Sensitization of 5xxx Series Aluminum Alloys Explored with an Adapted Johnson-Mehl-Avrami-Kolmogorov Model for Phase Evolution and Ultrasonics

In the designing of structural materials for air/water vehicles, properties such as specific weight, strength, and chemical stability are often among the deciding factors. Aluminum alloys (AA) are the material of choice for maneuverable and efficient vehicles due to their low density. Further, the 5xxx series aluminum-magnesium alloys (AA5xxx) are fit for structural applications because of their moderate-to-high strength, which can be further increased through strain hardening (yield strength and ultimate tensile strength can achieve several times above those of pure aluminum^1-2 ). At 3 wt% to 6 wt%, the magnesium content in the 5xxx series AA is above the solid solution limit, but, in as-received conditions, Mg atoms are generally found randomly distributed within the fcc structure of Al (the α phase). The temperature of the α/β phase boundary at this composition is too low (≈275°C, Figure 1[a]) to allow the formation of the expected amount of β phase at room temperature; the driving force is too low. In their as-manufactured state (metastable α phase), the 5xxx series AA have good corrosion resistance in salt water.

During use, however, structural materials are generally exposed to heat (through thermal radiation or conduction). In a metastable solid solution, the energy absorbed can lead to atomic migration and solid-state phase transformations. An alloy could thus gradually change its properties, sometimes rendering it unfit for the application for which it was designed. An example of such a case is the sensitization of the AA5xxx used in marine applications. When these alloys are exposed to heat as part of their normal operational environment, they phase separately. The thermal energy absorbed aids the diffusion of magnesium to the grain boundaries, and the formation of the β-phase (Al₃Mg₂), as indicated by the equilibrium phase diagram.³  In most environments, the transformation takes years, often decades, but in situations with higher thermal loading, the transformation can occur much faster. This process, initiated with the segregation of specific atoms at the grain boundaries accompanied by the formation of a new phase, is known as sensitization; the material becomes sensitive to its environment. The particular problem for marine vehicles built from AA5xxx is that the β phase formed during sensitization is anodic to the aluminum matrix.⁴  In the presence of seawater, the sensitized alloy becomes susceptible to intergranular corrosion (IGC), exfoliation, and stress-corrosion cracking (SCC) (Figure 1[b]). In addition, the Mg depletion in the matrix lowers the strength of the original alloy, which slowly transforms into a material with different properties.⁵ 

The current standard for measuring the susceptibility to IGC of sensitized AA5xxx is the ASTM nitric acid mass loss test (NAMLT) (a.k.a. the G67 test).⁸  A sample (2 in by 0.25 in by less than 1 in) cut out from the material to be investigated is submersed in a 70% nitric acid solution for 24 h for accelerated surface corrosion. Several specimens are often tested from one location. The mass loss due to corrosion divided by the surface area is reported. If the NAMLT measurement is greater than 25 mg/cm², the specimen is considered sensitized. The test is sensitive to the β phase present at the surface of the collected specimen, with expected variability among specimens from the same source. In addition, the β phase often decorates the grain boundaries of the alloy, which can result in the fallout of surface grains, especially in recrystallized alloys, producing an artificially large mass-loss value. The test results can thus be highly dependent on grain size and morphology, for alloys with an otherwise identical designation. While some find the test to be sufficiently reliable, others consider that it is not reproducible or not sufficiently sensitive to the microstructure and its connection to IGC susceptibility, and therefore not accurate. Additionally, the procedure is destructive, lengthy, and costly, clearly motivating new testing method developments. A special issue of NACE International Corrosion Journal was dedicated to the corrosion and environmental cracking of Al-Mg alloys. Comprehensive data compilations, analysis, and new NAMLT studies,⁹  new electrochemical studies, scrutiny of NAMLT results,¹⁰  repair techniques,¹⁰  as well as a comprehensive overview of the historical use and evolution of the alloys,¹¹  are found in the issue. Subsequent work^12-13  showed that several acoustic parameters of AA5456-H116 and AA5083-H116 are strongly dependent on the change accumulated in the alloys exposed to isothermal heating. A salient point about ultrasound, a powerful materials characterization tool,¹⁴  is its ability to detect transformations within the bulk, rather than just at the surface, as it integrates a much larger volume of the tested material than previous techniques. The DoS Probe (ElectraWatch, Charlottesville, VA) and electrical resistivity probe (Luna Inc., Roanoke, VA), for example, test only the surface of the sensitization-affected area, like NAMLT, and thus are highly dependent on the grain morphology of the exposed surface of the sample extracted. Through multiple methods, the mentioned study¹²  identified different ultrasonic parameters that can be utilized to build a new, on-site, nondestructive tool to quantitatively monitor the sensitization level in Mg-rich aluminum alloys, with possible extensions to other materials. The dependence of the wave speed and attenuation coefficient on sensitization, consistently measured on different materials, lends itself as a well-defined case study for studying the kinetics of β-phase growth during sensitization, if a predictive algorithm is to be formulated. Investigating the effect of variability in the alloy’s microstructure is the subject of future work. The current work is concerned with verifying the applicability of a model to the acoustic parameters which were shown to change with sensitization.

