# Hot Deformation Behavior and Dynamic Recrystallization of Ultra High Strength Steel

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## Abstract

**:**

^{−1}and a temperature of 800 to 1150 °C was conducted. Based on the experimental data, the material parameters were determined, the constitutive model considering the influence of work hardening, the recrystallization softening on the dislocation density, and the recrystallized grain size model were established. After introducing the model into the finite element software DEFORM-3D, the thermal compression experiment was simulated, and the results were consistent with the experimental results. The rule for obtaining forging stock with a uniform and refinement microstructure was acquired by comparing the simulation and the experimental results, which are helpful to formulate an appropriate forging process.

## 1. Introduction

^{−1}strain rate were obtained by single pass hot compression experiment. A constitutive equation considering work hardening and dynamic recrystallization softening during deformation was established. The dynamic recrystallization grain size model based on the fully crystalized microstructure was established. The research results provide theoretical guidance for the controlling of the microstructure during the high temperature deformation of the martensitic steel.

## 2. Experimental Procedure

^{−5}Mpa, as shown in the Figure 2, the specimens were heated to 1200 °C at a rate of 10 °C/s and were held at that temperature for 5 min. The temperature of the specimens was then reduced to the predetermined deformation temperature at a speed of 5 °C/s and was held for 3 min. Finally, the specimens were compressed until the engineering strain was 65% in the Figure 3. After the test, the specimens were immediately quenched with water.

_{3}(2%) + H

_{2}O (92%) was used to corrode the sample in a constant temperature water bath at 60 °C for 2 min. After that, it was quickly rinsed with water and cleaned with alcohol, then dried with a blower. The grain size of the middle of the sample was then observed and recorded.

## 3. Results and Discussions

#### 3.1. Discussion on Hot Deformation Behavior

_{0}is the height of the original specimen (mm); and R

_{0}is the height of the original specimen (mm). The true stress–strain curve can be revised by the above formula. The modified flow–stress curve is obtained in Figure 4.

#### 3.2. Establishment of Constitutive Model of Hot Deformation

^{−1}); R is the molar gas constant 8.314 (J/ (mol. k); Q is the hot deformation activation energy (J/mol); and T is the deformation temperature (K). In the case of high flow stress ($\alpha \sigma >1.2$), it can be expressed by Equation (6). When the flow stress is low ($\alpha \sigma <0.8$), it can be expressed by Equation (7). ${A}_{1}$, ${A}_{2},{n}^{\prime},$ and $\beta $ are material constants:

_{p})] with respect to 1/T and the partial derivative of $ln\dot{\epsilon}$ with respect to ln[sinh(σ

_{p})] were obtained when keeping strain rate and temperature unchanged, respectively. The average slope of $ln\dot{\epsilon}$−ln[sinh(σ

_{p})] was 8.786, and the average slope of ln[sinh(σ

_{p})]−1/T graph was 9050.6, which are also shown in Figure 6. As such, the deformation energy considering the effect of the temperature and strain rate is 661,118 J/mol.

_{p})] can be found in the Figure 7. The slope of the obtained straight line is 8.45, and this gives the stress index n of the material. The intercept lnA is 62.018 and gives a structure factor of A = 8.59 × 10

^{26}.

#### 3.3. Constitutive Equation of Hardening Part Considering Dynamic Recrystallization

^{−1}could be smoothed by the red curve. The strain–hardening rate curve corresponding to each rheological curve and can be obtained by Equation (13). Figure 9b shows a graph of the hardening rate decreasing sharply to zero with strain, from which the curve is concave. The difference between the saturated stress with the peak stress is only 0.5 Mpa.

_{0}is the initial dislocation density at which the strain is zero.

_{drv}$=\frac{U}{\Omega},\mathrm{and}$by combining Equations (15) and (16), we can determine Equation (17) for strain hardening by considering dynamic recovery during hot deformation.

