Design of a Novel Linear Shaped Charge and Factors Influencing Its

applied sciences

Article Design of a Novel Linear Shaped Charge and Factors Inﬂuencing its Penetration Performance

Xi Cheng 1, Guangyan Huang 1,*, Chunmei Liu 2 and Shunshan Feng 1

1 State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China; [email protected] (X.C.); [email protected] (S.F.) 2 First Research Institute of Ministry of Public Security of PRC, Beijing 100044, China; [email protected] * Correspondence: [email protected]; Tel.: +86-010-6891-5532

Received: 9 September 2018; Accepted: 8 October 2018; Published: 10 October 2018

Featured Application: This work provides a new type of linear shaped charge, and it is meaningful for the structural design of the novel linear shaped charge.

Abstract: In this paper, a novel linear shaped charge (LSC), called a bi-apex-angle linear shaped charge (BLSC), has been designed to investigate the improvement of penetration performance. Compared with a traditional single-apex-angle LSC, a BLSC, which consists of a small-apex-angle liner and a large-apex-angle liner, has been investigated by depth-of-penetration (DOP) test. The results show that the penetration depth of BLSC is 29.72% better than that of an ordinary LSC. An Eulerian method is applied to simulate the entire process of jet formation, as well as penetration on a #45 steel target. The effectiveness of the Eulerian model is demonstrated by the good agreement of the computational results with experimental observations. Furthermore, the numerical simulation is developed to investigate the inﬂuence of liner thickness, explosive type, combination of small and large apex angle, ratio of small to all apex angle liner, and standoff distance on the penetration performance of BLSCs. The suggested work and results can provide a guide and reference for the structural design of BLSC.

Keywords: shaped charge; Bi-apex-angle liner; inﬂuence factor; penetration performance

1. Introduction In some emergencies, such as suspect capture, emergency rescue, and fire rescue, the first question is how to quickly open an emergency passage. One of the most effective ways is using a metal jet formed by a linear shaped charge (LSC), which can break up obstacles and reduce collateral damage. Since the pioneering work of G. Birkhoff, the steady state theory of Birkhoff and the unsteady state theory of PER (Pugh, EichelBerger, and Rosstoker) have been widely used in studies of shaped charges. Most of the researches in this field are focused on conical shaped charges (CSCs) and there have been few publications about LSCs [1,2]. Zeng [3] proposed an unsteady theory of jet formation for end-initiated LSCs, and confirmed that the theory agreed well with experimental results in the case of a charge with constant thickness. With the development of numerical simulation technology, the mechanism of LSC jet formation has been further analyzed and researched. Lim established a steady-state analytical equation of motion of a LSC’s liner based on the modification of the original Birkhoff theory [4] and showed that compared with numerical simulation results created with Autodyn software, this analytical equation exhibited favorable results in a limited range. Lim also proposed a theoretical model to predict the behavior of an explosively driven flyer, and calculated the jet tip velocity based on the formation of an arc in the liner. Some researchers studied the characteristics of the

Appl. Sci. 2018, 8, 1863; doi:10.3390/app8101863 www.mdpi.com/journal/applsci Appl. Sci. 2018, 8, x FOR PEER REVIEW 2 of 12 Appl.Appl. Sci.Sci.2018 2018,,8 8,, 1863 x FOR PEER REVIEW 22 of 1212 studied the characteristics of the liner collapse line using a typical jet flight pattern of LSC [5–9]. For studied the characteristics of the liner collapse line using a typical jet flight pattern of LSC [5–9]. For the simulation method, smoothed particle hydrodynamics (SPH) was used to investigate the linerthe simulation collapse line method, using a typicalsmoothed jet flight particle pattern hydrodynamics of LSC [5–9]. For(SPH) the simulationwas used method,to investigate smoothed the formation process of a linear-shaped charge jet [10–12]. Miyoshi conducted a standoff test of a LSC particleformation hydrodynamics process of a (SPH)linear-shaped was used charge to investigate jet [10–12]. the Miyoshi formation conducted process of a a standoff linear-shaped test of charge a LSC that provided significant information about determining the optimal standoff distance and allowed jetthat [10 provided–12]. Miyoshi significant conducted information a standoff about test determ of a LSCining that the provided optimal significantstandoff distance information and allowed about the design of effective cutting plans for use with LSCs [13,14]. Vinko Škrlec experimentally determiningthe design of the effective optimal standoffcutting distanceplans for and use allowed with LSCs the design [13,14]. of effectiveVinko Škrlec cutting experimentally plans for use determined the effects of a mass of explosive, liner material and standoff distance on the penetration withdetermined LSCs [13 the,14 ].effects Vinko of Škrlec a mass experimentally of explosive, liner determined material theand effectsstandoff of dist a massance ofon explosive, the penetration liner depth of the LSCs [15,16]. materialdepth of andthe LSCs standoff [15,16]. distance on the penetration depth of the LSCs [15,16]. The shape of a shaped charge liner has great influence on the formation of metal jet and its TheThe shapeshape ofof aa shapedshaped chargecharge linerliner hashas greatgreat influenceinfluence onon thethe formationformation ofof metalmetal jetjet andand itsits penetration performance into a target. The researchers mainly focused on LSCs with a penetrationpenetration performance performance into into a target. a Thetarget. researchers The researchers mainly focused mainly on LSCsfocused with aon single-apex-angle LSCs with a single-apex-angle liner. This paper describes an experiment using bi-apex-angle linear shaped liner.single-apex-angle This paper describesliner. This an pa experimentper describes using an bi-apex-angle experiment usin linearg shapedbi-apex-angle charges linear (BLSCs) shaped for charges (BLSCs) for effective penetration. A typical BLSC is shown in Figure 1. The greatest effectivecharges penetration.(BLSCs) for Aeffective typical penetration. BLSC is shown A intypical Figure BLSC1. The is greatestshown differencein Figure distinguishing1. The greatest difference distinguishing a BLSC from the traditional LSC is a small-apex-angle liner that is added adifference BLSC from distinguishing the traditional a BLSC LSC is from a small-apex-angle the traditional LSC liner is that a small-apex-angle is added in an ordinary liner that LSC is added liner. in an ordinary LSC liner. In this paper, the penetration performance of a BLSC is tested by the Inin thisan ordinary paper, the LSC penetration liner. In performancethis paper, the of penetration a BLSC is tested performance by the depth-of-penetration of a BLSC is tested (DOP)by the depth-of-penetration (DOP) test, and the results show that its penetration depth is 29.72% better test,depth-of-penetration and the results show (DOP) that test, its penetrationand the results depth show is 29.72% that its better penetration than that depth of an is ordinary29.72% better LSC. than that of an ordinary LSC. The penetration performance of the BLSC and LSC is then Thethan penetration that of an performance ordinary LSC. of the The BLSC penetration and LSC isperformance then investigated of the by BLSC Autodyn-2D. and LSC Based is then on investigated by Autodyn-2D. Based on the validated numerical approach and models, we theinvestigated validated numericalby Autodyn-2D. approach Based and models, on the we va comprehensivelylidated numerical discussed approach the influencesand models, of liner we comprehensively discussed the influences of liner thickness, explosive type, a combination of small thickness,comprehensively explosive discussed type, a combination the influences of small of liner and thickness, large apex explosive angles, and type, a ratio a combination of small to allof small apex and large apex angles, and a ratio of small to all apex angle liners on the penetration performance of angleand large liners apex on theangles, penetration and a ratio performance of small to ofall BLSCs. apex angle The presentliners on study the penetration provides a performance guidance and of BLSCs. The present study provides a guidance and reference for the structural design of a BLSC. referenceBLSCs. The for present the structural study provides design of a a guidance BLSC. and reference for the structural design of a BLSC.

