Corrosion is the primary failure mechanism for sea-based structures, as it plays an important role in material degradation and structural integrity. The localized corrosion behavior is affected by the micromechanics and the electrochemistry of the material; however, there are very limited studies where both mechanisms are studied jointly, let alone relative to microstructural attributes, i.e., at the mesoscale. High-resolution strain maps are created on pre-loaded AA7050 in the transverse-short orientation via digital image correlation to identify strain accumulation with respect to the microstructure. Afterward, this material is subjected to a galvanic corrosion environment. In order to investigate the driving force for localized corrosion, the microstructure, the cathodic particles, the localized strain, and the evolution of surface topology caused by corrosion pitting are spatially characterized in the region of interest. The evolution of the corroded surface is tracked every 24 h throughout the 20 d of corrosion that the material was immersed in 0.6 M NaCl solution. Specifically, three representative sized cathodic particles are monitored throughout the corrosion study, to identify their evolution of pitting before and after the particles fallout from contact with the matrix. Finally, the relationship between strain and localized galvanic corrosion is quantitatively investigated using Gaussian process modeling to identify the underlying correlations. The results show that localized strains within ±3σ of the macroscopic residual strain do not affect the corrosion rate of the material; however, extreme values beyond that threshold associated with the cracking of the particle itself seem to heavily promote the growth of localized galvanic corrosion.

Throughout the years, aluminum alloys have been the material of choice for aerospace structural applications, especially AA7050-T7451 (UNS A97050(1)) given its high strength, high fracture toughness, and good resistance to several types of corrosion. As a result, it is commonly used in airframe and wing skins applications where high tension and compressive loads are present.1  The life of the material is conditioned by the corrosion it inevitably develops when the aircraft is exposed to saline environments. A particular type of corrosion that conditions the life of AA7050 is pitting associated with localized galvanic coupling.2-3  Pits have consistently shown to be the main source of cracks and therefore are the limiting factor on the life of the material4  or for determining potential life extensions of aging aircrafts. As a result, there is a persistent interest in the community to understand the mechanisms behind corrosion pitting and its eventual transition to cracking.5-7 

For aluminum alloys, pitting has been found to originate at particles that are cathodic relative to the surrounding matrix.8  For the 7xxx series Al alloys, the copper-based Al7Cu2Fe intermetallic particles have been consistently shown to generate a localized galvanic coupling with the surrounding matrix.9-10  The localized galvanic coupling, as well as the large size of these particles relative to other cathodic constitutive particles, develops an accelerated localized corrosion of the matrix that eventually evolves into pits. The anisotropy of rolled aluminum plates cause these particles to be aligned with the rolling direction (L), thus causing uniformly scattered pitting on the transverse-short (TS) plane.11  It follows that the TS orientation is the one most likely to show the earliest development of needle-like pitting, with features deep enough to evolve into cracks.12 

As crack initiation has been observed to occur at pits of around ∼50 μm in AA7050,13  it is of interest to identify the physical basis that drives corrosion during its early stages, that is, before corrosion pitting reaches a critical size. Some factors that have been demonstrated to affect the corrosion rate in materials are either mechanical in nature, such as surface roughness14  or grain boundary density,15  or electrochemical in nature, such as local Volta potential gradients16  or the electrochemical interaction between particles themselves.17 

From a mechanical perspective, the residual mechanical loads acting on the material have shown to affect the corrosion behavior. For a pitting morphology, it has been postulated that residual tensile loads encourage the pits to grow in a notch-like manner.18  Additionally, residual compressive loads left from surface processing and enhancement strategies, such as shot peening, have been proposed to impede corrosion evolution and help retard pit growth.19  However, most of the relationships between mechanical deformation and localized corrosion only measure the response of the material at the macroscale level, specifically during the manufacturing process.20-21  There have been only a few cases where localized deformation has been characterized and linked to corrosion via x-ray techniques for zones of ∼4 μm22  or electron microscopy analyses for zones under ∼1 μm.23  These types of characterizations yield very limited fields of view, especially considering that cathodic intermetallic particles (and therefore initial pit sizes) for this material usually have a maximum diameter of ∼10 μm.24 

As a result, little is known regarding the effect that both the localized deformation and the microstructure have on the origin and evolution of corrosion at the mesoscale level. Therefore, there is a need to examine areas spanning several cathodic particles, which would mean characterizing areas much larger than the ones seen in present literature. For this need, which is addressed in the present paper, it is necessary to map the microstructure, the micromechanical fields, and the localized galvanic corrosion of a sample for which the location of the particles are known, all of which would require specialized high-resolution methods. In order to better understand the relationship between strain localization and localized galvanic corrosion, this paper relies on characterization methods capable of mapping the local strain and corrosion of large areas at the mesoscale level.25-26  To capture the early stages of localized corrosion, the surface topology of the material is intermittently measured every day over the course of a 20 d period, in which the material is exposed to a galvanic corrosion environment. Using the quantitative results from these characterization procedures, a series of statistical methods is used to investigate the driving mechanisms behind galvanic corrosion.

