PENETRATION OF METAL-FABRICS COMPOSITES BY SMALL PROJECTILES L. I. Slepyan and M. V. Ayzenberg-Stepanenko

Transcription

1 Pesonal Amou Systems. Bitish Cow Copyight/MOD 998. PENETRATION OF METAL-FABRICS COMPOSITES BY SMALL PROJECTILES L. I. Slepyan and M. V. Ayzenbeg-Stepanenko The Institute fo Industial Mathematis 4 Yehuda Hanahtom Steet 84 P.O.B. 5 Bee-Shea 845 Isael ABSTRACT. Analytial and numeial solutions ae pesented desibing dynamis and fatue of omposite metal-fabi amou penetated by small poetiles (bullets and fagments). Compaison of one-dimensional and spatial axisymmeti models fo nonlinea dynamis of a ply is onduted and thei apabilities fo patial alulations ae disussed. A ompute model fo spatial dynamis of omposite amou is desibed as a basis fo a alulation tool speially designed to simulate penetation poesses in atual metal/fabis shields. Residual paametes of the poetile afte pefoation of the pimay metal amou ae obtained on the basis of expeimental data poessing and enegy onsideations. Compaison of alulation esults with test data fo atual steel-kela shields podued by the Isaeli Militay Industies Co. shows suffiient appliability of the tool. INTRODUCTION Thee ae aious types of light metal/fabi omposite amous onsisting of a had metal o eami plate as pimay amou and a laye of flexible extensible fabi plies as a seonday amou. The latte is epesented often by kela and dyneema. Fibeglass and othe omposites ae used as well. Suh an amou is intended to potet light ombat o ash-aying ehiles seuity doos abins and ontol ooms in boats and small ships et. against light ams []. The ole of pimay amou is not only to deease the impat enegy but notably to maximaize the aea of impat onto the seonday amou. This is ahieed by mushooming the poetile head duing penetation of pimay amou. Foming a plug sees this pupose as well. The seonday amou is intended to stop the defomed poetile due to the ability of the fabi to onsume the emaining kineti enegy of the bullet. Thee ae many woks deoted to desiption of impat and penetation egimes in dutile bittle and ombined tagets. In paallel with puely empiial appoahes whih usually hae found appliations thee ae some theoetial appoahes analytial and numeial (see fo example [ 6]). A aiety of ompute odes ae known (see fo example [5 Chapte 9 6 7]). Computational models fo detemining the esistane of textile stutues to ballisti impat ae pesented in [8 ]. A set of semi-empiial and puely analytial models fo detemining esistane of a single thead and a thead pakage has been poposed in [ 6]. An analytial solution fo the dynamis of a single thead unde a onentated impat [7] has eently been used in [4 5] to design a simple one-dimensional pefoation model. At least two aiables must be detemined oetly by a mathematial model: maximal stesses (o anothe itial aiable) and the esistane to the poetile motion. In this sense a weakness of the one-dimensional model is an essential misepesentation of these alues as funtions of time. In fat as an be seen below they tun out to be inaiable unde onstant poetile eloity and deease fast with the deease of the eloity. In ontast in axisymmeti fomulation whih seems to be muh lose to eality these alues inease in time unde onstant eloity. This an ompensate fo deease in the esistane foe (due to the deease in eloity) in a onsideable pat of the poetile path.

2 In the pesent pape ompaatie esults of alulations ae pesented fo one-dimensional and axisymmeti fomulations. Futhemoe a thee-dimensional axisymmeti model of multi-ply fabi is onsideed. The inestigation has foused on designing a fast omputation tool oiented to PC. The tool poides a quantitatie basis fo ompute solution of optimization poblems. Calibation of the tool has been done on the basis of a ompaison of alulation esults and expeiments onduted by the Roket Systems Diision (RSD) at the Isaeli Militay Industies Co.. ONE-DIMENSIONAL MODEL FOR FABRIC ARMOUR A linea o hadening-type nonlinea elasti thead is onsideed. Initially the thead is at est unstessed and plaed along a hoizontal line. Suddenly a point of it is foed to moe in the etial dietion with onstant eloity. Unde these onditions two types of waes popagate along the thead to the ight and to the left. One is a longitudinal wae popagating with eloity and the othe is a tansesal wae. The latte has the shape of a gowing wedge and D denotes its eloity. It is assumed that D <. This nonlinea poblem has a simple analytial solution [7]. It an be desibed as follows. The onsideed domain onsists of thee egions. In the fist s > t (s is the Lagange oodinate along the thead and t is time) the thead is hoizontal and at est. In the seond Dt < s < t the thead is also hoizontal but thee exists onstant tensile stess >. Also in this egion the patile eloity g is dieted towad the ental point. In the thid egion s < Dt the patile eloity is etial. Tensile stess in the thid egions is the same as in the seond. The goening equation fo the extensible flexible thead dynamis is: R R s t R s t () Hee is initial density is nonnegatie tensile stess and R is the position eto. The pimes and dots aboe denote deiaties with espet to the oodinate along the thead and time espetiely. The Lagange aiables ae used then the modulus R = is steth; is stain. In the following we intodue the modulus E [in geneal the seant modulus is meant: E = E()] by the elation E In these tems the wae eloities ae E D. () - () Q A sin A Tensile stess and the extenal etial foe Q ae whee A is the total oss-setion aea of the theads whih esist to the impat. In its tun stain satisfies the equation In the impotant ase of small stain that is fo a small / atio the asymptoti elations ae alid as follows: (4)

