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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However, these LCs were identified based on an engineering judgement of the authors, therefore, there could be other conditions that are better than them. In addition, the authors are of the view we should investigate the characteristics of LC conditions which achieve a straight crack while maintaining fracture toughness. Based on the above, the authors conducted Bayesian optimization for identifying the characteristics of the ideal LC conditions in this study. 2. Bayesian optimization 2.1. Numerical analysis In order to simulate welding and LC process, authors operated finite element analysis by the same method as our previous study [10, 11]. Fig. 2 shows the overview. At first, a welding process simulation was performed on a welded joint with 500 mm length, 500 mm width, and 50 mm thickness. The multilayer welding is 60 pass and X shaped groove, and simulated by sequentially coupled finite element analysis of heat transfer and thermoelastic plasticity, using the general-purpose finite element analysis software Abaqus. After welding process simulation, a specimen is extracted with 500 mm length, 100 mm width, and 50 mm thickness, and LC is applied on the both faces simultaneously. After LC, the specimen is applied a crack with 50 mm, which is composed with 44 mm length machine notch and 6 mm fatigue pre-crack. The machine notch shape meets the related requirement in ISO 12135. After machining notch, the residual stress of crack opening direction at the notch tip is obtained for fatigue pre-crack shape evaluation. If the residual stress distribution is constantly tensile through thickness, we evaluated that a straight crack was achieved and if the residual stress of the mid-thickness is compressive while that of the surface is tensile, we evaluated that the crack was bowing. After applying a crack with 50 mm, three point bending load was applied to the specimen and the evaluation value of critical CTOD was obtained. With this regards, the fracture was estimated to be occur when Weibull stress criterion reaches 1800 MPa. In specimen which did not mapped the residual stress, the critical CTOD evaluation value reaches 0.1 mm when Weibull stress 1800 MPa [12]. 2.2.1. Optimization process Bayesian optimization is a method based on the expected improvement (EI). The EI is calculated with the near calculation results and the distance. The value becomes high if the near calculation results are high and these distances are long, i.e., the variance is high. Fig. 3 shows the process of Bayesian optimization. First, based on the calculation history, the next point is selected based on EI. After some calculation, EI decrease due to low variance when calculation points become dense. By this decreasing, Bayesian optimization selects the next point of which surrounding is not searched. Bayesian optimization has high computational efficiency with comparing random search and grid search and can find the global solution than a steepest descent and Newton’s method. 2.2. Bayesian optimization

Fig. 2. Overview of finite element simulation of LC after multi-pass welding.