The Johnson-Mehl-Avrami-Kolmogorov (JMAK) model is often used to model processes where phase transformations occur, and kinetics parameters need to be quantified. Applications are wide: nanofabrication,¹⁵  additive manufacturing,¹⁶  hydrogen storage,¹⁷  environmental pollution,¹⁸  and various aluminum alloy studies,^19-20  being only some recent examples. In 2015, Steiner and Agnew²¹  proposed the use of the JMAK model for sensitization in 5xxx AA and fitted NAMLT data with the model. The authors further suggest the possibility for the JMAK model to be applied to ultrasonic or eddy currents nondestructive techniques for sensitization predictions. Later work added detailed images of β-phase precipitates, robust thermodynamics-based modeling for phase growth, and an extension of the JMAK model to high temperatures.²²  Both models were able to capture the functional behavior of sensitization in AA5083. The evolution of acoustic wave speed and attenuation coefficient are modeled here by combining the JMAK model’s phase kinetics with acoustics principles. A comparative study is performed, where the phase transformation rate constant, k, and the Avrami exponent, n, which together describe the β-phase dynamics, are determined for two different 5xxx series AA. The analysis could be extended to other materials undergoing such phase transformations, for example, stainless steel acquiring precipitates due to heat loading.²³ 

The JMAK equation describes nucleation and growth through an entire volume, where the old phase completely transforms into the new phase (x: 0 → 1). In the specific case of 5xxx AA sensitization, only a part of the volume transforms, with the new phase, Al₃Mg₂ (β phase), taking a maximum volume fraction of ≈20% (Figure 3) after the transformation is complete. The exact value can be extracted from the equilibrium phase diagram using the lever rule for a specific Mg composition (w) and temperature of the operational environment (RT, or room temperature). The JMAK equation is used to capture the effect of the transforming volume portion on the propagation of ultrasound in the mixed medium.

Other limits are given in Figure 4(c). It is important to note that R is not the same as x (in Equation [1]), but it depends on it.

Attenuation is more complex to model than wave speed in mixed media. Different processes, independent in nature, contribute to the energy loss of a propagating pulse. While attenuation due to absorption can be lumped in one volume, as is the speed case, scattering requires more detailed and specific modeling. All attenuation effects are combined here in one effective k. The difference in the k values extracted from speed and attenuation is therefore a qualitative measure of the contribution of scattering to attenuation.

Generic time-dependent curves for speed and attenuation coefficient are shown in Figure 5. Based on the phase transformation rate (which is temperature-dependent) and the geometry of growth, which are contained in Equations (8) and (14) as k and n, respectively, various C(t) and γ(t) profiles may result.

The measured changes in wave speed and attenuation coefficient of AA5083 and AA5456 due to isothermal temperature holds, reported in Chukunuwnye, et al.,¹²  are the subject of the current implementation of the adapted JMAK model of phase transformation kinetics during sensitization. The standard alloy compositions are 4.0 wt% to 4.9 wt% Mg for AA5083 and 4.7 wt% to 5.5 wt% for AA5456.²⁸  Measurements were taken at a fixed temperature, after incremental isothermal heating events, with two methods: resonant ultrasound spectroscopy (RUS) and pulse-echo (PE). Shear wave velocity results from RUS have very low errors, which is a characteristic to the method. The same is the case for longitudinal wave velocity results from PE. The attenuation coefficient was only measured with PE for longitudinal waves. New RUS measurements on pure Al₃Mg₂, reported later in this section, lead to a lower wave speed value for sensitized vs. unsensitized Al-Mg alloys for both shear and longitudinal waves, explaining the behavior of the wave speed as the sensitization level increases.

