Study on the Composite Structure of Aluminum Foam-Filled Thin-Walled Metal Tube to Reduce the Charge Overload inside the Projectile during the Penetration Process

When a projectile penetrates a target at high speed, the charge loaded inside the projectile usually bears a high overload, which will consequently severely affect its performance. In order to reduce the overload of the charge during the penetration process, the structure of the projectile was improved by adding two buffers at both ends of the charge. In this study, the mathematical expressions were first gained about the axial buffering force generated by the thin-walled metal tube, aluminum foam, and the composite structure of aluminum foam-filled thin-walled metal tube when they were impacted by the high-speed mass block through reasonable assumptions and stress analysis. During the experiment on the high-speed projectile penetrating reinforced concrete target, the acceleration curve of the charge and the projectile body were obtained. (e results show that the maximum overload that the charge was subjected to during the launch and penetration process was significantly reduced, and the change in overload, which the charge was subjected to during the penetration process, was also less obvious.


Introduction
Earth penetrating weapon (EPW) is used to strike deep underground targets. e process of destroying the target can be divided into two steps: first of all, EPW breaks through the protective layer of the target, when the EPW must have a high speed to make sure that it can get into the target; then, the EPW detonates the charge with the action of fuse to destroy the target. e charge suffers a very high shock overload when the EPW penetrates the protective layer at a high speed. ere are studies showing that the charge column deformed with cracks while suffering the high overload, which seriously affected its performance. Muthig and Arnold [1] shot the concrete target vertically with the cannon, recovered the ks22a charge inside it, observed its morphological change, and tested its performance.
e results show that the charge was broken and the sensitivity of the explosive was obviously reduced. e thin-walled metal tube and aluminum foam could absorb energy of the impact and collision through the elastic-plastic deformation and have the advantages of having the simple structure and stable operation [2][3][4]. e composite structure of aluminum foam-filled metal thinwalled tube can not only make up for the defect of instability and collapse of aluminum foam when used alone but also solve the problem of poor nonaxial load-bearing capacity of metal thin-walled tube under the impact. is composite structure has huge application potential in aerospace, rail transit, and other fields [5,6] for its independent carrying capacity, strong stability, high energy absorption efficiency, and working in extreme environments. e main content of this research is how to apply the advantages of foam aluminum and thin-walled metal tubes in the field of energy absorption to EPW to reduce the impact load of the charge during the penetration process. e methodology applied in this research is theoretical analysis and experimental verification: first of all, a theoretical analysis was conducted on the stress conditions of thin-walled metal tube, aluminum foam, and composite structure when they were impacted by high-speed mass block and expressions of the axial buffering force were presented in Section 2; then, we designed the thin-walled metal tube buffer and the composite-structured buffer, which were added to the ends of the charge. Finally, an experiment was conducted on the EPW penetration into reinforced concrete to verify the effectiveness of buffers for reducing the overload of the charge.

Buffering Force of in-Walled
Metal Tube under High-Speed Axial Impact. Subject in this section is shown in Figure 1. e high-speed impact mentioned in this section refers to the impact of the mass block speed ranging from 400 m/s to 800 m/s. e formula of tube buffering force is deduced by using the principal stress method. Steel was selected as the material of the metal tube; von Mises yield condition as the yield condition of the metal tube and Cowper-Symonds constitutive model as the constitutive model of the metal tube.
In order to obtain the formula of the buffering force, we made the following assumptions: the deformation of the mass block is ignored; (1) e stress of the metal tube along the direction of wall thickness is evenly distributed when the mass block hits the metal tube (2) Ignore the elastic deformation of the metal tube (3) e friction coefficient between the metal tube and the mass block does not change in the whole process e stress condition of the tube is shown in Figure 2(a) and the stress state at arbitrary radius (r) is shown in Figure 2(b). e force balance equation perpendicular to the tube wall: (1) e kinematic balance equation: Time: Get the acceleration: Substituting equation (4) into equation (1), we obtained equation (5) as follows: e force balance equation parallel to the tube wall: Substituting dl � dr/sinα into equation (6), ignore the infinitely small: Ignore the change of thickness, dt/dr � 0: Substituting equation (5) into equation (8), Mises yield criterion: According to Cowper-Symonds' description of the yield strength of materials [7,8] under dynamic loading, the relationship between the yield strength and strain rate of the material can be expressed by Combining equations (10)-(12), Substituting equation (13) into equation (9), 2 Shock and Vibration Integrating both sides of equation (15), we obtain Boundary condition: Substituting equation (17) into equation (16), Substituting equation (19) into equation (16), Axial stress (r � R 1 ): (23) e buffering force: (24) It can be seen from equation (24) that the size of the buffer force generated by the thin-walled metal tube is related to the parameters R 1 , R 2 , t, f, and α, which can be changed according to the actual needs to achieve the desired buffer effect.

