Kinetics of ceramic particulate penetration into spray atomized metallic droplet at variable penetration depth

Acta metall, mater. Vol. 42, No. 9, pp. 2955-2971, 1994

~

Pergamon

0956-7151(94)E0096-Y

Copyright © 1994ElsevierScienceLtd Printed in Great Britain.All rights reserved 0956-7151/94 $7.00 + 0.00

KINETICS OF CERAMIC PARTICULATE PENETRATION INTO SPRAY ATOMIZED METALLIC DROPLET AT VARIABLE PENETRATION DEPTH

J. ZHANG,Y. WU and E. J. LAVERNIA Materials Science and Engineering, Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92717, U.S.A. (Received 29 July 1993; in revised form 16 February 1994)

Abstract--The present study provides insight into the physical interactions that take place when an injected ceramic particulate collides with an atomized metallic droplet during spray atomization and deposition processing of particulate reinforced metal matrix composites. A model is developed to predict the extent of penetration for a given particulate velocity, and the critical velocity for complete penetration. In the model, the initial kinetic energy of the injected particulates or the atomized droplets is considered as the driving force for penetration; the change in surface energies and the work done by viscous drag in the droplet melt are considered as the forces resisting penetration. As examples, Al/graphite and AI/SiC systems are analyzed to demonstrate the applicability of the model. The influence of the particulate size and the fraction of solid phase in the atomized droplet on the critical velocity and the penetration depth is also examined.

1.

INTRODUCTION

Among the variety of processing techniques that have been developed to optimize the microstructure and properties of discontinuously reinforced metal matrix composites (MMCs), spray forming offers a unique opportunity to combine the benefits associated with fine particulate technology (e.g. microstructural refinement) with near-net shape manufacturing [1-7]. Spray forming generally involves highly nonequilibrium thermal and solidification conditions which renders it possible to modify the propertes of existing alloy systems and to develop novel alloy compositions including MMCs [6-10]. The injection of reinforcing ceramic particulates and the interactions of the particulates with the solidifying matrix are of importance in determining the resultant distribution and volume fraction of the reinforcing particulates and hence the mechanical behavior of MMCs. One of the most important interaction mechanisms is the penetration of ceramic particulates into atomized droplets. Accordingly, an effort is made in the present study to elucidate the transfer kinetics during the penetration of gas-injected ceramic particulates into spray atomized metallic droplets. The relevant ceramic particulate transfer phenomena associated with casting of discontinuously reinforced MMCs have been addressed by a number of investigators. Kacar et al. [I l] developed a model to study the influence of kinetic energy on the gas-toliquid transfer of ceramic particulates during centrifugal casting. The forces considered in the model included surface tension of liquid alloy, buoyancy

forces and centrifugal forces. The predicted critical centrifugal acceleration for particulate incorporation was compared with the experimental results obtained using a two-bucket centrifugal apparatus. Both the theoretical predictions and experimental results from the study of Kacar et al. [l l] revealed that the required critical centrifugal acceleration for complete incorporation of particulates into liquid alloy decreased with increasing particulate size. Rohatgi et al. [12] studied the energetics associated with an equilibrium transfer of ceramic particulates across a stationary gas-liquid planar interface as a function of the path of submersion during casting of particulate reinforced MMCs. The model was used to examine the gas-liquid transfer of particulates in a gas injection technique in which particulates were injected into a liquid alloy by the injection gun nozzle submerged below the melt surface and carrying a gas-particulate mixture. In the model, the driving force for the transfer of particulates from gas to liquid metal was considered to be the initial kinetic energy of the particulates. During the transfer, the kinetic energy was dissipated to overcome the changes in surface energy, buoyancy energy and potential energy due to gravity. It was found that the theoretical minimum injection velocity required for the transfer of particulates into the liquid alloy increased with decreasing particulate size, i.e. fine particulates required a higher injection velocity for transfer than coarse ones. Gupta et al. [13], and Wu and Lavernia [14] studied dynamic wettability and interaction mechanisms between gas-injected ceramic particulates and atomized metallic droplets during spray atomization and

2955

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ZHANG et al.: KINETICS OF CERAMIC PARTICULATE PENETRATION

deposition processing of particulate reinforced AI alloy MMCs, Gupta et al. [13] introduced the concept of dynamic wettability to explain the wetting behavior in spray deposited A1/SiC MMCs. They proposed that the wetting interaction of particulates with droplets took place under extremely non-equilibrium conditions since solidification of droplets continued during their flight to the deposition substrate. Gupta et al. [13] observed two types of interactions of SiC particulates with atomized droplets: penetration and surface rupture. In related studies, Wu and Lavernia [14] further investigated incorporation mechanisms of SiC particulates into rapidly solidified A1-4Si alloy droplets during spray atomization processing. Their experimental results revealed that the distribution and volume fraction of the SiC particulates in the penetrated droplets depended on the droplet size, the particulate size and the particulate initial velocity. The objective of the present work is to develop a theoretical model to predict the critical initial velocity for the penetration of ceramic particulates into metallic droplets that are in a liquid or semi-liquid state during spray atomization, and to predict penetration depth at a given initial velocity. The model is developed on the basis of conservation of energy. The driving force for penetration considered herein is the initial kinetic energy of particulates and droplets. The resistance forces to penetration include surface tension and viscous drag. The change of kinetic energy of the penetrating system is assumed to be totally dissipated by the change in the surface energies and the work done by the viscous drag. The applicability of the model is demonstrated by comparing computational results to those obtained experimentally with SiC and graphite particulates that interact with atomized AI droplets.

