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Numerical simulation and experimental validation of SiC nanoparticle distribution in magnesium melts during ultrasonic cavitation based processing of magnesium matrix nanocomposites
Accepted Manuscript Numerical simulation and experimental validation of SiC nanoparticle distribution in magnesium melts during ultrasonic cavitation based processing of magnesium matrix nanocomposites Shangyu Song, Xia Zhou, Li Li, Wuming Ma PII: DOI: Reference:
S1350-4177(14)00376-9 http://dx.doi.org/10.1016/j.ultsonch.2014.12.010 ULTSON 2763
To appear in:
Ultrasonics Sonochemistry
Received Date: Revised Date: Accepted Date:
26 September 2014 14 December 2014 15 December 2014
Please cite this article as: S. Song, X. Zhou, L. Li, W. Ma, Numerical simulation and experimental validation of SiC nanoparticle distribution in magnesium melts during ultrasonic cavitation based processing of magnesium matrix nanocomposites, Ultrasonics Sonochemistry (2014), doi: http://dx.doi.org/10.1016/j.ultsonch.2014.12.010
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
Numerical simulation and experimental validation of SiC nanoparticle distribution in magnesium melts during ultrasonic cavitation based processing of magnesium matrix nanocomposites
Shangyu Song, Xia Zhou **, Li Li, Wuming Ma State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024, P. R. China
First author's surname: Song; Corresponding author’s surname: Zhou Running head: Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
Address correspondence to (** Corresponding author): Xia Zhou, Engineering Dr., Prof. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024, P. R. China. Tel: +86-411-84706782 Fax: +86-411-84708400 E-mail: [email protected] http://gs1.dlut.edu.cn/Supervisor/Front/dsxx/new/Default.aspx?WebPageName=Z houX
Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
Numerical simulation and experimental validation of SiC nanoparticle distribution in magnesium melts during ultrasonic cavitation based processing of magnesium matrix nanocomposites Shangyu Song, Xia Zhou **, Li Li, Wuming Ma State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024, P. R. China Abstract A two-dimensional model coupling of the temperature field, flow field and pressure field of SiC nanoparticles reinforced AZ91D magnesium composite slurries fabricated by high-intensity ultrasonic stirring method is established. The multiphase flow mixture model is used to simulate the temperature field, flow field and pressure field of the semi-solid slurries. The effects of ultrasonic stirring parameters on the distribution of SiC nanoparticles in AZ91D magnesium alloy melt are simulated by using finite difference method. The simulation results show that the distribution uniformity of SiC nanoparticles in Mg melts is influenced by ultrasonic power and frequency as well as the ultrasonic processing time and depth of ultrasonic probe dipped into the melts, but the ultrasonic power and frequency have greater influence on particle distribution. In the present work, the magnesium matrix composite with uniform dispersion of SiC nanoparticles can be obtained when the ultrasonic power, the ultrasonic frequency, the depth of ultrasonic probe dipped into the melts and ultrasonic processing time are 2kW, 20kHz, 20-30mm and 120s, respectively. It has been proven that the similar uniform dispersion could be achieved under the optimal ultrasonic processing conditions although SiC particle sizes in the agglomerated SiC-nanoparticles varied between 30-300nm in diameter. Moreover, the microstructure and mechanical properties of the SiC nanoparticles reinforced AZ91D magnesium alloy based composites obtained experimentally are improved significantly by using the optimized ultrasonic processing parameters based on numerical simulation.
Key words: Magnesium matrix nanocomposite; Ultrasonic cavitation; Microstructure; Nanoparticle distribution; Finite difference method; Experiment
1 **
Corresponding author. Tel.: +86-411-84706782; Fax: +86-411-84708400. E-mail address: [email protected] (X. Zhou)
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
1. Introduction
Magnesium alloys are potential candidates for structural applications in aerospace, automobile, military, transportation and consumer industries where weight saving is of great importance because of their low density and high specific strength as well as good processing capabilities. In comparison with the unreinforced magnesium alloys, magnesium matrix composites reinforced with ceramic particles exhibit higher strength and stiffness, improved wear resistance, and increased resistance to creep and fatigue[1]. The mechanical properties of magnesium alloy matrix composites can be further enhanced by decreasing the sizes of ceramic particulates and/or matrix grains from micrometer to nanometer level. Many attempts have been directed in recent years towards the development of Mg-based composites with nanoparticles such as Al2O3, Y2O3, SiC, AlN [2-5]. In addition, the investigations by many researchers [2, 6−8] have shown that remarkable improvement of mechanical properties of magnesium based composites can be realized through the use of ceramic reinforcements at nano-length scale in Mg alloy matrix. Use of nanoparticles to reinforce magnesium alloy materials has inspired considerable research interest in recent years because of the potential development of novel composites with unique mechanical and physical properties. A uniform distribution of nanoparticle reinforcement in magnesium alloy matrix is the crucial factor to better mechanical properties of the magnesium alloy matrix nanocomposites [9]. However, the nano-sized particles pose serious difficulty in achieving a uniform dispersion because of their high viscosity, poor wettability in the magnesium alloy matrix and large surface-to-volume ratio. Nanoparticle clusters or agglomerates are usually formed in such composites due to various factors in the
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
fabrication process and these clusters or agglomerates significantly decrease the local mechanical properties of the Mg alloy matrix composites. Magnesium alloy matrix nanocomposites can be prepared by incorporating ceramic nanoparticles into matrix via powder metallurgy [6], disintegrated melt deposition [7], compocasting method [10], high intensity ultrasonic stirring [4,11] and microwave sintering route [12]. Among of them, the ultrasonic cavitation-based solidification processing is often preferred to other techniques for its capability in wetting and dispersing nanometer-sized particles in metal melts and for the capability in purifying the particle/melt composite slurries. However, only few studies have analyzed this dispersion technique and the appropriate modes of action [13−15], and these studies are mainly focused on the dispersion of nanoparticles in the polymer. Several researchers [16−19] reported that the processing parameters, namely, ultrasonic power, ultrasonic frequency, ultrasonic processing time and depth of ultrasonic probe dipped into the melts, exhibited significant effects on the microstructure and properties of metal matrix composites. In order to study the effect of ultrasonic cavitation-based stirring process parameters, all researchers follow the traditional experimental techniques, i.e., varying one parameter at a time while keeping others constant. For example, Cao et al [16] indicated that SiC bonded well with the magnesium alloy matrixes without forming an intermediate phase in SiC-reinforced Mg-(2,4) Al-1Si nanocomposites fabricated by high-intensity ultrasonic processing under the conditions of 4.0kW power out-put and 17.5kHz ultrasonic frequency as well as 25–31 mm in depth for the ultrasonic probe dipping into the melts. Wang et al [17] studied the effect of ultrasonic treatment time on particle distribution, microstructure and properties of micro-SiC particles reinforced magnesium matrix composites. Erman
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
et al [18] investigated the beneficial effect of ultrasonic vibration on the distribution of SiC nanoparticles in Mg alloy melts by microstructural evaluation and mechanical property measurement. Eskin et al [19] found out that tthe ultrasonic cavitation treatment combined with electromagnetic stirring can significantly improve the size and spatial distribution of ceramic particles in hypereutectic Al–Si alloy matrix composites. This conventional parametric design of experiment approach is time-consuming and calls for enormous resources. Hence efforts must be placed on developing effective, numerical analytical methods to study ultrasonic cavitation-based stirring process. Although there have been some numerical simulation reviews [20-22] of ultrasonic cavitation effects on the solidification microstructure of molten metal at present, the numerical simulation of SiC nanoparticle dispersion process in magnesium melts is rarely reported. As we all know, the high intensity ultrasonic treatment can significantly improve the distribution of nanoparticles in magnesium matrix nanocomposites and refine Mg matrix grains [23], while process parameters of ultrasonic vibration have a great influence on distribution uniformity of nanoparticles. In addition, there is still lack of a systematical research on the energy transfer between the ultrasonic horn and melt/particles, the ultrasonic propagation in melt/particles and nanoparticle distribution. Therefore, it is a challenging task to simulate SiC nanoparticle distribution in magnesium melts during ultrasonic cavitation based processing of magnesium matrix nanocomposites and to optimize the ultrasonic processing parameters. In this study, numerical simulation of the propagation of high intensity pressure waves in nanoparticles/magnesium melts has been conducted using Fluent 6.3.26 software when the high intensity ultrasonic vibration is applied to the nanoparticles/Mg melts. The objective of this work is to study the influence rules of ultrasonic power,
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
ultrasonic frequency and position of the ultrasonic vibration tool head on the SiC nanoparticle distribution in AZ91D Mg alloy melts to optimize the critical process parameters of the ultrasonic stirring by numerical simulation. The results obtained from the numerical simulation have been further validated experimentally by performing ultrasonic cavitation treatment of 1vol% nano-SiC reinforced AZ91D composites. The present research results could provide the effective theoretical guidance for obtaining excellent mechanical properties of magnesium nanocomposites.