Figure 1. Schematic of a bi-apex-angle linear shaped charge (BLSC). FigureFigure 1.1. SchematicSchematic ofof aa bi-apex-anglebi-apex-angle linearlinearshaped shapedcharge charge(BLSC). (BLSC). 2.2. ExperimentExperiment 2. Experiment TheThe schematicschematic ofof thethe BLSCBLSC isis shownshown inin FigureFigure2 ,2, where where d d1,1, 2a 2a11,, dd22,, 2a2a22, θ, δ,, andand HH areare thethe widthwidth The schematic of the BLSC is shown in Figure 2, where d1, 2a1, d2, 2a2, θ, δ, and H are the width ofof thethe small-apex-anglesmall-apex-angle liner, liner, the the small small apex apex angle, angle, the the width width of large-apex-angle of large-apex-angle liner, liner, the large the apexlarge of the small-apex-angle liner, the small apex angle, the width of large-apex-angle liner, the large angle,apex angle, the charge the charge slope slope angle, angle, the liner the thickness,liner thickness, and the and charge the charge height, height, respectively. respectively. apex angle, the charge slope angle, the liner thickness, and the charge height, respectively.

FigureFigure 2.2. SchematicSchematic ofof thethe BLSC.BLSC. Figure 2. Schematic of the BLSC.

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2.1.2.1. Preparation Preparation of of the the Bi-Apex-Angle Bi-Apex-Angle Liner Liner AA bi-apex-angle bi-apex-angle liner liner is is distinguished distinguished by by a a small-apex-angle small-apex-angle linerliner thatthat is is added added to to an an ordinary ordinary liner.liner. A A typical typical bi-apex-angle bi-apex-angle liner liner is is shown shown in in Figure Figure 3 3.3.. TableTableTable1 1 1shows showsshows the thethe related relatedrelated parameters parametersparameters of ofof the thethe BLSCBLSC liner. liner.

FigureFigure 3. 3. Bi-apex-angleBi-apex-angle liner liner used used in in the the experiment. experiment.

Table 1. Parameters of the BLSC liner. TableTable 1.1. ParametersParameters ofof thethe BLSCBLSC liner.liner.

d1 d2 θ 2a1 2a2 dd11 dd22 θθ 2a2a11 2a2a22 ◦ ◦ ◦ 55 mmmm 5 mm 10 10 mmmm 10 mm 10 10° 10°40 60 40° 40° 60° 60°

2.2.2.2. Experimental Experimental Bi-Apex-Angle Bi-Apex-Angle Linear Linear Shaped Shaped Charge Charge TheThe BLSCBLSCBLSC usedusedused in inin the thethe experiment experimentexperiment consisted consistedconsisted of of theof thethe main mainmain charge, charge,charge, a bi-apex-angle aa bi-apex-anglebi-apex-angle liner, liner,liner, and a andand shell, aa shell,asshell, shown asas shownshown in Figure inin FigureFigure4. The 4.4. main TheThe chargemainmain chargecharge was an waswas 8701 anan explosive, 87018701 explosive,explosive, which whichwhich was placed waswas placedplaced in a press inin aa mold presspress moldandmold subjected andand subjectedsubjected to a pressure toto aa pressurepressure load at loadload room atat temperature. roomroom temperature.temperature. The height TheThe height ofheight the main ofof thethe charge mainmain (H)chargecharge was (H)(H) 17 mm.waswas 17Because17 mm.mm. BecauseBecause of the design ofof thethe of designdesign bi-apex-angle ofof bi-apex-anglebi-apex-angle liner, the linlin masser,er, thethe of mass themass BLSC ofof thethe main BLSCBLSC charge mainmain decreased chargecharge decreaseddecreased by 1.1% bycomparedby 1.1%1.1% comparedcompared to an LSC toto charge anan LSCLSC under chargecharge the underunder same thethe density samesame and densitydensity the height andand thethe (H). heightheight The bi-apex-angle (H).(H). TheThe bi-apex-anglebi-apex-angle liner was linermadeliner waswas from mademade a 1.0 from mmfrom T2 aa 1.0 copper1.0 mmmm plank. T2T2 coppercopper The shellplank.plank. was TheThe made shellshell from waswaspolymeric mademade fromfrom methyl polymericpolymeric methacrylate methylmethyl methacrylate(PMMA).methacrylate It provided (PMMA).(PMMA). a 10 ItIt mm providedprovided standoff aa distance1010 mmmm standoff (thestandoff same distancedistance as the width), (the(the samesame and the asas inﬂuencesthethe width),width), of theandand shell thethe wereinfluencesinfluences neglected. ofof thethe shellshell werewere neglected.neglected.

FigureFigure 4. 4. ((aa)) Main Main charge; charge; ( (bb)) BLSC BLSC and and target. target.

