Numerical simulation of jet formation and penetration characteristics in multi-point initiation mode

2.1. Numerical simulation model

The shaped charge used in this paper was composed of main charge, liner and shell. The main charge is 40 mm in diameter, 60 mm in height and 40° in cone angle. The main charge was 8701. The liner was made of copper with a wall thickness of 1.6 mm. The shell was 2 mm thick and made of aluminum alloy. The 8-node polyhedral solid element in LS-DYNA software (Solid164) was used in the calculation model. The air domain, explosive and shaped charge structure adopt Euler element, and the shell and charge in cylindrical shell charge used Lagrange mesh. Thus, the model was calculated by fluid structure coupling method. At the same time, a 1/4 model was established to simplify the calculation. Fig. 1 shows the 1/4 finite element model of shaped charge and its components.

Fig. 11/4 finite element model of shaped charge and its components

a) Shell

b) Charge

c) Liner

d) Shaped charge

2.2. Material model and parameters

In order to better simulate the phenomena of liner collapsing, forming and perforating when interact with the shell charge, Johnson-cook material model with failure fracture criterion [4] was selected for liner and shell of charge, which takes into account the strain hardening, strain rate and temperature effect of material.

For von Mises yield stress model, the material yield stress is expressed as follows:

where: ${\stackrel{-}{\epsilon }}^p$ is equivalent plastic strain, ${\dot{\epsilon }}^{\mathrm{*}}$ is relative equivalent plastic strain rate, $T^{*}$ is relative temperature, $A$ is yield stress, $B$ is strain hardening, $n$ is strain hardening index, $C$ is strain rate correlation factor, $m$ is temperature correlation factor.

The expression of the fracture strain is expressed as follows:

where $D$ is the damage to a material element, $\mathrm{\Delta }{\epsilon }_y$is the increment of accumulated plastic strain, and ${\epsilon }_f$is the accumulated plastic strain to failure under the current conditions of stress triaxiality, strain rate and temperature. Failure occurs when $D=$1. Material parameters selected from reference [5].

The explosive of shaped charge was 8701, HIGH_EXPLOSIVE_BURN material model and JWL equation of state were selected, see in reference [3] for specific parameters. The explosive in the shell charge was TNT and ELASTIC_PLASTIC_HYDRO material model and IGNITION_AND_GROWTH_OF_REACTION_IN_HE were selected for the study on shock initiation characteristics. For air, Null material model and LINEAR_POLYNOMIAL equation of state were used. The material parameters were obtained from reference [5].

3.1. Analysis of jet forming process

The typical forming progress of SCJ was shown in Fig. 2. The initiation mode was center point initiation. From the numerical simulation results, it can be seen that at about 10.4 μs after initiation, most of the liner materials have completed the movement to the symmetrical plane. At this time, the jet after collision redistributes the energy. The jet gradually forms at the head, and the pestle body forms at the tail. Due to the velocity difference between the head and tail, the jet was stretched. The final shape of jet formed at about 34.6 μs after initiation, and the velocity of jet head was about 5500 m/s.

Fig. 2Shaped charge jet forming process with center point initiation

a)$t=$0 µs

b)$t=$ 12.6 µs

c)$t=$71 µs

a)$t=$21.2 µs

d)$t=$34.6 µs

Fig. 3 shows the propagation process of detonation front in the case of center point initiation. When $t=$0.2 μs, the spherical detonation front grows steadily and propagates to the unexploded explosive. When $t=$2.2 μs, the spherical detonation wave reaches the top of the liner and starts to impact and squeeze the liner; the element pressure on the top of the liner suddenly jumps to 20.7 GPa. When $t=$ 3.2 μs, the detonation products attached to the detonation wave continue to squeeze the liner, and the detonation wave begins to impact and squeeze the circumferential shell. When $t=$7.6 μs, the peak pressure of the detonation front is 31.6 GPa, and the converged detonation wave moves towards the liner direction. After a series of complex interactions, the new wave system and detonation products will have a new round of impact and extrusion on the liner, and the maximum front pressure is 38.9 GPa.

Fig. 3The propagation process of detonation front of center point initiation

a)$t=$ 0.2 µs

b)$t=$ 2.2 µs

c)$t=$ 3.2 µs

d)$t=$7.6 µs

3.2. Influence of initiation point

Based on the above model, numerical simulation under four initiation modes with 2, 4, 8 and 12 initiation points ($N$) was carried out respectively. The initiation points were distributed in a ring shape and the initiation radius was 20 mm. Fig. 4 shows the propagation state of detonation wave in charge and the pressure distribution on the upper surface of the liner.

When multi-point initiation was adopted, the detonation wave would converge and collide in charge, and the peak pressure on the upper surface of the liner was 23.68 GPa, 26.30 GPa, 26.74 GPa and 25.51 GPa respectively, which were significantly larger than that of single point initiation of 17.13 GPa. The distribution of detonation wave initiated by two points was asymmetric (Fig. 4(d)). With the increase of the number of initiation points, the pressure distribution on the upper surface of the liner was more uniform, which was closer to the effect of ring initiation.

Fig. 4The propagation process of detonation front of multi-point initiation

a)$N=$12

b)$N=$8

c)$N=$4

d)$N=$2

Fig. 5 is the variation of jet tip velocity with initiation point. The initial velocity of jet tip increases with the number of initiation points. Compared with single point initiation, the increment of initial velocity of jet head can reach 980 m/s, and the maximum increase amplitude of jet tip velocity can reach 15.63 %.

Fig. 5The variation of jet tip velocity with initiation point

3.3. Influence of initiation radius

In order to explore the influence of distribution radius of multiple initiation points on jet performance, the circular distribution radius $r$ of eight initiation points was selected, as shown in Fig. 6. The distribution radius $r$ is 4 mm, 8 mm, 12 mm, 16 mm and 20 mm respectively.

By extracting the pressure and impulse data of element (H5601) on the top of liner and drawing the curve in Fig. 7, it shows that the maximum pressure and impulse of element H 5601 are increasing with the increase of initiation radius. We can get enlightenment from the pressure propagation characteristics in Fig. 8.

As shown in the Fig. 8, the detonation wave generated at each initiation point was superimposed for the first time at 0.8 μs, and then gradually converged to the bottom of the charge and the unexploded area under the reflection of the shell; the detonation wave was superimposed at 2.6 μs to form a high pressure area, with an instantaneous high pressure of 119 GPa; as the high pressure superposition area of the initiation ring propagates downward along the central axis and acts on the charge. The top of the liner was then crushed and shaped.

Fig. 6Schematic diagram of initiation point position and pressure nephogram of liner (t= 6 μs)

Fig. 7The variation of maximum pressure and impulse at observation point with r (t= 6 μs)

Fig. 8Peak pressure variation of explosive detonation front under r= 20 mm condition

Fig. 9The change of jet tip velocity and jet length

As the radius of the initiation ring becomes smaller, that is, the initiation point is closer to the central axis, and the detonation wave does not grow sufficiently at the time of the first superposition, the instantaneous high pressure will decrease, and the overall impulse acting on the liner will also decrease. The change of jet tip velocity and jet length recorded in Fig. 9 can well reflect this rule. Theoretically, the bigger the radius of initiation ring is, the better jet state can be obtained.