2. THEORY OF PARTICULATE PENETRATION Figure 1 schematically shows the atomization of a molten alloy and the injection of reinforcing ceramic ""

i

mized :al droplets ceramic iculates ,'ted

/

~

0.4 q ~10

wb~/e

J

b --

tomization ;)Re

11 /

/

;omposite

roplets

/ Fig. 1. Schematic diagram showing the spray atomization of molten metal and the injection of ceramic particulates during spray atomization processing of MMCs.

particulates akin to spray atomization and deposition processing of MMCs. A detailed description of this synthesis methodology may be found elsewhere [5-10, 15-17]. During spray atomization and deposition, the molten alloy is energetically disintegrated into micrometer-sized droplets using high velocity jets of nitrogen gas inside an environmental chamber. Simultaneously, ceramic particulates, carried by a separate flow of nitrogen, are injected through two or four nozzles, perpendicular to the outline of the atomization cone. Possible interaction mechanisms between ceramic particulates and metallic droplets may be divided into three categories. First, a particulate may collide with a droplet and bounce back (Fig. 1). Second, a particulate may collide and attach to the surface of a droplet (surface rupture). Third, a particulate may partially or completely penetrate a droplet and remain within the droplet. In the present analysis, the emphasis will be placed on the third category of particulate/droplet interactions. 2.1. M o d e l assumptions

Three assumptions are introduced herein for the theoretical analysis. First, ceramic particulates are considered to be spheroidal and with a size much smaller than that of metallic droplets. This assumption is based on the fact that the reinforcing ceramic particulates that are encountered in spray processed MMCs, such as SiC and graphite, are generally of a size ranging from 3 to 15 pm in diameter, while spray atomized metallic droplets exhibit a spheroidal morphology with a diameter ranging from 100 to 300/~m in diameter [13, 14]. Accordingly, the curvature effect of droplet surface is neglected in comparison to that of the ceramic particulates. Second, it is assumed that the potential penetration of a particulate into a droplet would be likely to occur when the particulate collides with the droplet (Fig. 1) in three different configurations, depending on the angle between the path of the particulate and the penetration direction. These are described as follows. Case 1, an injected particulate collides with a passing droplet in front of the particulate [Fig. 2(a)]. The penetration of the particulate into the droplet occurs along the initial traveling direction of the particulate. The driving force for penetration is the initial energy of the particulate. Case 2, a droplet collides with a passing particulate inside the atomization cone [Fig. 2(b)]. The penetration occurs against the initial traveling direction of the droplet. The driving force for penetration is the initial kinetic energy of the droplet. Case 3, a particulate collides with a droplet at the angle. To maintain the problem tractable, the angle is assumed to be 45 ° [Fig. 2(c)]. The penetration occurs at an angle of 45 ° to the initial traveling direction of both the particulate and droplet. The driving force for penetration is the sum of the initial kinetic energy of both. Third, in all three cases, the collision is considered to be a completely inelastic head-on collision.

2957

ZHANG et eL: KINETICS OF CERAMIC PARTICULATE PENETRATION

1"

11 V2

Droplet Pa~icula

V1

(c) Case 3

(b) Case 2

(a) Case 1

Fig. 2. Collision and penetration of a ceramic particulate with a droplet (3 cases).

Therefore, the change of kinetic energy of the penetrating system is completely dissipated by the surface energy changes and the work done by drag forces along the penetration path after the collision. The penetration process of the particulate inside the droplet is modeled as one-dimensional deaccelerated motion with the penetrating particulate ultimately resting within the droplet. Fourth, the possible resistance sources considered to be operative are: the surface tension due to the creation of a particulate/droplet interface, and the viscous drag of the liquid metallic droplets. The metallic droplets are considered to be in a liquid or semi-liquid state with variable viscosity that is primarily dependent on magnitude of the solid fraction. The buoyancy and gravitational forces are not taken into account. Finally, neither the presence of a solid shell nor an oxidized layer is taken into account in the present analysis.

2.3. Change o f kinetic energy o f a colliding system Case 1. A particulate acquires its initial velocity, V1, through gas injection and travels towards an atomized droplet [Fig. 2(a)]. Collision between particulate and droplet occurs in front of the particulate. After the completely inelastic head-on collision, both the particulate and droplet move together at a velocity V'. Momentum conservation requires

or

V~ =

ml V1 ml + m2

(3)

where ml and m2 are the masses for the colliding particulate and droplet, respectively, which are given by 47zR3 mI = ~ p

2.2. Modeling approach

(4)

4xR~

On the basis of the aforementioned assumptions, the penetration process of an injected ceramic particulate in an atomized metallic droplet is a completely inelastic head-on collision (Fig. 2). In the aforementioned three cases of penetration, the kinetic energy for penetration primarily depends on the relative velocity between the colliding particulate and droplet along the penetration direction. The change in kinetic energy after the collision is completely dissipated by the change in the surface energies and the work done by the viscous drag of the droplet liquid. According to conservation of energy, the formulation of this process may be expressed by AEk + AEs = W~

(2)

ml Vl = (ml + m:)V~

(1)

where AEk is the kinetic energy change of the colliding system, AEs is the summation of the surface energy changes due to particulate penetration and Wv is the work done by the viscous drag of the droplet liquid along the penetration path.