2. Simulation of the ultrasonic cavitation based stirring treatments
2.1. Geometrical model based on high intensity ultrasonic stirring
Fig. 1 shows the schematic diagram of experimental setup used in the fabrication of SiC nanoparticle reinforced AZ91D magnesium alloy matrix composites by using high intensity ultrasonic treatment. The device consisted of a steel crucible, automatic temperature control heater, and high intensity ultrasonic transmission and gas protection components. The operating principle of the device was described as follows: first AZ91D Mg alloy was heated to melt in a preheated crucible, and next surface-modified and preheated SiC nanoparticles were added into the AZ91D melts. Then high intensity ultrasonic fields were applied to the SiC nanoparticles/Mg alloy melts to produce violent local disturbances, and finally the uniform distribution of SiC nanoparticles reinforced magnesium alloy matrix composites were obtained.
Fig. 1 and Fig. 2: (about here)
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
Since the ultrasonic vibration device had relatively large aspect ratio, its twodimensional model was built by using the Gambit software for the convenience of calculation. The model was meshed and solved by the triangular elements. In addition, the subdivision meshes were adopted at the entrance of the ultrasonic pressure wave, while the coarse grids are applied to other parts. The multi-grid approach can not only assure the simulation accuracy but also improve the calculative efficiency. Resolution of the fine and coarse mesh was 0.05mm and 0.1mm, respectively. And the final numerical model with the grid nodes of 71430 is shown in Fig. 2. In order to reduce the computational load, the geometric model of the crucible in the present study was appropriately scaled-down based on its actual geometry structure. The geometry parameters of the crucible were set to 100mm in inside diameter and 150mm in height, while the diameter of the ultrasonic probe is set to 20mm. The boundary surface composed of ha, hg and gf lines in the model represented the inner wall of the crucible, and the frame consisting of bc, cd and de lines in the model meant the part of the ultrasonic probe under the magnesium alloy melts, while line cd showed the end face of the ultrasonic probe. And ab and ef lines were the interfaces between the magnesium alloy melts in the crucible and the external protective gas. Table 1 shows the length of each side, the name and type of the boundary.
Table 1: (about here)
2.2. Establishment and solution of mathematical models
For ease of calculation, the following hypotheses were proposed in the present paper: ① the entire simulation system was adiabatic and no heat convection was considered;
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
② the magnesium alloy melt was an incompressible non-Newtonian fluid; ③ the effects of temperature variation on the density of SiC nanoparticles and magnesium alloy melts were neglected; ④ the jet stream generated by the collapse of cavitation bubbles was ignored. As linear wave propagation has been assumed and the shear stress has been neglected, the acoustic pressure can be obtained by solving the wave equation [24]: 1 1 ∂2P ∇ ∇P − 2 2 = 0 ρ ρc ∂t
(1)
where ρ is the density of the metal melt, c is the propagation velocity of the acoustic wave in melt, t is the time. In order to investigate the nanoparticle distribution in the metal melt after ultrasound processing, the mixture model [25] for two-phase flows was used. When using the mixture model with cavitation effects in FLUENT, the governing equations [26] of continuity, momentum and cavitation bubble mass fraction can be written as follows:
∂ρ ∂ + ( ρ ui ) = 0 ∂t ∂xi
(2)
∂ ( ρ ui ) ∂ ∂u ∂u ∂p ∂ + ( ρ ui u j ) = − + [( µ + µl )( k + j )] + ρ g i ∂t ∂x j ∂xi ∂x j ∂x j ∂xk
(3)
∂ ( ρw ) ∂ + (ρui w) = ∂ [(µ + µl ) ∂w ] + Re + Rc ∂t ∂x j ∂x j ∂x j
(4)
where the mixture density ρ is the function of the liquid density ρl , incompressible gas density ρg and vapor density ρ v , it is shown as below: 1
ρ
=
wv
ρv
+
wg
ρg
+
1 − wg − wv
ρl
(5)
where ρ is the mixture density, ui is the velocity at i direction, w is the mass fraction of cavitation bubbles, µ is the viscosity of the fluid, g i is the gravity component
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
at i direction, t is the time, v , g and l represent vapor state, gas state and liquid state, separately; Re and Rc are the generation ratio and compressive ratio of cavitation bubbles, respectively, and they are calculated using the growth of a single bubble based on the Rayleigh-Pleasset model [27]: d 2 R 3 dR 2 2σ + = P0 − Pv + 2 R0 dt 2 dt
ρ R
3k
R0 2σ 4η dR − − − P0 + Pv + Pm sin ωt R R dt R
(6)
where R and R0 are the instantaneous radius and initial radius of bubbles, respectively; P0 , Pv and Pm are the initial pressure outside cavitation bubbles, vapor pressure within
cavitation bubbles and acoustic pressure amplitude, respectively; σ is the surface tension; k is the polytropic exponent of the melt which is usually 3/4 and ω is the angular frequency of the acoustic wave which is given by ω = 2π f . In the present paper, the pressure-based solving method was adopted. The solving method for unsteady problems was first applied in the SiC/Mg composite melts, material property parameters and solution conditions were then set, and finally the nanoparticle distribution could be calculated on the basis of the velocity, pressure and temperature fields. Since time-domain computations were used for resolving the acoustic field, a very small time step of 1 × 10−4 s was used and the total solving time was 120s. The ultrasonic
pressure wave was applied at the pressure inlet boundary and it was expressed by the equation P = PA sin(2π ft ) . The ultrasonic wave used for simulation had a ultrasound
velocity of 4000m/s,
a ultrasound
wavelength
of 150mm, an amplitude,
PA = 2 − 10MPa , and a ultrasonic frequency, f = 20 − 40kHz . The SiC nanoparticles with a mean diameter varying from 30nm to 50nm, an average density of 3200kg/ m3 and a volume fraction of 1vol% were used as reinforcements, while the AZ91D
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
magnesium alloy was used as a matrix of composites and its property parameters are shown in Table 2 [24].
Table 2: (about here)
3. Results and discussion
3.1. Effects of ultrasonic power and frequency on SiC nanoparticle distribution
During the dispersion process of nanoparticle-agglomerates in magnesium alloy melts by high intensity ultrasonic stirring method, the ultrasonic frequency and power is a pair of critical process parameters. They determine the size and distribution of the acoustic pressure and velocity fields, while the pressure and velocity fields in turn have influence on nanoparticle distributions in magnesium alloy melts. Fig. 3a-e show the distribution of 1vol% SiC nanoparticles in Mg melts after 120s ultrasonic agitation while the ultrasonic power and frequency are in the range of 1.5 to 2.5kW and 20kHz to 40kHz, and the depth of ultrasonic probe dipped into the melts and ultrasonic processing temperature are 20mm and 900 K, respectively. The effect of different combinations of ultrasonic power and frequency on SiC nanoparticle dispersions was obvious. It can be seen from Fig. 3a and b that the frequency has an obvious effect on the distribution of nanoparticle-agglomerates whether in the radial direction away from the center of the ultrasonic horn surface at the melt/horn interface or in the axial direction away from the center of the ultrasonic horn end surface for a constant ultrasonic power of 2kW. The volume fractions of nanoparticle-agglomerates in the same location of Mg melts at the same time were
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
increasing with the increase of the ultrasonic frequency while they varied little when the frequency was increased to 30-40 kHz. However, the volume fractions of nanoparticles in the same location of Mg melts at the same time firstly decreased from 1.5kW to 2kW and then increased again at 2.5kW for a fixed frequency of 20kHz. This is because cavitation effects are enhanced with the increasing ultrasonic power and the cavitation effects will tend to be saturated after the ultrasonic power reaches a certain value. During this time, a lot of useless cavitation bubbles will appear when the ultrasonic power continue to increase and these cavitation bubbles can't completely collapse instantaneously. They just stay in resonance, burst when rising to the melt surface or form bubble screen on the vibration surface. All these will result in ultrasound attenuation and decrease of cavitation intensity [28]. Fig. 3c-e shows a comparison of the effects of different combinations of ultrasonic power and frequency on the frequency distribution of the SiC nanoparticle volume fraction. Results from the comparative analysis of Fig. 3c-e also have proved that the combination of 2kW ultrasonic power and 20kHz frequency was preferred for achieving a homogeneous distribution of SiC nanoparticles.
