible for a pit-to-crack transition.75  Also on prepitted AA subjected to fatigue at a single frequency and R-ratio, Co, et al., noted that cracks did not nucleate at the deepest pit or fissure. Similarly, cracks did not nucleate at the damage site with the highest individual pit mouth surface area or pit volume.24,-25  Finally, for prepitted martensitic steel UNS 17400 (UNS S17400(1)) tested under fatigue, a correlation between pit depth and crack initiation was found, however, in no case did a crack initiate from the deepest pit.118 

In an investigation considering active pit growth to crack initiation, Barter and Molent examined shot-peened AA under fatigue loading and noted that, although the sample had a large corrosion pit (442 μm deep), it was not as effective at initiating fatigue cracks in comparison to other, smaller pits on the metal. Additionally, it was noted that fatigue initiation occurred at many positions, both above and below the final crack plane and around the boundary of the pitting120  further indicating the strong influence of microgeometric features dominating instead of the total depth of the pit. It was postulated that this large pit did not have a sharp crack-like feature but was instead very rounded.120  Additionally, Horner, et al., noted that under constant load tests, cracks do not nucleate from the deepest pit nor the deepest part of the pit in dilute chlorides (i.e., ppm Cl) for turbine disk steel.16 

Overall, there is substantial experimental evidence indicating that the deepest pit does not necessarily nucleate a stable CF crack20,23-25,75,118-120  or SCC.45  Experimental evidence contradicts early interpretations (First Established Criteria for Crack Initiation From a Pit-Like Geometry section) that theorized beyond a critical propagating pit size, fatigue crack growth would dominate pit growth. As previously stated, it is important to remember the overall test duration of these studies is typically on the order of weeks to months. This further raises the question, as to whether deep pits are simply growing too fast for crack growth to be the dominant failure mode. However, this would indicate the need for a distribution of pit and crack growth rates describing the pit-to-pit variability (i.e., in a given environment, not all pits grow at the same rate nor are initiated at the same time) not accounted for in the previous model of Kondo.36  Additionally, as the deepest uniform pit is expected to have the highest stress concentration, it also suggests that the highest stress concentration may not be responsible for crack nucleation highlighting the potential importance of smaller pit features in comparison to the deepest part of the pit or other metrics such as strain.120  While pit depth and maximum stress values typically do not correlate with pit initiation, the localization of strain around corrosion features has been correlated with crack nucleation and the highest strain may not be associated with the deepest pit.15,-16,38,49,117,121-122  As such, other pit characteristics could influence strain localization and the overall pit-to-crack transition. The current available research on other pit characteristics relevant to the pit-to-crack transition will be subsequently described.

Increasing Aspect Ratio of a Smooth Ellipsoidal Pit Increases Stress Concentration

When α is considered, rather than just pit depth, a more refined model of a pit’s ability to concentrate stress is attainable; however, it still represents a simplified pit morphology and may miss the important features governing crack nucleation.120  Many researchers have postulated that pit depth does not fully capture the significant physical dimensions of a pit1,21-25,120  when examining the pit-to-crack transition, especially as experimental evidence does not support the deepest pit nucleating a crack25,118-119  (potentially due to prepitting of samples). Additionally, as many models incorporate a pit growth term, it should not be overlooked that α of a pit can change as a pit grows.117,121,123-124  Many pits observed, both in the field and laboratory exposures,47,-48,67,77  are not hemispherical as displayed in Figure 1, further necessitating a model that does not rely solely on hemispherical pits with a fixed α.

The Kondo criteria suggested a dependence of the pit-to-crack transition on the ratio of pit depth (a) to pit radius (c), α = a/c, shown schematically in Figure 4, making the assumption that the pit is circular on the surface and that the α stays the same as the pit grows.36  Kondo utilized the equation:
formula
where σa is the stress amplitude and Q is a shape factor (and a function of α). Kondo supported this criterion with CF experiments on 2.5 NiCrMoV and 3.5 NiCrMoV in water containing dissolved oxygen.36  Recent experimental research has explored the effects of α on fatigue life in combination with other factors and is contradictory74,108,119,124  as the highest α does not always nucleate a crack. Often, work that is focused solely on the effects of α is computational as it is easier to isolate a single variable.110,125-127  It is important to note for computational models assuming a homogeneous material, empirical localized corrosion/cracking studies to which they are compared often have a heterogeneous material. Heterogeneities (e.g., the microstructure) could explain deviations between the predictive models and experimental observation.
FIGURE 4.

Schematic of aspect ratio.

FIGURE 4.

Schematic of aspect ratio.

Close modal
Several groups have indicated that increasing α of a pit (creating a deeper, narrower pit; Figure 4) increases the stress concentration.83,110,126-129  An, et al., noted increasing α generally increased the stress concentration under linear elastic assumptions and static loading. It was noted that as the pit depth approached the thickness of the plate, this relationship became weaker and could even break down;110  however, the relationship between defect size and material size would further complicate an understanding of a pit-to-crack transition, but is out of the scope of consideration for this review. Cerit, et al., observed that changing α changed the location of the highest elastic stress concentration.127  For wide, shallow pits the maximum stress concentration occurs at the bottom of the pit. For hemispherical pits as well as the narrow, deep pits the maximum stress occurs near but just below the mouth of the pit on the walls of the pit. This is shown in Figure 5(a).127 
FIGURE 5.

(a) Variation in the location of the critical stress concentration as a function of aspect ratio. Figure reprinted with permission from Cerit, et al.127  (b) Variation in the location of the maximum principal strain as a function of aspect ratio. Figure adapted with permission from Turnbull, et al.15  It is noted that to investigate numerical values refer to original papers. The scale bar at the top of the image displays the overall trends present in the images with blue being the lowest stress or strain present and red being the highest. It is noted that loading in (a) and (b) is in different directions and labeled in the respective figures.

FIGURE 5.

(a) Variation in the location of the critical stress concentration as a function of aspect ratio. Figure reprinted with permission from Cerit, et al.127  (b) Variation in the location of the maximum principal strain as a function of aspect ratio. Figure adapted with permission from Turnbull, et al.15  It is noted that to investigate numerical values refer to original papers. The scale bar at the top of the image displays the overall trends present in the images with blue being the lowest stress or strain present and red being the highest. It is noted that loading in (a) and (b) is in different directions and labeled in the respective figures.

Close modal

It is also important to note that α influences the location of the maximum plastic strain.15,83,117,119,130  Turnbull and co-workers note that the location of crack nucleation and growth for SCC is caused by the localization of plastic strain below the mouth of the pit rather than at the pit base. This is accentuated in a deep U-shaped pit, as shown in Figure 5(b). Further, due to the surface acting as a free surface, the lack of constraint promotes strain localization near the surface.81  Interestingly, while initiation was favorable in the high-strain regions, propagation was more rapid from the base of the pit where the maximum stress is located as shown in Figure 5(b).15  The localization of strain toward the pit mouth presumably is in response to the applied stress, and, upon deformation, the strain redistribution suggests that a growing pit in a static stress field would inherently generate a dynamic strain rate (on the order of 10−8/s) and could be responsible for crack nucleation.15  Strain localization near the pit mouth has been shown to be important for SCC15  as well as for CF.131 

While the stress concentration increases as α increases, K and ΔK illustrate the opposite trend. Acuña, et al., modeled a pit-like crack with varying α and varied the angle between the stress and the pit-like crack plane introducing mixed loading conditions.125  They found that as α increased, the ΔKeq (combined ΔK from mode I and II cracking) required to transition increased. Additionally, as the angle between the applied stress and pit-like crack plane increased, the ΔKeq required to transition decreased.125  Acuña, et al., utilized the formulism for mode I cracking proposed by Raju and Newman132  that also indicates for a crack under tension an increased α increases the K. It is noted that the K dependence on α is also dependent upon the total thickness of the material;132  however, the thickness may not play a role when corrosion defects are much smaller than the thickness of the plate, typical of in-service damage. It is also important to remember that K is not valid for smooth objects and would make more physical sense if a stress concentration was utilized.81 

An increased α (a deep, narrow pit, Figure 4) leads to an increase in stress concentration83,110,126-129  and increasing α leads to an elastic stress concentration near the pit bottom with plastic strain concentration near the mouth.83,117,119,130  It is important to remember that most computational models do not consider chemistry within the pit and would be representative of a repassivated pit. Despite computational studies indicating preferential initiation for pits with higher α, experimental studies for CF have shown pits with the highest α do not always initiate a crack for an AA system133  or there is a lack of correlation between α and cracking for an Fe-based system.23  Experimental observations are also supported by Horner, et al., who noted that under static loading for disk turbine steel in dilute chlorides, pits with the highest α do not nucleate stable cracks. In general, Horner, et al., observed that increasing α caused cracks to nucleate on the wall of the pit rather than at the base of the pit, suggesting a controlling factor other than stress concentration.16  While a clear relationship between crack initiation and α would be useful, as with pit depth, α is not a complete description of the physical attributes of a pit. Many experiments and models rely solely on the physical shape of the defect, but the electrochemical nature of the pit may play a role. Also, the total shape of a pit, incorporating microscale features and chemistry, is a more comprehensive description of the pit-to-crack transition.