Buffering Force of Composite
Structure under the High-Speed Axial Impact. Due to the complexity, inhomogeneity, and uncertainty of aluminum foam, it is difficult to use mathematical models to express the stress changes of aluminum foam during the compression process. e empirical formula is usually gained based on a large number of experiment date for fitting. e failure of the open-cell aluminum foam under the high-speed impact is caused by plastic collapse, whose stress is determined by the yield stress of matrix material. e stress of plastic collapse can be expressed as follows: where C: constant, measured by test; ρ * : density of aluminum foam; ρ s : density of matrix material; and σ ls : yield stress of matrix material. e buffering force of cylindrical aluminum foam (F 1 ) when it is in the platform stage under the high-speed impact can be expressed as Shock and Vibration e composite structure of the thin-walled metal tube and aluminum foam could buffer the impact body through radial expansion of the metal tube and plastic deformation of the aluminum foam. It consists of three parts: frustum, thinwalled metal tube, and aluminum foam, with its structure shown in Figure 3. When the mass block impacts the frustum, the metal tube will generate elastic-plastic deformation in the radial direction, forming the axial buffer force. At the same time, the aluminum foam also absorbs part of the energy from impact when compressed, resulting in an axial cushioning force. So, the composite structure can contribute to forming a greater buffering force on the mass block.
Assuming that there is no interaction between the metal tube and the aluminum foam at the axial direction, the buffering force of the composite structure (F) can be expressed as follows:

Structural Parameters of the Projectile.
According to the theoretical analysis and the structure of the 125 mm EPW charge, we designed a thin-walled metal tube buffer filled with aluminum foam that was installed at the front end of the charge and a thin-walled metal tube buffer that was installed at the back end of the charge. Two buffers were installed into the 125 mm EPW, as shown in Figures 4 and 5, followed by the fired EPW with artillery. e acceleration date collected by the acceleration sensor 1# was treated as the overload of the charge during the test, and the acceleration date collected by the acceleration sensor 2# was treated as the overload of the projectile body during the test. By comparing the acceleration collected by the two sensors, we can verify whether the buffer can effectively reduce the overload of the charge. e target is made of reinforced concrete. Its length, width, and height are 2.5 m, 2.5 m, and 1.5 m, respectively.   Its compressive strength is 35 MPa. e diameter of reinforcement steel in reinforced concrete is 10 mm, and the reinforcement steel ratio was 1%. All parts were processed and assembled according to the designed drawings with the assembly drawing shown in Figure 6 (the total mass of the projectile was 27.2 kg).
Buffer No. 1 consisted of the thin-walled metal tube, aluminum foam, and frustum, as shown in Figures 7 and 8. Its structural parameters are listed in Table 1. Buffer No. 2 consisted of the thin-walled metal tube and frustum, as shown in Figures 9 and 10. Its structural parameters are listed in Table 2.
At the end of the experiment, we designed a device made of concrete to recover the launched projectile so that the data can be collected by the sensors. e installation of the experiment device in the shooting range is shown in Figure 11. e artillery muzzle was 100 meters away from the target. e board was placed behind the target with a thickness of 22 mm and a total of 11 layers. e recovery device was placed behind and on both sides of the board.

Experimental Procedures.
e experimental process is as follows: (1) Measure the quality of each part of the projectile.

