DETERMINATION OF FOCAL LENGTH FOR CUMULATIVE CHARGES WITH VARIOUS CONCAVITY SHAPES

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1 Internationa Journa of Mechanica Engineering and Technoogy (IJMET) Voume 8, Issue 11, November 217, pp , Artice ID: IJMET_8_11_114 Avaiabe onine at ISSN Print: and ISSN Onine: IAEME Pubication Scopus Indexed DETERMINATION OF FOCAL LENGTH FOR CUMULATIVE CHARGES WITH VARIOUS CONCAVITY SHAPES Vadimir Kovaevskyi, Dmitriy Modovan, Vadimir Chernobai, Saint Petersburg Mining University, Russia, 19916, Saint-Petersburg, 21 ine, 2 ABSTRACT This artice discusses an approach to determination of efficient penetration of cumuative "knife" (jet) generated by exposion of eongated cumuative charge (ECC) into destroyabe media. It is determined that the penetration depth of cumuative knife depends on optimum distance between ECC and destroyabe medium. Herewith, maximum penetration depth is achieved upon retaining of its integrity. An experimenta approach is proposed to determination of foca ength upon operation of ECC. Veocity gradient aong moving cumuative jet has been experimentay studied. Optimum foca ength shoud equa to the distance between ECC and obstace, when the jet is not yet separated from stamper. Foca engths for various types of ECC are theoreticay cacuated. Key words: eongated cumuative charge, cumuative knife (jet), foca ength, penetration depth, crater width, utimate deformation, materia pasticity, stamper-jet system. Cite this Artice: Vadimir Kovaevskyi, Dmitriy Modovan, Vadimir Chernobai, Determination of Foca Length for Cumuative Charges with Various Concavity Shapes, Internationa Journa of Mechanica Engineering and Technoogy 8(11), 217, pp INTRODUCTION Increase in oca impact of exposion is achieved by means of concavity in charge of various shape: conica, spherica, paraboic, etc. Charges of jet perforators and axia torpedoes have predominanty concavities of conica shape. Cumuative effect is significanty higher when the concavity surface is coated by thin metaic ining. Under the action of pressure of tens and hundreds of thousands megapascas produced by detonation of exposive charge, the concavity ining is compressed with high force from its top to base. Meta at interna ining surface fows generating thin and fast cumuative jet. In average, about 1 wt % of ining is transformed into cumuative jet, the remainder forms cigar-shaped rod, stamper, which moves at the end of the jet at decreased speed without editor@iaeme.com

2 Vadimir Kovaevskyi, Dmitriy Modovan, Vadimir Chernobai effective work, and it can infict damages being jammed in the generated channe. Cumuative jet shoud be generated in cavity free from dense materia or iquid. Cumuative jet is generated by active portion of cumuative charge directy adjacent to concavity and characterized by propagation of detonation products towards cumuative jet [1]. Detonation products of remaining passive portion of cumuative charge fy apart without affective work and generay infuence negativey on structures and environment. The portion of charge active portion increases by pacement of charge into massive she of soid and strong materia. The speed of head portion of cumuative jet achieves 8-1 km/s, the speed of tai portion is ower by severa times, and the speed of stamper does not exceed.5-.8 km/s. Cumuative jet during its fow is eongated and narrowed, its braking impact increases. Exerting high pressure onto obstace of tens and hundreds of thousands megapascas, the cumuative jet can generate a channe in stee with the ength by 3-4 times higher than the charge diameter and the average diameter is by 6-7 times ower than it. The channe depth generated in rock by cumuative jet is higher than that in stee and depends on structure and strength properties of rocks; in rocks saturated by iquids the channe depth is higher than in non-saturated rocks. Cumuative charges provide the highest generated depths when they are ocated at certain optimum distance from obstace, this distance is known as foca ength. Cumuative effect occurring upon impact of speciay designed charges is widey appied upon directed breakage of both metaic and reinforced concrete structures as we as rocks. Such simpe practices were initiay described in fundamenta works and subsequenty cited in numerous artices devoted to aspects of cumuative actions. Upon detonation of exposive charge without concavity a minor indent is observed in materia without obstace, and at sma distance between charge and obstace the impact sharpy decreases. Existence of concavity in charge provides concentration of energy density which is manifested by increase in indent depth in obstace. When the considered cumuative charge is removed from the obstace, the effect of exposion impact aso sharpy decreases. The use of metaic ining in cumuative charge eads to sharp increase in breaking impact, the penetration depth of cumuative jet significanty depends on the distance between cumuative charge and obstace. The differences in impact of cumuative charge without and with concavity metaic ining are reated with physica pecuiarities of impied modes of spatia concentration of energy density. In the first case the cumuative effect appears in generation of gas cumuative jet [2, 3] which is a fast-directed fow of exposion products with increased energy density (the speed of such jet can be even higher than the second cosmic speed km/s). However, such gas cumuative jet has reativey ow impact efficiency with regard to obstace, especiay at some distance from it, which is stipuated by fast expansion of gaseous exposion products due to non-uniform distribution aong the jet ength and existence of transversa osciations in jet. This eads to radia scatter and fast decrease in density of exposion products. At present jet generation of axiay symmetric cumuative charge has been studied in sufficient detais [4, 5]. Such processes as generation of cumuative knife in eongated cumuative charge (ECC), determination of their foca engths and penetration of cumuative knife into various obstaces are poory known, despite that the reevant knowedge is required for designing and efficient appication of such charges. According to the concusions in [6, 7], generation of directed main fracture predetermines nuceation of nuceus fracture, which mainy depends on the appied method of directed breakage editor@iaeme.com