Sharp Corrosion Features and Asperities may Increase Local Stress and Strain Concentrations

Often for computational studies, pits are considered to be ellipsoidal in nature with a defined α (Figure 4); experimentally, more complex shapes have been observed47,99,107,134  (Figure 1) and can impact the pit-to-crack transition by creating a local stress or strain concentration factor greater than would be predicted for a comparable smooth geometry. 3D finite element analysis (FEA) results have suggested the stress concentration around a pit increases as the pit changes from circular to elongated on the surface.16,22,126,129  Experimentally, it has been observed that pits can elongate, and the elongation can be influenced by surface roughness.47,135  Additionally, the orientation of the asymmetrical pits with respect to the loading direction cannot be neglected. Simulations from Huang, et al., and Burns, et al., indicated that a higher stress concentration was achieved for elongated pits when the long axis of the pit was perpendicular to the loading direction.22,129  Burns, et al., experimentally fatigued prepitted AA samples with similarly shaped pits and recorded where on the pits the crack initiated.22  Both the circular pit and the pit elongated perpendicular to the loading direction saw cracks primarily occur in the region of highest stress concentration at the center of the pit, as identified by 3D FEA. Pits elongated parallel to the loading direction did not exhibit location preferences for the cracks despite the concentration of stress in the corner of the pit. In general, SEM analysis showed fatigue cracks nucleated at microtopographic features, asperities (termed jut-ins in Burns, et al.22 ), and micropits. It was further hypothesized that cracks preferentially nucleate at these sites due to high plastic strain localization.22 

With computational advancements, researchers have begun examining nonhemispherical pits in simulation and modeling efforts. Mai and Soghrati utilized a two-dimensional (2D) phase field model (assuming plane stress, in which both the maximum von Mises stress and maximum principal normal strain occurred at the pit bottom) to examine stresses related to nonhemispherical pits under static loads and indicated sharper features concentrate stress to a higher level than blunt features (first column of Figure 6).80  It is important to note that chemical effects were incorporated for both the dissolution and fracture rates based on the metal ion concentration in the pit solution. Preliminary results displayed the initial pit shape played a role in the magnitude of the stresses near the pit bottom as well as the location of the highest stress. Narrow, deep features concentrated the stress more than rounder, blunter features. The simulations indicated these sharper features are more likely to form under tensile loading than shear loading. The precise dimensions defining a feature as sharp or blunt have yet to be quantitatively determined.80  Mai and Soghrati also noted that the plastic hardening modulus played a role in pit depth and K. When a plastic hardening modulus of 2 GPa to 10 GPa was compared, the K values were 18.9 MPa√m and 17.3 MPa√m respectively at the same crack depth. All of the shapes considered appeared to show the stress concentrated near the base of the pit or crack (Figure 6) due to the plane stress assumption.80 
FIGURE 6.

Phase field simulation of von Mises stress field around SCC emanating from nonhemispherical pits under tensile loading reprinted with permission from Mai and Soghrati.80 

FIGURE 6.

Phase field simulation of von Mises stress field around SCC emanating from nonhemispherical pits under tensile loading reprinted with permission from Mai and Soghrati.80 

Close modal
Zhu, et al., performed experiments and simulations on single crystal SS316L samples under constant, low elastic loads to examine pits and SCC emanating from pits.136  3D FEA indicated cracks emanated from pits at the location of the higher local elastic stresses and strains, which were dependent on the shape of the pit. In line with earlier simulation work from Horner, et al.,16  and Turnbull, et al.,14  Zhu, et al.,136  predicted the 3D strains to be highest closer to the mouth of the pit rather than the base.14,16,136  This location is consistent with the experimental results from Horner, et al.,16  Zhu, et al.,136  and others.103,117,119,137  Additionally, FEA from Xiang, et al., examined four different pit shapes under constant load: hemispherical, U-shaped (Figure 7[a]), V-shaped (Figure 7[b]), and semiellipsoid.83  They reported that the highest plastic strain areas were near the mouth of the pit for rounded pits, similar to that reported by Turnbull, et al.,14  Zhu, et al.,136  and Fatoba and Akid,138  but that the highest stresses were near the bottom of the pit implying stress is an inappropriate parameter for predicting crack initiation from a pit. When a V-shaped pit was considered, the highest strain was on the wall of the pit and located near the apex of the V as shown in Figure 7(b). Xiang, et al., still concluded that the cracks are most likely to nucleate near the pit mouth in the region of a higher strain. They also noted that, for hemispherical-shaped pits, the larger the depth-to-width ratio of a pit, the larger the stress concentration factor. The V-shaped pit exhibited the largest stress concentration of the shapes examined.83  Finally, Ma, et al.,139  indicated pit growth for cyclic-stressed A537 steel samples in 3.5 wt% NaCl showed anisotropic behavior with higher growth rates found in the direction perpendicular to the load axis. Static 3D FEA indicated localized plastic strain played an important role in pit growth as the anodic dissolution was linked to pit growth139  and showed similar influences of stress on overall pit depth which will subsequently be discussed. The existing research indicates pit shape will influence the likelihood of transitioning from a pit to a crack, with sharper features potentially contributing further to the concentration of strains. By understanding the localization of strain by pitting features, the localized strains can be compared to the critical strain threshold of a material which has been shown to be fairly independent of pit shapes for a given material.117 
FIGURE 7.

Plastic strain localization for (a) a U-shaped pit and (b) a V-shaped pit. Image reprinted from Xiang, et al.,83  under the CC BY-NC-ND license. It is noted that to investigate numerical values refer to original papers. The scale bar at the top of the image displays the overall trends present in the images with blue being the lowest strain present and red being the highest.

FIGURE 7.

Plastic strain localization for (a) a U-shaped pit and (b) a V-shaped pit. Image reprinted from Xiang, et al.,83  under the CC BY-NC-ND license. It is noted that to investigate numerical values refer to original papers. The scale bar at the top of the image displays the overall trends present in the images with blue being the lowest strain present and red being the highest.

Close modal
FIGURE 8.

Cellular automaton finite element approach to the changing strain distributions of a pit under stress. Image reprinted from Fatoba, et al.,121  with permission. It is noted that to investigate numerical values refer to original papers. The scale bar at the top of the image displays the overall trends present in the images with blue being the lowest stress present and red being the highest.

FIGURE 8.

Cellular automaton finite element approach to the changing strain distributions of a pit under stress. Image reprinted from Fatoba, et al.,121  with permission. It is noted that to investigate numerical values refer to original papers. The scale bar at the top of the image displays the overall trends present in the images with blue being the lowest stress present and red being the highest.

Close modal

Asperities—Pits are not always smooth-walled shapes and can have morphological features on the walls or base of the pit that influence the pit-to-crack transition. There is often strong experimental evidence that shows smaller asperities can be preferential nucleation sites for stable cracks in both SCC45  and CF23-25,45  scenarios. Cerit used 3D FEA to explore the static, elastic stress concentration effects of a secondary pit forming at the bottom of a primary pit.126  As α of the secondary pit increased (grew narrower and deeper), the stress concentration factor increased. This held true for various α of the primary pit. As the primary pit α increased, so did the stress concentration factor due to the secondary pit.126 

Experimentally, Burns, et al., examined pre-pitted AA pits with “jut-ins,” a scenario where the pit has grown such that a piece of material remains in a pit.1  They reported that fatigue crack initiation was observed at jut-ins and that initial growth rates from cracks emanating from these sites could vary by an order of magnitude. The variation was attributed to a nonuniform kind of crack front.1  More recent research by Co and Burns on precorroded AA reported that jut-ins were likely to initiate fatigue cracks.25  Further analysis by Burns, et al., for prepitted AA strongly suggested that local elastic macrostress concentrations and elastic-plastic micro strains, due to jut-in/micropit topography, and subsurface constituent particles, played the most significant role in fatigue crack formation. However, micropits caused higher local strain concentrations than jut-ins. Assuming that crack formation occurs at the highest strain location, these results are at odds with the experimental finding that most cracks form about jut-ins.22 

A similar result was seen by Fatoba, et al., who utilized a 2D cellular automaton approach to track changing stress distributions as a function of pit growth under a constant tensile load as shown in Figure 8.121  While local strain generally increased with pit depth and pit α, both of which increased with time, the effective stress was not observed to increase significantly beyond the yield strength of the material.121  As with other studies,16,22,126,129  the distribution of strain on the pit surface is not uniform, and, due to the low α, is concentrated near the bottom of the pit when calculated parallel to the loading direction.121  Overall, the significance of local elastic stress (previously examined up to a factor of 6)122,126,-127,140-142  and plastic strain (previously examined up to 10 fold)16,122,141,143  of microfeatures cannot be understated when considering the pit-to-crack transition.

Additional Factors

Pit location—On a larger scale, the position of the pit on the sample may play a role in the transition to a crack. Sabelkin, et al., electrochemically fabricated (prepitted) a pit on an AA tensile sample with a hole through its thickness and exposed it to fatigue loading.144  The location and shape of the pit (i.e., corner of the through hole or through the thickness of the sample on the hole, as seen in Figure 9) changed the time to transition. Whether the sample was fatigued in air or in salt water, for a given applied stress the through pit failed sooner than the corner pit. This difference is larger at lower applied stresses. In salt water at a stress of 55 MPa, the through pit initiated a crack 14,000 cycles earlier than a corner pit, while at 40 MPa the through pit failed 41,000 cycles earlier than the corner pit. This trend held for multiple AAs.76  Sabelkin hypothesized that if the stress concentration of the pit is considered, rather than the applied stress, the disparity in initiation cycles would shrink and the relationship reverses such that the corner pit fails sooner than the through pit for a specific stress concentration.144  Similarly, Joshi and Mall examined corner pits and through pits on AAs and reported that the corner pit transitioned at a lower stress in saltwater.145 
FIGURE 9.

(a) Through pit and (b) corner pit reprinted with permission from Sabelkin, et al.144 

FIGURE 9.