Fig. 3a-e: (about here)
3.2. Effects of the ultrasonic probe position on SiC nanoparticle distribution
Fig. 4a and b show the effects of different depths (25mm, 30mm and 40mm) of the ultrasonic probe into Mg melts on the distribution of 1vol% SiC nanoparticles along two special paths such as the radial direction away from the center of the ultrasonic horn surface at the melt/horn interface and the axial direction away from the center of the
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
ultrasonic horn end surface under the combination of 2kW and 20kHz at 110s. It can be seen that compared with the case of 20mm depth of the ultrasoinc probe into the melt (Fig. 3a and b), the volume fractions of SiC nanoparticles along the two directions described above were all tending to be zero when the depth of the probe in the melt was increased from 25mm to 40mm. It can be predicted that the cavitation development in the directions from the probe center to the bottom and both sides of the crucible is at the varying stages as the depth of the probe into the Mg melt increases, and this can be clearly seen from velocity distribution contours (Fig.5a-c) under the corresponding probe depths in the melt at the moment. It is obvious that when the probe depth in the melt is varied between 25mm to 40mm, the amplitude value and distribution for the probe depth of 25mm to 30mm in the melt are different from the case for the probe depth of 30mm to 40mm in the melt, indicating that the probe depth of 30mm might be a critical depth for the cavitation development and the uniform dispersion of nanoparticles.
Fig. 4a and b: (about here) Fig. 5a-c: (about here)
3.3. Effects of the ultrasonic agitation time on SiC nanoparticle distribution
Fig. 6a-e shows frequency distribution variations of 1vol% SiC nanoparticles in Mg melts with different ultrasonic agitation time under the immersed ultrasonic probe end of 30mm depth and the combination of 2kW and 20kHz while the other ultrasonic processing parameters are identical. It can be seen that the distribution of the nanoparticles at 80s was significantly improved with prolonging the ultrasonic
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
dispersion time, but it became more inhomogeneous when the ultrasonic time was extended to up to 160s. The best nanoparticle distribution uniformity was obtained at 120s.
Fig. 6a-e: (about here)
The above-mentioned analysis on the simulation results of the effects of different ultrasonic processing parameters on SiC nanoparticle distribution has shown that the distribution of SiC nanoparticles in the magnesium alloy melt is relatively homogenous under the addition of 1vol% of SiC nanoparticles to the Mg melt, the ultrasonic processing temperature of 900K, ultrasonic agitation time of 120s, the immersed ultrasonic probe end of 20-30mm depth, and the ultrasonic power of 2kW and ultrasonic frequency of 20kHz. Fig. 7a-d shows the magnitude contours of pressure, velocity and temperature fields as well as SiC nanoparticle distribution in the SiC/Mg composite slurries under the identical ultrasonic processing conditions of 30mm probe depth in the melt. It can be seen that there existed a gradual increasing pressure gradient from the sound source (Fig. 7a), a highly uneven velocity distribution (Fig.7b) and a relatively homogeneous temperature distribution in the composite slurries (Fig. 7c). Such varied three fields are favorable for the uniform distribution of reinforced SiC nanoparticles and it can be seen from Fig. 7d.
Fig. 7a-d: (about here)
3.4. Size effect of the dispersion process of nanoparticle agglomerates
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
As was mentioned above, nanoparticle-aggregates can be well dispersed in the magnesium alloy melt through the optimal ultrasonic processing parameters. In this section, further simulation on the dispersion of nanoparticle-aggregates with a larger particle diameter of 300nm in magnesium alloy melt was conducted under the conditions of the optimal ultrasonic processing parameters and thus the effect of the variation in particle size on ultrasonic dispersion was analyzed. Fig.8a-d shows the sound pressure, velocity and temperature fields and the frequency distribution of the SiC nanoparticle volume fraction at 120s, respectively. It can be seen from these figures that a similar uniform distribution of particle volume fraction can be obtained at the same time although both amplitude value and distribution of the sound pressure, velocity and temperature fields have both varied a little.
Fig. 8a-d: (about here)
The reason why increasing the size of SiC ceramic particles has a smaller effect on the uniform dispersion in the Mg melt under the optimal ultrasonic processing conditions may due to the combined effects of several factors. When the particle size increases, the contact area between the particles decreases and the number of adjacent molecules is less, resulting in the decrease of the van der Waals force between the particles. In addition, the liquid bridge can be formed between the particles and this is helpful to increase the capillary force, but the capillary force is generally much smaller than the van der Waals force. On the other hand, the number of voids and cavitation bubble nucleation will increase as the particle size increases and thus the cavitation intensity is increased.
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
4. Experimental validation
In this section, SiC nanoparticles reinforced AZ91D magnesium matrix composites were fabricated by ultrasonic cavitation based solidification method [29] and effects of ultrasonic variables on microstructure evolution of the composites were discussed. Fig. 9 shows a TEM image of AZ91D Mg alloy based nanocomposites along with selected area diffraction pattern (SADP). It can be seen from Fig. 9a that the nanometer-sized SiC particles or their clusters are well embedded in the area observed. Fig. 9b is the SADP from the marked A area in Fig. 9a, the corresponding diffraction pattern can be indexed as (111), (200), (220), and (311), and this matches well with the cubic β-SiC [30]. Fig.10 shows the effects of ultrasonic variables on microstructure formation in AZ91D magnesium matrix nanocomposites reinforced with volume fraction of 1% SiC nanoparticulates (1vol% n-SiCp/AZ91D). It can be seen that microstructures of the AZ91D matrix alloy changed significantly and SiC particles dispersion became more homogeneous with the increase of ultrasonic power and agitation time. As shown in Fig. 10a, there still existed the agglomeration of SiC nanoparticles in the Mg matrix after treated by ultrasonic vibration for 50s when the power and frequency of ultrasonic vibration are 1.5kW and 20kHz, respectively. Compared with the case of Fig. 10a, Fig. 10b has shown that the grain size of the AZ91D Mg matrix was refined and its average size was significantly smaller than that of the matrix treated by ultrasonic vibration for 50s when ultrasonic vibration time was extended to 120s with ultrasonic power and frequency remaining unchanged. Also the distribution of SiC particles became more uniform in Fig. 10b. It can be furtherly found from Fig. 10c that the grain size of the matrix alloy changed little and the best distribution of SiC particles in the matrix was obtained when the ultrasonic power was increased to 2kW with the ultrasonic time and
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
frequency remaining unchanged. It can be thus concluded that the ultrasonic power and ultrasonic time have great influence on the grain size of the matrix alloy and distribution of SiC particles based on the microstructural evolution of SiCp/AZ91D nanocomposites under different ultrasonic processing parameters shown in Fig. 10. On the one hand, the roles of the ultrasonic cavitation and acoustic streaming are strengthened with the increase of the ultrasonic power, resulting in the gradual refining of the matrix grains and brittle connected phase Mg17Al12 as well as the improved uniform dispersion of SiC particles. On the other hand, the ideal microstructure of the SiCp/AZ91D nanocomposite with an evenly particle distribution and grain refinement of matrix alloy can be obtained under the conditions of larger ultrasonic power and suitable ultrasonic vibration time. This is because that if the SiCp/AZ91D nanocomposite is subjected to ultrasonic vibration for fairly short processing times under the given ultrasonic power and frequency conditions, there's not enough time for the ultrasonic cavitation effect to give the full play to the particles dispersion, leading to the agglomeration of SiC particles; while if the composite is subjected to ultrasonic vibration for fairly prolonged processing times, the mechanical disturbance generated by high-intensity ultrasound can not work and the grain refinement effect of the matrix alloy is not obvious too since the matrix alloy has tended to be solidified.
Fig. 9a and b: (about here) Fig. 10a-c: (about here)
Fig. 11 shows the room-temperature mechanical properties of AZ91D magnesium alloy without ultrasonic processing and 1vol% SiCp/AZ91D magnesium matrix nanocomposites fabricated by the ultrasonic cavitation based solidification technique
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
with different ultrasonic parameters. From Fig.11, the nanosized SiC particles reinforced AZ91D magnesium matrix composite has shown an improvement in both 0.2% yield and ultimate tensile strengths as well as the elongation rate when compared to AZ91D magnesium alloy because of the addition of SiC nanoparticles into the Mg melt and suitable combinations of ultrasonic processing parameters. The significant improvement in the comprehensive mechanical properties of the SiCp/AZ91D magnesium matrix nanocomposites can be attributed to the grain refinement of the matrix alloy, the homogeneous distribution of SiC nanoparticles and less connected β phase (Mg17Al12)[31], as well as the increased interfacial bonding strength between the reinforcing particle and the matrix. Fractographs taken from the tensile fracture surfaces of
AZ91D
magnesium
alloy
and
1vol%
SiCp/AZ91D
magnesium
matrix
nanocomposites are shown in Fig.12. As shown in Fig. 12a, fracture surface of AZ91D Mg samples indicated the presence of cleavage steps and microscopically rough features. Different from the brittle fracture of AZ91D magnesium sample, the fracture surfaces of SiCp/AZ91D magnesium matrix nanocomposite samples in Fig.12b and c have revealed the mixed mode failure showing more evidences of matrix plastic deformation. Regions showing dimple-like ductile features were also observed, particularly in the SiCp/AZ91D magnesium matrix nanocomposite with uniform distribution of reinforcing SiC particles shown in Fig.12c. The mixed fracture behaviour of the SiCp/AZ91D magnesium matrix nanocomposites is largely due to the presence of clustered SiC particles and brittle eutectic phase Mg17Al12, particle debonding and localized microvoid coalescence as well as grain refinement in the matrix alloy.
