# 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

- Huang, C.Q.; Deng, J.; Wang, S.X.; Liu, L.L. An Investigation on the Softening Mechanism of 5754 Aluminum Alloy during Multistage Hot Deformation. Metals
**2017**, 7, 107. [Google Scholar] [CrossRef] - Sang, D.; Li, Y. The Hot Deformation Activation Energy of 7050 Aluminum Alloy under Three Different Deformation Modes. Metals
**2016**, 6, 49. [Google Scholar] [CrossRef] - Huang, C.-Q.; Liu, L.-L. Application of the Constitutive Model in Finite Element Simulation: Predicting the Flow Behavior for 5754 Aluminum Alloy during Hot Working. Metals
**2017**, 7, 331. [Google Scholar] - Brand, A.J.; Kalz, S.; Kopp, R. Microstructural simulation in hot rolling of aluminium alloys. Comput. Mater. Sci.
**1996**, 7, 242–246. [Google Scholar] [CrossRef] - Yanagida, A.; Yanagimoto, J. Formularization of softening fractions and related kinetics for static recrystallization using inverse analysis of double compression test. Mater. Sci. Eng. A
**2008**, 487, 510–517. [Google Scholar] [CrossRef] - Llanos, L.; Pereda, B.; Lopez, B.; Rodriguez-Ibabe, J.M. Hot deformation and static softening behavior of vanadium microalloyed high manganese austenitic steels. Mater. Sci. Eng. A
**2016**, 651, 358–369. [Google Scholar] [CrossRef] - Jiang, F.; Zhang, H.; Li, L.; Chen, J. The kinetics of dynamic and static softening during multistage hot deformation of 7150 aluminum alloy. Mater. Sci. Eng. A
**2012**, 552, 269–275. [Google Scholar] [CrossRef] - Pouraliakbar, H.; Pakbaz, M.; Firooz, S.; Jandaghi, M.R.; Khalaj, G. Study on the dynamic and static softening phenomena in Al-6Mg alloy during two-stage deformation through interrupted hot compression test. Measurement
**2016**, 77, 50–53. [Google Scholar] [CrossRef] - Mukhopadhyay, P.; Loeck, M.; Gottstein, G. A cellular operator model for the simulation of static recrystallization. Acta Mater.
**2007**, 55, 551–564. [Google Scholar] [CrossRef] - Beygelzimer, Y.E.; Spuskanyuk, A.V. The thick yield surface: Idea and approach for investigating its structure. Philos. Mag. A
**1999**, 79, 2437–2459. [Google Scholar] [CrossRef] - Raabe, D. Cellular automata in materials science with particular reference to recrystallization simulation. Annu. Rev. Mater. Res.
**2002**, 32, 53–76. [Google Scholar] [CrossRef] - Lin, Y.C.; Liu, Y.X.; Chen, M.S.; Huang, M.H.; Ma, X.; Long, Z.L. Study of static recrystallization behavior in hot deformed Ni-based superalloy using cellular automaton model. Mater. Des.
**2016**, 99, 107–114. [Google Scholar] [CrossRef] - Zheng, C.; Xiao, N.; Li, D.; Li, Y. Microstructure prediction of the austenite recrystallization during multi-pass steel strip hot rolling: A cellular automaton modeling. Comput. Mater. Sci.
**2009**, 44, 507–514. [Google Scholar] [CrossRef] - Kugler, G.; Turk, R. Study of the influence of initial microstructure topology on the kinetics of static recrystallization using a cellular automata model. Comput. Mater. Sci.
**2006**, 37, 284–291. [Google Scholar] [CrossRef] - Salehi, M.S.; Serajzadeh, S. Simulation of static recrystallization in non-isothermal annealing using a coupled cellular automata and finite element model. Comput. Mater. Sci.
**2012**, 53, 145–152. [Google Scholar] [CrossRef] - Zhang, Y.; Jiang, S.; Hu, L.; Zhao, Y.; Sun, D. Investigation on primary static recrystallization in NiTiFe shape memory alloy subjected to cold canning compression by coupling crystal plasticity finite element method with cellular automaton. Model. Simul. Mater. Sci. Eng.
**2017**, 25. [Google Scholar] [CrossRef] - Sitko, M.; Pietrzyk, M.; Madej, L. Time and length scale issues in numerical modelling of dynamic recrystallization based on the multi space cellular automata method. J. Comput. Sci.
**2016**, 16, 98–113. [Google Scholar] [CrossRef] - Chen, M.S.; Yuan, W.Q.; Li, H.B.; Zou, Z.H. Modeling and simulation of dynamic recrystallization behaviors of magnesium alloy AZ31B using cellular automaton method. Comput. Mater. Sci.
