Deposit Cooling and Solidification

One of the early predictions of the spray models was the result that successful spray deposition requires a partially solid-partially liquid spray in which 1 ~—f\(s) >0 (Ref 1). The droplets arriving at the surface of the deposit at velocities —50 to 100 m/s are predicted to be fully solid if small, fully liquid if large, and for the majority of the mass of the spray of intermediate size, partially solid and partially liquid on impact. Given the high thermal conductivity of metallic alloys, rapid thermal equilibration of all the deposited droplets is expected with a partially solid and partially liquid structure on the surface of the deposit. Initial models of the thermal behavior of the deposit were one dimensional and predicted that after deposition of the partially molten alloy, most of the subsequent cooling was caused by the high velocity gas, with only limited cooling taking place through the substrate--at least for material deposited some distance away from the substrate. The model predicted complete solidification times (10-200 s), that were confirmed by embedded thermocouple measurements (Ref 5). Later models, such as those of Grant et al. (Ref 17, 18) and Cai et al. (Ref 3), confirm the qualitative form of these results, as shown in Fig. 16 and 17. Models of thermal deposition were two dimensional, incorporating gas cooling from the side and top surfaces of the deposited billets (Ref 3, 29). For billets, the two-dimensional thermal models appear to capture the major features of the cooling and solidification process (Ref 29). After a short period of deposition, the temperature at the top surface of the deposit achieves a value corresponding to a partially molten surface. The depth of this incompletely solidified region increases, and at the center of the billet time required for complete solidification is tens of seconds. There is, however, a critical need for a three-dimensional thermal model for more complex shapes, such as a rotating tube (Ref 27, 29). In tube deposition, which is one of the major commercial applications of the technology (Ref 6, 7, 8, 9, 10, and 11), the thermal conditions are complex because the tube is subjected to additional cooling as it rotates into and out of the spray in the presence of the cooling gas stream. As a result, it is expected that for the same enthalpy in the spray, /(s), there will be a lower fraction of liquid on the surface of the deposit during spray forming of tubes than of billets.

700 O 650

Fig. 16 Numerically modelled and experimentally observed deposit temperatures (using infrared imaging) as a function of deposition time for Al-4Cu at two axial spray heights. Source: Ref 17

Fig. 17 Predicted temperature contours for a Cu-6Ti cylindrical billet as a function of deposition time. The enthalpy of the spray corresponds to a fraction of liquid (f) in the spray of 0.19. Note the depth of the partially solid region. Source: Ref 27

An initial two-dimensional model for the spray forming of tubes (Ref 27) captured one significant aspect of this geometry. In addition to the usual buildup of surface temperature with time after overcoming the initial chilling effect of the substrate, there was a second but opposite effect in the tube. As the length of the deposited tube grew, the cooling effect of the gas stream on the as-deposited tube resulted in a decrease in the surface temperature under the spray with time as shown in Fig. 18 (Ref 27). Also shown in Fig. 18 is the chilling effect of the tubular substrate, which causes rapid cooling of the deposit in contact with the mandrel even after extensive deposition. The limitations of the two-dimensional model for this geometry are clear from Fig. 18. The thermal model of a billet shows that the fraction of liquid on the surface of the deposit,/(d), approaches that in the spray,/(s) (Fig. 17).

Fig. 18 Isotherms modeled for In625 tube under a fraction of liquid in the spray of 0.46. Limitations of the two-dimensional model are clear, and acceleration of cooling in the later stages of deposition (due to the cooling effect of the gas stream on the as-deposited tube) are seen from the rapid decline of the partially solid region, even before termination of the spray which occurred after 64 s. Source: Ref 27

It should also be noted that with a rapidly rotating substrate, particularly in tubes, embedded thermocouple measurements are difficult to make (Ref 5). However, for plates sprayed under linear nozzles, embedded thermocouple measurements can be made, and these show close agreement with the thermal model (Ref 30) shown in Fig. 19 and 20. In particular two features of the process are shown in Fig. 20. First, the cooling rate in the solid-liquid phase field in the presence of a preheated steel substrate (to offset the chilling effect of a cold steel substrate) is low. The second feature is the thickness in the deposit (10% at 400 °C and 40% at 30 °C) during which the chilling effect of the substrate causes the deposit to form without the temperature rising above the solidus temperature. Under these conditions, the only liquid present is the transient liquid in the spray as it arrives at the surface of deposition. This transient liquid will disappear rapidly during thermal equilibration with the deposit, and the partially liquid region at the deposit will form only after the deposit is relatively thick (Fig. 18). This result is of major significance in the formation of a deposit of low porosity. Although this study pertains to continuous deposition, the experimental and modeling methods are applicable if the spray is oscillated in the growth direction, thereby allowing for additional cooling at the deposit surface when the spray is temporarily elsewhere. Similar conditions are inevitable in the manufacture of other shapes, most significantly tubes.

Fig. 19 Calculated and measured temperature versus time plots in spray formed plates using a linear nozzle. Source: Ref 30

o

o

Model pri Measurec

îdiction i

1

0

400 ÛC

substrat* •—

v 30 SG

steel sut

1 strate

i \ -—■—.

1-

0 0.2 0.4 0.6 0.0 1.0 Normalized distance from the bottom of the deposit

0 0.2 0.4 0.6 0.0 1.0 Normalized distance from the bottom of the deposit

Fig. 20 Calculated cooling rates in spray formed plates showing the chill layer. Source: Ref 30

0 0

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