# Integrated Image Processing Toolset for Tracking Direction of Metal Grain Deformation
## 5 Application for Tracking the Direction of Metal Grain Deformation
As an example of the implementation, FEA analysis was performed for a comparison, including deflection in the \(x\) (\(\delta_{x}\)), \(y\) (\(\delta_{y}\)), and \(z\) (\(\delta_{z}\)) directions and the shear deflection in the \(xy\) (\(\delta_{XY}\)), \(yz\) (\(\delta_{YZ}\)), and \(xz\) (\(\delta_{XZ}\)) directions (Figure 15). The strain vector at three specific locations, i.e., the compressive (A), combination (B), and tensile (C) stress areas, was assessed using a four-point bending test (Figure 16). After applying a deflection of 0.2 mm to the system according to the FEA analysis, uniform deformations of 0.511 \(\upmu\)m, 0.013 nm, and 0.511 \(\upmu\)m were expected to occur in regions A, B, and C, respectively. However, in the grain-level assessment using the proposed algorithm, the deformation did not occur in a uniform direction. As shown in Figure 16a, in the specific analysis in location A, where a compressive deformation of 0.511 \(\upmu\)m was expected to occur owing to the compressive stress, there was an internal compression with the maximum magnitude of 0.433 \(\upmu\)m. Likewise, at location B, where a deformation of 0.013 nm was expected owing to the compressive and tensile stresses, the compression and local shear stress of 0.154 \(\upmu\)m was observed at the top and 0.077 \(\upmu\)m at the bottom, as shown in Figure 16b. At location C, as shown in Figure 16c, where a deformation of approximately 0.511 \(\upmu\)m was expected owing to the tensile stress, the local shear stress on the grain of 0.232 \(\upmu\)m at the top and  
Figure 14: Implementation of the integrated toolsets for extracting the direction of grain deformation: (**a**) geometric meshing analysis on grain before deformation, (**b**) geometric meshing analysis on grain after deformation, (**c**) quiver plot of direction of metal grain deformation, and (**d**) O-grid generalization method to amplify the trend of direction signal. 0.310 \(\upmu\)m at the bottom was clearly observed. It is related to the normal and shear stress on a boundary in a homogeneous body corresponding to the boundary orientation [67]. This result implies that the deformation analysis obtained by the numerical-analytical approach of the stress-strain on specific structures is very difficult to apply at the grain level (Figure 17). However, the experimental approach to the stress-strain in a specific region using a metallographic observation can effectively provide a high spatial resolution for tracing the microscopic deformation at the grain level. Thus, it is suggested that the algorithm proposed in this study is a tool to quantitatively measure the micro-deformation at the metal grain level (Figures S16-S18). Figure 15: The results of numerical approach using FEA on structural simulation of 4-point bending test including deflection components in the \(x\) (\(\delta_{x}\), \(y\) (\(\delta_{x}\)), and \(z\) (\(\delta_{x}\)) directions and shear deflection in the \(xy\) (\(\delta_{XY}\)), \(yz\) (\(\delta_{YZ}\)), and \(xz\) (\(\delta_{XZ}\)) directions. Figure 16: The grain-level analysis of deformation direction for understanding the internal deformation trends on the grain area: (**a**) compressive stress area, (**b**) compressive and tensile stress area, and (**c**) tensile stress area.