## 3 Results and Discussions
For example, in case of the in-out pattern, only the heat source energy is applied to the center at the beginning of the deposition without any other heat additions. Figure 5b shows that the intensity of the temperature contour at the center becomes weaker as time proceeds. On the contrary, in other pattern cases, the heat is transferred from the adjacent depositions in addition to the heat source energy. In case of the out-in pattern, as shown in Figure 5c, the heat is concentrated toward the center of the deposition layer, showing a circular symmetric temperature distribution. The level of heat energy at the center is the highest  
Figure 8: Displacement distribution for the different deposition patterns (unit: m); (**a**) alternate, (**b**) in–out spiral, (**c**) out–in spiral, and (**d**) raster. The cross-section planes A–A and B–B were chosen for the analysis. among the cases considered in this study. Note that in Figure 5c the heat from the adjacent depositions is transferred toward the center before the heat source reaches the center point. The temperature histories of Figure 6 support this explanation as well. In Figure 6, the out-in case has the highest peak temperature (T = 1080 \({}^{\circ}\)C). The values of the peak temperature for the raster and the alternate are similar to each other and come next (T = 866 \({}^{\circ}\)C). The in-out case shows the lowest value of peak temperature (T = 759 \({}^{\circ}\)C). For such reasons, the largest thermal stress and thus bending are generated in the case of the out-in pattern. This can explain why the negative displacement in the center of the deposition layer is observed in the out-in case, different from the other cases. The results so far suggest that the deposition pattern significantly affects thermal profiles such as peak temperature, heat accumulation, cooling rate, and others. Therefore, the deposition strategy could have a significant influence on the formation of warpage and residual stress in the AM parts. In Figure 9, the warpage index is analyzed for the different deposition patterns along the diagonal direction. Note that the warpage index was determined by the normalized relative displacement by the substrate thickness. The relative displacement was calculated as the deflection in the z-direction at the corresponding position with respect to the minimum displacement (i.e., \(\mathrm{U_{z}-U_{z,min}}\)). Such an index was used to understand intuitively how much distortion is generated due to the AM deposition. The overall trend is that the minimum warpage is observed in the center, while the maximum warpage is located at the corner of the substrate. Another interesting finding is that the warpage for the out-in pattern is higher than other cases throughout the whole deposition path. In addition, the warpage for the out-in pattern is the most symmetric with respect to the center. This is mainly attributed to a circular symmetric temperature distribution due to its characteristic of the scanning path as described above. Note that a similar trend is also found in the Mises stress and displacement distributions in Figures 7 and 8, respectively. Different from the contour-type patterns (i.e., in-out and out-in), the line-type depositions (i.e., raster and alternate) have similar trends and values of warpage, as shown in Figure 9. Note that unlike raster deposition, the alternate scanning has an interval between each deposition. However, such a difference in the presence of intervals has little influence on the peak temperature Mises stress distribution, as analyzed above in Figures 6-8. Analysis in Figures 7 and 9 shows that the out-in case leads to the highest Mises stress and warpage. The line-type patterns (i.e., alternate and raster) do not show notable differences in residual stress and warpage. In the case of the in-out patterns, the values of maximum Mises stress and warpage have a tendency to be slightly lower than the line-type patterns.