# Deformation Behavior and Constitutive Model of 34CrNi3Mo during Thermo-Mechanical Deformation Process

^{*}

## Abstract

**:**

^{−1}–20 s

^{−1}. The results show that the flow stress of 34CrNi3Mo steel under high temperatures is greatly influenced by the deformation temperature and strain rate, and it is the result of the interaction between strain hardening, dynamic recovery, and recrystallization. Under the same deformation rate, as the deformation temperature increases, the softening effect of dynamic recrystallization and dynamic recovery gradually increases, and the flow stress gradually decreases. Under the same deformation temperature, with the increase of strain rate, the influence of strain hardening on 34CrNi3Mo steel is gradually in power, and the flow stress gradually increases. To predict the flow stress of 34CrNi3Mo steel accurately, a modified Arrhenius-type constitutive model considering the effects of strain, temperature, and strain rate at the same time was made based on the experiment data. On this basis, the evolution law of deformation activation and instability characteristics of 34CrNi3Mo steel were investigated, and the processing map of 34CrNi3Mo steel was established. The formability of 34CrNi3Mo steel under high temperature deformation was revealed, which provided a theoretical foundation of the equation of reasonable hot working process.

## 1. Introduction

## 2. Experiment

#### 2.1. Experiment Method

^{−1}, 1 s

^{−1}, 10 s

^{−1}, 20 s

^{−1}). In the experiment process, the amount of total strain of the compressed sample was set as 0.65, and the isothermal compression tests were carried out on 34CrNi3Mo cylindrical specimens with the help of Gleebel-3500 thermal simulation test machine, as shown in Figure 2.

_{0}= 1473 K, then cooled to the deformation temperature and kept there before deformation for 180 s to make the sample temperature uniform.

#### 2.2. Results and Analysis

## 3. Constitutive Model

#### 3.1. Arrhenius-Type Constitutive Model

^{−1}). Then, substituted into Equation (1), the relationship between flow stress σ and strain rate $\dot{\epsilon}$ can be approximately shown as,

_{1}is the material parameter.

_{1}.

_{1}and the material constant β. Therefore, under certain strain conditions, the test results under the same deformation temperature and different strain rates were linearly fitted according to Equation (5) and Equation (6), respectively, then the stress index n

_{1}and material constant β under different stress levels can be obtained.

_{1}, β, and stress level parameter α can be obtained under different conditions, as shown in Table 1.

_{1}in the research process of this paper, the value n

_{1}= 10.231 can be obtained through calculation. In a similar way, taking the average of the four lines as the value of β, thus β = 0.0662. According to the relationship between the material parameters n

_{1}and β, β = α·n

_{1}, the stress level parameter α=0.0064MPa

^{−1}can be obtained.

^{16}.

#### 3.2. Modified Arrhenius-Type Constitutive Model

^{2}of the fitted surface is 0.951. This proves the accuracy of fitting formula.

^{2}= 0.951.

^{−1}), the value of $K\left(\epsilon ,\dot{\epsilon}\right)$ decreases with the increase of deformation (ε > 0.1). However, when the strain rate is large ($\dot{\epsilon}$ ≥ 10 s

^{−1}), the value of $K\left(\epsilon ,\dot{\epsilon}\right)$ increases gradually with the increase of deformation (ε > 0.1). The functional expression of the function of $K\left(\epsilon ,\dot{\epsilon}\right)$ can be obtained through 3D surface fitting, as shown in Figure 13b. The fitting function is shown in Equation (18), and the correlation coefficient R

^{2}of the fitting results is 0.937.

^{2}= 0.999.

## 4. Thermal Deformation Behavior

#### 4.1. Evolution of Activation Energy

^{−1}to −607 kJ·mol

^{−1}under different deformation conditions and decreases with the increase of deformation temperature and strain rate. This indicates that the dislocation motion of 34CrNi3Mo steel is promoted by temperature under the high temperature. At the same time, the softening effect of temperature is obviously enhanced with the increase of deformation temperature. This will cause the dislocation density and the activation energy to decrease. Under the condition of high strain rate, the high deformation rate increases the shear stress and is favorable to the dislocation movement, thus reducing the dislocation density.

#### 4.2. Processing Map

_{max}.

_{max}. The energy dissipation factor is used to represent the ratio of microstructure conversion dissipation energy to ideal linear dissipation energy. According to the definition of the energy dissipation factor η and the Murty criterion [26], the power dissipation coefficient can be obtained as follows,

^{−1}.

## 5. Conclusions

^{−1}.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**True stress-strain curves of 34CrNi3Mo steel, (

**a**) T = 1073 K, (

**b**) T = 1223 K, (

**c**) T = 1323 K, (

**d**) T = 1373K.

**Figure 6.**The relation curve of $\mathrm{ln}\dot{\epsilon}-\mathrm{ln}\left[\mathrm{sin}\mathrm{h}\left(\alpha \sigma \right)\right]$.

**Figure 7.**The relation curve of $\mathrm{ln}\left[\mathrm{sin}\mathrm{h}\left(\alpha \sigma \right)\right]-\mathrm{ln}\left(1/T\right)$.

**Figure 8.**The relation curve of $\mathrm{ln}Z-\mathrm{ln}\left[\mathrm{sin}\mathrm{h}\left(\alpha \sigma \right)\right].$.

