## 3 Analysis and Design of Key Components
### High-Temperature and Ultrahigh-Pressure Simulation Test Cabin
#### 3.1.3 Analysis and Calculation of Wall Thickness
Plastic failure refers to the condition that, even though the local stress of the cylinder has exceeded the yield strength of the material and the material has undergone plastic deformation, as long as the cylinder material has not entered the full yield state, the container is not considered to have failed. Only when the whole container wall has completely undergone plastic deformation will the container fail [41; 42]. The material properties of a single-layer integral forged thick-walled cylinder include high strength and good plasticity. When all materials in the cylinder yield, the increase in plastic deformation of the material leads to strain hardening and wall thinning. When the effect of strain hardening is stronger than the effect of wall thinning, the bearing capacity of the cylinder is enhanced. When the two effects are equivalent, the bearing capacity of the cylinder reaches the limit. If the load is increased further, the influence of wall thinning is more significant, which results in a decreased bearing capacity of the cylinder. When a certain pressure is reached, the container bursts, and blasting failure occurs. The materials used in ultrahigh-pressure vessels are generally high-strength materials rather than ideal plastic materials; with increases in the internal pressure of the container, the material gradually yields and then enters the plastic deformation phase. Due to material strain hardening, the container carrying capacity increases until blasting, and the bearing pressure at this time is called the burst pressure. The blasting failure process for container materials is illustrated in Figure 6[39]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Mark** & **Intensity Index** & **Date** \\ \hline
35 CrNi3 MoVR & Yield strength & \(\geq\)857 MPa \\  & Strength of extension & \(\geq\)1060 MPa \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mechanical properties of 35 CrNi3 MoVR at 150 \({}^{\circ}\)C.  
Although there are many methods for calculating the blasting failure criterion for a thick-walled pressure vessel, the Faupel formula is most widely used in practical engineering, and its derivation proceeds is as follows [43; 44; 45; 46]:  
The yield pressure of the vessel in the full yield state is:  
\[p_{s}=\frac{2}{\sqrt{3}}R_{p0.2}\ln(K) \tag{2}\]  
where \(p_{s}\) is the full yield pressure, MPa; \(R_{p0.2}\) is the yield strength of the material at room temperature, MPa; and \(K\) is the ratio of the outside diameter to the inside diameter of the container. Therefore, the bursting pressure can be written as:  
\[p_{b}=\frac{2}{\sqrt{3}}R_{m}\ln(K) \tag{3}\]  
where \(p_{b}\) is the blasting pressure, MPa and \(R_{m}\) is the tensile strength of the material at room temperature, MPa. The formula for the calculation of burst pressure can be modified as follows:  
\[p_{b}=\frac{R_{p0.2}}{R_{m}}(\frac{2}{\sqrt{3}}R_{m}\ln(K))+(1-\frac{R_{p0.2}} {R_{m}})(\frac{2}{\sqrt{3}}R_{p0.2}\ln(K)) \tag{4}\]  
The final burst pressure is:  
\[p_{b}=(2-\frac{R_{p0.2}}{R_{m}})\frac{2}{\sqrt{3}}R_{p0.2}\ln(K) \tag{5}\]  
The wall thickness of the simulation test cabin designed in this paper was calculated with the Faupel formula (Equation (5)). Because the simulation test chamber operates in a high-temperature and ultrahigh-pressure environment, all cylinders are subjected to high temperature and high pressure at the same time. Therefore, when calculating the thickness of the test chamber wall, the thermal load should be converted into a certain pressure and included in the design pressure, which can be converted as shown in Equation (6). \[P_{D}=\phi(\frac{p_{b}}{n_{b}}) \tag{6}\]  
In this formula, \(P_{D}\) is the design pressure; because the design pressure of the cabin body should not be lower than its maximum working pressure, 1.08 times the working pressure should be used as the design pressure. \(\phi\) is the strength reduction coefficient of the material at the design temperature, which is calculated to be 0.9 according to Equation (1).