PSI - Issue 42

Mike Nahbein et al. / Procedia Structural Integrity 42 (2022) 433–440 Author name / Structural Integrity Procedia 00 (2019) 000–000

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Figure 5 displays the fracture surface and the run of the crack angle  calculated from the three potentials for a specimen with a secondary notch at the position of 60°, exactly between probe position 1 and 2, as second example. In the light microscope image of the fracture surface (Figure 5a), not all overload lines are marked. The early markers are only visible in the SEM and were therefore evaluated separately.

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b

Fig. 5. (a) Fracture surface and (b) calculated crack angle of a specimen with a crack initiation site at 60°. The colored lines correspond to the overload marks. The first overload marks are not marked in the fracture surface.

The crack angle can be detected safely at about 115,000 cycles, the corresponding crack size can be calculated with the new criterion to 3.36 %. An earlier detection of the crack size is not possible in this case because the first overload marks cannot be identified in this specimen. 4. Discussion The experiments have proofed the possibilities of the geometrical model suggested by Hartweg and Bär (2019) to detect the crack angle very fast and precise. Moreover, the advanced model allows the calculation of the crack size from the radius-coordinate of the normal vector. This is a big advantage because this new criterion for crack detection is uniquely defined in contrast to the scatter of the calculated crack angle. In addition to that, it is now possible to calculate the crack size itself independent of the position of crack initiation. For using the model independently of the starting position of the crack or e.g., for in-situ measurements, a mathematic correlation between the radius-coordinate of the normal vector n r and the crack size, i.e. the relative fractured surface a f /W f is needed. For the mathematic correlation, two formulas 2 formulas were adapted which are used for crack length calculation from potential data for single edge notched specimen: The first one (“JRF”) is referring to the “Johnson-Formula”, (Johnson 1965) which is often used to calculate crack length from potential drop data. The JRF bases on the non linear correlation between the relative broken area and the total area of the specimen a f /W f and the radius-coordinate of the normal vector n r as well as the half distance between the connection points of the potential probes y 0 and the size of the secondary starter notch a f,k /W f (see equation 3): � � � � = � � ∙ ⎩⎪⎨ ⎪⎧ ����� � � ∙� ∙� � � � �����(� � ��)∙�������� ��� � � ∙� ∙� � � � ���� � � ∙ ∙ � �� � ,� � �� ⎭⎪⎬ ⎪⎫ (3)