1. Introduction
Metallic materials are widely used in daily life, especially a variety of steel that have a very long history of research. It is known that there are many variables that can affect the properties of steels such as strength [
1]. Strength is the ability of a material to resist plastic deformation or fracture, and the strength properties such as tensile strength and plasticity of steels are usually dependent on chemical composition. In addition, the heat treatments, such as annealing, tempering and quenching, can effectively control the microstructure, grain size and defects, which are all closely related to the tensile properties of steels. In addition, the tensile properties are also affected by the service conditions such as working temperature and irradiation environment [
2]. To discover the inherent mechanism of how these variables affect the steels, researchers could only get the preliminary influence trends through the continuous experiments via changing a part of variables for a long time. A formula obtained with the traditional linear fitting regression is generally difficult to capture the exact correlations between relative variables and corresponding properties of steels, because they often have complex nonlinear relationships [
3].
With the vigorous development of computer technology, machine learning sprang up and became a powerful method for finding the patterns in high-dimensional data [
4]. Machine learning is actually an efficient statistical analysis method to capture the linear or nonlinear internal relationships by learning from empirical data [
5]. The common machine learning methods include artificial neural network (ANN) [
6,
7], support vector machine (SVM) [
8,
9], decision tree (DT) [
10] and so on. Nowadays, machine learning prompts data science and analytics to become a significant tool to find the desired causal relations in the material research [
11], and results in developing a new field termed as “Materials Informatics” [
12,
13] in recent years. Machine learning has been rapidly used in the fields of metals [
14,
15,
16,
17,
18], as well as polymers [
19], semiconductors [
20,
21], which fully demonstrates its powerful universality.
Meanwhile, in order to meet the needs of machine learning for big data [
22], many experimental data were collected and established databases such as MatNavi [
23], MatWeb [
24] and Matmatch [
25]. MatNavi contains a large amount of data about the fatigue and creep properties of various steels, which have been already used for machine learning model establishment and research. Agrawal et al. [
26] proved the practicality of machine learning for fatigue strength research with the Fatigue Data Sheet. Sourmail et al. [
27] correctly captured the important influence trends using the established models with ANN based on the Creep Data Sheet. Besides the fatigue and creep properties, a few machine learning models have been established to obtain the correlations between the tensile properties of steels and the important variables. Guo et al. [
28] used the ANN model to well characterize the relationships between the mechanical properties of maraging steels and composition, processing and working conditions. Fragassa et al. [
29] chose the metallographic factors as the input features and designed three kinds of machine learning methods to model the mechanical properties of cast iron.
However, for austenitic stainless steel (ASS), more attention is paid on the creep, fatigue and corrosion resistance [
30,
31,
32]. Besides the corrosion resistance, the mechanical properties such as strength of ASS are also important for their application and have drawn much attention in past decades. The tensile properties of ASS have been extensively studied both experimentally and theoretically. Sivaprasad et al. [
33] developed an artificial neural network model to correlate alloy composition and test temperature to tensile properties of 15Cr-15Ni-2.2Mo-Ti modified ASS. Desu et al. [
34] used test temperature and strain rates as descriptors to predict the tensile properties of ASS 304L and 316L using the ANN model. However, there are no general machine learning models to correlate chemical composition, heat processes and service conditions to tensile properties of ASS, and clarify how each variable affects the tensile properties of ASS.
In this work, we proposed a machine learning method using ANN to predict the tensile properties of ASS with the chemical composition, solution treatment conditions (heat processes) and test temperature (service condition) as descriptors. The models established by partial data in the database have high predictive accuracy for the remaining data and some new data outside the database. We also calculated the impact degrees of each variable with the mean impact value (MIV) method and predicted the influence trends of several important variables on tensile properties. Our results conform to the previous metallurgical theories, and the established models can guide us for further research and development of new ASS with the expected tensile properties.
Author Contributions
Conceptualization, Y.W. and X.W.; investigation, Y.W., X.L. and Z.X.; writing-original draft preparation, Y.W. and X.W.; writing-review and editing, X.L., Z.X., R.L., W.L., Y.Z. and Y.X.; supervision, X.W. and C.L. All authors have read and agreed to the published version of the manuscript.
