## 2 Crack Length Measurement with the DC-Potential Drop Method
### Investigation of Ferromagnetic Alloys-The Villari Effect  
Another effect influencing potential drop measurements on cyclic loaded ferromagnetic alloys is the Villari effect [37]. This effect, also known as inverse magnetostriction, is based on a change in the magnetic properties when a mechanical load is applied. The mechanical loading induces a current and thus a voltage in the sample [38]. This voltage depends on the rate of stress change d\(\sigma\)/dt and consequently, on the loading frequency and level. The potential changes of a crack free SEN specimen, made of an unalloyed steel (C45E) and loaded mechanically at a frequency of f = 20 Hz with an amplitude of 2 kN and 5 kN, are shown in Figure 4a,b, respectively. For better comparability, the same scaling has been selected in both diagrams. While only slight fluctuations in the potential can be seen at an amplitude of 2 kN, a load with an amplitude of 5 kN results in sinusoidal potential fluctuations with an oscillation range of approximately 4 \(\mu\)V.  
Figure 3: Change of the potential in a particle reinforced 6113 aluminum alloy tested under fully reversed loading conditions (R = \(-\)1) in dry nitrogen [36]. Due to the absence of oxygen, the crack flanks are not isolated and the crack length changes about 3 mm within a cycle. The force and potential curves are out of phase. The maximum and the minimum of the potential curve are located in the region of the greatest steepness of the loading curve, i.e., at the highest stress change rate d\(\sigma\)/dt at the zero crossing of the stress curve. In the case of samples with cracks, the superposition of crack opening effects and the Villari effect results in more complex potential hysteresis loops. A direct comparison of the potential curve of a sample made of ferritic steel C45E and one made of austenitic steel X5 CrNi18-10 with a crack length of about 6 mm each is shown in the Figure 5a. The ferritic steel shows a complex potential curve that is caused by the superposition of the crack opening that occurs synchronously with the load and the phase shifted Villari effect. The potential changes caused by the Villari effect are significantly higher than the effects caused by crack opening and closing. In Figure 5b, the corresponding hysteresis loops are shown. The austenitic steel has the maximum and minimum potential values at the force maximum and minimum, whereas the ferritic steel exhibits a completely deformed hysteresis loop with maximum and minimum values for the potential far away from the maximum and minimum loading. Figure 4: Change of the potential in an unalloyed ferritic steel (C45E) at loading frequencies of 20 Hz: (**a**) at low loading the potential remains nearly constant; (**b**) at higher loadings, a distinct change of the potential due to the Villari effect is visible. The maximum and minimum of the potential appear at the zero-crossing of the force where the change of the force per time is highest. Figure 5: Changes of the potential in a specimen of an austenitic (X5 CrNi18-10) and a ferritic (C45E) steel with cracks of about 6 mm length: (**a**) the austenitic steel shows only a change due to the crack opening and closing, the ferritic steel exhibits two maxima, the higher one is due to the Villari effect; (**b**) corresponding hysteresis loops showing the big potential change due to the Villari effect. In addition to the frequency and the load level, the crack length also influences the magnitude of the potential changes caused by the Villari effect. Figure 6 shows the potential change within a cycle measured on SEN specimens made of C45E and X5 CrNi18-10 tested at a test frequency of 10 Hz under fully reversed cyclic loading with a load amplitude of 4 kN as a function of the crack length. The austenitic steel shows a potential difference that increases slightly with increasing crack length. This is due to the contact of the crack flanks under compression loading, where the contact area increases with the crack length.