Polytetrafluoroethylene/aluminum (PTFE/Al) reactive material is a pivotal research object in the aerospace, military, and mechanical engineering fields and can release chemical energy (CE) under shock or impact. However, its relatively low mechanical strength limits its applications. The present paper proposes a Cu-PTFE/Al (73.5wt. %/26.5wt. %) double-layer liner that can form tandem explosive formed projectiles (EFPs) under the shock of shaped charges, which not only retains the strong penetration ability but also shows a more significant lateral enhancement effect through the deflagration reaction. Here, the preparation process of the PTFE/Al liner is given, and an analytical model for the Cu-PTFE/Al tandem EFP of the damage process against multi-spaced plates is established, revealing the penetration and deflagration-enhanced mechanisms. Subsequently, a two-step segmented numerical simulation for the penetration–deflagration coupling effects is conducted, and the time-space interaction process and damage results between kinetic energy penetration and CE deflagration are obtained. A series of experiments of tandem EFPs against spaced plates are conducted, including the different materials, thickness ratio, and standoff. Experimental results show that compared with Cu–Cu tandem EFP with the same condition, the penetration ability of Cu-PTFE/Al composite EFP is reduced, but the damage enhancement effect is greatly improved; the maximum damage area of a single plate is increased by 220.1%, and the average damage area of a single plate is increased by 76.2%. This study provides important reference data and a theoretical basis for the design of metal-reactive tandem EFPs.
I. INTRODUCTION
Polytetrafluoroethylene (PTFE) matrix reactive materials (e.g., PTFE/Al, PTFE/Ti, PTFE/Cu, and PTFE/Al/W) have a certain mechanical strength and can release chemical energy (CE) under the impact, forming deflagration reactions and releasing a large amount of gas products. In the past two decades, they have been widely used in national defense, aerospace, navigation, civil use, etc. fields.1–3 With the increasing popularity of reactive materials, many scholars have conducted a series of studies on PTFE matrix reactive materials, including their mechanical properties,4,5 energy release,6 and damage mechanisms.7–9 However, due to its poor mechanical properties compared with inert metal (e.g., Cu), how to improve its mechanical properties while ensuring the release of chemical energy has become one of the hot topics in recent research. Some scholars improve the mechanical properties of fluoropolymer-based reactive materials by improving the formulation10 or sintering process.11 However, existing research shows that the mechanical properties of PTFE matrix reactive materials, especially material ductility and tensile strength, still have a certain gap with traditional metal materials. Using reactive materials as the shaped charge liner, the penetration ability of the reactive jet formed is still small.12
A double-layer explosive formed projectile (EFP) is a new technology that has been developed in the last 20 years and is widely used to attack lightly armored targets or for oil extraction. Under the shaped charge impact, the double-layer metal spherical liner forms front-to-back tandem EFPs, which use the kinetic energy (KE) to achieve penetration and damage against the target.13,14 Specifically, under the small standoff, the precursor and trailing metal EFPs form a penetrator with a large aspect ratio that “occludes” each other, which is beneficial to the penetration depth of the target. Under the large standoff, the precursor and trailing metal EFPs form a separate penetrator so as to achieve “relay” penetration against the target, especially suitable for penetrating and damaging multi-layer spaced structures.15,16 Based on the above advantages, the double-layer metal spherical liner shaped charge has been widely studied in recent years. Cardoso and Teixeira-Dias17 studied the effects of EFP liner material and thickness, explosive mass, number of detonation points, and eccentricity on EFP performance. Faibish and Mayseless18 studied the formation and underwater motion behavior of the Tan-Ni double-layer spherical liner. By controlling the spacing between the precursor and trailing EFPs, the precursor EFP opened a channel in the water, thus ensuring the penetration ability of the trailing EFP into the target. Han et al.19 studied the EFP forming and penetration behavior of the Zr–Ta double-layer liner. The results showed that the EFP formed by the Zr–Ta double-layer liner had a relatively small length and diameter. What is more, the strongest speed and penetration ability of the EFP formed at the 6.0 CD ∼ 9.0 CD. Besides, the EFP also had an ignition effect on the target. The double-layer composite liner shaped charge designed by Weiman and Blache20 can form a tandem EFP in which the precursor material is Ta and the trailing material is Fe, which has the characteristics of a large aspect ratio and good flight stability. However, metal materials only have KE damage, and the perforation ability is weak, unable to cause large holes or ignite and detonate the internal structure of the target.
Therefore, this study proposes a new structure, a Cu-PTFE/Al double-layer liner with deflagration-enhanced damage effect, which is composed of an outer reactive liner and an inner Cu liner. Under the shaped charge effect, the double-layer liner forms tandem EFP, in which the precursor Cu EFP still uses its own KE to penetrate the plate and form a debris cloud behind the plate. Meanwhile, the trailing reactive EFP not only has KE but also undergoes a deflagration reaction during its movement, releasing a large amount of CE and gas products. Hence, with the reactive EFP following into the multi-spaced plates, it causes a deflagration-enhanced damage effect in the paced plate. This is a great benefit for penetrating the internal multi-layer structural parts of the aviation target and igniting the internal structures.
