# A Hybrid Method for Calculating the Chemical Composition of Steel with the Required Hardness after Cooling from the Austenitizing Temperature

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^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Hardness Model

#### 2.1. Dataset for the Model

_{A}), and cooling rate (CR). Additionally, four categorical independent variables describing the presence of ferrite, pearlite, bainite, and martensite in the steel structure were considered. The values of these variables were determined from the cooling curves presented in the CCT diagrams. The dependent variable of the model was the hardness of the steel obtained after cooling at a specified rate.

#### 2.2. Methods and Results

_{c3}+ 50 °C. The value of the end temperature of the A

_{c3}transformation during heating was calculated based on the chemical composition using a neural network. The neural network model for calculating the A

_{c3}temperature is presented in [51].

_{A}and CR.

## 3. Calculating the Chemical Composition of Steel

#### 3.1. ANN–GA Hybrid Model

- i = 1, 2,..., k;
- k = 1, 2,..., 5;
- w
_{HVi}—weighting coefficient for the hardness at the i-th cooling rate; - HVci, HVri—the calculated or required hardness for the i-th cooling rate;
- HV
_{min}, HVmax, the minimum and maximum hardness determined based on empirical data analysis; - x—vector of independent variables.

#### 3.2. Examples of Applications of the ANN–GA Model

## 4. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Variables | Minimum | Maximum | Mean | Std. Dev |
---|---|---|---|---|

C (wt%) | 0.10 | 0.68 | 0.32 | 0.14 |

Mn (wt%) | 0.25 | 1.80 | 0.79 | 0.33 |

Si (wt%) | 0.13 | 1.60 | 0.33 | 0.28 |

Cr (wt%) | 0 | 2.30 | 0.72 | 0.56 |

Ni (wt%) | 0 | 3.60 | 0.74 | 1.00 |

Mo (wt%) | 0 | 1.00 | 0.16 | 0.20 |

V (wt%) | 0 | 0.38 | 0.02 | 0.06 |

Cu (wt%) | 0 | 0.30 | 0.04 | 0.08 |

T_{A} (°C) | 770 | 1050 | 878 | 57 |

Mn + Cr | Mn + Cr + Ni | Cr + Ni | Mn + Ni | |
---|---|---|---|---|

Maximum (wt%) | 3.6 | 5.6 | 5.3 | 4.5 |

Dataset | Mean Absolute Error, HV | Standard Deviation of the Error, HV | Ratio of Standard Deviations | Pearson Correlation Coefficient |
---|---|---|---|---|

