# Modeling and Simulation of the Static Recrystallization of 5754 Aluminium Alloy by Cellular Automaton

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{−1}to 1 s

^{−1}at constant temperature and delay time.

## 1. Introduction

## 2. Experimental Procedure and Materials

^{−1}) were used. The compression process in the first pass ended when the compression deformation reached 35%. Then, compression continued at 35% until the compression process was finished. The delay times during interrupted compression varied between 5 s, 30 s, and 60 s. The samples were quenched immediately after the tests. The entire test process is shown in Figure 2.

## 3. Results and Discussion

#### 3.1. Static Softening Behavior of 5754 Aluminium Alloy

^{−1}. The stress-strain curves are characterized by the hopping type B bands at the delay time of 5 s and 60 s. The sawteeth oscillates between the upper and lower envelope curves of the stress, and the drop amplitude and density are not large. The feature of the hopping type B bands typically occurs at intermediate strain rates and temperatures. The most recognized microscopic mechanism of the PLC effect is dynamic strain aging, which is the dynamic interaction of solute atoms with movable dislocations. More details about the PLC effect of the aluminium alloy can be found in reference [28,29].

#### 3.2. SRX Kinetic Model of 5754 Aluminium Alloy

^{−1}), and $T$ is the absolute deformation temperature ($\mathrm{K}$).

#### 3.3. The Simulation of Static Recrystallization of 5754 Aluminium Alloy

#### 3.3.1. Deformation-Stored Energy

#### 3.3.2. Nucleation Model for Static Recrystallization

#### 3.3.3. Grain Growth Model

#### 3.4. The Construction of CA Model

## 4. Simulation Results of the CA Model

#### 4.1. The Initial Microstructure

#### 4.2. Deformation Temperature Effect

^{–1}, the strain of 0.35 and a delay time of 5 s are given in Figure 8. White areas are the initial grains, while dark areas represent the SRX grains as shown in Figure 8c,d. Obviously, the SRX nucleation first appeared on grain boundaries because of the high energy in this location. It can be concluded from Figure 8c,d that temperature provides the necessary energy for nucleation and grain growth, and the recrystallized volume fraction and the mean size of recrystallized grains are increased as the temperature increases. The recrystallized volume fraction is 17.87% at 350 °C and 21.89% at 450 °C, and the mean size of SRX grains also increases from 12.70 to 16.20 $\mathsf{\mu}\mathrm{m}$ as shown in Figure 8e. When the deformation temperature is high, the activity of dislocation increases, which provides a sufficient driving force to initiate SRX. In addition, a high deformation temperature enhances the thermal activation of atoms in the alloy for the progress of nucleation, which can effectively promote the development of SRX and greatly increase the recrystallized volume fraction. Meanwhile, high temperatures alter the state of the inside microstructure of the alloy by promoting the solubility of trace elements in the matrix, thereby reducing the inhibition caused by precipitation during the SRX, and increasing grain boundary mobility at the same time. Therefore, the growth of recrystallized grains will increase, and the grains will become larger.

#### 4.3. Strain Rate Effect

^{−1}and 86.06% at 1 s

^{−1}. However, the average grain size is slightly reduced with increasing strain rate and is 62.50 $\mathsf{\mu}\mathrm{m}$ at 0.1 s

^{−1}and 45.45 $\mathsf{\mu}\mathrm{m}$ at 1 s

^{−1}. During the hot deformation test, the dislocation density increases rapidly with an increasing strain rate, and a great quantity of deformation energy for recrystallization nucleation and grain growth is generated, which increases the recrystallized volume fraction. However, too much nucleation inhibits the growth of grains, and as a result, the average grain size decreases slightly. Therefore, improving the strain rate is propitious for increasing the volume fraction and size of recrystallized grains.

#### 4.4. Delay Time Effect

^{−1}are shown in Figure 10. Obviously, the recrystallized volume fraction and the recrystallized grain size increase with the increasing delay time, but the rate of increase gradually decreases. The recrystallized volume fraction is 21.89% at 5 s and 80.07% at 60 s, while the mean size of recrystallized grains also increases from 16.20 to 62.50 $\mathsf{\mu}\mathrm{m}$. Longer delay times provide sufficient time for the growth of recrystallization of grains. However, the process of grain growth is often accompanied by a reduction in energy. As the driving force of grain growth, the dislocation difference is gradually reduced to zero during the SRX, resulting in a gradual decrease in the rate of increase.

