The Continuous Cooling Transformation Diagram for 76

1. Introduction

To evaluate the performance of structural steels, understanding its microstructure after processing is crucial. The continuous cooling transformation (CCT) diagram of a steel plays an important role in providing information on the steel microstructure, as the information includes the start temperatures of phase transformation during cooling, as well as hardness. Since the actual CCT diagram varies significantly with material composition, the CCT diagram has to be constructed for each steel on the basis of experimental results. However, organizing the CCT information obtained for a specific steel is a highly experimental and time-consuming process, and it is difficult to immediately increase the amount of information.

For the prediction of a CCT diagram, there are several models for the transformation of the austenite phase during cooling. The commercial code JMatPro [1], which implements the Kirkaldy–Venugopalan model [2–5] assuming the additivity of time temperature transformation (TTT) diagram, is widely used. A model, that is an improved version of the Johnson–Mehl–Avrami–Kolmogorov (JMAK) model [6–8] has also been reported.

It has been shown that the CCT diagrams constructed using the addition rule can give erroneous estimates [9,10]. In addition to the refinement of transformation modeling, recent developments in data science have led to the prediction of transformation using machine learning and deep learning, as shown in . However, the number of reports that can show the overall CCT diagram is still limited because the prediction of Ac₃ temperature and the phase transformation start temperatures of ferrite (F), bainite (B), pearlite (P), and martensite (M) phases are evaluated separately using different data.

Table 1. Techniques used to predict transition temperature in previous studies.

Table 2. Steel grades listed in NRIM Atlas 1.

Trzaska has developed a linear regression formula [12], but it is not applicable to CG HAZ, the prediction models developed by Geng et al. are limited to Ni–Cr–Mo steels [16] and low alloy steels [17]. However, they do not predict the Ac₃ and critical cooling rate, which are essential for constructing the CCT diagrams for unknown materials as mentioned in the last paragraph of section 2.3. Miettinen et al. [21] used the critical cooling rate, which is expected to improve the accuracy in the prediction of a CCT diagram, but separate determination of intergranular components is required.

The toughness of a weld joint often deteriorates in the vicinity of the coarse-grained heat affected zone (CG HAZ), where the prior austenite grain size is the largest. For this reason, many CCT diagrams for welding have been developed for the CG HAZ, where the maximum temperature is between 1350°C and 1400°C. For example, CCT diagrams of structural steels for welding from Japan Iron and Steel Institute [22], NRIM CCT Atlas 1,2 [23–25] published by NRIM (now National Institute for Materials Science (NIMS)), and CCT diagrams for duplex stainless steels [26] are available. These CCT data must be useful for developing prediction models of CCT diagrams for CG HAZ.

On the other hand, with the progress of computational science and meso- and macro-scale computational techniques such as the CALPHAD (CALculation of PHAse Diagrams) method, the phase field method, and the finite element method, it has become common to consider the performance of structural materials according to the PSPP model (process, structure, property, and performance) [27]. It is now considered effective to consider the performance of materials. In Japanese SIP-MI projects [28,29], a number of workflows have been developed to consistently predict the material performance of weld HAZ on the basis of the PSPP concept [30–38]. Information on the microstructure of a material is crucial for the accurate material performance prediction using such workflows. To predict the microstructure of the weld HAZ, we have constructed a prediction model of the CCT diagram of an arbitrary composition from using experimental data by machine learning.

2. Building a prediction model of CCT diagram for weld HAZ

2.1. CCT diagram of steel and the thermophysical properties required for predicting the diagram

A schematic illustration of the CCT diagram is shown in Figure 1, where the horizontal axis is the time elapsed from the Ac₃ temperature during cooling and the vertical axis is the temperature. The solid lines in the figure are the transformation start temperatures for the F, P, B, and M and the dashed lines are the critical cooling rates for the F, P, and B, beyond which these phases do not appear. The critical cooling rates, which will be discussed later, are very important for drawing the CCT diagram. In order to predict the CCT diagram for a given composition, it is necessary to predict the following parameters: Ac₃, the critical cooling rates of F, P, and B, and the transformation start temperatures of F, P, B, and M at various cooling rates.