2.3.2.3. Depth Depth of of Penetration Penetration (DOP) (DOP) Experiment Experiment AnAn experimentexperimentexperiment using usingusing the the DOPthe DOPDOP method methodmethod was conducted waswas conductedconducted to investigate toto investigateinvestigate the penetration thethe performancepenetrationpenetration ◦ performanceofperformance a BLSC against ofof aa thatBLSCBLSC of against anagainst ordinary thatthat LSC. ofof anan The ordinaryordinary LSC had LSC.LSC. a constant TheThe LSCLSC 60 hadhadapex-angle aa constantconstant liner, 60°60° and apex-angleapex-angle the other liner,parametersliner, andand thethe were otherother the parametersparameters same as the werewere experimental thethe samesame asas BLSC. thethe experimentalexperimental The experimental BLSC.BLSC. setup TheThe experimentalexperimental is shown in Figure setupsetup 5isis. shownTheseshown shaped inin FigureFigure charges 5.5. TheseThese were shapedshaped centrally chargescharges initiated werewere through centrallycentrally a #8 initiatedinitiated electric throughthrough detonator aa at#8#8 one electricelectric end. detonatordetonator To measure atat onetheone penetration end.end. ToTo measuremeasure depth is importantthethe penetrationpenetration when studying depthdepth is theis importantimportant difference inwhenwhen penetration studyingstudying performance thethe differencedifference between inin penetrationthepenetration LSC and performanceperformance BLSC. A 45 steel betweenbetween target thethe was LSCLSC set to andand measure BLSCBLSC.. the AA penetration4545 steelsteel targettarget capability waswas setset of toto the measuremeasure two shaped thethe 3 × × penetrationcharges.penetration It had capabilitycapability a density ofof of thethe 7.85 twotwo g/cm shapedshapedand charges.charges. measured ItIt hadhad 300 a mma densitydensity (l) 100ofof 7.857.85 mm g/cmg/cm (w) 33 andand20 mm measuredmeasured (h). 300300 mmmm (l)(l) ×× 100100 mmmm (w)(w) ×× 2020 mmmm (h).(h). Appl. Sci. 2018, 8, 1863 4 of 12 Appl. Sci. 2018, 8, x FOR PEER REVIEW 4 of 12 Appl. Sci. 2018, 8, x FOR PEER REVIEW 4 of 12

Figure 5. (a) Main charge; (b) BLSC and target. FigureFigure 5.5. ((a)) MainMain charge;charge; ((bb)) BLSCBLSC andand target.target. 3. Numerical Simulation 3.3. Numerical SimulationSimulation 3.1.3.1. NumericalNumerical AlgorithmsAlgorithms 3.1. Numerical Algorithms TheThe numericalnumerical simulationsimulation isis carriedcarried outout inin softwaresoftware Autodyn.Autodyn. ThisThis softwaresoftware hashas beenbeen widelywidely The numerical simulation is carried out in software Autodyn. This software has been widely usedused to analyze analyze the the nonlinear nonlinear dynamic dynamic impacts impacts and andexplosions. explosions. It allows It allowsthe application the application of different of used to analyze the nonlinear dynamic impacts and explosions. It allows the application of different differentalgorithms algorithms such as Euler, such asLagrangian, Euler, Lagrangian, Arbitrary ArbitraryLagrangian Lagrangian Euler (ALE), Euler and (ALE), SPH andto solve SPH the to algorithms such as Euler, Lagrangian, Arbitrary Lagrangian Euler (ALE), and SPH to solve the solvefluid–structure the fluid–structure problems problems [17]. In[ 17this]. Incurren this currentt work, work, because because LSCs LSCs are are much much larger larger in in thethe fluid–structure problems [17]. In this current work, because LSCs are much larger in the longitudinallongitudinal direction direction than than in in other other two two directions, directions, they they can can be modeledbe modeled as a as plane a plane strain strain problem problem in a longitudinal direction than in other two directions, they can be modeled as a plane strain problem two-dimensionalin a two-dimensional space [space4,10,11 [4,10,11,14],14] and numerically and nume simulatedrically simulated using the using explicit the nonlinear explicit nonlinear dynamic in a two-dimensional space [4,10,11,14] and numerically simulated using the explicit nonlinear analysisdynamic softwareanalysis ANSYSsoftware Autodyn-2DANSYS Autodyn-2D version 17.2version (ANSYS 17.2 (ANSYS Inc.: Canonsburg, Inc.: Canonsburg, PA, USA, PA, 2016).USA, dynamic analysis software ANSYS Autodyn-2D version 17.2 (ANSYS Inc.: Canonsburg, PA, USA, By2016). using By the using multi-material the multi-material Eulerian Eulerian algorithm, algori thethm, whole the process whole includingprocess including the jet formation, the jet formation, flight of 2016). By using the multi-material Eulerian algorithm, the whole process including the jet formation, jet,flight slug of and jet, slug wing, and and wing, the impact and the on im thepact steel on targetthe steel was target reproduced. was reproduced. flight of jet, slug and wing, and the impact on the steel target was reproduced. 3.2.3.2. EstablishmentEstablishment ofof thethe SimulationSimulation ModelModel 3.2. Establishment of the Simulation Model AA numericalnumerical analysisanalysis modelmodel isis simplifiedsimplified toto two-dimensionaltwo-dimensional plane-symmetricplane-symmetric geometriesgeometries forfor A numerical analysis model is simplified to two-dimensional plane-symmetric geometries for efficientefficient calculation, calculation, as as shown shown in in Figure Figure6. The6. The geometrical geometrical parameter parameter in the in simulationthe simulation model model was thewas efficient calculation, as shown in Figure 6. The geometrical parameter in the simulation model was samethe same as the as one the inone the in DOP the test.DOP The test. charge The charge was 8701 was and 8701 it wasand centrallyit was centrally initiated initiated through through a simple a the same as the one in the DOP test. The charge was 8701 and it was centrally initiated through a detonatorsimple detonator at the bottom. at the bottom. simple detonator at the bottom.

