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Trans. Indian Inst. Met. Vol.57, No. 3, June 2004, pp. 283-296

MODELING OF HEAT FLOW AND SOLIDIFICATION DURING SPRAY DEPOSITION PROCESS P.Shukla, R.K.Mandal and S.N.Ojha Department of Metallurgical Engineering, Banaras Hindu University, Varanasi- 221 005, India E-mail address: [email protected] (Received 28 October 2002 ; in revised form 7 June 2004)

ABSTRACT The solidification behavior of droplets as well as spray-deposit of Al-4.5 wt% Cu alloy is simulated by modeling based on heat flow analysis. The model incorporates droplet dynamics and their thermal states during atomization process. The resultant spray enthalpy is used to analyze heat flow during solidification of the spray deposit. The effect of process variables like atomization pressure, melt superheat and nozzle to substrate distance on the solid fraction and enthalpy of the spray is analyzed. The results of modeling are compared with the experimentally determined thermal profile of the spray deposit. The results indicate that the cooling rate for a wide size range of droplets varies from 103-105 Ks-1 in contrast to a slow cooling rate of 1 to 10 Ks1 of the spray deposit. Empirical correlation between cooling rate of the spray deposit and the grain size has been established. It is inferred that cooling rate is not the sole determining factor in controlling grain size of the deposit during spray deposition process.

NOMENCLATURE

h

Symbol Description

Units

Ad

Surface area of droplet

m2

CD

Coefficient of drag

-

CL

Specific heat capacity per unit mass of liquid

CS

Specific heat capacity per unit mass of solid

Cpd

Specific heat per unit mass of droplet

CLS

Convective heat transfer coefficient at droplet gasinterface

W m-2 K-1

htop

Heat transfer coefficient at deposition surface

W m-2 K-1

hbot

Heat transfer coefficient at substrate-deposit interface

W m-2 K-1

Hd

Enthalpy of droplet per unit mass

J kg-1

&Hd

&Hf - (CL-CS)(TL-Td)

J kg-1

&Hf

Latent heat of fusion per unit mass

J kg-1

H

Enthalpy in the deposit per unit mass

J kg-1

J kg-1 K-1 J

kg-1

K-1

J kg-1 K-1

Specific heat per unit mass of solid-liquid mixture

J kg-1 K-1

d

Diameter of droplet

Om

fs

Solid fraction

-

fR

Solid fraction generated during recalescence

-

g

Acceleration due to gravity

m s-2

HSPRAY Spray enthalpy per unit mass J kg-1 k

Average thermal conductivity of the alloy W m-1 K-1

kg

Thermal conductivity of gas

W m-1 K-1

TRANS. INDIAN INST. MET., VOL. 57, NO. 3, JUNE 2004

ko

Partition coefficient

-

1. INTRODUCTION

md

Mass of droplet

kg

Pr

Prandtl number

-

Re

Reynolds number

-

Td

Temperature of droplet

K

Tg

Temperature of gas

K

TL

Liquidus temperature

K

TR

Recalescence arrest temperature

K

TS

Solidus temperature

K

TE

Eutectic temperature

K

TM

Melting point of pure solvent

K

TN

Nucleation temperature

K

Tgas

Temperature of atomizing gas

K

Tsub · T

Temperature of substrate

K

Cooling rate of droplet/preform

K s-1

Vg

Velocity of gas

m s-1

Vd

Velocity of droplet

m s-1

x

Distance solidified along growth axis

m

y

Distance in the preform

m

Y

Height of deposition surface

m

Deposition rate per unit area

kgs-1m-2

Spray deposition (SD) has emerged as a viable alternative to the casting and powder metallurgy routes of processing monolithic as well as composite materials 1-5. Its potential for producing near-net shape products has already been demonstrated in the past for different applications 6-7. Spray deposition involves atomization of a molten material by high velocity gas jets into a spray of micron-sized droplets which are subsequently propelled and deposited onto a substrate to produce preforms of desired shapes through maneuvering of the substrate. Owing to the heat transfer by forced convection between the droplets and the gas, rapid solidification effects are realized 8. This has been demonstrated based on the microstructural refinement and chemical homogeneity that are achieved in the spray deposits. For a given nozzle assembly, the atomization gas pressure, melt superheat and the nozzle to substrate distance are the process variables which influence the thermal state of the spray during flight and on the deposition surface. The former governs the nature of undercooling that a droplet experiences and the latter largely controls the microstructural characteristics of the preform. Hence there is a need for understanding the nature of microstructural evolution during SD process. In the past, several attempts have been made for modeling the various steps involved in SD 9-13 but an integrated and comprehensive model combining the process of atomization, droplet dynamics and thermal state of the deposition surface is limited in literature10. In the present work, an attempt has been made to develop an integrated approach by combining the outcome of the droplet dynamics with that of heat transfer on the substrate. This includes (a) experimental measurement of gas velocity between the substrate and nozzle exit (b) computing the velocity and temperature profile of different sized droplets as a function of flight distance and (c) determining the spray enthalpy at the deposition surface and the temperature profile of the deposit. Further, a comparison between the computed and measured temperature profile of the deposit has been carried out. The experiment conducted as part of this investigation has served two objectives. These include (a) supplementing the computed data based on model and (b) comparing the predicted behavior

