PSI - Issue 57

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

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Matthias Hecht et al. / Structural Integrity Procedia 00 (2019) 000 – 000

3.2. Cyclic stiffness degradation The stiffness degradation behavior, i.e., the displacement orthogonal to the surface, was measured on the upper side of the bowl by using a laser extensometer at three points. In radial direction, these measuring points were located on the inner ellipse of the adhesive.

Fig. 4 Cyclic stiffness degradation of the bowl specimens: (a) under pure vertical force loading, displacement measured at L 1, related to the vertical force component; (b) under pure horizontal force loading, displacement measured at L 2, related to the horizontal force component; (c) under combined loading without phase shift ( φ = 0°), displacement measured at L 3, related to the vertical force component; (d) under combined loading with phase shift ( φ = 90°), displacement measured at L 3, related to the vertical force component. The measuring positions were selected so that this was at the most highly stressed point under the load cases of pure vertical ( L 1) and pure horizontal loading ( L 2), as well as the combined loading without phase shift ( L 3), see Fig. 1. These were identified using the, for adhesives often used, modification of the von Mises equivalent stress according to Beltrami [20] via FE analysis. Then, the location of maximum stress was identified in the centroid of the first element row in the inner edge of the bowl. The failure point under combined loading with phase shift was quite similar to that without phase shift, resulting in the use of only three laser extensometers. After the tests, it was found on the fracture pattern of failed specimens that the location of cracking could be described with good approximation by the FE analysis under all loading conditions. The cyclic stiffness c̅ was then calculated using ̅ = ∫ ̅( ) ( +5) ( ) ∫ ̅( ) ( +5) ( ) . (6) For this purpose, five cycles were evaluated in more detail every 100 cycles. Due to the exclusively positive force and displacement curves, the stiffness was calculated via the mean value of the force F̅ and displacement u̅ within these five cycles, resulting in a measurement point for the stiffness c̅ every 100 cycles. Through these measurement points a fitting function is placed that consists of an exponential and linear term, Fig. 4. The stiffness normalized to the initial value is shown here over the normalized fatigue life. The behavior is similar under all loading conditions. At the beginning of the test, the stiffness drops very sharply, which can often be observed with adhesives or elastomers. Subsequently, the stiffness drop linearizes until the specimen gapes open at the end of the test, causing the stiffness to drop to a very low value. An exact correlation between the amplitude level and the stiffness decrease could not be identified due to noise.