## 3 Crack Detection and Crack Localization with Multiple PD Measurements
### Crack Detection in Round Bars  
The investigations for crack detection on notched round bars were carried out on specimens of a high-alloy steel (X8 CrNi18-9) with a diameter of 19.8 mm and a circumferential notch with a radius of 5 mm and a depth of 3.9 mm as shown in Figure 7a. To measure the potential, wires with a diameter of 0.2 mm were spot-welded to the specimen surface at a distance of 0.5 mm from the upper or lower edge of the notch (Figure 7b). The three measuring points were equidistantly arranged along the circumference of the sample with an angle of 120\({}^{\circ}\) in between two points, as shown in Figure 7c. The tests were carried out under fully reversed loading conditions with an amplitude of 35 kN and a frequency of 20 Hz. To mark the crack front on the fracture surface, overloads with a maximum load of 70 kN were applied at intervals of 5000 cycles, beginning after 10,000 cycles. In order to initiate cracks at defined positions, secondary notches in form of small laser-cuts were introduced into the notch root. A constant current was conducted via the clamps through the specimen. The three potentials were measured using the amplifiers of the control electronics (Doli EDC 580V). During the fatigue tests, the maximum and minimum value of the three potentials were recorded for each cycle. In order to compensate differences in the potentials due to small differences in the tap spacing and contact resistance, the relative potentials \(P_{i}\) were calculated as the quotient of the measured potential \(U_{i}\) and the mean value of the potential of the first 10 cycles \(U_{i,0}\) according to Equation (2):  
\[P_{i}=\frac{U_{i}}{U_{i,0}}, \tag{2}\]  
Figure 7: Setup of notched bar for multiple potential drop (PD) measurement: (**a**) drawing of the specimen; (**b**) position of the potential grips beside the notch; (**c**) position of the potential grips on the circumference. Figure 8a shows the fracture surface of a specimen with an additional laser cut at the position of potential 1. The overload lines are retraced in color on the image of the fracture surface. The run of the three relative potentials P1, P2, and P3 as a function of the crack area related to the sample cross-section is also shown in Figure 8a. The relative potential P1 shows a steeper increase compared to the values of P2 and P3, which show an almost identical increase. This clearly shows that the measured potential depends on the position of the potential probe and thus multiple potential measurements can be used to determine the location of crack initiation. [PERSON] and [PERSON] [23] developed a simple geometric model to locate the crack initiation site based on the three measured potentials. In this model, the relative potentials are treated as vectors that span a plane. In the crack-free sample, all relative potentials are equal and show the value \(P_{i}=1\). This results in a horizontal plane and the normal vector of this plane is parallel to the loading axis. When a single crack is initiated on the specimen circumference, the relative potentials \(P_{i}\) begin to differ and therefore the plane and thus the corresponding normal vector tilts in the direction away from the crack initiation site. The position of the crack in relation to potential probe P1 can be described by the angle \(\phi\) which is the opposite direction of the deflection of the normal vector. The angle \(\phi\) calculated from the potential data for the specimen from Figure 8a is shown in Figure 8b as a function of the cycle number. The scatter of the unfiltered raw data decreases with increasing cycle number and thus crack size. The scatter has already decreased significantly after 10,000 cycles. At this point the crack has propagated up to 1.48% of the total cross-sectional area. After 30,000 cycles with a relative crack area of 5.92%, the standard deviation is below \(5^{\circ}\).