PSI - Issue 53

Benjamin Möller et al. / Procedia Structural Integrity 53 (2024) 190–202 Author name / Structural Integrity Procedia 00 (2023) 000–000

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From Fig. 8a it becomes clear that the thickness changes significantly, not only from one specimen to the other, but also along the axis of a single specimen. The idea to consider this effect was to model every WAAM hollow structure specimen with a mean thickness of 4 mm, which is equal to the thickness of the section of the nominal geometry, and then apply a thickness correction factor to increase or decrease the peak stresses obtained from the FE simulations. To find those thickness correction factors, a series of five FE simulations under variation of the thickness was carried out with the following framework conditions:  The outer surface (envelope) of the FE model is set to ideal flat surface.  The thickness of the section is varied between the different simulations from 2 mm to 6 m, i. e. 2 mm, 3 mm, 4 mm, 5 mm and 6 mm has been applied.  The load applied is simultaneously in phase axial and bending (the same loading used for the testing and other simulations). The (von Mises) peak stresses obtained from these FE simulations are shown in Fig. 8b with respect to the thickness, giving information on the thickness effect. Then, the link to the equivalent stresses derived from the FE simulations of the tested specimens had to be created by thickness information for every single specimen. To derive this, the area of the mean section for each handlebar was calculated dividing the volume of each specimen, found using the Archimedes method, by the corresponding length of the hollow structure specimen. Assuming the external profile of each section to remain constant over its length, it was possible to obtain a value for the mean thickness of each specimen. All resulting values for the specimens came out to be in the range between 4 mm and 6 mm (the one highlighted in grey in the graphs from Fig. 8b). The relative differences of peak stresses in between the reference thickness (4 mm) and the real ones were below the 10 %. This has led to the thickness reduction factors to be smaller or equal to 1.1.

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Fig. 8. (a) Typical section of the segment; (b) comparison of sections; (c) thickness effect.

Concerning the second modelling aspect, the process to define the effect of the size and number of the elements for the FE simulation followed a similar procedure to the one described before, ending up in a convergency study. Under repetition of the same FE simulation, the effect of changing the size of the elements for every simulation on the peak stress was obtained. From this, meshing parameters have been chosen to be applied to the FE models of every (3d scanned) specimen, which contain a mesh refinement at outer surface and towards the fatigue-relevant notches. Further details on the FE simulation are given in section 3.2. A surface analysis was carried out to find the handlebar specimen with the most severe defect in terms of notch radius in the most stressed point. Two examples of this analysis are shown in Fig. 9, i. e. specimen HB_2D with measured notch radius of r notch ≈ 0.5 mm and a measured notch opening angle  notch ≈ 123 ° (Fig. 9a) and specimen HB_4U with r notch ≈ 0.9 mm and a measured notch opening angle  notch ≈ 140 °. The specimen HB_2D is the one that showed the most severe defect (the one with the smallest notch radius combined with a small notch opening angle). Therefore, this is the one that was used as a representative critical case for the hollow structure specimens of the motorcycle handlebar.