Prediction of Creep Rupture Life of 5Cr-0.5Mo Steel Using Machine Learning Models

Abstract

The creep rupture life of 5Cr-0.5Mo steels used in high-temperature applications is significantly influenced by factors such as minor alloying elements, hardness, austenite grain size, non-metallic inclusions, service temperature, and applied stress. The relationship of these variables with the creep rupture life is quite complex. In this study, the creep rupture life of 5Cr-0.5Mo steel was predicted using various machine learning (ML) models. To achieve higher accuracy, various ML techniques, including random forest (RF), gradient boosting (GB), linear regression (LR), artificial neural network (ANN), AdaBoost (AB), and extreme gradient boosting (XGB), were applied with careful optimization of hidden parameters. Among these, the ANN-based model demonstrated superior performance, yielding high accuracy with minimal prediction errors for the test dataset (RMSE = 0.069, MAE = 0.053, MAPE = 0.014, and R² = 1). Additionally, we developed a user-friendly graphical user interface (GUI) for the ANN model, enabling users to predict and optimize creep rupture life. This tool helps materials scientists and industrialists prevent failures in high-temperature applications and design steel compositions with enhanced creep resistance.

1. Introduction

The ever-growing global population continues to drive an increasing demand for energy to support technological advancements and industrial operations. This has led to a critical need for high-performance industrial components capable of extending machinery life and minimizing operational shutdowns. To achieve maximum operational efficiency, it is essential to assess the lifespan of components in industrial equipment, particularly those operating under high-temperature conditions. Power plants and petrochemical industries widely use Cr-Mo steels due to their excellent high-temperature performance [1]. Among these, 5Cr-0.5Mo steel is one of the most important alloys in the Cr-Mo steel family, extensively utilized in manufacturing high-temperature components for power generation devices [2]. The composition of the steel, particularly the addition of minor alloying elements, significantly affects its properties and performance [3,4]. Additionally, initial cooling conditions—such as cooling temperature and cooling rates—play a vital role in determining the resulting austenite grain size and hardness, which are critical factors influencing the steel’s mechanical behavior and service life [5]. Furthermore, the surrounding environment, in particular, applied stress during service is another decisive factor affecting the remaining life of components [6,7]. However, the interplay of these variables is complex and non-linear, making it challenging to establish a clear understanding through conventional experimental approaches. During prolonged exposure to elevated temperatures and sustained stress, materials undergo specific changes that can significantly affect their properties [8], particularly the remaining service life. The application of stress can result in localized stress concentrations [9], the development of dislocation networks [10], and phase transformations [11,12]. Additionally, exposure to high temperatures can alter phase fractions [11], promote the formation of secondary precipitates/carbides [13,14], and ultimately lead to a reduction in creep resistance [15]. While numerous experimental studies have investigated the effects of these factors on the microstructure and performance of Cr-Mo steels [11,16,17,18,19,20], a comprehensive analysis over broader intervals is lacking. Conducting such detailed experiments would require significant energy, resources, and time. Consequently, there is a pressing need for predictive modeling approaches that leverage existing data to forecast material behavior effectively. Some indirect methods have also been employed to estimate the creep rupture life, such as by analyzing the growth of oxide scales [21].

Researchers have utilized various machine learning (ML) models to predict various properties of metallic materials [22,23,24,25,26,27]. For example, Zhang et al. [28] predicted the creep rupture life of 316L stainless steel using linear regression (LR), random forest (RF), and artificial neural network (ANN) models. Similarly, Tan et al. [29] applied multiple models to predict the creep rupture life of 9Cr martensitic steels and compared their prediction accuracies. Xiang et al. [30] employed a deep-learning model to predict the creep rupture life of Fe-Cr-Ni alloys. The creep rupture life of low alloy steel was predicted by Wang et al. [31] by combining the ML model with genetic algorithms.

Although various ML methods have been applied to predict the properties of different materials, to the best of our knowledge, no significant research has been published on predicting the creep rupture life of 5Cr-0.5Mo steel using ML techniques, particularly artificial neural networks (ANN). This study aims to predict the creep rupture life of 5Cr-0.5Mo steel using multiple ML models and compare their accuracies using evaluation metrics such as root mean square error (RMSE), mean average error (MAE), mean average percentage error (MAPE), and R-squared (R²). The most accurate model will be identified and recommended. In addition to predicting creep rupture life, the model will assess the influence of each input variable on the output. Furthermore, a user-friendly graphical user interface (GUI) will be developed to facilitate practical applications.