Experimental values for the attenuation coefficient of the pure β phase were not available, because a large sample (not available) is needed to measure it accurately through PE. Thus, γ_β was allowed to vary during the fitting.

This quantity provides the expected wave speed for the mix, after the phases reach equilibrium, dependent only on the properties of the two phases and the final volume fraction achieved at a specific heat treatment temperature, R. With C_β,T = 2,902 m/s and C_β,L = 6,229 m/s (for shear and longitudinal waves, respectively) measured with RUS, and R extracted from the equilibrium phase diagram at a central w value of 4.5 and 5.5 Mg wt% for AA5083 and AA5456, respectively, at the corresponding temperature of the experiment, C(∞) can be calculated and compared to the measured saturation speed value for the samples used, directly. The results are listed in Table 1 for shear speed. Recall that ΔC = C_β − C_α. Note that, as different samples were used for each temperature test (columns), slight variations of their composition are expected, reflected in some differences in C_T(0). Moreover, while the AA5456 RUS samples were cut out of the same batch, the PE plate was sourced differently. Another effect that could also contribute to the difference between the measured and calculated C(∞) is the assumption that the Al matrix maintains the same properties through the transformation. Although Mg exists in very small amounts in the material at the start, and only a fraction of that amount is used in the formation of the β phase, it could have a small effect. In addition to the shear speed results in Table 1, the one set of data measured for longitudinal waves (from the PE measurement on AA5456—Figure 7[a]) provided measured C_L(0) = 6,365 m/s and C_L(∞) = 6,342 m/s; with an extracted R of 0.095, the calculated C_L(∞) is 6,351 m/s. Overall, the lowest temperature results concur very well; the large R-value is less sensitive to error in its estimation from the phase diagram. For the higher temperatures, where R is very small, the theoretical C(∞) is overestimated, but still lower than C(0), as it should.

Note that the equivalence of heating time to mass loss (in g/cm²), a standard sensitization measure for the NAMLT test, is done by rescaling the horizontal axis based on measurements for the specific material at the required temperature. The measured attenuation in Figure 7(b) has been presented as such in the source.¹²  The difference between the two representations captures the nonlinear scaling between heating time and mass loss. In the completely sensitized state reached after a long enough heating time, the measured quantities and the mass loss do not change, and the mass loss representation ends in a degenerate point.

The phase transformation rate constant (k) and Avrami exponent (n) found through the JMAK model for AA5083 and AA5456 at different sensitization temperatures are summarized in Table 2 and are also used in Figure 8. In the following discussion, temperature is categorized as low (120°C), moderate (175°C and 185°C), and high (240°C). Equations (16) and (17) are used to fit the various data shown in Figures 6 and 7.

At the lowest temperature, k for the two alloys is practically the same. The low k value at this temperature reflects the expected slow effect thermal energy has on the phase transformation. At moderate temperatures, the phase transformation rate is higher for both alloys. A differentiation in k becomes visible, being higher for AA5456, the alloy expected to have more Mg in composition. Further, the additional PE data on AA 5456 at the moderate temperature level allows for a close comparison. The extraction of k from the separate PE measurements of shear and longitudinal speed at 175°C reveals two remarkably close values (k_T = 0.110 and k_L = 0.105). The values are comparable to k_T = 0.15 measured through RUS for shear waves at 185°C. The difference may be attributed to the 10°C temperature difference and also to the AA5456 samples being from different sources. Over the temperature range of the present study, k continues to increase. It grows to the highest values at the highest temperature, 240°C, which is quite high for these alloys. The k value for AA5456 is the highest. From lowest to highest, k increases by a factor larger than ten. During the sensitization process at moderate and high temperatures, the differentiation in the k value indicates that a minute change in the magnesium composition can affect sensitization significantly. The behavior of k vs. temperature is further discussed in the Variation of k and n with T section.

The values of the Avrami exponent, n, are determined with larger errors. Given the range, n most likely spans between 0.5 and 2. This indicates 1D and 2D growth of the new phase^24-25  at lower temperatures, at grain boundaries (2D), and their intersections (1D). At the highest temperature, n is larger and has a larger range, indicating possible diffusion-controlled 3D growth, with nucleation and growth taking place at locations throughout the matrix (intragranular), not only at grain boundaries.