Fig. 11: (about here) Fig. 12a-c: (about here)
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
5. Conclusions
The optimized ultrasonic processing parameters are determined by the numerical simulation of ultrasonic cavitation based mixing and dispersing 1vol% SiC nanoparticles in AZ91D Mg melts when SiC particle size in the agglomerated SiCnanoparticles is in the range of 30-300nm in diameter. The combination of higher power and lower frequency has beneficial effects on uniform distributions of the pressure, velocity and temperature fields. The higher pressure and velocity fields with a relatively uniform distribution are obtained and thus SiC nanoparticles can be well-dispersed in the melt when the ultrasonic power, the ultrasonic frequency, the depth of ultrasonic probe dipped into the melt and ultrasonic agitation are 2kW, 20kHz, 20-30mm and 120s, respectively. Experimental results show that the SiCp/AZ91D magnesium matrix nanocomposites with improved mechanical properties can be fabricated by using the optimized ultrasonic processing parameters. This can be attributed to the combined effects of several factors, in which the uniform dispersion of SiC nanoparticles in the Mg melt is dominated by the ultrasonic cavitation while the grain refinement of Mg matrix composites can be achieved by the cavitation and acoustic streaming due to the uniform addition of SiC nanoparticles as grain refiners and dendrite fragmentation of Mg matrix under the ultrasonic processing conditions in the present paper. In addition, fractographs of the nanocomposites have revealed changes in fracture behavior from cleavage in the case of AZ91D magnesium alloy to mixed mode of fracture as a result of the presence of SiC nanoparticulates and the dominant effect of ultrasonic cavitation.
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
Acknowledgments
The authors gratefully acknowledge the financial supports from the National Nature Science Foundation of China (No. 11272072) and the Special Fund of State Key Laboratory of Structural Analysis for Industrial Equipment.
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by ultrasonic dispersion and their structure property relationship, Ultrason. Sonochem. 18 (2011) 120-126. [16] G. Cao, H. Konishi, X. Li, Mechanical properties and microstructure of SiCreinforced Mg-(2, 4) Al-1Si nanocomposites fabricated by ultrasonic cavitation based solidification processing, Mater. Sci. Eng. A 486 (2008) 357-362. [17] X.J. Wang, N.Z. Wang, L.Y. Wang, Processing, microstructure and mechanical properties of micro-SiC particles reinforced magnesium matrix composites fabricated by stir casting assisted by ultrasonic treatment processing, Mater. Des. 57 (2014) 638-645. [18] A. Erman, J. Groza, X.C. Li, H. Choi, G.P. Cao, Nanoparticle effects in cast Mg-1 wt% SiC nano-composites, Mater. Sci. Eng. A 558 (2012) 39-43. [19] G.I. Eskin, D.G. Eskin, Production of natural and synthesized aluminum-based composite materials with the aid of ultrasonic (cavitation) treatment of the melt, Ultrason. Sonochem. 10 (2003) 297-301. [20] P. Padhi, B.N. Dash, S.K. Kar, Process modeling of deagglomeration of ceramic nanoparticles in liquid metal during synthesis of nanocomposites, Journal of Nanotechnology 2011 (2011) Article ID 734013. [21] Z.W. Shao, Q.C. Le, J.Z. Cui, Z.Q. Zhang, Numerical simulation of standing waves for ultrasonic purification of magnesium alloy melt, Trans. Nonferrous Met. Soc. China 20 (2010) s382-387. [22] L. Nastac, Mathematical modeling of the solidification structure evolution in the presence of ultrasonic stirring, Metall. Mater. Trans. B 31 (6) (2010) 2818-2833. [23] X. Liu, Y. Osawa, S. Takamori, T. Mukai, Grain refinement of AZ91 alloy by introducing ultrasonic vibration during solidification, Mater. Lett. 62 (17) (2008)
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2872-2875. [24] Z.W. Shao, Q.C. Le, Z.Q. Zhang, J.Z. Cui, Numerical simulation of acoustic pressure field for ultrasonic grain refinement of AZ80 magnesium alloy, Trans. Nonferrous Met. Soc. China 21 (11) (2011) 2476-2483. [25] FLUENT. FLUENT 6.3.26 user manual guide, ANSYS Corporation, 2009. [26] A.K. Singhal, M.M. Athavale, H. Li, Y. Jiang, Mathematical basis and validation of the full cavitation model, J. Fluid Eng. 124 (3) (2002) 617-624. [27] M.S. Plesset, R.B. Chapman, Collapse of an initially spherical vapour cavity in the neighbourhood of a solid boundary, J. Fluid Mech. 47 (2) (1971) 283-290. [28] G.I. Eskin, Ultrasonic treatment of light alloy melts [M], 2nd Edition. New York: CRC Press, Taylor & Francis Group, 2014, pp. 26-69. [29] X. Zhou, D.P. Su, C.W. Wu, L.M. Liu, Tensile mechanical properties and strengthening mechanism of hybrid carbon nanotube and silicon carbide nanoparticle-reinforced magnesium alloy composites, J. Nanomater. 2012 (2012) Article ID 851862. [30] J.Z. Guo, Y. Zuo, Z.J. Li, W.D. Gao, J. L. Zhang, Preparation of SiC nanowires with fins by chemical vapor deposition, Physica E, 39(2) (2007) 262–266. [31] E.I. Barker, K.S. Choi, X. Sun, E. Deda, J. Allison, M. Li, J. Forsmark, J. Zindel, L. Godlewski, Microstructure based modeling of β phase influence on mechanical response of cast AM series Mg alloys, Comp. Mater. Sci. 92 (2014) 353–361.
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Figure and Table Captions
Fig. 1. Schematic of high intensity ultrasonic vibration device used in this study. Fig. 2. Meshing of ultrasonic stirring. Fig. 3. Effects of different combinations of ultrasonic power and frequency on SiC nanoparticle dispersions: (a) volume fraction variations in the radial direction, (b) volume fraction variations in the axial direction, (c) frequency distribution of particle volume fraction under the conditions of 1.5kW and 20kHz, (d) frequency distribution of particle volume fraction under the conditions of 2kW and 20kHz and (e) frequency distribution of particle volume fraction under the conditions of 2.5kW and 20kHz. Fig. 4. Effects of the ultrasonic probe position on the volume fraction distribution of SiC nanoparticles: (a) the radial distribution and (b) the axial distribution. Fig. 5. Velocity contours when the ultrasonic probe is immersed in SiC/Mg melts at different depths of (a) 25mm, (b) 30mm and (c) 40mm. Fig. 6. Effects of the ultrasonic agitation time on frequency distribution of SiC nanoparticle volume fraction: (a) 10s, (b) 50s, (c) 80s, (d) 120s and (e) 160s. Fig. 7. Contours of (a) pressure field, (b) velocity field, (c) temperature field and (d) SiC nanoparticle distribution in SiC/Mg composite melts by ultrasound. Fig. 8. Contours of (a) pressure field, (b) velocity field, (c) temperature field and (d) frequency distribution of SiC nanoparticle-aggregates with an average particle diameter of 300 nm. Fig. 9. TEM image and SADP of the AZ91D Mg alloy based nanocomposite reinforced with SiC nanoparticles: (a) TEM image of the composite; (b) SADP taken from the marked A area in Fig. 9a.
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
Fig.10. Microstructures of SiCp/AZ91D nanocomposites under the conditions of 20kHz ultrasonic frequency and other varied ultrasonic processing parameters: (a) 1.5kW, 50s; (b) 1.5kW, 120s; and (c) 2kW, 120s. Fig.11. Tensile properties of AZ91D Mg alloy and SiCp/AZ91D Mg matrix nanocomposites treated with different combinations of ultrasonic power and time of 1.5kW, 50s and 2kW, 120s at 20kHz. Fig. 12. SEM fractographs of (a) AZ91D magnesium alloy and 1vol% SiCp/ AZ91D magnesium matrix nanocomposite treated with different combinations of ultrasonic power and time of (b) 1.5kW, 50s and (c) 2kW, 120s at 20kHz. Table 1 Calculation model and boundary setting. Table 2 Property parameters of magnesium alloy.