(a) Through pit and (b) corner pit reprinted with permission from Sabelkin, et al.144 

Close modal

Another important scenario to consider is the K of a crack emanating from a pit. For a hemispherical pit, a significant increase in K due to the presence of the pit is readily apparent for cracks that are smaller than the pit size. When a crack is deeper than the pit but close to the pit base at its maximum depth there is a dip in the predicted K value toward the base of the pit compared to the situation with no pit.146 

Pit density—Having multiple pits within close proximity of one another concentrate local stresses and strains differently than a singular pit.49,111,147-148  Liang, et al.,147  investigated the influence of pitting location on the stress concentration factor and plastic strain in a 3D model. As presented in Figure 10, the location of the maximum equivalent plastic strain is influenced by the location of a neighboring pit and could change the location of a crack initiation.147  A similar, 3D peridynamic study of interacting pits was put forth by Chen, et al., and noted preferential crack growth due to interacting pits.148  Qualitatively, researchers have reported for AA and steel that areas of higher pit density are more likely to nucleate fatigue cracks but have not established a definitive relationship.114,118-119  This raises concerns for pit density and inhomogeneities in materials that are not traditionally accounted for in modeling and computational scenarios. Experimentally, on prepitted UNS S17400 exposed to fatigue loading, local pit density correlated well with crack initiation location; however, the most dense region of pitting was not always the location where cracking occurred.118  Finally, Fatoba and Akid noted that closer pits (smaller separate distance) yielded a decrease in crack initiation time and proposed a threshold separation distance in which pits further than this distance did not influence fatigue crack initiation time. The proposed threshold separation distance was based on interacting total and plastic strain fields between pits and also proposed to be material dependent.49 
FIGURE 10.

Influence of the location of multiple pits on the (a) elastic von mises stress and (b) equivalent plastic strain. Reprinted from Liang, et al.,147  under the CC BY-NC-ND license. It is noted that to investigate numerical values refer to original papers. The scale bar at the top of the image displays the overall trends present in the images with blue being the lowest stress or strain present and red being the highest.

FIGURE 10.

Influence of the location of multiple pits on the (a) elastic von mises stress and (b) equivalent plastic strain. Reprinted from Liang, et al.,147  under the CC BY-NC-ND license. It is noted that to investigate numerical values refer to original papers. The scale bar at the top of the image displays the overall trends present in the images with blue being the lowest stress or strain present and red being the highest.

Close modal

Overall, it is likely that no single metric directly correlates pitting with crack initiation but instead a combination of pitting characteristics that ultimately leads to cracking.24,118  It should also be noted that changes in pit shape and environment over the dynamic growing process (including dynamic stress and strain redistributions) are rarely reflected in the presented research and may prove to be integral in assessing the transition point.

Increasing Stress Decreases Pit-to-Crack Transition Time

Applied stress is one of the most influential variables for mechanical testing and has also been shown to influence the dissolution rates of metals.149-151  Additionally, much of the experimental pit-to-crack research, both prepitted and active corrosion, has been performed under fatigue and necessitates accounting not only for the magnitude of the applied load but the frequency and amplitude. Existing SCC research also indicates that residual stresses (i.e., those from welds or additive processes) may be sufficient in magnitude to induce SCC.152 

Applied Stress

Early research showed that increasing the load for the same defect shape will increase the stress concentration, local stresss, and K or ΔK, as well as increase the likelihood of a defect transitioning to a crack.16  Assuming crack formation will occur at the location of the highest strain, cracking would be more likely to initiate under higher applied loads and it has been noted for fatigue that increased applied load decreased transition time, or cycles, to failure.153-155 

Several studies have explored the effects of varying applied stress on the crack transition for steels in chloride solutions and indicated that increased applied stress decreased the pit-to-crack transition time. Akid aggregated available data on a variety of high-strength steels in the late 1990s and, as presented in Figure 11,156-163  the time to transition for fatigue of a specific alloy decreased as applied stress increased; plotting the time to transition vs. the applied stress was linear with a slope of −5. There was no strong dependence observed for steel type or exposure environment as many of the datasets displayed similar slopes despite the variance in loading frequencies, material types, and environments examined. Specifically, Nakajima and Tokaji investigated carbon steel in 3 wt% NaCl,163  Daubler, et al., investigated an iron-based superalloy in H2SO4,162  and Masahiro also investigated carbon steel in 3% NaCl.161  In all cases, increasing the applied stress decreased the time to the pit-to-crack transition. The overall scatter in the data arose due to loading mode (tension, torsion, or bending), test frequency, or pit depth.35  Externally applied stress and strain can also affect pit size and growth kinetics;133,143,164  however, detailed descriptions of the pit characteristics were not provided in the reviewed studies.
FIGURE 11.

Time to pit-to-crack transition vs. applied stress in chloride solutions from various authors with different loading conditions on varying steels. Based on Akid35  with data from the literature.156-163,325 

FIGURE 11.

Time to pit-to-crack transition vs. applied stress in chloride solutions from various authors with different loading conditions on varying steels. Based on Akid35  with data from the literature.156-163,325 

Close modal

The conclusions from recent fatigue research75,115,138  and static exposures165  are in line with the general relationship observed by Akid;35  that is, increasing the magnitude of the peak or static stress increases the likelihood of crack initiation. Sankaran, et al., made the observation that prepitted AA samples failed in fewer fatigue cycles as applied stress increased; this trend held true for four different pitting conditions. Despite the overall trend, there was still evidence that cracking did not initiate from the deepest pit or the deepest part of the pit.75  It should be noted that, as the time to initiation was not reported, differences in crack growth rate cannot be separated from the transition.75  Spencer, et al., examined SS304, coated with MgCl2, under a fixed displacement in a bent condition at varying values of RH and, in general, an increased stress resulted in increased crack density.165 

Turnbull, et al., noted that as the applied stress changes, so does the localization of stress and strain.15  As the applied stress is lowered, the stress distribution for a 3D FEA model around the pit shifts so that the larger elastic stresses concentrate toward the shoulder of the pit and away from the base. For a purely elastic material, analysis revealed that the stress patterns around the pit remained the same at all applied stress levels with the peak stress just below the surface of the pit along the line of symmetry.15  However, for a plastically deformed material at high applied stresses (or deep pits at lower stress), a plastic strain was localized near the pit mouth.15  Finally, it is important to remind the reader that applied stresses may influence the rate of corrosion166  as well as the overall shape and depth of a corrosion pit, which will be subsequently discussed in the Electrochemical, Environmental, and Metallurgical Influences on Pitting Characteristics section, further complicating the transition processes.

For mechanical fatigue and CF, factors such as the R-ratio and frequency of applied load should also be considered.35,155,167  Chlistovsky, et al., examined unpitted AA samples under fatigue loading in NaCl solution167  and as the R-ratio increased, the number of cycles to failure decreased following a linear relationship on a log-log plot. When an occasional compressive overload was introduced this linear relationship did not appear, and the lifetime of the sample was negatively impacted.167  Schönbauer, et al., examined the fatigue stress limit for a few select R-ratio values on prepitted samples of 12% Cr steel in dilute (ppm and ppb) chloride environments.155  They found that higher R-ratios had lower fatigue stress limits. This would seem to complement the work of Chlistovsky, et al.,167  as increasing R-ratio increased crack initiation. When observing the loading frequency for an array of existing research on varying steel types, Akid noted that a linear relationship can be found between time to transition and loading frequency when plotted on a log-log plot. As loading frequency was increased, the time to transition decreased, potentially due to an increase in mechanical deformation.35  The slopes for the different applied stress levels (1,200 MPa, 600 MPa, and 400 MPa) were all fairly equivalent and displayed an inverse trend with applied stress.35 

Any pit-to-crack transition model should account for the magnitude of the applied stress, as generally, increasing the applied stress decreases the time for the pit-to-crack transition. In the case of fatigue, the frequency also needs to be considered, as generally, increasing frequency decreased the time to transition. Finally, there are limited studies that solely look at the influence of R-ratio on the pit-to-crack transition and the field would benefit from the R-ratio being investigated alongside other factors reviewed in the sections: Pit Depth may not be the Sole Governing Factor for pit-to-crack Transition, Increasing Aspect Ratio of a Smooth Ellipsoidal Pit Increases Stress Concentration, Sharp Corrosion Features and Asperities may Increase Local Stress and Strain Concentrations, and Additional Factors.

Residual Stress

In addition to applied stress, the influence of residual stress may play a role in the pit-to-crack transition with increased tensile (positive) residual stresses decreasing the pit-to-crack transition time. Oltra and Vignal examined residual surface stress gradients at the interface between ferrite and austenite as it related to pitting.168  They found that at the grain boundary, a stress gradient between 20 MPa/µm and 32 MPa/μm was observed for most of the stable pitting that occurred in the electrochemically driven, high chloride environment. Others have observed cracking in scenarios where no external stress was applied.47,135  This suggests that residual surface stresses may play a role in the pit-to-crack transition, particularly in combination with crystallographic factors. Intuitively, a large externally applied stress may overshadow the effects of residual stress, but this combination of factors has yet to be thoroughly examined.169-172 

Historically, it has been observed that inducing compressive residual stresses, such as in shot peening, lessens the susceptibility of steel to pitting.173-174  It stands to reason that decreasing susceptibility to pitting would also decrease the susceptibility to SCC and this correlation has been experimentally observed. Turnbull, et al., explored the benefits of shot peening and predicted that a reduced net tensile stress range and mean stress occurred at the base of a pit in the shot-peened specimen. Therefore, the fatigue crack growth rate from a corrosion pit was reduced by the residual stress imposed by shot peening, and increased constraint to lateral crack propagation near the surface and its impact on stress intensity factor at the crack base was proposed.175  For SS316 in boiling magnesium chloride, several groups have shown that compressive residual stresses impeded SCC susceptibility while tensile residual stresses above some small threshold value were sufficient to induce SCC.176,-177  Zhang, et al., also noted that the microcracks tended to run perpendicular to the machining direction.177  Additionally, Zhang, et al., noticed a strong correlation between residual stress with crack density.177  It has also been suggested that the resultant microstructure in the near-surface peened alloy can play a larger role in determining crack growth behavior causing various periods of crack growth acceleration and deceleration.178  In the case of additively manufactured (AM) materials, samples with a nonuniform residual stress distribution on the exposed surface saw more severe cracking in areas of higher tensile residual stress and impeded cracking in areas where there was a compressive residual stress.152  Other researchers have noted that parts with higher tensile residual stresses show more evidence of SCC.152,179  There is some experimental evidence that the effects of residual stress can be obscured by applied stresses.135,169 

Many surface finishing and processing techniques that impart residual stresses can have effects on microstructure and, in the case of SS, can result in strain-induced martensite which can impact susceptibility to and the behavior of SCC.38,135,179-182  Surface finishing techniques such as grinding may also create surface defects that serve as preferential sites for pitting and thus increase SCC susceptibility.169  Grinding overall, can give rise to near-surface residual stress, introduce physical defects, plastic deformation, form a nanocrystalline layer, high local hardness, and the extent of these are dependent on the relevant alloy.38  Some of these aspects will be subsequently discussed in the Material and Microstructural Properties Influence Pit-to-Crack Transition section.