The proposed model is expected to provide significant benefits to the steel industry and materials engineers involved in the production of 5Cr-0.5Mo steels for high-temperature applications. Additionally, it will assist engineers working on the safety and reliability of power plant components.

2. Materials and Methods

2.1. Data Collection

The data required for the development of the model, including its training and testing phases, was obtained from the existing dataset provided by the National Institute for Materials Science (NIMS), Tsukuba, Japan. This dataset includes critical parameters such as the chemical composition, austenite grain size, non-metallic inclusion content, applied stress, service temperature, and the resulting creep rupture life of 5Cr-0.5Mo steel, as outlined in Supplementary File S1. The dataset has a yield strength range of 106–338 MPa and elongation values between 28% and 80%. A total of 237 datasets were obtained, out of which 191 were used for training the model, and the remaining 46 were used for testing the developed model. This widely accepted approach in machine learning, which allocates 80% of the dataset for training and 20% for testing, was chosen to achieve a balance between model learning and evaluation. This split ensures that the model has enough data to capture underlying patterns while preserving an independent test set for performance assessment. The statistical analysis of the data used for model training and testing is provided in

Table 1. Summary of the statistical data of 5Cr-0.5Mo steel for model training and testing.

Variable	Training Data				Testing Data
	Max	Min.	Mean	Std. Dev.	Max.	Min.	Mean	Std. Dev.
C (wt.%)	0.12	0.09	0.108	0.01	0.12	0.09	0.108	0.012
Si (wt.%)	0.37	0.27	0.331	0.012	0.37	0.27	0.33	0.035
Mn (wt.%)	0.56	0.44	0.499	0.035	0.56	0.44	0.499	0.048
P (wt.%)	0.022	0.007	0.016	0.048	0.022	0.007	0.015	0.005
S (wt.%)	0.01	0.005	0.007	0.005	0.012	0.005	0.007	0.002
Ni (wt.%)	0.083	0.043	0.060	0.003	0.083	0.043	0.060	0.015
Cr (wt.%)	5.02	4.61	4.84	0.016	5.02	4.61	4.84	0.150
Mo (wt.%)	0.52	0.49	0.503	0.151	0.52	0.49	0.504	0.010
Cu (wt.%)	0.13	0.05	0.072	0.031	0.13	0.05	0.073	0.030
Al (wt.%)	0.008	0.004	0.006	0.001	0.008	0.004	0.006	0.001
N (wt.%)	0.018	0.01	0.014	0.002	0.178	0.010	0.014	0.003
AGS (um)	6.9	4.8	5.97	0.587	6.9	4.8	5.97	0.580
Hardness (HRB)	90	75	81	5.620	90	75	81	5.588
NMI (wt.%)	0.2	0.03	0.086	0.045	0.2	0.03	0.086	0.044
Temp. (°C)	650	500	562	52.90	650	500	562	52.90
Stress (MPa)	216	29	89	50	265	29	95	58
Creep Life	5.12	1.37	3.64	0.99	5.06	1.58	3.62	1.00

.

2.2. Correlation Analysis

Pearson’s correlation coefficient was utilized to evaluate the relationship between input and output variables. The coefficient values range from −1 to +1, and these are visually represented in a heatmap, as shown in Figure 1. For better visualization, the color intensity corresponds to the magnitude of the linear relationships between the variables. A higher color intensity indicates a stronger relationship, with the strongest relationships, such as a variable’s correlation with itself, represented in red and having the maximum value of +1. Furthermore, relatively strong positive relationships, such as that of carbon (C) with phosphorus (P), aluminum (Al), nitrogen (N), austenite grain size, and hardness (HRB), are depicted in shades of red. However, the intensity is slightly lower as these coefficients are positive but less than +1, typically exceeding 0.5. From a metallurgical perspective, carbon enhances the hardness of steel by forming carbide precipitates and strengthening the ferrite matrix through solid solution strengthening. Additionally, higher carbon content facilitates martensite formation during quenching, further increasing hardness [4]. This direct positive effect on hardness (HRB) is also reflected in the heat map, with a correlation coefficient of 0.772. Conversely, the negative correlation of C (wt.%) with temperature is evident, aligning with the known phenomenon that higher temperatures adversely affect the strength imparted by carbon in steels. To aid in precise interpretation, the actual correlation coefficient values are displayed within each heatmap cell, providing a clearer understanding of the dependency between variables.

