Deep Learning to Predict Deterioration Region of Hot Ductility in High-Mn Steel by Using the Relationship between RA Behavior and Time-Temperature-Precipitation

: Reduction of area (RA) measurement in a hot ductility test is widely used to deﬁne the susceptibility of surface crack of cast steel, but the test is complex because it entails processes such as specimen fabrication, heat treatment, tensile testing, and analysis. As an alternative, this study proposes a model that can predict RA. The model exploits the relationship between precipitation and RA behavior, which has a major effect on hot ductility degradation in high-Mn steels. Hot ductility tests were performed using four grades of high-Mn steels that had different V-Mo compositions, and the RA behavior was compared with the precipitation behavior obtained from a time-temperature-precipitation (TTP) graph. The ductility deterioration of high-Mn steels shows a tendency to start at the nose temperature T N at which precipitation is most severe. Using this relationship, we developed a model to predict the hot ductility degradation temperature of high-Mn steels. T N was calculated using J-matpro software (version 12) for 1500 compositions of high-Mn steels containing the precipitating elements V, Mo, Nb, and Ti, and by applying this to a deep neural network (DNN), then using the result to develop a model that can predict T N for various compositions of high-Mn steel. The model was tested by comparing its predicted RA degradation temperature with RAs extracted from reference data for ﬁve high-Mn steels. In all ﬁve steels, the temperature at which the RA decreases coincided with the value predicted by the DNN model. Use of this model can eliminate the cost and time required for hot ductility testing to measure RA. accuracy of the T N was from and temperature-related datasets of high-Mn steels with the DNN model. Root mean square error (RMSE) was used to evaluate the accuracy of the


Introduction
During the conventional continuous casting process, the slab goes through bending and unbending zones. In the unbending zone, the stress accumulated on the slab can cause defects such as surface cracks. To quantify the susceptibility of surface crack of slab, the steel's hot ductility is measured using tensile tests at high temperatures. The tensile test that applies the thermal condition of continuous casting yields the reduction of area (RA), which is the rate of change in cross-sectional area at each temperature. RA can represent the hot ductility behavior.
Hot ductility can decrease (i.e., RA can decrease) in certain temperature ranges as a consequence of phase transformation that can form ferrite film, and of segregation that can deposit precipitates along austenite grain boundaries [1][2][3][4]. RA measurements to evaluate hot ductility require a complex experimental process that entails specimen fabrication, solution treatment, tensile test, measuring RA, and analyzing the data. However, the process is too slow and costly to be applied to all steel grades, so an alternative method to predict RA would be desirable. Methods to provide this ability have included simple linear regression [5], multiple linear regression [6], back-propagation neural network (NN) [7][8][9][10], from each, a cylindrical tensile specimen with a length of 90 mm and a diameter of 10 mm was fabricated along the casting direction in the area outside the shrinkage cavity. Tensile tests were performed using a Caster & Thermo-mechanical simulator (40334, Fuji electronic industrial, Saitama, Japan). The specimen was heated to 1250 • C at 10 • C·s −1 , held for 300 s for solution treatment, then cooled to the target temperature (T T = 600, 700, 800, 900, or 1000 • C) at 10 • C·s −1 . The specimen was held for 60 s at T T to stabilize the temperature, then the tensile test was conducted using strain rate of 5 × 10 −4 s −1 (Figure 1), which is a conventional continuous casting speed (5 × 10 −3 to 5 × 10 −4 s −1 ). All tensile tests were performed three times at each T T . Hot ductility was evaluated by RA measured from field emission scanning electron microscope (FE-SEM; JSM-7100F, JEOL Ltd., Tokyo, Japan) images of each fractured specimen after the tensile test. The FE-SEM images were also used to confirm the structure of the fracture surface. The microstructure of a vertical section of the fractured specimen prepared by using cutting machine was observed by electron backscatter diffraction (EBSD; Oxford, UK).