Material and Microstructural Properties Influence Pit-to-Crack Transition

The influence of microstructure on fatigue initiation sites in the absence of corrosion has been reviewed by McDowell and Dunne42  and highlighted the importance of microplasticity within individual grains as a key driving force for fatigue crack formation. Additionally, associated fatigue indicators relating grain-scale fatigue crack formation and microstructurally small fatigue crack growth were discussed.42  While extensively reviewed for fatigue initiation of smooth surfaces,42  a review of microstructural constituents and the influence on pit-to-crack transitions does not exist to the knowledge of the authors, however, certain aspects have been reviewed by Miller and Akid.178  Microstructural features have been shown to influence both the formation of pits134,183  as well as the pit-to-crack transition and crack propagation.17,25,35,86,116,153,184-193  The microstructural features of interest can be separated into (i) constituent particles, (ii) grain size and orientation, and (iii) grain phase.

Constituent Particles

As noted by McDowell and Dunne,42  the importance of constituent particles was highlighted for fatigue initiation (in the absence of corrosion) by Wang, et al.43  They analyzed the effects of various microstructure-scale features on maximum plastic shear strain range calculated using FEA. The calculated plastic shear strain range was generally higher proximate to a hard-particle matrix interface than at a grain interface. Even higher plastic strain concentration occurred at a complex cluster of hard particles.43  While explored for pure fatigue (without corrosion),42,-43  the role of constituent particles on SCC and CF initiation, to date, is still unclear.

Burns, et al., suggested that stress distributions in precorroded AA due to pit macrotopography interacted with local microtopographic strain concentration, perhaps further affected by the microstructure near the pit surface and influencing fatigue crack formation.22  This was further explored for precorroded AA7050,25  and it was determined that while corrosion features remained the dominant fatigue initiation point, the microstructure played an important role in combination with microtopography. First, as previously mentioned, the constituent particles influenced pitting characteristics. Second, constituent particles or stringers were commonly aligned in the rolling direction for AA7050. As the corrosion damage is known to form at these particles, it is likely that there will be constituents from a stringer proximate to the corrosion damage surface.25  Prior work studying isolated corrosion-induced fatigue crack formation sites demonstrated that there was a stringer of constituents close to the initiating feature in AA7075.1  Finally, Jones and Hoeppner note that for etched 7075 in 3.5 wt% NaCl under CF environments, constituent particles competed with corrosion pits as critical crack nucleation sites.46  Overall, these studies theorized that constituent particles are not independently governing the crack initiation process; however, the particles are suggested to be closely related to pit initiation and shape determination22,25  or competed with corrosion pits as CF crack nucleation sites.46 

In steel alloys, manganese sulfide (MnS) inclusions have been shown to influence the initiation of localized pitting corrosion,194-195  and the formation of these pits at MnS inclusions is influenced by applied stresses,116,139,184,195-197  which may impact the overall transition of a pit to a crack. Turnbull investigated a 3 NiCrMoV steel under static loading and indicated that MnS inclusions played a role in the shape and propagation of pits,45  thus influencing stress distributions and the subsequent pit-to-crack transition. Ma, et al., investigated CF initiation for A537 steel in 3.5 wt% NaCl and noted that pits typically formed at MnS and the shape and size of these pits were influenced by the presence of fatigue.139  However, while the overall stress distributions were influenced by pits formed at MnS inclusions,139  the role of the constituent particles, such as MnS, on crack initiation remains unclear.

In general, constituent particles for AA22,25  and Fe-based45  alloys can serve as an initiation point for localized corrosion features as well as play a potential role in stress concentration, however, the role in the pit-to-crack transition beyond a localized corrosion initiation site remains unclear.

Grain Orientation and Size

Generally, for fatigue crack growth in the absence of corrosion, reduction of the grain size improves resistance to fatigue initiation.198  A similar effect was observed by Jones and Hoeppner46  for etched specimens in a 3.5 wt% NaCl CF environment, who observed that reduced grain sizes extended their lifetime due to a slower pit-to-crack transition. It was hypothesized the slower transition was due to an increased number of grains within a given area interfering with fatigue crack transition and growth.46  In a separate study, Co and Burns found that in precorroded AA7050, fatigue-initiating grains were larger than the mean and median size grains; however, it was not the largest grain that initiated the crack.25  Looking further at grain characteristics in AA7050, it was concluded that only the misorientation angle relative to adjacent grains showed a correlation with the crack initiation location, and, even in this case, it was not always at the highest level of misorientation. That is, the grain size, extent of residual processing deformation, and grain orientation relative to the loading axis do not independently dictate the fatigue initiation site.25  Similarly, it was found when microstructure and corrosion features were investigated together in crystal plasticity models of corroded materials, a microstructure-based prediction of the mechanisms that drive crack initiation can be created and was shown to predict favorable locations for crack initiation for the same AA7050 system.199  FEA modeling has also served as a way to evaluate how corrosion influences the grain orientation.200-202  With 2D FEA modeling, Brewick and co-workers accounted for the effect of microstructure on the formation of a pit.200,-201  They concluded that microstructure contributes to the nonsymmetric shape of pits201  and reported that the maximum stress on the pit is sensitive to the microstructure. Additionally, pits were more likely to be found near a grain boundary, driven by the mismatch in elastic constants of the grain orientations on either side.200  Despite these advances, Brewick and co-workers200-201  do not comment on the influence of strain localization which has been shown to play an important role in the propagation of pits and crack nucleation. Chu, et al., similarly reported microcracks preferentially formed at pits on grain boundaries and other microstructural inhomogeneities such as pearlitic colonies and banded phases. However, when pits nucleated at grain boundaries, the cracks did not progress down the grain boundaries and were transgranular in nature.193  Ultimately, research has indicated crystallographic inhomogeneities and mismatch of elastic constants due to crystallographic misorientation may influence pit formation and the eventual transition.

The influence of grain size has also been investigated under fatigue,203  and SCC204-205  scenarios for other alloy systems, showing similar trends to AA, in that smaller grains reduce the initiation of cracks.203-204  Lu, et al., noted that in U-bend testing (static load) of SS304, refined grain sizes can reduce initiation in boiling MgCl2 exposure environments.204  Mochizuki and Mikami investigated SCC initiation in a microscopic model to evaluate the microscopic stress on the scale of the grains and microstructure utilizing the theory of crystal plasticity. The locations where microscopic stress concentrations occurred in the multiscale analysis were in good agreement with the locations of cracks observed in SCC tests for a 600 Nickel-based alloy.205  Finally, Bellefon and Duysen conducted elastic FEA focused on the influence of elastic anisotropies in face-centered cubic (fcc) alloys and pointed out that high local stress led to crack initiation; however, experimental validation is still being performed.190 

The importance of grain structure and size has been shown for fatigue without corrosion and for SCC and CF for various alloy systems. In general, for fatigue, SCC, and CF smaller grain sizes decrease the initiation of cracks and increase the pit-to-crack transition time period suggesting loading independence of grain size. Second, the grain boundary characteristics and underlying microstructure have been investigated together in crystal plasticity models with promising results for predicting initiation sites. Finally, for CF, misorientation angles, specifically high-angled grain boundaries, relative to adjacent grains, have been shown to be preferential sites for SCC initiation.

Grain Phase

Differences in grain phase can also play a role in the pit-to-crack transition leading to preferential pit initiation and differences in stress or strain distributions. For example, 2205 duplex SS samples manufactured in the transverse direction (TD) displayed the highest propensity toward atmospherically induced SCC.19  This was in line with higher strain and stress distributions in both ferrite and austenite in the TD. Bending along the TD results in larger strain and stress in the microstructure and a higher propensity toward corrosion and atmospherically induced SCC. The direction of bending deformation determines the extent and distribution of strain in the duplex microstructure.19  An example of the influence of the microstructure present in 2205 duplex SS on pitting morphologies is shown in Figure 1(h).206  Additionally, the distributions of stress and strain within 2205 duplex SS development of tensile strain occur initially in austenite and at interphase boundaries, and further extend into the ferrite with increasing load. Furthermore, heterogeneous strain fields within austenite grains indicated higher work-hardening behavior and lower stiffness of austenite than ferrite.207 

Investigations of SS304 in various chloride environments and loading conditions have shown cracks formed under high strain conditions (0.2%) inducing an elastic-plastic scenario and were linear in comparison to those formed at lower, elastic strain that showed branching (0.1%). This suggests that different microstructures led to varying strain and stress distribution within the metal matrix and influences pit-to-crack transitions.134  The role of martensite in pitting and SCC processes of SSs has been recognized as an important factor due to changes in material properties. In pitting studies of SS304, it has been suggested that deformed martensite structures introduced into the matrix during the polishing process can preferentially cause corrosion and crack nucleation.47-48  Ghosh and Kain investigated SCC initiation of SS304L in an H2SO4 and Cl environment as a function of surface machining, which formed different fractions of induced martensite.180  A high density of martensitic regions on the surface resulted in higher SCC susceptibility as the dissolution rate of martensite in a corrosive environment is higher than that of austenite. Increased martensite also increased the propensity for SCC crack initiation. It was suggested that nonsensitized SS undergo intergranular SCC in the high-temperature, high-purity aqueous environment of boiling water reactors due to the formation of martensitic structures.180  In a separate study, the martensite transformation effect plays the main role, and the stress corrosion sensitivity index increases with the increasing shot peening pressure.208  Additionally, it has been noted that greater concentrations of deformed martensite lead to a shorter crack initiation time209  and potentially lead to increased susceptibility to HE.210  Finally, as with 2205 duplex SS, the mechanical properties of martensite and austenite in austenitic SSs are different211  further influencing the local distribution of stresses and strains within a localized corrosion feature.