Figure 6. Numerical model of shaped charges: (a) LSC; (b) BLSC. FigureFigure 6.6. Numerical modelmodel ofof shapedshaped charges:charges: ((aa)) LSC;LSC; ((bb)) BLSC.BLSC. InIn thethe calculation, calculation, the the 8701 8701 explosive explosive is is used. used. The Th equatione equation of of state state (EOS) (EOS) of of the the 8701 8701 explosive explosive is In the calculation, the 8701 explosive is used. The equation of state (EOS) of the 8701 explosive Jones-Wilkins-LEEis Jones-Wilkins-LEE (JWL). (JWL). The linerThe materialliner material is made is ofmade T2 copper. of T2 Thecopper. mechanical The mechanical model of CU-OFHC model of is Jones-Wilkins-LEE (JWL). The liner material is made of T2 copper. The mechanical model of inCU-OFHC Autodyn in is regardedAutodyn asis T2regarded copper. as The T2 EOS copper. and strengthThe EOS ofand T2 copperstrength were of T2 Shock copper and were Streinberg Shock CU-OFHC in Autodyn is regarded as T2 copper. The EOS and strength of T2 copper were Shock Gruinan,and Streinberg respectively. Gruinan, The respectively. material of theThe steel material target of was the #45 steel steel; target itsdynamic was #45 responsesteel; its behaviordynamic and Streinberg Gruinan, respectively. The material of the steel target was #45 steel; its dynamic underresponse the behavior action of under the detonation the action wave of the can deto benation described wave using can thebe Johnson–Cookdescribed using (J–C) the Johnson– material response behavior under the action of the detonation wave can be described using the Johnson– model.Cook (J–C) An air material grid covered model. the An penetrator air grid covered ﬂying range. the penetrator The type of flying air model range. was The taken type from of Autodyn,air model Cook (J–C) material model. An air grid covered the penetrator flying range. The type of air model andwas thetaken Int Energyfrom Autodyn, of air is 2.068and the× 10 Int5. TheEnergy parameters of air is of 2.068 all material × 105. The models parameters used in theof all calculation material was taken from Autodyn, and the Int Energy of air is 2.068 × 105. The parameters of all material aremodels listed used in Table in the2[18 calculation,19]. are listed in Table 2 [18,19]. models used in the calculation are listed in Table 2 [18,19].

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Table 2. Parameters of material model.

Density C–J Detonation C–J Energy/unit C–J Pressure 3 A (kPa) B (kPa) R1 R2 W 3 8701 (g/cm ) velocity (m/s) volume (kJ/m ) (kPa) 1.713 5.242 × 108 7.768 × 106 4.2 1.1 0.34 7980 8.499 × 106 2.86 × 107 Density Shear modulus Yield stress Hardening Hardening Strain rate Thermal softening Melting Ref. strain rate Strain rate 3 #45 Steel (g/cm ) (kPa) A (kPa) constant B (kPa) exponent constant exponent temperature Tm (K) (/s) correction 7.83 7.59 × 107 3.5 × 105 3.2× 105 0.28 0.064 1.06 1.793 × 103 1.0 1st Order Density Shear modulus Yield stress Maximum Yield Hardening Hardening Derivative dG/dT Derivative Melting 3 Derivative dG/dP CU-OFHC (g/cm ) (kPa) A (kPa) stress (kPa) constant Exponent (kPa/K) dY/dp Temperature (K) 8.93 4.77 × 107 1.2 × 105 6.4 × 105 36 0.45 1.35 -1.798× 104 3.39 × 10-3 1.79 × 103 Thermal Density Adiabatic Pressure shift Reference Speciﬁc Heat Gamma Conductivity Int Energy (g/cm3) constant (kPa) Temperature (K) (J/kgK) Air (J/mKs) 0.001225 1.4 0 0 288.200012 717.599976 0 2.068 × 105 Appl. Sci. 2018, 8, 1863 6 of 12 Appl. Sci. 2018, 8, x FOR PEER REVIEW 6 of 12 Appl. Sci. 2018, 8, x FOR PEER REVIEW 6 of 12 4. Results Results 4. Results 4.1. Experimental Experimental Results 4.1. Experimental Results The LSC and BLSC exhibited excellent damage effects, as illustrated in Figure7 7.. The LSC and BLSC exhibited excellent damage effects, as illustrated in Figure 7.

Figure 7. ExperimentalExperimental results of shaped charges: ( a) LSC; ( b) BLSC. Figure 7. Experimental results of shaped charges: (a) LSC; (b) BLSC. To investigateinvestigate thethe penetration penetration depths depths of of the the LSC LSC and and BLSC, BLSC, the targetsthe targets were were cut vertically cut vertically along To investigate the penetration depths of the LSC and BLSC, the targets were cut vertically alongpenetration penetration cracks. cracks. Every Every target target was divided was divided into eight into parts.eight parts. Figure Figure8 provides 8 provides detailed detailed data about data along penetration cracks. Every target was divided into eight parts. Figure 8 provides detailed data abouttheabout penetration the the penetration penetration depth depth on depth each on on side each each of side everyside of of part.every every part.part.

FigureFigure 8. 8.Penetration Penetration depth depth of of shaped shaped charges: charges: (( aa))) LSC;LSC; LSC; ( b( b) )BLSC. BLSC.