Based on the above reaction mechanism, a two-step segmented numerical simulation is used to describe the reactive materials in the inert condition and reactive condition, respectively. A series of experiments of tandem EFPs against multi-spaced steel plates are conducted, including the different materials, thickness ratio, and standoff. Combining experimental and numerical simulation results, the unique damage mode and mechanism of the Cu-PTFE/Al tandem EFPs are revealed.
II. A PHENOMENOLOGICAL DESCRIPTION OF THE Cu-PTFE/Al TANDEM EFPS
A. Mechanism of deflagration-enhanced damage behaviors
This paper designs a Cu-PTFE/Al (73.5 wt. %/26.5 wt. %) tandem EFP that uses precursor Cu EFP to improve the penetration capability while exerting the deflagration-enhanced damage capability of reactive materials, whose mechanism can be divided into three steps:
Forming process. Under the loading of the detonation, the double-layered liner forms a tandem EFP composed of the precursor Cu EFP and the trailing reactive EFP. Because Cu has a higher density and better ductility, the precursor EFP formed is relatively dense and has good compactness. The reactive material has low density and poor ductility, so the trailing EFP formed has poor compactness, as shown in Fig. 1(a).
Penetration process. The precursor Cu EFP uses KE to penetrate the multi-spaced thin plates and generate a debris cloud. The debris cloud has a certain hole-expanding effect when penetrating the next layer of spacer plates. At the same time, part of the Cu EFP is consumed. The trailing reactive EFP passes through the KE pre-perforations, as shown in Fig. 1(b).
Deflagration process. After a certain period of time, a violent deflagration occurs in the trailing EFP. A large amount of CE and gas products are released, resulting in a deflagration-enhanced damage effect. At the same time, the deflagration seriously affects the penetration performance of the precursor Cu EFP, causing a decrease in the penetration ability of the remaining precursor Cu EFP. However, the remaining Cu EFP and reactive materials still have a certain speed and can cause combined KE and CE damage to the plates, as shown in Fig. 1(c).
Damage mechanism of Cu-PTFE/Al tandem EFP: (a) Forming process, (b) penetration process, and (c) deflagration process.
Damage mechanism of Cu-PTFE/Al tandem EFP: (a) Forming process, (b) penetration process, and (c) deflagration process.
The PTFE/Al reactive liner is prepared by cold pressing, sintering hardening, and other processes. The specific method is (1) the mixture of 73.5 wt. % PTFE powder (100 nm) and 26.5 wt. % Al powder (44 µm) is mixed in the mixer, and then the mixed powder is placed in a vacuum environment to dry for 24 h; (2) weigh the mixed powder, evenly sprinkle it into the mold, the molding pressure is 200 MPa, and the pressure holding time is 30 s; (3) the cold-pressed reactive liner sample is sintered in a nitrogen atmosphere at a maximum sintering temperature of 380 °C; and (4) put the sintered sample into the mold again for complex shape, complex pressure of 400 MPa, and holding time of 1960 s.
For mechanism considerations, the reactive liner suffers a strong shock wave, significant deformation, and intense friction between the PTFE matrix and Al particles, leading to the reactive EFP temperature rising greatly. Therefore, the PTFE matrix begins to decompose, and the corresponding decomposition products start to react with Al particles. However, what needs emphasis is that the shock-induced chemical reactions in the early stages are local and relatively mild. Only when these local reactions gradually increase to a certain extent does the reactive EFP cause the global chemical reactions to occur violently. In other words, the chemical reactions of reactive EFP could be divided into two steps, including the shock-induced local reaction and the subsequent global reaction. Commonly, the time from the shaped charge being initiated to the occurrence of the reactive EFP global reaction is defined as the reaction delay time τ.21 It is further mentioned that the reactive EFP is often assumed to be completely inert before the reaction delay time τ, but reacts instantaneously when reaching the time τ. This assumption is reasonable in dealing with macroscopic interaction problems. According to Ref. 22, for the PTFE/Al (73.5 wt. %/26.5 wt. %) reactive material, the reaction delay time τ is ∼166.5 µs.
B. Simulation models and material parameters
To better reveal the damage mechanism of Cu-PTFE/Al tandem EFPs against multi-spaced thin plates, the SPH and Lagrange coupled algorithms are utilized to perform simulations in AUTODYN-3D. Figure 2 shows the numerical model, in which the double-layer liner shaped charge is composed of SPH particles and the multi-spaced thin plates are described by Lagrange meshes. Based on the considerations of accuracy and efficiency, the SPH particle size of the composite liner shaped charge is 0.25 mm.23 Furthermore, according to the calculation results of grid size convergence in numerical simulation, it is more reasonable to use the Lagrange gradient grids for each steel plate, which change from 0.5 to 1.0 mm from center to edge. Finally, a fixed boundary condition is set at the edge of each steel plate, as shown in Fig. 2. Each part of the model interacts with each other through the interaction settings of AUTODYN.
The parameters of different materials are listed in Table I. It is noted that ρ is the density, G is the shear modulus, Ca, S1 are shock Hugoniot parameters, and Γ is the Grüneisen coefficient. Moreover, there is no use of failure and erosion in the present paper due to the SPH algorithm. The material parameters of Cu, 45# steel, and PTFE/Al are all from Refs. 24–26.
Parameters of PTFE/Al as inert material, Cu and steel.
