PSI - Issue 38

Matthias Hecht et al. / Procedia Structural Integrity 38 (2022) 251–259

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Matthias Hecht et al. / Structural Integrity Procedia 00 (2021) 000–000

4. Discussion In general, the fatigue strength of the adhesive bond depends on the loading condition. The slightly higher fatigue life under multiaxial loading with phase shift compared to the one without phase shift can be attributed to a critical plane oriented interacting local shear and normal stresses in the semi-ductile bond [16]. This behavior can be described by a suitable critical plane based hypothesis [19]. Under variable amplitudes a larger difference in endurable stress between tension and multiaxial loading compared to the equivalent Woehler lines under constant amplitudes is visible. This is so far an experimental, purely empirical observation, which should be investigated in more detail in the future. Furthermore, it can also be seen that the real damage sums in all loading conditions deviate strongly from the theoretical value of th = 1. The real damage sums that have been determined are plausible in comparison with known literature results on uniaxially loaded adhesively bonded joints with the same adhesive [10]. Up to now, a general valid allowable damage sum for the design of adhesively bonded joints could not be defined since it strongly depends on the loading condition. 5. Conclusion and Outlook Test results of adhesively butt-bonded double hollow cylinder specimens under tensile, torsional and multiaxial loading without and with phase shift were presented. The fatigue strength under constant and variable amplitudes depends strongly on the loading situation. The tests under variable amplitudes were performed with a Gaussian load spectrum. The real damage sums, which are based on the modified Palmgren-Miner hypothesis by retaining the slope of the Woehler line also after the knee point, are clearly below the theoretical value of one and depend strongly on the loading condition, so that damage sums valid for the test conditions can be suggested. Non-proportional loading under constant amplitudes does not reduce fatigue life. It even leads to a slight increase compared to proportional loading. For this critical plane based hypotheses corresponding the ductility of the bond [16, 19] seem to be suitable. For similar types of loads, the damage sums presented can be used for fatigue life prognosis. Acknowledgements The investigations presented here were supported by financial funding from the Federal Ministry of Economics and Technology (BMWi) via the Federation of Industrial Research Associations (Arbeitsgemeinschaft industrieller Forschungsvereinigungen Otto von Guericke e.V.) under grant 21.112 N. Technical and scientific support during the project was provided by the Research Association for Steel Application (FOSTA). The authors thank the AiF, the FOSTA and the members of the project committee for their support. References [3] J. Schijve, Fatigue of Structures and Materials, Dordrecht: Kluwer Acadamic Publishers, 2001. [4] A. Palmgren, "Die Lebensdauer von Kugellagern," VDI-Z 68, vol. 14, pp. 399-341, 1924. [5] K. L. Kotte and K. -G. Eulitz, "Data Pool Structural Integrity – Reliability of Lifetime Prediction Methods", Mat.-wiss. u. Werkstofftech, vol. 34, no. 9, pp. 836-842, 2003. [6] M. A. Miner, "Cumulative damage in fatigue", Journal of Applied Mechanics, vol. 12, no. 3, pp. A159-A164, 1945. [7] H. T. Corten and T. J. Dolan, „Cumulative fatigue damage“, Proceedings of the International Conference on Fatigue of Metals, pp. 235 246, London, 1956. [8] E. Haibach, Betriebsfestigkeit - Verfahren und Daten zur Bauteilberechnung, Wiesbaden: Springer-Verlag Berlin Heidelberg, 2006. [9] K.-G. Eulitz, P. Heuler and K. L. Kotte, "Lebensdauerabschätzung von Schweißverbindungen unter variablen Amplituden - Berechnung und Experiment", DVS-Bericht Nr.236, pp. 36-42, 2005. [10] H. Schmidt, "Schwingfestigkeitsanalyse struktureller Klebverbindungen unter Belastung mit variablen Amplituden", Technische Universität Darmstadt, Dissertation, Darmstadt, 2013. [1] E. Gassner, "Festigkeitsversuche mit wiederholter Beanspruchung im Flugzeugbau", Luftwissen 6, pp. 61-64, 1939. [2] C. M. Sonsino, "Principles of Variable Amplitude Fatigue Design and Testing", Journal of ASTM International, vol. 1, no. 9, October 2004.