3 () w u z Although expessions () and (5) ae alid only fo = onst they show that the esistane foe deeases fast as the eloity deeases. This is a onsequene of the one-dimensional fomulation of the poblem. Let * be the limiting tensile stess and ** the limiting aeaged ompessie stess. The stength onditions ae [we use the asymptoti elations (5)] whee B is the impat aea. Both * and ** an be itial fo amou design. In patiula the esistane Q is equied to be high enough to satisfy the ondition onening the allowed tansesal displaement of the ea. This displaement must be less than the fee spae behind the amou. Let us then assume that Q = B ** at the beginning of the impat t =. In this ase using the expession fo Q in (6) fo a aiable eloity and assuming that all the fibes wok simultaneously one aies at the equation whee m and ae the poetile mass and its initial eloity (with aount taken of the eatie impulse of the plug). The displaement following fom this equation is Note that this maximal displaement is six times lage than the theoetial minimum oesponding to the inaiable esistane foe B **. In fat the displaement is oeestimated beause the one-dimensional poblem is onsideed. As shown below the esistane foe deeasing due to the bullet deeleation ineases in time due to the axisymmeti geomety of the stutue. This leads to an essential deease in the displaement. Neetheless the esistane foe tends to zeo with the eloity.. AXISYMMETRIC FORMULATION AND COMPARATIVE RESULTS In the axisymmeti fomulation a flexible membane is onsideed whih does not esist ompessie stesses. This means that tangential stesses ae at zeo and only adial stesses ae still nonzeo. In this ase equation () takes the fom It an be ewitten in poetions on etial and adial axis (6) E B AE Q * * * (7) B dt d m 5 ** (8). B m w w t B B m t w max ** ** ** ) ( (9). st st R R R (5) A Q ~ ~ D ~ ~

4 whee pimes denote deiaties with espet to and u w E - u w. () z The equation fo the bullet motion is m W Q () whee Q = A z A= H is the bullet adius H is the fabis pakage thikness. The bullet-fabis ontat ondition is w( t) W(t). () Equations () - () togethe with zeo initial onditions [exept W ] wee numeially alulated using the expliit finite diffeene sheme. Gid paametes wee hosen fom the ondition of mesh dispesion minimization (see [8 9]). This appoah enables disontinuities and high gadients of the solution to be alulated with good auay. Conuent with this the one-dimensional poblem was simulated. Some ompaatie esults ae pesented in Figue. The alulations wee pefomed fo a onstant eloity at =. In Figues and 4 the esults oespond to bullet impat onto the fabis. In the alulated examples the following paametes wee used: bullet: = 49 m/s m = g = 5 mm; fabis: H = mm = g/m E = 6. 5 kg/m (the linea stess-stain diagam). These alues oespond to an AK-47 bullet and a omposite steel-kela amou. The initial eloity of the bullet is 7 m/s. Afte pefoation of.5 mm thik 6 BHN pimay steel amou its esidual eloity is 6 m/s [see below elation (7)]. With aount taken of the plug mass the eloity beomes 49 m/s. In ontast to the one-dimensional model whee the esistane foe Q is onstant in the axisymmeti ase it ineases with time (see Fig. ). Calulated efeene alue Q = N oinides with that obtained fom elations (5). The shapes fo one-dimensional and axisymmeti ases do not diffe too muh. Fig Vetial displaement w and esistane Fig. Vetial displaement w foe Qunde onstant eloity at = unde the bullet impat

5 In the ase of the bullet impat the alulated esults etial displaements (Fig. ) the bullet eloity and the esistane foe (Fig. ) and stains (Fig.4) show signifiant diffeene between one-dimensional (a) and axisymmeti (b) models. In the latte ase the bullet is stopped at t = 5.8 ms and w max =.49 m. In the fome the bullet eloity! when t! " wheeas w is integated and w max =.67 whih is moe than 5 times lage than in the axisymmeti ase. This esult oesponds to the same initial alues Q. (a) (b) (a) (b) Fig. Bullet displaement w eloity and esistane foe Q Fig. 4 Stains in oss-setions s time. PENETRATION INTO METAL-FABRIC ARMOURS. CALCULATION TOOL In this setion the alulation tool simulating penetation/pefoation of metal-fabi omposite amou by bullets is biefly desibed. Some examples of alulations ae pesented and disussed. The following main paametes ae taken into aount in the model and alulation tool: bullet weight and geomety thikness and hadness of the pimay amou weight and numbe of plies stength of plies and inte-ply oints (adhesie). Penetation by the bullet into omposite amou is aompanied by a numbe of phenomena that ae simulated by the tool: wae adiation fom the bullet-taget inteation aea fatue of ply oss-setions dynami delamination of plies and inte-ply fition. We use a likely assumption that the seonday amou does not influene the pefoation of the pimay amou and the poess unde onsideation an be diided into two suessie independent stages: pefoation of the pimay amou and penetation into the multi-ply fabis. Stage. Pefoation of thin metal plates At this stage the esidual bullet eloity afte pefoation of the pimay amou its exit mass and diamete ae estimated fom expeiments. A simple fomula fo ballisti limit bl and

