Effect of initiation manners on the scattering characteristics of semi-preformed fragment warhead

Xu-yang Wang,Xiang-shao Kong,*,Cheng Zheng,Wei-guo Wu

aKey Laboratory of High Performance Ship Technology(Wuhan University of Technology),Ministry of Education,Wuhan 430063,PR China

bDepartments of Naval Architecture,Ocean and Structural Engineering,School of Transportation,Wuhan University of Technology,Wuhan 430063,PR China

Keywords:Initiation manners Semi-preformed fragment warhead Deformation pattern

ABSTRACT The lethality of a semi-preformed fragment warhead is closely related to the expand velocity and spatial distribution of the fragments from ruptured metal casing.The topic of how to improve the utilization of charge of have been drawing great attention from researchers and designer in this filed.In present paper,in order to investigate the influence of charge initiation manners on the scattering characteristics of semi-preformed fragment warhead,the numerical simulations and experimental test are conducted.Firstly,the influence of grid density on numerical results is investigated,and a proper numerical model with relatively high accuracy and effectiveness is determined.Then,numerical simulations of three kinds of different initiation position of a semi-preformed fragment warhead are carried out.An experimental test of the explosion of a semi-preformed fragment warhead is carried out.By comparing and analyzing the numerical results and experimental data,it is found that the initiation manners have great influence on scattering characteristics of semi-preformed fragment warhead.The researcher work of this paper would provide an effective alternative method to optimize the design of warhead.

1.Introduction

The pre-controlled technology of fragments refers to controlling the size of fragments formed by the breaking of warhead with specific measures,which can enhance the lethality of warhead.The pre-controlled technology of fragmentation of cased charge is an important issue in the field of ammunition engineering and the design of protective structure.Great efforts have been made by scholars to study the scattering characteristics of preformed and semi-preformed fragments warhead from different aspects.With regard to the study of preformed fragments,many scholars have done plenty of work in theory,numerical simulation and test,while the research on semi-preformed fragments is rare[1].

In order to get the scattering method of pre-formed fragments,Li et al.[2]investigated the expanding and fragments crushing process of a HE shell by employing the explicit code ANSYS/LSDYNA.The initial velocity and scattering direction angle of fragments along case is determined.The gained results were basically in accord with the statistical results of recovery fragments in crushing experiments and empirical formula and consequently illustrate the accuracy of model simplification and calculation parameters.Peng et al.[3]used AUTODYN to simulate the fragment formation of semi-preformed fragment warhead,which external shell groove has different groove depth and width parameters,was carried out.After comparing and analyzing the simulation results,the effect rules of groove depth and width on the effective formation rate of semi-preformed fragment,average speed of semipreformed and mass loss were found out,thus the suitable groove width and depth were determined.In order to investigate the effect of groove parameters on the formation of semipreformed fragments,a numerical simulation of the fragmentation process of 50SiMnVB steel warhead was conducted by Liu et al.[4].The effect of different groove-parameters on casing-fracture was compared and analyzed.Besides,a method to determine the fracture trace and fracture probability of external grooved casing were proposed and verified by comparing with experimental results.

At present,researches mainly focus on the failure mechanism of the metal casing,the average velocity of the fragments and the influence of groove parameters on the scattering characteristics.There are few studies aiming to investigate the influence of different initiation manners on the fragmentation characteristic of a semi-preformed case.In this paper,by employing AUTODYN-3D,the three-dimensional numerical simulation of expanding and subsequent fragmentation process of a semi-preformed warhead is studied,the propagation of detonation wave in the dense charge and the velocity distribution of fragments are obtained under different initiation manners.Additionally,an experiment with the same explosive fragmentation geometry as modeled in the numerical simulation is conducted.The experimental data and theoretical data are compared with the numerical results,based on which the conclusions of present paper are drawn.

2.Numerical simulations

2.1.Numerical model

The warhead that used in numerical simulations in this paper is a cylindrical metal casing filled with TNTcharge,which is fabricated from steel#45.The internal diameter,the length and the wall thickness of the cylindrical casing is 50.5mm,130.4mm,and 6mm,respectively.Along both the length and circumference directions of the metalcasing 8 equal split grooves,whose depthis 3mm and the width is 2mm to control the size of semi-preformed fragments,are machined.It is estimated that the number of fragments from the case is 64.The mass of metal casing is 948.6 g,with a 400 g TNT charge filled inside it.

