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Introduction to metal matrix composites

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  • 1. Chapter 5 Centrifugal Casting of Metal Matrix Composites Abstract There are three major types of centrifugal casting used for the infiltration of molten metal into fibrous preforms. In this chapter, the infiltration of molten metal into fibrous preforms using centrifugal force is discussed theoretically and the predictions of the theory are compared with experimental results. We discuss the rotational speed necessary for infiltration to start, the pressure distribution in the preforms, the velocity of the infiltration front and other important parameters. When the volume fraction of fibers is not high, the pressure necessary for the infiltration of molten metal is low. This process is suitable for fabricating products which are symmetrical around a rotational axis, and uses simple and economical casting equipment. In addition to discussion of fibrous preforms, centrifugal casting of molten metal including ceramic particles is also discussed, focusing on the theory of the behavior of a ceramic particle in molten metal in the centrifugal force field. 5.1 Infiltration of Molten Metal Using Centrifugal Force If molten metal is rotated, centrifugal force will act on the molten metal. The force increases radially from zero at the rotation center. This force generates pressure in the molten metal, and the pressure increases with distance along the radius. This pressure can be used to infiltrate molten metal into a porous preform made of ceramic fibers or particles and thus produce composites [1–4]. In this process, when the volume fraction Vf of the preform is relatively low, the pressure needed for infiltration is not high. The apparatus is simple and economical, although the process is only suitable for the symmetrical products. However, when Vf of the preform is high, a high rotation number is needed, and the apparatus required to produce the rate will be large. Y. Nishida, Introduction to Metal Matrix Composites: Fabrication and Recycling, DOI 10.1007/978-4-431-54237-7_5, # Springer Japan 2013 91
  • 2. 5.1.1 Pressure Generated at the Surface of Preform There are three cases for the production of composites using centrifugal force as shown in Fig. 5.1. In Case 1, the preform is shaped like a pipe. Infiltration begins from the inner surface of the pipe. The infiltration front spreads to the outer surface of the pipe along the rotation radius. In Case 2, the volume of the preform is very small compared with the total volume of molten metal, and therefore the displace- ment of the inner surface of molten metal is negligible during infiltration. This means that the pressure generated on the inner surface of the preform is almost constant throughout infiltration. In addition, as the cross-section of the preform in Case 2 is constant, it is possible to apply a one-dimensional infiltration model to this case. In Case 3, the hatched area outside the fan-shaped molten metal also presses the preform, which means that the pressure generated in Case 3 is higher than in the other two cases. Therefore, the pressure which acts on the preform surface depends on the type of infiltration. A good starting point to develop the theory of centrifugal casting is to consider the infiltration of molten metal in the small angle a at the rotation center during preform preform preform container container container molten metal molten metal molten metal rotation center rotation center rotation center A a b c Fig. 5.1 Three major cases for the infiltration of molten metal by centrifugal casting 92 5 Centrifugal Casting of Metal Matrix Composites