Funding
This work is supported by the National Key Research and Development Program of China (2017YFE0302400 and 2017YFA0402800) the National Natural Science Foundation of China (11735015, 51871207, 51801203, 51671184, 51671185 and U1832206) and Anhui Provincial Natural Science Foundation (1908085J17).
Conflicts of Interest
The authors declare no conflict of interest.
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Figure 1.
Structure of a three-layer feedforward neural network.
Figure 2.
Schematic diagram of Back Propagation Neural Network (BPNN) model for predicting two tensile properties of austenitic stainless steels in this study.
Figure 3.
The number of units in the hidden layers influences the prediction of models on the training set and testing set: (a) yield strength (YS), (b) ultimate tensile strength (UTS) and (c) YS/UTS ratio. The black and red dots represent correlation coefficient (R) and root mean square error (RMSE) on the training set and testing set, respectively. We use the dotted lines to mark the selection of the optimal number of hidden units in every figure.
Figure 4.
Comparison between the predicted and original values on the training set and testing set for: (a) YS, (b) UTS and (c) YS/UTS ratio. X-axis is the original value of tensile properties, Y-axis is the predicted one and the equation of black line in these figures is (The more points concentrated near the black line, the more accurate the predicted values).
Figure 5.
Comparison between the predicted and original values of the unseen data outside the database for: (a) YS and (b) UTS.
Figure 6.
The absolute values of mean impact value (MIV) of each variable on two tensile properties: (a) YS and (b) UTS. The red and blue columns represent the positive and negative correlation, respectively (The higher the MIV value, the greater the effect on the corresponding tensile properties).
Figure 7.
The predicted influence trends of (a) carbon, (b) chromium, (c) nickel, (d) titanium, (e) niobium and (f) vanadium on YS and UTS. The red and blue dots represent the predicted values of UTS and YS respectively.
Figure 8.
The predicted influence trends of (a) temperature, (b) time of solution treatment and (c) test temperature on YS and UTS. The blue and red dots represent the predicted values of YS and UTS respectively.
Table 1.
The input variables of austenitic stainless steel in this research.
Number | Variables | Number | Variables |
---|
1 | Chromium (Cr, wt%) | 11 | Carbon (C, wt%) |
2 | Nickel (Ni, wt%) | 12 | Boron (B, wt%) |
3 | Molybdenum (Mo, wt%) | 13 | Phosphorus (P, wt%) |
4 | Manganese (Mn, wt%) | 14 | Sulfur (S, wt%) |
5 | Silicon (Si, wt%) | 15 | Cobalt (Co, wt%) |
6 | Niobium (Nb, wt%) | 16 | Aluminum (Al, wt%) |
7 | Titanium (Ti, wt%) | 17 | Solution treatment temperature (Ts, K) |
8 | Vanadium (V, wt%) | 18 | Solution treatment time (ts, s) |
9 | Copper (Cu, wt%) | 19 | Water-quenched or Air-quenched |
10 | Nitrogen (N, wt%) | 20 | Test temperature (Tt, K) |
Table 2.
Statistical parameters for the training and testing set with the optimal hidden units.
Tensile Properties | Hidden Units | Training | Testing |
---|
(83% of the Data) | (17% of the Data) |
---|
MAPE | RMSE | R | MAPE | RMSE | R |
---|
(%) | (MPa) | (%) | (MPa) |
---|
YS | 8 | 4.09 | 8.40 | 0.97 | 5.21 | 11.82 | 0.93 |
UTS | 11 | 1.76 | 10.69 | 0.99 | 3.56 | 28.54 | 0.93 |
YS / UTS | 6 | 4.80 | 0.025 1 | 0.93 | 5.91 | 0.035 1 | 0.86 |
Table 3.
Statistical parameters of predicted results for the new data.
Tensile Properties | MAPE (%) | RMSE (MPa) | R |
---|
YS | 9.61 | 5.27 | 0.95 |
UTS | 4.16 | 6.06 | 0.97 |
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