Figure 1. Schematic illustration of continuous cooling transformation (CCT) diagram for steel.

When the cooling rate is low, the transformation proceeds in the order of F, P, and B. In general, as the cooling rate increases, the transformation temperature decreases, the amount of F and P decreases, and the amount of B and M increases, resulting in an increase in hardness.

The procedure to construct a prediction model of a CCT diagram is as follows: (1) digitizing and organizing the CCT data, (2) predicting Ac₃, (3) predicting the critical cooling rate, (4) estimating the time and temperature of phase transformation at several cooling rates, and (5) drawing the comprehensive CCT diagram.

2.2. CCT diagram data: NRIM atlas 1

The CCT diagram depends on not only the composition but also the austenite grain size (austenitization conditions). However, the austenitization conditions often vary in the literature, and mixing all the austenitization conditions as training data may lead to inaccuracy. The CCT diagram data NRIM Atlas 1 [23,24] is intended for evaluating the microstructure of CG HAZ and contains 195 CCT diagrams for various types of steels, as shown in . All diagrams are created under the same austenitization conditions (peak temperature: 1350°C, holding time: 0 sec). Then, we used these 195 CCT diagrams as the training data to create the model for predicting the CCT diagram. The NRIM Atlas 1 data are also available on NIMS MatNavi [39].

Table 3. Mean and standard deviation of alloy compositions in wt%.

Histograms of the chemical composition of the steels in NRIM Atlas 1 are shown in Figure 2. Nitrogen (N) has not been measured in some steels and is treated as zero if not stated. As a result, about 150 steels have a nitrogen content of zero. The mean and standard deviation of the alloy compositions are shown in . All information on alloy composition is given in .

Figure 2. Histograms of elemental amounts listed in NRIM Atlas 1, (a) C, (b) Si, (c) Mn, (d) Cu, (e) Ni, (f) Cr, (g) Mo, (h) V, (i) N, (j) Nb.

Table 4. Coefficient of determination ( $R^{2}$ ), and the root mean square error (RMSE), and the mean absolute error (MAE) for Ac₃ temperature predictions using the NRIM Atlas 1 data.

First, CCT diagrams stored as printed data were scanned with high accuracy and stored as electronic data using a general-purpose digitizer. The obtained electronic data were used to create an approximate curve for the phase transformation start line of each steel. In the case of data not available owing to low cooling rate, the data were supplemented by transformation in which the transformation line was approximated by a monotonically increasing function. The validity of the CCT datasets was confirmed by comparing the obtained data with micrographs and so on.

Some CCT diagrams were excluded from 195 datasets. The effect of boron (B) is very large and should be included as a descriptor for prediction because of its possible effect of shifting the CCT line to the longer side; however, the insufficient description of the amount of B in NRIM Atlas 1 makes it difficult to evaluate its effect. Therefore, it was decided to exclude B from the explanatory variables and B-containing steels (15 steels) from the training data in the present study. We will discuss the effect of B in the next paper. Three steels with a high C content of 0.5 wt% or more have been excluded, due to the different transformation processes. Formation of some precipitates may affect the CCT diagram, because the CCT curves are determined by the solute content of each element just before the transformation. However, we consider the effect of precipitates is included in the non-linear model of the present study. Only four steels with a Nb content of 0.14 wt% or more have been excluded, because the content is too high compared with the commercial steels. In addition, questionable datasets were excluded (9 steels); then, dataset for 164 steels was used.

2.3. Machine learning algorithms and descriptor selection

Four machine learning algorithms, i.e. random forests [41], multiple regression, XGBoost, and support vector regression methods, have been tested and found that the random forests provided the best prediction performance. Thus, we used the random forests for the subsequent analysis. The random forests is an ensemble learning algorithm with decision trees as weak learners. The data were sampled to ensure that the data of the same steel grade are not included in both the training and test datasets at the same time (GroupKFold sampling). The hyperparameter of the random forests is the ratio of the descriptors used in each branch. Hyperparameters are optimized using a combination of grid search and Bayesian optimization techniques to select the best model.