WhereWhereP Pise is the the penetration penetration depth depth of ofexperimental experimental test. It It is is shown shown as: as: Where Pe is the penetration depth of experimental test. It is shown as: n nn PPi ∑Pi (1) =i=i=11 i PPe= i=1 (1)(1) Pe = nn e n 4.2. Numerical Simulation Results 4.2. Numerical Simulation Results 4.2. NumericalTypical jet Simulation formation Results and penetration processes of an LSC and BLSC are shown in Figure9. Typical jet formation and penetration processes of an LSC and BLSC are shown in Figure 9. After the explosion, the copper liner elements gradually moved to the symmetry plane and collapsed AfterTypical the jetexplosion, formation the and copper penetration liner elements processes gradually of an LSC moved and toBLSC the aresymmetry shown planein Figure and 9. under the action of the detonation wave. When the copper liner elements arrived at the collision point, Aftercollapsed the explosion, under the theaction copper of the linerdetonation elements wave gradually. When the moved copper toliner the elements symmetry arrived plane at theand the velocity of the outer liner elements was lower than that of the inner liner elements; hence, the outer collapsedcollision under point, the the action velocity of theof thedetonation outer liner wave elements. When wasthe copperlower thanliner thatelements of the arrived inner linerat the liner elements moved to the left of the collision point and formed a slug. At the same time, the inner collisionelements; point, hence, the the velocity outer liner of the elements outer movedliner elementsto the left wasof the lower collision than point that and of formedthe inner a slug. liner elements;linerAt elementsthe same hence, movedtime, the the outer to inner the liner rightliner elements ofelements the collision moved moved pointto to the the andleft right formedof ofthe the collision acollision jet. The point point remaining and and formedformed copper a jet.slug. liner Atelements, Thethe sameremaining which time, did copperthe notinner liner arrive liner elements, at elements the collision which moved did point, tonot the formingarrive right at of anthe the alae. collision collision Therefore, point, point forming the and colliding formed an alae. a liner jet. TheelementsTherefore, remaining were the dividedcopper colliding intoliner liner threeelements, elements parts: which were jet, slug, di didvided and not into alae. arrive three at parts: the collision jet, slug, point,and alae. forming an alae. Therefore,TheThe penetration the penetration colliding depths, depths,liner elements as as well well as aswere thethe di DOPDOPvided testtest into results three for for parts: the the LSC LSCjet, slug,and and BLSC, and BLSC, alae. are are graphically graphically illustratedillustratedThe penetration in Figurein Figure8, anddepths, 8, Figureand as Figure 9well shows as 9 theshows typicalDOP the test numericaltypical results numerical for results the ofLSC results jet formationand ofBLSC, jet andformation are penetrationgraphically and illustratedprocessespenetration describedin Figureprocesses by8, Autodyn.anddescribed Figure by Furthermore, 9 Autodyn. shows the Furthermore, Tabletypical3 shows numerical Table the 3 good resultsshows agreement theof jetgood formation betweenagreement theand penetrationexperimentbetween andtheprocesses numericalexperiment described simulation and numericalby Autodyn. outputs. simulation These Furthermore, indicate outputs. that Table These the adopted3 showsindicate numericalthe that good the constitutive agreementadopted betweenmodelsnumerical and the corresponding constitutiveexperiment models parametersand numericaland corresponding are ablesimulation to give parameters reliable outputs. predictionsare Theseable to giveindicate of penetration reliable that predictions the performance adopted of penetration performance of LSCs and BLSCs. numericalof LSCs and constitutive BLSCs. models and corresponding parameters are able to give reliable predictions of penetration performance of LSCs and BLSCs. Appl. Sci. 2018, 8, 1863 7 of 12 Appl. Sci. 2018, 8, x FOR PEER REVIEW 7 of 12

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FigureFigure 9. 9.Numerical Numerical simulation simulation ofof jet formation and and penetration penetration processes. processes.

TableTable 3. 3.Parameters Parameters of material model. model. Figure 9. Numerical simulation of jet formation and penetration processes. Type TypePs (mm) Ps (mm) PePe (mm) (mm) DifferenceDiffer (mm)ence (mm) Percentage Error Percentage Error Table 3. Parameters of material model. LSC LSC4.75 4.75 4.714.71 0.04 0.04 0.85% 0.85% BLSCType BLSCPs6.00 (mm) 6.00 Pe 6.116.11 (mm) 0.11Difference 0.11 (mm) 1.80% Percentage 1.80% Error LSC 4.75 4.71 0.04 0.85% 5. Parametric5. ParametricBLSC Influences Influences on6.00 on Penetration Penetration Performance Performance6.11 0.11 1.80% Based on our results, as well as the verified numerical constitutive models and the Based5. Parametric on our Influences results, as on well Penetration as the verified Performance numerical constitutive models and the corresponding corresponding parameters, the influences of liner thickness, explosive type, combination of small parameters, the influences of liner thickness, explosive type, combination of small and large apex and largeBased apex on angle, our ratioresults, of smallas well to all as apex the angleverified liner, numerical and standoff constitu distancetive models on the penetrationand the angle, ratio of small to all apex angle liner, and standoff distance on the penetration performance of performancecorresponding of BLSCs parameters, are further the influences discussed. of liner thickness, explosive type, combination of small BLSCsand are large further apex discussed.angle, ratio of small to all apex angle liner, and standoff distance on the penetration 5.1.performance Liner Thickness of BLSCs are further discussed. 5.1. Liner Thickness Based on the presented numerical simulation result of the BLSC, another four sets of Based5.1. Liner on Thickness the presented numerical simulation result of the BLSC, another four sets of penetration penetration scenarios with the liner thickness (δ) of 0.4 mm, 0.6 mm, 0.8 mm, and 1.2 mm are further scenariosBased with theon linerthe thicknesspresented (δnumerica) of 0.4 mm,l simulation 0.6 mm, 0.8result mm, of and the 1.2 BLSC, mm areanother further four complemented. sets of complemented. The other parameters, such as d1, 2a1, d2, 2a2, and θ, are shown in Table 1. penetration scenarios with the liner thickness (δ) ofθ 0.4 mm, 0.6 mm, 0.8 mm, and 1.2 mm are further The otherFigure parameters, 10 shows such the as velocity d1, 2a1, ddistribution2, 2a2, and ,of are jet shown with indifferent Table1 . liner thicknesses before complemented. The other parameters, such as d1, 2a1, d2, 2a2, and θ, are shown in Table 1. penetration.Figure 10 showsFigure the11 presents velocity the distribution relationship of jetbetween with different the liner liner thickness thicknesses and penetration before penetration. depth. Figure 10 shows the velocity distribution of jet with different liner thicknesses before FigureIt is obvious11 presents that thethe relationshipjet velocity is between getting higher the liner and thickness the total andlength penetration of jet and depth.slug is Itincreasing is obvious penetration. Figure 11 presents the relationship between the liner thickness and penetration depth. that the jet velocity is getting higher and the total length of jet and slug is increasing rapidly with the rapidlyIt is obvious with the that decrease the jet velocity of liner is gettingthickness. higher Thus, and the the BLSCtotal length with ofa 0.4jet andmm slug liner is increasinghas a better decrease of liner thickness. Thus, the BLSC with a 0.4 mm liner has a better penetration performance penetrationrapidly with performance the decrease than of liner others. thickness. But, Thus,taking the into BLSC account with athe 0.4 processingmm liner has technic a better and thanassemblingpenetration others. But, of aperformance takingBLSC, the into 0.6 accountthan mm others.liner the is processingrecommendedBut, taking technic into in thisaccount and paper. assembling the processing of a BLSC, technic the and 0.6 mm linerassembling is recommended of a BLSC, in thisthe 0.6 paper. mm liner is recommended in this paper.