#### 4.5. Validation of the CA Model

^{−1}are shown in Table 4. The recrystallized volume fraction and average grain size of the test material and CA model at different deformation temperatures, strain rates and delay times are shown in Figure 11 and Figure 12. It can be concluded from these figures that the predicted average grain size and recrystallized volume fraction agree well with the test data.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Flow curves resulting from different deformation parameters: (

**a**) 350 °C, 0.1 s

^{−1}; (

**b**) 350 °C, 1.0 s

^{−1}; (

**c**) 450 °C, 0.1 s

^{−1}; (

**d**) 450 °C, 1.0 s

^{−1}.

**Figure 4.**The contrast of the static softening fraction at different strain rates and deformation temperatures.

**Figure 5.**The relationship between $\mathrm{ln}\left(-\mathrm{ln}\left(1-{X}_{s}\right)\right)$ and $\mathrm{ln}t$.

**Figure 8.**The experimental (

**a**,

**b**) and CA (

**c**,

**d**) results for microstructures formed at deformation temperatures of 350 °C (

**a**,

**c**) and 450 °C (

**b**,

**d**); (

**e**) the variation of the recrystallized volume fraction and the mean grain size at temperatures of 350 °C and 450 °C.

**Figure 9.**The experimental (

**a**,

**b**) and CA (

**c**,

**d**) results for microstructures formed at a strain rate of 0.1 s

^{−1}(

**a**,

**c**) and 1.0 s

^{−1}(

**b**,

**d**); (

**e**) the variation of the recrystallized volume fraction and the mean grain size at strain rates of 0.1 and 1 s

^{−1}.

**Figure 12.**Comparison of the average grain size obtained from the tests and cellular automaton (CA) results at a temperature of 450 °C and strain rates of 0.1 and 1 s

^{−1}.

Chemical Elements | Mg | Mn | Si | Fe | Cr | Zn | Ti | Cu | Al |
---|---|---|---|---|---|---|---|---|---|

Content (wt. %) | 3.1 | 0.50 | 0.40 | 0.40 | 0.30 | 0.20 | 0.15 | 0.10 | Balance |

Parameter | $\mathit{b}$$\left(\mathit{m}\right)$ | $\mathit{\mu}$$(\mathit{G}\mathit{P}\mathit{a})$ | $\delta {\mathit{D}}_{0}$$({\mathit{m}}^{3}\xb7{\mathit{s}}^{-1})$ | ${\mathit{K}}_{\mathit{B}}$$(\mathit{J}\xb7{\mathit{K}}^{-1})$ | $\mathit{\nu}$ | $\mathit{\alpha}$ |
---|---|---|---|---|---|---|

Value | 2.6 × 10^{−10} | 26 | 8 × 10^{−14} | 1.38 × 10^{−23} | 0.33 | 0.5 |

**Table 3.**The physical parameters for 5754 aluminium alloy obtained by regression and used in this paper.

Parameter | $\mathit{Z}$ | ${\mathit{Q}}_{\mathit{a}}$$(\mathit{J}\cdot \mathit{m}\mathit{o}{\mathit{l}}^{-1})$ | ${\mathit{Q}}_{\mathit{b}}$$(\mathit{J}\cdot \mathit{m}\mathit{o}{\mathit{l}}^{-1})$ |
---|---|---|---|

Value | 1.56966 × 10^{6} | 73,220.3 | 108,000 |

**Table 4.**Comparison of the average grain size obtained from the tests and cellular automaton (CA) results.

Temperature/°C | Strain Rate/s^{−1} | CA Model/$\mathsf{\mu}\mathbf{m}$ | Experiment/$\mathsf{\mu}\mathbf{m}$ |
---|---|---|---|

450 °C | 0.1 | 62.50 | 64.17 |

1.0 | 45.45 | 47.91 |

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**MDPI and ACS Style**

Huang, C.; Jia, X.; Zhang, Z. Modeling and Simulation of the Static Recrystallization of 5754 Aluminium Alloy by Cellular Automaton. *Metals* **2018**, *8*, 585.
https://doi.org/10.3390/met8080585

**AMA Style**

Huang C, Jia X, Zhang Z. Modeling and Simulation of the Static Recrystallization of 5754 Aluminium Alloy by Cellular Automaton. *Metals*. 2018; 8(8):585.
https://doi.org/10.3390/met8080585

**Chicago/Turabian Style**

Huang, Changqing, Xiaodong Jia, and Zhiwu Zhang. 2018. "Modeling and Simulation of the Static Recrystallization of 5754 Aluminium Alloy by Cellular Automaton" *Metals* 8, no. 8: 585.
https://doi.org/10.3390/met8080585