# Numerical and Experimental Investigations of Laser Metal Deposition (LMD) Using STS 316L
## 4 Results and Discussion  
Figure 3a shows the position (point 1) where the pyrometer continuously measured the varying temperature for validating the numerical model. Figure 3b shows the temperature profile measured using a pyrometer (solid line) and the temperature calculated through the simulation model (dotted line) at point 1. The difference in the peak temperatures between the two temperature profiles is 6.5% at maximum and 4.1% at minimum. In Figure 3b, because point 1 is fixed at the height of the fourth layer, there are no temperature profiles from the first to the third layers. As mentioned in Section 2, the pyrometer cannot measure temperatures below 580 \({}^{\circ}\)C; therefore, the measured temperature profile in Figure 3b is shown as a straight line at 580 \({}^{\circ}\)C. In addition, some errors occurred at \(\sim\)580 \({}^{\circ}\)C because of electrical noise after the temperature decreased to this value. Figure 3b shows a difference of \(\sim\)5% on average between the peaks of the two temperature profiles. However, except for the temperature near the peaks, which were above the melting point of STS 316L (1400 \({}^{\circ}\)C), the measured and the simulated temperature profiles are almost identical. This indicates that the developed numerical model fits well. During the cooling process of each layer, the slope of the temperature profile at the melting point of STS 316L indicates the cooling rate when the molten powder solidifies. Note that the solid-liquid interface was simplified and assumed to be a melting point in this study. Therefore, the solidification parameters obtained at the melting point have an important effect on the characteristics of the microstructure morphology. In other words, it is important to obtain a continuous temperature history, including the melting point, of the cooling process through the simulation model. By doing so, quantified solidification parameters can be derived through the model. Figure 2: Mesh of numerical model for LMD simulation. Figure 4 shows the solidification map. The temperature gradient (G) (shown on the y-axis in the map) indicates the temperature difference at the solid-liquid interface and the growth rate (R) (shown on the x-axis) represents the travel speed of the solid-liquid interface. In the map, the G/R value determines the morphology of the microstructure and the cooling rate, expressed as G \(\times\) R, determines the size of the microstructure [22,23]. As shown in Figure 4, the morphology transforms from planar to cellular, cellular dendritic, columnar dendritic, and finally, equiaxed dendritic as the G/R value decreases. In addition, the higher the cooling rate, the finer is the microstructure that is formed and the more improved are mechanical properties such as the tensile strength and hardness [24, 25, 26]. Figure 4: Solidification map: effect of temperature gradient (G) and growth rate (R) on morphology and size of solidification microstructure [21]. Figure 3: Temperature measurement position and results; (**a**) Schematic diagram of temperature measurement position; (**b**) comparison of simulated and experimental results for temperature profile of deposits. In this study, G and R were calculated using a mathematical model validated through the measured temperature profiles. A deposit with the same configuration as the real deposit was built in the mathematical model. After calculating G and G x R by using the mathematical model, R was inversely derived. These parameters were all calculated at the spatial location where the temperature was passing through the last melting point in each layer. Figure 5 shows the cooling rate, temperature gradient, and growth rate depending on the height of the deposits. Figure 5a shows the locations where G and R were calculated. The sample size is 1.8 mm (W) \(\times\) 2.5 mm (H). The bottom is at 0.13 mm in the -Z direction from the base metal surface. The middle is at 0.88 mm in the +Z direction from the base metal surface. Figure 5b shows the changes in G x R, G, and R at each layer.