PSI - Issue 75

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

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could be correlated to cutting forces from a shell model. In the following a path is described using machine learning approaches.

3. Calculation of structural and notch stresses at the spot weld

In order to derive a correlation between structural and notch stresses, a simple and universal joint geometry was used. Two circular sheets with a diameter of d a and thicknesses t 1 and t 2 are joined with a spot weld with a diameter of d . The four dimensions are varied in the range 20 mm ≤ d a ≤ 50mm, 3mm ≤ d ≤ 7mm, 1mm ≤ t 1 , t 2 ≤ 3mm. Both circular sheets are coupled on their outer diameter with a kinematic coupling to a reference point that lies on the line of the rotational symmetry, but at a distance of 5 mm to the spot weld center, Figure 2. One reference point is fixed, allowing neither movement nor rotation, whereas at the other reference point three forces and three moments are applied. These forces and moments range between zero and a max. value that leads to a notch stress of approx. 1 MPa in the case of mean geometric dimension, i.e., d = 5mm, t 1 = t 2 = 2mmand d a = 35mm.

Fig. 2. Models, boundary conditions and load for the calculation of notch stresses (left) and nodal forces at the spot weld (right)

Two di ff erent types of parametric models are set up:

1. A model using hexahedron elements with quadratic shape function (Abaqus: C3D20) is used to derive notch stresses with a reference radius of r ref = 0 . 05 mm. The meshing of the notch is in agreement with the recommen dation given in [2]. The notch stress model is created and solved in Abaqus CAE. 2. A shell model using shells with linear shape function (Abaqus: S4 and S3R) is used to derive nodal forces. The spot weld is modeled as a hexahedron (Abaqus: C3D8) that is connected to the shell elements of the sheets with RBE3. The model is set up in ANSA and solved in Abaqus. Nodal forces as well as maximum principal notch stresses are derived for both models in which the 10 parameters (4 geometrical dimensions + 6 loads) are varied randomly, Figure 3. From the notch stress model, notch stresses as maximum principal stress are derived; from the structural stress models, 8 × 3 nodal forces at the nodes of the hexahedron. In addition, the location of the notch stresses is evaluated in cylindrical coordinates. Overall 963 models have been set up, solved, and evaluated. The derived notch and structural stresses, and angular coordinates are used for the training of the machine learning algorithms.

4. Machine learning model

A number of publications demonstrate the use of machine learning to predict crack initiation and propagation. However, most of them focus on mode I cracking. Wei Wang et. al [24] for instance use a dynamic Bayesian network to predict fatigue crack growth on a notched sample under uniaxial tension. Post et al. [12] looked at quasi-static damage initiation in carbon fiber reinforced plastics using two separate machine learning models for di ff erent aspects. The crack initiation load level is predicted using a tree-based classification model and a separate linear regression model is used to identify the crack angle and location.