To study the influence of different liner structures and materials (copper, steel, and tungsten) on the forming characteristics of multiple explosively formed projectile (MEFP) with integrated liner and shell designs, three types of liners with different structures were designed. LS-DYNA was used for numerical simulation, and the results show that the thickness change at the center of the liner has no obvious influence on the shape of the explosively formed projectile (EFP). However, the curvature radius of the liner has a significant influence on the shape of the EFP. When the liner material is copper and the curvature radius of the liner is greater than 8 mm, the EFP shape approximates an ellipsoidal or hemispherical shape and the EFP forming speed is between 1900 m/s and 2400 m/s. When the material of the liner is steel or tungsten and the curvature radius of the liner is thicker than 8 mm, the liner is not able to form projectiles in the shape of a sphere, ellipsoid, or long rod. By comparing the forming speed from 1#EFP to 4#EFP, it can be said that MEFP with integrated liner and shell design displays a certain pressurization effect. Research results show that, for small-caliber MEFP warheads, subject to the size of the warhead, when the liner is steel or tungsten, the detonation energy generated by the limited charge does not result in the liner forming an effective EFP. However, when the liner material is selected as copper, the EFP forming shape and speed are more appropriate.
During the Spanish Civil War from 1936 to 1939, the High-Explosive Antitank (HEAT) with a shaped charge effect began to be used. As a type of shaped charge projectile, explosively formed projectiles (EFP) began to appear in the 1970s. Multiple explosively formed projectile (MEFP) began to appear in the 1980s to improve the hit rate and damage probability of the projectile [
The research on the forming performance of the MEFP, according to the flying direction of the formed projectile, can be divided into two categories. In the first category, the liner is along the axial direction of the charge arrangement, and the formed projectile is scattered along the axial direction [
In the numerical simulation, firstly, the structured mesh of the designed circumferential MEFP warhead was generated using the ANSYS/ICEM (Integrated Computer Engineering and Manufacturing) meshing tool, and then the unstructured mesh generated by ANSYS/ICEM was generated and imported into HyperMesh for LS-DYNA preprocessing. Finally, it was submitted to the LS-DYNA solver for calculation.
To investigate the forming performance of the circumferential MEFP integrated design of the small-caliber shell and liner, the structural parameters of the three different types of MEFP warheads designed are listed in Table
MEFP warhead structure parameters of three different structure types.
Parameters | Liner center thickness | Inner wall curvature radius of liner ( | Outer wall curvature radius of liner ( |
---|---|---|---|
Charge height: 52 mm, charge diameter: 37.6 mm, shell thickness: 1.2 mm ( | 1.1 | 8 | 8 |
9 | 9 | ||
10 | 10 | ||
11 | 11 | ||
1.2 | 8 | 8 | |
9 | 9 | ||
10 | 10 | ||
11 | 11 | ||
1.3 | 8 | 8 | |
9 | 9 | ||
10 | 10 | ||
11 | 11 |
The three-dimensional (3D) model designed by the structural parameters of the MEFP warhead is shown in Table
Three-dimensional structure of MEFP warhead.
In the structure (Figure
At present, there are many commonly used finite element meshing software, such as HyperMesh, Finite Element Model Builder (FEMB), True Grid, and ANSYS/ICEM. In this study, first, ICEM was used for finite element structured mesh division, then the divided mesh file was imported into HyperMesh for preprocessing of finite element analysis, and finally, the numerical calculation was carried out using LS-DYNA. To reduce the amount of calculation in the numerical simulation, according to the symmetry of the MEFP warhead structure, a quarter finite element model was established, as shown in Figure
Finite element model.
The material model of the shell, explosive, and air is the same as that in Section
Materials parameters of liner.
Material | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Copper | 8.93 | 46.5 | 90 | 292 | 0.31 | 0.025 | 1.09 | 1356 | 293 | 2.02 | 0.39 | 1.49 |
Steel | 7.8 | 79 | 813 | 601 | 0.28 | 0.014 | 1.04 | 1723 | 293 | 1.67 | 0.46 | 1.33 |
Tungsten | 17.7 | 160 | 631 | 1258 | 0.092 | 0.014 | 0.94 | 1723 | 293 | 1.54 | 0.4 | 1.24 |
Single-point detonation was adopted in the numerical simulation, and the position of the detonation point is shown in Figure
Forming results: (a) The thickness of liner is less than the shell thickness. (b) Equal thickness of shell and liner. (c) The thickness of shell is less than the liner thickness.
Figure
The forming speed is shown in Table
Forming speed when the material of the liner and shell is copper.