m2 = ~ - -

P2

(5)

respectively. In equations (4) and (5), R and p denote the radius and density of the particulate; R 2 and P2 denote the radius and density of the droplet. The velocity change of the particulate during the collision is given by A V = V ~ - VI

(6)

or

AV =

m2

VI '

(7)

mj + m 2

The magnitude of the velocity change is considered as the initial velocity for the particulate to penetrate the droplet. The entire change in the kinetic energy of the colliding system due to the velocity change is given by

(

)2

AEk=½(ml+m2) m l m, + m 2 V1

- ½m1 V~

(8)

2958

ZHANG

et al.:

KINETICS

OF CERAMIC

or

PARTICULATE

PENETRATION

2.4. Surface energy change at variable penetration depth v;.

(9)

Case 2. In this case, an droplet collides with a passing particulate inside the atomization cone [Fig. 2(b)]. The penetration occurs against the initial traveling direction of the droplet. Using the same analysis as used in Case 1, the change of velocity and kinetic energy of the head-on colliding system [Fig. 2(b)] are given by V2

(10)

and V;

(11)

where V, is the initial velocity of the droplet. Case 3. In this case a particulate collides with a droplet at an angle. To maintain the problem tractable, the angle is assumed to be 45” [Fig. 2(c)]. The penetration occurs at an angle of 45” to the initial traveling direction of both the particulate and droplet. From Fig. 2(c), the velocity change and kinetic energy change along the penetration direction during the completely inelastic head-on collision can be derived to be AV = -+V,

+ V2)

The penetration of particulate inside droplet proceeds in the same way for all three cases. The surface energy and work done by droplet liquid drag during the penetration can be mathematically expressed in the same procedure. In order to calculate the surface energy change (AE,) and the work done by viscous drags in a droplet melt (WV), a free body diagram for a particulate during penetration is shown in Fig. 3. In this figure, x is the penetration axis and cp is the spherical coordinate (0 < cp < x). Both x and cp are related by

(12)

Since the size of particulates is much smaller than that of droplets but their density is on the same order of magnitude (Al, Sic, graphite considered here), m, is much smaller than m,. The term m2/(ml + m2) in equations (7) to (13) is approximately equal to unity. To that affect, equations (7)-(13) can be generalized as follows

x = R(l - cos cp).

(17)

Also in Fig. 3, x0 (corresponding to cp,) denotes the penetration depth that the particulate may achieve at an initial velocity V,, with x0 = R (q, = ~~12) for half-particulate immersion and x0 = 2R (cpo= rc) for complete particulate immersion. The immersed part of the particulate in the droplet at any penetration depth is outlined by sphere segment ABC, as shown in Fig. 3. The spherical zone bounded by surface ABC defines the wetted area (AA,,) of the particulate at the penetration depth x0; and the base plane of the sphere segment bounded by plane AC (normal to the penetration direction) represents the reduction in the interface area (AL&) between the droplet liquid and its surrounding gas environment. F, represents the x-component of the frictional drag due to the fluid shear (r) on the particulate and FP is the xcomponent of the pressure drag due to the normal pressure (p) on the particulate. The surface energy change results from the creation of an interface between the particulate and droplet, and a reduction in the surface of the droplet liquid during particulate penetration. During penetration the net change in the surface energy of the particulate-droplet system is given by [12] AE, = A&,+ BE,,+ AEpg

(18)

where AE,,, AE,, and AEPg are the relevant surface energy changes between the particulate and the droplet liquid, between the liquid and the gas, and

Case 1 (14)

vo AEk = -$

Case 3 R3pV;

(1%

where Case 1 Case 2 v. =

(16) i(Vl

+ V2) Case 3.

Fig. 3. Drag

forces acting

on a penetrating

particulate.

ZHANG et al.: KINETICS OF CERAMIC PARTICULATE PENETRATION between the particulate and the gas, respectively. They are given by AEpl = AApffpl

(19)

AElg = AAlgylg

(20)

AEpg = AApgypg

(21)

where ])pl, Ypg and y~gis the surface energy per unit area (surface tension) between particulate and liquid (droplet), particulate and gas, and liquid and gas, respectively, AApl, AApgand AA~gare the corresponding area changes. The wetted area of a particulate during its penetration is equal to the area reduction in the particulate/gas interface, i.e. AApg = -- AApl.

(22)

By substitution of equations (19)-(22) into equation (18), the surface energy change of the system is expressed as AEs = YlgAAIg-- Ylgcos 0 AApl

(23)

where Young's equation [18] Ypg= 7pl + Y~gcos 0

(24)

is used and 0 is the wetting angle between particulate and liquid. Both AAIgand AAo~may be readily calculated using Fig. 3. When a particulate penetrates a droplet by x0, the reduction in droplet surface is given by AAIg= - z ( R sin tp0)2

(25)

AAIg= - x R 2 ( 1 - cos2 ¢Po)

(26)

i.e.

particulates into the droplets reduces the surface energy. This process involves a time-dependent procedure and is discussed elsewhere [19]. For the case of SiC and graphite particulates in an A1 melt, in which the wetting angle is larger than 90 ° [11], the surface energy change given by equation (30) is primarily positive during penetration although the change is less than zero at the initial stages of penetration. The increase in surface energy (positive surface energy change) acts to resist the penetration of the particulates into the droplet. However, the resistance will become zero after the particulate is completely immersed into liquid droplet because no more new interface between particulate and droplet is created. 2.5. W o r k by viscous drag

