PSI - Issue 21

Taiko Aikawa et al. / Procedia Structural Integrity 21 (2019) 173–184 Taiko Aikawa/ Struc ural Integrity Procedia 00 (2019) 000 – 00

178 6

Fig. 7 Mis-orientation of neighbor two grains

The normal vector can be calculated by obtaining the Euler angle matrix from the data extracted by EBSD analysis. Euler angles can be expressed as a composite representation of rotation transformations about three axes fixed on a given plane. Here, it is regarded as the rotational transformation of {100} plane which is the cleavage plane of brittle fracture of iron. The xy -plane of 1 in Fig. 7 is the {100} plane before conversion, and it is assumed that this {100} plane has been converted to a specific orientation by the three conversions shown in Fig. 7. In the Eq. (2), a vector obtained by applying 3 rotation transformations to the original vector ( ) can be described as ( ′ ′ ′ ) . Using the above concept, the normal vector after conversion is obtained from the original normal vector (0, 0, 1). By substituting the z -axis vector (That is, the normal vector) (0,0,1) of the {100} plane before the coordinate conversion, the z -axis vector (Eq. (3)) of the {100} plane after the coordinate conversion is obtained. ( ′ ′ ′ ) = ( − − − + − + − ) ( ) (2) ( 1 2 3 ) = ( ) (3) Where, α , β and γ are the rotation angles shown in Fig. 7, ( ) is the vector before conversion, ( ′ ′ ′ ) is the vector after conversion, and ( 1 2 3 ) is the normal vector of the {100} plane after conversion. 1 2 3 4 Coordinate system before conversion rotation about z axis rotation about the converted y axis rotation about z axis after conversion3

Fig. 8 Conversion of the coordinates

2.4. Relationship between the orientation differences between crystal grains connected in the propagation direction and crack propagation characteristics