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
Table 1 Calculation model and boundary setting. Boundary line
Length/mm
Boundary conditions
Boundary type
ha
150
wall1
wall
ab
40
out
pressure-outlet
bc
20
deform1
wall
cd
20
inlet
pressure-inlet
de
20
deform2
wall
ef
40
out
pressure-outlet
fg
150
wall2
wall
gh
100
wall3
wall
Table 2 Property parameters of magnesium alloy. Density ρ(kg/m3)
Surface tension coefficient σ(N/m)
Initial pressure outside cavitation bubbles P0(Pa)
1820
0.564
1.013 × 105
Vapor pressure within cavitation bubbles Pv(Pa)
1000
24
Initial radius of cavitation bubbles R (µm)
1.0
Fluid viscosity
µ (Pa·s)
1.12 × 10-3
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Highlights • A two-dimensional model of high-intensity ultrasonic processing is established. • The model is coupled with the pressure, velocity and temperature fields. • SiC nanoparticles distribution in Mg melt under varied parameters is simulated. • The optimized high-intensity ultrasonic processing parameters are obtained. • The results obtained from numerical simulation have been verified by experiments.
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S1350-4177(14)00376-9 http://dx.doi.org/10.1016/j.ultsonch.2014.12.010 ULTSON 2763
To appear in:
Ultrasonics Sonochemistry
Received Date: Revised Date: Accepted Date:
26 September 2014 14 December 2014 15 December 2014
Please cite this article as: S. Song, X. Zhou, L. Li, W. Ma, Numerical simulation and experimental validation of SiC nanoparticle distribution in magnesium melts during ultrasonic cavitation based processing of magnesium matrix nanocomposites, Ultrasonics Sonochemistry (2014), doi: http://dx.doi.org/10.1016/j.ultsonch.2014.12.010
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
Numerical simulation and experimental validation of SiC nanoparticle distribution in magnesium melts during ultrasonic cavitation based processing of magnesium matrix nanocomposites
Shangyu Song, Xia Zhou **, Li Li, Wuming Ma State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024, P. R. China
First author's surname: Song; Corresponding author’s surname: Zhou Running head: Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
Address correspondence to (** Corresponding author): Xia Zhou, Engineering Dr., Prof. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024, P. R. China. Tel: +86-411-84706782 Fax: +86-411-84708400 E-mail: [email protected] http://gs1.dlut.edu.cn/Supervisor/Front/dsxx/new/Default.aspx?WebPageName=Z houX
Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
Numerical simulation and experimental validation of SiC nanoparticle distribution in magnesium melts during ultrasonic cavitation based processing of magnesium matrix nanocomposites Shangyu Song, Xia Zhou **, Li Li, Wuming Ma State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024, P. R. China Abstract A two-dimensional model coupling of the temperature field, flow field and pressure field of SiC nanoparticles reinforced AZ91D magnesium composite slurries fabricated by high-intensity ultrasonic stirring method is established. The multiphase flow mixture model is used to simulate the temperature field, flow field and pressure field of the semi-solid slurries. The effects of ultrasonic stirring parameters on the distribution of SiC nanoparticles in AZ91D magnesium alloy melt are simulated by using finite difference method. The simulation results show that the distribution uniformity of SiC nanoparticles in Mg melts is influenced by ultrasonic power and frequency as well as the ultrasonic processing time and depth of ultrasonic probe dipped into the melts, but the ultrasonic power and frequency have greater influence on particle distribution. In the present work, the magnesium matrix composite with uniform dispersion of SiC nanoparticles can be obtained when the ultrasonic power, the ultrasonic frequency, the depth of ultrasonic probe dipped into the melts and ultrasonic processing time are 2kW, 20kHz, 20-30mm and 120s, respectively. It has been proven that the similar uniform dispersion could be achieved under the optimal ultrasonic processing conditions although SiC particle sizes in the agglomerated SiC-nanoparticles varied between 30-300nm in diameter. Moreover, the microstructure and mechanical properties of the SiC nanoparticles reinforced AZ91D magnesium alloy based composites obtained experimentally are improved significantly by using the optimized ultrasonic processing parameters based on numerical simulation.
Key words: Magnesium matrix nanocomposite; Ultrasonic cavitation; Microstructure; Nanoparticle distribution; Finite difference method; Experiment
1 **
Corresponding author. Tel.: +86-411-84706782; Fax: +86-411-84708400. E-mail address: [email protected] (X. Zhou)
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
1. Introduction
Magnesium alloys are potential candidates for structural applications in aerospace, automobile, military, transportation and consumer industries where weight saving is of great importance because of their low density and high specific strength as well as good processing capabilities. In comparison with the unreinforced magnesium alloys, magnesium matrix composites reinforced with ceramic particles exhibit higher strength and stiffness, improved wear resistance, and increased resistance to creep and fatigue[1]. The mechanical properties of magnesium alloy matrix composites can be further enhanced by decreasing the sizes of ceramic particulates and/or matrix grains from micrometer to nanometer level. Many attempts have been directed in recent years towards the development of Mg-based composites with nanoparticles such as Al2O3, Y2O3, SiC, AlN [2-5]. In addition, the investigations by many researchers [2, 6−8] have shown that remarkable improvement of mechanical properties of magnesium based composites can be realized through the use of ceramic reinforcements at nano-length scale in Mg alloy matrix. Use of nanoparticles to reinforce magnesium alloy materials has inspired considerable research interest in recent years because of the potential development of novel composites with unique mechanical and physical properties. A uniform distribution of nanoparticle reinforcement in magnesium alloy matrix is the crucial factor to better mechanical properties of the magnesium alloy matrix nanocomposites [9]. However, the nano-sized particles pose serious difficulty in achieving a uniform dispersion because of their high viscosity, poor wettability in the magnesium alloy matrix and large surface-to-volume ratio. Nanoparticle clusters or agglomerates are usually formed in such composites due to various factors in the
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
fabrication process and these clusters or agglomerates significantly decrease the local mechanical properties of the Mg alloy matrix composites. Magnesium alloy matrix nanocomposites can be prepared by incorporating ceramic nanoparticles into matrix via powder metallurgy [6], disintegrated melt deposition [7], compocasting method [10], high intensity ultrasonic stirring [4,11] and microwave sintering route [12]. Among of them, the ultrasonic cavitation-based solidification processing is often preferred to other techniques for its capability in wetting and dispersing nanometer-sized particles in metal melts and for the capability in purifying the particle/melt composite slurries. However, only few studies have analyzed this dispersion technique and the appropriate modes of action [13−15], and these studies are mainly focused on the dispersion of nanoparticles in the polymer. Several researchers [16−19] reported that the processing parameters, namely, ultrasonic power, ultrasonic frequency, ultrasonic processing time and depth of ultrasonic probe dipped into the melts, exhibited significant effects on the microstructure and properties of metal matrix composites. In order to study the effect of ultrasonic cavitation-based stirring process parameters, all researchers follow the traditional experimental techniques, i.e., varying one parameter at a time while keeping others constant. For example, Cao et al [16] indicated that SiC bonded well with the magnesium alloy matrixes without forming an intermediate phase in SiC-reinforced Mg-(2,4) Al-1Si nanocomposites fabricated by high-intensity ultrasonic processing under the conditions of 4.0kW power out-put and 17.5kHz ultrasonic frequency as well as 25–31 mm in depth for the ultrasonic probe dipping into the melts. Wang et al [17] studied the effect of ultrasonic treatment time on particle distribution, microstructure and properties of micro-SiC particles reinforced magnesium matrix composites. Erman
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
et al [18] investigated the beneficial effect of ultrasonic vibration on the distribution of SiC nanoparticles in Mg alloy melts by microstructural evaluation and mechanical property measurement. Eskin et al [19] found out that tthe ultrasonic cavitation treatment combined with electromagnetic stirring can significantly improve the size and spatial distribution of ceramic particles in hypereutectic Al–Si alloy matrix composites. This conventional parametric design of experiment approach is time-consuming and calls for enormous resources. Hence efforts must be placed on developing effective, numerical analytical methods to study ultrasonic cavitation-based stirring process. Although there have been some numerical simulation reviews [20-22] of ultrasonic cavitation effects on the solidification microstructure of molten metal at present, the numerical simulation of SiC nanoparticle dispersion process in magnesium melts is rarely reported. As we all know, the high intensity ultrasonic treatment can significantly improve the distribution of nanoparticles in magnesium matrix nanocomposites and refine Mg matrix grains [23], while process parameters of ultrasonic vibration have a great influence on distribution uniformity of nanoparticles. In addition, there is still lack of a systematical research on the energy transfer between the ultrasonic horn and melt/particles, the ultrasonic propagation in melt/particles and nanoparticle distribution. Therefore, it is a challenging task to simulate SiC nanoparticle distribution in magnesium melts during ultrasonic cavitation based processing of magnesium matrix nanocomposites and to optimize the ultrasonic processing parameters. In this study, numerical simulation of the propagation of high intensity pressure waves in nanoparticles/magnesium melts has been conducted using Fluent 6.3.26 software when the high intensity ultrasonic vibration is applied to the nanoparticles/Mg melts. The objective of this work is to study the influence rules of ultrasonic power,
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
ultrasonic frequency and position of the ultrasonic vibration tool head on the SiC nanoparticle distribution in AZ91D Mg alloy melts to optimize the critical process parameters of the ultrasonic stirring by numerical simulation. The results obtained from the numerical simulation have been further validated experimentally by performing ultrasonic cavitation treatment of 1vol% nano-SiC reinforced AZ91D composites. The present research results could provide the effective theoretical guidance for obtaining excellent mechanical properties of magnesium nanocomposites.
