Introduction

Due to the dynamical nature and multiple rate-controlling variables, understanding oxidation behavior for alloys is a complex problem [1]. After Fukishima Diachi nuclear disaster in 2011, there is increasing interest towards finding oxidation resistant alloys to replace Zr based cladding materials. One of the leading candidates is FeCrAl alloy. FeCrAl alloys have good oxidation resistant at high temperatures exposure [2]. However, its durability at normal operating conditions needs further investigations. Furthermore, the sensitivity to compositional variations needs further understanding. To do so, a systematic and fast approach is necessary. Large number of experiments have been performed primarily at GE [2] and Oak Ridge National Laboratory [3] to understand the oxidation behavior of FeCrAl alloys in air, steam, and simulated boiling water reactor (BWR) at both normal water chemistry (NWC) and hydrogen water chemistry (HWC). Finding optimal composition of alloys through experiments with specific targeted property needs intensive resources and is time consuming as well. One alternative approach is to model oxidation mechanisms of alloys using ab initio, atomistic [4] and mesoscale [5] computational tools. Although these tools are effective to understand underlying physics of interest, it is almost impossible to obtain quantitative information to compare with experimental results. However, machine learning models can help accelerate composition optimization process. Machine learning codes built based on statistical approaches are used to predict targeted properties [6] from experimental datasets. This tool is particularly useful to optimize the composition in a fast and reliable fashion. The difficulty of interpretability of such machine learning models and the scarcity of dataset are major concern in the community.

In this work, we propose a combinatorial experimental and predictive optimization modeling approach that helps optimizing and accelerating alloy-designing process. Different chemical species with varying composition has diverse effect on the oxidation behavior of alloys. To design an oxidation resistant alloy, it is important to optimize its chemistry. The target is to obtain an optimized composition of FeCrAl alloy with low oxides mass gain. To do so, experimental dataset of mass change at different compositions is generated and later utilized to build predictive models. In addition to that, advanced material characterizations on the oxidized samples are performed to understand material chemistry. Experimental dataset is used to train machine learning codes and generate the predictive models relating targeted property with alloy composition.

Methodology

Experimental

Prior to air/steam testing, FeCrAl samples were polished using 600 grits, rinsed, dried, and weighted. Depending on the test, 4–6 samples were exposed side by side in a specially built vertical furnace. The entire test system was initially purged with argon for 30 min. The power was switched on, and the system was ramped with heating rate of 10 °C/min. Once the chamber reached the testing temperature, the argon was shut off and air/steam was introduced. Air (plain laboratory air) flow was 4 cubic feet per hour and steam flow was 2.5 g/min. The samples were exposed for 2–4 h at 1200 °C (high temperature oxidations) and 100 h at 400 °C (low temperature oxidation). After the exposure, the flow of air/steam was shut off and argon was introduced again to cool the system under argon atmosphere to ambient conditions. After the air/steam exposure, the samples were weighed to ambient conditions. The microstructure of tested samples was analyzed using transmission electron microscopy (TEM).

Computational

We leveraged two different approaches to build the predictive models [7] in this work, namely random forest (RF) and Bayesian Hybid models (BHM) [8]. Random Forest is a popular and widely used machine learning tool capable of tackling regression and classification tasks due to its ease of understanding and implementation [9]. GE Research’s in-house BHM is implemented on the same dataset for comparison [10]. Random forest is primarily chosen for its quick implementation and robustness to data quality. The BHM was chosen due it’s efficiency in low data regime. BHM also provides additional insights on uncertainty quantification and can be leveraged to obtain query points in the subsequent experimental runs. If \(M:X\to Y\) is the predictive model from the feature space X to output space Y, where features are the variables that we can measure and the output is the variable of interest (e.g., specific mass gain), then the optimization problem can be set up as \(\mathrm{arg}\underset{X}{\mathrm{min}}\left|M\left(X\right)\right|\). Thus, once a good predictive model is trained with available data, toolsets from optimization techniques [11] can be leveraged to obtain the composition towards minimizing specific mass change. Please note that Genetic Algorithm is used as optimization scheme. For the study conducted in the paper the input features (X) are, the weight % of Fe, Cr, Al, Mo and Ni, testing temperature, test duration. The output of interest is the specific mass change.

Both RF and BHM models were trained with 87 datapoints (combining high and low temperature oxidation) with varying chemical composition as features and specific mass gain as target variable. 80% of the datapoints were used as train the models while 20% were used to test them. The Normalized Root Mean Square Error (NRMSE) defined through Eq. (1–2) for RF and BHM are 1.80 and 3.20, respectively. Once we have achieved reasonable accuracy, the whole dataset, i.e., without the test-train split, is used to run the optimization models as the total number of datapoint is too low to cover the composition space.

$${\text{RMSE}}=\sqrt{\left\{\frac{1}{N}\sum_{i=1}^{N}{({y}_{i}-\widehat{{y}_{i}})}^{2}\right\}}$$
(1)
$${\text{NRMSE}}=\frac{\text{RMSE}}{{y}_{\text{max}}-{y}_{\text{min}}}$$
(2)