In general, performing cross-validation (CV) by dividing the data into training and validation data when the size of the available dataset is small will result in a large variation in the accuracy of the machine learning model depending on the sampling method [42]. To maximize the use of data on a small number of steels, we decided to use double cross validation (DCV) [43], which is a double nested structure of CVs. For the outer CV, we adopt the leave-one-out (LOO) method, where only one dataset is left for testing and the rest is used for training, to evaluate the generalization performance. In the inner CV, the data set with one point removed by LOO is used for 10-fold cross-validation to adjust the hyperparameters. The final prediction model is built by adjusting the hyperparameters using all the data. The R and Python languages were used for the analysis. The random forests function was implemented in the R library, and the LOO and data processing parts were implemented in R. The part related to drawing was implemented in Python. Since all the data are used as training data, it is difficult to evaluate the generalization performance. However, we believe that the results of repeated evaluations by excluding a single point in LOO are close to the prediction results obtained by treating all the data as unknown data. The flowchart for DCV is shown in Figure 3. When the number of data is small, there is a problem of large variation of model performance due to random sampling using general $k$ -fold CV. However, when DCV is used, variation is minimized because all data can be used for model building. The coefficient of determination $R^{2}$ is evaluated by solving Eq. (1).

Figure 3. Flowchart of DCV and construction of final model.

(1)

R^{2} = \frac{\sum_{i} {(y_{i}^{o b s} - y_{i}^{p r e d})}^{2}}{\sum_{i} {(y_{i}^{o b s} - \overline{y^{o b s}})}^{2}},

(1)

where $y_{i}^{o b s}$ and $y_{i}^{p r e d}$ are the observed and predicted values for $i$ th data, respectively, and the overline denotes the average of the values.

According to the experimental conditions of the NRIM CCT Atlas 1 [23], the data supervised in this study, the Ac₃ measurement is considered to be approximately equal to A₃ because the sample was heated slowly. In the CCT diagram measurements, the specimens were rapidly heated to 1350°C and immediately cooled. The cooling is given a thermal cycle similar to the temperature history measured at the heat affected zone during welding. The old austenite grain size was found to be about 100 $\mum$ . Figure 4 shows the procedure for predicting the CCT diagram. Using the alloy composition and the logarithmically transformed cooling rate as descriptors, we first predict the Ac₃ temperature, and the predicted temperature is used. Next, the critical cooling rates of F, P and B were predicted to determine the upper limit of the cooling rate for the transformation of each phase. The transformation start time was predicted between 1 and 1000 sec. The critical cooling rate was used to determine the presence of phase transformation. Then we added the cooling rate as a descriptor, and the transformation start temperatures and times for F, P, and B were predicted for 40 equally spaced cooling curves on a logarithmic scale, in the range below the critical cooling rate for each phase. For M, the transformation start temperature was predicted for all cooling rates. The prediction of the transformation start time near the nose has a larger prediction error owing to the smaller curvature of the CCT line. Therefore, the CCT curve at the tip of the nose was represented by connecting the intersection of the critical cooling rate line and the transformation start temperature line learned on the long side with a B-spline curve [44].

Figure 4. Procedure for predicting CCT diagram.

Figure 5(a) shows a two-dimensional histogram of all the data plotted for the ferrite phase used in this study, where the number of data points used for training is small in the high cooling rate and low-temperature region as shown in the red circle. In addition, only the transformation start data of low hardenable steels are available in this region. If the ferrite transformation temperature of high hardenable steel is predicted under such a condition, inaccurate prediction results are obtained in high cooling rate region as shown in the dotted line in Figure 5(b). Thus, it is very important to include an index to distinguish the presence of transformation by separately predicting the critical cooling rate. Therefore, as shown in Figure 5(b), the nose position of the transformation was determined by the critical cooling rate, and the prediction line of the transformation temperature was truncated above the critical cooling rate.

Figure 5. (A) Variation in the number of data in temperature-time space, and (b) difference between prediction lines with and without considering of critical cooling rate.

