## 3 Crack Detection and Crack Localization with Multiple PD Measurements
### Crack Detection in Single Edge Notched Specimens  
The investigations were carried out on SEN-specimens with a size of \(80\times 12\times 2.8\) mm made of aluminum alloy 7475 T761. The potential grips were spot-welded in a distance of 1.5 mm from the notch root. As shown in Figure 10a, potential probes were attached to the front (\(U_{F}\)), the rear (\(U_{B}\)), and the narrow (\(U_{N}\)) side of the sample. Figure 10b shows an optical micrograph of the spot-welded wires beneath the notch. Figure 10: Single edge notched (SEN)-specimen: **(a)** position of the potential grips on the specimen. The notch is located on the right side, the arrow characterizes the crack propagation direction (CPD); **(b)** micrograph of the laser-welded wires on the specimen surface. Figure 9: Data of an experiment without prior temperature stabilization: **(a)** run of the three relative potentials and the crack surface with marked crack extensions; **(b)** calculated angle \(\phi\) showing a crack initiation after about 110,000 cycles. The crack was initiated at an angle \(\phi\) of 103\({}^{\circ}\), the green square at N = 115,000 corresponds to a cracked area of 1.27%, the blue square at N = 130,000 to 4.8%. The specimens were cyclically loaded with a stress amplitude of 70 MPa and a frequency of 20 Hz under fully reversed loading conditions in a testing machine with parallel clamps. At intervals of 15,000 load cycles, overloads with an amplitude of 175 MPa were applied to mark the actual crack geometry on the fracture surface. The machine control and data acquisition were undertaken by a control electronics of the type Doli EDC 580 V.  
The measured potentials \(U_{F}\), \(U_{B}\), and \(U_{N}\) were normalized according to Equation (2) to the mean value of the first 10 cycles \(U_{F,0}\), \(U_{B,0}\), and \(U_{N,0}\), respectively. From the relative potentials \(\mathrm{P_{F}}\), \(\mathrm{P_{B}}\), and \(\mathrm{P_{N}}\) determined in this way, the quotients \(Q_{Front}\) and \(Q_{Back}\) were calculated according to Equation (3):  
\[Q_{Front}=\frac{U_{F}}{U_{N}},\text{ and }Q_{Back}=\frac{U_{B}}{U_{N}}, \tag{3}\]  
For an uncracked specimen at the beginning of the experiment, both quotients exhibit the value \(Q_{Front}=Q_{Back}=1\). When a crack is initiated, a change of the potential quotients depending on the crack initiation site takes place. In Figure 11, the possible changes of the potential quotients for three idealized crack initiation scenarios are sketched:  
* Figure 11a: When a crack is initiated near the frontside (backside) \(Q_{Front}\) (\(Q_{Back}\)) increases while \(Q_{Back}\) (\(Q_{Front}\)) decreases or remains constant. * Figure 11b: When a crack is initiated in the center of the notch root a decrease of both potential quotients takes place. * Figure 11c: When cracks are initiated on the front and backside at the same time, both quotients are rising. The formation of subsequent cracks can also be described based on the change of the potential quotients described above. In the following, this described criteria shall be applied on real experimental data. Figure 12a shows the fracture surface and the corresponding run of the potential quotients \(Q_{Front}\) and \(Q_{Back}\) of a sample with a crack initiated near the backside. The yellow lines show the crack fronts marked with overloads in an interval of 15,000 cycles. The marks of the first overload show a crack with a length of about 0.9 mm and a depth of 0.25 mm. The formation of the crack is shown by an increase of the potential quotient \(Q_{Back}\) and a decrease of the quotient \(Q_{Front}\). With further crack propagation the crack front becomes more and more straight and parallel to the notch and consequently the potential ratios are increasingly converging. Figure 11: Run of the potential quotients \(Q_{Front}\) and \(Q_{Back}\) for different crack initiation sites: (**a**) single crack on the front side; (**b**) single crack in the middle of the notch root; (**c**) two cracks on the front and the backside.