Uncovering the generic and alloy-specific governing parameters of deformation-induced martensitic transformation in austenitic steel

The database was further developed from a prior work [19] containing 2801 original datapoints from austenitic stainless steels (ASSs), such as the 201 series, 204 series, 301 series, 304 series, 309, 316, and also other related experimental alloys (Misc.). All these steels have a fully austenitic structure prior to deformation. In order to investigate the effect of the governing parameters on DIMT, the following features were included: strain, stress, strain rate, temperature, austenite grain size, driving force for α′-martensite transformation (DF_fcc-bcc), and driving force for ε-martensite formation (DF_fcc-hcp). α′-martensite fraction was the target to be predicted. In this database, α′-martensite fraction was mainly measured by saturation magnetization and x-ray diffraction (XRD) methods and the measurement error was less than 3% [20], satisfying the establishment of a reliable ML model. The database constitution is summarized in Table 1. Strain, stress, strain rate, and temperature were directly read from the related literature. The austenite grain size was most often taken from the reported values in μm, in some cases though grain size was given as an ASTM number, which were in such case transformed to μm based on ASTM E112 [21]. In other cases, the grain size was evaluated based on the micrographs reported in literature. Finally, in a few cases no grain size or microstructure information was provided in the original report, and in those cases the average value of the grain size in the database was used. Driving forces for both α′-martensite and ε-martensite were calculated by Thermo-Calc® software 2021b [22] using TCFE11 database [23]. The reason to include also ε-martensite is that DIMT is related to the stacking fault energy (SFE) which relates to DF_fcc-hcp [2]:where \(\rho\) is atom density in a close packed plane in moles per unit area; \(\Delta G^{\gamma \to \varepsilon }\) is the free energy for transformation from austenite to ε-martensite, which is equal to the negative value of DF_fcc-hcp. \(E^{{{\text{strain}}}}\) is the strain energy for the transformation from austenite to ε-martensite and \(\sigma^{\gamma /\varepsilon }\) is the interfacial energy of the γ and ε phase boundary. \(E^{{{\text{strain}}}}\) is generally neglected in austenitic steel and the parameters \(\rho\) and \(\sigma^{\gamma /\varepsilon }\) can be assumed to be constant [24]. The constitution of the PM parameters and the output in the database is shown in Fig. 1.

In the present work, a train–test split approach was applied where the dataset was randomly separated into a training dataset (80% of the data) and a test dataset (20% of the data). Normalization was applied to eliminate the difference in the numerical range among different input features, and the inputs are scaled to the range from 0 to 1. Based on the previous modeling results, it is found that the prediction of the trained ML model fluctuates for different partitions of the training and test sets; hence, multiple hold-out datasets were used to reliably evaluate the performance of the model [25]. The dataset was randomly divided into training and testing sets to develop 100 ML models, and model evaluation was performed by the squared correlation coefficient (R²), mean absolute error (MAE), and root mean square error (RMSE).

Six ML algorithms were applied to build the correlation between input features and the DIM fraction: (1) multilayer perceptron (MLP), a kind of artificial neural network, consisting of the neuron layers and the neuron clusters in each layer, which has been widely used to address material science challenges [26]; (2) support vector regression (SVR), a statistical learning regression algorithm based on structural risk minimization principle [27], suitable to develop models in the case of the small amount of samples; (3) decision tree regression (DTR), it belongs to the nonparametric models of supervised learning used for regression analysis, which originates from a binary tree that splits into more nodes to develop a decision tree [27]; (4) ensemble learning regression, including random forest regression (RFR), Adaboost (Ada), and XGBoost (XGB), a sort of multi-regression system, which integrates the multiple learners to complete the modeling [28]. The grid search technique is applied to optimize the hyper-parameters of each ML models, and the optimal hyper-parameter range and key hyper-parameters of 100 models for each ML algorithm are shown below: (1) MLP (activation = relu, solver = lbfgs, size of first hidden layer: 30, size of second hidden layer: 20); (2) SVR (penalty parameter C: 45–49, kernel function = RBF); (3) DTR (maximum depth of tree: 42–71); (4) RFR (number of estimators: 58–94); (5) Ada (number of estimators: 66–85, base estimator: DTR); (6) XGB (number of estimators: 33–42, learning rate = 0.1). The modeling implementation was conducted using Python and the Scikit-learn library. The prediction results of the testing set are shown in Fig. 2. It can be seen that the ensemble methods have better prediction accuracy than MLP, SVR, and DTR algorithms, which is consistent with the previous work [19]. Among the ensemble methods, random forest regression (RFR) obtains the largest MAE value, while Adaboost (Ada) and XGBoost (XGB) achieve similar accuracy in both MAE and R² values. Finally, XGBoost was selected as the final algorithm due to its slightly better performance.