Materials . | ρ (g/cm3) . | G (GPa) . | A (MPa) . | B (MPa) . | n . | C . | m . | Tm (K) . | Ca (km/s) . | S1 . | Γ . |
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PTFE/Al | 2.27 | 0.666 | 8.044 | 250.6 | 1.8 | 0.4 | 1.0 | 500 | 1.45 | 2.2584 | 0.9 |
Cu | 8.96 | 46.5 | 90 | 292 | 0.31 | 0.025 | 1.09 | 1356 | 3.94 | 1.49 | 2.02 |
Steel | 7.83 | 77 | 507 | 320 | 0.28 | 0.064 | 1.06 | 1793 | 4.57 | 1.92 | 2.17 |
Materials . | ρ (g/cm3) . | G (GPa) . | A (MPa) . | B (MPa) . | n . | C . | m . | Tm (K) . | Ca (km/s) . | S1 . | Γ . |
---|---|---|---|---|---|---|---|---|---|---|---|
PTFE/Al | 2.27 | 0.666 | 8.044 | 250.6 | 1.8 | 0.4 | 1.0 | 500 | 1.45 | 2.2584 | 0.9 |
Cu | 8.96 | 46.5 | 90 | 292 | 0.31 | 0.025 | 1.09 | 1356 | 3.94 | 1.49 | 2.02 |
Steel | 7.83 | 77 | 507 | 320 | 0.28 | 0.064 | 1.06 | 1793 | 4.57 | 1.92 | 2.17 |
Parameters of the JWL equation for materials.
. | ρ0 . | D . | Pcj . | A1 . | B1 . | |||
---|---|---|---|---|---|---|---|---|
Materials . | (g/cm3) . | (km/s) . | (GPa) . | (GPa) . | (GPa) . | R1 . | R2 . | ω . |
PTFE/Al | 2.27 | 5.2 | 21 | 15.9 | 0.0023 | 7 | 0.6 | 0.38 |
Explosive | 1.71 | 8.315 | 28.6 | 524.23 | 7.678 | 4.2 | 1.1 | 0.34 |
. | ρ0 . | D . | Pcj . | A1 . | B1 . | |||
---|---|---|---|---|---|---|---|---|
Materials . | (g/cm3) . | (km/s) . | (GPa) . | (GPa) . | (GPa) . | R1 . | R2 . | ω . |
PTFE/Al | 2.27 | 5.2 | 21 | 15.9 | 0.0023 | 7 | 0.6 | 0.38 |
Explosive | 1.71 | 8.315 | 28.6 | 524.23 | 7.678 | 4.2 | 1.1 | 0.34 |
C. Forming and damage behaviors
A numerical simulation of the forming behavior of the Cu-PTFE/Al tandem is carried out. The thickness of the inner Cu liner is 2 mm, and the thickness of the outer reactive liner is 3 mm. The forming process is shown in Fig. 3.
Forming process of Cu-PTFE/Al tandem EFP. (a) t = 0 µs, (b) t = 2.3 µs, (c) t = 5.5 µs, (d) t = 8.1 µs, (e) t = 21.0 µs, (f) t = 35.0 µs, and (g) t = 97.5 µs.
Forming process of Cu-PTFE/Al tandem EFP. (a) t = 0 µs, (b) t = 2.3 µs, (c) t = 5.5 µs, (d) t = 8.1 µs, (e) t = 21.0 µs, (f) t = 35.0 µs, and (g) t = 97.5 µs.
Since the strength and density of the PTFE/Al are much lower than those of Cu, under the detonation loading, the inner Cu liner and the outer reactive liner form an “occlusion” tandem EFP, which is the combination of the precursor Cu EFP and the trailing reactive EFP. Due to the high density and good ductility of the Cu material, a dense precursor EFP is formed. While the reactive material has low density, poor ductility, and is made of powder material pressed and sintered, expansion and scattering occur during the forming process, forming an “umbrella-shaped” trailing reactive EFP, and part of the reactive material in the tail is radially dispersed.
The forming morphology and material distribution of the Cu-PTFE/Al tandem EFP and the Cu–Cu tandem EFP under the 4.0 CD standoff are shown in Fig. 4. For the Cu-PTFE/Al tandem EFP, the diameter of the precursor Cu EFP in the condensed state is 13.5 mm, the diameter of the trailing reactive EFP in the condensed state is 33.4 mm, and the overall length of tandem EFP in the condensed state is 79 mm, while the diameter and length of the expanded divergent are larger, and the reactive material at the tail expands and diverges into a larger umbrella shape. The Cu–Cu tandem EFP maintains complete cohesion during the forming process, with almost no expansion or divergence. The diameter of the precursor Cu EFP is 24.1 mm, the diameter of the trailing Cu EFP is 34.4 mm, and the overall length of the tandem EFP is 40 mm. Compared with Cu–Cu tandem EFP, the Cu-PTFE/Al tandem EFP has a smaller diameter than the precursor Cu EFP, and the perforation of the first layer of the spaced plate is smaller. Because of the large difference in material density, the formed tandem EFP has a larger aspect ratio, similar to a “rod jet.”
Material distribution of tandem EFP: (a) Cu-PTFE/Al tandem EFP and (b) Cu–Cu tandem EFP.