3. Results and discussion

3.1. Performance evaluation

A comparison between the predicted results and the experimental data for Ac₃ temperature is shown in Figure 6 and the performance evaluation is shown in ., where R² is the coefficient of determination, RMSE is the root mean square error, and MAE is the mean absolute error. also includes the parameters evaluated in some references, where all Ac₃ data used in this study were predicted using the formulas [12,40] or machine learning model [13].

Figure 6. Prediction of Ac₃ temperatures.

Table 5. Coefficient of determination ( $R^{2}$ ), the root mean square error (RMSE), and the mean absolute error (MAE) for Ms temperature (martensite phase transition start temperature).

By comparing the prediction performance in this study with those in other references, we can see that the prediction accuracy in this study is higher than those in other references.

In all references, the Ms temperature was predicted when martensite was completely formed. In this study, however, performance in the region of constant Ms temperature with respect to time was also evaluated.

The results of the DCV method for the prediction of the critical cooling rates of (a) ferrite, (b) pearlite, and (c) bainite are shown in Figure 7. The performance of the training model for predicting the critical cooling rate for using unknown data is shown in . The accuracy of the prediction of the critical cooling rate for pearlite is slightly lower than that for the other phases. This might be due to the small number of data for pearlite and the fact that the accuracy of the experimental data is lower than that for the other phases, because it is difficult to detect the pearlite transformation only by dilatation measurement.

Figure 7. Prediction and verification results of critical cooling rate for various phases. ((a) F, (b) B, and (c) P).

Table 6. Coefficient of determination ( $R^{2}$ ) and the root mean square error (RMSE), the mean absolute error (MAE) for the model for critical cooling rate for various phases.

The data obtained in this study for the prediction of the start temperature of transformation for several cooling rates are shown in Figure 8. The prediction points for the same steel are presented continuously for different cooling rates. The performance of this prediction model for the transformation temperature is shown in , and we found that each start temperature was predicted with good accuracy of undefined ±30°C.

Figure 8. Prediction and verification results of transformation start temperature for various phases: (a) M, (b) F, (c) B, and (d) P.

Table 7. Coefficient of determination ( $R^{2}$ ), the root mean square error (RMSE), and the mean absolute error (MAE) for phase transition start points.

3.2. Evaluation of predicted CCT diagrams

A prediction model of the CCT diagram, constructed using the random forests method with double CV, was used to compare the CCT diagram calculated using the actual steel composition with the experimental results. In the evaluation, a prediction model was built by deleting one of the steels concerned. Several types of steel were selected according to their proof stress and their prediction results were compared with experimental results. ID-49 (SM50B), which is equivalent to SM490, was selected for the 490 MPa grade, ID-137 for the 590 MPa grade and ID-48 and 130 for the 780 MPa grade. The composition of each steel is shown in in section Appendix A.

Figure 9 shows the prediction results for each steel. The prediction model is generated by excluding the relevant steel and predicted the eligible steel. Good agreements of prediction results with the experimental results are obtained for each steel. When the LOO approach is used to evaluate the prediction performance for unknown data, a prediction model is built without the data concerned. However, in the end, the data for all steels were included in the prediction model, which meant that the model has also been adjusted for selected steels. Furthermore, the prediction performance is also expected to improve the prediction accuracy in the vicinity of the steel compositions.

Figure 9. Evaluated CCT diagrams for the alloys (a) ID-49, (b) 137, (c) 48, (d) 130. M(blue), F(red), B(green), and P(yellow).

When compared to other reports, it is difficult to evaluate the performance indicators alone because of the different steel grades handled and the variability in the number of data. Therefore, to evaluate the constructed model performance, results from this study were compared to JMatPro, which is a universally constructed and widely used model.

