Investigation on Interaction of Explosively Formed Projectile with Multi-layer Medium Targets

To investigate the influence of liner material, charge diameter and standoff on explosively formed projectile (EFP) penetrating into multi-layer targets, a large number of experiments were performed and the experimental data on crater diameter, hole diameter, crater depth and penetration depth were obtained. Meanwhile, the numerical simulation have been done to study the formation and penetration processes of all the EFP with AUTODYN software. The numerical results of penetration depth are in good agreement with the experimental ones. The results indicate that the optimal liner material of EFP to achieve a larger penetration hole diameter and depth are aluminum and copper, respectively.


INTRODUCTION
The impact resistance of concrete structures is of major importance in engineering application.In recent years, a large number of scholars investigated the intrinsic mechanisms on penetrating into concrete [1][2][3].Nia et al. [4] studied the resistance of concrete target against penetration of eroding long rod projectile.The analysis results show that there is a proportional relation between the strength of the target and the size of the incompressible zone.Smith et al. [5] developed a discrete modeling of ultra-highperformance concrete named CORTUF which can be used to simulate the behavior of protective CORTUF panels subjected to projectile penetration.In order to investigate the intrinsic mechanisms of mass loss for a projectile penetration into concrete, Guo et al. [6] carried out experiments on 30CrMnSiNi2A kinetic energy projectiles with an ogival nose penetrating concrete targets in the normal direction at a striking velocity of 843 m/s and 1400 m/s, respectively.Based on the experimental analysis and observations by using an optical microscope, energy dispersive X-ray detector and microhardness tester, evolution mechanisms of the microstructures induced by plastic deformation and high temperature during penetration were proposed.Warren et al. [7] designed experiments to recon deceleration date from projectile penetration into concrete targets with compressive strengths of 23MPa and 39MPa and two empirical penetration models that described deceleration kinetic energy divided by projectile mass were developed.A meshfree formulation under the reproducing kernel particle method was introduced by Sherburn et al. [8] for modeling the penetration and perforation of concrete slab.The accuracy of the formulation was confirmed by simulation.Wang et al. [9] investigated shaped charge penetrating into concrete targets experimentally, numerically and theoretically.Bian et al. [10] developed an elastoplastic damage model for concrete with an emphasis on the pressure dependence of volume change.The numerical results of penetrating into concrete targets by using the proposed model are in good agreement with the experimental results.Experimental and numerical investigations are conducted by Feng et al. [11] to study the dynamic response of a double-layered target of ultra-high-performance fibre reinforced concrete and armour steel subjected to an armour-piercing projectile impact.Yu et al. [12] investigated the energy absorption capacity of a sustainable Ultra-High Performance Fibre Reinforced Concrete (UHPFRC) under high velocity projectile impact.The experimental results indicate that, under high velocity projectile impact, the UHPFRC mixture with hybrid fibres shows a much better energy absorption capacity than the one with hooked steel fibres only, particularly in resisting the scabbing at the rear surface.
The penetrating into multi-layer targets is a complex mechanical problem which usually involves shock wave propagation, dynamic behavior of multi-layer targets, interactions between different layers and so on.Investigations on penetrating into multi-layer targets are far less than that of pure concrete targets.Zeng et al. [13] simulated the progress of penetrating obliquely multi-layer runway with anti-runway penetrator by the finite element code LS-DYNA 3D.The result indicated that the overturned angle of projectile could be reduced and the penetration depth increases when the centroid of projectile was moved ahead.The damage effects of the multi-layered target against reactive materials based shaped charge was studied in reference [14].
In the present investigations, due to lack of systematic experimental data, the intrinsic mechanisms of EFP penetrating into multi-layer targets are not understood clearly.We carried out a series of experiments of penetrating into multi-layer targets by EFP.Using both experiments and numerical simulations, we investigated the variation laws of crater diameter, hole diameter, crater depth and penetration depth with different liner materials, charge diameters and standoffs.

EXPERIMENTAL SCHEME
The charge with diameters of 100mm and 120mm are designed and Composition B with density of 1.6g/cm 3 is selected as the main charge in experiments.As shown in Figure 1, the length to diameter ratio of these shaped charge is 1:1.The cone angle of the liner is 120° and its wall thickness is uniformly 0.03D, for which liner materials include steel, copper and aluminum.Five kinds of standoffs (L=1D, 1.5D, 2D, 3D and 4D) are investigated respectively in this paper, which D is defined as charge diameter here.
The multi-layer targets consist of three layers in the experiments, as shown in Figure 2. The surface layer is concrete.Its density is 2.4g/cm 3 , compressive strength 30MPa and thickness 400mm.The middle layer is pebble.Its thickness is 300mm.The bottom layer is rammed earth.Its thickness is 400mm.
The typical experimental setup and result are shown in Figures 3. The values of crater diameter D1, hole diameter D2, crater depth H1 and penetration depth H are measured in the experiments as shown in Figure 4.The maximum and minimum values of D1 and D2 are recorded, and then the averages of maximum and minimum values are adopted to depict variation curves, as shown in Figures 5 and 6.