Training | 30.9 | 44.3 | 0.27 | 0.96 |

Validating | 33.6 | 46.4 | 0.28 | 0.96 |

Testing | 33.7 | 50.1 | 0.30 | 0.95 |

Verifying | 32.7 | 39.0 | 0.29 | 0.95 |

Transformation | ||||
---|---|---|---|---|

Ferritic | Pearlitic | Bainitic | Martensitic | |

ANN structure | MLP 10-8-1 | MLP 10-8-1 | MLP 10-10-1 | MLP 10-6-1 |

Training/No of epoch | BP/50, CG/330 | BP/50, CG/119 | BP/50, CG/188 | CG100 |

Metric | Dataset | Transformation | |||
---|---|---|---|---|---|

Ferritic | Pearlitic | Bainitic | Martensitic | ||

Accuracy | Training | 0.92 | 0.92 | 0.86 | 0.89 |

Validating | 0.91 | 0.92 | 0.86 | 0.86 | |

Testing | 0.89 | 0.91 | 0.84 | 0.86 | |

AUC | Training | 0.97 | 0.97 | 0.93 | 0.95 |

Validating | 0.96 | 0.97 | 0.92 | 0.94 | |

Testing | 0.96 | 0.97 | 0.91 | 0.93 |

**Table 6.**The required and calculated hardness of the steel after cooling at selected rates (Example 1).

Cooling Rate, °/s | Sum of the Errors, HV | |||||
---|---|---|---|---|---|---|

30 | 23 | 13 | 3 | 1 | ||

41Cr4 | 563 | 534 | 412 | 310 | 233 | - |

Target | 560 | 530 | 415 | 300 | 230 | - |

Solution | 550 | 530 | 451 | 291 | 232 | 57 |

Variables | 41Cr4 | Solution |
---|---|---|

C (wt%) | 0.40 | 0.42 |

Mn (wt%) | 0.60 | 0.58 |

Si (wt%) | 0.33 | 0.33 |

Cr (wt%) | 0.93 | 0.94 |

Ni (wt%) | 0.05 | 0.01 |

Mo (wt%) | 0.00 | 0.04 |

V (wt%) | 0.00 | 0.04 |

Cu (wt%) | 0.09 | 0.04 |

T_{A} (°C) | 850 | 841 |

**Table 8.**The required and calculated hardness of the steel after cooling at selected rates (Example 2).

Cooling Rate, °/s | Sum of the Errors, HV | |||||
---|---|---|---|---|---|---|

50 | 40 | 13 | 7 | 1 | ||

37Cr4 | 558 | 550 | 408 | 335 | 216 | - |

Target | 560 | 550 | 410 | 330 | 220 | - |

Solution 1 | 556 | 542 | 429 | 331 | 222 | 34 |

Solution 2 | 557 | 543 | 428 | 332 | 226 | 36 |

Solution 3 | 560 | 546 | 431 | 335 | 230 | 40 |

Solution 4 | 554 | 540 | 426 | 333 | 232 | 47 |

Solution 5 | 560 | 546 | 436 | 341 | 243 | 64 |

Variables | 37Cr4 | Solution 1 | Solution 2 | Solution 3 | Solution 4 | Solution 5 |
---|---|---|---|---|---|---|

C (wt%) | 0.38 | 0.40 | 0.40 | 0.40 | 0.40 | 0.40 |

Mn (wt%) | 0.74 | 0.50 | 0.69 | 0.87 | 0.93 | 1.30 |

Si (wt%) | 0.26 | 0.29 | 0.25 | 0.25 | 0.25 | 0.25 |

Cr (wt%) | 0.90 | 0.94 | 0.87 | 0.72 | 0.61 | 0.39 |

Ni (wt%) | 0.26 | 0.26 | 0.29 | 0.28 | 0.29 | 0.26 |

Mo (wt%) | 0.04 | 0.03 | 0.01 | 0.00 | 0.01 | 0.03 |

V (wt%) | 0.00 | 0.05 | 0.03 | 0.05 | 0.04 | 0.05 |

Cu (wt%) | 0.07 | 0.04 | 0.05 | 0.05 | 0.05 | 0.04 |

T_{A} (°C) | 880 | 843 | 835 | 832 | 831 | 832 |

**Table 10.**The required and calculated hardness of the steel after cooling at selected rates (Example 3).

Cooling Rate, °/s | Sum of the Errors, HV | |||||
---|---|---|---|---|---|---|

50 | 12 | 4 | 1.3 | 0.5 | ||

25CrMo4 | 498 | 392 | 294 | 266 | 200 | - |

Target | 500 | 390 | 290 | 260 | 200 | - |

Solution 1 | 500 | 391 | 290 | 266 | 198 | 9 |

Solution 2 | 496 | 399 | 289 | 269 | 194 | 29 |

Solution 3 | 499 | 390 | 292 | 248 | 209 | 24 |

Solution 4 | 495 | 395 | 293 | 248 | 206 | 31 |

Solution 5 | 490 | 390 | 291 | 273 | 192 | 32 |

Variables | 25CrMo4 | Solution 1 | Solution 2 | Solution 3 | Solution 4 | Solution 5 |
---|---|---|---|---|---|---|

C (wt%) | 0.22 | 0.25 | 0.25 | 0.32 | 0.30 | 0.21 |

Mn (wt%) | 0.64 | 1.20 | 1.00 | 0.59 | 0.50 | 1.41 |

Si (wt%) | 0.25 | 0.35 | 0.45 | 0.31 | 0.37 | 0.31 |

Cr (wt%) | 0.97 | 0.32 | 0.63 | 0.74 | 0.87 | 0.65 |

Ni (wt%) | 0.33 | 0.30 | 0.48 | 0.78 | 1.01 | 0.20 |

Mo (wt%) | 0.23 | 0.11 | 0.02 | 0.10 | 0.05 | 0.00 |

V (wt%) | 0.01 | 0.35 | 0.28 | 0.02 | 0.00 | 0.35 |

Cu (wt%) | 0.16 | 0.16 | 0.07 | 0.05 | 0.04 | 0.15 |

T_{A} (°C) | 875 | 910 | 900 | 846 | 849 | 903 |

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**MDPI and ACS Style**

Trzaska, J.; Sitek, W.
A Hybrid Method for Calculating the Chemical Composition of Steel with the Required Hardness after Cooling from the Austenitizing Temperature. *Materials* **2024**, *17*, 97.
https://doi.org/10.3390/ma17010097

**AMA Style**

Trzaska J, Sitek W.
A Hybrid Method for Calculating the Chemical Composition of Steel with the Required Hardness after Cooling from the Austenitizing Temperature. *Materials*. 2024; 17(1):97.
https://doi.org/10.3390/ma17010097

**Chicago/Turabian Style**

Trzaska, Jacek, and Wojciech Sitek.
2024. "A Hybrid Method for Calculating the Chemical Composition of Steel with the Required Hardness after Cooling from the Austenitizing Temperature" *Materials* 17, no. 1: 97.
https://doi.org/10.3390/ma17010097