**6. Numerical simulation for thixotropic plastic forming of composites**

To investigate thixoforming process with numerical simulation method, which is a nonlinear system, some assumptions are taken as follow: (1) The semi-solid material is assumed as a continuous and incompressible one. (2) The solid grains in semi-solid metal are uniformly distributed in liquid phase, and because of the large deformation in forming, the semi-solid material is considered as an isotropy uniform medium. According to the above assumptions, the material deformation in thixoforming is supposed as a rigid viscoplastic one.

The material adopted in this paper was SiCp/AZ61 composite, and the simulations were performed in thixo-forging and forging. The flow stress model of SiCp/AZ61 composite in thixo-forging is expressed as follow [Yan &Wang, 2011].

270 Mechanical Engineering

Fig.18 is the real stress test - a true strain curves and regression curve of the results of the comparison, Solid line is the experimental curve, dotted line is the calculation of one. The results calculated by multiple non-linear regression method are good agreement with experimental ones. So the proposed constitutive model has the higher forecast precision and

(a) 3vol.% SiCP/AZ61,570℃ (b) 6vol.% SiCP/AZ61,560℃

(c) 9vol.% SiCP/AZ61,530℃ Fig. 18. A comparison between true strain—stress curves of the test and regression curves

To investigate thixoforming process with numerical simulation method, which is a nonlinear system, some assumptions are taken as follow: (1) The semi-solid material is assumed as a continuous and incompressible one. (2) The solid grains in semi-solid metal are uniformly distributed in liquid phase, and because of the large deformation in forming, the semi-solid material is considered as an isotropy uniform medium. According to the above assumptions, the material deformation in thixoforming is supposed as a rigid

The material adopted in this paper was SiCp/AZ61 composite, and the simulations were performed in thixo-forging and forging. The flow stress model of SiCp/AZ61 composite in

thixo-forging is expressed as follow [Yan &Wang, 2011].

**6. Numerical simulation for thixotropic plastic forming of composites** 

practical significance.

viscoplastic one.

$$
\sigma = \exp(-8.27366 + 50.158f\_p - 296.55f\_p^{\
u} + 14253.359 \, / \, T)
$$

$$
\text{or } 0.053 \cdot \frac{1}{\varepsilon} \ge 0.242 \cdot \left(1 - \beta f\_L\right) 2.316 \cdot \left[1 + \left(2.1 \times 10^4 \, \varepsilon\right) 0.242 \, f\_p\right] \text{-0.505}\tag{12}
$$

where σ is the stress; ε the strain; z . the strain rate; T temperature; β constant(β=1.5); *pf* is Volume fraction of SiC particle; *Lf* is liquid volume fraction

For establishing material modal of SiCp/AZ61 composite in forging, true stress-strain curves at various temperature and strain rates were performed by mean of isothermal compression experiments.

In this study, the workpiece is formed by the close-forge method. The experiment set-up was shown in Fig.19. Fig.20 shows the workpiece, whose structure and flow character are complicated. Comparisons between forging and thixo-forging of the workpiece will be done and predicted in advance using numerical simulation. This is an effective method to instruct application of semi-solid forming technology into its practice production.

The same simulated parameters are used to analyze the differences of mechanics properties and flow rule between forging and thixo-forging processes. The materials are normal and semi-solid SiCp/AZ61 composite respectively. Environment temperature is 20℃, warm-up temperature of the die is 320℃. The friction model is constant shearing stress model, whose coefficient is 0.25. Billet size is ø50×18.5mm, which is meshed to 50000 tetrahedron elements. Stroke of up-die is 14mm.

Fig. 19. Experiment set-up

Fig. 20. SiCp/AZ61 composite workpiece

Study on Thixotropic Plastic Forming of Magnesium Matrix Composites 273

Fig. 24. shows the effective stress distributions at different volume fraction of SiC particle in thixo-forging process. The effective stress was increased with the increasing of volume

(a) Vol.3% SiCP/AZ61, 560℃ (b) Vol.6% SiCP/AZ61, 560℃ Fig. 24. Effective stress distributions at different volume fraction of SiC particle in thixo-

Fig. 25 shows temperature distributions at different volume fraction of SiC particle in thixoforging process. When the volume fraction of SiC particle was 3%, the fluctuation period of temperature was 558~561℃, whose changed value was small. When the volume fraction of SiC particle was 6%, the fluctuation period of temperature was 558~572℃, whose changed value was more greater than that of the former. It could be gained that the temperature

(a) Vol.3% SiCP/AZ61, 560℃ (b) Vol.6% SiCP/AZ61, 560℃

Fig.26 shows the traditional forging and thixo-forging workpieces of SiCp/AZ61 composite. The thixo-forging has better fill effect and surface finish quality of workpiece than the traditional forging, which could achieve near-end deforming with high quality of workpiece in the former. Those coincide with the simulation results, which indicate that semi-solid