  • 3. Case 1, as shown in Fig. 5.1a. The mass of this part is rmAdr and its acceleration is o2 r. The centrifugal force, dFc, which acts on the region r to r + dr shown in Fig. 5.1a, is given by: dFc ¼ rmAo2 rdr; (5.1) where rm is the density of the molten metal, A is the cross-sectional area of the fan- shaped molten metal with small angle a, and o is the angular velocity (¼ 2pN, where N is the number of revolutions per second or revolution number). 5.1.1.1 Case 1 Case 1 corresponds to Fig. 5.1a. By integration of Eq. (5.1) between r0 and r1, the force, Fc, is obtained as: Fc ¼ 1 3 rmao2 ðr3 1 À r3 0Þ; (5.2) where r0 and r1 are the locations of the inner surfaces of the molten metal and the preform during rotation. The pressure P1, which acts on the inner surface of the preform, is obtained by dividing Fc by the preform inner surface area ar1 at r ¼ r1. When the infiltration of molten metal into the preform starts, the location of the inner surface of the molten metal, rs(t), moves as shown in Fig. 5.2 and time- dependent P1(t) during infiltration is given by: P1ðtÞ ¼ 1 3r1 rmo2 ðr3 1 À ðrsðtÞÞ3 Þ: (5.3) We suppose that solidification of the molten metal does not occur during infiltration and that the molten metal is an incompressible liquid. When the location of the infiltration front in the preform once infiltration starts is rf (t), rs(t) is given by: rsðtÞ ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2 0 þ f ðrf ðtÞÞ2 À r2 1 n or ; (5.4) preform front container molten metal rotation center Fig. 5.2 Locations of the infiltration front and inner surface of molten metal during infiltration 5.1 Infiltration of Molten Metal Using Centrifugal Force 93
  • 4. where f is the porosity of the preform (¼ 1 À Vf). Substitution of Eq. (5.4) into Eq. (5.3) yields: P1ðtÞ ¼ rmo2 3r1 r3 1 À fr2 0 þ fððrf ðtÞÞ2 À r2 1Þg 3=2 h i : (5.5) This is the pressure which is applied to the inner surface of the preform during infiltration. 5.1.1.2 Case 2 Case 2 is shown in Fig. 5.1b. The volume of the preform is so small compared with the whole volume of the molten metal that the volume change of molten metal is negligible during infiltration. In this case, the location of the inner surface of the molten metal does not move during infiltration. Therefore, the pressure P1(t) in Eq. (5.3) is constant throughout infiltration, and by putting rs(t) ¼ r0 in Eq. (5.3), P1(t) becomes: P1ðtÞ ¼ 1 3r1 rmo2 ðr3 1 À r3 0Þ: (5.6) 5.1.1.3 Case 3 This case is shown in Fig. 5.1c. The cross-section of the molten metal column is constant and does not change with increasing r. In other words, as well as the fan- shaped metal with angle a, the hatched part of the molten metal also presses against the inner surface of the preform. By putting A ¼ constant in Eq. (5.1), the force which acts on the inner surface of the preform is given by: Fc ¼ 1 2 rmAo2 ðr2 1 À r2 0Þ: (5.7) In this case, as infiltration proceeds, the location of the inner surface of the liquid column moves. When the location is rs(t), the time-dependent P1(t) is given by: P1ðtÞ ¼ 1 2 rmo2 fr2 1 À ðrsðtÞÞ2 g; (5.8) and rsðtÞ ¼ r0 þ fðrf ðtÞ À r1Þ: (5.9) 94 5 Centrifugal Casting of Metal Matrix Composites
  • 5. Substituting Eq. (5.9) into Eq. (5.8), we obtain: P1ðtÞ ¼ 1 2 rmo2 ½r2 1 À fr0 þ fðrf ðtÞ À r1Þg2 Š: (5.10) 5.1.2 Infiltration Start Pressure The contact angle of a ceramic fiber with molten aluminum is usually higher than 90 . A certain pressure must be applied to the molten metal to induce infiltration. The pressure is called the “threshold pressure”, and was discussed in detail in Chap. 3. When the distribution of fibers is random, the threshold pressure Pc is given by: Pc ¼ À 4Vf g cos y df ð1 À Vf Þ ; (5.11) where g is the surface energy of the molten metal, y is the contact angle and df is the diameter of fibers. When P1(t) is smaller than Pc, infiltration cannot begin. The minimum revolution number necessary for infiltration is given by Eqs. (5.12) and (5.13): N ! 1 2p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3r1Pc rmðr3 1 À r3 0Þ s ðfor Case 1 and Case 2Þ (5.12) N ! 1 2p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2Pc rmðr2 1 À r2 0Þ s ðfor Case 3Þ (5.13) 5.1.3 Infiltration of Molten Metal into the Preform Ignoring fluid inertial contributions and preform compression, the flow of the fluid (molten metal) in the preform in the radial direction is governed by Darcy’s law in a centrifugal force field [5, 6]: @pðr; tÞ @r ¼ À mmuðr; tÞ K þ rmo2 r; (5.14) 5.1 Infiltration of Molten Metal Using Centrifugal Force 95
