Numerical simulation of macrostructure formation in centrifugal casting ...
INSTITUTE OF PHYSICS PUBLISHING
MODELLING AND SIMULATION IN MATERIALS SCIENCE AND ENGINEERING
Modelling Simul. Mater. Sci. Eng. 11 (2003) 651–674
PII: S0965-0393(03)63720-4
Numerical simulation of macrostructure formation in centrifugal casting of particle reinforced metal matrix composites. Part 2: simulations and practical applications Ludmil Drenchev1 , Jerzy Sobczak2 , Savko Malinov3 and Wei Sha3 1 2 3
Institute of Metal Science, 67 Shipchensky Prohod St., 1574 Sofia, Bulgaria Foundry Research Institute, 73 Zakopianska St., 30-418 Krakow, Poland Queen’s University of Belfast, School of Civil Engineering, Belfast BT7 1NN, UK
E-mail: [email protected], [email protected] and [email protected]
Received 12 March 2003, in final form 18 May 2003 Published 16 June 2003 Online at stacks.iop.org/MSMSE/11/651 Abstract Centrifugal casting is a widely applied method for production of graded metal matrix composites (MMCs). This paper discusses some aspects of the macrostructure management of centrifugally cast particle reinforced MMCs. A specially developed software product is applied for the analysis of many technological regimes for casting cylindrical sleeves of composite alloy A356 and SiC particles as reinforcing phase. A number of technological recommendations are made. Castings of aluminium alloy A356 and copper alloy C90300 with Ni coated graphite particles of diameter 100 µm introduced as reinforcing phase are discussed. Some typical and unusual casting structures are analysed using the specially developed software product. This software is based on the mathematical model described in detail in part 1.
Nomenclature A, B, C1 , C2 c Cm , Ceff CD c, cm , ceff d, d0 E = (Ex , Ey , Ez ) EG = (EGx , EGy , EGz ) ER FR 0965-0393/03/040651+24$30.00
constants heat capacity (J m−3 K−1 ) shape coefficient specific heat (J kg−1 K−1 ) thickness of solidified layer (m) mass force (N) gravity mass force (N) rotational component of the mass force (N) centrifugal force (N) © 2003 IOP Publishing Ltd
Printed in the UK
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FG FS FB FC fL g H h0 , hF i, j, k k, K L m n N, Nk N0 P = P (x, y, z) p p0 R1 R2 r r r0 ri S T TL TS T0 TP t t U UG UR V Vf v = (vx , vy , vz ) v0 v0 x = (x, y, z) x0 x y z
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force due to gravity (N) drag force (N) buoyant force (N) Coriolis force (N) relative mass fraction of liquid in two-phase zone gravity acceleration (m s−2 ) z-coordinate of the highest level of liquid metal in a rotating cup (m) heat exchange coefficient (W m−2 K−1 ) unit vectors over axes x, y and z, respectively numbers latent heat (J kg−1 ) particle mass (kg) normal unit vector particle concentration (vol%) initial particle concentration (vol%) function pressure (Pa) pressure on the inner surface of the liquid metal inner casting radius (m) outer casting radius (m) radius vector coordinate (m) inner radius of the liquid metal in a rotating cup (m) initial particle position (m) surface (m2 ) temperature (K) liquidus temperature of base alloy (K) solidus temperature of base alloy (K) initial mould temperature (K) pouring temperature (K) time (s) time increment (s) potential function potential function of gravity force potential function of rotational component of mass force volume (m3 ) volume fraction of particles (%) particle velocity (m s−1 ) initial particle velocity (m s−1 ) initial radial velocity of particle (m s−1 ) coordinate vector initial particle position coordinate (m) coordinate (m) coordinate (m)
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Greek symbols α, α1 , α2 , α3 , αB , αT ε λ λe λm , λC µ, µeff ρ ρL ρP ρm , k ω ω
heat exchange coefficients (W m−2 K−1 ) particle radius (m) constant effective thermal conductivity of casting (W m−1 K−1 ) thermal conductivity (W m−1 K−1 ) viscosity (Pa s) effective density of casting (kg m−3 ) density of liquid metal (kg m−3 ) density of single particle (kg m−3 ) mould density (kg m−3 ) cylindrical areas of casting vector of angular velocity (s−1 ) angular velocity (s−1 )
1. Introduction Sometimes the macrostructure of centrifugally cast metal matrix composites (MMCs) looks unusual, strange and difficult to explain in the framework of the conventional models. Here, such cast parts will be an object of consideration. Castings of aluminium alloy A356 (see table 1) and copper alloy C90300 (tin bronze, Sn: 8%, Zn: 4%, Ni, Pb, Sb, Fe) with Ni coated graphite particles of diameter 100 and 5 µm introduced as reinforcing phase will be discussed. Many castings of a cylindrical shape of 57 mm inner diameter, 92 mm outer diameter and 100 mm height were produced and investigated. Rotation speed was in a range of 800–1900 rpm. The heat exchange coefficient between the casting and the mould is calculated by relation (45), part 1. The values of h0 and hF vary depending on mould coating. 2. General relations obtained by the model To verify the model and to investigate the relations between the processing parameters of centrifugal casting and particle distribution many numerical experiments are carried out. Casting of cylindrical sleeves of composite alloy A356 (see table 1) and SiC particles as reinforcing phase is considered. Thermomechanical properties of the alloy and dimensions of mould and casting are listed in table 2. Sets of particular values of the parameters, related to the figures, are given in table 3. All analyses of particle distribution and structures given below are performed using a specially developed software product on the basis of the mathematical model presented in part 1. All numerical experiments are carried out with time of filling 1 s (pouring velocity 0.75 l s−1 ). It is assumed that the segregation of particles proceeds up to a maximal volume fraction equal to 52% for granular particles [1]. Table 1. Composition of A356 aluminium matrix (wt%). Si
Mg
Mn
Cu
Fe
Ti
Al
6.5–7.5
0.2–0.45
0.35
0.25
0.60
0.25
balance
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Parameter
Value and dimension
Latent heat Specific heat for base alloy Thermal conductivity for base alloy Density of base alloy
3.86 × 105
870–1180 J kg−1 K−1 73–151 W m−1 K−1
Viscosity of liquid metal Solidus temperature for base alloy Liquidus temperature for base alloy Heat exchange coefficient on inner casting surface Inner casting radius Inner mould radius
Parameter
Value and dimension
Specific heat for steel Thermal conductivity for steel Density of steel
452 J kg−1 K−1 76 W m−1 K−1
Specific heat for SiC Thermal conductivity for SiC Density of SiC
630 J kg−1 K−1 0.32 W m−1 K−1
J kg−1
2380–2700 kg m−3 (liquid–solid) (1.5–2.5) × 10−3 Pa s−1 580 ˚C 620 ˚C 60 W m−2 K−1 0.025 m 0.055 m
Heat exchange coefficient on outer mould surface Outer mould radius Length
7870 kg m−3
3230 kg m−3 130 W m−2 K−1 0.135 m 0.1 m
Table 3. Technological parameters for centrifugal casting at experiments which are shown in figures.
Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11
Initial mould temperature (˚C)
Pouring temperature TP (˚C)
Rotation speed ω (rpm)
Particle radius ε (µm)
Particle density ρP (kg m−3 )
h0 / h F (W m−2 ˚C−1 )
Initial particle concentration (vol%)
200 200 200 Varied 200 200 200 200 200 200 200
700 700 Varied 700 700 700 700 700 650 650 720
Varied 1800 1800 1200 1200 1200 1800 1200 1800 1800 1550
18 Varied 18 18 18 18 18 18 18 18 18
3230 3230 3230 3230 3230 3230 Varied 3230 3230 3230 3230
21 000/4200 21 000/4200 21 000/4200 21 000 /4200 21 000 /4200 Varied 21 000 /4200 21 000 /4200 21 000 /4200 21 000 /4200 21 000 /4200
15 15 15 15 Varied 30 15 15 15 15 8.7
Figure 1 shows the correlation between the rotation speed and particle distribution. Colour schemes here and below are the output of the software and they depict particle distribution or, temperature field in altitudinal casting cross section. The dashed line to the left on the screen indicates the axis of rotation and the right placed colour scale gives values of the parameter monitored. As the rotation speed increases, the thickness of the particle rich region at the outer casting surface decreases. In a thin layer on the casting outer surface the volume fraction of particles is equal to the initial value because of the rapid solidification of this volume. The maximal value of the volume fraction at the outer periphery increases with increasing speed but the minimal value near the particle free region slowly decreases. From the experiment discussed in [2] it was observed that the volume per cent of particles, both at the periphery and near the particle free region, increases with increasing speed. In that experiment the composite contains graphite particles, which have a lower density with respect to the liquid
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(a)
(b)
(c)
Figure 1. Correlation between rotation speed and final distribution of SiC particles. (a) Final distribution in middle cross section; (b) and (c) two-dimensional diagrams of final distribution.
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Figure 2. Correlation between particle size and final distribution of SiC particles in the middle cross section. 1—ε = 7 µm, 2—ε = 18 µm, 3—ε = 39 µm.
alloy and particles move to the inner casting surface, in the same direction as the moving solidification front. In the case considered here, SiC particles move against the solidification front. The effect of the particle size on the final distribution is shown in figure 2. It is evident from the figure that as the radius of particles increases, the thickness of the particle free region also increases. There is a critical radius for which all particles are accumulated in a layer at the outer casting surface. This layer has the maximum possible volume per cent of SiC (in our case 52%). Further increase of particle radius does not change the final distribution. Figures 3 and 4 depict how pouring temperature and initial mould temperature influence segregation. The higher values of these temperatures result in an enlargement of the size of the particle free region. Figure 5 shows the final particle distribution as a function of initial concentration. The initial concentration influences only details of the final volume fraction but the shape of the distribution remains the same. Figure 6 shows the correlation between the heat exchange coefficient and the particle distribution. The highest coefficient (see table 3) corresponds to a graphite coating, the middle to a boron nitride in water coating and the smallest to a fibrefrax coating. A higher heat exchange coefficient on the casting–mould interface results in a more uniform particle distribution. The increase of particle density, figure 7, has almost the same effect as the increase of rotation speed and radius of particles (see figures 1 and 2). Figures 8 and 9 show changes in particle distribution during solidification. Analysing the curves, one can see that after 5 s the solidification front moved from 55 to 48 mm, after 10 s to 43 mm and after 25 s to 32 mm. The comparison between the final distribution in the middle cross section and in a cross section at the end of cylindrical casting is shown in figure 10. There is a difference owing to the different thermal conditions in these two regions. Similar results can be easily seen on almost all colour schemes given. A comparison of the final particle distribution calculated by the offered mathematical model and the experimental results in [3] is shown in figure 11. Here the inner and outer radii of the casting are 45 mm and 60 mm, respectively, and the outer mould radius is 125 mm. Other technological parameters are as in table 3. The agreement between experimental and numerical results is acceptable.
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p
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p
p
(b)
(c)
Figure 3. Correlation between pouring temperature Tp and final distribution of SiC particles. (a) Final distribution in the middle cross section; (b) and (c) two-dimensional diagrams of the final distribution.
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(a)
0
0
0
(b)
T0
(c)
T0 Figure 4. Correlation between the initial mould temperature and the final distribution of SiC particles. (a) Final distribution in the middle cross section; (b) and (c) two-dimensional diagrams of the final distribution.
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(a)
(b)
(c)
Figure 5. Correlation between the initial concentration N0 and the final distribution of particles: (a) in the middle cross section; (b) and (c) two-dimensional diagrams of the final distribution.
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(a)
(b)
(c)
Figure 6. Correlation between the heat exchange coefficient (see equation (45), part 1) and the final distribution of SiC particles. (a) Distribution in the middle cross section; (b) and (c) twodimensional diagrams of the final distribution.