· Y S

Wetting angle degree

T

Density of spray deposit

kg m-3

Tg

Density of gas

kg m-3

Td

Density of melt

kg m-3

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SHUKLA, et al., : MODELING OF HEAT FLOW AND SOLIDIFICATION DURING SPRAY DEPOSITION PROCESS

with respect to microstructural characterisations of the preform vis-àvis those obtained by experiment. The results facilitate an insight into the microstructural evolution during SD process.

2. EXPERIMENTAL DETAILS 2.1 Gas Flow Measurement An indigenously designed convergent-divergent spray nozzle with a throat area of 20.5 mm2 and an exit to throat-area ratio of 3:1 was used to atomize the melt. A metallic flow tube having a concentrically aligned ceramic insertion is used to deliver the melt in the gas stream to promote atomization. The axial velocity of the gas was measured using a Pitot tube aligned below the nozzle exit. The static and stagnation ends of the Pitot tube were connected to a mercury manometer. The Pitot tube was traversed axially downward and the deflection in the mercury column was recorded at regular intervals of 5.0 mm at reservoir pressures of 0.8, 1.0 and 1.2 MPa. These measurements have provided data to calculate the gas velocity at a particular gas pressure and axial distance. 2.2 Atomization and Spray Deposition The atomization of the melt was carried out in nitrogen environment at reservoir pressures of 0.8, 1.0 and 1.2 MPa. The droplets were allowed to solidify during flight. The powder particles were collected at the bottom of the atomization chamber and sieved into various size fraction following ASTM standard B 214 procedure14. The sieve analysis data provided the median particle diameters in the size range of 60-70 Om and these were used in the analysis of the heat flux calculations on the deposition surface. In another experiment, a mild steel substrate was introduced at distances of 0.35 and 0.45 m along the spray axis. Two Chromel-Alumel thermocouples, centered along the axis of the spray and inserted through a fine hole in the substrate were used to measure the temperature profile within the deposit as shown schematically in Fig. 1. The hot junctions of the thermocouples were positioned at a height of 2.0 mm and 10.0 mm from the surface of the substrate. The output of the thermocouples was recorded during and after deposition using a Data

Fig. 1

: Schematic diagram of the spray deposition set-up.

Acquisition System having a response time of 1.0 sec. 2.3 Microstructural Examination The specimens for microstructural examination were machined from various locations of the spray deposit. These were polished using standard metallographic procedure and etched with Keller’s reagent consisting of 1.0 % HF. 1.5 % HCl, 2.5 % HNO3 in water. The microstructural examination was carried out using a Leitz optical metallograph. The size and size distribution of the grains were studied using quantitative metallographic procedure by using a VIDS Image Analyzer.

3. FORMULATION OF THE MODEL The consideration of heat transfer process associated with spray deposition involves two distinct but closely related steps. These include (1) atomization including flight of droplets till impingement and (2) deposition of the aggregate of undercooled droplets onto the substrate. The complexity of the atomization process and our limited understanding about the various phenomena involved preclude any analytical solution of the problem. Most of our understanding about the physical phenomena involved in spray forming and

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the effect of process parameters on size and size distribution of powders is based on experimental results. The size and size distribution of droplets produced during atomization at different atomization conditions is determined by characterizing the powders produced during atomization. The axial gas velocity as a function of distance from the nozzle exit (Cf. section 2.1) is measured and used as an input in solving the momentum equation to determine the velocity of droplets of different sizes. The relative velocity between the atomizing gas and the droplet determines the heat transfer coefficient at the dropletgas interface. This coefficient is used to calculate the time-temperature history of droplets by applying energy conservation equation. The thermal history of the droplet is used to evaluate the solidification behavior of the droplet by invoking solidification theory. A five-stage solidification regime comprising of (1) cooling in the liquid state till nucleation (2) recalescence of the undercooled droplet (3) segregated solidification (4) eutectic solidification and finally (5) cooling in the solid state has been considered. Size-dependent undercooling of droplets based on volume separation of nucleants15-16 existing in the melt has been employed. The above mentioned computations are performed initially on droplets of specific sizes. Subsequently, the characteristics of the spray are determined from the experimentally determined size of the droplets in the spray17. This includes the spray enthalpy, which is an input for the deposition stage and is used to calculate the thermal history of the deposit. A one-dimensional heat transfer model, using a finite difference method is employed to calculate the temperature of the deposit by establishing a heat balance between the incoming enthalpy of the spray and the heat dissipated from the deposit. All the parameters utilized as input in the model pertain to Al-4.5 wt. % Cu alloy. The physical properties of the gas are taken from Holman18 whereas those of Al-4.5 wt% Cu alloy from Swaminathan19 and are given in Appendix I.