2. Simulation of the ultrasonic cavitation based stirring treatments
2.1. Geometrical model based on high intensity ultrasonic stirring
Fig. 1 shows the schematic diagram of experimental setup used in the fabrication of SiC nanoparticle reinforced AZ91D magnesium alloy matrix composites by using high intensity ultrasonic treatment. The device consisted of a steel crucible, automatic temperature control heater, and high intensity ultrasonic transmission and gas protection components. The operating principle of the device was described as follows: first AZ91D Mg alloy was heated to melt in a preheated crucible, and next surface-modified and preheated SiC nanoparticles were added into the AZ91D melts. Then high intensity ultrasonic fields were applied to the SiC nanoparticles/Mg alloy melts to produce violent local disturbances, and finally the uniform distribution of SiC nanoparticles reinforced magnesium alloy matrix composites were obtained.
Fig. 1 and Fig. 2: (about here)
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
Since the ultrasonic vibration device had relatively large aspect ratio, its twodimensional model was built by using the Gambit software for the convenience of calculation. The model was meshed and solved by the triangular elements. In addition, the subdivision meshes were adopted at the entrance of the ultrasonic pressure wave, while the coarse grids are applied to other parts. The multi-grid approach can not only assure the simulation accuracy but also improve the calculative efficiency. Resolution of the fine and coarse mesh was 0.05mm and 0.1mm, respectively. And the final numerical model with the grid nodes of 71430 is shown in Fig. 2. In order to reduce the computational load, the geometric model of the crucible in the present study was appropriately scaled-down based on its actual geometry structure. The geometry parameters of the crucible were set to 100mm in inside diameter and 150mm in height, while the diameter of the ultrasonic probe is set to 20mm. The boundary surface composed of ha, hg and gf lines in the model represented the inner wall of the crucible, and the frame consisting of bc, cd and de lines in the model meant the part of the ultrasonic probe under the magnesium alloy melts, while line cd showed the end face of the ultrasonic probe. And ab and ef lines were the interfaces between the magnesium alloy melts in the crucible and the external protective gas. Table 1 shows the length of each side, the name and type of the boundary.
Table 1: (about here)
2.2. Establishment and solution of mathematical models
For ease of calculation, the following hypotheses were proposed in the present paper: ① the entire simulation system was adiabatic and no heat convection was considered;
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
② the magnesium alloy melt was an incompressible non-Newtonian fluid; ③ the effects of temperature variation on the density of SiC nanoparticles and magnesium alloy melts were neglected; ④ the jet stream generated by the collapse of cavitation bubbles was ignored. As linear wave propagation has been assumed and the shear stress has been neglected, the acoustic pressure can be obtained by solving the wave equation [24]: 1 1 ∂2P ∇ ∇P − 2 2 = 0 ρ ρc ∂t
(1)
where ρ is the density of the metal melt, c is the propagation velocity of the acoustic wave in melt, t is the time. In order to investigate the nanoparticle distribution in the metal melt after ultrasound processing, the mixture model [25] for two-phase flows was used. When using the mixture model with cavitation effects in FLUENT, the governing equations [26] of continuity, momentum and cavitation bubble mass fraction can be written as follows:
∂ρ ∂ + ( ρ ui ) = 0 ∂t ∂xi
(2)
∂ ( ρ ui ) ∂ ∂u ∂u ∂p ∂ + ( ρ ui u j ) = − + [( µ + µl )( k + j )] + ρ g i ∂t ∂x j ∂xi ∂x j ∂x j ∂xk
(3)
∂ ( ρw ) ∂ + (ρui w) = ∂ [(µ + µl ) ∂w ] + Re + Rc ∂t ∂x j ∂x j ∂x j
(4)
where the mixture density ρ is the function of the liquid density ρl , incompressible gas density ρg and vapor density ρ v , it is shown as below: 1
ρ
=
wv
ρv
+
wg
ρg
+
1 − wg − wv
ρl
(5)
where ρ is the mixture density, ui is the velocity at i direction, w is the mass fraction of cavitation bubbles, µ is the viscosity of the fluid, g i is the gravity component
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
at i direction, t is the time, v , g and l represent vapor state, gas state and liquid state, separately; Re and Rc are the generation ratio and compressive ratio of cavitation bubbles, respectively, and they are calculated using the growth of a single bubble based on the Rayleigh-Pleasset model [27]: d 2 R 3 dR 2 2σ + = P0 − Pv + 2 R0 dt 2 dt
ρ R
3k
R0 2σ 4η dR − − − P0 + Pv + Pm sin ωt R R dt R
(6)
where R and R0 are the instantaneous radius and initial radius of bubbles, respectively; P0 , Pv and Pm are the initial pressure outside cavitation bubbles, vapor pressure within
cavitation bubbles and acoustic pressure amplitude, respectively; σ is the surface tension; k is the polytropic exponent of the melt which is usually 3/4 and ω is the angular frequency of the acoustic wave which is given by ω = 2π f . In the present paper, the pressure-based solving method was adopted. The solving method for unsteady problems was first applied in the SiC/Mg composite melts, material property parameters and solution conditions were then set, and finally the nanoparticle distribution could be calculated on the basis of the velocity, pressure and temperature fields. Since time-domain computations were used for resolving the acoustic field, a very small time step of 1 × 10−4 s was used and the total solving time was 120s. The ultrasonic
pressure wave was applied at the pressure inlet boundary and it was expressed by the equation P = PA sin(2π ft ) . The ultrasonic wave used for simulation had a ultrasound
velocity of 4000m/s,
a ultrasound
wavelength
of 150mm, an amplitude,
PA = 2 − 10MPa , and a ultrasonic frequency, f = 20 − 40kHz . The SiC nanoparticles with a mean diameter varying from 30nm to 50nm, an average density of 3200kg/ m3 and a volume fraction of 1vol% were used as reinforcements, while the AZ91D
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
magnesium alloy was used as a matrix of composites and its property parameters are shown in Table 2 [24].
Table 2: (about here)
3. Results and discussion
3.1. Effects of ultrasonic power and frequency on SiC nanoparticle distribution
During the dispersion process of nanoparticle-agglomerates in magnesium alloy melts by high intensity ultrasonic stirring method, the ultrasonic frequency and power is a pair of critical process parameters. They determine the size and distribution of the acoustic pressure and velocity fields, while the pressure and velocity fields in turn have influence on nanoparticle distributions in magnesium alloy melts. Fig. 3a-e show the distribution of 1vol% SiC nanoparticles in Mg melts after 120s ultrasonic agitation while the ultrasonic power and frequency are in the range of 1.5 to 2.5kW and 20kHz to 40kHz, and the depth of ultrasonic probe dipped into the melts and ultrasonic processing temperature are 20mm and 900 K, respectively. The effect of different combinations of ultrasonic power and frequency on SiC nanoparticle dispersions was obvious. It can be seen from Fig. 3a and b that the frequency has an obvious effect on the distribution of nanoparticle-agglomerates whether in the radial direction away from the center of the ultrasonic horn surface at the melt/horn interface or in the axial direction away from the center of the ultrasonic horn end surface for a constant ultrasonic power of 2kW. The volume fractions of nanoparticle-agglomerates in the same location of Mg melts at the same time were
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
increasing with the increase of the ultrasonic frequency while they varied little when the frequency was increased to 30-40 kHz. However, the volume fractions of nanoparticles in the same location of Mg melts at the same time firstly decreased from 1.5kW to 2kW and then increased again at 2.5kW for a fixed frequency of 20kHz. This is because cavitation effects are enhanced with the increasing ultrasonic power and the cavitation effects will tend to be saturated after the ultrasonic power reaches a certain value. During this time, a lot of useless cavitation bubbles will appear when the ultrasonic power continue to increase and these cavitation bubbles can't completely collapse instantaneously. They just stay in resonance, burst when rising to the melt surface or form bubble screen on the vibration surface. All these will result in ultrasound attenuation and decrease of cavitation intensity [28]. Fig. 3c-e shows a comparison of the effects of different combinations of ultrasonic power and frequency on the frequency distribution of the SiC nanoparticle volume fraction. Results from the comparative analysis of Fig. 3c-e also have proved that the combination of 2kW ultrasonic power and 20kHz frequency was preferred for achieving a homogeneous distribution of SiC nanoparticles.