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(a)
(b)
(c)
Figure 7. Correlation between the particle density ρp and the final particle distribution (density of liquid ρL = 2390 kg m−3 ). (a) Distribution in the middle cross section; (b) and (c) two-dimensional diagrams of the final distribution.
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Figure 8. Distribution in the middle cross-section of SiC particles during solidification: (1) after 5 s, (2) after 10 s, (3) after 15 s, (4) after 20 s, (5) after 25 s (final distribution).
3. MMCs of A356 and graphite particles Below MMCs of aluminium alloy A356 matrix and Ni coated graphite particles of diameter 100 µm as reinforcing phase are considered. Because of the lower density of graphite, the particles move to the inner casting region. Three kinds of casting structures are analysed. 3.1. Casting A1 Usually, longer solidification time leads to a larger particle free zone in the casting. In figure 12 a cross section of a conventional MMC casting is shown. The initial concentration of particles is 18 vol%. Other parameters are as follows: rotation speed 1200 rpm, pouring temperature 750 ˚C, initial mould temperature 200 ˚C, filling time 3 s. Heat exchange coefficients h0 = 3000 W m−2 ˚C−1 and hF = 1420 W m−2 ˚C−1 are used. The heat exchange coefficients on casting surfaces z = 0 and z = H (see section 3.2 in part 1) are αB = 120 W m−2 K−1 , αT = 120 W m−2 K −1 , respectively. It is assumed that the maximal particle concentration in the liquid alloy is 48 vol%. The temperature field during solidification, the particle distribution and the movement of the solidification front as a function of time are simulated using the model. The final particle distribution in longitudinal section is given in figure 13. Here and on all screens from the software product the dashed line on the left marks the axis of rotation, and the colour scale gives values of different physical fields in the cross section. Comparison between figures 12 and 13 indicates a good agreement between numerical simulation and the experimental result. 3.2. Casting A2 A ring from the middle area of a casting with unusual structure is shown in figure 14. This case consists of a thin layer of maximal particle concentration, a large particle free region and shrinkage cavities between them. Metal matrix, reinforcing phase and all parameters are as before but initial particle concentration is 5 vol%. Another essential difference is in the heat exchange coefficients on casting surfaces z = 0 and z = H . In this case they are αB = 450 W m−2 K−1 and αT = 450 W m−2 K−1 , approximately four times larger. A thinner coating layer can give these larger values. It caused greater axial heat transfer. Figure 15 shows
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(a)
(b)
Figure 9. Two-dimensional diagrams of SiC particle distribution during solidification.
the arrangement of solid (blue), liquid (yellow) and two-phase (red) zones at time = 13 s. A hot spot formed in casting can be seen. Then, because of continuous cooling, shrinkage and insufficient feeding in the hot spot area a gas gap appears, figure 16. It is easier for this shrinkage defect to form at the boundary between particle free and particle rich zones because the particles have formed a non-plastic framework at the inner part of the casting where the temperature is lower. If the axial heat transfer is not so high and casting cooling runs predominantly by radial heat flow as in the previous case, such an effect will not happen.
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(c)
(d)
Figure 9. (Continued)
3.3. Casting A3 The next casting structure that is an object of our interest is given in figure 17. There are a lot of pores in the particle rich region, the sizes of which increase with the radius. In this case the particle concentration originally was 18 vol%, greater than for casting A2. Such a structure can be formed when the technological parameters are as for casting A2. Greater axial heat flow facilitates formation of a solid framework at the inner casting surface. Because of the
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(e)
(f)
Figure 9. (Continued)
greater initial content of graphite, the particle concentration decreases slowly from a maximal value on the inner surface to zero in the middle zone of the casting. The particle segregation in a centrifugal casting resembles the process of sedimentation. During this process there are four typical zones [4]: a particle free zone, a zone with the initial concentration, a transient zone where the concentration increases from initial to maximal and a zone with maximal concentration. The size of these zones changes during the segregation. In the casting discussed here, the particles and the solidification front move in the same
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Figure 10. Final particle distribution in different cross sections of the casting. 1—Z = 100 mm, 2—Z = 50 mm.
Figure 11. Comparison of particle distribution obtained theoretically (1) and experimentally (2) in [3].
Figure 12. Particle distribution in a casting fabricated using nominal technological parameters.
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Figure 13. Particle distribution according to numerical simulation.
Figure 14. Casting with a gas cavity.
direction: from the outer surface to the inner surface. The solidification front reaches the zone with initial concentration and the transient zone. The only difference in technological parameters between casting A2 and casting A3 was the initial concentration. In the case of casting A2 the particles succeeded in reaching maximal concentration and formed a non-plastic layer before the solidification front reached the particle rich zone. For that reason, shrinkage defects appear between free and rich zones. In the case of casting A3, the presence of a greater number of particles leads to the hindering of segregation and the solidification front reaches the particle rich zone before the establishment of maximal concentration in it. Because of the nonplastic framework formed and because of shrinkage, the solidifying metal ‘sucks up’ the liquid
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Figure 15. Hot spot formed at 13 s.
Gas cavity
Figure 16. Gas cavity according the numerical simulation.
between the graphite clusters and forms pores. These pores are larger in the regions where particle concentration is lower, i.e. the sizes of cavities increase with the radius. Here, the same amount of shrinkage defects as in casting A2 is distributed not in the free/rich boundary but in the rich zone.
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Figure 17. A casting with a porous particle rich zone.
Figure 18. Casting with intermediate region in the particle rich zone.