Material distribution of tandem EFP: (a) Cu-PTFE/Al tandem EFP and (b) Cu–Cu tandem EFP.
The axial velocity change curve of tandem EFP with time is shown in Fig. 5. By analyzing the change curve, the forming process can be divided into three stages, namely the collision stage, the propulsion stage, and the stretch flight stage.
In the collision stage, driven by detonation loading, the velocity of point 1 starts to increase when t = 2.98 µs and reaches the first peak value when t = 5.62 µs, at which point the axial velocity of point 2 increases rapidly. It can be seen that the collision of points 1 and 2 causes the KE exchange between the inner and outer liner, and the outer reactive liner is decelerated while the inner Cu liner is accelerated. This stage lasts about 6.96 µs.
In the propulsion stage, the driving effect of detonation loading can offset the flight resistance of the liner. When t = 12.68 µs, the point 1 and point 2 velocities reach their maximum. As can be seen from Fig. 5, there is a significant velocity difference between the center and edge of the double-layer liner, so the liner gradually stretches and closes to the axis. Due to the interaction of the inner and outer liner in the propulsion process, point 1 of the outer reactive liner has a relative backward thrust effect along the axis direction, so there is an obvious speed decrease at point 1 during the time period from t = 12.68 µs to t = 28.73 µs. This stage ends at t = 35.21 µs, which lasts 25.95 µs.
In the stretch flight stage, the tandem EFP is not fully formed, the aspect ratio is still large, and the double-layer liner is not fully closed. Due to the obvious velocity gradient inside the tandem EFP, it is always in a stretched condition. Moreover, due to the high density of the Cu EFP, reactive materials with lower density are gradually squeezed out of the Cu EFP tail during the closing process. The time for the tandem EFP to reach 4.0 CD standoff is 97.5 µs.
The process of Cu-PTFE/Al tandem EFP damaging spaced plates is shown in Fig. 6. At 97.5 µs, the tandem EFP reaches a 4.0 CD standoff, as shown in Fig. 6(a). The precursor Cu EFP first penetrates the spaced plates with its KE, resulting in central pre-perforation on the corresponding plates. Due to the large thickness of the first layer of the steel plate, the perforation is small, about 0.3 CD, and part of the reactive material is blocked from the central pre-perforation. As the penetration proceeds, the contact area between the precursor Cu EFP and the plate increases because of the lateral flow of the EFP tip. Then, after perforating the steel plate, the debris from the precursor Cu EFP and the steel plate forms a debris cloud, further enhancing the kinetic damage capability. Then the speed of the precursor Cu EFP decreases, the EFP tip expands, and it is caught up by the trailing reactive EFP, forming a penetrator with an outer layer of Cu and an inner core of reactive material, as shown in Fig. 6(b).
Process of Cu-PTFE/Al tandem EFP damaging spaced plates: (a) t = 97.5 µs, (b) t = 166.5 µs, (c) t = 300 µs, and (d) t = 1 ms.
Process of Cu-PTFE/Al tandem EFP damaging spaced plates: (a) t = 97.5 µs, (b) t = 166.5 µs, (c) t = 300 µs, and (d) t = 1 ms.
At 166.5 µs, the reactive material delay time τ is reached. The trailing reactive EFP with a certain forward velocity deflagrates violently among plates. At the same time, the unconsumed precursor Cu EFP still has penetration and expansion capabilities. Under the combined action of KE and CE, the deflagration-enhanced damage effect is achieved, as shown in Figs. 6(c) and 6(d).
However, the deflagration also interferes with the penetration of the precursor Cu EFP, resulting in a reduction in the penetration ability. Figure 7(a) shows the KE penetration damage results of the Cu-PTFE/Al tandem EFP to the spaced plate when the reactive EFP is an inert material. The inert tandem EFP can penetrate the seven-layer spaced plates by KE. The deflagration-enhanced damage results are shown in Fig. 7(b), which can only penetrate six layers of spaced plates. Table III shows the comparison of the damage area under the inert conditions and the reactive conditions.
Numerical results of Cu-PTFE/Al tandem EFP against spaced plates.