For the training dataset, the values of RMSE and R² are 0.025 and 99.3%, which indicates that the trained ML model has fully learned the “knowledge” from the training data. With respect to the testing set as shown in Fig. 3a, most data points lie on or close to the straight line with a slope of 1, indicating that the prediction results are in excellent agreement with the actual values for all kinds of grades. The RMSE and R² values of the whole testing dataset are 0.042 and 97.1%. Additionally, 479 of 541 testing data entries have the absolute errors between experimental and predicted values within 0.05, and no large deviations occur anywhere in the whole range of data, indicating that it has a good performance. The RMSE values for each grade are listed in Table 2. In order to further investigate the applicability, the trained model was applied for predictions on an unseen validation set containing alloys with other compositions or deformation conditions; the results are shown in Fig. 3b. For 204Cu, the validation alloy with new grain size (16.4 μm) and strain rate (3 × 10^–4 s⁻¹) was collected from Ref [29], and it has a higher DIM fraction compared to other 204Cu alloy (0.5–18 μm of grain size, 5 × 10^–4 s⁻¹ of strain rate) in the training set [30]. The 304SS validation alloy [31] with the new composition and a lower strain rate of 3 × 10^–3 s⁻¹ also has an obvious difference in DIMT behavior from 304SS alloy with strain rate of 3 × 10^–1 s⁻¹ and other alloys belonging to 304 series. Moreover, 301LN validation alloy [32] was deformed at a different strain rate compared to the other 301 grades. However, as illustrated in Fig. 3b, the trained model is capable of accurately predicting the DIM fraction for all of the validation cases (RMSE: 0.0558, R²: 93.5%), showing the excellent generalizability.

In this work, the ML method was applied to predict the DIM fraction in a very complex dataset containing a range of austenitic steel grades. However, the prediction accuracy is close to the previous studies that have only focused on one kind of austenitic stainless steels, such as AISI 304 [18] and AISI 301 [17]. Furthermore, compared to the work of Das et al. [16], the current dataset has a wider composition range and obtains a slight improvement in terms of R² value, i.e., 93.5% (present work) versus 88.3–95.6% (Das et al. [16]). Finally, the present prediction results are basically consistent with Ref. [19], but the amount of samples used in the current modeling process (2801 data points) is much less than in the previous study where synthetic data points were generated through physical modeling (16,500 data points).

After establishing the predictive model, we investigate the correlation between composition, PM features, and DIMT based on feature importance analysis for the ML models. According to the modeling results, the feature importance was slightly different for the above four ensemble algorithms, and since each algorithm had an excellent goodness of fitting, we use the average results of feature importance from the algorithms (i.e., Ada, RFR, XGB and DTR) as final feature importance, see Fig. 4a. With respect to composition, carbon and nitrogen have the strongest correlation with DIMT and thereafter Mn, Cr, Si. For PM features, the highest importance is related to stress and thereafter strain and temperature. Strain rate and austenite grain size show relatively low importance for DIMT compared with other features.

The correlation of each feature and DIMT has been generally analyzed for the whole dataset containing various grades of austenitic stainless steels in the last section, and it can be found that the correlation of some PM features varies among different steel grades. So, it is necessary to critically analyze the feature importance for the specific grades. In general, a ML model was supposed to be firstly trained by samples from the specific grades in order to obtain its importance analysis. But the sub-dataset of each steel grade does not contain enough samples and has the very narrow range of each feature, e.g., chemical composition, which increases the difficulty for training a reliable model. Instead in this work, a method is proposed to calculate the feature importance of the specific steel grade, in which samples of the target grade were removed from the dataset and a new feature importance was obtained from the new model trained by the rest of the samples. In this case, compared to feature importance of the whole dataset (Fig. 4a), a change of the importance value was attributed to the removed samples of the target grade. If the importance value of some features decreases, it indicates that these features are very important for target grade. Conversely, the increase in importance value represents a low correlation. This analysis method was applied to two series of austenitic stainless steels to investigate their respective feature importance, including 204 series (204Cu, 204 M, 204SS) and 301 series (301, 301L, 301LN), and it has been proved that 204 series has the higher austenite stability than 301 series according to the previous studies [57, 58]. Figure 6 displays the change of importance value for these selected grades. 301 series and 204 series display the totally different results. With respect to 301 series, stress greatly increases the correlation owing to the obvious reduction in importance value, and the strain and temperature become less important. This grade has the relatively low austenite stability owing to the low SFE value, e.g., \(\gamma_{{{\text{SFE}}}}\) = 14.7 mJ m⁻² for 301SS [57]. The low austenite stability indicates that transformation can start in a wide temperature range with a high upper temperature limit and has a low requirement for extra chemical DF from the decrease in temperature, resulting in a relatively low correlation of deformation temperature. Moreover, the nucleation sites, e.g., shear bands and ε-martensite, can be easily obtained when the applied strain is very small owing to the low SFE. So, the key point governing DIMT is applied stress that provides extra mechanical DF to transform nucleation sites into α′-martensite, instead of applied strain that produces nucleation sites. With respect to 204 series, the correlation of stress and strain slightly decreases and goes up, respectively. The deformation temperature’s correlation obtains an obvious increase considering the decrease in feature importance. Combining with feature importance of the whole dataset as shown in Fig. 4a, it can be seen that 204 series achieves a better balance among stress, strain, and temperature. This grade has a high austenite stability and high SFE, e.g., \(\gamma_{{{\text{SFE}}}}\) = 16.8 mJ m⁻² for 204SS [57]. The high SFE represents the difficulty for forming the new nucleation sites [24], and DIMT process may be more dependent on the existing sites. In this case, the applied stress is essential to provide mechanical DF to transform the stable nucleation sites with the high activation energy. In addition, a relatively large plastic strain is also important to produce the new nucleation sites for further martensite transformation. Moreover, 204 series have a low chemical DF_fcc-bcc, which also means the extra chemical DF from temperature reduction is important to induce transformation.