  • 6. where p(r, t) is the pressure in the preform, mm is the viscosity of the molten metal, K is the permeability, and u(r, t) is the radial superficial velocity which is the mass of molten metal which flows into the preform per unit time and unit area. 5.1.3.1 Case 1 The continuity equation for the radial direction in cylindrical coordinates is given by: rm r @fruðr; tÞg @r ¼ 0: (5.15) From Eq. (5.15), we obtain the following relationship: ruðr; tÞ ¼ CðtÞ ði:e:; it is a function of time onlyÞ: (5.16) Using Eq. (5.16), Eq. (5.14) is rewritten as: @pðr; tÞ @r ¼ À mm K CðtÞ r þ rmo2 r: (5.17) At a fixed time, it is possible to regard Eq. (5.17) as an ordinary differential equation with respect to r. Then, we can obtain the following solution: pðr; tÞ À P1ðtÞ ¼ À fmmCðtÞ K ln r r1 þ 1 2 rmo2 ðr2 À r2 1Þ; (5.18) where P1(t) is the pressure at r ¼ r1. As the pressure at r ¼ rf (t) (infiltration front) is Pc (the threshold pressure): Pc À P1ðtÞ ¼ À fmmCðtÞ K ln rf ðtÞ r1 þ 1 2 rmo2 fðrf ðtÞÞ2 À r2 1g: (5.19) Alternatively, we have the following relationship between infiltration front rf (t) and the superficial velocity uf (t) at the front: drf ðtÞ dt ¼ uf ðtÞ f : (5.20) If mm, K, rm and f are independent of t, substitution of Eqs. (5.16) and (5.19) into Eq. (5.20) yields the following ordinary differential equation: t ¼ ðrf ðtÞ r1 mmf2 rf ðtÞ lnðrf ðtÞ=r1Þ K½P1ðtÞ À Pc þ ð1=2Þrmo2fðrf ðtÞÞ2 À r2 1gŠ drf ðtÞ: (5.21) 96 5 Centrifugal Casting of Metal Matrix Composites
  • 7. It is difficult to obtain an analytical solution of this differential equation, but numerical integration can be used. The pressure distribution in the infiltrated region is obtained by substitution of C (t) from Eq. (5.18) into Eq. (5.19): pðr; tÞ ¼ P1ðtÞ À P1ðtÞ À Pc þ 1 2 rmo2 fðrf ðtÞÞ2 À r2 1g lnðr=r1Þ lnðrf ðtÞ=r1Þ þ 1 2 rmo2 ðr2 À r2 1Þ (5.22) Equation (5.22) gives the pressure distribution in the infiltrated region when the infiltration front is located at position rf(t). This relationship shows that the pressure is independent of f and K except for the threshold pressure Pc which depends on f. When this process is applied industrially, the thickness of the preform is finite. When the infiltration front reaches the outer surface of the preform (r ¼ rt), the infiltration stops and the pressure distribution in the infiltrated region changes instantaneously. Supposing that the framework of the fibrous preform is sufficiently rigid and does not deform in the infiltrated region, the centrifugal force, dFc, which acts on the metal of the region r to r + dr in the preform, is given by: dFc ¼ frmAo2 rdr: (5.23) When the preform thickness is L (¼ rt À r1), the pressure in the preform p(r) at r (r1 r rt) is given by: pðrÞ ¼ 1 3r1 rmo2 ½r3 1 À fr2 0 þ fðr2 t À r2 1Þg3=2 Š þ 1 3r frmo2 ðr3 À r3 1Þ: (5.24) When the amount of molten metal is small and all molten metal enters the preform before the infiltration front arrives at the outer surface of the preform, the pressure curve is given only by the second term of Eq. (5.24). 5.1.3.2 Case 2 This is the case where P1(t) is constant (¼ P0). The cross section of the preform is independent of r and constant. Therefore, the superficial velocity u(r, t) in Eq. (5.14) is also independent of r and expressed by u(t). The one-dimensional form of the continuity equation, which applies in this situation, is: @uðtÞ @r ¼ 0: (5.25) At a fixed time, it is also possible to regard Eq. (5.14) as an ordinary differential equation with respect to r. Then, we can obtain the following solution: 5.1 Infiltration of Molten Metal Using Centrifugal Force 97