#### 3.4. Constitutive Equation of Softening Part Considering Dynamic Recrystallization

_{ss}is steady state flow stress (MPa); X

_{s}is an apparent softening fraction.

_{ss}, which can be obtained through a hyperbolic sine equation. A part of the data is used to fit the hyperbolic sine equation because of the low-temperature stress–strain curve and the high-strain rate are in the unsteady state. The stress parameter α

_{s}is 0.0083, and the deformation activation energy Q

_{s}is 474,924 J/mol and can be obtained through the previous method. As shown in Figure 14, the relationship diagram of InZ-ln[sinh(ασ

_{ss})] is established. Through linear fitting, the structure factor of steady-state stress A

_{s}is 5.34 × 10

^{17}, and the stress index n

_{s}is 4.88.

#### 3.5. Grain Size Model of Dynamic Recrystallization

_{drex}represents the ordinate.

#### 3.6. Simulation and Experimental Results

## 4. Conclusions

- Amend the flow-stress curve through the friction correction formula to reflect the actual deformation process accurately.
- According to the constitutive equation below, the average relative error of the predicted flow stress and the experiment is 7.46%, which can be used for the finite element analysis of thermal deformation process.$${\sigma}^{H}={\sigma}_{p}\left[1-\mathit{exp}\left(-\Omega \epsilon \right)\right]\hspace{1em}\epsilon {\epsilon}_{p}$$$$\sigma ={\sigma}^{H}-{x}_{s}\left({\sigma}_{p}-{\sigma}_{ss}\right)\epsilon \ge {\epsilon}_{p}$$
- The following dynamic recrystallization grain size model can predict the change of recrystallization grain size during hot deformation well.$${D}_{drex}=1.159*{10}^{3}{\dot{\epsilon}}^{-0.124}exp\left(\frac{-54118.129}{RT}\right)$$
- After the above model is implemented, software can be used to simulate the thermal deformation process of the material. The simulation results are in good agreement with the experimental results.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**(

**a**) Schematic diagram of the sample before and after thermal compression; (

**b**) physical picture of the sample after compression.

**Figure 4.**The true stress–strain curves of the experiment modified under different deformation temperatures. (

**a**) 0.01 s

^{−1}; (

**b**) 0.1 s

^{−1}; (

**c**) 1 s

^{−1}.

**Figure 5.**The relationship between peak stress ${\sigma}_{p}$ and strain rate $\dot{\epsilon}$ (

**a**) and the relation curve of $ln\dot{\epsilon}$−$In{\sigma}_{p}$; (

**b**) the relation curve of $ln\dot{\epsilon}$−${\sigma}_{p}$.

**Figure 6.**The relationship between peak stress ${\sigma}_{p}$ strain rate$\dot{\epsilon}$and T; (

**a**) the relation curve of $ln\dot{\epsilon}$-ln[sinh(σ

_{p})]; (

**b**) the relation curve of ln[sinh(σ

_{p})]−1/T.

**Figure 8.**Schematic description of the change in the work-hardening rate with stress. Reproduced from [20], with permission from Elsevier, 2021.

**Figure 9.**(

**a**) The peak part of the flow curve at 1100 °C-0.1 s

^{−1}; (

**b**) the variation curve of the work-hardening rate with stress.

**Figure 10.**Schematic description of the flow behavior of the high-strength steel. Reproduced from [20], with permission from Elsevier, 2021.

**Figure 12.**Softening fraction curve and its fitting curve under different deformation conditions: (

**a**) 1000 °C-0.1 s

^{−1}; (

**b**) 1000 °C-1 s

^{−1}; (

**c**) 1150 °C-0.1 s

^{−1}.

**Figure 15.**Comparison chart of actual values and predicted values under different deformation conditions: (

**a**) 0.01 s

^{−1}; (

**b**) 0.1 s

^{−1}; (

**c**) 1 s

^{−1}.

**Figure 17.**(

**a**) The relation curve of $In\dot{\epsilon}$-lnD

_{drex}; (

**b**) the relation curve of 1/T-lnD

_{drex}(with error bars).

