Influence of the magnetic field on the distribution of SiC​p ​ in AZ91D composite

Guihong Genga,b,Shuge Yanga,c,Kunxia Weia,c,Wei Weia,c and Jing Hu a,c

aSchool of Materials Science and Engineering, Changzhou University, Changzhou 213164, P. R. China
b School of Materials Science and Engineering, Beifang University of Nantionalities, Yinchuan 750021, P. R. China
cSino-Russia Joint Laboratory of Functional Nanostructured Materials, Changzhou University, Changzhou 213164, P. R. China

Advanced Modelling and Simulation 2019, 1, 7–13. doi:10.26705/advmodsim.2018.1.1.7-13
Received 10 July 2018, Published 29 July 2019

Abstract

The model of the molten magnesium alloy with injection device was built to investigate the distribution of SiC particle in the uniform magnetic field. The device included a crucible, a magnetic field generator and a powder feeding tube. According to the L16 (4​4​ ) orthogonal array, sixteen cases were performed to study the effect of injection speed, the particle diameter, the injection angle and the magnetic field intensity on the particle distribution. The results showed that the injection speed was the first important factor affecting the particle homogenous distribution, subsequently the particle diameter, the injection angle and the magnetic field intensity in order. The optimal process parameters were the injection speed of 5m/s, the particle diameter of 120μm, the injection angle of 300 and the magnetic field strength of 0.5T, in which the uniform distribution of the particle can be well achieved.

Keywords: SiC​p/AZ91D composite, SiC particle distribution, magnetic field, numerical simulation, Orthogonal experimental

Introduction

Magnesium alloy has many excellent performances such as high modulus and good thermal conductivity, but low strength and resisting abrasion limit its industrial applications [1]. The comprehensive mechanical properties can be improved by the reinforced particles in the magnesium matrix composite [2,3], which was one of the best methods to achieve the good ability of high temperature creep resistance [4]. Many particle such as metallic particle (Ti) [5], intermetallic particle (MgZn​2​) [6] and ceramic particle (carbide (B​4C) [7-9], nitride (AlN) [10], oxide (Al​2O3​) [11,12]) was chose to reinforce the magnesium matrix.

SiC particle was excellent in wear resistance, impact resistance and high temperature mechanical properties. More attentions have been paid to SiC particle reinforced magnesium matrix composite. However, the process of SiC particle reinforced magnesium matrix composite by conventional crafts had one crucial problem with the inhomogeneous distribution of particles in the melt.

The particle trajectory and distribution can be altered by the magnetic field with different frequencies [13]. The distribution of particles cannot be directly and accurately known in the processing of magnesium matrix composites. It was found that WC​p exhibited a graded distribution along the depth direction of the metal matrix composites layer [14]. The injection velocity of particle had a mainly effect on the microstructure of coatings [15]. In the present, the FLUENT software was applied to simulate the process of the particle reinforced magnesium matrix composite in the uniform magnetic field. The process parameters for the particle uniform distribution were established.

Experimental methods

Experimental parameters

The chemical component of AZ91D was listed in Table 1. SiC particle was chosen as the reinforcement.

Table 1: The chemical composition (wt%) of AZ91D.

Al Zn Mn Si Cu Cr Ni Fe Mg
9.1 0.82 0.23 0.03 0.019 0.5 0.001 0.0025 Bal.
Figure 1 showed the injection process of SiC particle. The angle between the powder feeding tube and the upper surface of the melt was acute(30°, 40°, 50°, 60°). There were two magnetic poles on both sides of the melt to generate a uniform magnetic field whose direction was X-axis. The geometry parameters of the crucible were mentioned in Table 2.

Table 2: The crucible geometry parameters.

Parameters Value
Upper bottom diameter 27.27 mm
Lower bottom diameter 25 mm
Height 50 mm
Wall thickness 2 mm
Powder injection inner diameter 2 mm
The melt temperature was 950K for free of contamination and oxidation by Argon protection. After the crucible was filled with the molten magnesium alloy, each SiC particle charged 10​-9 coulombs was injected into the melt by the powder feeding tube.

[2456-279y-1-2-1]

Figure 1: Schematic diagram of SiCp injection process with the uniform magnetic field.

Orthogonal design

The injection angle, injection speed, particle diameter and magnetic field strength were considered for the process factors of the particle injection process. The four main factors were denoted as A to D respectively. Each factor had four levels indexed from 1 to 4, which represented the chosen values of the operating parameters as shown in Table 3.

Table 3: The orthogonal factors and levels.

Factors Levels Unit
1 2 3 4
A, Injection angle 30 40 50 60 °
B, Injection speed 3 4 5 6 m/s
C, Particle diameter 60 80 100 120 μm
D, Magnetic field strength 0.5 0.8 1.0 1.5 T

Principle of Numerical analysis

Governing equations

The molten magnesium alloy can be considered as many infinitely small liquid micelles, so the macroscopic melt properties can be seen as a continuous function of the liquid micelles. The governing equations in the simulation are written as

[2456-279y-2-1-i1.1]
(1)
[2456-279y-2-1-i1.2]
(2)

where v is fluid velocity vector, ρ is fluid density, F is volume force vector, P is the pressure and μ is the dynamic viscosity.