Material, Microstructure Characterization, and Strain Map

The material under investigation is AA7050 treated to the T7451 (AMS 4050), which was cut into dog-bone specimens in the TS orientation. A 48 mm × 10 mm × 1.6 mm specimen with a 10 mm long gauge section was electrodischarge machined from a rolled plate with the thickness of 1.6 mm parallel to the rolling direction, i.e., the load axis of the specimen is aligned to the transverse direction of the rolled plate. The specimen was designed in accordance to ASTM tensile standards,27  considering the constraints of the chamber sizes of the microscopes utilized throughout the paper. A full description of the geometry can be found in Mello, et al.28  For a complete analysis of the material, the microstructure, the intermetallic particles, the residual strain fields, and the topology resulting from surface corrosion were characterized over a region of interest (ROI), which is a 300 μm × 400 μm area located at the center of the sample. The ROI was delimited by a set of fiducial marks on the specimen surface via microhardness indentation.

The specimen was polished using a 1200 grit sand paper for 2 min followed by a NAPPAD cloth with 0.05 μm colloidal silica for 40 min to achieve a mirror-like surface. Once the specimen was polished, the ROI was delimited by placing fiducial markings at each corner with an automated LECO Microhardness Tester LM247AT with a force of 0.5 N, following ASTM Standard E92-16 to ensure the ROI does not include the region immediately adjacent to the indents to not influence the resulting mechanical behavior.29  As a visual orientation aid, two larger fiducial marks were placed on the lower left side of the ROI using a 1 N force. Both were placed 50 μm away from the delimited region’s edge. To characterize the microstructure, electron backscatter diffraction (EBSD) was performed on the ROI using a FEI Philips XL-40 scanning electron microscope (SEM) with the following acquisition settings: 25 kV accelerating voltage, spot size of 5, 17 mm working distance, 500× magnification, and 70° tilt. For the EBSD setup in the EDAX system, a gain of 13.59, black level 2.38, 75 ms exposure time, and a step size of 1.50 μm were used. The inverse pole figure map of the specimen in the TS orientation is shown in Figure 1(a), with an average grain diameter of 35 μm.

FIGURE 1.

Characterization of (a) the microstructure, (b) the cathodic Al7Cu2Fe particles, (c) the residual strain response, and (d) the surface roughness from corrosion (displayed for 10 d of corrosion on 3.5% NaCl solution).

FIGURE 1.

Characterization of (a) the microstructure, (b) the cathodic Al7Cu2Fe particles, (c) the residual strain response, and (d) the surface roughness from corrosion (displayed for 10 d of corrosion on 3.5% NaCl solution).

Close modal

The spatial location of the cathodic Al7Cu2Fe intermetallic particles was performed via energy-dispersive x-ray spectroscopy (EDX) using a FEI Quanta 3D FEG dual-beam SEM with the following settings: 30 kV accelerating voltage, spot size of 4, 8.2 mm working distance, and a 700× magnification, with a final resolution of 210 nm/pixel. The chemical mapping was done on the polished surface of the specimen and the zones with high content of copper and iron were concluded to be the cathodic particles of interest. The characterizations of the particles by EDX (Figure 1[b]) were in agreement with the grayscale SEM images of the ROI, as well as the characterizations observed in the literature.24,30  The area fraction of the particles was of 1.01%, the mean particle diameter was 2.56 μm, and the maximum particle size was 9.34 μm. Other secondary phase particles known to be cathodic relative to the surrounding matrix, such as MgZn2 (5 nm to 10 nm in diameter) or Al3Zr (20 nm to 50 nm in diameter),31-32  could not be characterized via the current EDX-SEM setup given their small size relative to the 210 nm/pixel resolution of the scan.