The numerical model is developed by employing the finite difference-engineering package AUTODYN,which is particularly suitable for the nonlinear dynamic problems,such as impact or explosion.The symmetry of the problem under consideration allows modeling one eighth of the whole metal casing and TNT charge,as shown in Fig.1.In order to reproduce the explosive fragmentation process,in which the casing material is plastically deformed and eventually ruptured by the driven load from the expansion of the inner charge,the Euler-Lagrangian method is adopted to model the phenomenon of explosively driven fragmentation.

The air is modeled with Euler grid.The size of grid is 100mm×100mm×100mm.The Euler method is ideally suited to handling large deformations and fluid flow,which has a good description of the formation,propagation and action process of shock wave.The metal casing is discrete with Lagrange grid and the size of the cubic grid is 0.5 mm.The Lagrange algorithm can cause a large distortion of the structural grid,but it has a clear description of the whole and local evolution process of the structure,which can truly present the whole process of the expansion of the metal casing,the crack expansion and the formation of fragments.

The rapid pressurization leads to the large deformations and eventual rupture of the metal casing at high strain rates.The Johnson-Cook constitutive relation[5]and the Gruneisen equation of state are selected to model the material behavior of the metal casing.

whereσYis the dynamic yield stress of the material.A,B,C,n and m are Johnson-Cook material constants,˙ε*=˙εp/˙ε0represents the effective plastic strain rate at a reference strain rate˙ε0=1s-1and the homologous temperature T*m= （T-Tr）/（Tm-Tr）,in which T is the material temperature,Tris the room temperature,and Tmis the melting temperature of material.

The material parameters used in the simulation are listed in Table 1.The failure mode should be defined in the AUTODYN to provide a suitable failure criterion for the casing material.In this study,the principal strain failure model and stochastic failure model based on the Mott[6]distribution is used to simulate the formation of natural fragments.

The JWL(Jones-Wilkins-Lee)equation of state is employed to describe the adiabatic expansion of the detonation products,which represents the pressure as a function of the volume and energy:

where A,B,R1,R2and w are constants of the TNT charge.P,v and e0are the detonation pressure,relative volume and specific internal energy,respectively.

The material parameters and properties used for the JWL equation are shown in Table 2.The ideal gas equation of state is selected to model the material behavior of the air.

2.2.The influence of grid density on the results

The major influence factor of the numerical results is the relative size of the computational model grid units(the ratio between the air domain size and the air domain grid),rather than the absolute mesh size of the model[7].By changing the mesh size of the air domain,we can change the model grid density.In this section,the grids of the air domain are set as 4mm,3 mm,2 mm,1.5 mm,1 mm,and 0.5 mm,respectively.The corresponding grid density of the model is 25,33,50,67,100 and 200,respectively.

Fig.2 shows the relation between the maximum velocity at the corresponding gauge point and the different grid density in the model.It is clearly shown that with the increase of grid density the maximum velocity of gauge point is increasing.However,the relation curve is tend to convergence when the mesh density is greater than 100.On the other hand,when the mesh density is greater than 100,the grid number and the computational cost increases rapidly.Therefore,under the premise of ensuring the numerical results to meet the actual demand precision,it is very important to select the appropriate grid density,which can avoid the excessive grid density and cause the unprovoked waste of computing resources.From the above analysis,the grid density of 100 is used in the numerical model.

Table 1 Material parameters of the metal casing.

Table 2 Material parameters used in the simulation for the TNT.

