PSI - Issue 75

Jörg Baumgartner et al. / Procedia Structural Integrity 75 (2025) 538–545 Jo¨rg Baumgartner / Structural Integrity Procedia 00 (2025) 000–000

542

5

Fig. 3. Example of calculation results for solid model (left) and shell model (right)

Giannella et al. [5] studied di ff erent regression network architectures for fatigue crack propagation analysis. They achieved good correlation between FEA based and machine learning predictions using very simple network structures. Yu et al [25] used machine learning to predict the fatigue curve of high-strength steel resistance spot welds using a simple regression model. The model consisted of two hidden layers, a linear layer and a ReLu activation function. A Broyden-Fletcher-Goldfarb-Shannon (BFGS) algorithm was used for optimization. FEA based data were used for model training, the FE-model represented a tensile shear test according to ISO 14324-2003, which means a mode I type loading. The sheet metal gauges, nugget diameter and specimen width were used as input parameters. With this approach, a good agreement between machine learning model prediction and physical tests was achieved. Based on the literature review, the machine learning model architecture used for this study of mode II / III cracking was kept as simple as possible. The model consists of two hidden layers with 52 nodes and a ReLU activation function each. A hyperparameter optimization study was conducted to achieve the best possible correlation between 3D model results and machine learning model prediction. As can be seen in Figure 4 and Figure 5 good correlation is achieved for the max. principal stress and the radial position of the highest stress. However, the correlation of the tangential and vertical position is yet poor (Figure 6 and Figure 7) This study shows that the approach assessing notch stresses based on structural stresses from a shell model leads to good results. Even though some scatter is present, a good correlation between numerically determined and estimated notch stresses is achieved. It should be mentioned that the dataset used for training and validation only contained 963 data points. Additional data points will likely improve the assessment reliability. The limited success in predicting the exact position of crack initiation can have multiple reasons and needs to be investigated further. A number of approaches have been attempted to improve correlation, such as using a separate regression machine learning model for each individual output and employing di ff erent activation functions in the hidden layers. Additionally, various cost functions were explored, including those with squares of inputs included. Unfortunately, none of these measures improved correlation. Small numbers might also contribute to this poor correlation; for instance, the z-coordinate varies only between -0.05 and + 0.05 (i.e. ± r ref ), which is a very small range. Normalizing the numbers should mitigate this problem somewhat, which is why z-score normalization was used. However, using angular coordinates in degrees might be a better choice than position coordinates in mm. This will also be the subject of further investigations. Finally, when examining the plot of z-coordinates (Figure 7), the results seem to jump between di ff erent levels. The cause is the regular mesh in the notch; the nodes are positioned exactly on the some z-coordinates. This suggests that using a classification model rather than a regression model might be a better choice, similar to the approach suggested by Wei Wang et al. [24] for failure in composites. 5. Discussion