The viscous drag which the droplet melt exerts on a penetrating particulate is generally a complex function of several factors, such as melt viscosity, particulate velocity and acceleration, particulate geometry and varying contact area between particulate and droplet. In the absence of an analytical solution to the drag forces present in this complex problem, a solid sphere moving through a creeping viscous flow [20] is adapted to model the penetration process of the particulate in the liquid droplet. Accordingly, the viscous drag forces exerted on the particulate during penetration arise from two sources: the normal pressure and the shear friction on the moving particulate surface. The normal pressure and tangential shear stress acting on the surface of a spherical particulate moving in a creeping fluid are given by [20]

and the increase in the wetted area is given by AApl =

f: °

dA

(27)

(28)

Integration of equation (27) gives AApj = 2nR2(l -- cos tpo).

(29)

Substituting equations (26) and (29) into equation (23), the surface energy change is expressed by

The sign of AEs depends on that of the sum inside the second pair of parentheses on the right hand side of equation (30), which means that the surface energy change relies on the penetration depth (q~0) and the magnitude of the contact angle (0) between the particulate and droplet. For those ceramic particulates, such as TiB2, whose contact angles with molten A1 are less than 90 ° [19], the surface energy change given by equation (30) is always negative during penetration, which means the incorporation of the

3r/V cos q~ 2R

(31)

z=

3r/V sin q~ 2R

(32)

where r/is the viscosity coefficient of the melt, V is the velocity of penetration particulate along the penetration path, R is the particulate radius, and tp is the spherical coordinate (0 ~
A E s = - n R 2 y l g ( 1 - cos q~0)(1 + cos tp0 + 2 cos 0).

(30)

p = and

where d A = ( 2 n R sin ~0) (R dq~).

2959

dF~ = ( p d A ) cos ~0

(33)

dF r = ( z d A ) sin go.

(34)

and

By substituting equations (28), (31) and (32) into equations (33) and (34), the resultant of two components given by the addition of equations (33) and (34) can be written as dFv = dFp + d F f = - 3 n R r I V sin ~o dq~.

(35)

The work done along the penetration path (0 ~
2960

ZHANG

et al.: KINETICS OF CERAMIC PARTICULATE PENETRATION Table 1. Physical properties of materials used in this study p (kg/m 3)

AI melt SiC Graphite

2385 3200 2000

0 (°)

Yl¢ (N/m)

r/ (Ns/rn 2)

References

134 152

0.914 ---

1.3 × 10 3 ---

[21] [11,22] [I 1, 22]

from the integration over the contact area of the particulate

W,=-3zrRrlf:°[Vfosintpdq~]dx.

(36)

In this equation the particulate velocity, V, along the penetration path is unknown. Considering the fact that penetration is a decelerated motion with V = IAVI at the beginning of the penetration and V = 0 at the end of the penetration, it is assumed that V takes the following distribution along the penetration path V=IAV,(1-~)

(37)

where IAVI is given by equation (14). Substitution of equations (17) and (37) into equation (36) yields Wv = -½7rR2~/IAVI(1 - cos tp0)2.

(38)

It can be seen from equation (38) that the work done by viscous drag is a function of the penetrating particulate size (R), the droplet melt viscosity (~/), the initial velocity of the particulate (110) and the penetration depth (¢P0).

to be positive, V0 is given in the following form by taking the positive square root in equation (41)

v0=

3(1 - cos ~o0):

8Rp 32Rp~,lg(l + cos tpo + 2 cos 0)-] 3(1 - cos tpo)3 J" (42)

From this equation, the relationships between the initial velocity and size of the particulate, between the velocity and penetration depth, and between the velocity and the viscosity of the droplet melt can be readily obtained. In addition, given any penetration depth (varying ¢P0), the required initial particulate velocity may be readily predicted using equation (42). For complete particulate immersion, the critical initial velocity that the particulate should possess may be obtained by taking ~00= 7z in equation (42) and substituting II0 with equation (16) for Cases 1 and 3 Case 1:

Vlcr=

~

3 I 17 + X/ ~ 2 - - 8Rp'IgC°S 3

(43)

2.6. Critical initial particulate velocityfor penetration and Cases I and 3. For Cases 1 and 3 (Fig. 2), substitution of equations (14), (15), (30) and (38) into equation (1) gives 2nR 3p V0z _ 3

nR

2ylg(1 - - COS([0) (1 + cos tp0+ 2 cos 0) = -½nR2r/(1 - c o s tp0)2V0. (39)

This equation can be rearranged to give a second order equation with respect to V0 in form of

0]

Case 3:

-3w/-2 [q + ;q2-8Rp'l~c°sO.]- V2. (44) 3

V, or -- -~--~p

On the other band, the penetration depth can be expressed as a function of the initial particulate velocity, the particulate size and the viscosity of droplet. By rearranging equation (42), one has x___oo= 71g(1 + cos O)

2Rp V2 _ lq(1 _ cos ~po)2Vo + yig(1 - cos ~Po)

2R

3

x(l+costPo+2cosO)=O. (40) The solution to by

v0=

x[l+;1'

'R-2

(2TIg+~/Vo)

]

(45)

Vo from the above equation is given where V0 is given by equation (16), and x0 denotes penetration depth which is given by equation (I 7) and xo/2R represents the normalized penetration depth, with

3(1 - cos tp0)2

× ~ +-

(2~1~+ ~Vo)

8Rp ~-

~(i---~

"

(41) Considering 0 > ~ / 2 (therefore cos0 <0) for the wetting of SiC and graphite particulates in molten A1 [11], the value given by the square root in equation (41) is generally greater than t/. Since V0 is required

x0 2R

0.5

(46)

for half-particulate immersion, and xo 2R for complete immersion.