atomizing gas is utilized to atomize the melt. As a result of this, there would be very little change in the velocity of the atomizing gas due to the energy consumed for atomization and hence the atomizing gas velocity measured without atomization can be used even for the case where atomization takes place. The solution of the momentum equation provides the velocity of the droplet. In the present analysis, only a one dimensional flow is considered and hence the radial component of the gas velocity has been ignored. Applying Newton’s law of motion on a droplet of diameter d in the vertical direction yields a generalized equation of the form.20 md

+ md g +

ρg ρd

md g

) (1)

with the initial condition that Vd = 0 at time t = 0. The first term on the right hand side of Eqn. (1) denotes the drag force, the second the gravitational force and the third the buoyancy force acting on the droplet. The drag coefficient CD arises because of flow separation around the droplet and is a function of the Reynolds number (Re). The expression for CD 21 for a wide range of Reynolds number varying from 0.1 < Re < 4000 is given by

C D = 0.28 +

6.0 21 + 0.5 Re Re

(2)

A velocity dependent heat transfer coefficient is obtained by the well-known correlation of Ranz and Marshall22. h=

kg d

(2.0 + 0.6 Re

0.5

Pr 0.33

)

(3)

A generalized heat balance equation for a droplet during solidification23 is given by

3.1 Droplet Dynamics and Thermal State In spray atomization, the atomizing gas transfers a part of its kinetic energy to disintegrate the melt into droplets and the remainder is used to accelerate the droplets towards the deposition surface. It has been reported17 that only about 3% of the energy of the

(

dVd 1 = − ρ g Ad C D Vg − Vd Vg − Vd dt 8

dH d dT df = C pd d − ∆H d s dt dt dt

Cpd and &Hd are given by

286

(4)

SHUKLA, et al., : MODELING OF HEAT FLOW AND SOLIDIFICATION DURING SPRAY DEPOSITION PROCESS

C pd = C L − (C L − C s ) f s

(5)

∆H d = ∆H f − (C L − C s )(TL − Ts )

(6)

The details of the solution are given by Shukla et al16. Recalescence arrest temperature TR is obtained by

The L.H.S. in eqn. (4) denotes the rate of change of enthalpy with time while the two terms in R.H.S. denote respectively the change in sensible heat of the droplet and the latent heat released as a result of solidification. Assuming a linear crystal growth velocity for low undercooling24 and a twinned spherical solidification interface given by Lee and Ahn12, the governing differential equation for heat transfer in a droplet assumes the following form C pd

(

6h Td − Tg ρd d

)

(7)

subject to the initial condition that Td = TL at x=0 and t=0. The growth velocity for highly undercooled melts shows a power law relationship with melt undercooling25. However, owing to lack of information regarding the value of Ki for highly undercooled melt, a linear relationship has been considered which is true for small to moderate degree of undercooling of the melt. The droplet temperature is obtained inserting the expression for crystal growth velocity into eqn. (7). The temperature profile during recalescence is obtained by

1 Td = TN − ki

 A1 x 3 A2 x 2     3 + 2 + A3 x + A4 t   

−3ki ∆H d 3ki ∆H d : A2 = : 3 2C pd d C pd d 2

A3 =

− 6 hki Tgas − T L − 6h : A4 = C pd ρ d d C pd ρ d d

(

)

The modeling of heat transfer during the deposition stage follows the solution of droplet heat transfer and their solidification behavior. The thermal condition of the mass median particle diameter is assumed to represent the thermal condition of the entire spray 17 and the total spray enthalpy is calculated based on this. On the basis of this assumption and with the mass flow rate of the melt known, the incoming spray enthalpy is calculated. The equation governing the heat transfer in the preform using an enthalpy formulation27 is given as

(8)

(9)

(10)

3.2 Heat Flow During Deposition

ρ

where the constants are defined as A1 =

1

 T − TR  (1− ko ) f s = 1 − (1 − f r ) M   TM − Td 

It must be emphasized that Schiel’s equation 26 assumes no diffusion in the solid state and complete mixing in the liquid phase with equilibrium at the liquid-solid interface. The temperature profile during the eutectic solidification and in the solid state is obtained by solving Eqn. (7) with relevant conditions.