Number of . | Inert damage . | Reactive damage . | . | Inert bulge . | Reaction bulge . | . | ||
---|---|---|---|---|---|---|---|---|
layers . | area (mm2) . | area (mm2) . | Area increase . | height (mm) . | height (mm) . | Bulge increase . | ||
First | 174.4 | 231.1 | 32.5% | ⋯ | ⋯ | ⋯ | ||
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Second | 409.5 | 452.4 | 10.5% | ⋯ | ⋯ | ⋯ | ||
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Third | 2310.7 | 2789.9 | 20.7% | 24 | 34 | 41.7% | ||
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Fourth | 1289.4 | 5276.4 | 309.2% | 23 | 41 | 78.3% | ||
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Fifth | 844.3 | 1638.7 | 94.1% | 15 | 21 | 40% | ||
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Sixth | 194.1 | 2083.7 | 973.5% | 15 | 22 | 46.7% | ||
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Sevnth | 280.4 | ⋯ | ⋯ | ⋯ | 12 | 17 | 41.7% | |
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Number of . | Inert damage . | Reactive damage . | . | Inert bulge . | Reaction bulge . | . | ||
---|---|---|---|---|---|---|---|---|
layers . | area (mm2) . | area (mm2) . | Area increase . | height (mm) . | height (mm) . | Bulge increase . | ||
First | 174.4 | 231.1 | 32.5% | ⋯ | ⋯ | ⋯ | ||
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Second | 409.5 | 452.4 | 10.5% | ⋯ | ⋯ | ⋯ | ||
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Third | 2310.7 | 2789.9 | 20.7% | 24 | 34 | 41.7% | ||
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Fourth | 1289.4 | 5276.4 | 309.2% | 23 | 41 | 78.3% | ||
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Fifth | 844.3 | 1638.7 | 94.1% | 15 | 21 | 40% | ||
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Sixth | 194.1 | 2083.7 | 973.5% | 15 | 22 | 46.7% | ||
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Sevnth | 280.4 | ⋯ | ⋯ | ⋯ | 12 | 17 | 41.7% | |
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It can be seen from Table III that the damage area of the six-layer spaced plates combined with CE and KE damage by Cu-PTFE/Al tandem EFP in the reactive condition is larger than the area of the KE penetration in the inert condition. The total damage area in the reactive condition is 12 472.2 mm2, and in the inert condition, it is 5502.8 mm2. The damage increase is 126.7%. In addition, the maximum bulge increase of a single plate is 78.3%. The deflagration of the reactive material greatly enhances the damage effect.
III. EXPERIMENTAL METHODS
A. Composite liner shaped charge
The shaped charge structure and the corresponding photograph are shown in Fig. 8. It can be seen that the shaped charge mainly includes the case, charge, baffle ring, and composite liner. The case is made of 45 No. steel with a thickness Hcase of 2 mm; the charge is fabricated by pressing the 8701 explosive with a pressure of 200 MPa. The final density, length Lc, and radius Rc of the charge are 1.7 g/cm3, 50 and 25 mm, respectively. The baffle ring is made of 45# steel, with a width δr of 5 mm and a thickness Hr of 2.5 mm.
The double-layer liner consists of an inner Cu liner and an outer reactive liner, respectively. The detailed structure and photograph of the composite liner are shown in Fig. 8. As can be seen, both the Cu and reactive liners adopt the standard spherical segment, with a diameter Φ of 45 mm and a curvature radius R of 45 mm. Generally, the Cu liner is obtained by the machining method from the Cu rod. The reactive liner is composed of PTFE powder and Al powder with a mass ratio of 73.5%/26.5%. It is noted that the double-layer liner is classified based on the thickness ratio of the outer liner to the inner liner (To/Ti). Specifically, the total thickness of the composite liner is 5 mm, and the thickness ratios To/Ti are chosen as 3/2, 7/3, and 4/7, respectively. Furthermore, a Cu–Cu double-layer liner with a thickness ratio of 3/2 is also used for comparison.
The reactive liner is prepared by cold pressing, sintering hardening, and other processes. The specific method is:
(1) The mixture of 73.5 wt. % PTFE powder (100 nm) and 26.5 wt. % Al powder (44 µm) is mixed in the mixer, and then the mixed powder is placed in a vacuum environment to dry for 24 h. (2) Weigh the mixed powder and evenly sprinkle it into the mold; the molding pressure is 200 MPa, and the pressure holding time is 30 s. (3) The cold-pressed reactive liner sample is sintered in a nitrogen atmosphere at a maximum sintering temperature of 380 °C. (4) Put the sintered sample into the mold again for a complex shape, a complex pressure of 400 MPa, and a holding time of 60 s.
B. Experimental setup
In order to study the coupling damage effect of Cu-PTFE/Al tandem EFPs on lightly armored targets, such as armored vehicles, helicopters, and other targets, a multi-spaced thin plate composed of ten layers 45# steel plates with a thickness distribution was designed. The thickness of the first two layers is 5 mm, the thickness of the last eight layers is 2 mm, and the distance between adjacent steel plates is 50 mm. The planar dimensions of each plate are 250 × 250 mm2. The experimental setup is shown in Fig. 9. The shaped charge is placed on the multi-spaced thin plates with a standoff. The damage behavior is recorded by a high-speed camera.
IV. RESULTS AND DISCUSSION
A. Influences of materials
First, the damage processes of Cu–Cu tandem EFPs and Cu-PTFE/Al tandem EFP to spaced plates are observed by high-speed photography comparatively, as shown in Figs. 10 and 11. It can be seen that the two fireballs at 30 µs show similar brightness and size. Then, the fireball with a height of 1056 mm and a width of 1481 mm is still above the spaced plates at the time of 270 µs in the case of the double-layer Cu liner shaped charge against spaced plates, as shown in Fig. 10(c). However, under the condition of the reactive composite liner shaped charge against spaced plates, the fireball at the time of 150 µs has increased to a height of 1056 mm and a width of 1481 mm, as shown in Fig. 11(c). It is worth noting that the fireball has expanded into the interior of the spaced plates in Fig. 11(c). For mechanism considerations, the Cu–Cu liner weighs 10 g more than the Cu-PTFE/Al liner, indicating the Cu–Cu tandem EFPs have a lower velocity compared with the Cu-PTFE/Al tandem EFPs. As such, the Cu–Cu tandem EFPs have not yet penetrated into the interior of the spaced plates at the time of 270 µs, and therefore the fire cannot spread to the interior of the spaced plates. By contrast, the spread of fireballs in Fig. 11(c) indicates that the Cu-PTFE/Al tandem EFPs with a higher velocity have penetrated into the spaced plates at a time of 150 µs, which is consistent with the numerical simulation results. Then, it can be found that the Cu–Cu tandem EFPs begin to penetrate the space plates at about 150 µs and get the fifth plate at the time of 450 µs. Furthermore, the t Cu–Cu tandem EFPs can hardly form the fireball in the spaced plates, and only some local light can be seen near the steel plates. In fact, the Cu–Cu tandem EFPs belong to the inert damage element, which does not occur during the penetration process, and the local lights are mainly from the KE impact behavior. While Figs. 10(d) and 11(c) show the different phenomena that the fireball obviously expands into the spaced plates, which indicates that the Cu-PTFE/Al tandem EFP has caused violent deflagration among the spaced plates.