2.3. Data Preprocessing

The normalization function was employed to scale all the data within the range of 0.1 to 0.9. This approach improved the stability and performance of the model by preventing the generation of complex or extreme values. The normalization process was carried out using Equation (1).

$${\mathrm{x}}_{\mathrm{n}}=\left({\displaystyle \frac{\left(\mathrm{X}-{\mathrm{x}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\right)\times 0.8}{\left({\mathrm{x}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{x}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\right)}}\right)+0.1$$

(1)

Here, x_n represents the normalized value, x_max is the maximum value, and x_min is the minimum value.

Once the optimal model was established, the normalized data were reverted to their original scale using Equation (2).

$$\mathrm{x}=\left({\displaystyle \frac{\left({\mathrm{x}}_{\mathrm{n}}-0.1)\times ({\mathrm{x}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{x}}_{\mathrm{m}\mathrm{i}\mathrm{n}}\right)}{8}}\right)+{\mathrm{x}}_{\mathrm{m}\mathrm{i}\mathrm{n}}$$

(2)

2.4. ML Methods

We applied six different machine learning (ML) methods to predict the creep rupture life of 5Cr-0.5Mo steel, each offering distinct advantages in model performance and applicability:

(i)

Random Forest (RF)—An ensemble learning method that constructs multiple decision trees and aggregates their predictions, effectively reducing overfitting and improving accuracy [32].

(ii)

Gradient Boosting (GB)—A boosting technique that sequentially enhances weak learners by correcting previous errors, making it highly effective for structured data [33].

(iii)

Linear Regression (LR)—A fundamental statistical approach that models relationships between variables based on linear assumptions. While simple and interpretable, it is less suited for capturing complex, non-linear patterns [34].

(iv)

Artificial Neural Networks (ANN)—Composed of interconnected layers of neurons that mimic brain-like processing, enabling deep learning and high accuracy, particularly for non-linear and high-dimensional data [35].

(v)

AdaBoost (AB)—A boosting technique that iteratively adjusts weights on misclassified instances, enhancing model robustness by improving weak classifiers [36].

(vi)

Extreme Gradient Boosting (XGB)—An advanced variant of GB that incorporates regularization techniques and computational optimizations, making it one of the most powerful ML models for structured datasets [37].

These methods differ in complexity and suitability and choosing the right ML technique based on data characteristics and problem requirements is crucial for achieving optimal predictive performance and meaningful insights.

These ML methods were first trained using a training dataset and then tested using a testing dataset. A schematic representation of the workflow for predicting the creep life of 5Cr-0.5Mo steels is illustrated in Figure 2.

2.5. Performance Evaluation

To evaluate the performance of each, metrics such as RMSE, MAE, MAPE, and R² values were calculated. The calculation formulas for RMSE, adj. R², MAE, and MAPE are presented in Equations (3), (4), (5), and (6) respectively.

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{1}{\mathrm{N}}}{\sum }_{\mathrm{i}=1}^{\mathrm{N}}({\mathrm{E}}_{\mathrm{i}}-{\mathrm{E}}_{\mathrm{p}}}{)}^2$$

(3)

$$\mathrm{A}\mathrm{d}\mathrm{j}\mathrm{u}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{d} {\mathrm{R}}^2=1-{\displaystyle \frac{(1-{\mathrm{R}}^2)(\mathrm{N}-1)}{\mathrm{N}-\mathrm{p}-1}}$$

(4)

$$\mathrm{M}\mathrm{A}\mathrm{E}={\displaystyle \frac{1}{\mathrm{N}}}{\sum }_{\mathrm{i}=1}^{\mathrm{N}}\left|{\mathrm{E}}_{\mathrm{i}}-{\mathrm{E}}_{\mathrm{p}}\right|$$

(5)

$$\mathrm{M}\mathrm{A}\mathrm{P}\mathrm{E}={\displaystyle \frac{1}{\mathrm{N}}}{\sum }_{\mathrm{i}=1}^{\mathrm{N}}\left|{\displaystyle \frac{{\mathrm{E}}_{\mathrm{i}}-{\mathrm{E}}_{\mathrm{p}}}{{\mathrm{E}}_{\mathrm{i}}}}\right|$$

(6)

Here, N = number of data, E_i = actual values, E_p = predicted values, p = number of independent variables i = variable i.