Overall, the influence of metal phase has been shown to be important in both duplex and austenitic SSs. Increased susceptibility to SCC initiation has been shown at the boundary between the two phases due to the difference in electrochemical activity. Additionally, different material phases change mechanical properties and combined with differences in electrochemical behavior, area concern for pit-to-crack transitions due to the enhanced initiation of corrosion features at metal phase boundaries and the potential for differences in localized stress and strain fields.

Hydrogen Embrittlement

H uptake into a susceptible metal can result in embrittlement, rendering it more susceptible to cracking and enhancing crack growth rates171,212-215  and can influence the pit-to-crack transition. Critically, H uptake can significantly reduce material ductility and cause cracking and catastrophic brittle failures at stresses below the yield stress of susceptible materials.216  While mechanisms related to HE are still under debate216-218  and not the sole focus of this paper, the deleterious effects of H on the mechanical performance of materials are widely accepted. Furthermore, it is commonly recognized that environmental effects and corrosion-induced H production and uptake likely also impact crack initiation.19,134,183,206,-207,219-225  Increased H production and uptake can occur at occluded sites86,224,226-229  and is influenced by the stress state.230-232  For example, H concentrations were mapped spatially, proximate to acidic corrosion pits formed in MgCl2 droplets, on an ultrahigh strength SS using a Scanning Kelvin Probe.228  As HE reduces mechanical strength and ductility and H is elevated in localized corrosion features, HE could influence the pit-to-crack transition. In 1969, Rhodes proposed that microcrack formation could be promoted by occluded pits facilitating H production and embrittling the material.222  A similar mechanism has been proposed as the source of microcracks in corrosion exposures.47,-48  Despite the studies related to H influences on corrosion, SCC, and CF separately, the influences of H on the pit-to-crack transition are seldom explored.

Of particular note, Burns and Gangloff investigated the influence of H on precorroded specimens in ambient temperature, humid, fatigue environments as well as low temperature, dry environments yielding quantitative fatigue crack formation and microstructure scale crack propagation kinetics for AA7075.233  It was hypothesized that localized corrosion prior to fatigue develops an H (or H-vacancy complex) concentration gradient about the pit surface and is shown schematically in Figure 12. Additionally, cracking kinetics (i.e., crack growth rate) when initiated near-pits was enhanced by H which could have dissolved in the microstructure prior to fatigue loading.233  The influence of H has also been investigated in steel systems. First, it was deduced by Örnek and Engelberg that H uptake was seen to lead to individual cracks branching from the crack front, suggesting HE acting in parallel to SCC at different sites in SS304.134  Second, in 2205 duplex SS HE increases with increased aging time, mainly caused by microstructural changes in the ferrite microstructure, and increased the overall length and number of observed SCC,19  potentially indicating a decreased time to transition from a pit to a crack. Further studies of H effects on the pit-to-crack transition included H uptake measurements by thermal desorption spectroscopy coupled with corrosion damage imaged by atomic force microscopy.234  It was concluded that corrosion damage starts with pitting and proceeds to interactions between pits, intergranular attack, and exfoliation. Hydrogen, produced during the corrosion process, was trapped in distinct states in the interior of the material. While the authors point out that yield strength is restored on the removal of the exfoliated layer, this study does not elucidate the role of hydrogen in the CF process.234  Overall, the potential interactions of H and material properties have been highlighted for the limited pit-to-crack studies19,134,233-235  warranting further study.
FIGURE 12.

H charging and vacancy injection during pit corrosion. The dashed box speculates a combination of H-vacancy complexes to form 100 nm voids containing atomic H and H2, where absorption into interstitial sites allows the H to diffuse into the material. Figure reprinted with permission from Burns and Gangloff.233 

FIGURE 12.

H charging and vacancy injection during pit corrosion. The dashed box speculates a combination of H-vacancy complexes to form 100 nm voids containing atomic H and H2, where absorption into interstitial sites allows the H to diffuse into the material. Figure reprinted with permission from Burns and Gangloff.233 

Close modal

It has also been realized that dislocations can play a role in the crack initiation process for smooth specimens under fatigue conditions.130,236-237  Furthermore, researchers have shown a stress field attractive interaction between H and dislocations;238  however, as pointed out by Burns and Gangloff, the attractive force between H-vacancy complexes and dislocations or hydrostatic stresses has not been studied233  and remains a field of future study for pit to-crack transitions. Finally, the phases present play an important role in pit-to-crack transitions potentially due to differences in H diffusion rates which have been shown to be different for austenitic SS.239-241  For example, deformation-induced martensite could increase pit-to-crack and SCC susceptibility in austenitic SS.242-243 

Overall, HE reduces material ductility and causes brittle crack formation. Localized corrosion sites typically have increased hydrogen concentrations, increasing the susceptibility to HE in the region surrounding the localized site. Various studies have theorized controlling mechanisms of hydrogen on crack initiation; however, the influence of H on the pit-to-crack still remains a critical area of study especially as proposed mechanisms for HE likely vary with material and environment.

Materials Processing

Materials processing has been shown to influence SCC initiation and pit-to-crack transitions for in-service alloys. Typically, materials processing will affect the overall microstructural features further influencing corrosion initiation and propagation, HE, and pit-to-crack transitions. There are many ways to process a material, and some of these processes have been shown to be both detrimental and beneficial for pit-to-crack and SCC resistance, including: thermal treatment,171,188,244  rolling of a material,171,209,245-249  shot peening,174-175,208  surface grinding,47-48,170,180,250  laser processes,172,204  and AM.152,251  All of these processes have the possibility to influence both stress distribution (Increasing Stress Decreases Pit-to-Crack Transition Time section) and materials’ properties (Material and Microstructural Properties Influence Pit-to-Crack Transition section) which could be detrimental or beneficial to pit-to-crack transitions. While an examination of all methods and their potential influences on the pit-to-crack transition areoutside the scope of this review, a brief summary of potential influences from one example materials forming technique, AM, will be put forth as an example, but is not meant to be an extensive review of this topic nor ignore substantial work in other processing techniques. For AM, important factors for corrosion propagation and resistance have been reviewed.252-253  A pictorial representation of the metallurgical effects is presented in Figure 13 from Sander, et al.252  There are many competing metallurgical effects for AM materials influencing pit-to-crack transitions. For example, refined grain sizes254  can reduce the propensity for crack propagation (Grain Orientation and Size section), but pit initiation at asperities (Additional Factors section), oxide inclusions,255-256  pores,257  and chemical segregation sites258  combined with elevated residual stresses152  (Residual Stress section) could increase the propensity to initiate and propagate a crack. While a detailed analysis of pit-to-crack transitions in AM materials is not present, recent work in boiling MgCl2 indicates a combined effect of H trapping in dislocation structures and residual stresses lead to crack initiation.152  As such, caution should be taken when applying pit-to-crack studies on wrought materials to AM materials.
FIGURE 13.

Summary of potential metallurgical effects from additive manufacturing. Reprinted from Sander, et al., 252  under CC BY-NC-ND. The figure includes data reported in the literature.252,319-324 

FIGURE 13.

Summary of potential metallurgical effects from additive manufacturing. Reprinted from Sander, et al., 252  under CC BY-NC-ND. The figure includes data reported in the literature.252,319-324 

Close modal

Electrochemical, Environmental, and Metallurgical Influences on Pitting Characteristics

The solution composition and concentration of the exposure environment (including thin film or full immersion conditions) influences the characteristics of pitting corrosion features and, as discussed in the sections: Pit Depth may not be the Sole Governing Factor for Pit-to-Crack Transition, Increasing Aspect Ratio of a Smooth Ellipsoidal Pit Increases Stress Concentration, Sharp Corrosion Features and Asperities may Increase Local Stress and Strain Concentrations, Additional Factors, Increasing Stress Decreases Pit-to-Crack Transition Time, Material and Microstructural Properties Influence Pit-to-Crack Transition, Hydrogen Embrittlement, and Materials Processing, can impact the pit-to-crack transition. There are many factors that influence localized corrosion as the process relies on an otherwise passive alloy to suffer a breakdown at discrete sites. Once initiated, a localized corrosion feature provides an occluded region that prevents mass transport between the interior localized corrosion solution and the exterior bulk solution. An autocatalytic process is started in which metal cations undergo hydrolysis, resulting in aggressive, acidic solutions (high concentration of H+) that destroy local passivity and create an actively corroding anode. Pit growth cannot continue without sufficient cathodic reduction current, and without a sufficient cathodic supply, a pit will not be able to produce sufficient metal cations to replace those lost by diffusion and the pit will repassivate.259 

Further, the shape and stability of pits have been theorized to be controlled by the local concentration of aggressive anions (i.e., presence of a salt film) which can be related to the overall cathodic current.260  As such, the exposure environment (i.e., bulk anion concentration, solution amount, etc.) can influence the cathodic current supply and the overall pit shape.