1.0

(47)

ZHANG et al.: KINETICS OF CERAMIC PARTICULATE PENETRATION Case 2. This case [Fig. 2(b)] can be analysed by following the procedure as used above. In this case, the driving force results from the initial velocity of droplets (I"2) which is generally determined by spray processing parameters. For a given V2, the penetration depth is calculated by x0 2R

(

71g(1 + cos 0)

R~__2_°v~)

\2yl~ + r/R~p2

× 1+

l+~RpV~ ~p~(l+cos0) 2 3' (48)

3. COMPUTATIONAL RESULTS AND DISCUSSION In order to provide insight into the relationship between the critical injection velocity of ceramic particulates, the penetration depth and other parameters during spray atomization of MMCs, the aforementioned formulation has been applied to the A1/SiC and A1/graphite systems. A1 alloy (in this study, 6061 AI alloy was used), SiC and graphite were selected as examples for the analysis because they have been widely used as constituents in MMCs [6-10]. The phyiscal properties for the three types of materials are listed in Table 1. In this table, p is the mass density, 7ts is the interface energy between the A1 alloy melt and the gas environment, and r/ is the viscosity of the Al melt. It has been noted that the viscosity of the AI alloy melt is a function of the solid fraction (f~, in volume fraction). Kattamis and Piccone [23] experimentally studied the rheological behavior of A1-4.5Cu-I.5Mg (wt%) alloy and found that the apparent viscosity of the semi-liquid A1 alloy may be dramatically increased with a small increase in the solid fraction. Kattamis and Piccone's viscosity data betweenf~ = 0.05 and 0,30 for A1-4.5Cu-I.5Mg alloy and Brandes' viscosity data [21] atf~ = 0.00 are used in the present study to simulate viscous behavior of 6061 AI alloy (Al-l.0Mg-0.6Si-0.28Cu-0.2Cr). The data are curve fitted and expressed as r / = 0.0013 + 0.3783f~ + 40.4738f ~ - 406.0482f 3 + 1533.9573f~- 1687.5581f~.

(49)

3.1. Effect of particulate size One of the most common concerns regarding particulate penetration during spray atomization processing of MMCs is the penetration ability of the particulates with different sizes. The required initial velocity for the particulates of different sizes at different penetration depths is predicted using equation (42) and the critical initial velocity required for complete particulate immersion is calculated using equations (43) and (44). Figure 4 shows the

2961

variation of the required initial velocity of the graphite particulates with particulate size at several penetration depths (Case 1). Also shown in the figure is the critical velocity (V~cr) for complete immersion of graphite particulate into the AI alloy droplet. In this figure, ~/is taken to be 0.0013 Ns/m 2 (corresponding to a pure liquid state with f~ = 0.00); 400= n/2 represents half-particulate penetration and ~00= n denotes complete particulate immersion. It is evident, as seen from the figure, that the critical velocity for complete immersion is approximately inversely proportional to the particulate size, which means that the smaller particulates would require higher initial velocity for complete immersion. On the other hand, the critical particulate size for complete immersion at any given initial particulate velocity can be readily determined from Fig. 4. For example, if the maximum velocity that the injected graphite particulates may acquire from the injection gas is 20 m/s, the minimum size of the graphite particulates for complete immersion is estimated to be d = 6 pm (Fig. 4), indicating that the particulates whose size is less than 6 pm may not be incorporated into droplets. Since the magnitude of the initial particulate velocity is determined by the injector, the requirement of the critical velocity provides a design criterion for the particulate injector to reach the velocity for complete particulate immersion. Figure 5 shows variation of the required initial velocity of SiC particulates with particulate size at different penetration depths (Case 1). The same dependency is observed for both Al/graphite and AI/SiC systems (Figs 4 and 5). However, it is also noted that the initial velocity for SiC particulates is less than that of graphite particulates for the same penetration depth. This is considered to be due to the high density and low wetting angle of SiC particulates in molten AI relative to those of graphite particulates [see equation (42) and Table 1]. Assuming that the particulates with different sizes travel towards droplets at the same initial velocity, the relationship between penetration depth and particulate size may be estimated using equation (45). Figures 6 and 7 show the variation in normalized penetration depth, Xo/2R, with particulate size for both graphite and SiC particulates, respectively (Case 1). It is seen that the penetration depth is proportional to the particulate size under the conditions used herein. In these two figures, Xo/2R = 1 indicates complete immersion. Once again, the critical particulate size for complete immersion can be readily determined for each initial velocity at the intersection point of the corresponding curve with Xo/2R = 1 (see Figs 6 and 7). Figures 8 and 9 shows the variation in normalized penetration depth, xo/2R, with particulate size of graphite particulates for Cases 2 and 3, respectively. In Figs 8 and 9, several different solid fractions in droplet liquid are considered to evaluate their effect on the penetration. In the two cases, a value of

G.

