Jia-yun Liu,Yong-xiang Dong,Xuan-yi An,Ping Ye,Qi-tian Sun,Qian Gao

State Key Laboratory of Explosion Science and Technology,Beijing Institute of Technology,Beijing,100081,China

Keywords:Reaction degree Explosive protection Compound structure Comprehensive experiment

ABSTRACT The explosive reaction degree and protection from explosions are concerns in the military field.In this work,the reaction degree of the composition B explosive was investigated experimentally.Multi-layered compound structures were used as barriers to weaken the blast loads.A comprehensive experiment using a high-speed camera and image processing techniques,side witness plates,and bottom witness plates was presented.Using the experimental fragment velocities,fragment piercing patterns,and damage characteristics,the reaction degree of the explosive impeded by different multi-layered compound structures could be precisely differentiated.Reaction parameters of the explosive obstructed by compound structures were obtained by theoretical analysis and numerical simulations.Unlike the common method in which the explosive reaction degree is only distinguished based on the initial pressure amplitude transmitted into the explosive,a following shock wave reflected from the side steel casing was also considered.Different detonation growth paths in the explosive formed.Therefore,all these shock wave propagation characteristics must be considered to analyze the explosive response impeded by compound structures.?2020 The Authors.Production and hosting by Elsevier B.V.on behalf of China Ordnance Society.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

1.Introduction

A conventional warhead typically requires an explosive charge detonation completely inside the steel casing.Recently,some warheads with novel structures were proposed to achieve controllable output using non-detonable layer structures in the explosive charges[1-3].Furthermore,the reaction degree of the composition B explosive caused by different shockwave impacts is crucial in areas such as warhead design,hazard assessment,storage of munitions,and safety and lethality considerations[4-6].A high explosive detonation loading-structure that consists of inert materials for protection in which the unreacted high explosive is protected is common in many fields,e.g.,the design of explosive confinements to avoid sympathetic detonation[7,8],the use of a single inert plate to attenuate the shock pressure in tests of high explosive shock sensitivity[9,10],the study of the detonation behaviors of double reactive cassettes[11],and the design of new warhead concepts to achieve controllable power outputs[1-3].Thus,understanding the output levels of the composition B explosive subjected to explosive effects with multi-layered compound structure protection is of interest.

It has been reported that the chance of sympathetic detonation can be reduced by using a high-impedance single-layer material as a confinement between the detonation explosive and unreacted explosive[7].Single layer structure material design guidelines for explosive confinements were outlined based on the elastic impedance of a candidate material using one-dimensional analysis and by calculating the pressure amplitude transmitted into the protected explosive.To handle shock wave resistance and attenuation,the structure type has developed from single panels to multilayered compound structures,which are used to improve the impact resistance by providing higher energy dissipation with less area density[12].

It is important for the designer to differentiate the same explosive with different output levels,especially in incomplete detonation applications,such as in novel warhead structure design or to find an efficient structure in a limited space to achieve maximum protection for the protected explosive.However,experiments that exclusively investigate the composition B explosive at a relative low output level have rarely been conducted.It is necessary to investigate the reaction degree of the explosive protected by different multi-layered compound structure subjected to detonation loading.

Fig.1.Details of the structures.

In this study,a series of experiments were carried out to differentiate the reaction degree of composition B subjected to attenuated detonation loading using multi-layered compound structures.The reaction degree of the protected explosive was tested in various ways:combining high-speed photography with a side witness plate to analyze fragment properties,measuring the fragment speeds via a speed test system,and characterizing the damage on side and bottom witness plates.The shock wave pressure amplitude transmitted into the protected explosive was studied theoretically and numerically.The numerical simulation for the pressure attenuation and transition was developed.The current findings can pave the way for further studies on the reaction degree of explosives and the structure design for explosive protection.

Fig.2.Experiment layout.

Fig.3.First group of fragments for specimen 1 and speed test method.

Fig.4.Second group of fragments at 866.45 and 1732.91μs for specimen 1.