Although this focus is not meant to disregard the immense work done by many others for full immersion conditions, it is likely that irregular shapes are more prevalent in thin film environments47,-48,67-68  due to the level of polarization and limited cathodic supply and will be the focus of the discussion within. Additionally, studies mentioned in Pit Depth may not be the Sole Governing Factor for Pit-to-Crack Transition, Increasing Aspect Ratio of a Smooth Ellipsoidal Pit Increases Stress Concentration, Sharp Corrosion Features and Asperities may Increase Local Stress and Strain Concentrations, Additional Factors, Increasing Stress Decreases Pit-to-Crack Transition Time, Material and Microstructural Properties Influence Pit-to-Crack Transition, Hydrogen Embrittlement, and Materials Processing sections will not be further detailed in this section. Furthermore, influences of stress and environment on pitting may become compounded when simultaneous influences are considered and the complex interactions between the environment and stress need to be considered.261 

Pit Shape

Varying exposure environments and alloy types can drastically influence the shape of a localized corrosion feature and, therefore, the pit-to-crack transition. Studies performed in simulated atmospheric environments have shown an influence of RH on pitting morphologies. For SS304 deposited with seawater and exposed at 40% RH,47-48  similar to a saturated MgCl2 brine,262  pits were irregularly shaped with a sharp, cross-hatched structure. At 76% RH, where a NaCl-rich brine forms,262  the observed pits were ellipsoidal with crystallographically faceted surfaces (Figure 1[e]).47-48  The difference in pit morphologies suggests the solution and water layer thickness may have an influence on the pH and concentration of metal cations in the pit.260  Another study by Street, et al., also observed pit morphology differences under droplets of pure MgCl2 with changes in RH.67  At 33% RH, pits were shallow dishes with regions that showed crystallographic etching with a deeper attack on one side and satellite pits (shown in Figure 1[f]) near the circumference. At 56% RH, the pits did not have a shallow dish region but instead showed narrow circular mouths. As increasing the RH will dilute the chloride present, the presence of differing morphologies at varying RH levels illustrates the influence of salt concentration on pitting morphologies under thin brine layers.67  Another pitting study on SS304 investigated pitting under droplets containing different compositions at a constant RH of 45%. MgCl2 droplets were observed to have spiral, etched growth, while an MgCl2 and NaCl mixture contained various pit morphologies including: a dish-shaped pit, shallow crevice-like attack under a salt crystal, and crevice-like attack containing a pit under a salt crystal.68  While it is important to understand environmental influences, the underlying microstructure of a steel system can have drastic influences on the pitting morphologies. For example, duplex stainless steel 2205 contains distinct ferrite and austenite regions, resulting in microgalvanic couples and results in selective dissolution of certain phases producing abnormal corrosion features (Figure 1[h]).206  Overall, studies on SS alloys indicate that RH, salt compositions, and salt concentrations significantly influence the pitting morphology with more irregular pits present at low RH exposure levels.

AAs are also known to pit in chloride environments263-266  and studies on environmental influences of pitting in aluminum and AAs have shown an influence of long-term exposure, material microstructure, and chemistry. In one example, when AA5005 was exposed to a seawater environment, pitting morphology increased in complexity as the exposure time increased. Only smooth hemispherical pits were observed in the early months of exposure; however, after 12 month, crystallographic pits and petal-like pit features also appeared.70  Similar pit shapes were also observed for AA6060 with the addition of dimple-like pits at long time periods indicating that time of exposure matters for corrosion features in AA.69  Pitting initiation in AAs has also been correlated with intermetallic particles and grain boundaries.74,99,194,267  For example, AA2024 was exposed to 0.5 M NaCl for 500 h and cross sections revealed two types of morphologies on the same alloy surface with abnormal features being generally associated with constituent particles.268  Overall, the time of exposure, exposure environment, and material microstructure including composition and grain orientation play significant roles in pit formation in AAs.

In low RH exposure testing and duplex microstructures, abnormal and sharper localized corrosion features have been observed.47,-48,67,-68,206  As discussed in the Sharp Corrosion Features and Asperities may Increase Local Stress and Strain Concentrations section, it is likely that sharper, irregular features will increase strain concentrations, increasing the likelihood of the pit-to-crack transition when compared to the critical strain threshold.117  Thus, it would follow that pit-to-crack transitions may be more likely in low RH environments or alloys with microgalvanic couples.

Pit Depth

Literature has noted the influence of the environment, surface finish, and stress on pit depth. Schindelholz and co-workers investigated pit depths on a mild steel at various RH levels and found that increasing exposure RH generally increased pit depths for NaCl, MgCl2, and artificial seawater solutions after 30 d of exposure.71,-72  Additionally, it is noted that at high RH, NaCl solutions exhibited a deeper pit depth in comparison to MgCl2 and artificial seawater solutions despite NaCl having a lower overall chloride concentration71,-72  potentially related to cathode availability.66  Srinivasan, et al., observed little to no difference in the deepest measured pit when changing RH.47,-48  Similarly, Street, et al., noted that pit depths in exposure environments below 48% RH had a comparable maximum pit depth regardless of geometry.67  While the dependence of pit depths with the environment remains unclear, it is important to note that RH and solution type can influence corrosion rates. For example, Schindelholz noted that below 50% RH, MgCl2 had a higher corrosion rate for mild steel in comparison to NaCl solutions while corrosion rates above 50% RH were relatively similar and even plateaued.269  While the kinetics of corrosion have widely been ignored in this study, it is important to remember that early research (First Established Criteria for Crack Initiation from a Pit-Like Geometry section) relied on rate competition between anodic dissolution and crack growth rate.

Deeper pits have also been observed on rougher surface finishes after exposure periods. Turnbull, et al., has also shown that surface finishes can influence pit depths of SS304 exposed to MgCl2, with a milled finish producing greater depths than ground finishes.135  Another study on SS304 and 316 alloys has also indicated rougher surface finishes had deeper observed pitting morphologies than smooth surface finishes.270 

In general, when an alloy has an external or residual stress pits are deeper.113,121,133,139,143,148,166,271-274  Also, elastic and plastic deformation can both promote metal dissolution. Based on bulk thermodynamics analysis, Gutman271  built a model describing mechano-electrochemical effects of metals. Based upon this model, local stress and strain distributions can lead to differences in the local anodic dissolution rate leading to changes in the pit geometry and, in turn, influence the local stress and strain distributions at every microregion of the pit surface.143,271  Experimental research from Ishihara, et al., indicated that increases in fatigue stress amplitude increases maximum pit depth.113  Research on SS304 in ferric chloride by Huang, et al., showed that applied stress increased the average pit depth compared to static conditions.133  Finally, it has been shown that plasticity can also play an important role in the pitting process, and the onset of plasticity can increase overall pitting depth.121  Overall, there are many influences on the depth of localized corrosion features and, as reviewed in the Pit Depth may not be the Sole Governing Factor for pit-to-crack Transition section, they can influence pit-to-crack transitions.

Finally, it is important to note that pit sizes on many passive alloys, such as austenitic SS, tend to reach a finite size at longer time periods in atmospheric environments.47,-48,66  In varying long-term field exposures of SS304 and SS316 compiled by Chen and Kelly, a bounding pit depth was observed even for samples exposed up to 26 y and served as justification for cathodic limitations on pit growth in atmospheric environments.66  The finite nature of pits observed in long-term field exposures is interesting to note as many early models for pit-to-crack transitions (First Established Criteria for Crack Initiation from a Pit-Like Geometry section) do not include finite growth of pits.

In general, deeper pits have been observed in high RH environments, on rougher surfaces, and in the presence of a stress. While deeper pits are found in these environments, as discussed in the Pit Depth may not be the Sole Governing Factor for Pit-to-Crack Transition section, pit depth may not be the sole determination of the pit-to-crack transition. There are compounding influences from deeper pits at high RH and pits containing more asperities in low RH environments further complicating the mechanistic interpretations of the pit-to-crack transition. Additionally, environment and material type influence the growth rate; however, in some alloy systems, finite pit values are observed for long times. The implications of these findings will be discussed further in the Discussion and Implications section.

Methods for Artificial Pit Creation

In order to study the pit-to-crack transition, a defect, either a localized corrosion feature or a mechanically formed pit, needs to be present on the surface. Pit-to-crack transition studies often involve the creation of pits electrochemically either by exposure to an accelerated solution,1,21,74-75  galvanostatic polarization,28  or potentiostatic polarization.23,76  It is important to consider that these techniques of growing pits can influence the shape and characteristics of a pit. Of particular note, Ghahari, et al., observed the difference in potentio- and galvano-static methods to grow pits via in situ synchrotron radiography on SS304 in 0.1 M NaCl.275  In their study, potentiostatically grown pits had a clearly defined and smooth perimeter. In contrast, galvanostatically grown pits were deeper but had a rougher surface and an etched perimeter.275  In pure aluminum (studied in 1 M NaCl) the level of potentiostatic polarization changed pit morphology276  further highlighting the importance of replicating the exposure environment with electrochemical methods. It was also noted by Zaid, et al., that anodic potentiodynamic polarization of AA6061 in 3.5 wt% NaCl did not match the morphology of fully immersed unpolarized exposures.277  Overall, if the underlying microstructure of the metal heavily impacts naturally grown pits, then strong electrochemical polarizations or differing chemical solutions can depart from the important, governing formation mechanisms and resultant features of a naturally formed pit.

Another important factor is the aggressive chemistry formed by natural, accelerated, or electrochemical (galvanostatic or potentiostatic) processes. While it is possible that in certain applications pits are formed during nonservice conditions and then the pit-to-crack transition occurs during service, there are still many applications where pit and crack nucleation occur in the same environment. As stated in the Electrochemical, Environmental, and Metallurgical Influences on Pitting Characteristics section, localized corrosion processes are largely an autocatalytic process and rely on metal ion hydrolysis to drive compositional differences between the localized feature and the bulk solution chemistry. Broadly, the pit environment can be very aggressive (i.e., low pH, high Cl, etc.) and differs radically from the bulk environment.259  Methods used to investigate the pit-to-crack transition can remove this aggressive environment for characterization purposes after pit formation. An example exposure environment for AAs is an ASTM G-341,22,-23,25,278  and ASTM G85.75  In both accelerated methods, the samples were exposed for various durations, cleaned, characterized for pitting characteristics, and then exposed to fatigue or CF. In these scenarios, while enhanced characterization of the localized corrosion features is gained, the aggressive solution created during localized corrosion formation is removed. Additionally, during this process, depending on the time required for characterization and/or the environment necessary for cleaning, hydrogen egress from the material is possible, potentially reducing the susceptibility for pit-to-crack transitions. While a good agreement for accelerated tests such as ASTM G-34278  is seen when comparing morphologies between lab and atmospheric exposures,23,279,-280  the connection of critical chemistries for localized corrosion propagation with the pit-to-crack transition is typically lost during the cleaning process. Thus, pits are often exposed to an aggressive environment, removed from that environment, and re-exposed to a corrosive environment to test the pit-to-crack transition causing concern regarding the aggressive chemistry that is present in the pit as it can be removed during this process.