  • 8. pðr; tÞ ¼ P0 À mmuðtÞ K ðr À r1Þ þ 1 2 rmo2 ðr2 À r2 1Þ: (5.26) As the pressure at the infiltration front r ¼ rf (t) is Pc, we obtain: P0 ¼ mmuðtÞ K ðrf ðtÞ À r1Þ À 1 2 rmo2 fðrf ðtÞÞ2 À r2 1g þ Pc: (5.27) Alternatively, the velocity of the infiltration front is given by: drf ðtÞ dt ¼ uðtÞ f : (5.28) Substitution of u(t) from Eq. (5.28) into Eq. (5.27) yields an ordinary differential equation: m3 þ m4rf ðtÞ m1 þ m2frf ðtÞg2 drf ðtÞ ¼ dt; (5.29) where m1 ¼ K P0 À Pc À rmo2 r2 1 2 ; m2 ¼ Krmo2 2 ; m3 ¼ Àmmfr1; m4 ¼ mmf: The solution of Eq. (5.29) depends on the sign (negative or positive) of m1. However, since we know P0 from Eq. (5.6), m1 is always negative. Then, the following solution is obtained: t ¼ n1 lnfðrf ðtÞÞ2 À n2 3g þ n2 ln rf ðtÞ À n3 rf ðtÞ þ n3 þ n4; (5.30) where n1 ¼ m4 2m2 ; n2 ¼ m3 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Àm2m1 p ; n3 ¼ ffiffiffiffiffiffiffiffiffiffi À m1 m2 r ; and n4 ¼ Àn1 lnðr2 1 À n2 3Þ À n2 ln r1 À n3 r1 þ n3 : By substituting uðtÞ from Eq. (5.26) into Eq. (5.27), we obtain: pðr; tÞ ¼ rf ðtÞ À r rf ðtÞ À r1 P0 þ 1 2 rmo2 ðr À r1Þðr À rf ðtÞÞ þ Pc r À r1 rf ðtÞ À r1 : (5.31) This equation gives the pressure distribution in the infiltrated region when the infiltration front is specified. The characteristic features of this equation are that the equation does not include f, and that the pressure distribution pattern is 98 5 Centrifugal Casting of Metal Matrix Composites
  • 9. independent of the volume fraction of fibers in the preform except for the depen- dence of the threshold pressure, Pc, on f. When the preform thickness is L, the pressure p(r) in the infiltrated region after the infiltration front reaches the outer surface of the preform is given by: pðrÞ ¼ P0 þ 1 2 frmo2 ðr2 À r2 1Þ; ðr1 r rtÞ: (5.32) 5.1.3.3 Case 3 This is the case shown in Fig. 5.1c. Since cross sectional variations can be neglected because of the cylindrical configuration, the superficial velocity u(r, t) in Eq. (5.14) is actually u(t) and the continuity equation in the one-dimensional form, Eq. (5.25), should also be valid in this case. At a fixed time, it is possible to regard Eq. (5.14) as an ordinary differential equation with respect to r, if mm, K and rm are independent of r. Then, we can get the following solution: pðr; tÞ ¼ P1ðtÞ À mmuðtÞ K ðr À r1Þ þ 1 2 rmo2 ðr2 À r2 1Þ; (5.33) where P1(t) is the pressure at r ¼ r1. As the pressure p(r, t) at r ¼ rf (t) in Eq. (5.33) is the threshold pressure Pc, we obtain: P1ðtÞ ¼ mmuðtÞ K ðrf ðtÞ À r1Þ À 1 2 rmo2 ððrf ðtÞÞ2 À r2 1Þ þ Pc: (5.34) Substitution of Eqs. (5.10) and (5.28) into Eq. (5.34) provides an ordinary differential equation, if mm, K, rm and f are independent of t. The solution is: t ¼ 1 2m3 ln fðrf ðtÞÞ2 þ m1rf ðtÞ þ m2g rf ðtÞ þ m6 rf ðtÞ þ m5 m4 þ m7; (5.35) where m1 ¼ 2fðfr1 À r0Þ 1 À f2 ; m2 ¼ Àr2 0 À f2 r2 1 þ 2fr0r1 À 2Pc=ðrmo2 Þ 1 À f2 ; m3 ¼ rmo2 Kð1 À f2 Þ 2mmf ; m4 ¼ m1 þ 2r1 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m2 1=4 À m2 p ; m5 ¼ 1 2 m1 À ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m2 1 4 À m2 r ; m6 ¼ 1 2 m1 þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m2 1 4 À m2 r ; and m7 ¼ À 1 2m3 ln ðr2 1 þ m1r1 þ m2Þ r1 þ m6 r1 þ m5 m4 5.1 Infiltration of Molten Metal Using Centrifugal Force 99
  • 10. Equation (5.35) gives the relationship between the location of the infiltration front rf (t) and time t. Alternatively, by substituting Eq. (5.34) into Eq. (5.33), we obtain the pressure distribution in the infiltrated region when the infiltration front is specified at rf (t): pðr; tÞ ¼ ðrf ðtÞ À rÞP1ðtÞ þ ðr À r1ÞPc rf ðtÞ À r1 þ 1 2 rmo2 ðr À r1Þðr À rf ðtÞÞ: (5.36) When the preform thickness is L (¼ rt À r1), the pressure in the preform after infiltration reaches the outer surface of the preform is: pðrÞ ¼ 1 2 rmo2 r2 1 À r0 þ fðrt À r1Þf g2 h i þ 1 2 frmo2 ðr2 À r1 2 Þ: (5.37) 5.1.4 Example Calculations The relationship between Vf and the permeability of the preform is needed for the calculation of infiltration. There are many theoretical equations for the permeability of porous media [7]. Among them, Langmuir’s equation [Eq. (5.38)] which applies to flow parallel to the fiber alignment and Happel’s equation [Eq. (5.39)] which applies to flow normal to fibers can be used to obtain the permeability of the preform. Generally the permeability calculated using these equations agrees well with experimental results. The equations are: K R2 ¼ 1 4Vf À ln Vf À 3 2 þ 2Vf À 1 2 Vf 2 ; (5.38) and K R2 ¼ 1 8Vf À ln Vf þ V2 f À 1 V2 f þ 1 ! ; (5.39) where R is the radius of the fiber. As the fiber distribution we used was random, the permeability of the preform was obtained by averaging the values of permeability calculated for flows parallel and normal to the fiber alignment. 5.1.4.1 Case 1 The advance of the infiltration front of molten aluminum (without solidification) calculated using Eq. (5.21) is shown in Fig. 5.3. The calculation was performed for 100 5 Centrifugal Casting of Metal Matrix Composites
