Modeling and Microstructure

The process of spray forming involves a series of steps in which a molten alloy at a selected superheat is disintegrated by high velocity gas atomization into a spray of rapidly cooled droplets possessing a range of sizes and thermal conditions. These droplets then impact on a substrate to give a high yield of a partially solid deposit of controlled shape. This deposit is cooled by the gas stream, and solidification is completed at much slower rates (comparable to those in ingot casting) than the initial cooling rates in the spray. The steps in the process are complicated, and many of them are not yet fully understood, which makes them unpredictable at least from first principles. The process has, however, been modeled, and some understanding of the microstructure characteristics of spray formed alloys has been obtained (Ref 2).

The successful models, which include those of Mathur et al. (Ref 1, 12), Lavernia et al. (Ref 13, 14), Trapaga et al. (Ref 15), Tsao and Grant (Ref 16), Grant et al. (Ref 17, 18) and others (Ref 19, 20, 21), combine detailed numerical models (for those processes in which the physics is well understood) with empirical input parameters for the other processes or steps that cannot, as yet, be modeled. The model developed at Drexel University is illustrated in Fig. 11 (Ref 3, 12). It shows the preset process parameters (e.g., metal superheat, gas pressure, metal flow rate, and gas to metal ratio [GMR]) and the measured (empirical) parameters (e.g., the gas velocity field, the particle size distribution [PSD], the radial mass flux distribution [RMF], and the droplet sticking efficiency [SE]). At the present time, none of the last four parameters can be predicted reliably from first principles. The atomization stage is similar to gas atomization in powder production and has been reviewed in detail by Lawley (Ref 22, 23), Yule and Dunkley (Ref 24), and Lavernia and Wu (Ref 5). Modeling methods are available for predicting gas flow fields using numerical techniques (Ref 19); physics-based methods are available for estimating the mean particle size in gas atomization (Ref 25); and empirical methods are available for predicting the PSD, such as those of Lubanska (Ref 26). However, these methods, when tested in spray forming studies, do not appear to be sufficiently reliable to be useful in modeling the detailed thermal processes intrinsic to spray forming. In addition, the current models of gas atomization do not address the angular dependence of particle density in the spray.

Fig. 11 Flow chart of the Drexel University model of spray forming illustrating empirical inputs and predicted outputs. Source: Ref 3

To overcome these difficulties, it has been found necessary in experimental studies of spray forming to measure all the required empirical parameters in gas atomization. One such parameter is the gas velocity field in the spray chamber, usually determined by Pitot tube measurements in the absence of a stream of molten metal (Fig. 12). Results of empirical determinations of the measured PSD and RMF of the alloys investigated at Drexel University and at the Naval Surface Warfare Center (NSWC) were reported and analyzed by Cai et al. (Ref 3, 27). The method used was to spray the alloys (nickel-base alloy In625, high-strength low-alloy steel, and Cu-6Ti) under a range of gas pressures, metal flow rates, and superheats in a modified Osprey facility at NSWC. The height of the chamber was extended to ensure that solidification of the largest droplets was complete before capture in a series of concentric tubular collectors (Fig. 13). Concurrently, this experiment yielded measurements of the RMF (Ref 3). Analysis of these observations showed a general tendency for the mass mean particle size to fall with increased radial distance from the axis of the spray, as shown in Fig. 14 (Ref 27). Empirical results such as these can then be fitted to descriptive equations in order to model the spray conditions of the alloys in the same facility at NSWC and in a similar facility at Drexel University. A comparable experimental investigation of PSD and RMF for tin, steel, and copper was conducted by Uhlenwinkel and Bauckhage (Ref 28).

Fig. 12 Axial gas flow velocities as a function of distance measured in the Osprey facility at Drexel University for nitrogen gas at different preset atomization gas pressures

Fig. 13 Schematic of system for collecting fully solidified particles from a spray cone for measurement of radial mass flux and particle size distribution. The distance of fall (standoff distance) has been increased from that used in spray forming to ensure a fully solidified spray at the collector. Source: Ref 3, 17

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Radial distance, mm

Fig. 14 Measured mass median particle diameter and standard deviation of the log normal distribution as a function of radial distance for Cu-6Ti sprayed at a GMR of 0.68, metal flow rate of 0.32 kg/s, and superheat of 120 °C. Source: Ref 27

With current heat and mass transfer techniques, it is possible to predict the velocity and cooling rate of an individual droplet of a given size in flight to the substrate (Fig. 11) (Ref 5, 6, 7, 8, 12, 13, 14, 15, 16, 17, and 18). By integration of the resultant heat content of all the droplets in the PSD, it is then possible to calculate the enthalpy of the spray at the moment of impact onto the growing deposit. If it is assumed that thermal and chemical equilibrium are achieved rapidly after deposition, an equivalent value of the effective fraction of liquid in the spray,/(s), can be calculated. This calculated value of/(s) is a more meaningful physical parameter than the integrated enthalpy in the spray from which /(s) is derived. With the use of empirical values of the PSD and gas flow fields, the predicted values of/(s) should be reliable. The fraction of liquid on the surface of the deposit, /(d), under the spray for a billet shaped preform is predicted to be very close to the calculated fraction of liquid in the spray. However, for other geometries such as tubes, the fraction of liquid on the deposit can be less than that in the spray by virtue of cooling of the deposit when it rotates out of the spray and into the gas stream.

To calculate the rate of growth of the deposit, various inputs are needed. The first of these is the rate of arrival of metal from the spray at each point on the substrate surface. Cai and Doherty (Ref 3, 29) have developed a full three-dimensional shape model that can predict the rate of growth at all points on the deposit, assuming a known sticking efficiency. Examples of the predicted shapes are reproduced in Fig. 15. The shape model can be developed further to delineate the substrate motion required to give specific shapes—including those of complex geometry such as a curved tube where, by altering the substrate motion, a uniform wall thickness was designed (Ref 3, 29). These predictions do, however, require a knowledge of the sticking efficiency of the droplets onto the deposit.

Fig. 15 Predicted shapes for spray deposited billets as a function of deposition time and for a curved tube sprayed onto a 100 mm diam mandrel with appropriate substrate motion using the three-dimensional shape model. Ref 27
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