PSI - Issue 42

Takumi Ozawa et al. / Procedia Structural Integrity 42 (2022) 730–737 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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2.2.4. Objective function Equation (1) shows the objective function used in this study.   2 2 min Y ISO 0.1 0.1 Y MIN , 0 . . O F         −  −  = +          

(1)

where,  ISO is the critical CTOD obtained from the process in ISO standard.  0.1 is a value of 0.1 mm,  min is the minimum residual stress for crack opening direction at the notch tip and  Y is the yield stress of the weld metal, i.e. 444 MPa. Fig. 5 shows the value of this objective function for each  ISO and  min . The value of the objective function decrease when  ISO is near 0.1 mm and  min is higher than  Y . The authors searched the LC condition of which objective function is small with Bayesian optimization. 2.3. Optimization result Fig. 6 shows the calculation history. Some groups were formed by the analysis result and the characteristics of LC. The stress of the left group were low, therefore, these fatigue precrack will be bowing. In this group, compression areas were significantly high or low, or the distance from the future crack tip was significantly long. If compression area is high, the applied LC strain will be low due to the constraint condition of the load limit. If that is low or the distance is long, the LC effect on the stress distribution at the notch tip will be limited. Therefore, the stress of the left group became low. The distance from the future notch tip of the lower right group is zero, i.e. the LCs of this group compress in contact with the future crack tip like traditional ones, and these evaluation value of the critical CTOD is low. Therefore, the authors believes that such LC conditions affect Weibull stress significantly and underestimate the fracture toughness excessively. The upper right group has sufficient the residual stress and the critical CTOD evaluation value of near 0.1 mm. These compression areas and the distance from the future crack tip had values with a certain range. The authors are of the view that LC conditions of this group is better, i.e. , will achieve a straight fatigue precrack while maintaining the fracture toughness. Fig. 7 shows the relationship between objective function and each parameter. As shown in the Fig. 7, the ideal LC conditions needed the compression area from 500 to 700 mm 2 and the distance from 2 to 6 mm. On the other hand, other parameters, such as aspect ratio and corner dimensions, had not much effect on the objective function. This means complicated shapes are not necessary for the ideal LC conditions.

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0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

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Critical CTOD [mm]

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-500

0

500

1000

Minimum stress at notch tip [MPa]

Fig. 5. Values of the objective function.