PSI - Issue 42

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

439

7

The second formula (“TRF”) was proposed by Tiedemann (2016). This root-based formulation shows a better performance especially for short crack length compared with the Johnson-formula. The TRF does not use the distance of the potential probes, but two other parameters: The inclination of the fitted curve correlates with the variable q, whereas the exponent t describes the curvature. Moreover, the broken area of the secondary notch a f,k is used (see equation 4). � � � � = ∗ � � + � �,� [� � ] (4) Figure 6 shows the relative fractured area af/Wf as a function of the radius-coordinate of the normal vector n r for specimens with different locations of the initial crack. The data points show only a small scatter especially at higher crack length which is mainly due to different crack geometries. On all data points a mathematical adjustment of the JRF and TRF formula (equation 3 and 4) was undertaken. In case of the JRF formula the half distance between the connection points of the potential probes y 0 and for the TRF formula the parameters q and t were used as adjustment parameters.

0.4

0.3

a f,i /W f,i

0.2

MN-02 0°-10k-1 MN-09 30°-10k-1 MN-10 30°-10k-1 MN-11 15°-10k-1 MN-12 15°-10k-1

0.1

Parameters of TRF: q = 0.14540 ± 0.00223 t = 0.67181 ± 0.01553 a f,k = 2.08159*10 -7 m 2

TRF JRF

0.0

0

1

2

3

4

5

n r,i

Fig. 6. Fitting curves of JRF and TRF in comparison.

The two fitted curves in figure 6 show that both formulas can be used to describe the mathematic correlation between the relative fractured area a f /W f and the radius-coordinate of the normal vector n r . The TRF shows a better correlation (corrected R 2 -value = 0.967) compared with the JRF (corrected R 2 -value = 0.949). This result clearly indicate that the length of a crack initiated at the surface of a notched round bar can be calculated out of the three measured potential drops with a high accuracy. The multiple potential measurement is excellently suited not only to determine the location of the crack, but also the size of the crack, independent of the location of the crack initiation site on the circumference of the specimen. 5. Conclusions The investigations have shown that with the advanced model introduced in this work the location of the crack initiation site as well as the crack length can be calculated from three simple potential drop measurements. This opens new possibilities in fatigue tests on specimens with a round cross-sectional area. Beside the crack initiation lifetime crack propagation data can be easily gathered from the potential drop measurements. This allows a defined pre