2.Experimental setup

2.1.Multi-layered compound structures

Multi-layered compound structures were designed to contain a high-strength material layer to stop the detonation products and prevent other layers from being destroyed directly,to contain a porous material to improve the shock wave attenuation and energy absorption capability,and to contain an intermediate-impedance material to strengthen the structure and reduce the area density.The multi-layered compound structures were placed in a cylindrical steel casing.One side next to the multi-layered compound structure contained the explosive for normal detonation,which was initiated by the primary explosive column 8701 and a detonator.The other side contained the composition B explosive to be protected.Four specimens were designed and tested,as shown in Fig.1,all the units in this figure were millimeter.

Table 1Fragments speed results in each specimen.

Fig.5.Side witness plate after perforation with the small patterns removed.

The total thickness of the multi-layered compound structures was calculated through an empirical equation based on experimental results as follows[13]:

whereρACis the density of the detonation explosive,dACis the diameter of the detonation explosive,HACis the height of the detonation explosive,and d0,K1,K2are constants[13].This equation is applied for a single layer structure and explosive detonations without an outside steel casing to calculate the minimum thickness of the material layer to prevent the protected explosive from being initiated(for a cylindrical charge).Assuming that there is an equivalent conversion relationship between these materials,a rough estimate for a definite structure of the detonation explosive can be acquired.Since the situation of interest is different because of the outside steel casing,two total structure thicknesses were designed.The calculated results(for a 15 mm thickness)were used to explore the effect of the multi-layer structure with double thickness(30 mm)to ensure the protected explosive can be prevented from reacting dramatically.

Fig.6.Number of piercing holes to compare the outputs of the protected explosive.

The following materials were considered in this study.The detonation and protected explosives were composition B.This explosive has a density of 1.70 g/cm3,a detonation velocity of 8480 m/s,and a Chapman-Jouguet energy per unit volume of 1.51×107 kJ/m3.The primary explosive column,which was constructed of 8701[14],was a cylinder with a diameter of 15 mm and a height of 15 mm.AISI 1045 steel(45#steel)was used as the metal casing.The AISI 1045 steel density was 7.85 g/cm3,its elastic modulus was 210 GPa,its Poisson’s ratio was 0.3,its yield strength was 345 MPa,its tensile strength was 450 MPa-685 MPa,and its failure strain was 18%.Four materials were used to construct the multi-layer structure:2024 Al(density of 2.78 g/cm3),AISI 1045 steel,polyurethane foam(density of 80 kg/m3),and isostatic graphite(density of 1.91 g/cm3).All of these materials were fabricated from a commercially available source.

2.2.Experimental method

The experimental test setup consisted of four regimes that were used to evaluate the different reaction degrees of the composition B explosive from different aspects,and the experiment layout is shown in Fig.2.The velocities of the fragments formed from the steel casing were measured with two velocity measurement targets.It was assumed that the velocities of the fragments did not decrease before reaching the target.The velocity measurement target was made of wood board(～1.5 mm thick)and copper wire(～0.13 mm in diameter),so the slowing down of the fragments during penetration of the two plates were not significant.The distance of the two velocity measurement targets was 22 cm.The first velocity measurement target was placed 1.5 m from the specimen.

The side witness plate was used to determine the piercing pattern formed by the fragments.The middle of the plate faced the casing vertically,and the distance was 0.8 m.Fragments traveling at an angle of 60°impacted the plate,and the size of the side plate was 900 mm×900 mm×1 mm.

A high speed camera was used to record the images during detonation.The bottom witness plates which were constructed of LY-12Al and Q235 steel were stacked together on a support base.The support base had a space for the deformation of the bottom witness plates,and it was constructed of Q235 steel,as shown in Fig.2(b).The bottom witness plates’sizes were the same:170 mm×170 mm×5 mm.The height of the specimen to the ground was 700 mm.

Four tests were carried out for the specimens shown in Section 2.1.For comparison,the testing conditions were the same in each test.After each test,the side and bottom witness plates were obtained.