dTd df s k i (T L − Td ) = Hd dt dt

−

dTd = 0 i.e. when the rate of release of dt latent heat slows down and equals the heat dissipated into the quenching medium. After the end of recalescence, further solidification of the droplet involves solute segregation. The fraction of solid generated during this mode by solidification can be predicted by Scheil’s equation.

setting

∂  ∂T ∂H = k  ∂y  ∂y ∂

  

(11)

where at time t = 0 and y = 0, T = Tspray corresponding to the deposition distance. The average thermal conductivity (k) is the mean of thermal conductivity of liquid and solid melt. Enthalpy has been used in the above formulation to take into account the change in heat content as a result of solidification. The computational domain in the y direction (growth direction) is of length Ydep and is the deposit height formed during the deposition 287

TRANS. INDIAN INST. MET., VOL. 57, NO. 3, JUNE 2004

period. In a chosen computational time interval (say t), the increment in height is y = t ( Ydep/tdep). At the end of each time increment, the temperature of the instantaneous topmost surface is put equal to Tspray corresponding to the current deposition distance. At the bottom surface of the deposit, a heat flux balance yields k

∂T = hbot [T − Tsub ] ∂y

(12)

At the top surface of the growing deposit, the heat balance is given by

H =

f sC s (T − Ts ) + (1 − f s )C L (T − TS )

+ (1 − f s )∆H f + C S (TS − TE ) for TS < T < TL (15) H =

CS(T – TE)

for T < TS (16)

In eqns. (14-16), the reference temperature for enthalpy measurement is TE, the eutectic temperature. The enthalpy term consists of the sensible heat of the solid till T = TS, the heat of fusion &Hf, sensible heat of the solid-liquid between TL & TS and the sensible heat of the liquid above TL.

4. RESULTS AND DISCUSSION (13)

4.1 Droplet Velocity and Thermal State

In eqns. (11-13), H is the net enthalpy input at the top surface of the deposit and is equal to the difference between the enthalpies of the incoming • spray and the topmost layer of the deposit and Y is the deposition rate per unit area. In the absence of measured values of heat transfer coefficient, in the present investigation a value of 1100 W m-2 K-1 has been used for hbot during the deposition stage. A convective heat transfer coefficient (htop) value of 200 W m-2 K-1 during the deposition stage and 100 W m-2 K-1 during natural cooling in the postdeposition stage has been used. The spray impinging on the substrate imparts a high value of heat transfer coefficient (hbot) because of the intimate contact between the deposit and the substrate during the deposition process. Similar values have been reported by other investigators17. The gas velocity at the deposition surface falls to a value close to around 50 ms-1. At this value of gas velocity, the forced convective heat transfer at the top surface (htop) has been reported to be around 200 W m-2 K-1 by Estrada and Duszczyk28 while a lower value is reported when the gas is turned off because then the cooling occurs by natural convection. These values are commensurate with those reported by other investigators17. Enthalpy and temperature are related by the following relationships. H = + ∆H f + C S (TS − TE )

for T > TL (14)

The measured gas velocity showed an exponential decay with distance with a velocity decay profile represented by an equation of the form Vg = A + Be

 z − zo     C 

(17)

where the constants A, B, zo and C are 15.88, 376.06, 0.0326 and 0.080 respectively in appropriate units for a reservoir pressure of 1.0 MPa. The gas velocity measurements were repeated three times and the error was within ±2 %. The mass flow rate of the gas through the atomizer was measured by a rotameter connected on-line and calibrated for an inlet gas pressure of 1.20 MPa in a mass flow rate range of 0.61-6.1 kg min-1 of nitrogen gas. The variation in velocity of different-sized droplets as a function of flight distance computed using eqn. (1) is presented in Fig. 2. A comparison of the velocity profiles of a wide size range of droplets in the spray shows that a 20 Om droplet attains a maximum velocity of 230 m s-1 in less than 0.1 m compared to a maximum velocity of 100 m s-1 of a 160 Om size droplet attained at a flight distance of 0.15 m. Other intermediate size droplets show a similar behaviour. Larger size droplets, due to their large inertia, are observed to accelerate and decelerate slowly at greater flight distance compared to small size droplets. The temperature profiles of different size droplets as a function of flight distance are

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0.15 m. The droplet of 160 Om remains in a mushy state till a much larger distance. Droplets of intermediate sizes show similar behaviour. 4.2 Spray Characteristics

presented in Fig. (3). These are obtained by employing Eqn. 7 with appropriate modifications corresponding to the solidification condition mentioned in Section 3.0. Prior to solidification, the droplets in the spray are subjected to different undercooling depending upon their size. The present work, based on the analysis of nucleant free fraction of droplets in gas atomization process, facilitates to predict the size dependent undercooling of droplets. Considering droplet size limits of 10 and 180 Om for homogeneous and heterogeneous nucleation condition respectively, the expression for size dependent nucleation potency of droplets can be obtained as f(S) = a + bd–1.16 The undercooling achieved by two widely different size droplets of 20 and 160 Om is 175 and 10 K respectively. Fig. 3 shows the five distinct stages of cooling and solidification for the 20 Om droplet where complete solidification takes place at a flight distance of about