**Figure 9.**The fitting relationship curve between strain and material parameters: (

**a**) α-ε; (

**b**) n-ε; (

**c**) Q-ε; (

**d**) A-ε.

**Figure 10.**The predicted results of flow stress, (

**a**) T = 1073 K; (

**b**) T = 1223 K; (

**c**) T = 1323 K; (

**d**) T = 1373 K.

**Figure 11.**The value of α(ε,T) under different deformation conditions: (

**a**) the experimental results, (

**b**) the fitting results.

**Figure 12.**The value of n(ε,T) under different deformation conditions: (

**a**) the experimental results, (

**b**) the fitting results.

**Figure 13.**The value of K(ε, $\dot{\epsilon}$) under different deformation conditions: (

**a**) the calculation results, (

**b**) the fitting results.

**Figure 14.**The value of b(ε,T) under different deformation conditions: (

**a**) the calculation results, (

**b**) the fitting results.

**Figure 16.**The predicted results of the modified Arrhenius-type model: (

**a**) T = 1073 K, (

**b**) T = 1223 K, (

**c**) T = 1323 K, (

**d**) T = 1373 K.

**Figure 17.**The relative error curves of the prediction results: (

**a**) the Arrhenius-type model, (

**b**) the modified Arrhenius-type model.

**Figure 18.**The evolution of activation energy: (

**a**) ε = 0.15, (

**b**) ε = 0.3, (

**c**) ε = 0.45, (

**d**) ε = 0.6.

**Figure 19.**The processing map under the different strain conditions: (

**a**) ε = 0.15, (

**b**) ε = 0.3, (

**c**) ε = 0.45, (

**d**) ε = 0.6.

Temp./K | 1073 | 1223 | 1323 | 1373 | Average |
---|---|---|---|---|---|

n_{1} | 15.873 | 10.425 | 7.7972 | 6.8264 | 10.231 |

β | 0.0605 | 0.0654 | 0.0676 | 0.0713 | 0.0662 |

α | 0.0038 | 0.0062 | 0.0087 | 0.0104 | 0.0064 |

Temp./K | 1073 | 1223 | 1323 | 1373 | Average |
---|---|---|---|---|---|

n | 8.51745 | 7.75401 | 6.5601 | 6.0217 | 7.2133 |

Strain Rate/s^{−1} | 0.1 | 1 | 10 | 20 | Average |
---|---|---|---|---|---|

Q | 443.084 | 398.4061 | 357.6501 | 376.2161 | 397.4488 |

Strain | Q/MPa | n/MPa | LnA | α |
---|---|---|---|---|

0.05 | 399.1256 | 7.38668 | 38.27542 | 0.00969 |

0.1 | 400.6295 | 7.40179 | 38.36398 | 0.008 |

0.15 | 402.4933 | 7.46533 | 38.45559 | 0.00724 |

0.2 | 402.38308 | 7.42159 | 38.43599 | 0.00684 |

0.25 | 402.62062 | 7.36242 | 38.53199 | 0.00659 |

0.3 | 397.44876 | 7.2133 | 38.09718 | 0.00647 |

0.35 | 391.81027 | 7.05774 | 37.64784 | 0.00638 |

0.4 | 386.26765 | 6.93568 | 37.16344 | 0.00634 |

0.45 | 381.4456 | 6.82569 | 36.74357 | 0.00634 |

0.5 | 378.517 | 6.78605 | 36.51825 | 0.00632 |

0.55 | 375.50975 | 6.72715 | 36.24138 | 0.00633 |

0.6 | 376.62529 | 6.77065 | 36.36216 | 0.00633 |

B_{0} | B_{1} | B_{2} | B_{3} | B_{4} | B_{5} | B_{6} |

0.01209 | −0.07008 | 0.40198 | −1.32864 | 2.54498 | −2.59908 | 1.08967 |

C_{0} | C_{1} | C_{2} | C_{3} | C_{4} | C_{5} | C_{6} |

7.64236 | −10.40617 | 139.43461 | −761.53963 | 1911.63147 | −2288.30462 | 1068.61673 |

D_{0} | D_{1} | D_{2} | D_{3} | D_{4} | D_{5} | D_{6} |

442.8039 | −1133.84 | 11,184.9 | −50,811.3 | 115,013 | −128,989 | 57,596.7 |

E_{0} | E_{1} | E_{2} | E_{3} | E_{4} | E_{5} | E_{6} |

1.10 × 10^{17} | −2.03 × 10^{18} | 2.21 × 10^{19} | −1.06 × 10^{20} | 2.43 × 10^{20} | −2.67 × 10^{20} | 1.14 × 10^{20} |

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**MDPI and ACS Style**

Jia, X.-D.; Zhou, Y.; Wang, Y.-N. Deformation Behavior and Constitutive Model of 34CrNi3Mo during Thermo-Mechanical Deformation Process. *Materials* **2022**, *15*, 5220.
https://doi.org/10.3390/ma15155220

**AMA Style**

Jia X-D, Zhou Y, Wang Y-N. Deformation Behavior and Constitutive Model of 34CrNi3Mo during Thermo-Mechanical Deformation Process. *Materials*. 2022; 15(15):5220.
https://doi.org/10.3390/ma15155220

**Chicago/Turabian Style**

Jia, Xiang-Dong, Ying Zhou, and Yi-Ning Wang. 2022. "Deformation Behavior and Constitutive Model of 34CrNi3Mo during Thermo-Mechanical Deformation Process" *Materials* 15, no. 15: 5220.
https://doi.org/10.3390/ma15155220