Digital image correlation (DIC)33  was used to quantify the local residual strain after deformation of the material. This technique relies on a high-contrast speckle pattern that is applied on the surface of interest and tracked during/after deformation to determine the local strains in the material. The resolution of the resulting strain map is dependent on the size of the pattern, and different patterning methods are available according to the individual needs of the experiment.34  Because it is of interest to resolve strain at the sub-micrometer level, a titanium nano-particle speckle was applied on the surface of the specimen and SEM images were used to track its deformation. The patterning methodology for titanium nano-particles is based on Tracy, et al.,35  and a full description of the procedure, as well as examples, can be seen in Mello, et al.36  Once the speckle pattern was placed on the ROI, the material was tensile loaded to 2% total strain and unloaded to a residual macroscopic strain of 1.56% using a 6.7 kN electromechanical Mark-10 ESM-1500 force test stand. The force indicator has a ±0.1% accuracy with a resolution of 5 N. The load was administered via displacement-controlled loading at a rate of 2 mm/min, and the macroscopic strain response was measured with an Epsilon extensometer model 3542.

The ROI was divided into nine regions and separately scanned via SEM before and after deformation with the following acquisition settings: 10 kV accelerating voltage, spot size of 4, 10 mm working distance, and 700× magnification. Each SEM scan had a 69 nm/pixel resolution, with ∼15 pixels per μm. All images underwent ex situ spatial distortion and magnification corrections by taking a reference image of a certified grid with known dimensions alongside every SEM scan to quantify spatial distortions and uncertainty. The correction is particularly necessary for images that have been scanned days apart and therefore have slight discrepancies in the reported magnification values. More details on the procedure can be seen in Mello, et al.37  The nine sets of images were post-processed using Correlated Solutions software, VIC-2D.38  Each DIC analysis was performed using subset size of 6.8 μm (111 pixels), with a step of 0.2 μm (3 pixels). The DIC outputs were stitched together for a full strain field view of the ROI. The resulting in-plane strain components were characterized across the ROI, as shown in Figure 1(c) for the εxx component of strain (aligned with the loading axis of the specimen, which is the horizontal axis in the figure).

Galvanic Corrosion Assessment

After loading, unloading, and subsequent residual strain field characterization, the specimen was subjected to a galvanic corrosion environment. The specimen was coupled to a M6 × 16 Type 316L stainless steel (SS; UNS S31603) screw by means of a 0.5 mm Type 316L SS wire wrapped around one end of the specimen, which ensured the macroscopic coupling would be far away from the ROI located at the center of the specimen. Furthermore, the use of the wire minimizes the shared contact surface between the Type 316L SS cathode and the AA7050 anode to <1% of the total specimen surface. The full specimen-wire-screw arrangement was then subjected to galvanic corrosion by fully submerging it in an aerated 3.5 wt% (0.6 M) NaCl solution at pH 5.6 for 24 h periods, for a total corrosion duration of 20 d (480 h), without any external voltage control. When excessive corrosion product was observed in the NaCl solution, which occurred about every 6 d, the solution would be replaced with a fresh batch of NaCl solution. After each 24 h period of corrosion, the sample was taken out of the solution, rinsed, and sonicated with an ultrasonic cleaner (Sper Scientific) using distilled water, isopropyl alcohol, acetone, and methanol, with a duration of 480 s for each solution. The sample was carefully dried with compressed air between each cleaning agent. Once cleaned, the surface roughness of the specimen was characterized.

In between each galvanic corrosion session, the specimen was characterized for spatial pitting in the ROI via a confocal microscope and qualitative view of pitting around particles via SEM imaging. It should be noted that after Day 10, the specimen underwent further cleanup to remove carbon buildup observed at the surface, possibly generated by the repeated SEM imaging. Several instances of cleaning and SEM imaging were done to achieve a good characterization with the least amount of oxides at the surface, with no particle fallout being observed after each instance. The entire surface roughness was characterized via confocal laser scanning microscopy (CLSM) using a Zeiss LSM 880 upright confocal microscope with a 561 nm laser wavelength and a Plan APO 10×/0.45 objective. A step size of 1 μm in the z-direction and a resolution of 0.74 μm in the x-y directions were used. To ensure a high-resolution scan, the size of the pinhole used to block out-of-focus light was set to a maximum allowable Airy unit (AU) of 1 AU so that only the first dark ring in the Airy disk stemming from the diffraction pattern of the point light source is captured (1 AU = distance from the center of the major peak to the first minimum), which leads to a high signal-to-noise ratio. To maximize the gradient of the grayscale confocal images, the laser was set to 100% intensity, with an optical gain of 554, a digital offset of 0, and a digital gain of 1. The entire ROI was segmented into 20 areas and scanned with a pixel dwell time of 2 μs, after which the images were stitched. The first and last slices of the full z-stack were manually determined by checking that the maximum brightness of the highest and lowest points within the ROI was captured by the upper and lower slices, respectively.

