PSI - Issue 58

Mikkel L. Larsen et al. / Procedia Structural Integrity 58 (2024) 73–79

79

M.L. Larsen et al. / Structural Integrity Procedia 00 (2024) 000–000

7

Table 2. Non-proportionality levels for varying phase shifted loading for four points of interest.

Phase-shift 0 degrees

NP1 NP2 NP3 NP4

0.00 0.00 0.00 0.00 22.5 degrees 0.00 0.01 0.04 0.03 45 degrees 0.00 0.03 0.18 0.13 90 degrees 0.01 0.09 0.96 0.73

As seen from Tab. 2, the non-proportionality levels vary considerably between the four points. As expected, at 0 degrees phase-shift in the loading, the local stress state will also be proportional, predicting values close to 0. However, when increasing the phase-shift of the loading only points NP 3 and NP 4 exhibit non-proportionality values above 0. This is due to the location of the points. As seen in Fig. 3, NP 1 and NP 2 are located close to the neutral-line considering the F V force. Thus, the bending forces from this load are not large enough to result in normal stresses perpendicular to the weld, causing non-proportionality. Point NP 3 and NP 4 are exposed to stresses from both the F V and F H loading, leading to higher levels of non-proportionality, when phase-shifting the forces. The results from the non-proportionality analysis can be used to optimize weld locations and determine if better weld classes are required at special places in the structure. In this paper, a lifting arm in a mower structure has been tested and a digital twin has been developed using the finite element method. The first FE model was observed to be too sti ff . The cylindrical joint at the pinned connection was replaced by an equivalent spring support and parameter based-model updating was performed. The updated model was more accurate and the root-mean-square error was reduced by 39 to 68 %. Using the accurate updated FE model, the non-proportionality of the stress states at four locations of the lifting arm has been investigated based on a principal component-based measure of non-proportionality. Four simulated load cases have been investigated and the results show that the levels of non-proportionality are largely dependant on the load case and the location of the critical point. 5. Conclusions

Acknowledgements

This work has been supported by the Innovation Fund Denmark, grant number 2053-00003b. The authors are grateful to Carsten Stjernfelt from Dewesoft who has kindly lent us the Dewesoft measuring system. Furthermore, the authors would like to thank lab technicians Hans-Henrik Olsen and Kasper Wolfhagen at Kverneland Group Kerteminde for their help with performing and setting up the experiments conducted in the paper.

References

Arora, V., 2011. Comparative study of finite element model updating methods. Journal of Vibration and Control 17, 2023–2039. Bolchoun, A., Kaufmann, H., Sonsino, C.M., 2015. Numerical measures of the degree of non-proportionality of multiaxial fatigue loadings. Frattura ed Integrita` Strutturale 9, 238–252. DNV, 2021. DNV-RP-C203 - Fatigue design of o ff shore structures. Recommended Practice. DS / EN, 2007. Eurocode 3: Design of steel structures - Part1-9: Fatigue. Standard DS / EN 1993-1-9. Danish Standards. Gurney, T.R., 1979. Fatigue of welded structures. Cambridge University Press, Cambridge England New York. Hobbacher, A.F., 2016. Recommendations for Fatigue Design of Welded Joints and Components. Springer International Publishing. Larsen, M.L., Baumgartner, J., Clausen, H.B., Arora, V., 2022a. Multiaxial fatigue assessment of welded joints using a principal component-based measure for non-proportionality. International Journal of Fatigue , 106731. Larsen, M.L., Baumgartner, J., Clausen, H.B., Arora, V., 2022b. A new constant amplitude equivalent principal component analysis-based method for non-proportionality quantification of variable amplitude loaded welded joints in large-scale structures. International Journal of Fatigue , 107008. Maddox, S.J., 1991. Fatigue strength of welded structures. Abington Pub, Cambridge, England. Pejkowski, Ł., 2017. On the material's sensitivity to non-proportionality of fatigue loading. Archives of Civil and Mechanical Engineering 17, 711–727. Sonsino, C.M., 2019. Influence of material ductility on fatigue life under multiaxial proportional and non-proportional normal and shear stresses, in: ICMFF12 - 12th International Conference on Multiaxial Fatigue and Fracture, p. 17001.