PSI - Issue 39

Deborah Weiß et al. / Procedia Structural Integrity 39 (2022) 139–147 Author name / Structural Integrity Procedia 00 (2019) 000–000

146

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Second, the influence of different loading angles α on the crack growth rate is analyzed and visualized in Fig. 5. Up to a crack length of 54 mm, a pre-crack is initiated under cyclic Mode I loading with a maximum force of 2.5 kN and an R -ratio of 0.1. Then the loading device is reclamped and the test is subsequently continued with the same maximum force of 2.5 kN. With an increase of the loading angle α , the amount of Mode II at the crack tip increases. Thus, the cyclic equivalent stress intensity factor Δ K v as well as the crack growth rate decreases. With the help of the cyclic equivalent stress intensity factor Δ K v , it is possible to describe the loading situation at a crack tip as a function of K I and K II already presented in chapter 2. According to Erdogan and Sih (1963) Δ K v can be described by the following equation: = cos � 0 2 � � 2 � 0 2 � − 3 2 sin( 0 ) � (6) In addition, the number of load cycles from reclamping to a total crack length of 72 mm is noted in Table 1. It can be observed that the number of load cycles increases with increasing loading angle α, which can also be explained by the circumstance that the crack propagation after reclamping takes longer with increasing amount of Mode II. Furthermore, the crack growth rate is lower with higher loading angle α .

Table 1. Average number of load cycles in relation to the loading angle α . loading angle α 15° 30° 45° 60°

∅ number of load cycles

75°

90°

82191

129270

174049

220742

672671

3416993

3.4. Numerical Validation In the aforementioned sections it could be illustrated that the MTS-criterion is also applicable for thin structures. This means, as far as the crack propagation direction is concerned, these thin structures behave in the same way as the standard specimens with a thickness of 10 mm. With this knowledge, the existing numerical programs like A DAPCRACK 3D using the σ 1 ’-criterion, which is the three-dimensional analogue of the two-dimensional MTS criterion, can still use this criterion to predict crack propagation in thin structures as well, Schöllmann (2001).

Fig. 6. Experimentally determined crack path (left); numerically determined crack path (right) and comparison of the experimental and numerical results of the crack path (middle) for a loading angle of 75°. Fig. 6 shows the experimentally and the numerically determined crack path as well as the comparison of the experimental and the numerical results of the crack path for the loading angle α = 75°. For better illustration, the crack path predicted by the simulation program is highlighted in red color. The comparison with the experimental result underlines that it is possible to predict the crack path by numerical crack growth simulation.