## 3 Results and Discussion
### Effects of Grain Boundaries and Grain Orientations  
Figures 17-19 show the FE results of the considered conditions in order to observe the influences of the grain boundaries and grain orientations when the Grain Size Ratio (\(G_{R}\)) was 0.75. In other words, the average number of grains across the specimen was 1.3 (single-grain) under all the conditions. In LG1, all of the grain orientations were along the x-axis, which showed that the micro-extrusion pin was curved. This result indicated that, when there was no influence from the grain orientation, the grain boundaries alone could significantly affect the curvature. It could be observed that the grain boundaries were not symmetric along the x-axis, causing the specimen to flow  
Figure 16: The micro-extrusion results comparison between the EX1 and EX2 conditions. Figure 17: The micro-extrusion results of the considered conditions (LG1–LG4). nonuniformly into the extrusion die. This behavior implied that the asymmetric grain boundaries were the primary driving mechanism of the bending. In LG2, the effect of the grain orientation (+45\({}^{\circ}\) from the x-axis) of the bottom grain was coupled with the influence of the asymmetric boundaries. The ECI values of both LG1 and LG2 were similar (same curvature); thus, the effect of grain orientation was not observed here. However, when the bottom grain orientation was rotated +90\({}^{\circ}\) from the x-axis (LG3), the ECI values slightly increased from 6.90% to 7.17%. As a result, the grain orientation must be dramatically changed in order to see the curvature effect. When the bottom grain orientation was rotated-45\({}^{\circ}\) from the x-axis (or \(-\)90\({}^{\circ}\) opposite to LG2), the ECI values were reduced from 6.90% to 3.09%, which helped to straighten the micro-extrusion pin. This result also confirmed that the grain orientation must be significantly changed in order to see the curvature effect. In the direction of the curvature, the curvature increased with an increase in the amount of grain orientation mismatch. However, if the orientation mismatch was in the opposite direction to the curvature, the curvature decreased according to the amount of grain orientation mismatch. Figure 18 shows the conditions (LG5 to LG8) that take into account the effects of the grain orientations from the middle and top grains. Considering LG5 and LG6, it could be noted that both the middle and top grain orientations did not affect the curvature. Similarly, the middle grain orientations (LG7 and LG8) did not affect the curvature when compared with LG1. As a result, the bottom grain orientations significantly affect the curvature. Since the bottom grain was located at the high deformation (reduced diameter) and opening area, this implied that only the grain orientations at the high strain and opening area influenced the curvature. This phenomenon could also be observed in Figure 19, where the middle and top grain orientations did not show any effects on the curvature. Figure 19: The micro-extrusion results of the considered conditions (LG9–LG12). Figure 18: The micro-extrusion results of the considered conditions (LG5–LGS). Based on the results from Figures 16-19, it could be stated that the grain boundary of the high strain and die opening area was the dominating factor for single-grain billet conditions. Since the actual metallic grain shapes were not symmetric and the grain orientations were random, the grain boundary dominated. The combination of the grain shapes (grain boundaries), grain sizes, and grain orientations dictate the direction of the curvature. In the EX2 case, there was only one single grain at the bottom of the billet. As a result, the change of grain orientation (+75\({}^{\circ}\) to the extrusion direction) of the bottom grain caused the extruded pin to curve to the right. In the other single-grain cases, the curvature was mainly influenced by the initial bottom grain boundaries.