Fig. 3a-e: (about here)
3.2. Effects of the ultrasonic probe position on SiC nanoparticle distribution
Fig. 4a and b show the effects of different depths (25mm, 30mm and 40mm) of the ultrasonic probe into Mg melts on the distribution of 1vol% SiC nanoparticles along two special paths such as the radial direction away from the center of the ultrasonic horn surface at the melt/horn interface and the axial direction away from the center of the
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
ultrasonic horn end surface under the combination of 2kW and 20kHz at 110s. It can be seen that compared with the case of 20mm depth of the ultrasoinc probe into the melt (Fig. 3a and b), the volume fractions of SiC nanoparticles along the two directions described above were all tending to be zero when the depth of the probe in the melt was increased from 25mm to 40mm. It can be predicted that the cavitation development in the directions from the probe center to the bottom and both sides of the crucible is at the varying stages as the depth of the probe into the Mg melt increases, and this can be clearly seen from velocity distribution contours (Fig.5a-c) under the corresponding probe depths in the melt at the moment. It is obvious that when the probe depth in the melt is varied between 25mm to 40mm, the amplitude value and distribution for the probe depth of 25mm to 30mm in the melt are different from the case for the probe depth of 30mm to 40mm in the melt, indicating that the probe depth of 30mm might be a critical depth for the cavitation development and the uniform dispersion of nanoparticles.
Fig. 4a and b: (about here) Fig. 5a-c: (about here)
3.3. Effects of the ultrasonic agitation time on SiC nanoparticle distribution
Fig. 6a-e shows frequency distribution variations of 1vol% SiC nanoparticles in Mg melts with different ultrasonic agitation time under the immersed ultrasonic probe end of 30mm depth and the combination of 2kW and 20kHz while the other ultrasonic processing parameters are identical. It can be seen that the distribution of the nanoparticles at 80s was significantly improved with prolonging the ultrasonic
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
dispersion time, but it became more inhomogeneous when the ultrasonic time was extended to up to 160s. The best nanoparticle distribution uniformity was obtained at 120s.
Fig. 6a-e: (about here)
The above-mentioned analysis on the simulation results of the effects of different ultrasonic processing parameters on SiC nanoparticle distribution has shown that the distribution of SiC nanoparticles in the magnesium alloy melt is relatively homogenous under the addition of 1vol% of SiC nanoparticles to the Mg melt, the ultrasonic processing temperature of 900K, ultrasonic agitation time of 120s, the immersed ultrasonic probe end of 20-30mm depth, and the ultrasonic power of 2kW and ultrasonic frequency of 20kHz. Fig. 7a-d shows the magnitude contours of pressure, velocity and temperature fields as well as SiC nanoparticle distribution in the SiC/Mg composite slurries under the identical ultrasonic processing conditions of 30mm probe depth in the melt. It can be seen that there existed a gradual increasing pressure gradient from the sound source (Fig. 7a), a highly uneven velocity distribution (Fig.7b) and a relatively homogeneous temperature distribution in the composite slurries (Fig. 7c). Such varied three fields are favorable for the uniform distribution of reinforced SiC nanoparticles and it can be seen from Fig. 7d.
Fig. 7a-d: (about here)
3.4. Size effect of the dispersion process of nanoparticle agglomerates
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
As was mentioned above, nanoparticle-aggregates can be well dispersed in the magnesium alloy melt through the optimal ultrasonic processing parameters. In this section, further simulation on the dispersion of nanoparticle-aggregates with a larger particle diameter of 300nm in magnesium alloy melt was conducted under the conditions of the optimal ultrasonic processing parameters and thus the effect of the variation in particle size on ultrasonic dispersion was analyzed. Fig.8a-d shows the sound pressure, velocity and temperature fields and the frequency distribution of the SiC nanoparticle volume fraction at 120s, respectively. It can be seen from these figures that a similar uniform distribution of particle volume fraction can be obtained at the same time although both amplitude value and distribution of the sound pressure, velocity and temperature fields have both varied a little.
Fig. 8a-d: (about here)
The reason why increasing the size of SiC ceramic particles has a smaller effect on the uniform dispersion in the Mg melt under the optimal ultrasonic processing conditions may due to the combined effects of several factors. When the particle size increases, the contact area between the particles decreases and the number of adjacent molecules is less, resulting in the decrease of the van der Waals force between the particles. In addition, the liquid bridge can be formed between the particles and this is helpful to increase the capillary force, but the capillary force is generally much smaller than the van der Waals force. On the other hand, the number of voids and cavitation bubble nucleation will increase as the particle size increases and thus the cavitation intensity is increased.
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
4. Experimental validation
In this section, SiC nanoparticles reinforced AZ91D magnesium matrix composites were fabricated by ultrasonic cavitation based solidification method [29] and effects of ultrasonic variables on microstructure evolution of the composites were discussed. Fig. 9 shows a TEM image of AZ91D Mg alloy based nanocomposites along with selected area diffraction pattern (SADP). It can be seen from Fig. 9a that the nanometer-sized SiC particles or their clusters are well embedded in the area observed. Fig. 9b is the SADP from the marked A area in Fig. 9a, the corresponding diffraction pattern can be indexed as (111), (200), (220), and (311), and this matches well with the cubic β-SiC [30]. Fig.10 shows the effects of ultrasonic variables on microstructure formation in AZ91D magnesium matrix nanocomposites reinforced with volume fraction of 1% SiC nanoparticulates (1vol% n-SiCp/AZ91D). It can be seen that microstructures of the AZ91D matrix alloy changed significantly and SiC particles dispersion became more homogeneous with the increase of ultrasonic power and agitation time. As shown in Fig. 10a, there still existed the agglomeration of SiC nanoparticles in the Mg matrix after treated by ultrasonic vibration for 50s when the power and frequency of ultrasonic vibration are 1.5kW and 20kHz, respectively. Compared with the case of Fig. 10a, Fig. 10b has shown that the grain size of the AZ91D Mg matrix was refined and its average size was significantly smaller than that of the matrix treated by ultrasonic vibration for 50s when ultrasonic vibration time was extended to 120s with ultrasonic power and frequency remaining unchanged. Also the distribution of SiC particles became more uniform in Fig. 10b. It can be furtherly found from Fig. 10c that the grain size of the matrix alloy changed little and the best distribution of SiC particles in the matrix was obtained when the ultrasonic power was increased to 2kW with the ultrasonic time and
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
frequency remaining unchanged. It can be thus concluded that the ultrasonic power and ultrasonic time have great influence on the grain size of the matrix alloy and distribution of SiC particles based on the microstructural evolution of SiCp/AZ91D nanocomposites under different ultrasonic processing parameters shown in Fig. 10. On the one hand, the roles of the ultrasonic cavitation and acoustic streaming are strengthened with the increase of the ultrasonic power, resulting in the gradual refining of the matrix grains and brittle connected phase Mg17Al12 as well as the improved uniform dispersion of SiC particles. On the other hand, the ideal microstructure of the SiCp/AZ91D nanocomposite with an evenly particle distribution and grain refinement of matrix alloy can be obtained under the conditions of larger ultrasonic power and suitable ultrasonic vibration time. This is because that if the SiCp/AZ91D nanocomposite is subjected to ultrasonic vibration for fairly short processing times under the given ultrasonic power and frequency conditions, there's not enough time for the ultrasonic cavitation effect to give the full play to the particles dispersion, leading to the agglomeration of SiC particles; while if the composite is subjected to ultrasonic vibration for fairly prolonged processing times, the mechanical disturbance generated by high-intensity ultrasound can not work and the grain refinement effect of the matrix alloy is not obvious too since the matrix alloy has tended to be solidified.
