## 4 Conclusions  
In this paper, an effective numerical calculation method was obtained through the model test of the projectile penetrating the liquid tank and the numerical calculation verification with the experimental data. The deformation and failure modes of the projectile after penetration at attack angles, the trajectory and attitude change of the projectile in water were explored, and the load strength on the side walls and the failure modes of the front and rear plates during the penetration of the projectile into the water tank were analyzed. The main conclusions are as follows:  
1. There are four basic failure modes after the projectile penetrating the liquid cabin at attack angles: asymmetric mushrooming at the nose, side erosion, overall plastic bending and fracture. The overall plastic bending and fracture are mainly related to the L/D ratio, initial attack angle and initial projectile velocity; at low velocities, the main failure occurs during the penetration into the front plate; at high velocities, the main failure occurs during the penetration into the water.
2. In the case of the rod projectile with a L/D ratio of 2 and a velocity of 1600 m/s, the projectile was more prone to overall deformation at the attack angles in the range of 15-30\({}^{\circ}\). At low velocities, the overall plastic bending deformation occurred, whereas with the increasing velocity, fracture failure occurred; when the attack angle was above 30\({}^{\circ}\), the failure mode of the projectile was side erosion, but as the initial velocity increased, the range of the attack angle that led to the overall deformation of the projectile also expanded. The larger the L/D ratio, the more easily the projectile undergoes overall plastic bending failure.
3. After the projectile entered the water at an attack angle, the overturning moment was generated due to the uneven force on the projectile, and the projectile was at a state of constant overturning. Due to the change of the position contacting with the water, the projectile overturned many times, and projectile yaw occurred; the yaw direction was mainly affected by the initial attack angle and projectile attitude.  
Figure 20: Plastic hinge line in the rectangular plate.  
* After the water entry of the projectile, the side walls of the water tank were mainly affected by three stages of loading: the initial shock wave pressure loading, the cavitation loading and the cavity collapse loading. As the attack angle increased, the peak load of the initial shock wave pressure on the front plate increased gradually, whereas the initial shock wave pressure load on the rear plate decreased gradually.
* After the penetration of the projectile into the water tank, the failure modes of the front plate were mainly shear plugging, thin film bulging deformation and tearing failure. At certain velocities, with the increasing attack angle, the front plate underwent tearing along the plastic hinge line; under small attack angles, the tear was \"I\" shaped, and under large attack angles, it was \"X\" shaped; the rear plate mainly underwent dishing-bulging deformation; when the rear plate approached the ballistic limit, annular breaches and circumferential cracks were produced.  
Literature review, K.W. and Y.L.; writing--original draft preparation, K.W., H.H. and D.L.; writing--review and editing, K.W., D.L. and H.H.; experiment performance, Y.L. and K.W.; experiment analysis, K.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China, grant numbers 51979277, 52271338, 52101378.  
Not applicable.  
The authors would like to thank the editor, associate editor, and the anonymous reviewers for their helpful comments and suggestions that have improved this paper.  
The authors declare no conflict of interest.