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# Introduction to metal matrix composites

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### Introduction to metal matrix composites

1. 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. 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. 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. 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. 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 : (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. 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 1g drf ðtÞ: (5.21) 96 5 Centrifugal Casting of Metal Matrix Composites
7. 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  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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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