PSI - Issue 21

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

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Grain map (colored for neighbour orientation angle area within 15 degree)

Fig. 5 EBSD analysis results

2.3. Twist angle calculation method As mentioned in chapter 1, a previous study (Nakanishi et al., 2018) reported that the energy required for brittle crack propagation depends on the mis-orientation of grain boundaries that the crack runs across. When the difference in the grain boundary orientation is classified into three independent components, the grain boundary having a large component of the twist angle requires a large amount of energy for crack propagation and acts as a resistance against crack propagation (Fig. 5). From this point of view, the results of this experiment will be discussed in this section. That is, for each process of TMCP and NQT, information on the crystal orientation of the crack propagation plane was extracted using EBSD analysis data, and the twist angles to run across were calculated for each crack propagation direction. The detailed method is shown below. First, the normal vector of the {100} plane in each Grain is obtained by EBSD data, then the normal vector of the crystal plane is projected with respect to the crack propagation direction ( x - z plane), finally the twist angle can be obtained by the calculation of the inner product of the projected two dimensional vector. As shown in Fig. 6, the grains 1 and 2 are arranged in the direction of the y -axis. Let n 1 = ( a x , a y , a z ) be the normal vector of the {100} face of the crystal grain 1, and let n 2 = ( b x , b y , b z ) be the normal vector of the {100} face of the crystal grain 2. The vectors obtained after projecting each to the y -axis direction (to x - z plane), which is the crack propagation direction, are N 1 = ( a x , a z ) and N 2 = ( b x , b z ). Since the angle Ψ between these two vectors is the twist angle, the twist angle is mathematically determined by Eq. (1) derived from the inner product calculation formula. = −1 ( ∙ + ∙ √( 2 + 2 )( 2 + 2 ) ) (1) Rotation Tilt Twist

Fig. 6 Three components of grain boundary orientation difference