Hot Ductility Test
The hot ductility test was performed on four high-Mn steels that had different contents of V and Mo (Table 1). A vacuum melting furnace was used to produce 30 kg ingots, then from each, a cylindrical tensile specimen with a length of 90 mm and a diameter of 10 mm was fabricated along the casting direction in the area outside the shrinkage cavity.
Tensile tests were performed using a Caster & Thermo-mechanical simulator (40334, Fuji electronic industrial, Saitama, Japan). The specimen was heated to 1250 °C at 10 °C•s −1 , held for 300 s for solution treatment, then cooled to the target temperature (TT = 600, 700, 800, 900, or 1000 °C) at 10 °C•s −1 . The specimen was held for 60 s at TT to stabilize the temperature, then the tensile test was conducted using strain rate of 5 × 10 −4 s −1 (Figure 1), which is a conventional continuous casting speed (5 × 10 −3 to 5 × 10 −4 s −1 ). All tensile tests were performed three times at each TT. Hot ductility was evaluated by RA measured from field emission scanning electron microscope (FE-SEM; JSM-7100F, JEOL Ltd., Tokyo, Japan) images of each fractured specimen after the tensile test. The FE-SEM images were also used to confirm the structure of the fracture surface. The microstructure of a vertical section of the fractured specimen prepared by using cutting machine was observed by electron backscatter diffraction (EBSD; Oxford, UK).

Calculation of Time-Temperature-Precipitation diagram
The TTP and the equilibrium precipitation fraction diagram were calculated using J-MatPro software (version 12, Sente Software Ltd., Guildford, UK). The variables used in the calculation were same with the conditions used in the hot ductility test, and the other

Calculation of Time-Temperature-Precipitation Diagram
The TTP and the equilibrium precipitation fraction diagram were calculated using J-MatPro software (version 12, Sente Software Ltd., Guildford, UK). The variables used in the calculation were same with the conditions used in the hot ductility test, and the other conditions were set to represent the conditions used in the process of continuous casting. The quenching temperature was set to 1250 • C, which is the solution-treatment temperature in the experiment, and the grain size was set to 1000 µm, which is the size observed in general high-Mn steel. To consider the deformation-induced precipitation behavior, the deformation conditions were used in the calculation. The deformation temperature was set to 850 • C, which is the midrange temperature of conventional bending-unbending region (temperature range: 700 to 1000 • C), and the strain was set to 0.05 considering the maximum total strain during continuous casting process (total strain range: 0.02 to 0.05). The strain rate was set to 5 × 10 −4 s −1 , as in the experiment. If variables related to deformation are changed, the time taken for completion of precipitation changes, but it does not significantly affect the T N , so changes to the values of these variable for T N extraction are not constrained. T N that corresponds to matrix M(C, N) precipitation was extracted from the calculated TTP diagram to consider the dynamic precipitates [19].

Hot Ductility Behavior of V-Mo Added High-Mn Steel
To investigate the high-temperature ductility behavior according to the addition of V and Mo, the RA graphs ( Figure 2) were obtained for the four steel grades. All had a low RA < 50% over the entire T T range, but the addition of V or V-Mo significantly affected the RA behavior. The hot ductility was lower in Steels A, B, and C, including precipitating elements, than in the reference steel (Steel ref) at all T T ; this difference is related to the precipitation hardening and the retardation of dynamic recrystallization behavior due to the precipitation and solute effect [20][21][22].   The EBSD results ( Figure 3) of Steel ref show increase in the fraction of dynamic recrystallized grains as T T increased from 800 to 900 • C. In contrast to Steel ref, no recrystallized grains were observed in Steels A and B at T T = 800 • C. When the T T increases to 900 • C, a few recrystallized grains were found in the vicinity of fracture surface in steel A (black arrow in Figure 3e-1), but still no recrystallization clearly in steel B. This indicates that recrystallization was suppressed due to the addition of V or V-Mo. This trend can also be seen in the fracture surface ( Figure 4). Steel ref has dimples distributed throughout the fracture surface, whereas Steel A and B exhibit brittle intergranular fracture behavior at T T = 800 • C. At T T = 900 • C, the amount of dimple increased in Steel ref compared to T T = 800 • C, and some of dimples were found in Steel A. In the case of Steel B, it shows a brittle fracture surface through complete intergranular fracture as at T T = 800 • C. This recrystallization behavior is consistent with the hot ductility result of Figure 2, and therefore, steels A and B have lower hot ductility than Steel ref at temperatures < T T = 900 • C.
Steels B and C with the same V content had similar RA behavior despite presence of Mo content in steel C, and both had the lowest RA. This result implies that V has a greater degrading effect than Mo on high-temperature ductility. When high-Al and TWIP steels include >0.3 wt.% V, fine precipitates of about 4 to 5 nm form and degrade the hot ductility. Furthermore, if the V content is increased to ≥0.5 wt.%, the hot ductility is further reduced due to precipitation-free zones, because precipitates form along grain boundaries [15]. The behavior of RA in this study has a similar trend to the degradation of hot ductility due to the increase in V content. The average compositions of V at the segregation area in Steel A and B were about 0.57 and 0.93 wt.%, respectively ( Figure 5). The density of precipitates and the segregation of V were significantly higher in Steel B than in Steel A. The high level of V content in the segregation region of Steel B not only promotes the formation of precipitates, but also inhibits recrystallization due to the solute effect, leading to lower hot ductility [21,22].