The spray characteristics represent the aggregate effect of droplets comprising the spray under different atomizing conditions. The sieve analysis of the atomized powders at atomization pressures of 0.8, 1.0 and 1.2 MPa yielded the mass median particle diameters of 74, 64 and 60 Om respectively. The temperature of these particle sizes at the desired deposition distance was used to calculate the spray enthalpy. The spray characteristics at deposition distances of 0.35 and 0.45 m are shown in Table 1. A lower spray temperature and consequently higher solid fraction at larger deposition distance is observed. The effect of gas pressure on the spray enthalpy at various deposition distances is presented in Fig. (4) while the effect of superheat on the incoming spray enthalpy is presented in Fig. (5). These figures are used to calculate the enthalpy of the incoming spray at different deposition distances and degree of superheat and is used as an input in Eqn. (11). It is seen that the spray enthalpy decreases with an increase in the deposition distance owing to the fact that a longer flight time of the droplet to travel larger deposition distance facilitates heat removal and consequently a decrease in the incoming spray enthalpy. The relationship between atomization gas pressure and incoming spray enthalpy however depends on two opposing tendencies. A higher atomization pressure leads to an increase in the gas

Fig. 3

Fig. 4

Fig. 2

: Variation in gas and droplet velocity for a wide size range of droplets (Gas exit velocity=384 ms-1

: Temperature profile of two widely different sized droplets during cooling from a melt superheat of 100 K.

289

: Effect of gas pressure on the spray enthalpy at different deposition distances.

TRANS. INDIAN INST. MET., VOL. 57, NO. 3, JUNE 2004

Table 1 THE SPRAY CHARACTERISTICS AT DEPOSITION DISTANCES OF 0.35 AND 0.45 m.

Deposition Distance (m)

Spray Temperature (oC)

Solid Fraction (fS)

Spray Enthalpy (kJ kg-1)

0.35

632

0.62

212

0.45

600

0.84

104

content impinging on the top surface of the preform, a judicious choice of melt superheat and atomization gas pressure can produce preforms of optimum shape and the desired microstructure of the spray-deposit. 4.3 Cooling Rate of the Spray-Deposit

Fig. 5

: Effect of melt superheat on the spray enthalpy at different deposition distances.

exit velocity and reduces the size of droplets due to more efficient atomization29. Hence the spray enthalpy is determined by the relative magnitude of these opposing effects. The variation in spray enthalpy with melt superheat (Fig.5) shows that the spray enthalpy at a particular deposition distance increases with melt superheat. At a deposition distance of 0.35 m, the spray enthalpy fraction increases from 0.60 to about 0.80 as the melt superheat is increased from 100 K to 200 K. The magnitude of this change is significant when compared with the effect of atomising gas pressure on incoming spray enthalpy (Fig.4) where there is a marginal change in spray enthalpy owing to changing gas pressure. It is thus inferred that at a given deposition distance, the melt superheat has a significantly greater influence on the incoming spray enthalpy than atomization gas pressure. This has practical utility from an engineering point of view. It is easier to vary melt superheat than to increase gas pressure because of the associated problem of excessive pipeline pressure. Since the shape and microstructure of the preform depends upon the liquid

A comparison of the measured and calculated temperature profiles at a nozzle to substrate distance of 0.35 m (exp. 1) and 0.45 m (exp. 2) is depicted in Fig. (6) and Fig. (7) respectively. The thermocouples Tc1 and Tc2 record the temperature in the preform at 2.0 mm and 10.0 mm respectively from the substrate surface. The deposition time is 19.0 s in exp. 1 and 34.0 s in exp. 2. The thermocouple Tc1 attains a stable profile earlier than Tc2 because it is embedded earlier in the growing preform. Tc1 in expt.1 records temperature close to 580 oC while Tc2 records about 615 oC during the deposition period. There is difference between the measured and calculated values of the temperature during the initial stage of deposition and also in the post deposition stage. During the initial stage of the deposition, the thermocouples are the first to be covered by the spray because of their protrusion over the substrate and a cap of solidified alloy is formed. Therefore the temperature rise recorded is kinky. The perform gradually builds to a height to finally embed the thermocouples and thereafter the measured and calculated values coincide. Termination of deposition is manifested by a sharp change in the slopes of the two curves. The temperature profile in the post deposition regime does not exhibit an exponential decay profile as reported by other investigators30. This difference could be due to the use of a water-cooled copper substrate and consequently a higher value of heat transfer coefficient in their investigations compared to a mild

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Fig. 6

: Computed and measured temperature at a deposition distance of 0.35 m.