"El, B

;-? . . . . 20.0

Voc r V S . R at q~o=~

- " - B ' - it

---O-- ~/4 -- • - - ~/2 - -El- 3~/4

Xo=R(1-coSq~o) at

°'°'e--eo - o . - e . ~ . 9 . . . . ; - - , . . . . . ?-0.0 . . . . I . . . . . . . "",,0.0 5.0 10.0 15.0 Particulate Radius R (pro)

10.0

20.0

30.0

40.0

Penetration Depth

~=0.0013 Ns/m 2

~g=0.914 N/m

AI/Graphite 0=152 °

25.0

Fig. 4. Variation in initial velocity (V0) of graphite with paritculate size (R) for different penetration depths (Case 1).

_¢

¢1

O

•

0

2

u

>

A

50.0

60.0

5.0

10.0

15.0

0.0

(K

5.0

Q "O.

10.0 R (pro)

0- O-.,•..Q . ~ - ~ .

15.0

Vlcr

.-.-.ll.- g

- - - e - - ~/4

20.0

--In

Penetration Depth

AI/SiC 0=134 °

25.0

Fig. 5. Variation in critical initial velocity (V0) of SiC particulate with particulate size (R) for different penetration depths (Case 1).

>

v

20.0

25.0

30.0

35.0

40.0

z

~H

Z

C >

-]

'-o >

©

z ,.q

o.

> Z

N

O~ tO

to

ZHANG et al.: KINETICS OF CERAMIC PARTICULATE PENETRATION 250 m/s was calculated for the velocity of droplets

(V2) and 20m/s for the droplets (V~) [24]. Figure 8 shows that all ceramic particulates entrapped by the atomized metallic droplets could penetrate the droplets and could be embedded inside the droplets no matter how large the initial velocity of the penetrating particulates (Case 2). In Case 2, as long as the particulates enter the atomization cone at any initial velocity (Fig. 1), the extent of penetration would primarily depends on the magnitude of velocity of the atomized droplets. Figure 8 demonstrates that the driving force for the penetration of ceramic particulate into the droplets due to the droplet velocity was so large that it made it possible for all particulates of different sizes to penetrate into the colliding droplets. In Case 3 (Fig. 9), the kinetic energy of the atomized droplets played a dominant role in the penetration of particulates into the droplets since the droplet velocity was much larger than that of particulates. The extent to the penetration of particulates into droplets depends on the size of the particulates. At a solid fraction of 0.25 in the atomized droplets, which most frequently happened when the particulates were injected into the atomization cone at the predetermined location [13 17], the completed immersion of particulates occurred only to those particulates whose size was larger than 10/~m (R = 5 pm, Fig. 9).

3.2. Effect of solid fraction The aforementioned discussion of the penetration behavior of SiC and graphite particulates in Figs 4-7 was based on the assumption that the droplets are in a pure liquid state. In fact, the interactions between the injected ceramic particulates and the atomized metallic droplets take place in a non-equilibrium state during spray atomization and therefore some solidification products are present inside the atomized droplets [13, 14]. Therefore, it is reasonable to consider the atomized droplet to be in a semi-liquid state. The semi-liquid droplets may be characterized by a variable viscosity since there is a close relationship between viscosity and solid fraction [23]. The viscous drag exerted by droplets on penetrating particulates may be dramatically increased by an relatively small increase in viscosity due to the presence of solid phases in the semi-liquid droplet [equation (49)]. Figure 10 shows a comparison between the work done by the viscous drag [Wv, see equation (38)] and the surface energy change [AEs, see equation (30)] as a function of solid fraction [equation (49)]. When droplets are in a pure liquid state and the solid fraction is very small, as illustrated in Fig. 10, the resistance to particulate penetration results primarily from the surface tension. At this point, the initial kinetic energy of particulates is largely transformed to ovecome the surface energy change during penetration. As a result, the viscous drag resistance of the pure liquid droplet to the penetration is relatively small and may be safely

2963

neglected. However, the viscous drag resistance may become comparable to the surface tension resistance as the solid fraction increases, primarily depending on the magnitude of the initial velocity of particulates (Fig. lO). Figure 11 illustrates the variation of critical velocity as a function of solid fraction for complete immersion of graphite particulate with a size range from 1.5 to 10/~m (Case 1). From this figure, the effect of solid fraction on the required critical veloctiy for complete particulate immersion can be readily estimated. For example, the critical velocity required for complete immersion of a 5 #m graphite particulate into a pure liquid droplet is estimated to be 22 m/s; however, the critical velocity is approximately doubled when the solid fraction is increased from fs = 0 to 0.05. From Fig. 11, the possibility for a graphite particulate to penetrate into a droplet may be increased by increasing particulate size and velocity or by controlling the viscosity in droplets. Of the three variables, the viscosity of droplets plays a dominant role since a small increase in the solid fraction may induce a significant increase in viscous resistance. The solid fraction at which particulates collides with droplets may be controlled through adjusting the position of the injection nozzle along the atomization cone during spray atomization and co-injection. Figures 12 and 13 show the variation of critical velocity required for the immersion of graphite and SiC particulates as a function of particulate sizes at different solid fractions, respectively (Case 1). Figure 14 illustrates the variation in normalized penetration depth, Xo/2R, with particulate size of graphite particulates (Case 1). In this figure, several different solid fractions in droplet liquid are considered to evaluate their effect on the penetration.

