CHEN Kui(陳奎)，LI Wei-bing(李偉兵)，WANG Xiao-ming(王曉鳴)，LI Wen-bin(李文彬)，CHEN Chuang(陳闖)

(ZNDY of Ministerial Key Laboratory，Nanjing University of Science and Technology，Nanjing 210094，Jiangsu，China)

Introduction

Aiming at different targets on the battlefield，a multimode warhead can form corresponding mode penetrator to attack them efficiently by setting initiation mode，single-point or annular multi-point initiation，and so on.Since the multimode shaped charge warhead has lots of advantages compared with other warhead，so it has a good prospect of application in the field of smart munitions，intelligent weapons，hard structure munitions，top-attack-missiles，etc.Considering the difficulty to implement the annular initiation in reality，the technology of multi-point initiation is increasingly used in the formation of penetrator and paid close attention.JIANG，et al introduced annular multi-point initiation and made EFP formed by central-point initiation converted into jetting penetrator charge(JPC)［1－2］.Bourne，et al studied variable multi-point initiation;they established that，with the increase of number of initiation points，for example exceeding 4，the penetrator form was similar to the result obtained by a traditional annular initiation［3］.But the problem about the matching relationship between the initiation points and charge diameter，as well as the influence of the initiation points on the penetrator formation need to be further studied.

This paper studies the multi-pointinitiation schemes for the shaped charge warhead with arc-cone liner and different charge diameter of 100 mm，200 mm，300 mm and 400 mm numerically by using LSDYNA software，analyzes the effect of number of initiation points on the penetrator formation，finds out the minimum number of initiation points，and obtains a curve equation representing the relation between the number of initiation points and charge diameter by using polynomial fitting.

1 Structure Model and Numerical Simulation Scheme

The structure of the shaped charge is shown in Fig.1.The charge diameterDkcan be taken as 100 mm，200 mm，300 mm and 400 mm respectively，the charge heightHis 0.9Dk，and the liner is designed as an arc-cone，whose curvature radiusRis 0.45Dk，the cone angle 2αis 145°，and the liner thicknessTis 0.038Dk.In order to study the influence of the number of initiation points on the penetrator formation，six initiation schemes are set，i.e.4，6，8，10，12 or 36 initiation points are equally spaced in the surface of the largest annular radius of shaped charge.

Fig.1 Structure of shaped charge

2 Numerical Simulation Results and Analyses

Considering the distortion of grid due to the high strain rate and high overload in the process of penetrator formation，ALE algorithm is adopted in the simulation for the explosive，liner and air，while Lagrange algorithm is used for the shell，and the fluid-solid coupling algorithm is used for their interaction［4］.In the simulation，the material parameters and calculation model of all parts are shown in Tab.1.

Tab.1 Material parameters and calculation model

The formation conditions of penetrator in each initiation scheme are obtained by numerical simulation.For comparison，the penetrator formation condition at the stand-off distance of 3 times of charge diameter is selected，and the penetrator formation parameters in four different charge diameters are listed in Tab.2.In the table，L，L/d，v1，v2andv'represent the penetrator length，length-diameter ratio，tip velocity，tail velocity and velocity decline，respectively.

Analyzing these parameters in each initiation scheme，it can be seen that JPC lengthL，length-diameter ratioL/d，tip velocityv1and velocity gradientv'all increase with the number of initiation points，as shown in Fig.2，and，when the number of initiation points changes from 12 to 36，JPC length changes a little for 4 charge diameters.The changes of formation parameters are shown in Tab.3.

Fig.2 Formation parameters of penetrator vs.number of initiation point in different schemes at standoff distances of 3 Dk

Table 3 shows that，comparing with annular initiation scheme，JPC parameters only increase little，all less than 5%，when the minimum numbers of initiation points are taken for four typical charge diameter.But，comparing with the case of 10 initiation points for 300 mm charge diameter，the scheme of 8 initiation points has a larger parameter change，and the scheme of 9 initiation points is the best，because its JPC length，length-diameter ratio，tip velocity，tail velocity and velocity gradient are only changed 2.81%，2.18%，2.20%，1.95% and 4.00%，therefore，9 can be taken as the minimum number of initiation points for the charge diameter of 300 mm.

