PSI - Issue 17

Moritz Hartweg et al. / Procedia Structural Integrity 17 (2019) 254–261 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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4

P 1 = U 1 / U 0,1 P 2 = U 2 / U 0,2 P 3 = U 3 / U 0,3

1.15

1.05 relative potential drop P i 1.10

1.00

0

5

10

15

20

25

broken area [%]

Fig. 3. Increase of the three potentials as a function of the fractured area for a crack emanation from the position of potential probe 1.

For the initiation of a single crack, the crack initiation site can be determined using a simple geometrical model illustrated in figure 4. The relative potentials P 1 , P 2 and P 3 are treated as a vector. In the beginning of the experiment, without a crack all three relative potentials have the same value P i = 1 resulting in the same length for the three vectors (Figure 4a). As a result, the vectors span a horizontal plane and the normal vector of the plane is parallel to the loading direction. With the initiation of a crack, the vectors elongate by different amounts. Consequently, the spanned plane and with it the normal vector tilts away from the propagating crack (Figure 4b). The position of the crack initiation site is given as the opposite angle of the normal vector projected on the x-y-plane (dashed line in figure 4b).

Fig. 4. Illustration of the geometrical model for the determination of the crack initiation from the measured relative potentials. (a) uncracked specimen, (b) specimen with a crack near potential probe 2

The angles for the specimen shown in figure 2 calculated with the model are shown in figure 5a. The raw unfiltered data are shown in light grey, the red line represents the data filtered with a moving average over 100 data points. The colored vertical lines are connected with the colored overload marks in figure 2. It is clearly visible that the scatter of the raw data is decreasing with increasing crack length. The scatter was quantified by calculating the standard deviation in an interval [N-50, N+50] of the raw data and was assigned to the cycle number N. The run of the standard