## 6 Airtightness Sealing Performance and Failure Analysis
### Sealing Failure Process  
For one point on the contact surface, the contact pressure p during evacuation consists of the initial contact pressure \(p_{0}\) and the additional contact pressure \(p_{a}\) induced by the vacuum pressure \(p_{v}\):  
\[p=p_{0}+p_{a}=p_{0}+\
u p_{v}/(1+\
u) \tag{5}\]  
where \(\
u\) is the gasket [PERSON]'s ratio. As mentioned before, theoretically, the sealing fails once the contact pressure is lower than the vacuum pressure:  
\[p\leq p_{v} \tag{6}\]  
However, whether the gasket is in the initial state of pre-compression or the squeezed state of evacuation, there are differences in contact pressure at each point on the contact surface. Therefore, it is more reasonable to explain the seal failure on the contact surface using Equation (7).  
\[p_{max}\leq p_{v} \tag{7}\]  
where \(p_{max}\) is the maximum contact pressure on the contact surface.  
To illustrate the sealing failure process of the gasket-in-groove, Figure 13 plots the \(p_{max}\) path at the gasket-gasket contact surface with different \(p_{imax}\). Overall, the path may  
Figure 12: Relationship of initial maximum contact pressure versus separation pressure and failure pressure.  
be divided into two phases. (i) Path OA\({}_{1}\) (OA\({}_{2}\), OA\({}_{3}\), OA\({}_{4}\), OA\({}_{5}\)) represents the gasket pre-compression phase before vacuum pressure loading, and \(p_{max}\) mainly depends on the gasket compression. (ii) Path A\({}_{1}\)D\({}_{1}\) (A\({}_{2}\)D\({}_{2}\), A\({}_{3}\)D\({}_{3}\), A\({}_{4}\)D\({}_{4}\), A\({}_{5}\)D\({}_{5}\)) represents the vacuum pressure loading phase, in which \(p_{max}\) is determined by a combination of the vacuum pressure and the initial contact pressure. In this stage, as the vacuum pressure increases, \(p_{max}\) on the contact surface shows a tendency to first increase sharply (sub-stage 1), then decrease slowly (sub-stage 2), and then decrease dramatically (sub-stage 3). For sub-stage 1 (A\({}_{1}\)B\({}_{1}\), A\({}_{2}\)B\({}_{2}\), A\({}_{3}\)B\({}_{3}\), A\({}_{4}\)B\({}_{4}\), A\({}_{5}\)B\({}_{5}\)), the lateral squeezing of the gasket by the vacuum pressure results in a rapid increase in \(p_{max}\) near the inside contact surface with increasing vacuum pressure and exceeds \(p_{max}\). For sub-stage 2 (B\({}_{1}\)C\({}_{1}\), B\({}_{2}\)C\({}_{2}\), B\({}_{3}\)C\({}_{3}\), B\({}_{4}\)C\({}_{4}\), B\({}_{5}\)C\({}_{5}\)), as the vacuum pressure increases further, \(p_{max}\) near the outside end of the contact surface falls slowly, while \(p_{max}\) near the inside end of the contact surface rarely varies. Overall, \(p_{max}\) exhibits a slow descending at the contact surface. Additionally, in this stage, it is observed that the outside contact surface begins to separate and expand inside gradually; i.e., the contact length of the contact surface gradually decreases. For sub-stage 3 (C\({}_{1}\)D\({}_{1}\), C\({}_{2}\)D\({}_{2}\), C\({}_{3}\)D\({}_{3}\), C\({}_{4}\)D\({}_{4}\), C\({}_{5}\)D\({}_{5}\)), the contact surface separation extends near its inside, and the increase in vacuum pressure results in a sharp decrease in \(p_{max}\) in this area. When \(p_{max}=0\), the gasket sealing fails.  
The above analysis reveals that the sealing failure of the gasket-in-groove may also be considered a gradual variation process in \(p_{max}\) along the contact surface. Before the evacuation, the gasket is compressed by various external forces, which causes the initial contact pressure on the contact surface generated by the gasket rebound force. During the evacuation, the gasket deformation induced by vacuum pressure causes a redistribution of contact pressure on the contact surface, and \(p_{max}\) also changes accordingly; i.e., it shows a trend of increasing, then slowly decreasing, and then sharply decreasing. When \(p_{max}=0\), the sealing fails and air leakage occurs.