3 Determination of Foca Length for Cumuative Charges with Various Concavity Shapes 2. METHODS Taking into account the aforementioned, upon interaction of ECC with destroyabe materias and rocks it is mainy required to consider direct penetration of cumuative knife into various media and generation of nuceus fracture (stress concentrator). On the basis of data in [4, 8] the penetration depth of cumuative knife is the higher, the higher is its ength irrespective of destroyabe materia. In its turn the ength of cumuative knife is determined by the distance between charge and destroyabe materia. The higher is this distance, the onger is the cumuative knife. However, it can be eongated infinitey, since for each concavity ining (copper, stee, auminum, brass) there exists utimate vaue of knife eongation; when it is achieved, the materia is fragmented. Efficiency of fragmented cumuative knife, as shown in [9, 1], decreases significanty due to scatter of eements. The distance of the highest efficiency of cumuative knife is known as foca ength. It was demonstrated in [11, 12, 13] that foca ength is such distance at which cumuative knife is fragmented. One of the methods of experimenta determination of foca ength is the impact of cumuative charge on wedge. This method is schematicay iustrated in Fig. 1. Figure 1 Experimenta determination of foca ength. 1 - ECC; 2 - eectric detonator; 3 - stee wedge;4 -hoder Upon ECC impact on wedge a channe is generated in it, its sizes are finay determined by the distance from the wedge to the charge. Maximum sizes of the channe (depth and width of opening) are obtained at the distances between charge and obstace (wedge) equaing to foca ength. The tests were performed with three standard sizes of ECC: ECC-1 ( d =6.75 mm), ECC-2 ( d charge = 9 mm) and ECC-3 ( d charge = 4.3 mm). A charges were comprised of a copper tube with shaped concavity fied with octogene. 3. RESULTS The tests were performed with a stee wedge with the thickness of 25 mm, the wedge ange ( ) corresponded to the incination ange of ining front equaing to ECC-1: 18 ; ECC-2: 25 ; ECC-3: 21. Figures 2 and 3 iustrate variation of channe sizes as a function of distance between charges and wedge. charge editor@iaeme.com

4 Vadimir Kovaevskyi, Dmitriy Modovan, Vadimir Chernobai Distance to charge, m, 1-3 Figure 2 Carter width as a function of distance to charge (ECC). (1 ECC 1; 2 ECC 2; 3 ECC 3) Penetration depth, m, 1-3 Carter width, m, 1-3 Figure 3 Penetration depth (1-3 m) as a function of distance to charge (1-3 m) (ECC) (1 ECC 1; 2 ECC 2; 3 ECC 3) The foca ength can be cacuated. With this aim et us consider physica effect which determines the foca ength. The generated cumuative jet moves to obstace and is eongated due to speed gradients. Herewith, when the stresses between jet eements exceed critica vaues the jet is fragmented. The impact of singe jet eements on obstace is significanty ower than that of integer jet due to ower kinetic energy and ower cumuative ength. Therefore, the foca ength is the distance at which the jet is not yet fragmented. Moreover, the jet shoud not be separated from stamper since the cumuative kinetic energy of "jet-stamper" is higher than that of the jet itsef. On the basis of the aforementioned we assume that the foca ength between charge and obstace is such distance which is ower than that when the jet is separated from stamper. It is known [5] that the jet speed varies ineary aong its ength: 1 x, (1) Distance to charge, m, editor@iaeme.com

5 Determination of Foca Length for Cumuative Charges with Various Concavity Shapes where is the speed of jet head, is the dimensioness coefficient determined by the speed gradient, x is the distance from the head of cumuative jet, is the initia jet ength. In order to determine the speed gradient aong the jet a series of tests was performed with breaking of spaced stee pates with the thickness from 1. to 2. mm. It was assumed that the speed of simuated eement of cumuative jet after breaking of pate equaed to the speed of jet eement at the distance from the jet head equaing to the thickness of the broken pate. Chronophotography of breaking of spaced obstaces (pates) ocated at equa distances from charge is iustrated in Fig. 4. Figure 4 Impact of cumuative knife on spaced obstaces ( =4*1-6 s) 4. DISCUSSION Processing of chronophotography demonstrated that varied from.78 for ECC-2 to.75 for ECC-3. Determination of stamper jet ength is simiar to determination of jet vaue: t ULT, (2) where is the jet effective ength, is the utimate speed of jet penetration into ULT obstace, t is the current time. Destruction of stamper jet system, that is, jet separation from stamper, occurs after achievement of critica deformations in the system materia. Deformation is determined as foows:, (3) Substituting Eq. (3) into Eq. (2) for utimate case of system destruction we obtain the foowing: ULT t ULT, (4) where t ULT is the time of destruction of stamper jet system editor@iaeme.com