4. MMC of C90300 and graphite particles The density of alloy C90300 is approximately three times greater than the density of alloy A356. Particles of 5 µm diameter were used as the reinforcing phase. 4.1. Casting C1 An actual MMC casting of the copper alloy matrix is shown in figure 18. This casting has a free zone at the outer part of casting, a graded zone (with non-constant particle distribution)
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Figure 19. Numerically simulated final particle distribution.
at the central casting region and a zone of maximal graphite content at the inner periphery. The technological parameters are as follows: rotation speed 1800 rpm, pouring temperature 1200 ˚C, initial mould temperature 400 ˚C, initial particle concentration 13 vol%. Here, heat transfer parameters ensured the solidification front moved faster than the outer boundary of the particle rich region. For this reason an area with non-uniform distribution is present in the particle rich zone. The heat exchange coefficients between the casting and the mould are estimated as: h0 = 4000 W m−2 K−1 and hF = 1420 W m−2 K−1 . Figure 19 shows the final particle distribution, simulated by the software product developed on the basis of the model discussed in part 1 for the above technological parameters. 4.2. Casting C2 An atypical casting structure is given in figure 20. In this casting, the particle rich zone was stratified. The technological parameters are as follows: rotation speed 1200 rpm, pouring temperature 1030 ˚C, initial mould temperature (according to measurements) 350 ˚C, initial particle concentration 13 vol%, pouring time 4 s. The heat exchange coefficients between casting and mould were estimated as h0 = 740 W m−2 K−1 and hF = 500 W m−2 K−1 . When the pouring temperature is high enough, the melt stays liquid longer after filling, which provides better adhesion to the mould as in the case of casting C1. Here, the lower values of heat exchange coefficients àre due to the absence of good adhesion. The reason for this is low pouring temperature. In fact, the metal was in the two-phase zone during the mould filling and the solidification started the moment it reached the mould surface. Formation of good thermal contact was hindered. This structure formation process is simulated numerically. Because of the low pouring temperature (approximately equal to the liquidus temperature), solidification starts at the beginning of mould filling. A particle rich layer with the initial concentration is formed in the outer part of the casting. Then, because of decreasing heat flow between the casting and
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Figure 20. Casting with stratified particle rich zone.
the mould, movement of the solidification front becomes slower than the particle movement and a particle free zone appears in the middle section of the casting. All this can be seen in figure 21, which shows the simulated particle distribution 14 s after filling. The next particle rich zone is formed in the inner casting area where the particle concentration is greater than the initial value. Figure 22 shows the final particle distribution formed at 56 s when melt solidification is finished. Comparison of the modelling result and actual casting structure (see figure 20) shows good accuracy of the numerical simulation. The two particle rich zones are not well formed in the actual casting (figure 20). This is because of turbulent filling of the mould cavity with liquid without overheating and actually non-uniform cooling of the outer casting surface. Our model does not consider turbulent flow at the mould filling and considers uniform cooling of the outer casting surface. For these reasons stratified particle rich zones obtained by numerical simulation are well shaped. 4.3. Casting C3 A graded structure is typical for centrifugal casting of particle-reinforced composites. The potential for obtaining such structures is one of the main features of this technology. However, a uniform distribution can also be produced for a special set of main technological parameters. Such an atypical casting is shown in figure 23. The main parameters are as follows: rotation speed 800 rpm, pouring temperature 1020 ˚C, initial mould temperature 300 ˚C, initial particle concentration 6.8 vol%. A special parameter indicating the condition for particle non-movement effect in centrifugal casting is introduced in [5]: µeff CH = 1 (1) µA Here adapted viscosity (the effective viscosity of slurry, see section 3.1.4, part 1) is calculated by µeff = µ(1 + 2.5Vf + 10.05Vf2 )
(2)
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Figure 21. Particle distribution in the Cu–Gr system 14 s after filling. The solidification is not completed.
Figure 22. Particle distribution in the Cu–Gr system 56 s after filling. The solidification is completed.
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Figure 23. Casting with uniform particle distribution.
µ is the viscosity of liquid metal matrix, and Vf is particle volume fraction. The parameter µA reflects the influence of forces (centrifugal and/or buoyancy), which act in a direction opposite to the drag force. This is named [5] attached viscosity and is defined as follows: (3) µA = ωε 2 ρP |ρP − ρL | where ω is rotation speed, ε is particle radius, ρP and ρL are particle and liquid density, respectively. The relation CH 1 (i.e. µeff µA )
(4)
means that the drag force has a great value compared to other forces determining the particle movement and because of this the particles will not move in fact (particle velocity will be extremely small). In this case, because of the relatively short period of time for solidification, the particle distribution is close to homogeneous. Usually CH < 2 × 102 but for the technological regime related to the casting in figure 23 the parameter CH = 2686. 5. Conclusions The structure formation in centrifugally cast MMCs is a complicated process, defined by a number of physical phenomena. It depends on many factors and technological parameters. Small deviations in processing parameters can cause essential differences in casting structure. The application of a comprehensive and accurate software product for numerical simulation of the casting process provides a large potential for understanding the process, reduces the time for trials and is a powerful tool for increasing effectiveness. Using the mathematical model described in part 1 a software product is developed. Many numerical experiments, which are carried out applying this software, indicate that the volume fraction of the reinforcing phase at different zones of casting is a strong function of rotation speed and particle size. Initial mould temperature and pouring rate have less significant influence on the final distribution. Thermal management is a very essential tool for controlling the casting macrostructure. Choosing different values for the heat exchange coefficient (by means of mould coating), particle size, rotation speed and pouring time, the final particle distribution can be controlled in a wide range. A very good correlation between experimental results and model simulations for a variety of cases is demonstrated. The model can be used for optimization of technological regimes of casting production.