All CCT diagrams used in the present study were also predicted using JMatPro, assuming an austenitization temperature of 1350°C. The prior austenite grain size was set to 100 $\mum$ , which was the same assumption our prediction was based on as mentioned in section 2.3. Then data conversion was carried out for the results obtained, using the Ac₃ temperature of each steel as the reference for the cooling start time. As for the fraction of the formed phases, since the experimental values in NRIM Atlas 1 were obtained with a standard of 1%, the same standard was used in the JMatPro calculation. Figure 10 shows one example where the CCT diagram of ID-48 steel was predicted. Figure 9(c) shows good prediction accuracy, whereas F and B are shifted to the long time side in JMatPro, and the temperature for prediction tends to be high. Figure 11 shows the two-dimensional histograms of ferrite transformation start temperature in NRIM Atlas 1 (experimental), predicted in this study and using JMatPro for all steels. It can be seen that the overall prediction of the transformation start time derived from JMatPro shifts to the longer time side and higher temperatures.

Figure 10. CCT diagram evaluated using JMatPro for the alloy of ID-48 for Ac₃(black), M(blue), F(red), and B(green).

Figure 11. 2-D histograms of ferrite phase transition start temperature at various cooling rates for all target steels, predicted (a) in present study and (b) using JMatPro.

4. Summary

Although CCT data provide a wealth of information on the cooling rate dependent phase transformation of steels, the amount of available experimental data is not sufficient and is difficult to increase. In the present study, a prediction model for CCT diagrams of weld HAZ was developed using machine learning techniques with existing experimental data on CCT diagrams as training data. The data were carefully extracted from the literature, digitized, and validated with respect to the accuracy of individual data. In constructing the machine learning model, we adopted the method of predicting the transformation start temperature and the critical cooling rate separately, and created the prediction model using the DCV method that maximizes the use of a small number of data. As a result, we were able to construct a prediction model with higher accuracy for a wider range of steel products than in the case of using previous prediction models. The CCT diagram prediction model developed in this study has already been implemented in a system named MInt [28,29] that we have built under the concept of the PSPP model and can be connected to various computational workflows. The model is expected to contribute to the accurate understanding of microstructure information of materials. A hardness prediction model [45] which was developed by one of our authors (T.K.) will be implemented in the future.

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Source: https://www.tandfonline.com/doi/full/10.1080/27660400.2022.2123262?src=

The Continuous Cooling Transformation Diagram for 76

1. Introduction

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Table 1. Techniques used to predict transition temperature in previous studies.

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Table 2. Steel grades listed in NRIM Atlas 1.

2. Building a prediction model of CCT diagram for weld HAZ

2.1. CCT diagram of steel and the thermophysical properties required for predicting the diagram

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2.2. CCT diagram data: NRIM atlas 1

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Table 3. Mean and standard deviation of alloy compositions in wt%.

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Table 4. Coefficient of determination ( R 2 ), and the root mean square error (RMSE), and the mean absolute error (MAE) for Ac3 temperature predictions using the NRIM Atlas 1 data.

2.3. Machine learning algorithms and descriptor selection

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3. Results and discussion

3.1. Performance evaluation

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Table 5. Coefficient of determination ( R 2 ), the root mean square error (RMSE), and the mean absolute error (MAE) for Ms temperature (martensite phase transition start temperature).

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Table 6. Coefficient of determination ( R 2 ) and the root mean square error (RMSE), the mean absolute error (MAE) for the model for critical cooling rate for various phases.

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Table 7. Coefficient of determination ( R 2 ), the root mean square error (RMSE), and the mean absolute error (MAE) for phase transition start points.

3.2. Evaluation of predicted CCT diagrams

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4. Summary

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Table 4. Coefficient of determination ( $R^{2}$ ), and the root mean square error (RMSE), and the mean absolute error (MAE) for Ac₃ temperature predictions using the NRIM Atlas 1 data.

Table 5. Coefficient of determination ( $R^{2}$ ), the root mean square error (RMSE), and the mean absolute error (MAE) for Ms temperature (martensite phase transition start temperature).

Table 6. Coefficient of determination ( $R^{2}$ ) and the root mean square error (RMSE), the mean absolute error (MAE) for the model for critical cooling rate for various phases.

Table 7. Coefficient of determination ( $R^{2}$ ), the root mean square error (RMSE), and the mean absolute error (MAE) for phase transition start points.