Precipitation Behavior in V-Mo and V Steels
The difference in RA between Steel A and Steel B at T T = 900 • C can be explained by the variation in precipitation behavior according to the V content, and the calculated TTP diagram and equilibrium fraction diagram were used for this purpose. When the content of V was increased from 0.3 to 0.5 wt.%, the T N of the TTP curve increased from 800 to 850 • C, and the time to the onset of precipitation decreased ( Figure 6a). However, the addition of Mo did not affect the change in T N ; the precipitate fraction diagram ( Figure 6b) has a similar trend. In addition, the precipitation-initiation temperature T PI also increased from 1050 • C to~1110 • C by increasing content of V. The addition of Mo only serves to increase the volume fraction of precipitates; it does not affect T PI . Metals 2022, 12, x FOR PEER REVIEW 6 of 16

Precipitation Behavior in V-Mo and V Steels
The difference in RA between Steel A and Steel B at TT = 900 °C can be explained by the variation in precipitation behavior according to the V content, and the calculated TTP diagram and equilibrium fraction diagram were used for this purpose. When the content of V was increased from 0.3 to 0.5 wt.%, the TN of the TTP curve increased from 800 to 850 °C , and the time to the onset of precipitation decreased ( Figure 6a). However, the addition of Mo did not affect the change in TN; the precipitate fraction diagram ( Figure 6b) has a similar trend. In addition, the precipitation-initiation temperature TPI also increased from ~1050 °C to ~1110 °C by increasing content of V. The addition of Mo only serves to increase the volume fraction of precipitates; it does not affect TPI.
The tendencies of change in the TTP TN and TPI corresponded in the TT range, in which RA rapidly decreases. In Steel A, RA decreased rapidly to <10% from TT = 900 to 800 °C, and the calculated TN was 800 °C. In Steel B, the RA decrease started at a higher temperature than in Steel A, and the TN was 850 °C, which is higher than in Steel B. Increase in TPI and TN due to the increase in the V content is correlated with an increase in the temperature at which the decrease in RA begins.
This phenomenon can also be explained by the strain-stress curve at TT = 900 °C, at which the difference in RA is largest ( Figure 7). Steel A with a low TN has similar yield stress (YS) and ultimate tensile stress (UTS) to Steel ref that lacks precipitation-fostering elements, but Steel B with a relatively high TN has higher YS and UTS than Steel A due to the precipitation strengthening at TT = 900 °C. Therefore, the RA decrease starts in the region in which the formation of precipitates is concentrated, and this correlation means that the precipitation phenomenon of high-Mn steel and the change in its RA behavior are closely related.  diagram and equilibrium fraction diagram were used for this purpose. When the content of V was increased from 0.3 to 0.5 wt.%, the TN of the TTP curve increased from 800 to 850 °C , and the time to the onset of precipitation decreased (Figure 6a). However, the addition of Mo did not affect the change in TN; the precipitate fraction diagram (Figure 6b) has a similar trend. In addition, the precipitation-initiation temperature TPI also increased from ~1050 °C to ~1110 °C by increasing content of V. The addition of Mo only serves to increase the volume fraction of precipitates; it does not affect TPI.
The tendencies of change in the TTP TN and TPI corresponded in the TT range, in which RA rapidly decreases. In Steel A, RA decreased rapidly to <10% from TT = 900 to 800 °C, and the calculated TN was 800 °C. In Steel B, the RA decrease started at a higher temperature than in Steel A, and the TN was 850 °C, which is higher than in Steel B. Increase in TPI and TN due to the increase in the V content is correlated with an increase in the temperature at which the decrease in RA begins.
This phenomenon can also be explained by the strain-stress curve at TT = 900 °C, at which the difference in RA is largest (Figure 7). Steel A with a low TN has similar yield stress (YS) and ultimate tensile stress (UTS) to Steel ref that lacks precipitation-fostering elements, but Steel B with a relatively high TN has higher YS and UTS than Steel A due to the precipitation strengthening at TT = 900 °C. Therefore, the RA decrease starts in the region in which the formation of precipitates is concentrated, and this correlation means that the precipitation phenomenon of high-Mn steel and the change in its RA behavior are closely related.  The tendencies of change in the TTP T N and T PI corresponded in the T T range, in which RA rapidly decreases. In Steel A, RA decreased rapidly to <10% from T T = 900 to 800 • C, and the calculated T N was 800 • C. In Steel B, the RA decrease started at a higher temperature than in Steel A, and the T N was 850 • C, which is higher than in Steel B. Increase in T PI and T N due to the increase in the V content is correlated with an increase in the temperature at which the decrease in RA begins.
This phenomenon can also be explained by the strain-stress curve at T T = 900 • C, at which the difference in RA is largest (Figure 7). Steel A with a low T N has similar yield stress (YS) and ultimate tensile stress (UTS) to Steel ref that lacks precipitation-fostering elements, but Steel B with a relatively high T N has higher YS and UTS than Steel A due to the precipitation strengthening at T T = 900 • C. Therefore, the RA decrease starts in the region in which the formation of precipitates is concentrated, and this correlation means that the precipitation phenomenon of high-Mn steel and the change in its RA behavior are closely related.

