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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. Appl. Sci. 2018, 8, 1863 3 of 12 Appl.Appl. Sci.Sci. 20182018,, 88,, xx FORFOR PEERPEER REVIEWREVIEW 33 ofof 1212 2.1.2.1.
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