The model configurations were optimized by minimizing these error metrics. Various configurations were tested. The configuration yielding the minimum error was identified as the optimal setup.

3. Results and Discussion

3.1. ML Methods and Their Predictability

We optimized hyperparameters such as the learning rate, momentum term, number of hidden layers, and neurons for different models, selecting the parameters that yielded the lowest prediction errors. The performance of each model was then evaluated using RMSE, MAE, MAPE, and R², with the results presented graphically.

Figure 3a illustrates the RMSE, MAE, and MAPE values for the training dataset, while Figure 3b presents the corresponding values for the testing dataset. Since R² can reach a maximum value of 1, it is displayed separately in Figure 3c for both the training and testing datasets across all models.

For the testing dataset, the ANN model demonstrated the highest accuracy, achieving RMSE = 0.069, MAE = 0.053, MAPE = 0.014, and R² =1. These results highlight the exceptional capability of the ANN model in predicting the creep rupture life of 5Cr-0.5Mo steel with the highest accuracy.

Given the superior performance of the ANN model, it was utilized to predict the influence of various input parameters on the creep rupture life of 5Cr-0.5Mo steel. We will now provide a detailed discussion of the results obtained from the ANN model.

3.2. Prediction of the Effect of Input Variables on Creep Rupture Life

The ANN-based GUI, developed using Java (1.4), generates a large volume of results through sensitivity analysis by systematically varying input parameters and assessing their impact on the output. However, due to the vast number of possible variations, it is impractical to represent all results comprehensively. To maintain clarity and relevance, we selectively present only two key sensitivity analyses that provide the most insightful or significant findings related to the study objectives. This ensures that the results remain interpretable and aligned with the research focus.

The dataset used for training and testing the model consisted of a limited number of entries. Despite this, the model was effectively trained to predict the creep rupture life of 5Cr-0.5Mo steel with high accuracy. For example, the dataset included only a few values for applied stress and corresponding time-to-rupture data. Specifically, for 650 °C, stress values were limited to 29, 37, 47, and 61 MPa, while for 500 °C, higher stress values such as 137, 157, 177, and 216 MPa were available. The developed model, however, was capable of making predictions for nearly 100 different stress values ranging from 29 MPa to approximately 275 MPa across all temperatures (500 °C, 550 °C, 600 °C, and 650 °C), even in the absence of experimental data for some of these combinations.

Figure 4 provides a comparison between the experimental and predicted results, illustrating the effect of stress on time-to-rupture values at these temperatures. Figure 4a demonstrates that the experimental data closely align with the predictions of the ANN model, with points lying on the same trend line. Figure 4b–d depict the relationship between stress and time-to-rupture at constant temperatures of 550 °C, 600 °C, and 650 °C, respectively. From a metallurgical perspective, at a constant temperature, the applied stress inversely affects the creep rupture life of 5Cr-0.5Mo steel. The magnitude of the applied stress significantly influences the microstructural changes occurring at that particular temperature. In some cases, stress can induce phase transformations, such as the transformation from austenite to martensite, a phenomenon known as transformation-induced plasticity (TRIP) [38]. Higher applied stress facilitates greater dislocation movement, thereby promoting early deformation and reducing the creep rupture life. Interestingly, the model effectively captured the trends in time-to-rupture as a function of stress, even without being explicitly provided with metallurgical principles underlying these variations. This capability underscores the robustness of the developed ANN model.

As the temperature increases, dislocation motion becomes easier, leading to a reduction in the material’s strength. This effect of temperature was accurately predicted by the developed ANN model, with the predictions closely aligning with the experimental values. Although the experimental dataset includes only a limited number of data points for these conditions, the ANN model successfully predicted creep life for 100 different data points within the same temperature range. The high accuracy of the model’s predictions is evident from the results shown in Figure 5, where the predicted values align closely with the expected trends. Similarly, the ANN model can provide accurate predictions for different applied stress levels to estimate the creep rupture life of 5Cr-0.5Mo steel. This enables the assessment of the remaining creep life of components made from this steel at specific temperatures and under any given applied stress condition.