3.Numerical simulation results and analysis

3.1.The influence of different initiation position on detonation wave propagation

In the numerical simulations,three kinds of different conditions are considered,among which the initiation points of TNTcharge are altered.(1)Center point initiation,(2)symmetrical point initiation at 1/4 and 3/4 position,(3)symmetrical point initiation at top and bottom end,which are shown in Figs.3-5,respectively.The different position of the initiation point have influence on the propagation way of detonation wave and the subsequent pressure that exerted on the inner wall of the casing,resulting in divergence in the fragment velocities and scattering direction among different cases,as shown in Figs.3-5.When the explosive is initiated,the detonation wave travels outward in a semi-spherical or spherical form,and the interface between the reactive explosive and the unreactive explosive forms an obvious peak of detonation pressure.The initial wave reaches the cylindrical wall of the casing at t=4.0μs,and then is reflected by the metal casing.The reflected wave and the subsequent wave interact on the inner wall of the casing and produces a high-pressure region.The pressure of this area is much higher than the yield strength of the metal casing and drives the cylindrical casing deforms outward and eventually rupture.

In the conditions of symmetrical point initiation,with the further propagation of the detonation waves along the length direction of the cylindrical metal casing,the detonation waves are reflected and then converged at the center area of the casing.A local high-pressure region.With the decreasing of the symmetry detonation point distance,the weaker the detonation wave superposition is,and the phenomenon of the Mach reflection emerged.With the further development of the detonation wave,the volume of detonation products expands continuously,and the intensity of the subsequent reflected wave decreases dramatically.According to Figs.3(d)-5(d),when the initiation point is more close to the end of the metal casing,the higher detonation pressure at this region can lead to the more rapid expansion of the metal casing,companying the leakage of detonation products from the broken casing.Therefore,the closer the detonation point is to the end,the less time it takes for the pressure inside the casing to reach a uniform condition[8].

3.2.The influence of initiation manner on the velocities of fragments

Under the load from internal detonation pressure,radial expansion occurs firstly at the metal casing near the detonation point in all three modes.It can be seen from Figs.3-5 that the expansion velocity of the middle part of the metal casing reaches its maximum value when the initiation point located at the central point.The expand velocities gradually decreases along the length direction.It appears a “shuttle”shape of the broken casing.The deformation pattern of the metal casing is closely related to the location of the initiation.When the initiation point is symmetrical at top and bottom end,the expanded metal casing shows a “vase”shape.For the detonation waves converge at the center are of the casing,the expansion speed at the center part of the casing is faster than the other area.

Under the three different ways of initiation,the shell of the casing is prone to stress concentration in the groove area due to sharp abrupt change.Cracks firstly occurred in the groove area.The existing of velocity gradient in different area of the metal casing along its length direction leads to the rupture of the metal casing from the grooves area continuously.As shown in Fig.6,it can be clearly seen that under the three different ways of initiation,the metal casing all forms 64 preformed fragments with similar size along the groove,and reach the purpose of forming semipreformed fragments.

The axial distribution of the initial velocity of the semipreformed part fragments that formed in the three different initiation modes is investigated by comparing with the end face at the bottom as the datum.As shown in Fig.7,with the increasing of height,the fragments velocity increases firstly and then decreases.The velocity of preformed fragments reaches the maximum value in the center area.When the detonation point is closer to the end face of the metal casing,the superposition effect of the detonation wave in the middle part of warhead is stronger,resulting in the higher velocity of the fragments in this region.

The maximum velocity(vmax)and average velocity(vave)of semi-preformed part fragments under different ways of detonation are shown in Table 3.Compared with the initiation at the center point,the maximum and average velocity of the fragments increased by 3.77%and 1.75%respectively when the symmetrical point initiation at 1/4 and 3/4 height.While the maximum and average velocity of the fragments are increased by 10.72%and 1.10%respectively when the symmetrical point initiation at top and bottom end.It is seems that when the detonation point is closer to the end of the metal casing,the velocity of fragments is tend to higher.However,the average velocity of the fragments has not changed much.