Comparing k and n from the wave speed profile and the attenuation coefficient (when the same technique is used, at the same temperature, on the same sample), allows for evaluating the contribution to k of the scattering component of attenuation. The overall k extracted from attenuation (PE measurements on AA5456—Figure 7[b]) is k = 0.460±0.090. The value is approximately four times larger than that extracted from either longitudinal or shear wave speed (they are the same) for that sample. The value for n from the attenuation data is 1.997±0.299. Both k and n, being larger, capture an earlier saturation in the JMAK behavior of the attenuation compared to that of the wave speed (5 d vs. 30 d to reach saturation). Multiple processes, such as absorption, scattering, and mode conversion, can generally contribute to the loss of amplitude in various degrees. At normal incidence, mode conversion is not expected for the PE sample that had a 1/7 aspect ratio (thickness/length), but the other two mechanisms are present. Scattering grows with the number and size of interfaces, which increase predominantly in the nucleation and early-growth zones of the JMAK model. The process has a powerful effect on the attenuation, which increases rapidly and early. In the growth zone that follows, contributions to scattering are smaller, as the generation of new interfaces is not the dominant process any longer; absorption becomes dominant instead. If the attenuation coefficient is different for the different phases, we expect γ to continue to change past the nucleation zone. The slight dip in γ that occurs after saturation (not possible to capture with the current γ JMAK fit) past the ≈5 d peak may imply that the β phase has an attenuation due to absorption that is slightly lower than that of the α phase. In contrast, the speed reaches saturation at the end of the growth zone, being sensitive only to the overall volume ratio of the different phases, and not to where and how the new phase is distributed. The JMAK model for wave speed captures the volume-ratio transformation in time, while that for attenuation has two regimes, with the first (nucleation and early growth) being the most significant. This is an important characteristic of the attenuation coefficient, which may be useful in discriminating different stages of sensitization evolution with an eventual probe developed for such measurements.

Under a constant driving force, the phase transformation rate, k, is predicted to follow the Arrhenius equation for reaction rates. The ln(k) is linear with 1/T, with the slope being the effective activation energy for nucleation and growth combined, divided by the universal gas constant. Previous studies using JMAK to interpret NAMLT results for AA5083 saw, indeed, the expected linear dependence,^21-22  but with different slopes for different temperatures. It was inferred in the second study that, due to changes in kinetics, a lower activation energy is responsible for the much lower slope at higher temperatures. For the high-temperature range, two temperatures were used: 150°C and 200°C. They correspond to a 1/T value of 2.36 × 10⁻³ K^–1 and 2.11 × 10⁻³ K⁻¹, respectively, points which can be found in Figure 8.

Values of k extracted from those two studies are combined with the shear and longitudinal wave speed k results from the current study in Figure 8(a). Both quantities (mass-loss by NAMLT and acoustic wave speed), while of a different nature, reflect the volume fraction of the β phase, generally as a simple rule of mixtures. The Acoustic ln(k) at high temperatures and the NAMLT ln(k) at low temperatures appear to be part of an almost linear behavior for both AA5083-H116 and AA5456-H116. A notable difference appears with the AA5083 NAMLT data of a different temper (H131). Note that H131 is worked to three times the hardness of H116 (both by cold strain hardening): 3/8 vs. 1/8 of the fully hardened temper. In the low-temperature range, all tempers show similar slopes. Above 100°C (1/T: 2–2.5 × 10⁻³ K⁻¹), the slope for H131 is dramatically lower. Factors that could contribute to the lower slope are: (i) Intragranular activity is expected to increase with temperature. With a higher dislocation density, such as that of H131,²⁹  activation energy is lower. Thus, the slope for H131 is lower than that of H116 (the latter being captured by the acoustics data in the higher temperature range). (ii) By nature, NAMLT (testing the surface) and ultrasonic measurements (testing the bulk) have different sensitivities. NAMLT is not as sensitive to intragranular crystallization. The measurement is dependent on the particulars of the exposed surface, which varies significantly. In contrast, sound waves propagate through the bulk and integrate the phase volume distribution throughout the material. Thus, the k values from NAMLT data at high temperatures may be underestimated due to under-detected intragranular β phase.