Prediction Model for Time-Temperature-Precipitation Nose Temperature
The experimental results in Section 3.1 confirmed the correlation between hot ductility and the TTP diagram in high-Mn steels. This relationship indicates that if the T N is known, the RA decrease temperature can be predicted without complicated hot-ductility tests. Therefore, a model that can predict the temperature at which RA decreases was produced by utilizing a TTP diagram database for various high-Mn steel compositions.

Prediction Model for Time-Temperature-Precipitation Nose Temperature
The experimental results in Section 3.1 confirmed the correlation between hot ductility and the TTP diagram in high-Mn steels. This relationship indicates that if the TN is known, the RA decrease temperature can be predicted without complicated hot-ductility tests. Therefore, a model that can predict the temperature at which RA decreases was produced by utilizing a TTP diagram database for various high-Mn steel compositions.
To obtain a database of TN, TTP diagrams of ~1500 high-Mn steel compositions were calculated and the composition used in calculation included one or more of precipitating elements V, Mo, Ti, and Nb. Contents of elements that do not significantly affect TN in carbide formation were fixed by referring to the composition of steels used in the experiment: Si = 0.02, P = 0.015, S = 0.003, Al = 0.02, N = 0.005. When the TTP diagram could not be calculated because the content of the elements required for precipitation was too low, that composition was excluded. When the alloy included only Mo, which forms a precipitate by combining with other elements (mainly V), the TTP diagram could not be calculated, so this composition was also excluded. To consider the precipitation effect due to deformation, the deformation conditions mentioned in Section 2.2 were used. These calculations yielded 610 ≤ TN ≤ 1030 °C.
Variables cannot be directly compared in the analyzed results when variables have different ranges. To overcome this problem, each variable was normalized and standardized using MinMaxScaler to scale all data into the range 0 to 1. To predict the TN corresponds to supervised learning with both input and output values, and it uses the regression approach because prediction of real numbers or vectors is required. In this study, a DNN model [23,24] (Figure 8) was used to predict the TN for various compositions of high-Mn steels. The input layer consisted of six compositional variables: C, Mn, Nb, Ti, V, and Mo. The hidden layer consisted of four dense layers and transformed the nonlinear hidden characteristics of the input data to linear characteristics. The output layer was composed of one layer and was designed to predict TN. When the TTP diagram could not be calculated because the content of the elements required for precipitation was too low, that composition was excluded. When the alloy included only Mo, which forms a precipitate by combining with other elements (mainly V), the TTP diagram could not be calculated, so this composition was also excluded. To consider the precipitation effect due to deformation, the deformation conditions mentioned in Section 2.2 were used. These calculations yielded 610 ≤ T N ≤ 1030 • C.
Variables cannot be directly compared in the analyzed results when variables have different ranges. To overcome this problem, each variable was normalized and standardized using MinMaxScaler to scale all data into the range 0 to 1. To predict the T N corresponds to supervised learning with both input and output values, and it uses the regression approach because prediction of real numbers or vectors is required. In this study, a DNN model [23,24] (Figure 8) was used to predict the T N for various compositions of high-Mn steels. The input layer consisted of six compositional variables: C, Mn, Nb, Ti, V, and Mo. The hidden layer consisted of four dense layers and transformed the nonlinear hidden characteristics of the input data to linear characteristics. The output layer was composed of one layer and was designed to predict T N .
