PSI - Issue 75

Kris Hectors et al. / Procedia Structural Integrity 75 (2025) 102–110 Hectors et al. / Structural Integrity Procedia (2025)

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Fig. 6: Illustration of the bottom-up meshing strategy to obtain a volumetric mesh from the specimen cross-section, the applied boundary conditions and loading.

3.4. Mesh convergence study To ensure that the accuracy of the solution is independent of the mesh element size, a mesh convergence study was performed. The stress within the notch directly correlates to the mesh element size in the notch partition, as well as the element size in the circumferential direction. Maintaining an aspect ratio close to one necessitates a large number of circumferential seeds. However, this leads to exceedingly thin wedge elements in coarser meshed regions. Consequently, a trade-off was made to maintain a reasonable number of circumferential seeds, albeit at the expense of a diminished aspect ratio. The mesh convergence study consisted of a total of 15 models with reducing mesh element sizes. It tested convergence for the maximum principal stress in the notch and resulted in a convergence point for which the notch region and circumference contained 50 elements. The mesh density at selected convergence point results in an element size of 13 within the notch region. This is smaller than the distance between two sampling points of the profile scan, reinforcing the conclusion that the mesh indeed converged. The maximum elastic notch stress σ is depicted against the notch and circumferential seeding in Fig. 7. 3.5. The elastic stress concentration factor A finite element analysis was conducted for 177 specimens. However, the irregularities in the profile led to the formation of extremely fine mesh elements in some models. As a result, only 151 model were considered valid. This further proves the complexity of constructing qualitative finite element models from raw scan data. From the maximum notch stress σ obtained for each model, the stress concentration factor was calculated as / . The nominal stress is calculated with the applied bending moment , the section modulus and the nominal diameter at the notch root as defined in Equation (2). = = 32 3 (2) The results, presented in Fig. 8 show the -values obtained for every specimen. A mean value and standard deviation of = 2.20 ±0.15 are found. The mean value deviates significantly from the theoretical value of 1.875. This theoretical value was obtained from an idealized finite element model with the nominal dimensions, highlighting the importance of accounting for the as-machined geometry. Notably, certain specimens exhibit -values far exceeding the average value. For instance, specimen N35 was more closely examined due to its exceptionally high value of . N35’s measured notch parameters exhibited no significant deviations from the other specimens with respect to the influence of their values on the as can be observed from Fig. 9 . But N35’s profile exhibits an irregularity that narrows the opening angle, shown in Fig. 10, thereby causing a higher stress concentration in the notch root. This is not visible in Fig. 9 because of how the notch opening angle was measured. The measurements of the opening angle and root radius were based on the global notch geometry. Therefore, the measurements did not reflect this discontinuity in the profile. This example illustrates why incorporating the complete profile scan can yield more accurate results compared to relying solely on measured notch parameters.