3.Experimental results

3.1.Fragment speed characterization

Fig.3(a)shows that fragments appeared after detonation at 182.41,228.01 and 273.61μs,as recorded by high-speed camera.In the present work,the high-pass filter was used to make the fragments more obvious comparing to the black background as shown in Fig.3(b),and the median filter was used to reduce noise as shown in Fig.3(c).Finally,the fragments at different moments were converted into different colors as shown in Fig.3(d).Clear fragment propagation trajectories were obtained.The fragments propagated along a straight line,so photographs from three different times were included in one image(the red,green and blue points represent data from 182.41,228.01 and 273.61μs,respectively).After calibrating the camera,the fragment speeds were measured,as shown by the dashed line in Fig.3(d).Taking multiple measurements and using the average value as the results,the maximum speed of these fragments for specimen 1 was 1804 m/s,and the maximum difference of the speed test results was 25 m/s.The fragments that were observed during this time were called the first group of fragments.

Fig.4 shows the fragments that appeared after detonation at 866.45μs for specimen 1.Most of the first group of fragments impacted the side witness plate,whereas the other slower and larger fragments were observed using the high-speed camera;these fragments were called the second group of fragments.The fragment size of the second group were relatively large and easily distinguished in the image.Taking multiple measurements and using average value as the results,the maximum speed of the second group of fragments for specimen 1 was 1091 m/s,and the maximum speed difference of the second grope of fragments was 32 m/s.

Two groups of fragments could be distinguished by speed and shape using the high-speed camera.A speed test system was also used in this experiment.Table 1 lists the results for each specimen from the two test methods.

Fig.7.Photographs of bottom witness plate after protected explosive impact.

Fig.8.Graphical illustration of initial parameter determination.

Since the speed test system could only record one maximum speed in a limited area,this method could only be used for verification in this experiment.The fragment speed test results showed that the speed of the second group of fragments yielded a different reaction degree of the protected explosive.The order of the reaction degree of the specimens with composition B were as follows:specimen 3＞specimen 1＞specimen 2＞specimen 4,and the protection efficiency of the multi-layered compound structures subjected to the explosive effects were in the opposite order.

Fig.9.Finite element specimen and calculating results.(a)Lagrangian model.(b)Experimental[17]and numerical simulation results for AISI 1045 steel.

Table 2JWL coefficients for TNT.

3.2.Side witness plate damage characterization

Fig.4 shows the perforation characteristics of the side witness plate formed by two groups of fragments.Because the perforation characteristics on the side witness plate were formed by two groups of fragments,we could match the different pattern characteristics to the two groups by combining the relative positions of the high-speed photography bright spots and the recovered side witness plate holes.The bright spots corresponding to the interactions of the first group of fragments with the target plate were weak,and the perforations of the corresponding position of the side witness plates were small and shallow.The second group of fragments created strong bright spots when interacting with the target plate and formed larger holes at the positions of the bright spot.

After calibration and calculation,holes pierced by the fragments whose area larger than 2 mm2were considered.The hole size was not taken into account for comparisons when comparing the number of the penetration holes,and the median filter can ignore the small penetration holes.This is because the formation of natural fragments is random and the size of the holes in side witness plate cannot reflect the real size of the fragments due to the oblique impact of the fragments.By calculating the parameter value(in the‘median_filter’function in MATLAB)in one working condition,we can get an acceptable result that could ignore the black area smaller than the definite value,as shown in Fig.5(a).Then we used the same parameter value to process the other working condition results.The results are shown in Fig.5.

Fig.10.2D Lagrangian model for multi-layered compound structure.

By comparing the number of penetration holes in the simplified pattern in Fig.5,the reaction degrees of the protected explosives were obtained,as shown in Fig.6.It was assumed that more piercing fragments produced by the casing corresponded to a larger output of the protected explosive.The number of penetration holes in specimen 4 is much smaller than other three working conditions.The hole number of specimens 1 and 3 were comparable,and both of them were larger than that of specimen 2.The results were consistent with the fragment speed test results.Since the formation of natural fragments is random,and the side witness plate can only interact with a part of fragment fields,the number of the piercing holes can be used as an auxiliary judgment indicator.