The program in this experiment was implemented using the Keras library using Python (version 3.5.2, Python Software Foundation, Wilmington, DE, USA) and TensorFlow (version 2.0, Google Inc., Mountain View, CA, USA) as backends, and the experiment was conducted in a Windows 10 64-bit environment with an Intel i7-6700K processor (Intel Corporation, Santa Clara, CA, USA) and two GeForce GTX 1080 Ti graphics cards (NVIDA Corporation, Wilmington, DE, USA). First, hyper-parameter values that represent optimal prediction accuracy were found by applying various environments while training the proposed model. Of the 1468 sets of data used in the experiment, 80% were used for training and 20% for testing. The accuracy of the T N prediction was measured from composition and temperature-related datasets of high-Mn steels with the DNN model. Root mean square error (RMSE) was used to evaluate the accuracy of the prediction. Metals 2022, 12, x FOR PEER REVIEW 8 of 16 Figure 8. Neural network architecture for predicting nose temperature.
The program in this experiment was implemented using the Keras library using Python (version 3.5.2, Python Software Foundation, Wilmington, DE, USA) and TensorFlow (version 2.0, Google Inc., Mountain View, CA, USA) as backends, and the experiment was conducted in a Windows 10 64-bit environment with an Intel i7-6700K processor(Intel Corporation, Santa Clara, CA, USA) and two GeForce GTX 1080 Ti graphics cards (NVIDA Corporation, Wilmington, DE, USA). First, hyper-parameter values that represent optimal prediction accuracy were found by applying various environments while training the proposed model. Of the 1468 sets of data used in the experiment, 80% were used for training and 20% for testing. The accuracy of the TN prediction was measured from composition and temperature-related datasets of high-Mn steels with the DNN model. Root mean square error (RMSE) was used to evaluate the accuracy of the prediction.
In the proposed DNN model, RMSE and leaky ReLU were used as the cost function and the activation function, respectively. The batch size of the most accurate DNN model was 64, and Adam Optimizer [25] and a learning rate of 0.0001 were used for training. An optimal model to avoid overfitting was obtained by using drop out and early stopping [26] techniques with keep probability = 0.85. While the proposed model was being trained, the input and output values were randomly shuffled every epoch. In machine learning, one epoch refers to the period in which all data values included in the training dataset enter the prediction model once, then the weight value is updated. Finally, the RMSE of the proposed DNN model on the training and test data were 7.030 °C and 7.082 °C, respectively. Prediction results were applied to the training and evaluation data generated by the proposed model ( Figure 9). The error of the predicted value compared to TN was ± 7 °C, so the reliability of the predicted values is very high. In the proposed DNN model, RMSE and leaky ReLU were used as the cost function and the activation function, respectively. The batch size of the most accurate DNN model was 64, and Adam Optimizer [25] and a learning rate of 0.0001 were used for training. An optimal model to avoid overfitting was obtained by using drop out and early stopping [26] techniques with keep probability = 0.85. While the proposed model was being trained, the input and output values were randomly shuffled every epoch. In machine learning, one epoch refers to the period in which all data values included in the training dataset enter the prediction model once, then the weight value is updated. Finally, the RMSE of the proposed DNN model on the training and test data were 7.030 • C and 7.082 • C, respectively. Prediction results were applied to the training and evaluation data generated by the proposed model ( Figure 9). The error of the predicted value compared to T N was ±7 • C, so the reliability of the predicted values is very high. The predicted TN values in the proposed model were compared with the RA data of three high-Mn steels, as obtained in a hot ductility test (Figure 10). The values in the proposed model were almost identical to the TN obtained from the software calculation, and this value corresponds to the temperature at which the RA value decreases. This result indicates that the proposed model gives reasonable predictions of the RA degradation temperature.  The predicted TN values in the proposed model were compared with the RA data of three high-Mn steels, as obtained in a hot ductility test (Figure 10). The values in the proposed model were almost identical to the TN obtained from the software calculation, and this value corresponds to the temperature at which the RA value decreases. This result indicates that the proposed model gives reasonable predictions of the RA degradation temperature.