Experimental
Results. e velocity of the projectile was 832 m/s when it hit the target. e projectile penetrated into the reinforced concrete target plate, then 11 layers of wood target, and finally into the recovery device with a depth of 0.5 m. e recovered projectile and the penetrated reinforced concrete target are shown in Figure 13.
Two buffers were taken out of the recovered projectile and their structural parameters were measured, as shown in Figure 14.
e expanding length of the thin-walled metal tube in buffer No. 1 was 13.785 mm. e thickness of the compressed aluminum foam in buffer No. 1 was 6.215 mm (before the penetration process: 18 mm), the diameter was 56 mm (before the penetration process: 51.2 mm), and the volume compression 62.8%. e expanding length of the thin-walled metal tube in buffer No. 2 was 1.21 mm. Figures 15(a) and 15(d) show the original and filtered waveforms collected by the acceleration sensor 1# and acceleration sensor 2# during the launching    Shock and Vibration process. From the filtered waveforms, it can be seen that the peak value of the main wave in the waveform chart collected by the sensor 1# was 11140 g and the pulse width was 12.45 ms; the peak value of the main wave in the waveform chart collected by the sensor 2# was 13770 g and the pulse width was 12.68 ms, which means that the maximum overload received by the charge during the launch process was reduced by 19.1% after the buffers were installed in the projectile. e trends of the waveforms collected by sensor 1# and sensor 2# were basically the same. As the propellant burns, the chamber pressure increased rapidly, reaching a peak in 0.015 seconds, and so did the projectile acceleration value. As the projectile moved forward, the chamber pressure as well as the projectile acceleration value decreased.  When the projectile exited the artillery muzzle, a large amount of gunpowder gas leaked, and the thrust acting at the bottom of the projectile rapidly decreased. erefore, the acceleration value also quickly dropped to zero. Due to the sudden unloading of the gunpowder gas and the opening of the tail, the combined tensile stress and air resistance led to the negative acceleration value. Figures 16(a) and 16(d) show the original and filtered waveforms collected by the acceleration sensor 1# and acceleration sensor 2# during the penetration process. From the filtered waveforms, it can be seen that the peak value of the main wave in the waveform chart collected by the sensor 1# was 40380 g and the pulse width was 4.62 ms; the peak value of the main wave in the waveform chart collected by the sensor 2# was 69010 g and the pulse width was 0.77 ms, which showed that the maximum overload received by the charge during the penetration process was reduced by 41.5% after the buffers were installed in the projectile.

Penetration Process.
It could be seen from Figure 16 that the overload of the sensor 1# during the penetration process changed more smoothly, while the overload of the sensor 2# during the in-walled metal tube Frustum Figure 9: Structure of the buffer No. 2. Shock and Vibration 7 penetration process changed more drastically. A comparison of Figures 15 and 16 can show that the projectile and its charge were subjected to a larger overload during the penetration process than during the launching process. Based on the test results, we could conclude that (1) at the end of the experiment, buffer No. 1 produced a large amount of plastic deformation, while buffer No. 2 produced only a small amount of plastic deformation, which indicates that buffer 1 plays the major role in buffering and energy absorption; (2) after two buffers were installed at both ends of the charge, the maximum overload that the charge was subjected to during the launch and penetration process was significantly reduced, and the change in overload was also more gentle. e above test results show that the buffer with the composite structure can effectively reduce the impact load of the 125 mm EPW charge during the penetration process.
rough reasonable structural design, the composite structure of foamed aluminum-filled thin-walled metal tube can be applied to the protection of high-speed projectile charges.
In the published research results, there is no research on applying this composite structure of aluminum foam-filled metal thin-walled tube for the protection of projectile charges. At present, the relevant research mainly covers the following two areas: one is the study on the low-and medium-speed impact represented by the drop-weight impact method; the second is the High-speed impact research  e impact velocity of the composite structure in these two test methods did not reach the penetration velocity of the projectile (above 800 m/s). For the protection of high-speed projectile charges, a buffer device made of nylon or rubber are often installed at the front end of the charge. Shock and Vibration

Conclusion
In terms of theoretical and practical aspects, the main conclusions of this work can be summarized as follows: (1) A theoretical analysis was made on the dynamic response of the thin-walled metal tube and composite structure of aluminum foam-filled thin-walled metal tube under the impact of high-speed mass block was theoretically analyzed, together with some assumptions put forward. Based on these assumptions, we derived the expression of the buffer force of the thin-walled metal tube (F d ) and the composite structure aluminum foam and thin-walled metal tube (F) through the formula derivation. (2) According to the results of theoretical analysis and combining the structure of the 125 mm EPW, a design was conducted on a buffer with a composite structure of foamed aluminum-filled thin-walled metal tubes with specific dimensions. It was then installed at the front end of the charge. e penetrating concrete test was carried out with the projectile equipped with the buffer. e test results show that the overload on the charge was significantly reduced after the buffer was installed. It is obvious that this composite structure can be applied to the protection of high-speed penetration projectile charges.

Data Availability
e data used to support the findings of this study are included within the article.

Conflicts of Interest
e authors declared that they have no conflicts of interest regarding the publication of this work.  Shock and Vibration