While difficult to capture, it is thought that chemistry within localized corrosion features can play an important role in the pit-to-crack transition.281  Additionally, bulk chemistry in application environments can change rapidly (e.g., diurnal cycles and wetting and drying events) in comparison to the lifetime of an application (potentially hundreds of years).282  If dry-out occurs, the re-initiation of the localized corrosion feature becomes more difficult in comparison to initiation on a bare surface.281  Finally, experts in the field of corrosion have agreed that under static loading of austenitic SSs, the environment within the pit is necessary for crack initiation, and that crack initiation would occur from an actively propagating pit, rather than a repassivated one.281  An alternative attempt at simulating pits was applied by the introduction of the defects of the electric discharge machine.26,283,-284  However, this resulted in smooth pit surfaces often not representative of real-life pitting scenarios and potentially resulted in changes to the near-surface properties.285 

Overall, there are various methods to create localized corrosion features and these processes influence the formation of pits. First, the solution composition and concentration influence the shapes of pits and can induce ellipsoidal crystallographically faceted surfaces, rough cross-hatched structures, spiral morphologies, crevice-like attacks under a salt crystal, or petal-like structures. In controlled atmospheric environments, lower RH typically exhibits pits with rough cross-hatched surfaces while pits in higher RH exposure environments had crystallographic attack. Exposure to various solutions also influenced the overall α of the samples with low RH environments typically having shallow pits. Second, the overall pit depth can be influenced by the solution properties with various trends noted. Finally, it is noted that electrochemical methods to induce pits into a surface also change the various aspects of a pit and often do not replicate the morphologies that are commonly seen in field or controlled exposures.

The current review showcases a variety of factors such as pit characteristics, applied stress, and material microstructure, and how that influences the pit-to-crack transition. The importance of these factors has not been exhaustively explored nor has the potential for complex interactions between the factors and implications for the pit-to-crack transition. Future experimental work should further examine the impact of these factors, separately and in combination, to better inform modeling and simulation efforts and ultimately build toward a reliable and realistic model that can be used for predictions of crack initiation.

Summary of Knowledge

Experimental research has detailed important localized corrosion and loading features that lead to a pit-to-crack transition. Current models do not fully capture these important features nor allow for the extrapolation from a given material and environment combination. While early research (First Established Criteria for Crack Initiation from a Pit-Like Geometry section) such as the Kondo criterion set forth a foundation exploiting the notion of competing rate theory between pit growth and crack growth, early models should be used with caution when extrapolating the underlying principles. Substantial research on the pit-to-crack transition has been performed and reviewed within; however, the applicability of early models and mechanistic understanding of the pit-to-crack transition is lacking, limiting the extension of experimental results and validated models, requiring the creation of newer, more detailed models.

It has been widely shown that increasing the depth of a corrosion feature, irrespective of loading conditions or material property, will increase the stress concentration, as presented in the Pit Depth may not be the Sole Governing Factor for Pit-to-Crack Transition section. While this may be the case, experimental evidence has shown that the deepest pit does not necessarily initiate a stable SCC or CF crack. This has been shown for constant loading scenarios16,45  and fatigue24-25,75,118  as well as both iron-based45,118  and aluminum systems24-25,75  indicating this phenomenon is valid for many loading states and material systems. Another geometric property of interest identified by early research is the pit aspect ratio, α, and, similar to pit depth, increasing α increases the stress concentration of a pit. However, increasing α for pits in an AA system133  or Fe-based system16,23  does not correlate with crack initiation and indicates that bulk corrosion features cannot solely be used to identify when a crack will nucleate. At this point, it is worth noting again that some experimental methods remove the corrosive environment within the localized corrosion feature for advanced characterization. Despite this fact, when the corrosive environment is not removed, there is still evidence that neither the deepest pit nor the deepest part of the pit, initiates critical cracks in structures.120  Thus, there is significant evidence that bulk corrosion metrics (i.e., pit size, α) are insufficient to completely define the crack initiation process, in contrast to early research and models necessitating the further study of microfeatures within a localized corrosion feature and incorporation in models.

The importance of local stress and strain (both elastic and plastic) of microfeatures, instead of bulk stress, K, or ΔK calculations, have been shown to play a role in crack nucleation. Work from Turnbull and co-workers15  correlated crack nucleation near the mouth of a static pit with the highest plastic strain distribution. Further strain localization has also been shown to be important for CF.131  As reviewed in Sharp Corrosion Features and Asperities may Increase Local Stress and Strain Concentrations section, the idea of plastic stress and strain distributions has been furthered beyond hemispherical representations of a pit and extended to scenarios with asperities or localized corrosion features. Experimentally, fatigue cracks have been observed to nucleate at prepitted microtopographic features, jut-ins, and micropits for AA1,22,25  and were correlated with high plastic strain localization at these sites.22  Typically, computational studies investigating stress and strain distributions within a corroding feature are performed under static stress without the presence of a corrosive environment. As plastic strains have been shown to play a role in initiation, dynamic strain rates could also influence crack nucleation, thus the incorporation of dynamic simulations accounting for active corrosion and fatigue are needed. Certain models do include chemical considerations for active corrosion80,148  or growth is simulated by element removal,15,83  however, the growth of microfeatures in a pit combined with a stress field resulting in nonzero plastic strain rates has yet to be explored. Furthermore, while certain models consider chemical reactions connected to pit growth,80,148  they typically do not include information regarding HE (Hydrogen Ebrittlement section) nor cathodic reactions which could influence critical conditions inside a localized corroding feature (described in the Electrochemical, Environmental, and Metallurgical Influences on Pitting Characteristics section) due to competing pits sharing the same cathode.286 

It is no surprise that increasing the overall applied stress increases the likelihood of transition as covered in the Increasing Stress Decreases Pit-to-Crack Transition Time section. While the general trend was presented, the location of crack nucleation with increased applied stress may change due to potential changes in the localization of stress and strain.15  For fatigue scenarios, increasing the R-ratio increased crack initiation. While increasing the R-ratio or stress increases the likelihood of transition, the dominating initiation point (i.e., pit depth, microfeatures, etc.) is not typically noted and it is unknown if increasing applied stress will change the preferential initiation point when microfeatures are present.

Other considerations for preferential nucleation sites were reviewed in the Material and Microstructural Properties Influence Pit-to-Crack Transition section. First, while constituent particles, grain orientation, grain size, and grain phase are considered preferential nucleation sites for pure fatigue and localized corrosion sites, the role of these variables in nucleating a stable SCC or CF remains unclear. For example, Jones and Hoeppner noted that for etched 7075 in 3.5 wt% NaCl under CF environments constituent particles competed with corrosion pits as critical crack nucleation sites.46  Additionally, Co and Burns found that in precorroded AA7050, grains initiating fatigue cracks were larger than the mean and median size grains; however, the largest grain did not initiate a crack.25  Thus, similar to pit depths and α, singular material and microstructural properties do not correlate with SCC or CF initiation. Next, HE was reviewed as hydrogen uptake can significantly reduce material ductility and lead to cracking at stresses below the yield stress. While evidence exists that HE can play a role in the pit-to-crack transition as reviewed in the Hydrogen Embrittlement section, direct detection of hydrogen in materials and HE influences remains a challenge, limiting current understanding of H influences on the pit-to-crack transition. Finally, environmental and material influences on localized corrosion growth were presented in the Electrochemical, Environmental, and Metallurgical Influences on Pitting Characteristics section and highlighted the differences in electrochemical phenomena that can cause idealized (i.e., hemispherical) geometries and rougher, microfeatures. It was identified, that while methods exist in some alloy systems to replicate complicated geometries in a controlled manner, the critical environment during growth is sometimes removed. Experts have agreed that for initiation under static loading, the environment within the pit is necessary for crack initiation, and that crack initiation would occur from an actively propagating pit, rather than a repassivated one,281  however, the exact conditions needed for this transition or if these conditions are necessary for CF remain unexplored.

Prevailing Knowledge Gaps

Understanding the pit-to-crack transition, in terms of transition time and governing mechanisms, remains a critical challenge in many scientific and engineering applications. The existing research of the pit-to-crack transition has not yet developed a reliable, mechanistic-based method for predicting the pit-to-crack transition but has provided a foundation for future research into the area.

High-fidelity, time-dependent, 3D modeling of localized corrosion features in relevant environments, including the influence of internal and external stresses, is necessary for the development of mechanistic models describing the pit-to-crack transition. Critically, an understanding of morphologies (Figure 1) and mechanisms, coupled with the operating environments is needed. The ever-changing local environments due to active corrosion, ambient conditions, and stress/strain redistribution make this a particularly challenging, dynamic problem. Additionally, there is a lack of fundamental thermodynamic and kinetic understanding of the effect of elastic stresses or strains and plastic strain on dissolution, including how stress affects anodic dissolution SCC mechanisms from pre-existing corrosion features.287  Finally, it is important to note that such models are needed in 3D as the distribution of stresses and strains are dependent upon the loading direction125,146  and potentially cause preferential growth in different directions in comparison to a 2D model.

