# Research on the Mechanism and Dynamic Characteristics of Intermitt Failure of Electrical Connectors
## 4 Simulation Case
### Dynamics of Intermittent Failure Under Different Contact Pressures  
The creep and stress relaxation of the electrical connector elastic socket will cause a loss of contact pressure. According to Hertz theory and the G-W model, the decrease in the contact pressure directly leads to decreases in the contact area. The relationship  
Figure 11: Intermittent failure evolution throughout the device life.  
Figure 10: Contact resistance curve under different degradation stages.  
between the total contact area \(A\) and the contact pressure \(F_{N}\) proposed in reference [19] is expressed as  
\[\frac{A}{F_{N}}\approx\left(\frac{r}{\sigma}\right)^{1/2}\frac{3.3}{E^{*}} \tag{16}\]  
where \(E^{*}\) denotes the equivalent Young modulus, \(r\) denotes the deformation of asperities, and \(\sigma\) denotes the relative curvature.  
According to the positive correlation between the total contact area \(A\) and the number of contact spots \(N\), the correlation between contact pressure \(F_{\rm N}\) and conductive spots number \(N_{c}\) can be expressed as.  
\[N_{c}\propto\left(\frac{R}{T}\right)^{1/2}\frac{3.3}{E^{*}}\eta F_{N} \tag{17}\]  
where \(\eta\) is constant and \(R\) denotes the curvature radius of asperities.  
There is a positive correlation between \(F_{\rm N}\) and \(N_{c}\) according to Equation (18). Thus, it is reasonable to simulate the different contact pressure through modulating the number of conductive spots.  
Let \(N_{\rm c}\) be 10 and 1 separately, and the other parameters remain as in Table 1; the simulation results are the contact resistance curves shown in Figure 12a,b.  
It is seen that the duration of intermittent failure under 1 conductive spot is greater than the duration of intermittent failure under 10 conductive spots, and the number of intermittent failures under 1 conductive spot is less than the number of intermittent failures under 10 conductive spots.  
To further analyze the dynamic behaviors of intermittent failure, large amounts of simulations are conducted under the same condition. In the simulations, the number of conductive spots is increased from 1 to 10 with the step length of 1. The average number of intermittent failures \(\overline{N_{l}}\) and the average duration of intermittent failures \(\overline{D}_{I}\) vary with the number of conductive spots, as shown in Figures 13a and 13b, respectively.  
From Figure 13, with an increase in the number of conductive spots, the average number and duration of intermittent failure are generally decreasing. Considering the positive correlation between the number of conductive spots and the contact pressure, it can be concluded that the increase in contact pressure can resist external stress, thereby reducing the probability of intermittent failure. In contrast, with the creep and stress relaxation of the elastic component increasing, the electrical connectors are more likely to suffer intermittent failure. The conclusion that an increase in contact pressure can improve the electrical connector reliability is consistent with the conclusions mentioned in reference [13].  
Figure 12: Contact resistance curves for different numbers of conductive spots.  
By comparing Figures 12 and 13, it can be observed that there is no strong correlation between the number of intermittent faults and Nc. This is because the change in the number of conductive spots leads to changes in both aspects. On the one hand, the increase in the number of conductive spots indicates that the electrical contact performance is good. On the other hand, the increase in the number of conductive spots is also likely to cause fluctuations in contact resistance, especially loading the condition of vibration stress. Therefore, the relationship between the number of conductive spots and the number of intermittent faults still needs further study.