EFP no. | |||||
---|---|---|---|---|---|
1#EFP | 2097 m/s | 2085 m/s | 2072 m/s | 2135 m/s | |
2#EFP | 2205 m/s | 2151 m/s | 2134 m/s | 2186 m/s | |
3#EFP | 2358 m/s | 2264 m/s | 2184 m/s | 2189 m/s | |
4#EFP | 2273 m/s | 2176 m/s | 2138 m/s | 2177 m/s | |
1#EFP | 2077 m/s | 2051 m/s | 2042 m/s | 2085 m/s | |
2#EFP | 2197 m/s | 2140 m/s | 2131 m/s | 2141 m/s | |
3#EFP | 2334 m/s | 2230 m/s | 2164 m/s | 2175 m/s | |
4#EFP | 2257 m/s | 2145 m/s | 2130 m/s | 2131 m/s | |
1#EFP | 2067 m/s | 2005 m/s | 1997 m/s | 2034 m/s | |
2#EFP | 2165 m/s | 2126 m/s | 2115 m/s | 2097 m/s | |
3#EFP | 2329 m/s | 2192 m/s | 2136 m/s | 2121 m/s | |
4#EFP | 2241 m/s | 2139 m/s | 2090 m/s | 2082 m/s |
From Table
Comparison of forming speed of different structure types: (a) comparison of forming speed of 1#EFP; (b) comparison of forming speed of 2#EFP; (c) comparison of forming speed of 3#EFP; (d) comparison of forming speed of 4#EFP.
As shown in Figure
From Table
Comparison of forming speed of different structure types: (a) comparison of forming speed of
As shown in Figure
When the shell thickness of the integral MEFP warhead remains unchanged and the curvature radius of the liner remains unchanged, only the thickness at the center changes for three different types of MEFP warheads. Therefore, the influence of thickness change at the center on the change of forming speed can be obtained from the forming speed list shown in Table
Comparison of forming speed of different thickness of liner center: (a) comparison of forming speed of 1#EFP; (b) comparison of forming speed of 2#EFP; (c) comparison of forming speed of 3#EFP; (d) comparison of forming speed of 4#EFP.
As shown in Figure
The material in the finite element model of the MEFP warhead established in the third part was chosen as steel, and the remaining boundary conditions of the numerical simulation were set to be the same as for Section
Formed results: (a) the thickness of the liner is less than the shell thickness; (b) equal thickness of shell and line; (c) the thickness of shell is less than the liner thickness.
In Figure
The forming speed is shown in Table
Forming speed when the material of the liner and shell is steel.
EFP no. | |||||
---|---|---|---|---|---|
1#EFP | 2327 m/s | 2352 m/s | 2362 m/s | 2374 m/s | |
2#EFP | 2409 m/s | 2454 m/s | 2484 m/s | 2506 m/s | |
3#EFP | 2375 m/s | 2455 m/s | 2496 m/s | 2521 m/s | |
4#EFP | 2315 m/s | 2393 m/s | 2432 m/s | 2455 m/s | |
1#EFP | 2283 m/s | 2309 m/s | 2333 m/s | 2341 m/s | |
2#EFP | 2391 m/s | 2422 m/s | 2451 m/s | 2475 m/s | |
3#EFP | 2365 m/s | 2421 m/s | 2466 m/s | 2494 m/s | |
4#EFP | 2301 m/s | 2362 m/s | 2407 m/s | 2428 m/s | |
1#EFP | 2255 m/s | 2270 m/s | 2294 m/s | 2308 m/s | |
2#EFP | 2334 m/s | 2383 m/s | 2418 m/s | 2442 m/s | |
3#EFP | 2320 m/s | 2389 m/s | 2434 m/s | 2461 m/s | |
4#EFP | 2267 m/s | 2337 m/s | 2376 m/s | 2399 m/s |
From Table
Comparison of forming speed of different structure types: (a) comparison of forming speed of 1#EFP; (b) comparison of forming speed of 2#EFP; (c) comparison of forming speed of 3#EFP; (d) comparison of forming speed of 4#EFP.
In Figure
From Table
Comparison of forming speed of different structure types: (a) comparison of forming speed of
In Figure
When the shell thickness of the integral MEFP warhead remains unchanged and the liner curvature radius remains unchanged, only the thickness at the center changes for three different types of MEFP warheads. Therefore, the influence of thickness change at the center on the change of forming speed can be obtained from the forming speed list shown in Table
Comparison of forming speed of different thickness of liner center: (a) comparison of forming speed of 1#EFP; (b) comparison of forming speed of 2#EFP; (c) comparison of forming speed of 3#EFP; (d) comparison of forming speed of 4#EFP.