Simulation assumption

The process of particles injection was taken into as a transient model. The position and velocity of the particles changed with a time. In order to ensure an accurate and convergent simulation process, the assumptions were put forward as the followed:

  1. The molten magnesium alloy is a viscous and incompressible fluid.
  2. SiC particles do not collide with each other.
  3. The particles are rigid solid balls. The density of SiC particle is 3.2 g/cm​3 .
  4. The particles do not react chemically with the molten magnesium alloy.

The force analysis of the particles in the melt

It was necessary to analyze the force of the particles in the melt to investigate the distribution of particles. The SiC particles were exerted by the buoyancy, the gravity, the Lorentz force and the drag force in the melt as shown in Fig. 2.

[2456-279y-1-2-2]

Figure 2: Diagram of the forces acting on the particle. Fb, Fg, Fl and Fd represented the buoyancy, the gravity, the Lorentz force and the drag force, respectively.

The forces acting on the particle were described by the following equations:

[2456-279y-2-1-i1.3]
(3)
[2456-279y-2-1-i1.4]
(4)
[2456-279y-2-1-i1.5]
(5)
[2456-279y-2-1-i1.6]
(6)

where F​b , F​g , F​l and F​d represented the buoyancy, the gravity, the Lorentz force and the drag force respectively. R was the particle radius, ρ was the melt density, ρ​p was the particle density, q was the particle charge, v(t) was the speed of SiC particle in the melt, B was the magnetic induction, and η was the viscosity of the melt. The gravity of particles was constant. The density of the magnesium alloy melt was related to the temperature and the melt temperature was kept to a constant value during the injection of particles. Therefore the buoyancy of the particles in the melt was constant. Both of the Lorentz force and the drag force acting on the motion of particles were only taken into considered.

According to the second Newton law, Eqs. (1)-(4) can be rewritten as:

[2456-279y-2-1-i1.7]
(7)

where θ was the angle between the powder feeding tube and the upper surface of the melt. The movement distance of particle in z-axis direction was expressed by z (​ t ​ ) with the time ​ t , ​ which was described by:

[2456-279y-2-1-i1.8]
(8)

Eq. (7) was substituted by Eq. (3) - (6), integrated with the Eq. (9) and (10).

[2456-279y-2-1-i1.9]
(9)
[2456-279y-2-1-i1.10]
(10)

The relationship between the depth of the particle in the melt and the time was obtained:

[2456-279y-2-1-i1.11]
(11)
where

It can be found that the following factors have an effect on the injection depth of the particle in the melt from the Eq. (11):

  1. The initial velocity of particles;
  2. The diameter of particles;
  3. The melt viscosity;
  4. The magnetic field intensity.

Boundary conditions

It was necessary to set the reasonable temperature boundary condition and particle motion boundary condition for the solution of the equilibrium equations. The temperature of the melt and the crucible remained 950K during the injection of particles.

The layers of the melt

The molten magnesium alloy was divided into five layers as shown in Fig. 3.

[2456-279y-1-2-3]

Figure 3: Diagram of layering the molten magnesium alloy

The standard deviation was calculated by the particle’s concentration of each layer to quantify the particle’s distribution in the molten magnesium alloy. The smaller the standard deviation of the particles concentration, the more uniform the particles distribution in the melt. Otherwise, the particles were not evenly distributed. The standard deviation was defined as:

[2456-279y-2-1-i1.12]
(12)

where ​ i was the number of the layers in the melt, ​ x was the average concentration of particles each layer.

Results and Discussion

Analysis of the orthogonal tests

According to the orthogonal array designed in Section 3, showed the L16(4​4) orthogonal design scheme for studying the process parameters. All the cases were calculated by the Fluent software. The last column in the Table 4 was the standard deviation.

Table 4: The Orthogonal tests of L16 (44), and the standard deviation.

Cases A B C D Standard deviation
1 1 1 1 1 666.5
2 1 2 2 2 915.1
3 1 3 3 3 1987.1
4 1 4 4 4 410.9
5 2 1 2 3 4143.0
6 2 2 1 4 2750.0
7 2 3 4 1 886.5
8 2 4 3 2 1466.0
9 3 1 3 4 4535.4
10 3 2 4 3 1089.4
11 3 3 1 2 146.2
12 3 4 2 1 953.4
13 4 1 4 2 2798.1
14 4 2 3 1 2582.7
15 4 3 2 4 1308.5
16 4 4 1 3 2319.8

Table 5 showed the effect of the process factors on the uniformity of the distribution of particles. Because the standard deviation was used to quantify the particle distribution uniformity, the level with a smaller k was better than other levels. Therefore the order of the influences on the uniformity was B, C, A and D. The optimal process parameter for the best uniformity of particles distribution was B​3C4A1​D1​ , in which the standard deviation was 158.5.

