PSI - Issue 66

Carl H. Wolf et al. / Procedia Structural Integrity 66 (2024) 26–37 8 Carl H. Wolf, Sebastian Henkel, Christian Düreth, Maik Gude and Horst Biermann / Structural Integrity Procedia 00 (2025) 000–000

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3.3. Evaluation of the displacements To explain the measurement procedure, the determination of the energy release rate is demonstrated using the example of a #160 specimen, which was loaded with F tension = 2.75  2.25 kN and F compression = 0.5 kN, at N = 25,000 load cycles, cf. Figure 7. As with the steel specimens tested in reference [9], the portion of the Mode II displacement  4 , T in the total displacement  4 is difficult to recognize in the measurement set-up, see Figure 7c. By separating the displacements according to direction, it can be clearly seen in the evaluation of the displacement that a Mode II-dominated Mixed Mode loading is present. The displacements  4 , T caused by the Mode II loading are significantly larger in comparison to the displacements  4, S caused by the Mode I loading, see Figure 7a and c. The course of the displacement also shows that the extreme values of the Mode I and Mode II loading occur at the same time, i.e. there is an in-phase loading. The evaluation of the equivalent energy release rate over the crack growth rate for this specimen at N = 25,000 load cycles is comparable with the crack growth data from Sutton [8] for fatigue crack propagation in an epoxy polymer, cf. blue measuring points and black line in Figure 7f. The examination of the individual portions shows that the energy release rate of the Mode II loading is significantly larger than the Mode I energy release rate, see Figure 7b and d. Both Mode I and Mode II portions are included in the calculation of the equivalent energy release rate so that the data can be compared with the literature. 3.4. Fatigue crack growth In the crack growth plots ( Figure 8 ), the crack growth rate is plotted versus the energy release rate  G . The results are compared with the determined Paris law from references [8, 16, 12]. In Figure 8 a strong scatter of the crack growth rates can initially be recognized. This may be caused by a small scatter in the measurement of the crack tip position using CrackPy [7], which results in scatter in the crack growth rates. Comparing the energy release rates of the FE calculation  G eq, FE with the equivalent energy release rates determined using the virtual measuring clip  G eq, Clip , differences can be recognized, cf. circles and rectangles in Figure 8 e. The energy release rates determined using the FE calculation are larger than the equivalent energy release rates determined using the virtual measuring clip. The measured values of the FE calculation approximate the Paris law of Sutton's epoxy resin [8]. However, the results of the FE calculation are only to be understood as a guide value due to the assumption of a symmetrical crack path and a linear elastic material model. It is therefore possible that not all effects occurring due to the loading are represented due to the specimen geometry. This becomes particularly clear in the individual analysis of the Mode I and Mode II energy release rates of the virtual measurement clip  G I and  G II, cf. Figure 8 a and c. The Mode II energy release rates for uniaxial loading all correspond to a mutual scatter band, cf. Figure 8 c. The evaluation of the Mode I energy release rates under uniaxial loading, on the other hand, shows a clear trend: the crack growth rate decreases as the fabric weight increases, cf. Figure 8 a. A comparison of the determined equivalent energy release rates under uniaxial loading confirms this trend, cf. circles in Figure 8 e. The specimens with a lower fabric weight have lower crack growth rates, cf. red and orange circles in Figure 8 e, compared to the specimens with a high fabric weight, cf. green circles in Figure 8 e. On the one hand, it can be concluded from this result that the FE calculation may not reflect all the effects of the loading. On the other hand, the trend of the lower crack growth rate due to the higher fabric weight is recognizable, which is also reflected in the results of the FE calculation. Under biaxial loading, the data scatter is larger compared to uniaxial loading, cf. Figure 8b, d, and f. Nevertheless, some trends can be identified. In addition to the effects already described under Mode I loading with regard to the crack growth rate, i.e. caused on the one hand by the Mode I portion of the loading (Figure 8b) and on the other hand by a mutual scatter band due to the Mode II loading (Figure 8d), which can also be recognized in the consideration of the equivalent energy release rate (Figure 8f), it becomes clear that the crack growth rate is reduced as a result of the compressive loading. The increasing compressive loading impedes crack opening and thus reduces the Mode I portion of fatigue crack growth. At the same time, the compressive loading leads to a minimization of the Mode II loading by