Fig. 7

: Computed and measured temperature at a deposition distance of 0.45 m.

steel substrate without a cooling arrangement used in the present case. On the basis of the computed temperature profiles, the cooling rate at a distance of 2.0 mm, 10.0 mm and the deposition surface in exp. 1 and exp. 2 are calculated and are shown in Fig. 8 and Fig. 9 respectively. It is worthwhile to note that at a distance of 2.0 mm from the bottom of the deposit, an initial cooling rate of 2.5 K s-1 is experienced due to the initial rapid heat loss to a cold substrate. As the deposit height builds up, the incoming heat flux is not readily dissipated, leading to a gradual decrease in the cooling rate. The cooling rate shows a sharp increase at the termination of deposition and attains a peak value of about 5 K s-1 which then decreases and levels out at about 3 K s-1. The deposition surface experiences heating during the deposition process. The cooling/heating rate is calculated on the basis of

difference in temperature between the present and past values at a given location. The present value of temperature at the deposition surface is close to the average spray temperature while the past value includes the effect of heat dissipation. The difference in these values is initially large but gradually decreases as the heat dissipation through the substrate decreases with time. The heating rate changes to cooling rate when the deposition process is terminated and then a peak cooling rate of 8 K s-1 is achieved. The cooling rate then decreases in a similar fashion to a constant value of about 3 K s-1. The larger drop in the cooling rate of the deposition surface as compared to the location closer to the bottom surface is due to the sudden removal of incoming heat source at the top surface while the bottom still continues to receive heat from the over

Fig. 8

: Variation in cooling rate with time in the preform at a deposition distance of 0.35 m

Fig. 9

: Variation in cooling rate with time in the preform at a deposition distance of 0.45 m.

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lying preform material. The cooling rate profile at 10.0 mm from the bottom is also shown on the same graph. The lower cooling rate at this location, compared to the bottom surface is because of its proximity to the continuous heat source at the top. Interestingly, the nominal difference in the cooling rates experienced by the different surfaces gives an insight into the nature of evolution of microstructures in spray deposited materials which is dealt in the following section. The computed cooling rate curve for exp. 2 is of a similar nature. The cooling rate at the bottom surface in this case is lesser due to the reduced heat transfer rate at the bottom surface resulting from the smaller temperature gradient across the preform-substrate interface as a result of lower spray temperature. 4.4 Microstructural Features The microstructures of the spray formed alloy at a deposition distance of 0.35 m are shown in Fig. 10 (a,b,c). The height of the spray deposit was 3.5 cm. These microstructures invariably show equiaxed grain morphology of the primary C-phase at different locations in the spray deposit. Even though the spray deposited alloy shows considerable uniformity in grain size, small variation in grain size is observed at different locations in the deposit in the transverse direction. The bottom section of the deposit reveals maximum grains in the size range of 12 to 40 Om with a mean grain size of 25 Om. At this location, a mixed grain size distribution consisting of smaller grains coexisting with larger ones is observed. Absence of splat boundaries at the bottom surface indicates that either the spray contained sufficient amount of liquid to check the immediate freezing of droplets or the heat transfer coefficient at the deposit-substrate interface was sufficiently low, resulting in reduced heat loss. The grain size increases with increasing distance toward the middle section of the spray deposit. In the middle section of the deposit, the grain size distribution becomes more uniform with majority of grains lying between 25 to 35 Om with a mean grain size of 30 Om. The grain size continues to increase even above the middle section upto 30 mm from the bottom. A small decrease in grain size is observed in the top portion on the preform. In the top section, the mean grain size is observed to be 28 Om. As in the bottom

Fig. 10 : Micrographs showing equiaxed grain morphology in spray deposited alloy (a) bottom (b) middle and (c) top section. The deposition distance is 0.35 m.

section, both smaller and larger grains are also visible in the top portion of the deposit. A mixed type of grain size distribution at the bottom and top portions of the deposit and a uniform distribution at the middle seems to evolve due to two different types of solidification conditions at these locations. As the results of modeling in Figs.(6&7) indicate, a liquid pool builds up on the deposition surface during