Case Study for Prediction Model
To test the validity of the prediction model, data from 21 high-Mn steels that contained at least one of Nb, Ti, V, and Mo were collected from the literature [14,[27][28][29][30][31][32][33][34][35], and applied to the prediction model. The TN in the TTP diagram calculated from J-matpro software were compared with the result in the prediction model, and the values matched well ( Figure 11). To compare the RA behavior with the results from the prediction model, five high-Mn steels representing the composition of each precipitating element contained were selected from reference data [14,[27][28][29][30][31][32]. Few references present data that show RA behavior in experiments on high-Mn steel, so data were not available for all compositions. The composition of the five selected high-Mn steels were low Nb, high Nb, V, Nb-Ti, and Nb-V containing steels (Table 2).

Case Study for Prediction Model
To test the validity of the prediction model, data from 21 high-Mn steels that contained at least one of Nb, Ti, V, and Mo were collected from the literature [14,[27][28][29][30][31][32][33][34][35], and applied to the prediction model. The T N in the TTP diagram calculated from J-matpro software were compared with the result in the prediction model, and the values matched well ( Figure 11). To compare the RA behavior with the results from the prediction model, five high-Mn steels representing the composition of each precipitating element contained were selected from reference data [14,[27][28][29][30][31][32]. Few references present data that show RA behavior in experiments on high-Mn steel, so data were not available for all compositions. The composition of the five selected high-Mn steels were low Nb, high Nb, V, Nb-Ti, and Nb-V containing steels ( Table 2).
The temperature at which RA decreases and the value predicted by the DNN model matched well for all steels (Figure 12). The high-Mn steel that includes both Nb and V ( Figure 12e) has a TTP diagram that is divided into two sections, in contrast to other steels, which all had one nose. The predicted value in the DNN model corresponds to the T N with a sharper bend, but RA deteriorated in both sections.   Figure 11. Comparison of nose temperatures with reference compositions.
The temperature at which RA decreases and the value predicted by the DNN model matched well for all steels (Figure 12). The high-Mn steel that includes both Nb and V (Figure 12e) has a TTP diagram that is divided into two sections, in contrast to other steels, which all had one nose. The predicted value in the DNN model corresponds to the TN with a sharper bend, but RA deteriorated in both sections.

TTP Nose Temperature Prediction Model Using Linear Regression
Before the DNN model was applied, the relationship between TN and RA for 1500 high-Mn steel compositions was expressed as a linear equation by using simple multiple regression. The composition ranges (wt.%) used in the calculation of the TTP diagram were: 0. (1) However, this regression equation had low reliability of R 2 = 0.58, and it cannot obtain an accurate TN for comparison with observed RA behavior. Therefore, a TN prediction model that uses a nonlinear predictive analysis method is required; for this purpose, a DNN model was developed.

Relationship between TTP Nose and RA in General Carbon Steel
Results confirmed that in high-Mn steels, the TN and the RA-lowering temperature coincide, so this study investigated whether this relationship can be applied to carbon steels that had various compositions. The RA data for about 87 carbon steel compositions

Relationship between TTP Nose and RA in General Carbon Steel
Results confirmed that in high-Mn steels, the T N and the RA-lowering temperature coincide, so this study investigated whether this relationship can be applied to carbon steels that had various compositions. The RA data for about 87 carbon steel compositions were collected from literature data [2,5,[23][24][25][26], and a TTP diagram drawn from Jmatpro software was calculated from the collected composition data. Then, T N information was extracted from the calculated TTP diagram and compared with the RA data. The deformation condition did not affect T N , therefore it was set to the same value as that of the high-Mn steel. To determine the correlation between the calculated TTP diagram-T N and the RA behavior, the RA behavior of five representative compositions among the collected 87 data were compared with the TTP diagram (Table 3, Figure 13) [24,35,36,41,42].  Figure 13) [24,35,36,41,42].
In contrast to high-Mn steels, which consist of a single austenite phase, carbon steel undergoes austenite-ferrite phase transformation during cooling. Therefore, the TTP curve is divided into two parts around the A3 temperature and has a discontinuous shape. In particular, the formation of proeutectoid ferrite has a greater effect than precipitation on the deterioration of hot ductility in carbon steel. The RA degradation temperature is closer to A3 than to the TTP nose ( Figure 13).