Figure 10. Velocity distribution of different liner thickness. FigureFigure 10. 10.Velocity Velocity distribution distribution of of different different liner liner thickness. thickness. Appl. Sci. 2018, 8, x FOR PEER REVIEW 8 of 12

Appl. Sci. 2018, 8, 1863 8 of 12 Appl. Sci. 2018, 8, x FOR PEER REVIEW 8 of 12

Figure 11. Penetration depth of BLSCs with different liner thickness.

5.2. Explosive Type FigureFigure 11. 11.Penetration Penetration depth depth of of BLSCs BLSCs with with different different liner liner thickness. thickness. Based on the penetration performance of the BLSC with 0.6 mm liner, another four sets of DOP 5.2. Explosive Type 5.2.tests Explosive on steel Typetargets with the explosives of COMP B, C-4, TNT, and LX-19 were further simulated. TableBased 4 shows on the the penetration corresponding performance parameters of the of BLSCthese withexplosives 0.6 mm [20]. liner, Figure another 12 shows four sets the of velocity DOP Based on the penetration performance of the BLSC with 0.6 mm liner, another four sets of DOP testsdistribution on steel with targets the withabove the five explosives different of explosives COMP B, befo C-4,re TNT, penetration. and LX-19 Figure were 13 further further simulated. illustrates tests on steel targets with the explosives of COMP B, C-4, TNT, and LX-19 were further simulated. Tablethe sectional4 shows thepenetration corresponding cracks, parametersand the values of these of penetration explosives depths [ 20]. Figureare shown 12 shows in the theparentheses. velocity Table 4 shows the corresponding parameters of these explosives [20]. Figure 12 shows the velocity distribution with the above ﬁve different explosives before penetration. Figure 13 further illustrates distribution with the above five different explosives before penetration. Figure 13 further illustrates the sectional penetration cracks, andTable the 4. values Parameters of penetration of four explosives. depths are shown in the parentheses. the sectional penetration cracks, and the values of penetration depths are shown in the parentheses. Parameters COMP B C-4 TNT LX-19 Table 4. Parameters of four explosives. Density(g/cm3) Table 4. Parameters 1.717 of four explosives.1.601 1.630 1.942 ParametersA (kPa) COMP 5.24 B × 108 C-4 6.10 × 108 TNT 3.71 × 108 LX-19 1.64 × 109 Parameters COMP B C-4 TNT LX-19 B (kPa)3 7.68 × 106 1.30 × 107 3.21 × 106 1.86 × 107 Density(g/cmDensity(g/cm) 3) 1.717 1.717 1.6011.601 1.6301.630 1.9421.942 A (kPa)R1 5.24 × 104.28 6.10 × 104.58 3.71 ×4.15108 1.64 ×6.5109 A (kPa) 5.24 × 108 6.10 × 108 3.71 × 108 1.64 × 109 B (kPa)R2 7.68 × 101.16 1.30 × 101.47 3.21 ×0.95106 1.86 ×2.7107 B (kPa) 7.68 × 106 1.30 × 107 3.21 × 106 1.86 × 107 R1W 4.20.34 4.50.25 4.150.3 6.50.55 R2R1 1.14.2 1.44.5 0.954.15 2.76.5 C–J Detonation velocity (m/s) 7,980 8,190 6,930 9,208 WR2 0.341.1 0.251.4 0.30.95 0.552.7 C–J Energy/unit volume (kJ/m3) 8.50 × 106 9.00 × 106 4.30 × 106 1.15 × 107 C–J Detonation velocityW (m/s) 7,9800.34 8,1900.25 6,9300.3 9,2080.55 C–JC Energy/unit form alae volumeJ Pressure (kJ/m (kPa)3) 8.50 2.95× 10 6× 107 9.00 2.80× 10 ×6 107 4.30 2.10× 10 ×6 107 1.15 4.30× 10× 7107 C–J Detonation velocity (m/s) 7,980 8,190 6,930 9,208 C form alae J Pressure (kPa) 2.95 × 107 2.80 × 107 2.10 × 107 4.30 × 107 C–J Energy/unit volume (kJ/m3) 8.50 × 10 6 9.00 × 106 4.30 × 106 1.15 × 107 C form alae J Pressure (kPa) 2.95 × 107 2.80 × 107 2.10 × 107 4.30 × 107

FigureFigure 12. 12.Velocity Velocity distribution distribution of of different different explosives. explosives.

Figure 12. Velocity distribution of different explosives. Appl. Sci. 2018, 8, 1863 9 of 12 Appl. Sci. 2018,, 88,, xx FORFOR PEER PEER REVIEW REVIEW 9 of9 12of 12

-10-10 -5 -5 0 0 5 5 10 10 -2-2 -2 -2

00 0 0

22 2 2

44 4 4

66 6 6

88 8 8 8701 8701 (9.40) (9.40) 1010 COMP COMP B (14.25)B (14.25) 10 10

PenetrationDepth(mm) C-4 (8.70)

PenetrationDepth(mm) C-4 (8.70) 12 12 12 TNT TNT (13.10) (13.10) 12 LX-19 LX-19 (6.30) (6.30) 1414 14 14

1616 16 16 -10-10 -5 -5 0 0 5 5 10 10 （） CrackCrack width width （mmmm）

FigureFigure 13. 13.Penetration Penetration depth of BLSCs BLSCs with with different different explosives. explosives. Figure 13. Penetration depth of BLSCs with different explosives.