As shown in Figure
The material in the finite element model of the MEFP warhead established in the third part was chosen as tungsten, and the remaining boundary conditions of the numerical simulation were set to be the same as in Section
Forming results: (a) the thickness of the liner is less than the shell thickness; (b) equal thickness of shell and line; (c) the thickness of shell is less than the liner thickness.
As shown in Figure
The forming speed is shown in Table
Forming speed when the material of the liner and shell is tungsten.
EFP no. | |||||
---|---|---|---|---|---|
1#EFP | 1569 m/s | 1595 m/s | 1610 m/s | 1622 m/s | |
2#EFP | 1733 m/s | 1779 m/s | 1812 m/s | 1833 m/s | |
3#EFP | 1729 m/s | 1787 m/s | 1824 m/s | 1850 m/s | |
4#EFP | 1612 m/s | 1651 m/s | 1679 m/s | 1690 m/s | |
1#EFP | 1541 m/s | 1568 m/s | 1586 m/s | 1597 m/s | |
2#EFP | 1694 m/s | 1745 m/s | 1772 m/s | 1806 m/s | |
3#EFP | 1682 m/s | 1752 m/s | 1788 m/s | 1813 m/s | |
4#EFP | 1585 m/s | 1625 m/s | 1653 m/s | 1669 m/s | |
1#EFP | 1511 m/s | 1540 m/s | 1558 m/s | 1571 m/s | |
2#EFP | 1658 m/s | 1705 m/s | 1738 m/s | 1768 m/s | |
3#EFP | 1660 m/s | 1706 m/s | 1748 m/s | 1780 m/s | |
4#EFP | 1559 m/s | 1600 m/s | 1630 m/s | 1644 m/s |
From Table
Comparison of forming speed of different structure types: (a) comparison of forming speed of 1#EFP; (b) comparison of forming speed of 2#EFP; (c) comparison of forming speed of 3#EFP; (d) comparison of forming speed of 4#EFP.
As shown in Figure
From Table
Comparison of forming speed of different structure types: (a) comparison of forming speed of
As shown in Figure
When the shell thickness of the integral MEFP warhead remains unchanged and the liner curvature radius remains unchanged, only the thickness at the center changes for three different types of MEFP warheads. Therefore, the influence of thickness change at the center on the change of forming speed can be obtained from the forming speed list shown in Table
Comparison of forming speed of different thickness of liner center: (a) comparison of forming speed of 1#EFP; (b) comparison of forming speed of 2#EFP; (c) comparison of forming speed of 3#EFP; (d) comparison of forming speed of 4#EFP.
As shown in Figure
From Tables
Comparison of forming speed of different structure types and different materials: (a) comparison of forming speed of
In Figure
From Tables
Comparison of forming speed of different structure types and different materials: (a) comparison of forming speed of
In Figure
From the forming speed list shown in Tables
Comparison of forming speed of different thickness and different materials of liner center: (a) comparison of forming speed of
In Figure
To study the influence of different materials on the forming characteristics of different structural types of circumferential MEFP warheads, three structural types of circumferential MEFP warheads were designed: the warheads in which the thickness of the liner was smaller than that of the shell, those in which the thickness of the liner and the shell was equal, and those in which thickness of the liner was greater than that of the shell. Three materials, copper, steel, and tungsten, were used to simulate the designed circumferential MEFP warhead. The results show that when the material of the liner and shell is copper, the forming effect of EFP worsens with an increase in the curvature radius of the liners. The forming results of the three types of circumferential MEFP warheads are similar, and the forming effect is appropriate when the radius of curvature of the liner is between 9 and 10 mm; when the material of the liner and shell is steel and tungsten, the liner will not be able to form projectiles with spherical, ellipsoidal, or long rod shapes with an increase in the curvature radius (when the diameter is greater than or equal to 8 mm), and the forming results of the three types of circumferential MEFP warheads are similar. For the small-caliber MEFP warhead, if the material of the liner and the shell is selected as copper, the liner curvature radius is between 9 mm and 10 mm; if the material of the liner and the shell is selected as steel and the liner curvature radius is greater than 8 mm, the forming speed of the projectile is large, but the liner cannot form a better-shaped projectile. If the liner and the shell material are selected as tungsten, and the liner curvature radius is greater than 8 mm, the forming speed of the projectiles is slow, and the liners cannot form a better-shaped projectile.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare no conflicts of interest.
This work was financially supported by the Science and Technology on Electromechanical Dynamic Control Laboratory, China (no. 6142601200408).