## 6 Airtightness Sealing Performance and Failure Analysis
### Contact Pressure Distribution  
The contact pressure \(p\) distribution on the gasket-gasket contact surface was only discussed since FEM results show that the air-leakage path in this study occurred mostly on the gasket-gasket contact surface. Figure 10 shows the distribution of the initial contact pressure \(p_{0}\) along the gasket-gasket contact surface with different joint gaps (i.e., 9.873 mm, 9.647 mm, 9.423 mm, 9.205 mm, and 8.985 mm, corresponding to an initial maximum contact pressure \(p_{inmax}\) of 20.0, 40.0, 60.0, 80.0, and 100.0 kPa, respectively). Figure 10 indicates that \(p\) is symmetrically distributed in a \"W\" shape along the gasket centerline, and the contact pressure at both ends of the contact surface is significantly higher than that in other locations due to the presence of the inner holes in the gasket and the grooves between the gasket legs. The findings indicate that the contact surfaces at the ends of the gasket have the strongest sealing capacity due to stress concentration, and the contact stress in the ends determines the sealing capacity of the gasket-in-groove. Nevertheless, it is worth noting that the initial contact pressure has an increasing trend with a decreasing joint gap, which implies that the magnitude of initial contact pressure for the same gasket depends mainly on its compression.  
Figure 11 shows the contact pressure \(p\) distribution on the gasket-gasket contact surface with different vacuum pressure \(p_{v}\) (only one case with a \(p_{inmax}\) of 100.0 kPa is  
Figure 10: Initial contact pressure distribution along the gasket–gasket contact surface with different joint gaps. (S represents the distance from the symmetry axis of the gasket, negative values represent one side close to vacuum pressure, and positive values represent one side far from vacuum pressure).  
Figure 9: Air-leakage path.  
described since other cases have similar trends). It is observed that \(p_{v}\) has a significant effect on \(p\) distribution, and the specific details are as follows:  
1. As \(p_{v}\) increases to 17.7 kPa, \(p\) distribution is still approximately in a \"W\" shape, but the variations are slight except for a remarkable decrease in the peak contact pressure on the outside (i.e., the region in the range of \(S=-\)7.0-0 mm) and a significant increase in the peak contact pressure on the inside (i.e., the region in the range of \(S=0\)-7.0 mm);
2. As \(p_{v}\) increases to 41.5 kPa, \(p\) distribution is no longer in a \"W\" shape, and the peak contact pressure on the outside decreases rapidly. However, it is still higher than \(p_{v}\). Noted that \(p\) in some areas of the outside (i.e., the region in the range of \(S=-\)5.5-0 mm) shows a significant increasing trend, while \(p\) on the inside changes little;
3. As \(p_{v}\) increases to 60.2 kPa, the peak contact pressure on the outside drops below \(p_{v}\), but \(p\) in this range of \(S=-\)5.5-0 mm increases further. Note that \(p\) on the outside end decreases to 0, indicating that the sealing in this region begins to fail and the contact surface starts to be separate. However, it is found that the contact pressure variation on the inside remains relatively slight;
4. As the \(p_{v}\) increases to 79.8 followed by 101.0 kPa, the contact surface separation gradually expands toward the inside, and accordingly, the contact length rapidly decreases and eventually reduces to 0, which means that the sealing fails and air leakage occurs.  
The above analysis reveals that gasket sealing failure is a gradually developing process rather than a transient process from a macroscopical view. More specifically, the air-leakage failure is a gradual separation process of the contact surfaces until vacuum pressure exceeds the contact pressure at each location of the contact surface.