An in-house MATLAB code was developed to reconstruct the surface from the grayscale stacked images obtained from the confocal microscope. The topographic height was calculated based on a procedure proposed by Jordan, et al.,39  with the main equation being repeated here for completeness:

formula

where h(xi, yj) is the topographic height, I(xi, yj, zk) is the depth response (image intensity) for each pixel of the stack z1 to zn, dz is the step size of the scanning on z, zk is the stack number, and FWHM is the full width at half maximum (that is, the width of the Gaussian distribution of I(xi, yj, zk) at 0.5Imax).

Once the topology was calculated for all corrosion days, they were offset based on a global zero reference height to account for the evolution of the surface during the corrosion process (as the CLSM reports topology centered around the median height). The tallest feature seen on Day 1 was set as the zero-reference point (because it is the least corroded feature), and the subsequent corrosion profiles were offset by Δhn + 1 based on the average and maximum depth differences between the topographic heights h of Day n and Day n + 1, such that:

formula

for which 〈·〉 are the Macaulay brackets, (i.e., 〈x〉 = x if x > 0, and 0 otherwise). The maximum depth difference seen on the first half of Equation (2) ensures that the evolution of the deepest features is properly captured and that feature either keeps growing deeper or remains the same. The mean depth difference seen on the second half of Equation (2) ensures the proper description of surface recession, that is, the surface evolution only describes material degradation from corrosion and that material addition is not possible, as the surface undergoes thorough cleaning.

Additionally, to account for variations in flatness resulting from specimen mounting, the overall slope of the surface was calculated and removed from the reconstructed maps. A representative image of the surface topology within the ROI displaying localized pitting is shown in Figure 1(d) after 10 d of exposure to the galvanic environment. All surface maps reconstructions on the ROI were verified with lower-resolution scans from a Zygo ZeGage 3D optical profilometer and higher-resolution SEM scans from the field-emission SEM FEI Nova NanoSEM 630. The SEM images ensured the correct regions in the CLSM maps displayed the highest degree of pitting, but further provided a high-resolution view of the characteristic features of pitting around the microstructural features. All SEM scans used a spot size of 3.0, a voltage of 5.0 kV, and a working distance of 5 mm.

The SEM scans shown in Figure 2 provide the overall evolution of corrosion within the ROI every 5 d. The fiducial marks can still be seen after all 20 d of corrosion, albeit they are less noticeable by the end of the experiment. By the look of the degradation of these reference points, the surface seems to experience diffusion-controlled dissolution of the metal exposed to the NaCl solution. At these reference points, the surface seems to recede steadily and at a slow rate, which is indicative of steady mass transport from the surface of the material into the solution, which would be characteristic of a diffusion-driven process. By looking at the scans of the ROI in Figure 2, no grain boundary attack is seen as corrosion takes place, inferring that the material does not experience significant intergranular corrosion. Knowing that the smaller cathodic secondary phase particles tend to cluster at grain boundaries,11  it can be concluded that the main source of attack is the Al7Cu2Fe particles. However, associated with a slight uniform corrosion, pitting can be observed throughout the area. In fact, it can be seen that this type of corrosion begins very early in the experiment and evolves in a nonhomogeneous manner, with some areas corroding faster and wider than others. Also, because the macroscopic coupling between the Type 316L SS wire and the specimen was ∼24 mm away from the ROI, high-rate mechanisms such as fissure corrosion32  were not observed at the ROI.

FIGURE 2.

Overview of corrosion evolution within the ROI via SEM imaging. Pre-existing voids are indicated with white arrows, showing slow corrosion rates from surface area exposure. Grain boundary attack is not observed. Pitting is further examined from the particles highlighted in the image of Day 1.

FIGURE 2.

Overview of corrosion evolution within the ROI via SEM imaging. Pre-existing voids are indicated with white arrows, showing slow corrosion rates from surface area exposure. Grain boundary attack is not observed. Pitting is further examined from the particles highlighted in the image of Day 1.

Close modal

The quantitative measurement of the corroded surface via confocal microscopy can be seen in Figure 3. These measurements show that pitting becomes significant at Day 10 of corrosion, with pits being about 10 μm deeper than the overall surface. In particular, there is a distinct pit near the center of the ROI that exhibits a sizable growth at Day 15 and onward. It should be noted that to prevent skewed results from the use of these quantitative maps, the fiducial marks delimiting the ROI have been removed from the corrosion maps, hence the empty squares at each corner of the maps seen in Figure 3. Furthermore, the nonhomogeneous way in which corrosion progresses makes it necessary to distinguish between areas affected and unaffected by the coupling of the cathodic particles with the anodic matrix.