Fig. 9a and b: (about here) Fig. 10a-c: (about here)
Fig. 11 shows the room-temperature mechanical properties of AZ91D magnesium alloy without ultrasonic processing and 1vol% SiCp/AZ91D magnesium matrix nanocomposites fabricated by the ultrasonic cavitation based solidification technique
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
with different ultrasonic parameters. From Fig.11, the nanosized SiC particles reinforced AZ91D magnesium matrix composite has shown an improvement in both 0.2% yield and ultimate tensile strengths as well as the elongation rate when compared to AZ91D magnesium alloy because of the addition of SiC nanoparticles into the Mg melt and suitable combinations of ultrasonic processing parameters. The significant improvement in the comprehensive mechanical properties of the SiCp/AZ91D magnesium matrix nanocomposites can be attributed to the grain refinement of the matrix alloy, the homogeneous distribution of SiC nanoparticles and less connected β phase (Mg17Al12)[31], as well as the increased interfacial bonding strength between the reinforcing particle and the matrix. Fractographs taken from the tensile fracture surfaces of
AZ91D
magnesium
alloy
and
1vol%
SiCp/AZ91D
magnesium
matrix
nanocomposites are shown in Fig.12. As shown in Fig. 12a, fracture surface of AZ91D Mg samples indicated the presence of cleavage steps and microscopically rough features. Different from the brittle fracture of AZ91D magnesium sample, the fracture surfaces of SiCp/AZ91D magnesium matrix nanocomposite samples in Fig.12b and c have revealed the mixed mode failure showing more evidences of matrix plastic deformation. Regions showing dimple-like ductile features were also observed, particularly in the SiCp/AZ91D magnesium matrix nanocomposite with uniform distribution of reinforcing SiC particles shown in Fig.12c. The mixed fracture behaviour of the SiCp/AZ91D magnesium matrix nanocomposites is largely due to the presence of clustered SiC particles and brittle eutectic phase Mg17Al12, particle debonding and localized microvoid coalescence as well as grain refinement in the matrix alloy.
Fig. 11: (about here) Fig. 12a-c: (about here)
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
5. Conclusions
The optimized ultrasonic processing parameters are determined by the numerical simulation of ultrasonic cavitation based mixing and dispersing 1vol% SiC nanoparticles in AZ91D Mg melts when SiC particle size in the agglomerated SiCnanoparticles is in the range of 30-300nm in diameter. The combination of higher power and lower frequency has beneficial effects on uniform distributions of the pressure, velocity and temperature fields. The higher pressure and velocity fields with a relatively uniform distribution are obtained and thus SiC nanoparticles can be well-dispersed in the melt when the ultrasonic power, the ultrasonic frequency, the depth of ultrasonic probe dipped into the melt and ultrasonic agitation are 2kW, 20kHz, 20-30mm and 120s, respectively. Experimental results show that the SiCp/AZ91D magnesium matrix nanocomposites with improved mechanical properties can be fabricated by using the optimized ultrasonic processing parameters. This can be attributed to the combined effects of several factors, in which the uniform dispersion of SiC nanoparticles in the Mg melt is dominated by the ultrasonic cavitation while the grain refinement of Mg matrix composites can be achieved by the cavitation and acoustic streaming due to the uniform addition of SiC nanoparticles as grain refiners and dendrite fragmentation of Mg matrix under the ultrasonic processing conditions in the present paper. In addition, fractographs of the nanocomposites have revealed changes in fracture behavior from cleavage in the case of AZ91D magnesium alloy to mixed mode of fracture as a result of the presence of SiC nanoparticulates and the dominant effect of ultrasonic cavitation.
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
Acknowledgments
The authors gratefully acknowledge the financial supports from the National Nature Science Foundation of China (No. 11272072) and the Special Fund of State Key Laboratory of Structural Analysis for Industrial Equipment.
References
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by ultrasonic dispersion and their structure property relationship, Ultrason. Sonochem. 18 (2011) 120-126. [16] G. Cao, H. Konishi, X. Li, Mechanical properties and microstructure of SiCreinforced Mg-(2, 4) Al-1Si nanocomposites fabricated by ultrasonic cavitation based solidification processing, Mater. Sci. Eng. A 486 (2008) 357-362. [17] X.J. Wang, N.Z. Wang, L.Y. Wang, Processing, microstructure and mechanical properties of micro-SiC particles reinforced magnesium matrix composites fabricated by stir casting assisted by ultrasonic treatment processing, Mater. Des. 57 (2014) 638-645. [18] A. Erman, J. Groza, X.C. Li, H. Choi, G.P. Cao, Nanoparticle effects in cast Mg-1 wt% SiC nano-composites, Mater. Sci. Eng. A 558 (2012) 39-43. [19] G.I. Eskin, D.G. Eskin, Production of natural and synthesized aluminum-based composite materials with the aid of ultrasonic (cavitation) treatment of the melt, Ultrason. Sonochem. 10 (2003) 297-301. [20] P. Padhi, B.N. Dash, S.K. Kar, Process modeling of deagglomeration of ceramic nanoparticles in liquid metal during synthesis of nanocomposites, Journal of Nanotechnology 2011 (2011) Article ID 734013. [21] Z.W. Shao, Q.C. Le, J.Z. Cui, Z.Q. Zhang, Numerical simulation of standing waves for ultrasonic purification of magnesium alloy melt, Trans. Nonferrous Met. Soc. China 20 (2010) s382-387. [22] L. Nastac, Mathematical modeling of the solidification structure evolution in the presence of ultrasonic stirring, Metall. Mater. Trans. B 31 (6) (2010) 2818-2833. [23] X. Liu, Y. Osawa, S. Takamori, T. Mukai, Grain refinement of AZ91 alloy by introducing ultrasonic vibration during solidification, Mater. Lett. 62 (17) (2008)
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Figure and Table Captions
Fig. 1. Schematic of high intensity ultrasonic vibration device used in this study. Fig. 2. Meshing of ultrasonic stirring. Fig. 3. Effects of different combinations of ultrasonic power and frequency on SiC nanoparticle dispersions: (a) volume fraction variations in the radial direction, (b) volume fraction variations in the axial direction, (c) frequency distribution of particle volume fraction under the conditions of 1.5kW and 20kHz, (d) frequency distribution of particle volume fraction under the conditions of 2kW and 20kHz and (e) frequency distribution of particle volume fraction under the conditions of 2.5kW and 20kHz. Fig. 4. Effects of the ultrasonic probe position on the volume fraction distribution of SiC nanoparticles: (a) the radial distribution and (b) the axial distribution. Fig. 5. Velocity contours when the ultrasonic probe is immersed in SiC/Mg melts at different depths of (a) 25mm, (b) 30mm and (c) 40mm. Fig. 6. Effects of the ultrasonic agitation time on frequency distribution of SiC nanoparticle volume fraction: (a) 10s, (b) 50s, (c) 80s, (d) 120s and (e) 160s. Fig. 7. Contours of (a) pressure field, (b) velocity field, (c) temperature field and (d) SiC nanoparticle distribution in SiC/Mg composite melts by ultrasound. Fig. 8. Contours of (a) pressure field, (b) velocity field, (c) temperature field and (d) frequency distribution of SiC nanoparticle-aggregates with an average particle diameter of 300 nm. Fig. 9. TEM image and SADP of the AZ91D Mg alloy based nanocomposite reinforced with SiC nanoparticles: (a) TEM image of the composite; (b) SADP taken from the marked A area in Fig. 9a.
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
Fig.10. Microstructures of SiCp/AZ91D nanocomposites under the conditions of 20kHz ultrasonic frequency and other varied ultrasonic processing parameters: (a) 1.5kW, 50s; (b) 1.5kW, 120s; and (c) 2kW, 120s. Fig.11. Tensile properties of AZ91D Mg alloy and SiCp/AZ91D Mg matrix nanocomposites treated with different combinations of ultrasonic power and time of 1.5kW, 50s and 2kW, 120s at 20kHz. Fig. 12. SEM fractographs of (a) AZ91D magnesium alloy and 1vol% SiCp/ AZ91D magnesium matrix nanocomposite treated with different combinations of ultrasonic power and time of (b) 1.5kW, 50s and (c) 2kW, 120s at 20kHz. Table 1 Calculation model and boundary setting. Table 2 Property parameters of magnesium alloy.
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
Table 1 Calculation model and boundary setting. Boundary line
Length/mm
Boundary conditions
Boundary type
ha
150
wall1
wall
ab
40
out
pressure-outlet
bc
20
deform1
wall
cd
20
inlet
pressure-inlet
de
20
deform2
wall
ef
40
out
pressure-outlet
fg
150
wall2
wall
gh
100
wall3
wall
Table 2 Property parameters of magnesium alloy. Density ρ(kg/m3)
Surface tension coefficient σ(N/m)
Initial pressure outside cavitation bubbles P0(Pa)
1820
0.564
1.013 × 105
Vapor pressure within cavitation bubbles Pv(Pa)
1000
24
Initial radius of cavitation bubbles R (µm)
1.0
Fluid viscosity
µ (Pa·s)
1.12 × 10-3
Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
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Study on ultrasonic cavitation based dispersion of nanoparticles in Mg melts
Highlights • A two-dimensional model of high-intensity ultrasonic processing is established. • The model is coupled with the pressure, velocity and temperature fields. • SiC nanoparticles distribution in Mg melt under varied parameters is simulated. • The optimized high-intensity ultrasonic processing parameters are obtained. • The results obtained from numerical simulation have been verified by experiments.
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