Moreover, the impact of the most critical alloying elements, C and Si, on creep rupture life can also be accurately predicted using the ANN model. C forms various metal carbides, such as M₂₃C₆, which precipitate and disperse within the matrix [39]. These carbides effectively hinder dislocation motion and restrict the movement of lath boundaries [40,41], thereby enhancing the material’s resistance to deformation and ultimately increasing the creep rupture life. Additionally, coarse carbides can contribute to strengthening through Ostwald ripening, which further improves the creep rupture life of the steel [42]. Si also significantly influences the creep rupture life under fixed temperature and stress conditions. The positive effect of Si arises from its ability to lower the stacking fault energy, which promotes the formation of deformation twins [43]. These stacking faults and twins act as barriers to dislocation motion, thereby delaying the rupture of the steel and enhancing its creep resistance. A similar beneficial effect of Si on creep rupture life at 550 °C has been reported in previous studies [44]. Figure 6 illustrates the precise predictions of the model regarding the effect of C content (Figure 6a) and Si content (Figure 6b) on creep rupture life at 550 °C and under a fixed stress of 98 MPa. This predictive capability allows users to estimate the creep rupture life of steel with a known C content or to evaluate how C content influences creep life at a specific temperature or applied stress. Such insights are particularly useful for optimizing alloy compositions for desired performance under varying service conditions.

3.3. Prediction of the Combined Effect of Two Variables on Creep Rupture Life

The combined effect of two input variables, such as temperature and stress, is often complex and challenging to predict due to their intricate interdependencies. However, the developed ANN model successfully predicted this combined effect with remarkable accuracy, as demonstrated by the contour plots in Figure 7. These plots clearly illustrate the model’s capability to capture and represent the interplay between temperature and applied stress in determining the creep rupture life, further validating its predictive robustness and utility in practical applications.

The inverse relationship between stress and temperature on creep rupture life is clearly depicted in the single-variable graphs (Figure 4 and Figure 5). Additionally, the combined inverse effect of both temperature and stress is illustrated in the contour plot (Figure 7a), where the highest creep rupture life values are observed at lower stress levels (50–100 MPa) and lower temperatures (500–550 °C). This trend aligns well with the literature, as at higher values of both stress and temperature, dislocation motion becomes easier and faster, leading to earlier rupture and a subsequent decrease in creep rupture life.

Similarly, the combined effect of C and Si content on the creep rupture life is also accurately predicted. The contour plot in Figure 7b illustrates those higher levels of C and Si result in longer rupture times for 5Cr-0.5Mo steel. This prediction is consistent with the literature [45,46], as Si and C contribute to the formation of precipitates/carbides that hinder dislocation motion, thereby delaying fracture and enhancing creep strength. In addition, the combined effects of other input parameters can also be predicted. However, to maintain conciseness, the corresponding graphs are not included in the manuscript. To illustrate the combined effect of carbon and phosphorus, a contour plot is provided as a supplementary Figure S1, demonstrating that an increased phosphorus content enhances creep rupture life due to the formation of precipitates. Likewise, the interactions between all minor alloying elements can be precisely estimated for nearly 100 different scenarios, a level of detail that is not achievable through experimental methods. This underscores the reliability and effectiveness of the developed ANN model.

3.4. Quantitative Estimation of the Effect of Temperature and Stress

The quantitative effects of both temperature and stress were also evaluated using the ANN model, as presented in

Table 2. Effect of temperature on the Creep Rupture life under 29 MPa stress.

Temperature	Time to Rupture	Difference
5Cr-0.5Mo steel at 500 °C	5.576	-
5Cr-0.5Mo steel at 550 °C	5.567	−0.009
5Cr-0.5Mo steel at 600 °C	5.024	−0.543
5Cr-0.5Mo steel at 650 °C	3.709	−1.315
Experimental value 650 °C	3.849
Absolute Error in prediction	3.849 − 3.709 = 0.14
Percentage Relative Error	0.14/3.849 * 100 = 3.64%

and

Table 3. Effect of applied stress on the Creep Rupture life at 500 °C.