**Figure 19.**Distribution of volume fraction of DRX at$\dot{\epsilon}$ = 0.1 s

^{−1}under different deformation temperatures: (

**a**) 900 °C, (

**b**) 1000 °C, (

**c**) 1100 °C, (

**d**) 1150 °C.

**Figure 20.**Microstructure of the alloy under the deformation strain rate of 0.1 s

^{−1}at various temperatures: (

**a**) 900 °C, (

**b**) 1000 °C, (

**c**) 1100 °C, (

**d**) 1150 °C.

**Figure 21.**Histogram of the simulated recrystallization volume fraction and the average grain size after compression deformation and microstructures under the deformation temperature of 1100 °C with strain rates of (

**a**) 0.1 s

^{−1}, (

**b**) 1 s

^{−1}.

**Figure 22.**Histogram of the simulated recrystallization volume fraction and the average grain size after compression deformation and microstructures under the deformation temperature of 900 °C with strain rates of (

**a**) 0.1 s

^{−1}, (

**b**) 1 s

^{−1}.

Strain Rates s^{−1} | Deformation Temperature | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

800 °C | 900 °C | 1000 °C | 1100 °C | 1150 °C | ||||||

${\mathit{\sigma}}_{\mathit{p}}$ | ${\mathit{\epsilon}}_{\mathit{p}}$ | ${\mathit{\sigma}}_{\mathit{p}}$ | ${\mathit{\epsilon}}_{\mathit{p}}$ | ${\mathit{\sigma}}_{\mathit{p}}$ | ${\mathit{\epsilon}}_{\mathit{p}}$ | ${\mathit{\sigma}}_{\mathit{p}}$ | ${\mathit{\epsilon}}_{\mathit{p}}$ | ${\mathit{\sigma}}_{\mathit{p}}$ | ${\mathit{\epsilon}}_{\mathit{p}}$ | |

0.01 | 312.6 | 0.356 | 174.7 | 0.315 | 97.9 | 0.274 | 52.1 | 0.262 | 47.9 | 0.200 |

0.1 | 340.8 | 0.367 | 218.6 | 0.334 | 130.2 | 0.308 | 83.9 | 0.271 | 68.1 | 0.250 |

1 | 354.2 | 0.368 | 252.6 | 0.355 | 180.7 | 0.311 | 129.1 | 0.274 | 101.8 | 0.253 |

Strain Rates s^{−1} | Deformation Temperature | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

800 °C | 900 °C | 1000 °C | 1100 °C | 1150 °C | ||||||

k | n | k | n | k | n | k | n | k | n | |

0.01 | - | - | 2.39 | 2.29 | 1.58 | 1.03 | 0.96 | 0.81 | 1.48 | 1.18 |

0.1 | - | - | 0.73 | 1.82 | 1.45 | 1.12 | 0.74 | 2.17 | 2.21 | 2.39 |

1 | - | - | 0.71 | 1.45 | 3.15 | 2.22 | 1.77 | 1.81 | 1.23 | 1.51 |

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**MDPI and ACS Style**

Zhong, L.; Wang, B.; Hu, C.; Zhang, J.; Yao, Y.
Hot Deformation Behavior and Dynamic Recrystallization of Ultra High Strength Steel. *Metals* **2021**, *11*, 1239.
https://doi.org/10.3390/met11081239

**AMA Style**

Zhong L, Wang B, Hu C, Zhang J, Yao Y.
Hot Deformation Behavior and Dynamic Recrystallization of Ultra High Strength Steel. *Metals*. 2021; 11(8):1239.
https://doi.org/10.3390/met11081239

**Chicago/Turabian Style**

Zhong, Liping, Bo Wang, Chundong Hu, Jieyu Zhang, and Yu Yao.
2021. "Hot Deformation Behavior and Dynamic Recrystallization of Ultra High Strength Steel" *Metals* 11, no. 8: 1239.
https://doi.org/10.3390/met11081239