6 Vadimir Kovaevskyi, Dmitriy Modovan, Vadimir Chernobai Utimate deformations, which destroy stamper jet system, are determined by utimate pasticity of ining materia (copper) and, hence, do not depend on charge type, they are constants for a considered charges (ECC). Anaysis of Eq. (4) demonstrates that the time of ULT utimate deformation and system destruction is determined by the ratio. The distance L, when the jet is separated from stamper, can be considered as foca ength and to determine as foows: L tult ULT ULT, (5) It is shown in [2] that the utimate pasticity of copper ( i =.6) is determined as foows: i 2 n 3, (6) At such i ULT =.68, and foca engths wi equa to 9 mm for ECC-1, 7 mm for ECC-2, 5 mm for ECC-3, which agrees with the experimenta data. 5. CONCLUSIONS Maximum penetration depth of cumuative knife is achieved upon retaining of its integrity. Foca ength is the distance between ECC and obstace when the jet is not yet separated from stamper. Efficiency of ECC can be determined experimentay by the penetration depth and channe opening width generated upon impact of these charges on metaic wedge. REFERENCES [1] Savenkov, G.G., Barakhtin, B.K. and Rudometkin K.A. Mutifracta anaysis of structura modifications in a cumuative jet. Technica Physics, 6(1), 215, pp [2] Chang-bin, Y. Basting cumuative damage effects of underground engineering rock mass based on sonic wave measurement. Journa of Centra South University of Technoogy, 14(2), 27, pp [3] Yingguo, H., Wenbo, L., Ming, C., Peng, Y. and Jianhua, Y. Comparison of bast-induced damage between prespit and smooth basting of high rock sope. Rock Mechanics and Rock Engineering, 47(4), 214, pp [4] Lavren`t`ev, M.A. Kumuyativnyi zaryad i printsipy ego raboty [Cumuative charge and principes of its operation]. Uspehi mat. nauk, XII(4), 1957, pp [5] Orenko, L.P. Ed. Fizika vzryva [Physics of exposion], Vo Moscow: Fizmatit, 22. [6] Kopakov, V.I., Savchenko, G.G., Mazur, A.S. and Rudomyotkin, K.A. Chisennoe modeirovanie funktsionirovaniya udinennogo kumuyativnogo zaryada po zheezobetonnoi pregrade [Numerica simuation of impact of eongated cumuative charge reinforced concrete obstace]. Zhurna tekhnicheskoi fiziki, 85(1), 215, pp [7] Babkin, A.V., Kopakov, V.I., Ohitin, V.N. and Seivanov, V.V. Chisennye metody v zadachakh fiziki bystro protekayushchikh protsessov [Numerica methods in probems of fast processes]. Moscow: Bauman MGTU, editor@iaeme.com

7 Determination of Foca Length for Cumuative Charges with Various Concavity Shapes [8] Huang, J., Ma, Y., Huang, K. and Zhao, J. Anaysis of Aperture Shape Changing Trend Base on the Shaped Charge Jet Penetration through the Stee Target. Asia Simuation Conference: proceedings. Part I: Communications in Computer and Information Science, 27-3 October, China: Springer, pp [9] Pebecca, M., Leeavanichku, B. and Leeavanichu, C. Survey of four damage modes for concrete. Sandio Report/ SAND , 29, 8 p. [1] Gachenko, Yu.P. Ob effekte kumuyatsii pri razrushenii gornykh porod dekontsentrirovannymi zaryadami [On cumuative effect upon destruction of rocks by deconcentrated charges]. Zapiski Gornogo institute, 171, 27, pp [11] Kopakov, V.I., Savchenko, G.G., Mazur, A.S. and Rudomyotkin, K.A. Chisennoe modeirovanie funktsionirovaniya udinennogo kumuyativnogo zaryada po zheezobetonnoi pregrade [Numerica simuation of impact of eongated cumuative charge reinforced concrete obstace]. Zhurna tekhnicheskoi fiziki, 85(1), 215, pp [12] Rumyantsev, B.V. Coective penetration of cumuative jets into britte materias. Technica Physics, 6(4), 215, pp [13] Kurchin, G.S., Vokhmin, S.A. and Kytmanov, A.A. Viyanie formy geoogicheskogo kontakta na veichinu poter` pri otrabotke prikontaktnykh zon [The infuence of shape of geoogica contact on osses upon processing of near-contact areas]. Zapiski Gornogo instituta, 223, 217, pp [14] Kumar, A. and Gupta, A. K. Deformation and Detachment of Carbon Tetra Choride Dropet in the Presence of Different Concentration of Surfactant from Soid Substrate. Internationa Journa of Advanced Research in Engineering and Technoogy, 6 (7), 215, pp [15] Petr Aexeevich Demenkov, Maxim A. Karasev and Dmitry N. Petrov, Predicting Land- Surface Deformations During The Construction of Underground Faciities of Compex Spatia Configuration, Internationa Journa of Civi Engineering and Technoogy, 8(11), 217, pp editor@iaeme.com