Result and discussion

FeCrAl class alloys are of interest as an accident tolerant nuclear fuel cladding material. Therefore, operational conditions of interest are long duration exposure in boiling water reactors at low temperature (~ 400 °C) for simulating regular operation conditions, and high-temperature exposure (~ 1200 °C) for short time simulating accidents scenarios. The fact that fuel cladding is exposed to steam environment towards the top of the reactor makes understanding oxidation behavior during steam exposure of great importance. In our previous work, we applied machine learning (ML) using experimentally collected data to predict mass change for a certain composition of Fe, Cr and Al. While specific mass change is conventionally used as the primary matrix for quantitatively expressing oxidation of the alloy, it is not the only matrix to understand oxidation behavior. Instead of blindly following and trusting the predictions from ML at different compositions of Al and Cr in FeCrAl alloy (Fig. 1a), we analyzed the oxide scale experimentally to understand oxidation. This step is critical for integrating any ML tools with experimental results. For the purpose of this study, we choose Fe–21Cr–5.5Al as the composition of interest for both low temperature (400 °C) and high temperature (1200 °C) applications. Figure 1b describes this point in high confidence region as this composition was used to train the ML model. The alloy showed resistance to oxidation at low temperature (400 °C) for 100 h of exposure in steam. The external oxide layer primarily formed of Cr and there is an Al-oxide layer underneath. The oxide layer stays intact at 400 °C with small mass gain. The passive oxide layer forms a protective scale that prevents catastrophic oxidation at 400 °C. Therefore, this composition can be used as cladding material from oxidation resistance point of view during normal operating temperature.

Fig. 1
figure 1

A combinatorial machine learning and material characterization of FeCrAl alloy oxidation after 100 h at 400 °C. The specific mass gain is plotted using BHM (a) along with the uncertainty (b) at each composition. SEM (c) and TEM (d) are performed of Fe-21Cr-5.5Al composition along with a vertical line-scan (e) of oxide scale as indicated in the yellow line in (d)

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During an accident scenario in the reactor, temperature rises very high within a short duration. The cladding material must resist oxidation for as long as possible. In addition to that, the integrity of the clad should not change. Therefore, the same composition was tested at high temperature as well to understand its applicability as an accident tolerant fuel cladding material. At 1200 °C, Fe–21Cr–5.5Al lost mass in high-temperature steam environment after 2 h. The oxide layer was clearly seen to fall off exposing bare alloy. We also performed TEM at a region where the oxide layer is stuck to the surface. A clear gap was noticed in some parts of the alloy (Fig. 2c). The oxide layer is primarily composed of Al-oxide on top of a Fe–Cr rich region.

Fig. 2
figure 2

A combinatorial machine learning and material characterization of FeCrAl alloy oxidation after 2 h at 1200 °C. The specific mass gain is plotted using BHM (a) along with the uncertainty (b) at each composition. SEM (c) and TEM (d) are performed of Fe–21Cr–5.5Al composition along with a vertical line-scan (e) of oxide scale as indicated in the yellow line in (d)

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From the specific mass change data generated by experiments at GE and trained machine learning models, an optimized composition of FeCrAl alloys at both high and low temperature steam exposure is predicted. In our previous work, we demonstrated the ability of random forest (RF) and Bayesian hybrid model (BHM) to predict mass change given the composition. Using the same methods, the FeCrAl alloy composition is optimized at (1) 1200 °C for 2 h and (2) 400 °C for 100 h. Table 1 shows the optimized compositions for both the cases. Experimentally, we have explored that a small fraction of Ni (> 0 and < 2 wt%) and Mo (> 0 and < 3 wt%) addition to FeCrAl has effects on oxidation resistance. Therefore, the concentration of Ni and Mo is also optimized in this work. One significant insight from the optimized compositions is the need for higher concentration of Al at high temperature applications than low temperature regime. BHM predicts 1.69 wt% less Cr content for high temperature oxidation compared to its counterpart at low temperature. On the contrary, the Al is observed to increase by 1.63 wt% for high temperature. This can be explained through the dissociation theory of Cr2O3 at high temperature. [12]

Table 1 Optimized composition of FeCrAl alloy for minimum mass gain during high temperature and low temperature oxidation
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To visualize the optimized composition predicted by the models and compare it with the training data range, we use radar plots (Fig. 3). The radar plots provide an efficient means of studying the optimized composition against the existing training set used in the surrogate model. Each highlighted radial axis in the radar plot refer to different elements in the composition. The concentric circles represent the numerical values of the composition indicated with discretization of 20%. Any composition of the alloy can be represented as a pentagon shape formed by the vertices which are dictated by the elemental composition percentage. For our current study, the radar plots are used to contrast the optimized alloy composition against the training set used to develop the model. The hollow quadrilateral marked in non-blue colors represents (red for BHM and multiple shades of red for RF) the optimized solution while the different shades of blue ones are training set compositions. The dark regions indicate availability of high-density training set. The compositions predicted as oxidation resistant alloys lives within the bounds of the training dataset for both the models.

Fig. 3
figure 3

Radar plot of the optimized composition for oxidation at 400 °C, 100 h (a, b) and 1200 °C, 2 h (c, d) as obtained from BHM (a, c) and Random Forest (b, d)

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Conclusion

FeCrAl class alloys are one of the leading candidates for replacing Zr-based cladding material in nuclear reactors. The oxidation resistance of the alloy is conventionally tested and quantified by specific weight gain during exposure in oxidizing environment. In this work, we showed the ability of machine learning based optimization tools to predict alloy composition that will provide good oxidation resistance during high and low temperature oxidation. The predictive ability of the model depends on the availability of the dataset and hence it can never be treated as ultimate truth. But the optimized compositions guide us towards the regions of interest where more experiments need to be carried out to train predictive modeling better. Furthermore, along with specific mass change, advanced characterization using SEM, TEM needs to be implemented to understand the effect of oxidation in various compositions. If needed, only looking at mass change as target variable may not be enough to understand oxidation resistant alloy. But the guidance towards optimized composition space that is proposed help reduce the number of experiments that needs to be carried out to reach to the best composition of interest. For this study we proposed separate compositions for low temperature regular reactor operation and high temperature accidental case. Going forward, a multi-objective optimization can be formulated with the goal of finding a material that is oxidation resistant is both the conditions.