A mathematical explanation is also given to clarify the great variation in importance of strain, stress, and temperature based on the Pearson’s coefficient. As shown in Fig. 7a, stress obtains a higher linear correlation than strain and temperature, showing that stress should contribute more to the development of the ML model, which is consistent with the feature importance in Fig. 4. When removing the samples belonging to the 301 series from the dataset (Fig. 7b), the correlations of DIMT with strain and temperature increase and stress decrease (Fig. 7a), indicating that stress has a very strong correlation with α′-martensite fraction in 301 series. When removing the 204 series from the dataset (Fig. 7c), stress obtains a higher correlation, but the values of strain and temperature reduce compared to the whole dataset, also indicating that strain has a relatively higher correlation to α′-martensite transformation as compared to the 301 series.

With respect to strain rate and grain size, these factors show the decrease in importance values, indicating that they are both important for these two kinds of austenitic stainless steels. Generally, according to statistical analysis, 301 series are very different from 204 series in terms of DIMT behavior. 301 series with the low austenite stability is only highly related to applied stress, but 204 series have a higher requirement for the induction of martensite transformation, and strain, stress, and temperature all show high correlation. For the chemical composition, there are basically no obvious changes. Only a change occurs for molybdenum, and its importance reduces for 204 series because this grade contains very low level of molybdenum [29, 30]. The importance of carbon and nitrogen increases in 301 series, indicating the high correlation to DIMT.

In the previous work of Ref. [19], a prediction model for DIMT was developed combining physical-based modeling and ML method. In order to improve the robustness of the trained ML model, a large dataset was built combining experimental data and physical modeling data using Olson-Cohen model, which provides the new methodology to combination of physical-based method and ML. The present work selects another combination method that introduces numerous related PM features into the original experimental dataset for model training, as listed in Table 1. For the prediction accuracy, the current result is very close to that of previous work, e.g., the RMSE of testing set (0.0420 vs. 0.0415), 301 series (0.0451 vs. 0.0479), and 304 series (0.0372 vs. 0.0380). But it is worth noting that the present dataset only contains 2801 samples which is significantly smaller than that of previous dataset consisting of 16,500 samples. Furthermore, in order to compare in a fair way, a new ML model was trained based on present dataset, but using features of previous work, i.e., composition, strain, and temperature. From the results in Fig. 8; it can be seen that ML models trained by present features are clearly improved than those using the previous features for each algorithm. The good performance can be interpreted by fully mining the existing data using additional PM features. In the present work, in addition to strain and temperature used in the previous work, stress, strain rate, and grain size and two kinds of DF were also included in the dataset; especially, applied stress is found to be the most important feature for DIMT prediction according to the importance analysis and previous studies [4, 16, 36] and strongly controls the DIMT process. The introduction of such crucial features aids to lower the requirement for the number of samples for training a robust model, also contributing to alleviating the small sample problem. For correlation analysis, in the previous work, strain and temperature show the very strong correlation, which is much higher than the composition. A large gap exists between PM features (strain and temperature) and composition, implying the absence of other related features. The present study introduces these missing features into modeling process and displays a whole roadmap for the correlation between various PM features and DIMT, contributing to a better understanding of PM mechanism.