**2017**, 136, 163–172. [Google Scholar] [CrossRef] - Wang, L.; Fang, G.; Qian, L. Modeling of Dynamic Recrystallization of Magnesium Alloy using Cellular Automata Considering Initial Topology of Grains. Mater. Sci. Eng. A
**2017**, 711, 268–283. [Google Scholar] [CrossRef] - Azarbarmas, M.; Aghaie-Khafri, M. A New Cellular Automaton Method Coupled with a Rate-dependent (CARD) Model for Predicting Dynamic Recrystallization Behavior. Metall. Mater. Trans. A
**2018**, 49, 1916–1930. [Google Scholar] [CrossRef] - Li, X.; Li, X.; Zhou, H.; Zhou, X.; Li, F.; Liu, Q. Simulation of dynamic recrystallization in AZ80 magnesium alloy using cellular automaton. Comput. Mater. Sci.
**2017**, 140, 95–104. [Google Scholar] [CrossRef] - Chen, M.S.; Yuan, W.Q.; Lin, Y.C.; Li, H.B.; Zou, Z.H. Modeling and simulation of dynamic recrystallization behavior for 42CrMo steel by an extended cellular automaton method. Vacuum
**2017**, 146, 142–151. [Google Scholar] [CrossRef] - Zheng, B.; Ertorer, O.; Li, Y.; Zhou, Y.; Mathaudhu, S.N.; Tsao, C.Y.A.; Lavernia, E.J. High strength, nano-structured Mg-Al-Zn alloy. Mater. Sci. Eng. A
**2011**, 528, 2180–2191. [Google Scholar] [CrossRef] - Filatov, Y.A.; Yelagin, V.I.; Zakharov, V.V. New Al-Mg-Sc alloys. Mater. Sci. Eng. A
**2000**, 280, 97–101. [Google Scholar] [CrossRef] - Matsuda, K.; Ikeno, S.; Terayama, K.; Matsui, H.; Sato, T.; Uetani, Y. Comparison of precipitates between excess Si-type and balanced-type Al-Mg-Si alloys during continuous heating. Metall. Mater. Trans. A
**2005**, 36, 2007–2012. [Google Scholar] [CrossRef] - Lohmar, J.; Bambach, M.; Hirt, G. Comparison of Semi-empirical and Dislocation Density based Material Equations for Fast Modeling of Multistage Hot Working of Steel. Procedia Eng.
**2014**, 81, 268–273. [Google Scholar] [CrossRef] - Jiang, F.; Zhang, H.; Su, J.; Sun, Y. Constitutive characteristics and microstructure evolution of 7150 aluminum alloy during isothermal and non-isothermal multistage hot compression. Mater. Sci. Eng. A
**2015**, 636, 459–469. [Google Scholar] [CrossRef] - Zhemchuzhnikova, D.А.; Lebyodkin, M.A.; Lebedkina, T.A.; Kaibyshev, R.O. Unusual behavior of the Portevin-Le Chatelier effect in an AlMg alloy containing precipitates. Mater. Sci. Eng. A
**2015**, 639, 37–41. [Google Scholar] [CrossRef] - Ma, P.C.; Zhang, D.; Zhuang, L.Z.; Zhang, J.S. Effect of alloying elements and processing parameters on the Portevin-Le Chatelier effect of Al-Mg alloys. Int. J. Miner. Metall. Mater.
**2015**, 22, 175–183. [Google Scholar] [CrossRef] - Fernández, A.I.; López, B.; RodríGuez-Ibabe, J.M. Relationship between the austenite recrystallized fraction and the softening measured from the interrupted torsion test technique. Scr. Mater.
**1999**, 40, 543–549. [Google Scholar] [CrossRef] - Sheppard, T.; Duan, X. Modelling of static recrystallisation by combining FEM with empirical models. J. Mater. Process. Technol.
**2002**, 130, 250–253. [Google Scholar] [CrossRef] - Toloui, M.; Serajzadeh, S. Modelling recrystallization kinetics during hot rolling of AA5083. J. Mater. Process. Technol.
**2007**, 184, 345–353. [Google Scholar] [CrossRef] - Ivasishin, O.M.; Shevchenko, S.V.; Vasiliev, N.L.; Semiatin, S.L. A 3-D Monte-Carlo (Potts) model for recrystallization and grain growth in polycrystalline materials. Mater. Sci. Eng. A
**2006**, 433, 216–232. [Google Scholar] [CrossRef] - Hallberg, H.K. Approaches to Modeling of Recrystallization. Metals
**2011**, 1, 16–48. [Google Scholar] [CrossRef] [Green Version] - Lee, H.W.; Im, Y.T. Numerical modeling of dynamic recrystallization during nonisothermal hot compression by cellular automata and finite element analysis. Int. J. Mech. Sci.
**2010**, 52, 1277–1289. [Google Scholar] - Humphreys, F.J.; Hatherly, M. Recrystallization and Related Annealing Phenomena, 2nd ed.; Elsevier: New York, NY, USA, 2004; pp. 219–224. [Google Scholar]
- Kremeyer, K. Cellular Automata Investigations of Binary Solidification. J. Comput. Phys.
**1998**, 142, 243–262. [Google Scholar] [CrossRef] - Ulam, S. Sets, Numbers, and Universes: Selected Works; MIT Press: Cambridge, MA, USA, 1974. [Google Scholar]

**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 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**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