FIGURE 3.

Overview of surface roughness evolution within the ROI via confocal microscopy. Pitting becomes significant after 10 d of corrosion.

FIGURE 3.

Overview of surface roughness evolution within the ROI via confocal microscopy. Pitting becomes significant after 10 d of corrosion.

Close modal

To track the behavior of the areas affected by this coupling, the ROI was segmented into two types of areas: particles and matrix. For this purpose, the EDX particle map seen in Figure 1(b) was used as a baseline segmentation mask. Because the material surrounding the intermetallic particles is directly affected by the local electrochemistry, a sensitivity analysis of the outward radius size moving from the perimeter of the particles into the matrix, as part of the local galvanic coupling, was performed on both the strain field and the surface roughness maps. It was observed that a threshold radius equal or larger than 11 pixels (1.2 μm) away from the borders of the particles resulted in a saturation of results (minimal variation of segmented values) and is deemed suitable for the purposes of this study. To ensure the proper separation of the matrix affected and unaffected by the cathodic particles, a threshold radius equal to the mean particle radius, 1.28 μm, was used.

This new mask with added threshold around the particles was used to segment the strain map seen in Figure 1(c). The overall cumulative distribution function (CDF), seen in Figure 4, indicates that the regions comprised of and in the vicinity of the particles have higher localized strains and therefore more extreme strain gradients that pinpoint weak material spots and could possibly facilitate corrosion damage. Additionally, the average axial strain in the delimited area containing the particle is slightly lower than the average axial strain at the matrix. This results from the fact that the particles are stiffer than the matrix and therefore little to no strain is seen on the particles; in fact, the load is transferred to the surrounding matrix, thus explaining the high-localized strains seen in the vicinity of the particles and captured in the maximum tail of the CDF plot.

FIGURE 4.

CDF comparison of the axial strain in the matrix (black) versus the axial strain in the vicinity of the particles (red). The mean strain near the intermetallic particles is 1.5% and is lower than that of the matrix; also the extreme strains are found near the particles, showing that the hard particles concentrate strains around their surrounding matrix.

FIGURE 4.

CDF comparison of the axial strain in the matrix (black) versus the axial strain in the vicinity of the particles (red). The mean strain near the intermetallic particles is 1.5% and is lower than that of the matrix; also the extreme strains are found near the particles, showing that the hard particles concentrate strains around their surrounding matrix.

Close modal

To further explore the corrosion at the cathodic particles with high strains, three similarly sized particles exhibiting axial strain localizations beyond 3% were tracked throughout the entire corrosion analysis; their locations are pinpointed on the SEM scan for Day 1 in Figure 2. Particles 1, 2, and 3, with an equivalent diameter of 7.46 μm, 8.34 μm, and 8.10 μm, respectively, exhibited a maximum local axial strain of 3%, 4%, and 7%. Given that the maximum particle diameter observed within the ROI was of 9.34 μm, all of these particles are on the upper end of the particle size distribution.

High-resolution SEM scans were taken to capture the evolution of these three particles over the 20 d period in which this material was subjected to a coupling of AA7050 with Type 316L SS. These images help pinpoint the exact day when particle fallout occurs, thus delimiting up to which day the localized galvanic coupling between the particle and the matrix significantly contributes to localized corrosion. Figure 5 shows the evolution of Particle 1 with fallout occurring at Day 9. Similarly, Figure 6 shows the evolution for Particle 2 with fallout occurring at Day 8, and Figure 7 shows the evolution for Particle 3 with fallout occurring at Day 5.

FIGURE 5.

Corrosion evolution of the intermetallic Particle 1 during 20 d of corrosion. The corrosion rate diminishes after particle fallout and afterward no significant pitting evolves from this particle.

FIGURE 5.

Corrosion evolution of the intermetallic Particle 1 during 20 d of corrosion. The corrosion rate diminishes after particle fallout and afterward no significant pitting evolves from this particle.

Close modal
FIGURE 6.

Corrosion evolution of the intermetallic Particle 2 during 20 d of corrosion. The corrosion rate diminishes after particle fallout and afterward no significant pitting evolves from this particle.

FIGURE 6.

Corrosion evolution of the intermetallic Particle 2 during 20 d of corrosion. The corrosion rate diminishes after particle fallout and afterward no significant pitting evolves from this particle.

Close modal
FIGURE 7.