In conjunction with improved localized corrosion modeling, modeling of HE and subsequent material property changes requires further study. Specifically, understanding dynamic plastic strain induced by HE occurring at occluded environments could play an important role in determining crack initiation sites. Additionally, the interaction of overlapping distributions of applied stress, pit concentrated macrostress, local microtopography, and microstructure, plus local material changes due to stress (i.e., deformation-induced phase changes) and HE,19,134,183,206-207,219-225,288  is needed in order to have a further understanding of the pit-to-crack transition. After the creation of improved, dynamic models informing HE, these models could help predict local stress and strains, potentially governing the pit-to-crack transition. It is again important to reiterate that K calculations are not appropriate for pits due to the mathematical formulation of K or for small cracks due to strain localization-induced plasticity, which causes a breakdown of LEFM conditions, and careful consideration of the local, plastic material properties is necessary.80 

Aspects of a pit-to-crack model that incorporate crack propagation could be extended to modeling of stable SCC and CF propagation and failure. While a complete understanding of the chemistry at occluded sites, such as pits and crack tips, remains elusive,287,289-290  developed models for pit-to-crack transitions could help reach this goal. Although there has been substantial progress in defining local chemical compositions and electrochemical conditions of crack tip solutions, understanding of the exact mechanical properties of passive films at crack tips is lacking287  and requires further investigation. Modeling of the pit-to-crack transition can also be applied to the electrochemical effects of both short and long cracks38  enabling the connection between governing microscale processes across many time and length scales to engineering-scale metrics. Further, models will not only help identify governing mechanisms but will also enable the assessment of mitigation and repair strategies prior to implementation.

As simulation and modeling capabilities continue to advance, there is an increased opportunity to include the aforementioned factors and potential interactions; however, the quantification and validation of predicted transitions and important factors remain a challenge. In order to validate models, experimental investigation of the pit-to-crack process is needed and many studies typically rely on the creation of prepitted materials25,27,45,75,155  rather than actively corroding specimens. Therefore, a need exists to create realistic localized corrosion features that are representative of in-service environments in laboratory time scales. While techniques to create localized corrosion defects exist, they often do not replicate in-service corrosion damage, do not create complex geometries presented in Figure 1, or can change the damage state at the near surface of the induced defect.285  Additionally, experimental parameters required to create single defects could vary by alloy and environment and have not been sufficiently validated. Thus, improved, accelerated creation of localized corrosion features is needed. While the use of a prepitted alloy allows the quantification of pit characteristics on the micron and submicron level prior to crack initiation,25,291,-292  in-service pit-to-crack transitions potentially occur from an actively corroding material requiring experimental testing while monitoring both in situ pitting characteristics on the submicron scale as well as crack initiation. Quantifying such a dynamic process is nontrivial and is identified as a need for understanding the pit-to-crack transition

Experimental quantification of local H concentrations at microscopic features and the influence on microstructure is also identified as a critical need for understanding the pit-to-crack transition. Strong gradients in H concentration on a length scale of 0.05 µm to 5 µm and stress state can govern crack growth293  and potentially the pit-to-crack transition. There exists a challenge in modeling and characterization of H damage necessary to understand governing mechanisms293  and improved methods for quantification on the length scale of interest (<5 µm) are needed. Additionally, hydrogen may be enriched by electrochemical and chemical reactions occurring during localized corrosion features.86,226-229,293  As such, prepitting a sample could allow for sufficient hydrogen diffusion241  prior to experimental determination of the pit-to-crack transition potentially influencing both the location of and time to the transition. Finally, it is unclear whether accelerated pitting techniques will create similar dissolved H concentrations as in-service conditions.

Pit-to-crack research has focused heavily on optical and white light interferometry measurements, as well as a select few microscopy techniques, such as x-ray computed tomography (XCT).16,-17,99-108  Although there have been advancements in XCT, there are substantial limitations to the technique. The temporal and spatial resolution of XCT is limited294  and is likely not imaging finer details (i.e., <10−6 m) that may prove to be important to the pit-to-crack transition, such as asperities and microcracking in a pit as presented in Figure 1. Other microscopy techniques have undergone recent advances and have been utilized in the study of SCC and could help improve the understanding of pit-to-crack transitions. Of particular note, tunneling electron microscopy has been utilized in ex situ characterizations of SCC scenarios.90  Recent advances in liquid cell TEM have allowed for advanced exploration of corrosion and SCC phenomena;92,295-304  however, in order to image properly (i.e., allow transmission of electrons), it is likely that 2D samples would need to be utilized influencing stress/strain distributions and localized corrosion propagation. Finally, advancements in cryogenic techniques to probe chemical differences in corrosion and batteries also provide a unique path forward.289,305,-306 

Another technique of interest includes modified atomic force microscopy (AFM) which has been utilized to understand crack tip H distributions.288,307  Additionally, AFM and high-speed AFM have been utilized to investigate localized corrosion features and SCC propagation.94,308,-309  As a result, AFM could give important insight into the pit-to-crack transition. While the aforementioned techniques are likely to yield 2D information regarding pit-to-crack transition phenomena, APT can provide 3D information (both elemental and H measurements).86,98,305,310-311  Despite the 3D nature of APT, the measurements are made on a highly localized scale (∼10−7 m) and could limit the application. Additional techniques that could be utilized in investigations of the pit-to-crack transition include small angle x-ray scattering106  and MicroLaue diffraction using focused synchrotron x-ray probes.293 

It is important to note that a majority of experimental studies on the pit-to-crack transition are performed under fatigue1,20,22-27,32,35,37,44,59,62,75,113-120,144,153-155,167,312  and it is not clear if the transition will be governed by the same phenomena or features under constant load or constant K scenarios. It is not immediately evident that CF fatigue research can directly translate to static scenarios due to generally faster crack growth rates in fatigue and influences of loading on pit formation.125,132,166,313  Additionally, advection imposed by fatigue can cause chemistry differences in highly localized features at the crack tip,53  potentially influencing the aggressive nature of the solution (i.e., chloride concentration, pH, etc.) and thus local H concentrations. H production and uptake are promoted if the crack tip strain rate is sufficient to repeatedly fracture the passive film. Thus, inducing a crack tip strain rate, such as a rising crack mouth opening displacement test, can promote cracking that is not otherwise caused by quasistatic K loading.293  Similarly, loading ratio has been shown to influence H distributions ahead of a crack tip,231  and it is unknown if similar phenomena would be present in H uptake from localized corrosion features.

To date, pit-to-crack studies typically utilize dilute environments resulting in electrochemical properties and pit geometries that may differ from what is present in more concentrated electrolytes common to atmospheric exposure conditions. Sodium chloride is commonly utilized as a simulant in laboratory settings for corrosive operating scenarios, however, specifically for atmospheric or marine scenarios, the composition can vary widely. For example, sea salt brines include many constituents, including magnesium chloride which is dominant in brine at low RH262,282  and can change solution and electrochemical properties.314,-315  It has been shown that corrosion in sea salt at low RH levels creates pits that are morphologically different from those created by an exclusively sodium chloride environment.47,-48  Additionally, it is unclear if there is a significant impact of RH on crack growth rates. Further, atmospheric scenarios typically present a thin water layer (i.e., <900 µm depending on environment316-317 ) and can further influence localized corrosion features and crack growth rate.41,318  While these phenomena have been studied separately, the influence of changing brine conditions and thin water layer thicknesses have not been significantly studied in pit-to-crack transitions or for short crack growth. Finally, the role of the corrosive environment within the pit should be mentioned. It remains unclear if there is a critical strain localization combined with electrochemical properties (i.e., potential, pH, chloride concentration) that would be necessary to initiate an SCC or CF crack and how that changes with bulk environments.

Overall, there has been significant work related to the pit-to-crack transition as discussed in the Important Factors Influencing the Pit-to-Crack Transition section and summarized in the Summary of Knowledge section. There is a clear challenge to improve our knowledge of the fundamental mechanisms involved in the pit-to-crack transition and subsequent growth of SCC or CF from corrosion features. While suggested knowledge gaps in this section are numerous, it is hoped the review and suggested future research will improve our understanding of the complex processes presented within.

Understanding the underlying mechanisms and governing aspects of the pit-to-crack transition remains a critical challenge in many engineering applications and is limiting the accurate predictions and quantification of failures. Additionally, models attempting to describe the pit-to-crack transition are typically empirical in nature and hinder the extrapolation of their findings to other systems or environments. Further, principles from mechanical fatigue and CF are often transferred to static, SCC conditions without proper justification. In order to inform upon the pit-to-crack transition in current and future applications, mechanistic-based models are needed.

Despite significant efforts in quantifying pit-to-crack transitions, a mechanistic understanding of pit-to-crack transitions is still lacking and key areas of further research were identified:

  • It is important to create realistic, 3D, dynamic models of localized corrosion features, including microfeatures and potential imposed strain rates, that can closely represent in-service damage

  • Further validation of created models is necessary. Critically, the creation of representative, in-service localized corrosion features, with an aggressive local environment is required for some applications

  • The determination of combined critical chemistry values with critical stress/strain (or stress intensity) and plastic stress/strain maximum for static and fatigue scenarios is needed

  • The improved modeling of hydrogen embrittlement and the interaction with both pit macrostrain and microstrain induced by asperities is critical, especially on length scales of interest (i.e. <10 µm) is needed

  • The influence of loading state (i.e., fatigue vs. static) as well as the exposure environment, specifically in marine conditions, are identified areas of future study

(1)

UNS numbers are listed in Metals & Alloys in the Unified Numbering System, published by the Society of Automotive Engineers (SAE International) and cosponsored by ASTM International.

This article has been authored by an employee of National Technology & Engineering Solutions of Sandia, LLC under Contract No. DE-NA0003525 with the U.S. Department of Energy (DOE). The employee owns all rights, titles, and interests in and to the article and issolely responsible for its contents. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this article or allow others to do so, for United States Government purposes. The DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan https://www.energy.gov/downloads/doe-public-access-plan. This document is SAND2022-17025 J.

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Published by AMPP. This is an open access article under the CC BY 4.0 license (https://creativecommons.org/licenses/by/4.0/).