Fig.11.Time histories of burn fraction for different specimens.

3.3.Bottom witness plate damage characterization

Fig.7 shows the bottom witness plate damage characterization of specimens 1,2,3,and 4.The first layers of specimens 1,2,and 3 were totally penetrated.The areas surrounding the holes were flat,indicating that they were pierced rapidly.The second layers for the three specimens showed large deformations and perforations.For specimens 1 and 3,the number of cracks and the deformation degree were easily distinguished.For specimen 4,the first and second layers of the bottom witness plate only showed deformation,and no perforation occurred.

Because the holes of the first layer of the bottom witness had almost the same diameter in specimens 1-3,the second layer bottom witness plates were used to obtain a qualitative comparison.Specimen 3 had a greater number and larger cracks around the holes than specimen 1.Specimens 1 and 2 were not significantly different in appearance.The protected explosive output level ranking was as follows:specimen 3＞specimen 1≈specimen 2＞specimen 4,and the protection capability order of specimens 1,3,and 4 were consistent with the previous results.

4.Theoretical analysis and numerical simulation

4.1.Detonation loading and shockwave propagation mechanisms

Three processes can determine the pressure amplitude transmitted into the protected explosive.First,the detonation pressure is produced by the first layer explosive and transmitted into the first layer of the multi-layered compound structures.Second,a shock wave propagates through the solid material.Third,the shock wave transmits to another layer material and reflects back to itself.When it encounters another layer,this process repeats.

For the first process,conducting a one-dimensional analysis,the conservation of momentum equation for the shock wave propagation is as follows:

where the USis the velocity of propagation of the shock wave.Ahead of the shock front,the pressure is P0,the density isρ0,and the particles velocity is U0.Behind it,the pressure is P,the density is ρ,and the particle velocity is UP.

The following equation is used to relate USand UP,

where the data for the constants C0and S1data are available for many solid materials[14].A relation between P and UPin the solid metal material,such as for AISI 1045 steel(the green line),can be acquired,as shown in Fig.8.

The equation for the conservation of mass,momentum,and the energy was combined with the Chapman-Jouguet condition and the equation of state(the polytropic gas law was used in this study)for the detonation products to fully describe the detonation process[15].Steel’s mechanical impedance is higher than those of the explosive products,and thus,the shock wave will reflect back to the detonation products.The relation between P and UPfor the detonation products is as follows:

where the UDis detonation speed,which was previously tested for different explosives[15],κis the polytropic gas constant,ρ01is the density of the explosive,and Pjcan be calculated as follows:

Fig.8 shows plots of Eq.(4)for TNT(the orange line)and composition B(Comp.B)(the blue line)in the detonation products.Since the pressure and the velocity at the interface of the two materials should be equal,the intersection of two P-UPloci denotes the initial parameters,as shown in Fig.8.The intersection point coordinates are(1.056,46.290)and(0.778,30.886).

For the second process,the shock wave attenuation in the solid material is determined by the type of explosive,the distance that the shockwave has traveled through the material,and the material in which the shockwave is traveling[15].It is difficult to obtain an analytical solution for the shock attenuation in solid materials.However,many experiments have been conducted.In this study,the finite element method was used to calculate the pressure attenuation,and the correlation between the numerical calculations and experimental results was satisfactory over a short distance(0-10 mm).This is shown in Section 4.2.

For the third process,the best way to treat the transfer of the wave from one medium to another is to use the impedance matching technique[15].This method can provide the right relation while the shock wave transmits through the interface of the two materials.The shock wave transmits from the higher impedance material to the lower impedance materials,and thus,the shock pressure amplitude diminishes in the lower impedance material.Since we considered shock wave attenuation,the value must be determined using the numerical simulation.