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Acknowledgment Dr Sha’s contribution to this work is sponsored under the Royal Academy of Engineering’s Global Research Award Scheme. References [1] [2] [3] [4] [5]
Liu Q, Jiao Y, Yang Y and Hu Z 1996 Metall. Mater. Trans. B 27 1025–9 Kang C G, Rohatgi P K, Narendranath C and Cole G 1994 ISIJ Int. 34 247–54 Lajoye L and Suery M 1988 Int. Symp. on Advances in Cast Reinforced Metal Composites Drenchev L, Sobczak J and Sobczak N 2002 Colloids and Surfaces 197 A203–11 Drenchev L and Sobczak J 2001 Trans. JWRI 30 437–42
MODELLING AND SIMULATION IN MATERIALS SCIENCE AND ENGINEERING
Modelling Simul. Mater. Sci. Eng. 11 (2003) 651–674
PII: S0965-0393(03)63720-4
Numerical simulation of macrostructure formation in centrifugal casting of particle reinforced metal matrix composites. Part 2: simulations and practical applications Ludmil Drenchev1 , Jerzy Sobczak2 , Savko Malinov3 and Wei Sha3 1 2 3
Institute of Metal Science, 67 Shipchensky Prohod St., 1574 Sofia, Bulgaria Foundry Research Institute, 73 Zakopianska St., 30-418 Krakow, Poland Queen’s University of Belfast, School of Civil Engineering, Belfast BT7 1NN, UK
E-mail: [email protected], [email protected] and [email protected]
Received 12 March 2003, in final form 18 May 2003 Published 16 June 2003 Online at stacks.iop.org/MSMSE/11/651 Abstract Centrifugal casting is a widely applied method for production of graded metal matrix composites (MMCs). This paper discusses some aspects of the macrostructure management of centrifugally cast particle reinforced MMCs. A specially developed software product is applied for the analysis of many technological regimes for casting cylindrical sleeves of composite alloy A356 and SiC particles as reinforcing phase. A number of technological recommendations are made. Castings of aluminium alloy A356 and copper alloy C90300 with Ni coated graphite particles of diameter 100 µm introduced as reinforcing phase are discussed. Some typical and unusual casting structures are analysed using the specially developed software product. This software is based on the mathematical model described in detail in part 1.
Nomenclature A, B, C1 , C2 c Cm , Ceff CD c, cm , ceff d, d0 E = (Ex , Ey , Ez ) EG = (EGx , EGy , EGz ) ER FR 0965-0393/03/040651+24$30.00
constants heat capacity (J m−3 K−1 ) shape coefficient specific heat (J kg−1 K−1 ) thickness of solidified layer (m) mass force (N) gravity mass force (N) rotational component of the mass force (N) centrifugal force (N) © 2003 IOP Publishing Ltd
Printed in the UK
651
652
FG FS FB FC fL g H h0 , hF i, j, k k, K L m n N, Nk N0 P = P (x, y, z) p p0 R1 R2 r r r0 ri S T TL TS T0 TP t t U UG UR V Vf v = (vx , vy , vz ) v0 v0 x = (x, y, z) x0 x y z
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force due to gravity (N) drag force (N) buoyant force (N) Coriolis force (N) relative mass fraction of liquid in two-phase zone gravity acceleration (m s−2 ) z-coordinate of the highest level of liquid metal in a rotating cup (m) heat exchange coefficient (W m−2 K−1 ) unit vectors over axes x, y and z, respectively numbers latent heat (J kg−1 ) particle mass (kg) normal unit vector particle concentration (vol%) initial particle concentration (vol%) function pressure (Pa) pressure on the inner surface of the liquid metal inner casting radius (m) outer casting radius (m) radius vector coordinate (m) inner radius of the liquid metal in a rotating cup (m) initial particle position (m) surface (m2 ) temperature (K) liquidus temperature of base alloy (K) solidus temperature of base alloy (K) initial mould temperature (K) pouring temperature (K) time (s) time increment (s) potential function potential function of gravity force potential function of rotational component of mass force volume (m3 ) volume fraction of particles (%) particle velocity (m s−1 ) initial particle velocity (m s−1 ) initial radial velocity of particle (m s−1 ) coordinate vector initial particle position coordinate (m) coordinate (m) coordinate (m)
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Greek symbols α, α1 , α2 , α3 , αB , αT ε λ λe λm , λC µ, µeff ρ ρL ρP ρm , k ω ω
heat exchange coefficients (W m−2 K−1 ) particle radius (m) constant effective thermal conductivity of casting (W m−1 K−1 ) thermal conductivity (W m−1 K−1 ) viscosity (Pa s) effective density of casting (kg m−3 ) density of liquid metal (kg m−3 ) density of single particle (kg m−3 ) mould density (kg m−3 ) cylindrical areas of casting vector of angular velocity (s−1 ) angular velocity (s−1 )
1. Introduction Sometimes the macrostructure of centrifugally cast metal matrix composites (MMCs) looks unusual, strange and difficult to explain in the framework of the conventional models. Here, such cast parts will be an object of consideration. Castings of aluminium alloy A356 (see table 1) and copper alloy C90300 (tin bronze, Sn: 8%, Zn: 4%, Ni, Pb, Sb, Fe) with Ni coated graphite particles of diameter 100 and 5 µm introduced as reinforcing phase will be discussed. Many castings of a cylindrical shape of 57 mm inner diameter, 92 mm outer diameter and 100 mm height were produced and investigated. Rotation speed was in a range of 800–1900 rpm. The heat exchange coefficient between the casting and the mould is calculated by relation (45), part 1. The values of h0 and hF vary depending on mould coating. 2. General relations obtained by the model To verify the model and to investigate the relations between the processing parameters of centrifugal casting and particle distribution many numerical experiments are carried out. Casting of cylindrical sleeves of composite alloy A356 (see table 1) and SiC particles as reinforcing phase is considered. Thermomechanical properties of the alloy and dimensions of mould and casting are listed in table 2. Sets of particular values of the parameters, related to the figures, are given in table 3. All analyses of particle distribution and structures given below are performed using a specially developed software product on the basis of the mathematical model presented in part 1. All numerical experiments are carried out with time of filling 1 s (pouring velocity 0.75 l s−1 ). It is assumed that the segregation of particles proceeds up to a maximal volume fraction equal to 52% for granular particles [1]. Table 1. Composition of A356 aluminium matrix (wt%). Si
Mg
Mn
Cu
Fe
Ti
Al
6.5–7.5
0.2–0.45
0.35
0.25
0.60
0.25
balance
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L Drenchev et al Table 2. Thermomechanical properties of A356/SiC and size of mould and casting.