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deposition. The spray on the deposition surface after the deposition has progressed for some time, impinges on a pool of liquid under relatively steady condition. The spray impinges on this liquid pool, which stabilizes its impact and provides sufficient freezing time and consequently uniform and larger grains. In contrast, at the top and bottom regions, unsteady deposition conditions prevail due to abrupt termination and commencement of deposition. As a result of this and the smaller freezing time at these locations, a mixed grain microstructure with a smaller mean grain size is produced. Alternatively, it has been reported30 that smaller particles which are in a fully solidified state at the time of impingement may act as a nucleation site for the surrounding melt. The solidified particles undergo annealing and their boundaries are not discernible in the final microstructure. Because of the high temperature annealing, microstructural coarsening would further influence the grain size of the deposit. The occurrence of a mixed grain microstructure could be the result of finer grain formed during annealing surrounded by larger grains formed by the nucleation caused by the solidified particle. The solidified particles act as efficient nucleation sites on locations which have a low liquid content to check their re-melting. The bottom and top surface of the deposit are locations of low liquid content on the deposition surface. A considerable grain refinement is noticed at different locations in the deposit at a deposition distance of 0.45 m. The height of the deposit in this case is 30 mm. The mean grain size increases from 12 Om in the bottom section to 15 Om in the middle. A mixed type of grain size distribution is more pronounced in the bottom section. As in the previous case, the mean grain size decreases to 10 Om in the top portion of the deposit. In the present investigation the average computed cooling rate at different locations within the preform is shown in Fig. 11. The average cooling rate is calculated with the help of the following expression

T − TS T&avg = max tf

(18)

where Tmax is the maximum temperature attained at a location during the deposition process. The cooling rates calculated using Eqn. (18) are the average cooling rates at a particular location throughout the

Fig. 11 : Computed average cooling rate across the deposit at deposition distances of 0.35m and 0.45 m.

deposition and post-deposition regime. The average cooling rate is used to gain an understanding about the variation in the grain size within the deposit. The average cooling rate has a high value (~ 15 oC s -1 ) at the bottom of the deposit (y = 0 mm). This is due to the initial chilling effect of the substrate. The cooling rate drastically falls to a value of around 2.5 oC s-1 at about 1.0 mm from the substrate. Thereafter, it gradually increases with increasing deposit height, attaining a value of 5 oC s-1 at the top of the deposit in exp. 1 and 7 oC s-1 in exp. 2. The average cooling rate at a particular location is higher in exp. 2 because of the lower freezing time. The cooling rate increases with deposit height because the contribution of the increase in Tmax with deposit height is larger than the corresponding change in tf. Attempts have been made to establish an empirical relationship between an average cooling rate and grain size.10,13,31-32 Empirical correlations for cooling rate and secondary dendrite arm spacing are reported in literature10 to be of the form DAS = AT& −n

(19)

where DAS denotes the dendrite arm spacing, T& is the cooling rate and A and n are constants. For 7075-Al alloys, reported values of A and n as 45 Om (K s-1)-n and 0.25 respectively10. For other alloys, a similar relationship is reported with different values of the constant. Although the physical significance of such a relationship is not clear, nevertheless this

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relationship is useful for the prediction of the scale of microstructure based on thermal measurements. Grain size measurements were made by these investivators at the same locations and a correlation between the average cooling rate and the grain size established. In the case of spray formed alloys, the grain size is taken as the primary dendrite spacing. In the present investigation, the values of A and n are calculated to be 36.28 and 0.265 respectively for a deposition distance of 0.35 m by using the measured grain size and calculated cooling rate in Eqn. (19). However when these values are used to estimate the grain size variation at a deposition distance of 0.45 m, there is appreciable error. For example, using the estimated values of A and n, a mean grain size of 15 Om would be obtained under a cooling rate of 28 K s-1. Such large values of cooling rate are not encountered during spray deposition as observed from the thermal profile of the deposit. If the data for cooling rate and grain size obtained at a deposition distance of 0.45 m is fitted into a power law relation (Eqn. 19), the values of A and n obtained are 56.2 and 0.81 respectively. It is therefore inferred that cooling rate is not the sole determining factor in controlling grain size. In expt. 1, where a sufficient liquid pool exists at the top, it is proposed that re-melting of dendrites leads to a reduction in the available nucleation sites. At a larger deposition distance of 0.45 m, grain coarsening is reduced as a result of insufficient liquid.33 5.

CONCLUSIONS

(4) The microstructure of the spray deposit shows equi-axed grain morphology of the primary phase. The microstructure of the spray deposit does not appear to be governed solely by the cooling rate associated with the spray deposition process.

ACKNOWLEDGEMENT One of the authors (Prashant Shukla) wishes to thank the Council for Scientific and Industrial Research (CSIR), India for the financial assistance provided under the CSIR Research Grant No. 9/13/963/2000 under which this work was carried out.

REFERENCES 1.

Lavernia E J, and Grant N J. Mat. Sci. Engg., 98 (1988) p. 381

2.

Lavernia E J, Ayers J D, and Srivatsan T S Int. Mat. Rev. 37(1) (1992) p. 1

3.

Lawley A, Mathur P, Apelian D, and A. Meystel, Powder Metall., 33(1990) p.109

4.