Results of Crater Diameter D1
For different charge diameters, with the increase of standoffs, the variation trend of crater diameter which caused by EFP with steel liner or copper liner are nearly the same, as shown in Figure 5. Crater diameters formed by EFP with steel liner increase firstly and then decrease with the increase of standoffs; Table 1 illustrate that, when the charge diameters are 100mm and 120mm respectively, the corresponding maximum values of crater diameters are 7.6D and 7.5D; for the same standoff, crater diameter formed by EFP with 120mm diameters are larger than that formed by EFP with 100mm.Crater diameters formed by EFP with copper liner decrease firstly and then increase with the increase of standoffs; when the charge diameters are 100mm and 120mm respectively, the corresponding maximum values of crater diameters are 5.5D and 6.7D.Except for 1.5D standoff, crater diameters caused by EFP with aluminium liner vary slightly with the increase of standoffs; when charge diameters are 100mm and 120mm respectively, the corresponding maximum values of crater diameters are 6.2D and 6.3D; for the same standoff, crater diameter formed by EFP with 120mm diameters are larger than that formed by EFP with 100mm.When standoffs are lower than 2D, crater diameters caused by EFP with steel liner, aluminium liner and copper liner decrease in sequence.In the case of standoffs are greater than 2D, crater diameters caused by EFP of steel liner decrease rapidly with the increase of standoffs and crater diameters caused by EFP with aluminium liner are the largest.

Results of Hole Diameter D2
It is obvious from Figure 6 that, for different charge diameters, with the increase of standoffs, the variation trend of hole diameter which caused by EFP with steel liner or copper liner are nearly the same.Hole diameters formed by EFP with steel liner increase firstly and then decrease with the increase of standoffs; when the charge diameters are 100mm and 120mm respectively, the corresponding maximum values of hole diameters are 1D and 0.9D, as set out in Table 2. Hole diameters caused by EFP with copper liner decrease with the increase of standoffs; the maximum value of hole diameter is 0.6D for both 100mm and 120mm charge diameters.Among different liner materials, hole diameters caused by EFP with copper liner are the smallest.There are no stable variation laws of hole diameter which caused by EFP with aluminium liner; when the charge diameters are 100mm and 120mm respectively, the corresponding maximum values of hole diameters are 1.3D and 1.7D.For different liner materials and constant charge diameters, hole diameters caused by EFP with aluminium liner are the largest.It indicates that the EFP with aluminium liner is suitable for penetrating larger hole diameters.

Results of Crater Depth H1
From Table 3 we can find that crater depths caused by EFP with steel liner decrease with the increase of standoffs; when the charge diameters are 100mm and 120mm respectively, the corresponding maximum values of crater depths are 1.7D and 1.6D; for the same standoff,   4, when the charge diameters are 100mm and 120mm respectively, the corresponding maximum values of penetration depths are 5.6D and 5.8D.In the case of 100mm charge diameters, the maximum value of penetration depths caused by EFP with copper liner is 9.5D.In the case of 120mm charge diameters and 4D standoff, EFP with copper liner through the multi-layer targets and penetrating into the soil below multi-layer targets, the maximum value of penetration depths is 10.6D.Due to the low density and plasticity, penetration performance of EFP with aluminium liner is poor.EFP with aluminium liner are not through the upper layer of multi-layer targets.When the charge diameters are 100mm and 120mm respectively, the corresponding maximum values of penetration depths are 1.6D and 2.6D.For different liner materials and constant charge diameters, penetration depths caused by EFP with copper liner, steel liner and aluminium liner decrease in sequence.It indicates that the EFP with copper liner is ideal for larger penetration depths.