Tab.3 Changes of formation parameters

3 Effect of Detonation Wave on Liner in Multi-point Synchronization Initiation

The action of detonation wave on the liner and the liner collapse are analyzed numerically.In Tab.4，the deep-colored area on top of the liner represents the maximum detonation pressure area.The detonation pressure acting on the liner varies with the increase of number of initiation points.

From Tab.4，it can be observed that the configuration of detonation waves formed by shaped charge of 100 mm in diameter is significantly different from the others on the liner，it is superimposed，and take up a larger area in the whole detonation region;while the other three shaped charges form almost the same detonation waves in the same initiation scheme.Compared the waves formed by four shaped charges in each initiation scheme，it is obvious that the configurations of the detonation waves formed in the scheme of 4 initiation points have great difference，while the wave configurations in other schemes are different a little bit only.

The maximum detonation pressures acting on the liner for different shaped charges are shown in Fig.3.With the increase of number of initiation points，the pressure increases rapidly first，then gradually.Though the detonation pressure formed in 8-point initiation scheme is slightly larger than that in 10-point scheme in Fig.3(a)and 3(c)，it is caused by the calculation method and has a little effect on the overall trend;therefore，it can be ignored.For different charge diameter，the number of initiation points to make the detonation pressure tend to smooth is not the same points.It is 6 in Fig.3(a)，8 in(b)，8 to 10 in (c)，taken as 9，and 10 in(d).When the number of initiation points is selected as above，compared with the annular 36-point initiation，the detonation pressures only increase by 2.3%，2.6%，2.2%and 1.9%for 4 kinds of shaped charges.Thus，it can be found that the minimum number of initiation points to substitute for annular initiation is 6，8，9 and 10，respectively.

Tab.4 Detonation waves propagating to liner in different initiation schemes

Fig.3 Detonation pressure vs.number of initiation points in different charge diameters

According to the detonation wave theory，each initiation point produces a single spherical wave;the waves from all initiation points spread at the same velocity，and they will interact with each other.Since the elements of liner with the same radical size are impacted by the detonation pressure，and the detonation waves deformed in each initiation program reaching to the liner are in different times，so the elements of liner with different speeds.With the increase of number of initiation points，the distance between any two initiation points and the time that the detonation waves interact with each other becomes shorter，also the interaction area is thicker，resulting in the maximal detonation pressure acting on the liner changes a little.

The minimum number of initiation points to substitute for annular initiation is shown in Fig.4，and the polynomial fitting curve equation can be written as

Fig.4 Change of n with Dk

wherenis the minimum number of initiation points，whileDkis the charge diameter of shaped charge，in mm.

4 Experiment Validation

An X-ray imaging experiment was carried out for the shaped charge of 100 mm in diameter［5］.The center initiation can form the mode of EFP，and the 6-point initiation forms JPC.Comparing the results of the simulation and experiment，as shown in Tab.5，the experiment data is better in agreement with the simulation.It shows that the material parameters and calculation model used in the simulation are appropriate and the conclusion of the simulation is credible.In the table，v1is the tip velocity of penetrator，v2is the tail velocity，Lis the length，andL/dis the length-diameter ratio.

Tab.5 Comparison of simulation and experiment results

5 Conclusions

1)The influence of the number of initiation points on penetrator parameters in 4－，6－，8－，10－，12－and 36－point initiation schemes is studied numerically，and it is found that the minimum number of initiation points to substitute for the traditional peripheral initiation is 6，8，9 and 10，respectively，for four kinds of charge diameter.

2)The maximum detonation pressures acting on the liner in different schemes are analyzed.It is found that the configuration of the detonation wave formed in 4-point initiation scheme differs with those in other schemes greatly，and the waves formed in other schemes have almost the same configuration.It is also found that the minimum number of initiation points to substitute for annular initiation is also 6，8，9 and 10，respectively，for four kinds of charge diameter.

3)The polynomial fitting curve representing the relation between the minimum number of initiation points and the charge diameter is obtained.It can be as a reference for the optimized design of multimode warhead in the future.

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