  • 11. a preform made from alumina short fibers. The following data were also used in this calculation: r0 ¼ 0.07 m, r1 ¼ 0.12 m, f (¼ 1 À Vf) ¼ 0.87, rm ¼ 2.38 Â 103 kg/ m3 , R (¼ df/2) ¼ 1.85 Â 10À6 m, g ¼ 0.893 Pa m, y ¼ 160 and mm ¼ 0.984 Â 10 À3 Pa s. The minimum revolution number N for the infiltration is 19.74 rev/s, as calculated from Eq. (5.12). Figure 5.3 shows that if the revolution rate is slightly higher than the minimum value, infiltration will be continuous. The pressure distribution in the infiltrated region obtained from Eq. (5.22) is shown in Fig. 5.4 for N ¼ 50 rev/s. The pressure distribution curves are convex towards lower pressures, because the second derivative of Eq. (5.22) is always positive and Fig. 5.3 Relationship between infiltrated distance and time for a range of rotational speeds for Case 1 Fig. 5.4 Change with time of pressure distribution in the infiltrated region for Case 1 when N ¼ 50 rev/s 5.1 Infiltration of Molten Metal Using Centrifugal Force 101
  • 12. proportional to o2 . The preform surface pressure decreases quickly as the infiltra- tion advances, and the intermediate part of the pressure distribution curve falls below the threshold pressure. Nevertheless, infiltration continues, because the threshold pressure is needed only to wet fibers with molten metal, and the pressure at the infiltration front always remains constant at the threshold pressure. After wetting, the molten metal does not separate from the preform, even if the pressure becomes lower than the threshold pressure, unless enough work for the separation is supplied to the molten metal/fiber interface. When the preform thickness is L and the infiltration front reaches the location r (t) (the outer surface of the preform), the pressure distribution curve shown in Fig. 5.4 for N ¼ 50 rev/s is changed instantaneously to that of Fig. 5.5. Only the preform surface pressure remains constant, and the pressure in the infiltrated region rises quickly and becomes stable. In this calculation, in the cases of L ¼ 0.04 and 0.05 m, all liquid metal enters into the preform and a cavity is formed near the inner surface of the preform, because of the lack of liquid metal. 5.1.4.2 Case 2 Figure 5.6 shows the relationship between time and the advance of the infiltration front obtained from Eq. (5.30). The front advances faster than in Case 1, because the preform surface pressure remains constant throughout the infiltration. The pressure distribution curves are shown in Fig. 5.7 for N ¼ 50 rev/s. The pressure distribution curves in this case are also convex toward lower pressure, because the second derivative of Eq. (5.31) is also positive and proportional to o2 . The pressure distribu- tion curves for finite preform thickness cases are shown in Fig. 5.8 for N ¼ 50 rev/s. In Case 2, even if the preform thickness is different, the pressure distribution curve is the same, and the curve depends only on the revolution number. Fig. 5.5 Pressure distribution in the infiltrated region for Case 1 after the infiltration front reaches the outer surface of the preform when N ¼ 50 rev/s 102 5 Centrifugal Casting of Metal Matrix Composites
  • 13. 5.1.4.3 Case 3 Figure 5.9 shows the relationship between time and the advance of the infiltration front obtained from Eq. (5.35) for Case 3. The front advances faster than in Case 1 and slower than in Case 2 for a particular revolution number. The pressure distri- bution curves obtained from Eq. (5.36) are shown in Fig. 5.10 for N ¼ 50 rev/s. These curves are also convex toward lower pressure. Regions having lower pressure than the threshold pressure appeared at t ¼ 0.163 s in Fig. 5.10. The pressure Fig. 5.6 Relationship between infiltrated distance and time for a range of rotational speeds for Case 2 Fig. 5.7 Change with time of pressure distribution in the infiltrated region for Case 2 when N ¼ 50 rev/s 5.1 Infiltration of Molten Metal Using Centrifugal Force 103