NUMERICAL RESULTS
REMAP technology of the software AUTODYN is used to investigate the formation and penetration of EFP.The formation process of the EFP is simulated by Euler approach as shown in Figure 9.Then, the simulation results of EFP are imported and remapped into the Lagrange approach with local mesh refinement in the vicinity of the axis of the target as shown in Figure 10.The JWL, polynomial, porous and compaction equation of state are introduced to describe the Composition B, concrete, pebble and earth respectively.The transmit boundary condition is used between different target layers.Under the impact of the detonation wave, the liner moves inward and generates EFP. Figure 11 illustrates the EFP parameters, including the velocities, lengths and diameters of EFP in different standoffs.It is clear from Figure 11 that the EFP elongation with the increase of standoffs and the velocity gradient decrease with the length increase.In the case of 3D standoff, the fracture occurs in the neighbor of the EFP empennage.In the condition of 1D and 2D standoffs, the tip velocity of EFP with copper liner is similar to the velocity of EFP with steel liner.When the standoffs are 3D and 4D, for the same standoff, the tip velocity of EFP with copper liner is lower than steel liner.It is mainly caused by the velocity discontinuity of EFP with steel liner in the neighbor of the empennage.Due to the high ductility of copper, in the 3D and 4D standoffs, The EFP copper liner is continuous.However, The EFP with steel liner is fractured, as shown in Figures 11 and 12 5 shows the penetration depths by comparing numerical results with experimental ones.The maximum error of penetration depths caused by EFP is only 9.7%.It also demonstrates that the numerical techniques such as boundary conditions, mesh size, equations of state and so on are reasonable in this paper.
Compared with penetrating single concrete target, the interfacial effect exists obviously in the penetration of EFP into multi-layer targets, as shown in Figure 14.By the neighbor of the interface between concrete and pebble, the diameter of penetrating hole on the pebble side narrows locally, as shown in the location of P1.By the neighbor of the interface between pebble and rammed earth, the diameter of penetrating hole on the rammed earth side enlarges locally, as shown in the location of P2.Under the influence of rarefaction wave, in the interface of pebble and rammed earth, the pebble generates ductile perforation and part of pebble invades rammed earth.and depth (H) are aluminium and copper, respectively.
3. Formation laws of crater diameter, hole diameter, crater depth and penetration depth with the variations in liner materials, charge diameters and standoffs are different.Therefore it is of great significance to take into comprehensive consideration all the impact factors to optimize the design of EFP. 4. All the experiments performed in this paper to investigate penetrating into multi-layer targets by EFP are also simulated numerically.The numerical results of penetration depth are in good agreement with the experimental ones.

Figure 6 :
Variation trend of D2 with different standoffs (a) D=100mm.(b) D=120mm 3.4.Results of Penetration Depth H It is clear from Figure 8 that penetration depths caused by EFP with steel liner increase with the increase of standoffs; as shown in Table

Figure 9 :
Figure 9: The typical simulation results of EFP formation

Figure 12 :
The EFP with copper liner and 120mm charge diameters under different standoffs; (a) 1D standoff.(b) 2D standoff.(c) 3D standoff.(d) 4D standof Among different liner materials, for the same standoff, the tip velocity of EFP with aluminium liner is the highest, the length of EFP with aluminium liner is the shortest and the tail of EFP with aluminium liner is the smallest (Figures 11-13 ).

Figure 13 :
The EFP with aluminium liner and 120mm charge diameters under different standoffs; (a) 1D standoff.(b) 2D standoff.(c) 3D standoff.(d) 4D standoff Table Figure 14: (a) Penetration results of EFP with steel liner materials and 120mm diameters in 4D standoff.(b) Penetration results of EFP with copper liner materials and 120mm diameters in 4D standoff4.CONCLUSIONSFollowing conclusious can be drawn from experimental and simulation analysis of EFP penetrating into multi-layer targets: 1. Crater diameters and depths formed by EFP with steel liner are the largest under condition of standoffs lower than 2D, however, when standoffs are greater than 2D, the crater diameters and depths formed by EFP with aluminium liner are the largest.2. The optimal liner material of EFP to achieve a larger penetration hole diameters (D2)

Table 1 :
Experimental results of crater diameter with different liner materials, charge diameters under different standoffs (mm)

Table 2 :
Experimental results of hole diameter with different liner materials, charge diameters under different standoffs (mm)

Table 3 :
Experimental results of crater depth with different liner materials, charge diameters under different standoffs (mm) crater depth formed by EFP with 120mm diameter is larger than 100mm charge's.When the charge diameters are 100mm and 120mm respectively, the corresponding maximum values of crater depths caused by EFP with copper liner are 1.3D and 1.4D.For 100mm and 120mm charge diameters respectively, the maximum values of crater depths caused by EFP with aluminium liner are 1.6D and 1.5D.As shown in Figure7, crater depths formed by EFP with steel liner are the largest under condition of standoffs lower than 2D.When standoffs greater than 2D, crater depths caused by EFP with aluminium liner are the largest.Among different liner materials, crater depths caused by EFP with copper liner are the smallest.

Table 4 :
Experimental results of penetration depth with different liner materials, charge diameters under different standoffs (mm)

Table 5 :
Comparison between numerical and experimental results of penetration depth