## 4 Dynamic Testing
### Light Oxidation
#### 4.2.1 Light Oxidation: Statistical Mapping of the _U-I_ Characteristics  
For each of these zones, we have drawn up statistical representations of the current-voltage characteristics, as shown in Figures 12-14 under different test conditions.  
Overall, the results show high resistance characteristics. Maximum voltages reach 5 V (or even more).  
In all these statistical representations, we note a predominant main characteristic, marked in red, which shows a linear behavior. All around, other less frequent characteristics can be observed. They are non-linear, dispersed, and highly resistant. Characteristic dispersion and maximum voltage values increase with oxide thickness.  
These maps also allow us to conclude the following:  
* The majority of the dominant voltage-current characteristics (in red) observed are linear, which confirms the results of previous studies conducted by SNCF and GeePs [18,19]. These studies showed that the characteristics \(U_{\epsilon}=f(I)\) remain linear as long as the current does not exceed 1 A.
* The effect of current is noticeable: (i) This trend is reflected in a decrease in the maximum voltages reached as the current increases.  
Figure 11: Statistical analysis of contact resistances \(R(t)\) obtained for the two ‘clean’ rails as a function of current intensity, showing median values of contact resistances (\(\bullet\)) and their IQR intervals (I).  
* Increasing current also tends to reduce the dispersion of characteristics.
* However, the effects of force and speed are less obvious to evidence from these data.  
Figure 12: Statistical maps of current–voltage characteristics obtained on zone L1, with an average oxide thickness of 4 \(\upmu\)m, for different current intensities (20 mA, 50 mA, and 100 mA, at \(f\) = 2300 Hz), forces (200 N and 400 N), and speeds (10 cm/s and 25 cm/s).  
Figure 13: Statistical maps of current–voltage characteristics obtained on zone L2, with average oxide thickness 12.1 \(\upmu\)m for different current intensities (20 mA, 50 mA, and 100 mA, at \(f=2300\) Hz), forces (200 N and 400 N), and speeds (10 cm/s and 25 cm/s).  
Anomalies can be observed in certain maps. An example is shown in Figure 15 (upper part, red box). This map corresponds to measurements obtained in zone L3 with a current intensity of 20 mA at a force of 200 N and a speed of 10 cm/s. It shows the  
Figure 14: Statistical maps of current–voltage characteristics obtained on the L3 zone, with an average oxide thickness of 8.6 \(\mu\)m, for different current intensities (20 mA, 50 mA, and 100 mA, at\(f\) = 2300 Hz), forces (200 N and 400 N), and speeds (10 cm/s and 25 cm/s).  
presence of certain pairs of points (\(U,I\)) in quadrants 2 and 4. This means that there are situations where the current \(I\) is positive while the voltage \(U\) is negative, or vice versa. These singularities could be explained either by the presence of noise in the signal, as shown by the chronograms presented in the lower part of Figure 15 (circled in red), or by the existence of a significant phase shift between \(I\) and \(U\). Such anomalies remain relatively infrequent in relation to the total number of periods considered.