Fig. 25. Temperature distributions at different volume fraction of SiC particle in thixo-

distribution in the latter was worse than that in the former.

fraction of SiC particle.

forging process

forging process

Fig.21 and Fig.22 give the filling stages simulated results in forging and thixo-forging processes respectively. Compared with the two kind of forming processes, it can be concluded that both had the basically identical deformation processes. In the initial stage, the hexagon hole in central section of workpiece was extruded and the rest moved in the rigid motion shown in Fig.21a, Fig.22a. As the stroke increased, metal deformation entered into the second stage, in which metal flowed from central to around in the extrusion pressure, and the cetral protruded and bottom platforms were formed (Seen Fig.21b, Fig.22b). In the last stage, the metal could be filled up claw easily in thixo-forging process, and could not be filled up claw in forging process (Seen Fig.21c, Fig.22c). Therefore, forging was more difficult in filling cavity than thixo-forging.

Fig. 21. Filling stages simulated results in thixo-forging process

Fig. 22. Filling stages simulated results in forging process

Fig. 23. shows the effective stress distributions at different temperatures in thixo-forging process. The effective stress distribution was more uniform and its value was smaller with the increasing of forming temperature, which was contributed from the excellent fluidity of semi-solid composite.

Fig. 23. Effective stress distributions at different temperatures in thixo-forging process

Fig.21 and Fig.22 give the filling stages simulated results in forging and thixo-forging processes respectively. Compared with the two kind of forming processes, it can be concluded that both had the basically identical deformation processes. In the initial stage, the hexagon hole in central section of workpiece was extruded and the rest moved in the rigid motion shown in Fig.21a, Fig.22a. As the stroke increased, metal deformation entered into the second stage, in which metal flowed from central to around in the extrusion pressure, and the cetral protruded and bottom platforms were formed (Seen Fig.21b, Fig.22b). In the last stage, the metal could be filled up claw easily in thixo-forging process, and could not be filled up claw in forging process (Seen Fig.21c, Fig.22c). Therefore, forging

Fig. 23. shows the effective stress distributions at different temperatures in thixo-forging process. The effective stress distribution was more uniform and its value was smaller with the increasing of forming temperature, which was contributed from the excellent fluidity of

(a) 530℃ (b) 560℃

Fig. 23. Effective stress distributions at different temperatures in thixo-forging process

was more difficult in filling cavity than thixo-forging.

Fig. 21. Filling stages simulated results in thixo-forging process

Fig. 22. Filling stages simulated results in forging process

semi-solid composite.

Fig. 24. shows the effective stress distributions at different volume fraction of SiC particle in thixo-forging process. The effective stress was increased with the increasing of volume fraction of SiC particle.

Fig. 24. Effective stress distributions at different volume fraction of SiC particle in thixoforging process

Fig. 25 shows temperature distributions at different volume fraction of SiC particle in thixoforging process. When the volume fraction of SiC particle was 3%, the fluctuation period of temperature was 558~561℃, whose changed value was small. When the volume fraction of SiC particle was 6%, the fluctuation period of temperature was 558~572℃, whose changed value was more greater than that of the former. It could be gained that the temperature distribution in the latter was worse than that in the former.

Fig. 25. Temperature distributions at different volume fraction of SiC particle in thixoforging process

Fig.26 shows the traditional forging and thixo-forging workpieces of SiCp/AZ61 composite. The thixo-forging has better fill effect and surface finish quality of workpiece than the traditional forging, which could achieve near-end deforming with high quality of workpiece in the former. Those coincide with the simulation results, which indicate that semi-solid

Study on Thixotropic Plastic Forming of Magnesium Matrix Composites 275

deformation process was proposed. The constitutive equation of SiCp/AZ61 composites was obtained with the multiple nonlinear regression method based on data of thixotropic compression test. The calculated results were good agreement with the experimental ones. It

Numerical simulation can provide a help for the analysis of thixoforging process, and behavior of metal flow has been obtained. The effective stress distribution was more uniform and its value was more smaller with the increasing of forming temperature. The effective stress was increased with the increasing of volume fraction of SiC particle. The temperature distrubition was worse with the increasing of volume fraction of SiC particle. The differences between traditional forging and thixo-forging processes were analyzed. Results indicated that thixo-forging was better in filling cavity than forging. So the complicated workpiece can be done once in thixo-forging. Numerical simulation results are

This research was supported jointly by grant # 50465003, # 50765005 and # 51165032 from the National Natural Science Foundation of China, Innovative Group of Science and Technology of College of Jiangxi Province and the Jiangxi Province Education Commission

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**8. Acknowledgement** 

Foundation.

**9. References** 

SiCp/AZ61 composite has good flow property, and can be used to form complicated workpiece.

(a) Traditional forging workpiece (b) Thixo-forging workpiece

Fig. 26. Traditional forging and thixo-forging workpieces of composite