Table 5: ∑the standard deviation for the indicator

Parameters A B C D
K1 3979.6 12143.0 5882.5 5089.1
K2 9245.5 7337.2 7320.0 5325.4
K3 6724.4 4328.3 10571.2 9539.3
K4 9009.1 5150.1 5184.9 9004.8
k1 994.9 3035.8 1470.6 1272.3
k2 2311.4 1834.3 1830.0 1331.4
k3 1681.1 1082.1 2642.8 2384.8
k4 2252.3 1287.5 1296.2 2251.2
R 1316.5 1953.7 1346.6 1112.5
Order B > C > A > D
Optimal combination B3C4A1D1

Analysis of the particle distribution

The optimal process parameter derived from the orthogonal test was simulated using the Fluent software. Case 3, case 9, case 14 in the orthogonal experiments were compared with the optimal case. Fig. 4 showed the macroscopic distribution of the particles. It was found that the particles were agglomerated in the upper and distributed less in the lower part of the melt in Fig. 4(a). It was attributed that the injection angle of particles was small and the injection speed was large, so the particles had a large velocity in the non-z axis direction, and the particles tended to stay in the upper part of the melt. Fig. 4(b) showed that the particles gathered at the bottom and the particles were inhomogeneously distributed. The magnetic field intensity was large, and the particle injection speed was small, resulting in limiting the ability to change the particle trajectory. The larger the injection angle, the easier the particles entering the melt. As shown in Fig. 4(c), the particles were agglomerated at the bottom, and the voids appeared on the left side of the melt. The particles were distributed evenly without agglomeration of the particle. The uniform distribution of particles can be achieved under the optimal process parameter in Fig. 4(d).

[2456-279y-1-2-3]

Figure 4: The macroscopic distribution of particles: (a) Case 3: 5 m·s-1, 100μm, 30° and 1.0 T, (b) Case 9: 3 m·s-1 , 100μm, 50° and 1.5 T, (c) Case 14: 4 m·s-1 , 100μm, 60° and 0.5 T, (d) the optimum example: 5 m·s-1 , 120μm, 30° and 0.5 T.

Fig. 5 showed the changes of particles concentration in each layer’s melt. The particles concentration in case 3 had large changes in the diagram, and the particles concentration was the maximum value at the fifth layer of the melt. The trend of particle concentration of case 9 and case 14 was gradually decreasing. This was consistent with the macroscopic distribution of the particle. As for optimization example, the particles concentration changed little, and the particles were evenly distributed in all layers.

[2456-279y-1-2-5]

Figure 5: The particle concentration in each layer.

In order to observe the distribution of particles in the melt, a slice of 20 mm from the bottom was taken. Fig. 6 showed that the distribution of particles of 20 mm's layer in the melt. Fig. 6(a) showed that particles appeared slightly aggregated in the middle and voids appeared on the right side. Fig. 6(b) showed that particles appeared large area of the gap. Due to inhomogeneous distribution of particles, it would make the mechanical properties of magnesium matrix composite decline. As showed in Fig. 6(c), particles were aggregated in the lower part. Fig. 6(d) indicated that the uniform distribution of the particles can be obtained under the optimum process parameters.

[2456-279y-1-2-6]

Figure 6: The particles distribution on the layer of 20 mm: (a) Case 3: 5 m·s-1 , 100μm, 30° and 1.0 T, (b) Case 9: 3 m·s-1 , 100μm, 50° and 1.5 T, (c) Case 14: 4 m·s-1 , 100μm, 60° and 0.5 T, (d) The optimum example: 5 m·s-1 , 120μm, 30° and 0.5 T.

Conclusions

In the present,the model of the molten magnesium alloy with injection device was built to investigate the distribution of particles in the uniform magnetic field. The numerical simulation provided a better understanding of particle distribution status in the molten magnesium alloy. The following conclusions can be made.

  1. The force of the particles in the melt was analyzed. The SiC particles were subjected to buoyancy, gravity, Lorentz force and drag force in the melt. Initial velocity of the particles, particle diameter, melt viscosity and magnetic field intensity had an effect on the injection depth of the particles.
  2. Through the orthogonal tests, the impact sequence of the process parameters for the particle distribution was B > C > A > D, which was the injection angle>the injection speed>the particles diameter>the magnetic field intensity. The optimal combination of the best uniformity is B​3​C​4A1D1​ , which was the injection speed of 5m/s,the particles diameter of 120μm,the injection angle of 30° and the magnetic field intensity of 0.5 T.
  3. The case with the optimum parameter was running and compared with the three representative cases in the orthogonal experiments. The uniform distribution of the particles can be achieved under the optimum parameters.

Acknowledgements

The authors are grateful to be supported by the National Natural Science Foundation of China under Grant No. 51561001, the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), the Top-notch Academic Programs Project of Jiangsu Higher Education Institutions (TAPP), the Ministry of Education and Science within the framework of the project No. 16.1969.2017/PCh and the Science and Technology Bureau of Jiangsu Province, P.R. China under grant No. BY2016029-19.

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