Corrosion evolution of the intermetallic Particle 3 during 20 d of corrosion. The corrosion rate is steady after particle fallout, yet afterward significant pitting evolves from this particle.

FIGURE 7.

Corrosion evolution of the intermetallic Particle 3 during 20 d of corrosion. The corrosion rate is steady after particle fallout, yet afterward significant pitting evolves from this particle.

Close modal

It can be seen from Figures 5 and 6 that the corrosion rate near the location of Particle 1 and Particle 2 diminishes after fallout occurs, which suggests that the main driving mechanism behind pitting of these areas was electrochemically based, whereas Figure 7 shows just the contrary: Particle 3 evolves into the giant pit seen in Figure 3 thus dominating the corrosion profile, which means that there is another significant mechanism driving corrosion at this point. It is worth noting that the localized corrosion at Particle 3 keeps growing at a steady rate after particle fallout occurs, with the pitting exhibiting sudden growth at Day 17.

As previously mentioned and shown in Figure 8, a pit that formed around Particle 3 dominates the corrosion profile of the material within the ROI. This pit is expected to continue growing at longer corrosion times until it reaches a critical size of ∼50 μm where it is likely to evolve into a crack, based upon observations in literature.13  Upon examination of the DIC strain fields relative to Particle 3, heavily localized strain can be seen next to the particle, as seen in Figure 9. Given that the specimen has an average residual strain of 1.6%, the observed localized strain around this particle is ∼4× higher than the macroscopic strain, with an average local value of 6% and a maximum value of 14%. The extreme 14% maximum value arises from the cracking of the particle during loading (comparing Figures 9[a] and [b]), and thus this level of strain is only seen at the crack itself (Figure 9[c]), while the strain field quickly diminishes down to 6% moving away from the crack. The corrosion pit arising from this particle shows a final depth of ∼34 μm on Day 20 relative to the initial depth at Day 1.

FIGURE 8.

Overview of the pitting that evolved from Particle 3 after 20 d of corrosion, relative to (a) the overall ROI via CLSM, (b) the relative surface topology (zoom-in region from [a]), and (c) qualitative features via SEM imaging. This pit dominates the corrosion profile.

FIGURE 8.

Overview of the pitting that evolved from Particle 3 after 20 d of corrosion, relative to (a) the overall ROI via CLSM, (b) the relative surface topology (zoom-in region from [a]), and (c) qualitative features via SEM imaging. This pit dominates the corrosion profile.

Close modal
FIGURE 9.

Overview of the cathodic particle where the worst pitting originated (a) before loading, (b) after loading (with crack), and (c) with the localized strain. The extreme strain values beyond +3σ of the strain distribution (3.5%) arise from particle cracking.

FIGURE 9.

Overview of the cathodic particle where the worst pitting originated (a) before loading, (b) after loading (with crack), and (c) with the localized strain. The extreme strain values beyond +3σ of the strain distribution (3.5%) arise from particle cracking.

Close modal

In an effort to investigate how the heterogeneous strain field correlates to the localized galvanic corrosion for the entire ROI, the strain maps were spatially compared to the topology maps for the corrosion profile and a statistical analysis was performed on a point-by-point basis to outline any trends between corrosion and strain. A principal component analysis (PCA) was performed using R40  with all of the in-plane strain variables resulting from the DIC characterization, εxx, εyy, εxy, ε1, ε2, as well as calculated strains used in literature to predict failure, εvm and γmax.41  From the PCA analysis, it was found that the two most representative strain variables of the mechanical condition of the material were the longitudinal strain, εxx, and the shear strain, εxy, mapped onto the first and second axes of the PCA, respectively. The cumulative projected inertia (the sum of the variances of the variables) for these two axes is 85.51%, which means that the first and second axes of the PCA (i.e., the bases vectors) jointly retain ∼86% of the variation in the data and properly capture the overall shape and distribution of the data cloud. These two variables of strain will be used for correlating the micromechanical fields, in terms of εxx and εxy, to the spatial pitting exhibited by the localized galvanic corrosion process.

Gaussian process (GP) modeling42  was selected as an appropriate statistical approach for probabilistic regression by fitting a distribution over functions to identify the relationships between the experimentally acquired data. In this case, it was desired to infer a surface response of corrosion given localized strains, such that corrosion = f(εxx, εxy). It is worth noting that GP modeling takes into account multivariate spatial correlations by using covariance function kernels; i.e., it takes into account the effect that the neighboring values have on a specific point. This is particularly useful for datasets where the data points are spatially interdependent (clustered). In this study, in which corrosion is heavily localized, spatial cross-correlations of the data are of paramount importance. Unfortunately, the GP modeling of a dataset of size n has a complexity of O(n3) with storage demands of O(n2). This means that the computational solving times increase quadratically as more data are evaluated during the GP modeling. As a result, most GP algorithms are limited to dataset sizes of magnitudes between 102 and 104 spatial points.