Parameter
Value and dimension
Latent heat Specific heat for base alloy Thermal conductivity for base alloy Density of base alloy
3.86 × 105
870–1180 J kg−1 K−1 73–151 W m−1 K−1
Viscosity of liquid metal Solidus temperature for base alloy Liquidus temperature for base alloy Heat exchange coefficient on inner casting surface Inner casting radius Inner mould radius
Parameter
Value and dimension
Specific heat for steel Thermal conductivity for steel Density of steel
452 J kg−1 K−1 76 W m−1 K−1
Specific heat for SiC Thermal conductivity for SiC Density of SiC
630 J kg−1 K−1 0.32 W m−1 K−1
J kg−1
2380–2700 kg m−3 (liquid–solid) (1.5–2.5) × 10−3 Pa s−1 580 ˚C 620 ˚C 60 W m−2 K−1 0.025 m 0.055 m
Heat exchange coefficient on outer mould surface Outer mould radius Length
7870 kg m−3
3230 kg m−3 130 W m−2 K−1 0.135 m 0.1 m
Table 3. Technological parameters for centrifugal casting at experiments which are shown in figures.
Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11
Initial mould temperature (˚C)
Pouring temperature TP (˚C)
Rotation speed ω (rpm)
Particle radius ε (µm)
Particle density ρP (kg m−3 )
h0 / h F (W m−2 ˚C−1 )
Initial particle concentration (vol%)
200 200 200 Varied 200 200 200 200 200 200 200
700 700 Varied 700 700 700 700 700 650 650 720
Varied 1800 1800 1200 1200 1200 1800 1200 1800 1800 1550
18 Varied 18 18 18 18 18 18 18 18 18
3230 3230 3230 3230 3230 3230 Varied 3230 3230 3230 3230
21 000/4200 21 000/4200 21 000/4200 21 000 /4200 21 000 /4200 Varied 21 000 /4200 21 000 /4200 21 000 /4200 21 000 /4200 21 000 /4200
15 15 15 15 Varied 30 15 15 15 15 8.7
Figure 1 shows the correlation between the rotation speed and particle distribution. Colour schemes here and below are the output of the software and they depict particle distribution or, temperature field in altitudinal casting cross section. The dashed line to the left on the screen indicates the axis of rotation and the right placed colour scale gives values of the parameter monitored. As the rotation speed increases, the thickness of the particle rich region at the outer casting surface decreases. In a thin layer on the casting outer surface the volume fraction of particles is equal to the initial value because of the rapid solidification of this volume. The maximal value of the volume fraction at the outer periphery increases with increasing speed but the minimal value near the particle free region slowly decreases. From the experiment discussed in [2] it was observed that the volume per cent of particles, both at the periphery and near the particle free region, increases with increasing speed. In that experiment the composite contains graphite particles, which have a lower density with respect to the liquid
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Figure 1. Correlation between rotation speed and final distribution of SiC particles. (a) Final distribution in middle cross section; (b) and (c) two-dimensional diagrams of final distribution.
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Figure 2. Correlation between particle size and final distribution of SiC particles in the middle cross section. 1—ε = 7 µm, 2—ε = 18 µm, 3—ε = 39 µm.
alloy and particles move to the inner casting surface, in the same direction as the moving solidification front. In the case considered here, SiC particles move against the solidification front. The effect of the particle size on the final distribution is shown in figure 2. It is evident from the figure that as the radius of particles increases, the thickness of the particle free region also increases. There is a critical radius for which all particles are accumulated in a layer at the outer casting surface. This layer has the maximum possible volume per cent of SiC (in our case 52%). Further increase of particle radius does not change the final distribution. Figures 3 and 4 depict how pouring temperature and initial mould temperature influence segregation. The higher values of these temperatures result in an enlargement of the size of the particle free region. Figure 5 shows the final particle distribution as a function of initial concentration. The initial concentration influences only details of the final volume fraction but the shape of the distribution remains the same. Figure 6 shows the correlation between the heat exchange coefficient and the particle distribution. The highest coefficient (see table 3) corresponds to a graphite coating, the middle to a boron nitride in water coating and the smallest to a fibrefrax coating. A higher heat exchange coefficient on the casting–mould interface results in a more uniform particle distribution. The increase of particle density, figure 7, has almost the same effect as the increase of rotation speed and radius of particles (see figures 1 and 2). Figures 8 and 9 show changes in particle distribution during solidification. Analysing the curves, one can see that after 5 s the solidification front moved from 55 to 48 mm, after 10 s to 43 mm and after 25 s to 32 mm. The comparison between the final distribution in the middle cross section and in a cross section at the end of cylindrical casting is shown in figure 10. There is a difference owing to the different thermal conditions in these two regions. Similar results can be easily seen on almost all colour schemes given. A comparison of the final particle distribution calculated by the offered mathematical model and the experimental results in [3] is shown in figure 11. Here the inner and outer radii of the casting are 45 mm and 60 mm, respectively, and the outer mould radius is 125 mm. Other technological parameters are as in table 3. The agreement between experimental and numerical results is acceptable.
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p
p
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Figure 3. Correlation between pouring temperature Tp and final distribution of SiC particles. (a) Final distribution in the middle cross section; (b) and (c) two-dimensional diagrams of the final distribution.
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(a)
0
0
0
(b)
T0
(c)
T0 Figure 4. Correlation between the initial mould temperature and the final distribution of SiC particles. (a) Final distribution in the middle cross section; (b) and (c) two-dimensional diagrams of the final distribution.
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Figure 5. Correlation between the initial concentration N0 and the final distribution of particles: (a) in the middle cross section; (b) and (c) two-dimensional diagrams of the final distribution.
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Figure 6. Correlation between the heat exchange coefficient (see equation (45), part 1) and the final distribution of SiC particles. (a) Distribution in the middle cross section; (b) and (c) twodimensional diagrams of the final distribution.