Stress	Time to Rupture	Difference
5Cr-0.5Mo steel under 30 MPa	5.576	-
5Cr-0.5Mo steel under 50 MPa	5.575	−0.001
5Cr-0.5Mo steel under 100 MPa	4.656	−0.919
5Cr-0.5Mo steel under 130 MPa	3.789	−0.867
5Cr-0.5Mo steel under 150 MPa	3.204	−0.585
5Cr-0.5Mo steel under 200 MPa	1.913	−1.291
5Cr-0.5Mo steel under 216 MPa	1.706	−0.207
Experimental value under 216 MPa	1.737
Absolute Error in Prediction	1.737 − 1.706 = 0.031
Percentage Relative Error	0.031/1.737 * 100 = 1.78%

. The temperature was incremented in intervals of 50 °C, ranging from 500 °C to 650 °C, and the relative percentage error for the predictions was calculated to be very low at 3.64%. Similarly, Table 3 highlights the quantitative effect of stress on the creep rupture life of 5Cr-0.5Mo steel, with stress values increased in varying intervals. The relative percentage error for stress predictions was just 1.78%, demonstrating the high accuracy and reliability of the developed ANN model. The percentage relative error was calculated by using the formula given in Equation (7).

$$\mathrm{P}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{g}\mathrm{e} \mathrm{R}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{v}\mathrm{e} \mathrm{E}\mathrm{r}\mathrm{r}\mathrm{o}\mathrm{r}={\displaystyle \frac{\mathrm{A}\mathrm{c}\mathrm{t}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}-\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{d}\mathrm{i}\mathrm{c}\mathrm{t}\mathrm{e}\mathrm{d} \mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}}{\mathrm{A}\mathrm{c}\mathrm{t}\mathrm{u}\mathrm{a}\mathrm{l} \mathrm{V}\mathrm{a}\mathrm{l}\mathrm{u}\mathrm{e}}}\times 100$$

(7)

3.5. Graphical User Interface

Figure 8 presents the graphical user interface (GUI) of the developed ANN model, designed to predict creep rupture life based on 16 input variables. The GUI enables users to input infinite parameter combinations for precise predictions and dynamically visualize output variations as inputs are modified. It allows for analyzing the impact of individual variables by varying one while keeping others constant and evaluating the combined effect of two variables to gain deeper insights. Additionally, users can optimize specific parameters to achieve target creep rupture life, assess the relative importance of each variable, and compare predictions across multiple input configurations for a comprehensive evaluation of material compositions and operating conditions.

The GUI is highly user-friendly and intuitive, requiring no prior knowledge of machine learning, which makes it ideal for industrial applications. The model predicts the creep rupture life in terms of the logarithm of time to rupture—a critical parameter for materials scientists to evaluate, optimize, and select material compositions. This capability supports material design, process optimization, and failure prevention in high-temperature applications.

3.6. Optimization of Inputs to Get Maximum Creep Rupture Life

The developed GUI can optimize input parameters for superior performance. The highest experimental creep rupture life in the dataset was 152,683 h. However, using the optimization module within the GUI, the model predicted a significantly higher creep rupture life of 410,865 h (log 5.6137, as shown in Figure 9), showcasing the potential of ANN-driven optimization in identifying material configurations beyond the experimental limits.

The optimization process systematically adjusted the 16 input parameters—material compositions (e.g., C, Si, Mn, S, Ni, etc.), operating conditions (e.g., stress and testing temperature), and material properties (e.g., Rockwell hardness, AGS)—to find the most favorable combination for extended creep rupture life. This capability highlights the ANN model’s proficiency in capturing complex nonlinear interactions among multiple variables. The ability to achieve a creep rupture life significantly higher than the experimental maximum underscores the utility of this tool for advanced material research and engineering applications.

4. Conclusions

In conclusion, this study employed six different machine learning models—Gradient Boosting (GB), Random Forest (RF), Linear Regression (LR), Extreme Gradient Boosting (XGB), AdaBoost (AB), and Artificial Neural Network (ANN)—to predict the creep rupture life of 5Cr-0.5Mo steel. Among these, the ANN model demonstrated the highest efficiency, achieving minimal prediction errors for the test dataset (RMSE = 0.069, MAE = 0.053, MAPE = 0.014, and R² = 1. The developed ANN model effectively predicted the influence of composition, including minor alloying elements such as carbon and silicon, as well as the effects of temperature and applied stress. It accurately captured both the impact of individual input variables and the combined effects of two variables, such as temperature and stress, or alloying elements like carbon and silicon. Additionally, a user-friendly graphical user interface (GUI) was developed, enabling engineers and industry professionals to optimize alloy composition based on the desired creep rupture life of 5Cr-0.5Mo steel.