3.3. Relationship between penetration depth and particulate velocity The maximum penetration depth for a particulate at a given initial velocity may be estimated using equations (45) and (48). Figures 15 and 16 shows the variation in penetration depth with initial velocities for graphite and SiC particulates, respectively (Case 1). When droplets are in a pure liquid state (r/= 0.0013 Ns/m2), the penetration depth for both graphite and SiC particulates is a approximately linear function of the initial velocity of the particulates. As the solid fraction increases, the dependency evidently grows due to the brief increase in viscous drag. This can be clearly seen from Figs 14-16 which illustrate curves for the penetration depth vs the initial velocity when a fraction of solid is present in the atomized droplet (f~ = 0.10).

3.4. Comparison with experimental results Interaction mechanisms between gas-injected SiC particulates and atomized A1 droplets have been

0.0

0.0

0.2

0.4

0.6

®°

I

o"

oi ~

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I

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,

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/~

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15rn/s

10 m/s

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•

/

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25.0

Fig. 6. Variation in penetration depth (Xo/2R) o f graphite particulate as a function o f particulate size R (Case 1).

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0

N

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Fig. 7. Variation of penetration depth (Xo/2R) o f SiC particulate as a function of particulate size (Case I).

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fit.

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Fig. 8. Variation of penetration depth (Xo/2R) of graphite particulate as a function of particulate size (Case 2).

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Fig. 10. Ratio of work done by viscous drag (W,) to surface tension resistance (AE,) as a function of solid fraction (f~) during complete immersion of a graphite particulate,

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Fig. 11. Variation of critical veloctiy (V~cr) with solid fractions (f~) in droplet for complete immersion of a graphite particulate (Case 1).

0.0 0.00

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100.0

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250.0

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400.0

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Fig. 12. Variation o f critical velocity (Vt¢~) required for complete immersion o f graphite particulate as a function of particulate size (R) at different solid fractions in droplet (Case I).

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25.0

Fig, 14. Variations in penetration depth (xo/2R) with graphite particulate sizes for different solid fractions (Case 1).

x

e¢

1.5

2.0

0.0

,

:'

,

,

,

,

,

,

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=

,

°

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,

,

V I ( m/s )

,

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,

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,

g

I

,

,

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,

,

,

,

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f=0.10

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100.0

,

.o

,

,

,

150.0

AI/Gr

Fig. 15. Variations in penetration depth (x~/2R) with initial velocity (Vo) for graphite particulate for different solid fractions and particulate sizes (Case 1).

0.0

0.2"

0.4

0.6

0.81

1.0

z

rn

c

Q

z

> Z 0

ZHANG et al.: KINETICS OF CERAMIC PARTICULATE PENETRATION

rationalized on the basis of differences in density. Comparison between Figs 12 and 13 shows that the higher the density of penetrating particulates, the higher the likelihood that the particulates will penetrate and become completely immersed into the droplets. This finding is consistent with theoretical and experimental results discussed elsewhere [14, 19]. The second observation that is evident from Fig. 17 is that larger SiC or graphite particulates populated the droplet surfaces, whereas small particulates were present in the interior of the droplets, the latter observation suggesting the presence of droplet penetration. This observation appears to be in conflict with the results obtained from the present model which predicts that for the particulates with the same initial velocity, the larger the particulates are, the more likely they are to penetrate droplets. This apparent discrepancy may be rationalized from the assumptions that were used in the development of the model. The model developed herein does not take into account the transfer of thermal energy from molten droplets to ceramic particulates. Accordingly, in the model formulation it is implied that both large

reported by Wu and Lavernia [14], and those between graphite particulates and AI droplets have been reported by Perez [25] and Wu et al. [14, 19]. The results on the A1/SiC composite powders from these studies [14, 19, 25] reveal that small SiC particulates are generally found in the interior of the powders while relatively large SiC particulates are seen at the surface [14, 19]. Figure 17 shows optical microstructures of A1/SiC and A1/Gr from collected over-spray powders that were obtained during spray atomization and deposition [14, 19, 25]. The first observation that is evident from Fig. 17 is that the volume fraction of SiC particulates in the droplet is higher than that of graphite particulates, which implies that the penetration in the AI/SiC system is easier than that in the AI/Gr system. This observation is in agreement with the aforementioned computational analysis. From the model developed in the present study, SiC particulates need a smaller critical initial velocity to penetrate droplets relative to that required for graphite particulates. On the other hand, for a given initial velocity, the difference in penetration capability between SiC and graphite particulates can also be 1.0

..o""

/'" /,." i

0.8

..."

i/~t";

"'g

0.6

8.4 fs=O.O0 •

---0-

fs=O, lO

R=2.5 ~rn

---o-

-~E3- - 5.0 I~m ¢

0.2

0.0

,

0.0

,

,

I

20.0

,

,

,

I

2969

---m- - 5.0 I~m

7.5 I~m

,

~

,

40.0

2.5 rim

•

I

60.0

,

,

7.5 IJm

,

I

80.0

~

,

,

100.0

V 1 (m/s)

Fig. 16. Variations in penetration depth (xo/2R) with initial velocity (II0) for SiC particulate for different solid fractions and particulate sizes (Case 1).