4.Experimental test

4.1.The average speed of fragments

The detonation-driven expansion and fragmentation of the metal cylindrical casing is a complex transient nonlinear dynamic problem involving detonation of the explosive,propagation of shock waves,and rupture of the metal cylinder.The classical model used to calculate the ultimate velocity of fragments was proposed by Gurney in 1943[9].Considering the difference exists in the semi-preformed fragments and the natural fragments,the energy utilization coefficient S is introduced by the researchers based on the numerical simulations and experimental studies[10,11].The revised expression of the Gurney formula is as follows,

where vfis the fragment velocity.EGis Gurney energy in the limit of in finite expansion[12].C and M are mass of TNT and metal casing,respectively.R and L are radius and length of the internal size of the metal casing respectively.If fragments are the preformed fragments or semi-preformed fragments,S=0.75.For the natural fragments,S=1.

where D is the detonation velocity of TNT.γ=3 is the polytropic gamma of the detonation products.σyis yield stress of the metal casing.P0is detonation pressure,P0=PCJ（ρ0/ρCJ）γ,PCJ= ρ0D2/（γ+1）, ρCJ= （γ+1）ρ0/γ,where PCJand ρCJare the pressure and density of the detonation products in the Chapman-Jouguet state,andρ0is the density of the unexploded TNT charge.

For TNT charge,the velocity of explosion is D=6880 m/s and P0=1580kg/m3[13].The yield stress of metal casingσy=355MPa.The average velocity of the semi-preformed fragments can be obtained by Eq.(3).

By comparing the results from numerical simulation and the average speed calculated by modified Gurney formula,it is found that the error of fragments average speed are 5.49%,3.84%and 4.47%respectively under three different ways of detonation.

4.2.The maximum velocity of fragments

According to the numerical results,the case of initiating at both end of the preformed warhead is selected as the target of the experimental test.In the test,the structure of the metal casing,the TNT charge and initiating position are the same with the conditions that used in the numerical simulation.The solid metal casing of experimental model is shown in Fig.8.

As shown in Fig.9,detonators are arranged at both ends of the TNT explosive,and it is detonated at both ends simultaneously to ensure the symmetry distribution of fragments along its height direction.In order to measure the speed of the fragments,two target nets are arranged on the periphery of the metal casing,as shown in Fig.10.When the fragments fly to the target network areas and interrupt the connection lines,the velocity of fragments can be obtained by measuring the signal time difference of front and back target networks,that is,the velocity measured by the target networks is the maximum fragment speed.In the experimental test,the velocity obtained by the measuring device is vf=1428.6m/s.

According to the measuring principle of the velocity test device,the obtained fragment velocity is the maximum value.The whole process of fragmentation of the semi-preformed warhead is clearly presented in the numerical simulation.A very interesting phenomenon shows that the fragment with highest velocity is not the semi-preformed part,but is the fragment formed from the part located under the groove,as shown in Fig.11.The maximum value of fragment that obtained in the numerical simulation is vf=1480.6m/s.Therefore,the maximum velocity error of the fragment in the test and the numerical simulation is 3.64%.A part of the fragments from metal casing is collected after explosion,as shown in Fig.12,The size and mass of most fragments is close to eachother.It is evident that the metal casing is ruptured from the grooves.

Table 3 The comparison of semi-preformed part fragments velocity under three different ways of initiation.

5.Conclusions

For the semi-preformed fragment warhead,the influence of grid density on numerical results is firstly carried out,and then the effectiveness of numerical simulation is verified.On this basis,the influence of different ways of initiation on the propagation of detonation wave and the velocity of fragments is compared and analyzed by conducting numerical simulations.Conclusions of the present paper are listed as follow.

(1)Under the premise of ensuring the numerical results to meet the actual demand precision,it is very important to select the appropriate grid density,which can avoid the excessive grid density and cause the unprovoked waste of computing resources.It is evident that the numerical imitation result of the cylindrical metal casing filled with TNT charge in this paper is already converge when the grid density of model is 100.

(2)The position of charge initiation point has great influence on the fragment velocity and scattering direction.When the charge is initiated at both end simultaneously(the third condition),the maximum velocity of the semi-preformed fragment is increased dramatically.For the detonation wave from different initiation points in the charge would interact with each other and then would be strengthened due to superposition effect at the central part of the metal casing.

(3)By comparing with the value of average speed calculated by modified Gurney formula with the results from numerical simulations,it is found that the error of fragments average speed is not more that 5.5%under three different detonation conditions.The maximum velocity error of the fragments in the test and the numerical simulation is 3.64%when the case of initiating at both end of the preformed warhead.

Acknowledgments

The paper is supported by the Joint Foundation project for Young Scientists of Ministry of Education(6141A02033108)and National Natural Science Foundation of China(11502180).