PSI - Issue 51

Kenichi Ishihara et al. / Procedia Structural Integrity 51 (2023) 62–68 K. Ishihara and T. Meshii / Structural Integrity Procedia 00 (2022) 000–000

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the past. In other words, function f which gives heat source parameters ( a , b , c ) from welding speed v and heat power Q and the molten shape W and D by DL was developed. Engineering framework to inverse analysis method of molten shape by deep learning was shown in Fig. 1. 2. Heat source model and TDA method As aforementioned, Goldak’s double-ellipsoidal heat source model (GDE model), shown in Fig. 2 and equation (1) as below was considered in this study. � = 6√3 � √ � e�� �−3 � � � e�� �−3 � � � e�� �−3 � � � � (1)

y

c

c f

r

a

z

b

x

Fig. 2. Goldak’s double-ellipsoidal heat source model.

For the TDA method, there are two options: Finite element analysis (FEA) and the theoretical solution. In this work, the theoretical solution was used for machine learning because FEA takes amount of time, and the temperature dependence of material properties are small, and experiencedly, the infinite plate solution can be applied to the thickness of the actual structure. In this study, Fachinotti’s TDA close-formed equation (CF equation; Fachinotti, 2009) as shown equation (2)-(4) below, which uses GDE model as heat source model, was used for TDA. � � = � + 3√3 √ � ×� e��� −3 � 12 � � + � − −3 � 12 � � + � � �12 � � + � �12 � � + � ×� � � �1− � �+ � � �1+ � �� � � (2) � = � � ; � � = e�� � −3� � � 12 � � + � � � �12 � � + � � (3) � = � � ; � �=erf ⎢ ⎢ ⎡ ⎣ � 2 � � ��12 � � + � � ⎦ ⎥ ⎥ ⎤ (4) Note that, in equation (1)-(4), subscript i of parameters q i , c i , F i represents i = f when the position z is ahead of the welding beam, and i = r when the position z is behind the welding beam. And GDE parameters used in CF equation assumes c f = a and c r = 4 c f , F f = 2 c f / ( c f + c r ), F r = 2 - F f (Fachinotti, 2009). Thus, for the DL model function, heat source parameters ( a , b ) will be focused only.