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Figure 7. Correlation between the particle density ρp and the final particle distribution (density of liquid ρL = 2390 kg m−3 ). (a) Distribution in the middle cross section; (b) and (c) two-dimensional diagrams of the final distribution.
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Figure 8. Distribution in the middle cross-section of SiC particles during solidification: (1) after 5 s, (2) after 10 s, (3) after 15 s, (4) after 20 s, (5) after 25 s (final distribution).
3. MMCs of A356 and graphite particles Below MMCs of aluminium alloy A356 matrix and Ni coated graphite particles of diameter 100 µm as reinforcing phase are considered. Because of the lower density of graphite, the particles move to the inner casting region. Three kinds of casting structures are analysed. 3.1. Casting A1 Usually, longer solidification time leads to a larger particle free zone in the casting. In figure 12 a cross section of a conventional MMC casting is shown. The initial concentration of particles is 18 vol%. Other parameters are as follows: rotation speed 1200 rpm, pouring temperature 750 ˚C, initial mould temperature 200 ˚C, filling time 3 s. Heat exchange coefficients h0 = 3000 W m−2 ˚C−1 and hF = 1420 W m−2 ˚C−1 are used. The heat exchange coefficients on casting surfaces z = 0 and z = H (see section 3.2 in part 1) are αB = 120 W m−2 K−1 , αT = 120 W m−2 K −1 , respectively. It is assumed that the maximal particle concentration in the liquid alloy is 48 vol%. The temperature field during solidification, the particle distribution and the movement of the solidification front as a function of time are simulated using the model. The final particle distribution in longitudinal section is given in figure 13. Here and on all screens from the software product the dashed line on the left marks the axis of rotation, and the colour scale gives values of different physical fields in the cross section. Comparison between figures 12 and 13 indicates a good agreement between numerical simulation and the experimental result. 3.2. Casting A2 A ring from the middle area of a casting with unusual structure is shown in figure 14. This case consists of a thin layer of maximal particle concentration, a large particle free region and shrinkage cavities between them. Metal matrix, reinforcing phase and all parameters are as before but initial particle concentration is 5 vol%. Another essential difference is in the heat exchange coefficients on casting surfaces z = 0 and z = H . In this case they are αB = 450 W m−2 K−1 and αT = 450 W m−2 K−1 , approximately four times larger. A thinner coating layer can give these larger values. It caused greater axial heat transfer. Figure 15 shows
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Figure 9. Two-dimensional diagrams of SiC particle distribution during solidification.
the arrangement of solid (blue), liquid (yellow) and two-phase (red) zones at time = 13 s. A hot spot formed in casting can be seen. Then, because of continuous cooling, shrinkage and insufficient feeding in the hot spot area a gas gap appears, figure 16. It is easier for this shrinkage defect to form at the boundary between particle free and particle rich zones because the particles have formed a non-plastic framework at the inner part of the casting where the temperature is lower. If the axial heat transfer is not so high and casting cooling runs predominantly by radial heat flow as in the previous case, such an effect will not happen.
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(c)
(d)
Figure 9. (Continued)
3.3. Casting A3 The next casting structure that is an object of our interest is given in figure 17. There are a lot of pores in the particle rich region, the sizes of which increase with the radius. In this case the particle concentration originally was 18 vol%, greater than for casting A2. Such a structure can be formed when the technological parameters are as for casting A2. Greater axial heat flow facilitates formation of a solid framework at the inner casting surface. Because of the
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(f)
Figure 9. (Continued)
greater initial content of graphite, the particle concentration decreases slowly from a maximal value on the inner surface to zero in the middle zone of the casting. The particle segregation in a centrifugal casting resembles the process of sedimentation. During this process there are four typical zones [4]: a particle free zone, a zone with the initial concentration, a transient zone where the concentration increases from initial to maximal and a zone with maximal concentration. The size of these zones changes during the segregation. In the casting discussed here, the particles and the solidification front move in the same
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Figure 10. Final particle distribution in different cross sections of the casting. 1—Z = 100 mm, 2—Z = 50 mm.
Figure 11. Comparison of particle distribution obtained theoretically (1) and experimentally (2) in [3].
Figure 12. Particle distribution in a casting fabricated using nominal technological parameters.
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Figure 13. Particle distribution according to numerical simulation.
Figure 14. Casting with a gas cavity.
direction: from the outer surface to the inner surface. The solidification front reaches the zone with initial concentration and the transient zone. The only difference in technological parameters between casting A2 and casting A3 was the initial concentration. In the case of casting A2 the particles succeeded in reaching maximal concentration and formed a non-plastic layer before the solidification front reached the particle rich zone. For that reason, shrinkage defects appear between free and rich zones. In the case of casting A3, the presence of a greater number of particles leads to the hindering of segregation and the solidification front reaches the particle rich zone before the establishment of maximal concentration in it. Because of the nonplastic framework formed and because of shrinkage, the solidifying metal ‘sucks up’ the liquid
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Figure 15. Hot spot formed at 13 s.
Gas cavity
Figure 16. Gas cavity according the numerical simulation.
between the graphite clusters and forms pores. These pores are larger in the regions where particle concentration is lower, i.e. the sizes of cavities increase with the radius. Here, the same amount of shrinkage defects as in casting A2 is distributed not in the free/rich boundary but in the rich zone.
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Figure 17. A casting with a porous particle rich zone.
Figure 18. Casting with intermediate region in the particle rich zone.