4.2.Numerical simulation and analysis

To explore the reaction degree of the protected explosive in the experiment and the characteristics of shock wave transmission,numerical simulations were performed.The numerical simulation software used in this study was AUTODYN[16].The detonation interacted with the solid material,and the shockwave attenuation characteristics in a single layer material were first studied.AUTODYN 2D was subsequently used to reproduce the reacting grade and the pressure characteristic transmitted into the protected explosive under the experimental conditions.

4.2.1.Pressure characteristic in single layer material.Based on experimental studies of shockwave attenuation in solid materials[17-20],the pressure characteristics in a single layer material subjected to detonation loading were studied.The structural parameters used in the simulation were consistent with their impact tests results[17,18].

The TNT explosive used in a previous experimental study[17]was a cylinder with a density of 1.56 g/cm3,diameter of 40 mm,and a height of 50 mm.The single layer of AISI 1045 steel was also a cylinder in contact with the TNT with a diameter of 70 mm and height of 50 mm.For the numerical approach,procedure of the simulations was considered[24].The TNT and single layer steel plate were modeled as a solid mesh of about 20,000 elements and 60,000 elements,respectively,as shown in Fig.9(a).The typical mesh size was 1 mm for both of the TNT and steel plate,and the accuracy of the calculation results and time were acceptable.All Lagrange method was used to calculate.Self-interaction was used to calculate these two Lagrange parts’interaction.A detonation plane was used to initiate the TNT at the top of the column.For the TNT with a density of 1.56 g/cm3,the state coefficients of the Jones-Wilkins-Lee(JWL)equation are given in Table 2[21].The equation of state of AISI 1045 steel was used in the Shock model,the Johnson Cook model was used as the strength model,and the coefficients were taken from the AUTODYN library.Fig.9(b)shows the simulation results.

The initial pressure at the interface was consistent with the theoretical results presented in Section 4.1.The initial pressure amplitude calculated by the theoretical and numerical simulation were 30.89 and 30.19 GPa,respectively.For the structures considered in this study,the region within a 10-mm distance was the region of the interest,and the simulation yielded good estimates,as shown in Fig.9(b).

With increasing distance,the relative error increased,and the calculation results yielded an overestimate compared to the experimental results.This maybe because the Shock equation of state used by steel in this situation cannot work well when the pressure decreased.With the steel casing outside,the rare wave effect would be smaller,and the numerical simulation results would be satisfied over a longer distance.For the pressure attenuation in Al 2024 and polyurethane foam,the comparison between experimental and numerical simulation results showed similar trends to those for AISI 1045 steel.

Fig.12.Time histories of shock pressure transmitted into the protected explosive.

4.2.2.Reacting level and the multi-layered compound structures.The Lee-Tarver ignition and growth model[23]can be used to describe the expansion and detonation of the explosive,so both layers of the Comp.B explosive in the casing(described in Section 2.1)used this model.The primary explosive column 8701 used the Jones-Wilkins-Lee(JWL)equation of state[22],and a detonation point was used to simulate the detonator in the experiment.The material model coefficients for the explosive were taken from the AUTODYN material library.Other solid material models were used based on the simulations presented in Section 4.2.1.The structural parameters were the same as those in Section 2.1.The grid size,element type and interaction were the same as those in Section 4.2.1.A detonation point was set at the top of the 8701.Other methods like SPH and Euler-Lagrange methods were tried to calculate the same problem previously,considering the pressure contour pattern and the calculation time,all Lagrange method were finally used.Fig.10 shows one of the simulation models(specimen 1).Gauges 20-27 were set in the same position in the second layer explosive,and gauges were set in the structure.

Comparing the time histories of the burn fraction(α,indicating the reaction grade of the explosive;the value was between 0 and 1,where 1 corresponds to a complete output of the energy)[23]at different distances in the protected explosive,the output level of the protected explosive was obtained.The results are presented in Fig.11.

Fig.13.Shock wave pressure contour in the protected explosive.