Because the maps used in this paper contain over 9 million points each (meaning that the dataset has a magnitude of ∼106), a special GP model utilizing stochastic variational inferences (SVI), specifically designed for big datasets, was used.43  This method further improves computational run times by segmenting the dataset into batches and solving each of them in a parallel manner. Any values beyond ±3σ were removed from their respective datasets to improve the normal distribution of the data. It should be noted that the use of the whole spectrum beyond 3σ does not affect the fitting results because only ∼1,000 points lie beyond 3σ and the other 9 million points actually drive the fitting process, but unnecessarily slow down the GP modeling because it significantly widens the data ranges to evaluate during each iteration. A Matérn 5/2 covariance function kernel with noise (to account for variance) was used, along with a learning step rate of 0.2, a learning momentum of 0.9, 100 inducing inputs, and a mini-batch size of 20,000. Because the GP modeling algorithm is an iterative process, the variance of the kernel can be set up by the user. In this case, the local variance was enforced to be 1 × 10−5, which yields a 95% confidence bound of ±2 × 10−6 around the local normalized value. The results from the GP-SVI modeling can be seen in Figure 10.

FIGURE 10.

Corrosion trends relative to the longitudinal strain, εxx, and the shear strain, εxy, fit using Gaussian process modeling. The maximum corrosion values converge around the average strain values, showing no statistically significant correlation between high strain values and deeper corrosion.

FIGURE 10.

Corrosion trends relative to the longitudinal strain, εxx, and the shear strain, εxy, fit using Gaussian process modeling. The maximum corrosion values converge around the average strain values, showing no statistically significant correlation between high strain values and deeper corrosion.

Close modal

The inferred GP fitted response shows that the high corrosion levels within the ROI occur at approximately the mean values of strain, εxx and εxy, with values of 1.6% and 0%, respectively. The fitted response also shows that pure axial strain εxx coupled with little to no shear strain εxy exhibits higher amounts of corrosion. The GP model response also shows that, in general, high strains do not translate into high corrosion levels, and that the relationship between localized galvanic corrosion and localized strain does not change much over time. This would suggest that high strain values or local amounts of stored strain energy are not necessary conditions for local galvanic corrosion; that is, absolute or relative amounts of strain with respect to the surrounding material do not foster galvanic corrosion.

On the other hand, when looking at the largest pit dominating the corrosion in the ROI, high strain values can be seen in the vicinity of the cathodic particle. Further discussion of these localized strain values is necessary. Looking at the axial strains, the +3σ maximum strain for the ROI is 3.5%. About 99% of the strains in the ROI are below 3.5%, as seen in Figure 4. The localized strain, seen at the dominating pit, has a residual axial strain ≥6%, which is almost twice the +3σ strain value and almost four times the average strain experienced in the material (1.6%). Therefore, the data from the dominating pit were not used during GP modeling, because they contained extreme values of strain. In fact, this was the only cathodic particle excluded from the ROI analysis. All of the other particles had neighboring strains within the ±3σ threshold limits, mainly because they did not experience cracking at or near the particle. It is also likely that the cracking of Particle 1 is the source of the deep localized pitting seen during the early days of corrosion (Day 5 onward).

Particles 2 and 3 were part of the GP modeling, and as seen from both the SEM scans and the confocal profiles, no significant pit growth occurred at either of them. Both locations, representing particles 2 and 3, only developed pit growth while the cathodic particle was present, and the pit evolution greatly slowed down once particle fallout occurred. These two locations show that, even if hard particles encourage high localized strains at the neighboring soft matrix, as seen in Figure 4, it is rather the local galvanic coupling and not the strains that drives corrosion, as seen in Figure 10. In other words, particles are responsible for both high strains and deeper corrosion, but the high strains do not necessarily lead to deeper corrosion. The only case where strains actually translate into corrosion is when they arise from particle cracking, which is a very isolated case and therefore is not a mechanism captured by the GP fit nor the CDF plots.