4. MMC of C90300 and graphite particles The density of alloy C90300 is approximately three times greater than the density of alloy A356. Particles of 5 µm diameter were used as the reinforcing phase. 4.1. Casting C1 An actual MMC casting of the copper alloy matrix is shown in figure 18. This casting has a free zone at the outer part of casting, a graded zone (with non-constant particle distribution)
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Figure 19. Numerically simulated final particle distribution.
at the central casting region and a zone of maximal graphite content at the inner periphery. The technological parameters are as follows: rotation speed 1800 rpm, pouring temperature 1200 ˚C, initial mould temperature 400 ˚C, initial particle concentration 13 vol%. Here, heat transfer parameters ensured the solidification front moved faster than the outer boundary of the particle rich region. For this reason an area with non-uniform distribution is present in the particle rich zone. The heat exchange coefficients between the casting and the mould are estimated as: h0 = 4000 W m−2 K−1 and hF = 1420 W m−2 K−1 . Figure 19 shows the final particle distribution, simulated by the software product developed on the basis of the model discussed in part 1 for the above technological parameters. 4.2. Casting C2 An atypical casting structure is given in figure 20. In this casting, the particle rich zone was stratified. The technological parameters are as follows: rotation speed 1200 rpm, pouring temperature 1030 ˚C, initial mould temperature (according to measurements) 350 ˚C, initial particle concentration 13 vol%, pouring time 4 s. The heat exchange coefficients between casting and mould were estimated as h0 = 740 W m−2 K−1 and hF = 500 W m−2 K−1 . When the pouring temperature is high enough, the melt stays liquid longer after filling, which provides better adhesion to the mould as in the case of casting C1. Here, the lower values of heat exchange coefficients àre due to the absence of good adhesion. The reason for this is low pouring temperature. In fact, the metal was in the two-phase zone during the mould filling and the solidification started the moment it reached the mould surface. Formation of good thermal contact was hindered. This structure formation process is simulated numerically. Because of the low pouring temperature (approximately equal to the liquidus temperature), solidification starts at the beginning of mould filling. A particle rich layer with the initial concentration is formed in the outer part of the casting. Then, because of decreasing heat flow between the casting and
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Figure 20. Casting with stratified particle rich zone.
the mould, movement of the solidification front becomes slower than the particle movement and a particle free zone appears in the middle section of the casting. All this can be seen in figure 21, which shows the simulated particle distribution 14 s after filling. The next particle rich zone is formed in the inner casting area where the particle concentration is greater than the initial value. Figure 22 shows the final particle distribution formed at 56 s when melt solidification is finished. Comparison of the modelling result and actual casting structure (see figure 20) shows good accuracy of the numerical simulation. The two particle rich zones are not well formed in the actual casting (figure 20). This is because of turbulent filling of the mould cavity with liquid without overheating and actually non-uniform cooling of the outer casting surface. Our model does not consider turbulent flow at the mould filling and considers uniform cooling of the outer casting surface. For these reasons stratified particle rich zones obtained by numerical simulation are well shaped. 4.3. Casting C3 A graded structure is typical for centrifugal casting of particle-reinforced composites. The potential for obtaining such structures is one of the main features of this technology. However, a uniform distribution can also be produced for a special set of main technological parameters. Such an atypical casting is shown in figure 23. The main parameters are as follows: rotation speed 800 rpm, pouring temperature 1020 ˚C, initial mould temperature 300 ˚C, initial particle concentration 6.8 vol%. A special parameter indicating the condition for particle non-movement effect in centrifugal casting is introduced in [5]: µeff CH = 1 (1) µA Here adapted viscosity (the effective viscosity of slurry, see section 3.1.4, part 1) is calculated by µeff = µ(1 + 2.5Vf + 10.05Vf2 )
(2)
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Figure 21. Particle distribution in the Cu–Gr system 14 s after filling. The solidification is not completed.
Figure 22. Particle distribution in the Cu–Gr system 56 s after filling. The solidification is completed.
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Figure 23. Casting with uniform particle distribution.
µ is the viscosity of liquid metal matrix, and Vf is particle volume fraction. The parameter µA reflects the influence of forces (centrifugal and/or buoyancy), which act in a direction opposite to the drag force. This is named [5] attached viscosity and is defined as follows: (3) µA = ωε 2 ρP |ρP − ρL | where ω is rotation speed, ε is particle radius, ρP and ρL are particle and liquid density, respectively. The relation CH 1 (i.e. µeff µA )
(4)
means that the drag force has a great value compared to other forces determining the particle movement and because of this the particles will not move in fact (particle velocity will be extremely small). In this case, because of the relatively short period of time for solidification, the particle distribution is close to homogeneous. Usually CH < 2 × 102 but for the technological regime related to the casting in figure 23 the parameter CH = 2686. 5. Conclusions The structure formation in centrifugally cast MMCs is a complicated process, defined by a number of physical phenomena. It depends on many factors and technological parameters. Small deviations in processing parameters can cause essential differences in casting structure. The application of a comprehensive and accurate software product for numerical simulation of the casting process provides a large potential for understanding the process, reduces the time for trials and is a powerful tool for increasing effectiveness. Using the mathematical model described in part 1 a software product is developed. Many numerical experiments, which are carried out applying this software, indicate that the volume fraction of the reinforcing phase at different zones of casting is a strong function of rotation speed and particle size. Initial mould temperature and pouring rate have less significant influence on the final distribution. Thermal management is a very essential tool for controlling the casting macrostructure. Choosing different values for the heat exchange coefficient (by means of mould coating), particle size, rotation speed and pouring time, the final particle distribution can be controlled in a wide range. A very good correlation between experimental results and model simulations for a variety of cases is demonstrated. The model can be used for optimization of technological regimes of casting production.
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Acknowledgment Dr Sha’s contribution to this work is sponsored under the Royal Academy of Engineering’s Global Research Award Scheme. References [1] [2] [3] [4] [5]
Liu Q, Jiao Y, Yang Y and Hu Z 1996 Metall. Mater. Trans. B 27 1025–9 Kang C G, Rohatgi P K, Narendranath C and Cole G 1994 ISIJ Int. 34 247–54 Lajoye L and Suery M 1988 Int. Symp. on Advances in Cast Reinforced Metal Composites Drenchev L, Sobczak J and Sobczak N 2002 Colloids and Surfaces 197 A203–11 Drenchev L and Sobczak J 2001 Trans. JWRI 30 437–42