High-speed sequence of the Cu–Cu tandem EFP against spaced plates: (a) t = 0 µs, (b) t = 30 µs, (c) t = 270 µs, (d) t = 450 µs, (e) t = 1800 µs, and (f) t = 6000 µs.
High-speed sequence of the Cu–Cu tandem EFP against spaced plates: (a) t = 0 µs, (b) t = 30 µs, (c) t = 270 µs, (d) t = 450 µs, (e) t = 1800 µs, and (f) t = 6000 µs.
High-speed sequence of the Cu-PTFE/Al tandem EFP against spaced plates: (a) t = 0 µs, (b) t = 30 µs, (c) t = 150 µs, (d) t = 210 µs, (e) t = 2100 µs, and (f) t = 6000 µs.
High-speed sequence of the Cu-PTFE/Al tandem EFP against spaced plates: (a) t = 0 µs, (b) t = 30 µs, (c) t = 150 µs, (d) t = 210 µs, (e) t = 2100 µs, and (f) t = 6000 µs.
In addition, with time lapsing, the fireball above the spaced plates gradually extinguishes, and a dark smoke zone is formed in the case of Cu–Cu tandem EFPs against spaced plates. However, for the Cu-PTFE/Al tandem EFP, the fireball is still bright at 6000 µs, which is due to the chemical reaction of reactive materials being sputtered outside the spaced plates. The comparison of multi-space plate damage results is shown in Fig. 12.
Experimental results of Cu–Cu tandem EFP and Cu-PTFE/Al tandem EFPs.
Tables IV and V show the damage of tandem EFP to each plate layer, respectively. The results show that the Cu–Cu tandem EFPs perforate all ten-layer steel plates, but the Cu-PTFE/Al tandem EFPs only perforate six-layer steel plates, which is the same as the numerical simulation result. The penetration difference is mainly due to the following reasons: on the one hand, for the Cu-PTFE/Al tandem EFPs, the reactive liner undergoes a violent deflagration during the penetration process, which affects the penetration capability of the precursor Cu EFP. On the other hand, for the Cu–Cu tandem EFPs, both the precursor and trailing Cu EFPs have strong penetration ability, so they can penetrate all the spaced plates by relay.
Experimental results of Cu-PTFE/Al tandem EFPs against spaced plates.a
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To/Ti = 3/2.
Experimental results of Cu–Cu tandem EFPs against spaced plates.a
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To/Ti = 3/2.
The plate damage area data are statistically calculated, and the measurement method is as follows:28 (1) programming via Python and adding rulers for the rupturing area image. (2) Select a reference line on the image to weight the red–green–blue (RGB) channel values on the reference line. Then perform grayscale conversion and image segmentation, as shown in Figs. 13(a) and 13(b). (3) Through gray processing and segmentation, the damage area is separated. The image noise is processed, and the damage area is calculated from the pixel points, as shown in Figs. 13(c) and 13(d).
Damage area measurement method: (a) Damage area with ruler, (b) RGB component, (c) gray value histogram, and (d) calculate area.
Damage area measurement method: (a) Damage area with ruler, (b) RGB component, (c) gray value histogram, and (d) calculate area.
Figure 14 shows the comparison of the damage area of each plate and the total damage area of the tandem EFPs. It can be seen that the damage area of the first two steel plates caused by Cu–Cu EFP is larger than that of Cu-PTFE/Al EFP. This is caused by the different forming morphologies of the two EFPs. It can be seen from Fig. 4 that for the Cu-PTFE/Al EFP under the 4.0 CD standoff, the width of the precursor Cu EFP is about 13.5 mm, and the width of the trailing reactive EFP is about 33.4 mm. The width of the precursor Cu EFP formed by the Cu–Cu EFP is about 24.1 mm, which is an increase of 78.5% compared to the former, and the width of the trailing Cu EFP is about 34.4 mm. The wider precursor Cu EFP creates a larger damage area in the first two plates, and the density of the trailing Cu EFP is greater than that of the reactive EFP, which is more conducive to hole expansion in the first two plates. In addition, it can be seen from Table III and Fig. 7 that when the reactive material delay time τ is reached, less reactive material flows into the interior of the first two layers of plates, and the deflagration enhancement effect on the plate is weakly enhanced.
Damage area of each layer of plates caused by different tandem EFPs.