Also to be noted is that, while a change in the effective activation energy is expected at higher temperatures, a trigger point (1/T ≈ 2.7 × 10⁻³ K⁻¹) where the activation energy changes abruptly, by a factor of six, is unlikely. Rather, based on the new data, a gradual change in the slope appears to take place. Moreover, the intercept for the ln(k) vs. 1/T NAMLT H131 high-temperature data, a parameter that depends on factors such as nucleation rate, diffusion, and the precipitate aspect ratio is orders of magnitude lower for H131 than the other alloys,²²  a change that is not justified.

Intergranular activity at high temperatures should be paired with signs of 3D growth, i.e., higher n values. While it could be argued that the n value found here is higher, indicative of partial 3D growth contributions, the errors in n are quite high and don’t allow for a clear conclusion (Figure 8[b]). Errors for n from Steiner and Agnew²¹  are not available, and no n values are given for the two higher temperature points in the NAMLT study.²²  Note that there is a fourth alloy investigated in Steiner and Agnew,²¹  AA5083-H321 (cold strain-hardened and low-temperature stabilized to 2/8 of the fully hardened temper), with values of ln(k) overlapping with those of AA5083-H131 (not shown in Figure 8[a] to avoid congestion) and with an n ≈ 1.5 from the NAMLT data for all four heat-treatment temperatures tested between 40°C and 70°C (or 1/T of 3.2 × 10⁻³ K⁻¹ and 2.9 × 10⁻³ K⁻¹, respectively).

• Changes in ultrasonic speed and attenuation due to sensitization for 5083 and 5456 aluminum alloys have been investigated by adapting the JMAK model for ultrasonic wave propagation. Several key points emerged. The phase transformation rate constant, k, obtained from wave-velocity data is higher for AA5456 than for AA5083 for the same temperature of sensitization, reflecting that AA5456 reaches the full sensitized state earlier than AA5083. Also, k increases nonlinearly with the temperature of sensitization for both alloys, following closely the Arrhenius equations for the same alloy type and heat treatment of NAMLT data at lower temperatures. The Avrami exponent, n, lies in the 1 to 2 range expected for 1D to 2D growth, indicating the growth of the beta phase to be mostly at grain boundaries and intersections of grain boundaries. At the highest temperature of sensitization, n is higher, suggesting the occurrence of 3D growth.

• The saturation observed in the attenuation coefficient reflects an attenuation process that is dominated by scattering at the matrix/beta phase interfaces in the nucleation and early-growth zones. The behavior differs from that of the speed, where the phase volume fraction that continues to grow up to saturation affects the effective wave speed in the heterogeneous material past nucleation. Parallel studies engaging ultrasonics, imaging, and NAMLT on samples from the same location can be used to calibrate the saturation limits observed in the two ultrasonic quantities. Additional tests at lower sensitization temperatures may be added to verify the extension of the k derived from ultrasonic speed in the lower-temperature zone of the Arrhenius plot.

• Capturing the global behavior of ultrasonic parameters in sensitized alloys needs to be validated by additional measurements on alloys that are differently sourced. Statistics will help clarify if volume-testing, offered by ultrasonics, provides the necessary predictability to overcome the uncertainties of surface-detection methods. Further, a signature behavior specific to each material will be cataloged. In addition, other physical quantities that are affected by the growth of the β phase, such as specific heat, could be similarly modeled and added to increase the robustness of a predictive model. The process could be applied to other alloys that undergo similar phase transitions, such as stainless-steel acquiring carbide precipitates. The model could also be applied to explain sensitization reversal.⁶  Efforts continue to add to the multiple aspects of the sensitization mechanism in these aluminum alloys, such as understanding early-stage localized corrosion of AA5083-H111 at the dynamic waterline³⁰  or detailing the localized corrosion chemistry as a function of wetting time.³¹  Ultimately, this work, with new findings and potential extensions, could yield an efficient nondestructive probe used for on-site^32-33  tests, providing a simpler solution to monitoring sensitized materials. The technique could be coupled with routine ultrasonic structural testing, further reducing the overall structural health monitoring burden.

The authors thank Rob Kelly from the University of Virginia for providing the pure β phase sample used for the RUS measurements of β phase wave speed. All authors are grateful for the institutional support received while working on the project. G. Petculescu and S.P. Kharal acknowledge support from the Louisiana Department of Transportation, Grant No. 360098.