The results showed that both specimens 1 and 3 underwent a dramatic reaction(αreached 1),while specimen 4 only had a slight reaction(αdid not exceed 0.04).The initial pressure amplitude can be acquired by the gauges in the explosive,as shown in Fig.12.For specimens 1 and 3,the initial pressure amplitudes were 4.8 and 2.5 GPa,respectively,whereas the initial pressure amplitude in specimen 4 was 1.0 GPa.The differences between specimens 1 and 3 were as follows:(1)for the time at which the explosive completely reacted at the same location,specimen 3 was earlier than specimen 1;and(2)for the rate of increase of burn fractionα,specimen 3 at the 20# and 22# gauges approached a value of 1 more quickly than specimen 1.Thus,specimen 3 would output all of the energy in a shorter time than specimen 1,and specimen 3’s final output was the largest.The reaction degree was consistent with the experimental results.

If only the pressure amplitude transmitted into the protected explosive is considered,specimen 1 should have the higher output level than specimen 3.However,specimen 1 had a lower output level.This implied that only considering a one-dimensional pressure amplitude was not sufficient to explain the final output level when the pressure amplitude was not very low.Fig.13 shows the 2D shock wave propagation contour of the protected explosive in specimens 1 and 3 at 6.25,7.25,8.25,9.25,10.25 and 11.25μs.

The results showed that different multi-layered compound structures changed the pressure that was transmitted into the protected explosive.Specimen 1’s high pressure location changed from outside to inside,while specimen 3’s high pressure location transferred from left to right.The plane shape growing path had a more complete reaction efficiency than that in specimen 1,and this caused specimen 3 to exhibit the most dramatic reaction of these three specimens.

The time at which the pressure changed significantly was from 7.25 to 8.25μs,and thus,the pressure propagation characteristics in the multi-layered compound structures during this time were studied,as shown in Fig.14.

Fig.14.Shock wave pressure contour in the multi-layered compound structure.

The results showed that due to the steel casing,the reflected shock wave impacted the multi-layered compound structures again after the first detonation wave loading.Between 7.25 and 8.10μs,in specimen 1,the subsequent impact high pressure did not transmit into the protected explosive,whereas in specimen 3,the subsequent impact created a high pressure in the structure that had already affected the protected explosive.This implied that the multi-layered compound structures would not only influence the first impact pressure amplitude transmitted in to the explosive but would also affect the arrival time and pressure amplitude of the subsequent high pressure impact.All of these factors determined the final output level of the protected explosive.The mechanical impedance sequence can influence the entire shock wave propagation process,including the speed,reflection,and transmission characteristics,which would lead to different detonation growth paths in the protected explosive.

5.Conclusion

A series of detonation loading impact experiments were carried out to compare the reaction degree of the composition B explosive,which was protected by multi-layered compound structures.The experimental results showed that the reaction degree could be differentiated by three aspects.(1)Fragment velocity:two groups of fragment velocities could be acquired via a high-speed camera using image processing techniques,and the reaction degree of the protected explosive was related to the velocity of the second group of fragment.(2)Fragment piercing patterns on side witness plate:combining the high-speed camera and the fragment piercing patterns on side witness plate,the piercing number related to the second group of fragments could be acquired.(3)Damage characterization on bottom witness plates:this was used to compare the reaction degree of the explosive qualitatively.

Theoretical analysis and numerical simulations were carried out to explore the different reaction degrees of the explosive,which were related to the different multi-layered compound structures.The results indicated that only judging the reaction degree on the initial pressure amplitude transmitted into the protected explosive could not explain the reaction degree order in the experimental results.The following shock wave that was reflected by the side casing also must be considered,for after this shock wave was transmitted through the different multi-layered compound structures,different detonation growth paths formed in the protected explosive.This also influenced the final output of the explosive.

Declaration of competing interest

We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

Acknowledgment

The authors are very grateful for the support received from the National Natural Science Foundation of China(No.11872121).