2970

ZHANG et al.: KINETICS OF CERAMIC PARTICULATE PENETRATION

i

Fig. 17. Optical micrograph showing the presence of (a) SiC and (b) graphite particulates in AI/SiC and A1/Gr droplets processed using spray atomization.

and small particulates will experience identical thermal environments during penetration. In practice, however, the differences in heat transfer effects between large and small particulates may be significant during penetration. In particular, heat absorption by the particulate as it enters the droplet may cause local solidification, which would abruptly arrest its penetration by raising the viscosity of the liquid metal. This effect may be pronounced for large particulates, which absorb more thermal energy relative to that absorbed by smaller particulates. Accordingly, the extent of solidification in droplets that are impinged by large particulates will be higher than that present in droplets that are impinged by small particulates, with a concomitant increase in resistance

to particulate penetration. This phenomenon may be explained using the results shown in Figs 8, 9 and 14, It can be seen from these three figures that the magnitude of solid fraction in droplets dominates the extent of penetration (i.e. depth). Along the line of Xo/2R equal to unity (Figs 8, 9 and 14), which describes a condition for complete immersion of a penetrating particulate into a droplet, the minimum particulate size that is required for complete particulate immersion into a droplet increases as the solid fraction in droplets increases. Qualitative analysis of the results shown in Figs 8, 9, and 14 suggests that the larger the size of the penetrating particulates, the higher the amount of thermal energy that the particulate absorbs from the droplet, and thus, the higher the volume fraction solidified and the higher the resistance to penetration. This suggestion is in agreement with the experimental results shown in Fig. 17 in which the number of large particulates is smaller than that of small particulates in the interior of a droplet. Another factor which may influence penetration behavior is the angular momentum effect when an injected ceramic particulate collides with a traveling droplet along an off-axis. In the present model formulation, penetration was assumed to occur when a particulate collided with a droplet along the same axis (head-on), that is, only linear momentum transfer occurred during the collision, and hence angular momentum was not considered. During an off-axis collision, however, an angular momentum for either particulate or droplet may be generated. If the angular momentums of both particulate and droplet rotate in the same direction (e.g. clockwise or counterclockwise) during collision, penetration will be enhanced. However, if the angular momentums of droplet and particulate are in opposite directions, the resultant forces will tend to drive particulate and droplet into separate paths. The angular momentum effect was not taken into account in the present work to maintain the model formulation tractable. This is an area of further study. 4. CONCLUDING REMARKS The penetration behavior of graphite and SiC particulates into atomized metallic droplets during spray atomization may be predicted using a kinetic approach. By considering the surface energy change and viscous drag, the present model reveals that the critical velocity and the minimum particulate size for complete particulate immersion was a function "of particulate size and solid fraction in droplets. Three cases were studied according to three particulatedroplet head-on collision directions in which: (I) a particulate collides with a passing droplet in front of the particulate and the penetration of the particulate into the droplet occurs along the initial traveling direction of the particulate; (2) a droplet collides with a moving particulate inside the atomization cone and in this case penetration of the particulate into the

ZHANG et al.: KINETICS OF CERAMIC PARTICULATE PENETRATION droplet occurs against the initial traveling direction of the droplet; (3) a particulate collides with a droplet at an angle of 45 ° and the penetration of the particulate into the ceramic droplet occurs at an angle of 45 ° to the initial traveling direction of both particulate and droplet. From the computational results of M/graphite and A1/SiC systems using the model developed herein, the following observations may be summarized. 1. The critical initial velocity of graphite and SiC particulates for complete particulate immersion into atomized AI droplets is inversely proportional to particulate size (Cases 1 and 3). The particulate penetration depth at a given particulate velocity, however, is proportional to the particulate size. At a given initial velocity, the minimum particulate size required for complete particulate immersion may be estimated from a critical velocity versus particulate size graph and it is found that large particulates have more opportunity for complete immersion into the collided droplets than that of small particulates. 2. The resistance to particulate penetration dramatically increases with increasing solid fraction in the semi-liquid droplets. The kinetic energy of the penetrating particulates due to an initial velocity (Case 1) is primarily dissipated to ovecome the surface tension resistance during penetration when the atomized droplets are in a complete liquid state. Once a fraction of solid in the droplets is present, however, the fluid viscous drag is sharply increased with increasing solid fraction. When the solid fraction is as low as 0.01, the fluid viscous drag becomes comparable with the surface tension resistance. 3. The critical velocity required for complete immersion of SiC particulate into the A1 alloy droplet is tess than that of graphite particulate with the same size. The difference in penetration behavior between SiC and graphite particulates may be ascribed to the relatively high density of SiC particulates and small contact angle between SiC and molten A! in comparison with those of graphite particulates (Case 1). The difference may also result from different effects of droplet-to-particulate heat transfer on penetration between SiC and graphite particulates. Acknowledgement--The authors gratefully acknowledge the

financial support of the United States Army Research Office (Grant No. DAALO3-92-G-0181).

2971

REFERENCES

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5. 6. 7. 8. 9. 10. 11.

(edited by T. F. Bernecki), p. 329. ASM International, Materials Park, Ohio (1992). T. S. Srivatsan and E. J. Lavernia, J. Mater. Sci. 27, 5965 (1992). E. J. Lavernia, S A M P E Q. 22, 2 (1991). E. J. Lavernia, J. A. Ayers and T. S. Srivatsan, Int. Mater. Rev. 37, 1 (1992). I. A. Ibrahim, F. A. Mohamed and E. J. Lavernia, J. Mater. Sci. 26, 1137 (1991). M. Gupta, F. A. Mohamed and E. J. Lavernia, Metall. Trans. 23A, 831 (1992). R. J. Perez, J. Zhang, M. N. Gungor and E. J. Lavernia, Metall. Trans. 24A, 701 (1993). A. S. Kacar, F. Rana and D. M. Stefanescu, Mater. Sci. Engng A 135, 95 (1991).

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