Grant P S, Prog. Mat. Sci., 39 (1995) p.497

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Singer A R E, Int. J. Powder Metall., 21(3) (1985) p. 219

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Leatham A G, Ogilvy A, and Elias L, Spray FormingCommercialization and Applications, Spray Forming: Science, Technology and Applications Seminar, San Francisco, USA, APMI (1992)

7.

Prichard P D, Dalal R P, Spray Cast - XTM Superalloys for aerospace applications, Superalloys (eds. S.D. Antonovich et al), TMS, Warrendale, Pennyslvania (1992) p. 205

8.

Anantharaman T R, and Suryanarayana C, J. Mater. Sci., 6 (1971) p.1111

9.

Mathur P, Annavarapu S, Apelian D, and Lawley A Mater. Sc. Engg., A142, (1991) p.261

The following conclusions are drawn from the present investigation: (1) The cooling rate of the spray deposit varies from 1-10 Ks-1. (2) The maximum temperature recorded at a location of 10.0 mm is 580 oC and 615 oC at a deposition distance of 0.35 and 0.45 m respectively indicating that a larger spray enthalpy at a smaller deposition distance leads to a higher temperature of the preform. (3) The melt superheat largely determines the incoming spray enthalpy compared to atomization gas pressure.

10. Lavernia E J, Gutierrez E, Szekely J, and Grant N J, Int. J. Rapid Solidification, 4 (1988) p.89 11. Grant P S, Cantor B, and Katgerman L, Acta Metall. Mater., 41 (1993) p. 3097 12. Lee E, and Ahn S, Acta. Metall. Mater., 42 (1984) p.3231 13. Mathur P, Apelian D, Lawley A, Acta Metall., 37 (1989) p. 429

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24. Cahn J W, Hilling W B, and Sears G W, Acta Metall., 12 (1964) p.1424

15. Drehman A J, and Turnbull D, Scripta Metall., 15 (1981) p.543

25. Herlach D M, Mat. Sci. & Engg. R12 (1994) p. 213

16. Shukla Prashant, Mandal R K, and Ojha S N, Bull. Mat. Sci. 24(5) (2001) p. 547 17. Lavernia E J, and Wu Y, Spray Atomization and Deposition, John Wiley and Sons, England (1996) . 18. Holman J P, Heat Transfer, McGraw Hill Book Company, New Delhi, 1989 p. 644 19. Swaminathan C R, Met. Trans., 23B (1992) p. 651 20. Szekely J, Fluid Flow Phenomena in Metals Processing, Academic Press, N.Y., (1979) 21. Clift R, Grace J R, and Weber M E, Bubbles, Drops and Particles, Academic Press, N.Y., (1978) 22. Ranz W E, and Marshall W R, Chem. Engg. Prog., 439 (1952) p. 173 23. Levi C G, and Mehrabian R, Metall. Trans., 13A (1982) p.23

26. Flemings M C, Solidification Processing, McGraw Hill, New York (1974) 27. Crank J, Free and Moving Boundary Problems, Clarendon Press, Oxford (1984) 28. Estrada J L, and Duszczyk J, J. Mater. Sci. 25 (1990) p.1381 29. Srivastava V C, and Ojha S N, P/M Science and Technology Briefs 3(3) (2001) p.7 30. Bewlay B P, and Cantor B, J.Mater. Res., 6(7) (1991) p.1433 31. Annavarapu S, Apelian D, and Lawley A, Metall. Trans. A 19A (1988) p. 3077 32. Mathur P, Annavarapu S, Apelian D, and Lawley A, Mater. Sci.& Engg. 142A (1991) p. 261 33. Annavarapu S, and Doherty R D, Acta. Metall. Mater 43 (1995) p.3207

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APPENDIX I Thermo-physical properties of Al-4.5 wt % Cu alloy Heat of fusion

(&Hf)

3.48 ˆ 103 J kg-1

Density

(Td)

2800 kg m-3

Specific heat of liquid

(CL)

982 J kg-1 K-1

Specific heat of solid

(Cs)

900 J kg-1 K-1

Surface energy

(USL)

1.31 ˆ 10-2 J m-2

Thermal conductivity of liquid

(kl)

97.8 W m-1 K-1

Thermal conductivity of solid

(ks)

211.4 W m-1 K-1

Melting temperature of Al

(TM)

934 K

Liquidus temperature

(TL)

919 K

Solidus Temperature

(TS)

833 K

Eutectic temperature

(TE)

821 K

Equilibrium partition coefficient

(ko)

0.14

Specific heat

(Cpg)

1.04 J kg-1 K-1

Thermal conductivity

(kg)

2.6 ˆ 10-2 W m-1 K-1

Density

(Tg)

1.16 kg m-3

Kinematic viscosity

(µg)

1.78 ˆ 10-5 N s m-2

Thermo-physical properties of N2 gas

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