PSI - Issue 68

Ritsuki Morohoshi et al. / Procedia Structural Integrity 68 (2025) 701–707 R. Morohoshi et al. / Structural Integrity Procedia 00 (2024) 000–000 5 deviation of 5° or less from the reference grain are selected and registered in search . If the reference grain is ′ and the candidate grains are , no edges are generated. Next, the matching of the triple junctions at grain boundaries is performed. First, among all the triple junctions at grain boundaries, extract those for which all three grains that form the triple junction are already registered in search . Then, treat the three grains as nodes in search and calculate their respective successor nodes. From the set of successor nodes, identify the combinations that form a new triple junction. If there is only one candidate, it is adopted as the next triple junction. If there are two or more candidates, they are discarded for simplicity in this case. At this stage, the tracking of grain boundary triple junctions over time is complete, allowing the calculation of the displacement of these triple junctions. The next step is to extend this displacement calculation to the entire EBSD image. Simply put, the displacements of the triple junctions are spatially regressed. Simultaneously, each deformation is verified to be a small deformation. For the purpose of linear regression, an affine transformation matrix was defined and used. As a supplementary note, the matching of triple junctions is, of course, not guaranteed to be 100% successful. To exclude errors, any points that do not fall within the 95% confidence interval during the linear regression using the affine transformation matrix were excluded. To determine whether the regression was successful, rather than defining an error function for discussion, the validity of the regression was assessed more simply. Specifically, the affine transformation matrix obtained from the regression was applied to the entire EBSD image across all loads, transforming the basis where the EBSD image is defined. The validity of the regression was then checked by confirming whether the positions of the grains before and after the transformation remained in the same location. The results show that the regression using only the affine transformation was sufficient(fig. 7). Since the deformations are small, the strain tensor and rotation tensor can be separated. It is important to note that when there is a rigid body rotation component, it becomes necessary to apply a correction to the crystal orientation in the EBSD data. Given that the affine transformation alone was sufficient in the

705

Fig. 5: Overlay of grain bound ary, notched test, loaded horizontally. Black is at 105N, Red is at 115N.

Fig. 6: Crystalline grain tracking

(a) Notch

(b) Shear

(c) Uniaxial

(d) Notch affined (e) Shear affined (f) Uniaxial affined

Fig. 7: Movies of overlay of grain boundaries with affine transformation