Starting from the four layers of plate, the damage area of Cu-PTFE/Al EFP is significantly larger than that of Cu–Cu EFP. The change in this trend reveals the different damage mechanisms of the two tandem EFPs. After reaching the reaction delay time τ, the trailing reactive EFP releases CE, causing obvious deflagration-enhanced damage effects on the plate. The total damage area caused by Cu–Cu EFP is 13 767.7 mm2, and the average damage area of a single plate is 1376.8 mm2. The total damage area caused by Cu-PTFE/Al EFP is 14 554.6 mm2, and the average damage area of a single plate is 2425.8 mm2. Compared with the Cu–Cu EFP, the damage area of a single plate is increased by 76.2%, the total damage capacity is increased by 5.7%, and the maximum damage area of a single plate increases by ∼220.1%. The total damage area of the plate obtained by numerical simulation is 12 472.2 mm2, the average damage area of a single plate is 2078.7 mm2, and the deviation of the damage area of a single plate from the experimental value is about −14.3%, which further proves the effectiveness of the numerical simulation.
B. Influences of thickness ratio
Tables VI and VII show the damage effects of tandem EFPs with different thickness ratios at 4.0 CD standoff when other experimental conditions remain unchanged. Fig. 15 shows the comparison of the damage area of each plate and the total damage area of the EFPs.
Experimental results of tandem EFPs with To/Ti = 7/3.
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Experimental results of tandem EFPs with To/Ti = 4/1.
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Damage area of each layer of plates caused by tandem EFP with different thickness ratios.
Damage area of each layer of plates caused by tandem EFP with different thickness ratios.
Comparing Tables IV, VI, and VII, it can be seen that the thickness ratio To/Ti of the reactive liner to the Cu liner has a significant impact on the tandem EFP damage spaced plates. When the To/Ti = 7/3, the tandem EFP can still penetrate the six-layer plates, but the bulge behind the seventh layer plate is smaller than when the To/Ti = 3/2. When the thickness ratio is further increased to To/Ti = 4/1, the tandem EFP can only penetrate the five-layer plates, and the sixth-layer plate shows a bulge on the back but is not penetrated. As the thickness ratio To/Ti increases, the penetration ability of tandem EFP decreases. Figure 16 shows the forming condition and material distribution of tandem EFP with different thickness ratios under the 4.0 CD standoff.
Forming condition and material distribution of tandem EFP with different thickness ratios: (a) To/Ti = 4/1, (b) To/Ti = 7/3, and (c) To/Ti = 3/2.
Forming condition and material distribution of tandem EFP with different thickness ratios: (a) To/Ti = 4/1, (b) To/Ti = 7/3, and (c) To/Ti = 3/2.
Figure 17 shows the material distribution of tandem EFPs with different thickness ratios in the spaced plates when the reaction delay time τ is reached. It can be seen that when the time is 166.5 µs, To/Ti = 4/1 tandem EFP reaches the fifth layer plate, the precursor Cu EFP is almost exhausted, and only the trailing reactive jet remains for deflagration. The reactive material in the plate is mainly concentrated between the third layer and the fifth layer, so the final damage is only to the five-layer plates, and the deflagration-enhanced damage effect on the third and fourth layer plates is particularly obvious. The total damage area of the tandem EFP with To/Ti = 4/1 to the five-layer spaced plates is 10 540.9 mm2, and the average damage area is 2108.2 mm2. Compared with the case of To/Ti = 3/2, the total damage is reduced by 27.6%, and the average damage area decreases by 13.1%.
To/Ti = 7/3 tandem EFP penetrates four-layer plates, and the trailing reactive EFP mass can be approximately linearly distributed between the four-layer plates. Compared with To/Ti = 3/2 tandem EFP, although the reactive material mass increases, the precursor Cu EFP KE perforation diameter is smaller. The total damage area of the tandem EFP with To/Ti = 7/3 to the five layers of spaced plates is 10 991.6 mm2, and the average damage area is 1831.9 mm2. Compared with the case of To/Ti = 3/2, the average damage area decreased by 24.5%.
C. Influences of standoff
In order to further study the influence of standoff on the tandem EFPs deflagration-enhanced damage behaviors while keeping other conditions the same, experiments are carried out by changing the standoff to 4.0 CD, 5.0 CD, and 6.0 CD, respectively. The thickness ratio is To/Ti = 3/2. Tables VIII and IX show the damage effects of tandem EFPs with different standoffs.
Experimental results of 5.0 CD standoff.a
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To/Ti = 3/2.
Experimental results of 6.0 CD standoff.a
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To/Ti = 3/2.
Comparing Tables IV, VIII, and IX, it can be seen that when the standoff increases, the penetration ability of the tandem EFP gradually increases. When the standoff is 4.0 CD, the tandem EFP penetrates a total of six layers of the steel plate, causing a certain bulge to the seventh steel plate; when the standoff is 5.0 CD and 6.0 CD, the tandem EFP penetrates seven-layer plates. In these two standoff conditions, the damage effects of the steel plates on the seventh and eighth layers are shown in Fig. 18. It can be seen that under the 5.0 CD standoff, when the precursor Cu EFP penetrates the seventh steel plate, the penetration ability has almost reached the limit, and the remaining Cu EFP causes traces of sputtering and ablation on the steel plate. Part of the scattered precursor Cu EFP penetrated the seventh steel plate and caused some bulge damage on the eighth steel plate. For the case where the standoff is 6.0 CD, the remaining precursor Cu EFP is still capable of penetrating the seventh steel plate, forming a complete central perforation, and causing bulging damage on the eighth steel plate.