  • 14. distribution curves obtained using Eq. (5.37) are shown in Fig. 5.11 for various finite preform thickness at N ¼ 50 rev/s. Until the infiltration front arrives at the outer surface of the preform, the preform surface pressure changes as given in Fig. 5.10. When the front arrives at the preform outer surface, the change in the preform surface pressure stops and the pressure distribution in the infiltrated region becomes that shown in Fig. 5.11. Fig. 5.8 Pressure distribution in the infiltrated region for Case 2 after the infiltration front reaches the outer surface of the preform when N ¼ 50 rev/s Fig. 5.9 Relationship between infiltrated distance and time for a range of rotational speeds for Case 3 104 5 Centrifugal Casting of Metal Matrix Composites
  • 15. 5.1.5 Examples of Composites Fabricated Using Centrifugal Force In this section we summarize a previous study where the feasibility of centrifugal force for the infiltration of molten metal into preforms was examined and the composites obtained were characterized [8]. A schematic of the apparatus used is Fig. 5.10 Change with time of pressure distribution in the infiltrated region for Case 3 when N ¼ 50 rev/s Fig. 5.11 Pressure distribution in the infiltrated region for Case 3 after the infiltration front reaches the outer surface of the preform when N ¼ 50 rev/s 5.1 Infiltration of Molten Metal Using Centrifugal Force 105
  • 16. shown in Fig. 5.12. A preheated graphite container with a uniform cross section was used. The container was balanced by a counterweight. A preheated alumina short fiber preform was set on the bottom of the container which was rotated. When the rotational speed reached the target value, molten pure aluminum was poured into a pouring device concentric with the rotation shaft and a composite was produced. The experimentally obtained relationship between the rotational speed and the infiltrated distance for different volume fractions of fiber and initial preform thickness is shown in Fig. 5.13. The diameter for the preform was 24 mm, and the initial thicknesses of the preforms were 20 mm for Vf ¼ 6 %, 19 mm for Vf ¼ 9 %, and 18 mm for Vf ¼ 13 %. The infiltrated distances for Vf ¼ 6 % and preform graphite container graphite pipe pouring device Fig. 5.12 Schematic of the apparatus used to generate centrifugal force for the infiltration of aluminum Fig. 5.13 Relationship between the pressure generated and infiltrated distance. The initial thicknesses of the preforms are 20 mm for Vf ¼ 6 %, 19 mm for Vf ¼ 9 %, and 18 mm for Vf ¼ 13 %. The compressive deformation of preforms is neglected 106 5 Centrifugal Casting of Metal Matrix Composites
  • 17. 9 % were either zero or 100 %. That is, in the case of Vf ¼ 6 %, infiltration did not advance at 65 kPa (N ¼ 10 rev/s) but fully advanced at 70 kPa (N ¼ 11 rev/s). For Vf ¼ 9 %, infiltration did not take place at 70 kPa (N ¼ 16 rev/s), but occurred fully at 85 kPa (N ¼ 17 rev/s). For Vf ¼ 13 %, the molten metal advanced a little and then stopped at 160 kPa (N ¼ 26 rev/s), but advanced much further at 230 kPa (N ¼ 32 rev/s). Since the preheat temperatures of the preform and graphite con- tainer were 703 and 673 K, respectively, the infiltration velocity was slow in this case and the metal solidified during infiltration. Pressure higher than 300 kPa was needed for full infiltration for the Vf ¼ 13 % preform. The structural characteristics of samples are presented in Figs. 5.14 and 5.15. A partially infiltrated sample with Vf ¼ 13 % is also shown in Fig. 5.14. The preform also contained many particles, because the quality of the alumina/silica fibers was not high. The minimum pressures for the start of infiltration were obtained from this experiment and are listed in Table 5.1, along with the threshold pressure values calculated theoretically using Eq. (5.11). Both sets of values are in agreement. Fig. 5.14 Macrostructures of alumina/silica short fiber reinforced aluminum composite samples fabricated using centrifugal force 5.1 Infiltration of Molten Metal Using Centrifugal Force 107
