PSI - Issue 57

Matthias Hecht et al. / Procedia Structural Integrity 57 (2024) 581–588 Matthias Hecht et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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4. Discussion The specimens loaded multiaxially under variable amplitudes show that a phase shift of φ = 90° leads to a higher fatigue life compared to a proportional loading which is in line with the investigations from [10] under constant amplitudes. Thus, it can be seen that a non-proportional loading leads to a lifetime extension of the bowl specimen under constant and under variable amplitudes. This differs for the butt-bonded hollow cylinder specimens with the same adhesive, where a non-proportional loading has only a small life-extending effect [16]. The reason for this different result is of empirical nature; however, it might be connected to following differences between the bowl specimen and the butt-bonded hollow cylinders: ▪ The differences consist in the highly inhomogeneous stress state of the bowl specimen, ▪ a transient position of the most highly stressed location of the adhesive layer over one cycle and ▪ a different ratio between the normal and the shear stresses. ▪ Furthermore, the crack on the bowl specimen starts very early and the remaining fatigue life is characterized by the crack propagation, which is not the case on the butt-bonded hollow cylinder specimen. Non proportionality might act different in these two phases. Which of these four effects, or which combination of these four effects, leads to the different fatigue life behavior due to a non-proportional loading in the comparison between bowl specimen and butt-bonded hollow cylinder specimen cannot be precisely identified with the current experimental data. The cyclic stiffness degradation curves show the same behavior under all the test series investigated. At the beginning, the stiffness drops very sharply, which is due to the very high stress gradient in the adhesive layer, causing a crack to form very early on the inside of the bowl. Subsequently, the stiffness decreases linearly, indicating a constant crack propagation rate. Since this crack growth dominates the fatigue life of the bowl specimens and does not dominate the fatigue life of the butt-bonded hollow cylinder specimens, this may also explain the significantly steeper slope of the Gassner lines of the bowl specimens compared to the butt-bonded hollow cylinder specimens [16]. Investigations under constant amplitudes using a thermographic camera [10] showed that the stiffness decreases very strongly as soon as the crack has progressed to the outer edge of the bowl, which is also evident from the stiffness curve determined here. It is of interest that the progression of cyclic stiffness degradation under non-proportional loading resembles those of the other loading conditions. This suggests that the effect of the transient position of the stress hot spot over a cycle has no influence on the stiffness degradation or the crack growth. 5. Conclusion and Outlook The fatigue tests of the bowl specimens provide necessary information on the material performance under variable amplitude and multiaxial, non-proportional loading that are necessary to perform a reliable numerical assessment of the fatigue strength of adhesively bonded components, such as a vehicle body structure. In the case of a multiaxial loading, a phase shift of φ = 90° leads to an increase in fatigue life. Specimens with a quasi homogeneous stress state and the same adhesive do not show this behavior [16]. This might be explained by four differences between the specimen types. These are for the bowl specimen: ▪ Highly inhomogeneous stress state ▪ Changing position of the most highly stressed location of the adhesive layer over one cycle ▪ Different ratio between the normal and the shear stresses ▪ Early crack initiation and long crack propagation on the bowl specimen, which is shown by an early drop in stiffness degradation at the beginning of the test under all loading conditions. A precise identification of these four possible influences could not be determined within these investigations and should be made on further specimen types. In the future, a method will be developed to estimate the fatigue life of the bowl specimen under the shown complex loading conditions using structural stress approaches [21,22]. The experimental results presented in this paper are going to be used as validation data for this new method.