Damage to the seventh and eighth steel plates caused by tandem EFP under different standoffs: (a) 5.0 CD and (b) 6.0 CD.
Damage to the seventh and eighth steel plates caused by tandem EFP under different standoffs: (a) 5.0 CD and (b) 6.0 CD.
The numerical simulation results of tandem EFP forming under different standoffs are shown in Fig. 19. The experimental results of each layer of steel plates under different standoffs are shown in Fig. 20. It can be seen that, on the one hand, as the standoff increases, the tandem EFP aspect ratio increases. The precursor Cu EFP also gradually elongates and separates from the trailing reactive EFP. Therefore, when the trailing reactive EFP undergoes a deflagration, the impact on the precursor Cu EFP gradually decreases, resulting in an increase in the penetration capability of the tandem EFP. On the other hand, as the standoff increases, the EFP forming time increases. While the reaction delay time τ remains unchanged when the reactive material starts to deflagrate, the number of spaced plate layers will increase. With the elongation of the trailing reactive EFP, less mass of reactive material enters the plate, which weakens the deflagration-enhanced damage effect.
Forming state and material distribution of tandem EFP with different standoffs: (a) 4.0 CD, (b) 5.0 CD, and (c) 6.0 CD.
Forming state and material distribution of tandem EFP with different standoffs: (a) 4.0 CD, (b) 5.0 CD, and (c) 6.0 CD.
Damage area of each plate caused by tandem EFP with different standoffs.
When the standoff is 4.0 CD or 5.0 CD, the maximum damage area caused by the tandem EFP is on the fifth steel plate. When the standoff is 6.0 CD, the maximum damage area caused by the tandem EFP is on the fourth steel plate. Under the 5.0 CD and the 6.0 CD conditions, compared with the 4.0 CD conditions, the maximum single-layer damage area decreases by 11.4% and 27.2%, respectively. The average single-layer damage area decreases by 12.1% and 24.3%, respectively.
V. CONCLUSIONS
By analyzing the Cu-PTFE/Al tandem EFP forming process and the damage process of multi-spaced thin plates, the tandem EFP penetration and deflagration-enhanced damage mechanisms are revealed. Considering the nonself-sustaining reaction characteristics of reactive materials, a two-step segmented numerical simulation for Cu-PTFE/Al tandem EFP impacting spaced plates is developed. The influencing factors of the Cu-PTFE/Al tandem EFP deflagration-enhanced damage mechanism are further discussed in terms of the materials, thickness ratio, and standoff. The effectiveness of the numerical simulation is verified at the same time. The main conclusions are as follows:
Compared with Cu–Cu tandem EFP in the same condition, the penetration ability of Cu-PTFE/Al tandem EFP is reduced, but the deflagration-enhanced damage effect is greatly improved. Through the combined effect of KE and CE, the maximum damage area of a single plate is increased by 220.1% compared with the Cu–Cu condition. The average damage area of a single plate is increased by 76.2%, and the total damage area is increased by 5.7%.
The deflagration-enhanced damage ability of Cu-PTFE/Al tandem EFP mainly depends on the coupling between the KE perforation generated by the precursor Cu EFP and the CE released by the deflagration of the trailing reactive EFP. Under the conditions studied in this paper, as the thickness ratio of the reactive liner to the Cu liner increases, the penetration ability of the precursor Cu EFP weakens and the perforation diameter decreases. Although the reactive material entering the multi-layer plates increases, the total damage capability decreases. As the standoff increases, the precursor Cu EFP elongates, the penetration ability increases, and the number of plate penetrations increases. However, under the same reaction delay time τ, the mass of reactive materials entering the spaced plates decreases, leading to a decrease in the deflagration-enhanced damage capability.
The two-step segmented simulation method can effectively simulate the penetration–deflagration coupling damage effect of Cu-PTFE/Al tandem EFP on multi-spaced thin plates. The number of damage interval plate layers obtained by numerical simulation is consistent with the experimental value. The total damage area and the average damage area of a single plate differ by no more than 15%, which provides an effective means for revealing the deflagration-enhanced damage mechanism of Cu-PTFE/Al tandem EFP.
ACKNOWLEDGMENTS
This research is supported by the National Natural Science Foundation of China (Grant No. 12172052) and the Science and Technology Innovation Program of Beijing Institute of Technology (Grant No. 2022CX01020), and the authors would like to acknowledge these foundations for their financial support.
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
Cheng-hai Su: Conceptualization (equal), Data curation (equal), Methodology (equal), Validation (equal), Visualization (equal), Writing - original draft (equal) and Writing - review & editing (equal). Yuan-feng Zheng: Data curation (equal), Methodology (Equal) and software (Equal). Shi-peng Wang: Investigation (equal), Validation (equal) and Visualization (equal). Ao-xin Liu: Conceptualization (equal), Supervision (equal) and Visualization (Equal). Hai-fu Wang: Data curation (equal), Formal analysis (equal) and Writing-review & editing (equal).
DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request.