  • 18. 5.2 Centrifugal Casting of Particle Dispersed Molten Metal When molten metal which contains ceramic particles is cast in a centrifugal force field, the particles tend to segregate because of the density difference between the molten metal and the ceramic particles. Here, we discuss the movement of the particles and the forces which act on the particles. To simplify the model, solidifi- cation will be neglected. A particle having density rp and radius Rp is present in molten metal having density rm. The centrifugal force, which is proportional to the rotating radius r, is acting on the particle. The equation for the force, Fc, which acts on the particle as a result of the acceleration, o2 r is similar to Eq. (5.1): Fc ¼ 4 3 pR3 pðrp À rmÞo2 r: (5.40) If the particle moves with very low velocity in the molten metal, as shown in Fig. 5.16, Stokes’ drag formula will be applicable [9]. The viscous drag is given by: Fv ¼ À6pmmRp dr dt ; (5.41) where Fv acts on the particle in the opposite direction to the centrifugal force, and has a negative sign. mm is the viscosity of the molten metal. The fundamental expression of the movement of an object is: [force] ¼ [mass] Â [acceleration]. For the particle, the total force is Fc + Fv. Thus, we obtain the following differential equation: Fig. 5.15 Microstructure of alumina/silica short fiber reinforced aluminum composites fabricated using centrifugal force Table 5.1 Comparison of threshold pressures Vf (%) Pc (kPa) (theoretical) Pc (kPa) (experimental) 6 57.9 66 9 89.7 81 13 135.6 156 108 5 Centrifugal Casting of Metal Matrix Composites
  • 19. 4 3 pR3 pðrp À rmÞo2 r À 6pmmRp dr dt ¼ 4 3 pR3 prp d2 r dt2 : (5.42) Gravity is neglected, because the gravity is much smaller than the centrifugal force. The solution of Eq. (5.42), i.e., the location of the particle as a function of time, is: r ¼ r0 exp À9mm þ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 81m2 m þ 16ðrp À rmÞrpR4 po2 q 4Rprp 8 : 9 = ; t 2 4 3 5; (5.43) where r0 is the initial location of the particle. The solution is a simple exponential function. If the particle goes far away from the rotating center, the velocity of the particle will increase and Stokes’ drag formula (equation (5.41)) will be invalid, because the formula is only valid when the Reynolds number around the particle is less than 0.5. Examples of calculations using Eq. (5.43) are shown in Figs. 5.17 and 5.18. In these calculations, the particle is a spherical SiC particle with density rp ¼ 3.15 Â 103 kg/m3 ; the density rm of the molten aluminum is 2.38 Â 103 kg/m3 and the viscosity of the molten aluminum mm ¼ 0.948 Â 10À3 Pa s. Figure 5.16 shows the movement with time of particles with different radii, Rp, when the revolution number N is 10 rev/s. Equation(5.43)givesthedimensionlessdisplacementratioofthelocationoftheparticle to its initial location r/r0, which represents the movement of the particle. When the particle radius is 1 mm (i.e., the diameter is 2 mm), the particle quickly moves away from the rotating center. However, when the particle radius is 0.1 mm, the particle will move slowly. Figure 5.17 shows the displacement ratio, r/r0 of a particle of radius 0.1 mm, for different revolution numbers N. When N ¼ 5 rev/s, the particle essentially remainsatitsinitiallocationfortheentire300s.However,whenNislargerthan15rev/s (900 rpm), the particle moves quickly. However, Eq. (5.43) is quite different to “Stokes’ law” which gives: dz dt ¼ 2R2 pðrp À rLÞg 9mL ; (5.44) Fc Fv Rp particle Fig. 5.16 Viscous drag, Fv, and centrifugal force, Fc, which act on a particle during centrifugal casting of particle reinforced molten metal 5.2 Centrifugal Casting of Particle Dispersed Molten Metal 109
