# Altering the Supply of Shielding Gases to Fabricate Distinct Geometry in GMA Additive Manufacturing
## 2 Results and Discussion
### Mathematical Model
The voltage dropped in the cathode sheath is at least 12 V. While measurements show that the cathode fall voltage is higher for He than Ar [35], the presence of oxygen and metal vapor is expected to ensure that the cathode fall voltage is approximately the same for both gas mixtures. The anode fall voltage is low and can be neglected. The volumetric enthalpy (which is equal to \(\rho h\)) for the gas mixtures is shown in Figure 9:1 In the presence of metal vapor, it is similar for both mixtures--around 4-5 \(\times\) 10\({}^{5}\) J/m\({}^{3}\) for typical arc temperatures of up to 12,000 K.  
The arc radius is given by  
Figure 9:2  
Using the current parameters and V = 4 V (based on the difference between the measured voltage and the cathode fall voltage), \(\rho h\) = 4 \(\times\) 10\({}^{5}\) J/m\({}^{3}\) (based on an average temperature of about 7000 K), and \(v_{z}\) = 70 m/s, \(\sigma\) is calculated as 2.9 mm, which is close to the observed width of the ternary blend arc. Note that the calculation is only approximate (it neglects radiative losses, for example); moreover, arc width estimates from the photographic images are also only approximate. The binary blend arc is longer, as can be seen by comparing Figures 2 and 3. This implies the velocity and temperature will be lower near the workpiece. The value of \(\rho\)h will be similar, but we can use \(v_{z}\) = 50 m/s, which yields \(\sigma\) = 3.4 mm. The lower \(v_{z}\) is justified by the similar viscosity (Figure 16) for the two gas mixtures in the presence of iron vapor. The viscosity determines the radial spread of the flow momentum--a high viscosity leads to a more rapid decrease in the velocity as the distance from the wire increases. Thus, we estimate the arc radius is 30% smaller for the ternary blend than for the binary blend. Figure 9:3 Volumetric enthalpy for the ternary and binary blends and for 50 mol% mixtures of each blend with metal vapor, as a function of temperature. The surface tension data for 420 and 500 ppm oxygen concentrations were used in the simulation. Figure 17 shows the simulations of the melt pool regions. The binary blend, with lower heat flux and higher oxygen concentration, had a shallow and wide penetration, while the ternary blend had a deep and narrow penetration, consistent with the experimental results. Figure 18 shows the molten pool velocity contour plot in an x-z plane. The high heat input caused the higher velocity for the ternary blend (3 cm/s) compared to the binary blend (2.3 cm/s) in the z-direction, thus causing the variation in weld bead size. The flow direction reverses as the temperature lowers, due to the surface tension parameters. Figure 9:4 Viscosity for the ternary and binary blends and for 50 mol% mixtures of each blend with metal vapor, as a function of temperatures [19; 20; 21]. Figure 9:5 Melt region comparison for (**a**) a 500 ppm oxygen concentration with low heat flux, representing the binary blend, (**b**) 420 ppm oxygen concentration with high heat flux, representing the ternary blend. The simulation accurately predicted the shape of the molten pool for the binary blend. However, for the ternary blend, the height of the melt pool differed somewhat from the experimental results. The droplet parameters (droplet velocity and droplet diameter) play an important role in accurately predicting the melting pool shape [36; 37]. The droplet frequency is inversely proportional to the droplet diameter and droplet detachment cycle time. In general, if the droplet detachment cycle time is small, the droplet frequency is large. However, a larger droplet frequency entails a smaller droplet diameter. Thus, the tri-mix blend resulted in a smaller diameter droplet in the experimental results, but in the simulation, the same droplet velocity and the droplet diameter were considered for both blends, which may have produced this discrepancy. Our future work will focus on experimentally evaluating the droplet parameters, mainly the droplet velocity and droplet diameter, to accurately model the weld\(-\)bead shape.