Interestingly enough, the cavities left by these two particles seemed to blend with the surrounding matrix as time progressed. This brings up the question of whether there is a real difference between the corrosion at the matrix and corrosion resulting from the particles, specifically after particle fallout occurs. Figure 11 shows a comparison of the accumulated corrosion depths at the matrix (black) versus the accumulated corrosion depths at the intermetallic particles (red). The characterization maps in Figure 1 were segmented into particles and matrix using Figure 1(c) as a mask and an added radius around the particles equal to the average particle radius, 1.28 μm. It can be seen that initially (Day 3) both zones exhibit similar corrosion depth values, but eventually the corrosion at the particles grows deeper and larger, showing the greatest difference right after all of the particles have fallen out (Day 9). Once the particles are gone, the difference diminishes, but still the particles show deeper corrosion than the surrounding matrix, as can be seen in Figure 11 for Day 12, Day 15, and Day 18. In other words, the particles leave cavities that further corrode deeper than the average matrix; however, the rate at which each cavity grows varies. It is therefore of interest to identify the mechanisms behind such variations.

FIGURE 11.

CDF comparisons of the corrosion on the matrix (black) versus corrosion at the particles (red). The mean corrosion near the intermetallic particles is deeper than at the matrix, especially right after the particles fallout (Day 9), showing that the localized galvanic coupling is the main factor behind deeper corrosion, with other mechanisms driving corrosion beyond Day 9.

FIGURE 11.

CDF comparisons of the corrosion on the matrix (black) versus corrosion at the particles (red). The mean corrosion near the intermetallic particles is deeper than at the matrix, especially right after the particles fallout (Day 9), showing that the localized galvanic coupling is the main factor behind deeper corrosion, with other mechanisms driving corrosion beyond Day 9.

Close modal

One postulated mechanism behind the rate of corrosion is the available surface area exposed to the electrolytes.44  A good way of investigating the corrosion rate at large areas is by looking at preexisting voids in the material. In the ROI, one can see several large voids on the lower right section (Figures 2 and 3). These voids were not a product of corrosion and were present prior to the specimen being subjected to the galvanic corrosion environment. Figures 2 and 3 show that the corrosion at these voids is steady and relatively slow, especially in contrast with the localized corrosion at the cathodic particles. In this case, one can conclude that although the exposed surface area plays a part in corrosion, its corrosion rate is relatively slow and therefore is not the only parameter driving localized galvanic corrosion.

As a result, it can be postulated that localized pitting originates at the cathodic particles, especially at the ones where cracking occurred during loading. During the early days of corrosion, pitting undergoes accelerated growth because of the electrochemical interaction between the particles and the matrix, that is, until particle fallout occurs (usually around Day 10). Once the electrochemical coupling is no longer present, the surface roughness (exposed surface area) along with the high residual strains at the pits (partially resulting from the cracking of the particle itself) are the two mechanisms driving the localized corrosion of the material.

A TS-oriented specimen from an AA7050-T7451 rolled plate was coupled to stainless steel and subjected to 20 d of galvanic corrosion in a 3.5% NaCl solution. The localized corrosion, as well as the localized strains, cathodic particles, and microstructure morphology were characterized for a 300 μm × 400 μm ROI at the center of the specimen. Three similarly sized particles were tracked daily via SEM scanning and confocal measurements. The quantitative maps arising from these characterizations were spatially matched and analyzed via GP modeling and matrix/particle sectioning. From the analysis of the characterizations done on the ROI, the following can be concluded:

  • For the overall ROI, within ±3σ values of the characterized strain distribution, the localized corrosion is independent from localized strains, and relatively higher levels of stored strain relative to the microstructural attributes do not translate into deeper corrosion pits. This has been verified by the surface response obtained from GP modeling.

  • In one instance, a region with maximum strain within the ROI caused by crack formation in an intermetallic particle during loading accelerated pit growth and dominated the corrosion profile of the ROI. At this location, the values of the characterized strains were much greater than +3σ of the strain distribution in the ROI, resulting from the particle cracking.

  • Cathodic particles have been verified to be the main source of corrosion pitting, which is statistically significant compared to the corrosion occurring at the surrounding matrix. The evolution of corrosion pits is initially driven by the electrochemical interaction between the particle and the matrix; after the pit growth causes the particles to fallout from the matrix, the corrosion process is driven by the diffusion-driven dissolution of the surface and the extreme residual strains from the cracking of the particle itself.

(1)

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

Trade name.

The authors gratefully acknowledge funding from the Office of Naval Research, N00014-14-1-0544 under program manager Mr. Bill Nickerson. Dr. Andy Schaber is thanked for his help with the surface roughness characterization procedure. Additionally, we thank Prof. Jimmy Burns (UVA) for helpful discussions.

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