  • 20. where g is the gravitational acceleration, rL and mL are the density and viscosity of the fluid, respectively. The z-axis is taken as the gravity direction. In this equation, the acceleration is constant, although it is o2 r in the centrifugal force field. In actual centrifugal casting, solidification of metal occurs along with the movement of particles. The solidification in this case is very complicated and it is very difficult to analytically calculate the behavior, because solidification depends Fig. 5.18 Curves of displacement ratio r/r0 with time for various values of revolution number N; particle radius is 0.1 mm Fig. 5.17 Curves of displacement ratio r/r0 with time for various particle radii; revolution number N is 10 rev/s 110 5 Centrifugal Casting of Metal Matrix Composites
  • 21. on the shape of container (mold), the composition of the alloy and on other factors. In addition, Eq. (5.43) is the model of the movement for a single particle only. When the number of particles is large, we should consider the interaction between particles. Then, the apparent viscosity mapp must be used instead of the real viscosity of the molten metal; the apparent viscosity increases when the number of particles increases, and is given by [10]: mapp ¼ mmð1 þ 5 2 Vf þ 10:05V2 f Þ: (5.45) This mapp can then be used instead of mm in Eq. (5.43). Centrifugal casting with solidification in the presence of solid particles was discussed numerically by Panda et al. [11]. They showed that the segregation of particles in the alumina particles/aluminum or silicon carbide particles/aluminum systems depends on the size of particle, rotational speed, heat transfer coefficient at the casting/mold interface and volume fraction of particles. Examples of the application of centrifugal casting to composites include copper alloy/graphite particle composites, which were developed by Kim et al. to improve tribological properties of the inner surfaces of products [12]. Functionally graded composites were also developed in TiB2 or TiC particles/aluminum alloy systems by Kumar et al. [13]. References 1. Sugishita, J.: Fabrication and properties of centrifugally cast surface composites based on Al-11%Si alloy. J. Jpn. Foundry Eng. Soc. 57, 102–107 (1985) 2. Tsunekawa, Y., Okumiya, M., Niimi, I., Yoneyama, K.: Centrifugally cast aluminum matrix composites containing segregated alumina fibers. J. Mater. Sci. Lett. 7, 830–832 (1988) 3. Tsunekawa, Y., Okumiya, M., Niimi, I., Maeda, T.: Improvement of bending strength in aluminum alloy matrix composites containing short alumina fibers by centrifugal force. J. Jpn. Inst. Light Met. 40, 7–12 (1990) 4. Nishida, Y., Ohira, G.: Modelling of infiltration of molten metal in fibrous preform by centrifugal force. Acta Mater. 47, 841–852 (1999) 5. Geiger, G.H., Poirier, D.R.: Transport Phenomena in Metallurgy, p. 48. Addison-Wesley, Reading (1980) 6. Collins, R.E.: Flow of Fluids Through Porous Materials. Reinhold Publishing Corp, New York (1961) 7. Jackson, G.W., James, D.F.: The permeability of fibrous porous media. Can. J. Chem. Eng. 64, 364–374 (1986) 8. Nishida, Y., Shirayanagi, I., Sakai, Y.: Infiltration of fibrous preform by molten aluminum in a centrifugal force field. Metall. Mater. Trans. 27A, 4163–4169 (1996) 9. Geiger, G.H., Poirier, D.R.: Transport Phenomena in Metallurgy, p. 71. Addison-Wesley, Reading (1980) 10. Schowalter, W.R.: Mechanics of Non-Newtonian Fluids, p. 288. Pergamon, London (1978) References 111
  • 22. 11. Panda, E., Mehrotra, S.P., Mazumdar, D.: Mathematical modeling of particle segregation during centrifugal casting of metal matrix composites. Metall. Mater. Trans. 37A, 1675–1687 (2006) 12. Kim, J.K., Kestursatya, M., Rohatgi, P.K.: Tribological properties of centrifugally cast copper alloy-graphite particle composite. Metall. Mater. Trans. 31A, 1283–1293 (2000) 13. Kumar, S., Sarma, V.S., Murty, B.S.: Functionally graded alloy matrix in situ composites. Metall. Mater. Trans. 41A, 242–254 (2010) 112 5 Centrifugal Casting of Metal Matrix Composites

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