## 3 Experimental and Numerical Simulation Data Analysis
### Numerical Simulation Results
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{\
\begin{tabular}{c} **Thickness of** \\ **Cylindrical Shell** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Explusive** \\ **(gTNT)** \\ \end{tabular} } & \multicolumn{8}{c}{**Deformation under Different Distances (\%)**} \\ \cline{3-10}  & & **0 mm** & **5 mm** & **10 mm** & **15 mm** & **20 mm** & **25 mm** & **30 mm** & **35 mm** & **40 mm** \\ \hline
8 & 16 & 4.0 & 3.8 & 3.2 & 2.2 & 1.7 & 0.8 & 0.2 & & \\
8 & 29 & 13.1 & 12.3 & 10.4 & 7.5 & 5.7 & 3.0 & & & \\
14 & 80 & 4.0 & 3.9 & 3.5 & 3.1 & 2.8 & 2.1 & 1.8 & & \\
14 & 145 & 13.0 & 12.5 & 11.9 & 10.8 & 9.1 & 7.5 & 6.2 & & \\
20 & 223 & 4.1 & 4.0 & 3.9 & 3.7 & 3.3 & 3.0 & 2.8 & 2.5 & \\
20 & 403 & 13.5 & 13.2 & 13.0 & 12.2 & 11.3 & 10.5 & 9.5 & 8.4 & 7.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The numerical simulation of 20# steel. Figure 11: Time\(-\)history diagram of shell failure under 41.6 g TNT. Figure 10: Pressure and time curve of the blast wave. (Units 1, 2, and 3), with positions of 0 mm, 4 mm, and 8 mm. Unit 1 is the inside surface of shell, Unit 2 the middle section, and Unit 3 the outer side of the shell. It obtains the time history law of the radial stress, hoop stress, and axial stress of three points. Figure 12 shows the time history curves of radial stress of three point and experimental fracture. The shell is in the state of compressive stress in radial, hoop, and axial directions at the initial stage of the explosion shock wave loading and unloading (about the time period of 12-25 us), but the compressive stress and response time decrease gradually in the radial, hoop, and axial directions from the inside to the outer surface. The Unit 3 point of the shell changed to a tensile stress state after a short-time hoop compressive stress. There are two reasons for this: One is the high strength and short time of the radial loading of the shell by the blast shock wave, which causes an extremely high hydrostatic stress for a short period of time (2-3 us). The other is the high speed of the radial propagation of the stress wave in the shell, which results in the time of less than 2 us for the stress wave passing through the whole shell, as well as a period of about 90 us for the radial expansion vibration of the shell. Therefore, the one-quarter period of the structure response is much larger than the time of the stress wave passing through the whole shell wall. In the initial stage of radial deformation (about 15-25 us for the blast loading), the radial, hoop, and axial stresses are compressive stress in a certain range near the inside surface, while the shell is in the tensile stress state in a certain range near the outer surface. With the increase of the radial deformation of the shell, the pressure of the explosion shock wave is gradually unloaded, the stress wave inside the shell is gradually reduced, and the axial and hoop stress state of the shell is gradually changed from the compressive stress state to the tensile stress state within a certain range of the inner surface. However, the tensile stress on the outer surface of the shell is greater than that on the inner surface for a considerable period of time (about 100 us). The results show that the internal stress state of the shell is controlled by the high-intensity explosive shock wave load and the radial deformation of the shell. This is a remarkable difference from the normal axisymmetric static stress state. In addition, the axial tensile stress is smaller than the hoop tensile stress in the local radial deformation process of the shell. Figure 13 shows the metallography of 20# shell before experiment. Figure 14 shows the cross-section diagram of recovered fragments of the shell during the solid filling loading of RDX/TNT.