AccordingAccording to to these these figures, figures, it should it should be notedbe note thatd thethat penetration the penetration depth depth is a result is a ofresult a multitude of a According to these figures, it should be noted that the penetration depth is a result of a ofmultitude factors such of factors as jet tip such velocity, as jet tip jet length,velocity, velocity jet length, distribution velocity distribution and so on. and The so jet on. tip The velocities jet tip of multitude of factors such as jet tip velocity, jet length, velocity distribution and so on. The jet tip BLSCsvelocities with of 8701, BLSCs COMP with B,8701, and CO TNTMP are B, and much TNT higher are much than thosehigher with than C-4those and with LX-19. C-4 and The LX-19. jet/slug velocities of BLSCs with 8701, COMP B, and TNT are much higher than those with C-4 and LX-19. lengthsThe jet/slug of BLSCs lengths with of 8701, BLSCs COMP with 8701, B, and COMP TNT B, are and also TNT longer are also than longer those than of the those others. of the As others. shown The jet/slug lengths of BLSCs with 8701, COMP B, and TNT are also longer than those of the others. inAs Figure shown 13, in the Figure penetration 13, the depthpenetr ofation BLSC depth with of COMP BLSC Bwith is the COMP deepest, B is followedthe deepest, in turnfollowed by that in of As shown in Figure 13, the penetration depth of BLSC with COMP B is the deepest, followed in BLSCsturn by with that TNT, of BLSCs 8701, C-4,with andTNT, LX-19, 8701, whichC-4, and is LX-19, the smallest. which is Although the smallest. the jet/slugAlthough length the jet/slug of BLSC turn by that of BLSCs with TNT, 8701, C-4, and LX-19, which is the smallest. Although the jet/slug withlength LX-19 of BLSC is not with the shortest, LX-19 is itnot has the the shortest, minimal it has penetration the minimal depth, penetration indicating depth, that indicating the velocity that has length of BLSC with LX-19 is not the shortest, it has the minimal penetration depth, indicating that greaterthe velocity influence has ongreater the penetration influence on depth the penetration of BLSC than depth jet/slug of BLSC length. than jet/slug length. the velocity has greater influence on the penetration depth of BLSC than jet/slug length. 5.3.5.3. Combinations Combinations of of Small Small and and Large Large ApexApex AnglesAngles 5.3. Combinations of Small and Large Apex Angles TheThe influence influence of of small small and and large large apex apex angle angle is is further further discussed discussed in in this this part. part. Figure Figure 14 14 shows shows the The influence of small and large apex angle is further discussed in this part. Figure 14 shows numericalthe numerical results results of BLSC of with BLSC 0.6 with mm thick0.6 mm liner, thick COMP liner, B asCOMP the explosive B as the andexplosive different and combinations different thecombinations numerical of results small apexof BLSC◦ angle◦ with (2a◦1 =0.6 30°, mm 40°,◦ thick 50° and liner, 60°, COMP respectively) B as the and explosive large apex and angle◦ different (2a◦ 2 of small apex angle (2a1 = 30 , 40 , 50 and 60 , respectively) and large apex angle (2a2 = 60 , 80 and combinations of small apex angle (2a1 = 30°, 40°, 50° and 60°, respectively) and large apex angle (2a2 100=◦ 60°,, respectively). 80° and 100°, respectively). = 60°, 80° and 100°, respectively).

Figure 14. Penetration depths of different combinations of small and large apex angles. FigureFigure 14. 14.Penetration Penetration depths depths of of different different combinations combinations of of small small and and large large apex apex angles.angles. Appl.Appl. Sci. Sci. 20182018, ,88, ,x 1863 FOR PEER REVIEW 1010 of of 12 12

It shows that, (i) with the small apex angle increasing, the penetration depth shows a trend of increaseIt shows before that, a decrease; (i) with theand small(ii) with apex the angle large increasing, apex angle the increasing, penetration the depth penetration shows adepth trend showsof increase a trend before of increase a decrease; before and decreasing (ii) with theas we largell. The apex reason angle is increasing, that whenthe thepenetration small apex depthangle startsshows increasing, a trend of the increase jet velocity before is decreasinggetting slower as well. but the The jet reason mass is is becoming that when bigger. the small Therefore, apex angle the penetrationstarts increasing, depth thebecomes jet velocity deeper. is gettingWith the slower small butapex the angle jet mass further is becoming increasing, bigger. the jet Therefore, velocity dropsthe penetration dramatically depth and becomes the penetration deeper. With depth the smalldecreases. apex angleThe part further liner increasing, with large the apex jet velocity angle mainlydrops dramaticallyforms the wing and and the the penetration slug. Therefore, depth decreases. when the Thelarge part apex liner angle with starts large increasing, apex angle the mainly part thatforms forms the wingeffective and slug the penetrating slug. Therefore, into a when steel thetarget large speeds apex up, angle resulting starts increasing,in a deeper thepenetration part that depth.forms effectiveWith the slug large penetrating apex angle into further a steel increasing target speeds, the mass up, resulting of effective in a deeperslug decreases, penetration resulting depth. inWith a smaller the large penetration apex angle furtherdepth. increasing,It should thebe massnoted of that effective to make slug decreases,the charge resulting height inH aremain smaller constant,penetration the depth. differences It should of the be notedexplosive that mass to make vari thees chargefrom 30.4 height g/200 H remainmm to 40.4 constant, g/200 the mm differences and this cannotof the explosivebe ignored. mass varies from 30.4 g/200 mm to 40.4 g/200 mm and this cannot be ignored.

5.4.5.4. Ratio Ratio of of Small Small to to All All Apex Apex Angle Angle Liners Liners

TheThe effect ofof linersliners with with different different ratios ratios of smallof small to all to apex all apex angle angle (n = d (1n/d =2 d) on1/d2 penetration) on penetration depth depthis further is further explored explored using BLSCs using with BLSCs 0.6 mmwith thick 0.6 mm liner, thick COMP liner, B as COMP the explosive, B as the small explosive, apex angle small of ◦ ◦ apex50 , largeangle apex of 50°, angle large of apex 100 , angle and n of= 0.3,100°, 0.4, and 0.5, n 0.6,= 0.3, and 0.4, 0.7, 0.5, respectively. 0.6, and 0.7,Figure respectively. 15 represents Figure the15 representspenetration the performance penetration of performance BLSCs with of different BLSCs valueswith different of n. values of n.

-10 -5 0 5 10 -2 -2

0 0

2 2

4 4

6 6

8 8 n=0.3 (10.55) 10 n=0.4 (12.10) 10 n=0.5 (14.25)

Penetration Depth(mm) n=0.6 (8.70) 12 12 n=0.7 (9.65)

14 14

16 16 -10 -5 0 5 10 Crack width(mm) FigureFigure 15. 15. PenetrationPenetration depth depth of of BLSCs BLSCs with with different different ratios ratios of of small small to to all all apex apex angles. angles.

