PSI - Issue 5

Jürgen Bär et al. / Procedia Structural Integrity 5 (2017) 793–800 Jürgen Bär et al. / Structural Integrity Procedia 00 (2017) 000 – 000

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cycles only a slight extension of the corner crack is visible. However, after the first 20,000 cycles in all four specimens, independent of the notch depth, nearly the same crack size is measurable. In the following 20,000 cycles (crack propagation from 20,000 cycles up to 40,000 cycles) the cracks propagate dominantly in the notch root forming an ellipsoidal crack. However, the crack size after this period is different depending on the notch depth. A comparison between the specimen with a notch depth of 1 mm and the specimen with the 2 mm notch shows that one of the edge cracks of the latter has extended to nearly the double size. In the specimen with a notch depth of 3 mm even a through-the-thickness crack front was formed after these 40,000 cycles. The investigations demonstrate that the crack propagation in the notch root (z-direction) is faster than the propagation on the surface (x-direction). This higher crack propagation rate is probably caused by notch stresses and the interaction of the two edge cracks. The notch depth determines the crack propagation in the notch root, leading to a higher propagation rate and to a faster merging of the two edge cracks.

Fig. 5. Short cracks initiated in the notch. Left: notch depth 1 mm, right: notch depth 2 and 3 mm. The crack extension in the notch root and the specimen surface was measured in a SEM. The color gives the size after the given cycle-numbers.

To investigate the differing propagation of the short cracks in the notch root and on the specimen surface in more detail, finite element calculations have been undertaken. Therefore, two quarter elliptical cracks with a crack length in the notch root of c=1 mm and on the specimen surface of a = 0.5 mm were incorporated in a specimen with a notch depth of 1 mm. The stress profiles in the notch root and on the specimen surface were calculated in an elastic FEM calculation. The calculated stress concentration factors, i.e. the calculated local stress divided by the nominal stress applied on the specimen, are shown in figure 6. The stress concentration factor of the notched specimen without any crack is shown as a dashed blue line. The calculated stress concentration factor in the notch root (red line in figure 6) is nearly 8 at the crack tips and decreases to about 4.5 between the cracks. This means that in the cracked notch root the stress concentration factor is always higher than in the specimen without cracks. The increased stress leads to a higher crack propagation rate and promotes the initiation of new cracks in the notch root. In case of the specimen surface (green line in figure 6) the stress concentration at the crack tip is slightly higher compared to the value of the uncracked specimen and decreases within 1 mm nearly to the level of the nominal stress. These results support the observations of the fatigue experiments, which already showed that the crack propagation in the notch root is faster than on the specimen surface. Hence, the prolongation of the crack along the notch root until the formation of a through-the-thickness crack front is the process to focus on.