Others
RA prediction is necessary to minimize cracks in the slab by avoiding the low-ductility temperature in the bending and unbending step during continuous casting. Previous RA prediction studies were performed on steels with RA behavior of U/V type [11,12] and N/W type [13]. However, in this study, a method to predict the RA of high-Mn steels with excellent high strength, high toughness, and formability was proposed. Studies to evaluate high-temperature properties were insufficient to guide actual production of high-Mn steels. Additional data collection and related studies must be conducted to generalize the RA prediction model developed here. In contrast to high-Mn steels, which consist of a single austenite phase, carbon steel undergoes austenite-ferrite phase transformation during cooling. Therefore, the TTP curve is divided into two parts around the A 3 temperature and has a discontinuous shape. In particular, the formation of proeutectoid ferrite has a greater effect than precipitation on the deterioration of hot ductility in carbon steel. The RA degradation temperature is closer to A 3 than to the TTP nose ( Figure 13).

Others
RA prediction is necessary to minimize cracks in the slab by avoiding the low-ductility temperature in the bending and unbending step during continuous casting. Previous RA prediction studies were performed on steels with RA behavior of U/V type [11,12] and N/W type [13]. However, in this study, a method to predict the RA of high-Mn steels with excellent high strength, high toughness, and formability was proposed. Studies to evaluate high-temperature properties were insufficient to guide actual production of high-Mn steels. Additional data collection and related studies must be conducted to generalize the RA prediction model developed here.
Even with the same composition in the collected RA data, the RA behavior and precipitation behavior are different depending on the experimental conditions such as solution T T and cooling rate. For example, the cooling rate affects the size of precipitates, and this size has a great influence on RA. However, these factors are not included in the current prediction model, which was derived from the precipitation behavior during isothermal holding, i.e., in the equilibrium state, so the model may not be applicable to a case that considers all experimental variables. Therefore, the model might or can be modified to include continuous cooling precipitation (CCT) in the non-equilibrium state.
The TTP diagram data used in this study are calculation-based, and it is necessary to investigate the accuracy of the TTP data through experiments. The current study applied the equilibrium state calculation, verification of the reliability is required by comparing the experimental result with the calculated data reflecting the conditions in the non-equilibrium state.
Four precipitation elements (Nb, Ti, V, Mo) were considered in the current model. However, in practice, the precipitate composition that affects RA in high-Mn steel is much more varied than the conditions considered here. In particular, the current model mainly considered the effect on carbide, with the nitrogen composition fixed, but nitrides such as AlN and TiN also affect the hot ductility of high-Mn steel. Therefore, changes in nitrogen composition should also be considered in future studies.
Finally, the current model can only extract the temperature at a point where the RA decreases. However, to be useful for the actual continuous-casting process, the model must use a range of temperatures to avoid during unbending, so data to predict the RA degradation range must be collected.

Conclusions
In this study, a DNN was used to develop a model that can predict the RA deterioration temperature by exploiting the relationship between the RA behavior and the T N at which precipitation rate is highest. The model is intended for use as a substitute for complex hot-ductility experiments.
The relationship between RA behavior and T N could be confirmed by comparing the hot ductility test for high-Mn steel that includes the precipitating elements V and Mo to the TTP diagram calculation results from J-matpro software (version 12). This relationship was used to propose a model that can predict the T N for various compositions of high-Mn steel using a DNN by extracting the T N for 1500 compositions of high-Mn steel in which the precipitation elements were expanded to include V, Mo, Nb, and Ti. The proposed DNN model had RMSE = 7.030 • C on the training data and 7.082 • C on the test data; i.e., error of the predicted value relative to the magnitude of T N (~850 • C) is ±7 • C, which indicates that the reliability of the prediction is very high. To verify the validity of the predictive model, measured RA of five high-Mn steels that represented each precipitationelement composition was compared with the RA degradation temperature obtained from the proposed prediction model. For all five steel grades, the temperature at which the RA deteriorates was consistent with the values predicted by the model.
The DNN model proposed in this study is currently applicable only to high-Mn steels, and the RA behavior should be predicted separately using other models for steel types with phase transformation such as carbon steel. Moreover, the model was developed from data obtained in the equilibrium state, so it must be extended to consider the non-equilibrium state. In addition, the model should be modified to consider additional precipitating elements that affect RA behavior.
To verify the accuracy of the TTP data obtained from calculation, investigation through experiments on high Mn steel is being designed, and related contents will be introduced in the next study.

Data Availability Statement:
The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.

Conflicts of Interest:
The authors declare no conflict of interest.