ItIt should should be be noted noted that that the the mass mass of of explosive explosive changes changes as as the the n n charges. charges. Taking Taking a a 200 200 mm mm long long BLSCBLSC as as an an example, example, the the mass mass of of explosive explosive is is41.32 41.32 g, g,40.55 40.55 g, 39.54 g, 39.54 g, 38.31 g, 38.31 g and g and 36.86 36.86 g when g when n = 0.3,n = 0.4, 0.3, 0.4,0.5, 0.5,0.6, 0.6,and and 0.7, 0.7, respectively. respectively. Figure Figure 15 15 illustrates illustrates the the sectional sectional penetration penetration cracks cracks and and the the penetrationpenetration depths depths are are shown shown in in the the parentheses. parentheses. Taking Taking the the energy energy efficiency efﬁciency and and the the penetration penetration performanceperformance into into account, account, a a BLSC BLSC with with nn == 0.5 0.5 may may be be the the best. best.

5.5.5.5. Standoff Standoff Distance Distance TheThe standoff standoff distance distance (S) (S) is is the the distance distance between between a a BLSC BLSC and and a a target. It It is is also also an an important important factorfactor that that influences inﬂuences the penetrationpenetration performanceperformance of of BLSCs. BLSCs. The The efﬁciency efficiency of of the the BLSC BLSC is is increased increased to toa certaina certain standoff standoff distance, distance, which which is calledis called the the optimal optimal standoff standoff distance. distance. With With a 0.6 a mm 0.6 thickmm thick liner, COMP B, 2a = 50◦ and 2a = 100◦, and n = 0.5, the penetration performance of BLSCs is simulated liner, COMP1 B, 2a1 = 50° 2and 2a2 = 100°, and n = 0.5, the penetration performance of BLSCs is simulatedwith different with S different (S = 4, 6, S 8, (S 10, = 4, and 6, 128, 10, mm, and respectively.) 12 mm, respectively.) AsAs cancan bebe seen seen from from Figure Figure 16, for16, the for tested the constructiontested construction of the BLSCs, of the the BLSCs, greatest the penetration greatest penetrationdepth is about depth 14.25 is mm,about and 14.25 this mm, is achieved and this at is the achieved standoff at distance the standoff of 10 mm.distance It should of 10 be mm. noted It shouldthat there be arenoted two peaksthat there on the are penetration two peaks depth-standoff on the penetration distance curves.depth-standoff However, distance there is notcurves. yet a However, there is not yet a full understanding about the formation of these two peaks. The possible Appl. Sci. 2018, 8, 1863 11 of 12 Appl. Sci. 2018, 8, x FOR PEER REVIEW 11 of 12 fullreason understanding is that the velocity about the gradient formation in the of jet these form twoed peaks.by the TheBLSCs possible is different reason from is that the the one velocity that is gradientformed by in thethejet ordinary formed byLSCs, the BLSCsand this is differentleads tofrom a different the one thatdistribution is formed pattern by the ordinaryof penetration LSCs, andperformance. this leads to a different distribution pattern of penetration performance.

Figure 16.16.Penetration Penetration depth depth of of BLSCs BLSCs with with different different standoff standoff distance: distance: (a) Penetration (a) Penetration depth ofdepth various of standoffvarious standoff distance; distance; (b) Sectional (b) Sectional penetration penetration crack. crack. 6. Conclusions 6. Conclusions The penetration performance of a novel linear shaped charge, BLSC, is discussed in this paper. The penetration performance of a novel linear shaped charge, BLSC, is discussed in this paper. Compared with the ordinary LSC with a constant 60◦ apex-angle liner, the BLSC, which contains a 40◦ Compared with the ordinary LSC with a constant 60° apex-angle liner, the BLSC, which contains a small-apex-angle liner and a 60◦ large-apex-angle liner, greatly improves the efficiency of the main 40° small-apex-angle liner and a 60° large-apex-angle liner, greatly improves the efficiency of the charge energy. With a 1.0 mm liner thickness, 8701 explosive, and 10 mm standoff distance, the DOP main charge energy. With a 1.0 mm liner thickness, 8701 explosive, and 10 mm standoff distance, tests show that the penetration performance of the BLSC is 29.72% better than that of an ordinary LSC the DOP tests show that the penetration performance of the BLSC is 29.72% better than that of an for a #45 steel target. ordinary LSC for a #45 steel target. The results from the numerical simulations in a multi-material Eulerian algorithm of penetration The results from the numerical simulations in a multi-material Eulerian algorithm of performance are all in good agreement with the DOP tests, thus verifying the feasibility and penetration performance are all in good agreement with the DOP tests, thus verifying the feasibility effectiveness of the presented Eulerian model. and effectiveness of the presented Eulerian model. For the BLSC with 0.6 mm thick liner, COMP B as an explosive, small apex angle of 50◦ and 100◦, For the BLSC with 0.6 mm thick liner, COMP B as an explosive, small apex angle of 50° and respectively, n = 0.5, and S = 10 mm is recommended to attain the best penetration performance on a 100°, respectively, n = 0.5, and S = 10 mm is recommended to attain the best penetration #45 steel target. The greatest penetration depth is about 14.25 mm. performance on a #45 steel target. The greatest penetration depth is about 14.25 mm. All the results provide a guide and reference for the structural design of BLSC. All the results provide a guide and reference for the structural design of BLSC. Author Contributions: X.C. wrote the article; G.H. and S.F. contributed to scientific discussions; C.L. proposed theAuthor original Contributions: idea. X.C. wrote the article; G.H. and S.F. contributed to scientific discussions; C.L. proposed Funding:the originalThis idea. research was funded by [the National Natural Science Foundation of China] grant number [11772059],Funding: This and [theresearch National was Keyfunded Research by [the and National Development Natu Programral Science of China]Foundation grant numberof China] [2017yfc0822300]. grant number Conflicts[11772059], of Interest:and [theThe National authors declareKey Research no conflict and of interest. Development Program of China] grant number [2017yfc0822300].

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