6 esidual eloity has been poed (see []) by test data poessing on the basis of enegy onsideation. The tests onduted by the RSD onsisted of seen seies of a numbe of shots in eah by M-6 and AK-47 bullets onto amou plates of aious thiknesses and hadnesses. The test and poessing esults fo M-6 bullets ae pesented in the Table. Table N seies H (m) #$% (m/s) (m/s).. (m/s) / Hee H and BHN ae the plate thikness and the Binell hadness numbe whih wee inaiable fo the uent test seies while the bullet initial eloity and the esidual eloitiy ae aeaged alues oe all the shots in the uent seies. In the data poessing the atio of enegies m and BHN. H. d (d is the bullet alibe) was used and the following dependene was poed: BHd.. bl bl. (4) m Fomula (4) gies the best appoximation to test esults if the empiial onstant is: fo an M-6 bullet (m =.6 kg d =.56 m) and = fo an AK-47 bullet (m =.97 kg d =.76 m). The last olumn of the Table shows good auay of the theoetial appoximation. Stage. Dynamis and penetation of the multi-ply fabi amou The mehanial model of the multi-ply is as follows. The fabis is assumed to onsist of a numbe of thin flexible plies onneted by an adhesie. The following onditions and assumptions ae onsideed to be alid in the poblem fomulation: & the plies ae thin membanes as desibed in Setion ; & the tension stess-stain diagam = () of a ply is not speified in adane; & a ply fails unde the ondition that the tensile stain ahiees a gien limiting alue; & the adhesie funtions in tension-ompession and shea as massless isoelasti spings; & the nomal and shea stess-stain diagams in the adhesie ae not speified in adane; & nomal/shea flaking is ealized unde the ondition that nomal/shea stesses eah gien limiting alues; & dy fition between plies ealizes afte shea flaking unde ompessie stesses. Multi-ply pakage dynamis is desibed by the axisymmeti model () modified with aount taken of the inte-ply inteation: u f f w h h h S S s - N h h h N (5) s z s s z z

7 whee u (t) and w (t) ae adial and etial displaements of the -th ply f is the fabis density h is the thikness of the dy ply h s (t) is the uent distane between the +-th and -th plies S and N z ae - and z-poetions of sums of nomal and tangential stesses in the adhesie between neighboing plies. In-ply stess in a uent ply oss-setion is alulated fom the following expession: '* ) '( lim + t t t + t (6) whee is elongation () lim is the limiting stain and t () is the moment of fatue of a uent oss-setion of the -th ply. Stesses in the adhesie oespond to simila elations. An algoithm and oesponding ompute tool fo alulation of this poblem hae been designed on the basis of an expliit finite diffeene sheme. Stability and mesh dispesion minimization onditions ae eealed in the alulation poess. The tool as was examined has fast CP-time (fo examples below it is in the inteal fom to 8 min fo PC-586). Calibation of the tool has been ompleted by the ompaison of alulation esults with tests onduted by the RSD and in this way effetie moduli and stengths of plies and adhesie wee ealuated. Some esults of numeial simulations of penetation into metal-fabi amou ae pesented in Figues 5 6 and 7 (see also examples in []). The pimay amou is had steel plate (H = 4mm BHN=5). The seonday multi-ply amou is manufatued of (a) Kela-49 and (b) Kela-9 fabis with the same thikness (with aount taken of adhesie):.5 mm the same aeal density of the ply:.5 kg/m and tensile stength limit:.75 GPa. The Young moduli ae diffeent: (a) GPa and (b) 6 GPa. Configuations ae shown in Fig. 5 of two shields of Kela-49 and Kela-9 and of the same aboe-mentioned pimay amou unde penetation by M-6 bullets (the ply position oesponds to boundaies between light and dak stips). The latte stops the bullet at t = 77 ms and plies ae boken though while the fome is ompletely pefoated at t = 4 ms with the bullet esidual eloity V es = 7 m/s. (a) (b) (b) Fig. 5 Steel-kela omposite tagets (np = 4) s. an M-6 bullet

8 The same onfiguations ae shown in Fig. 6 fo the ase of these amous penetated by AK-47 bullets. The shield of Kela-9 stops the bullet at t = 8.5 ms and plies wee boken though the shield of Kela - 49 was pefoated at t = 6.5 ms with V es = 67 m/s. (a) (b) Fig. 6 Steel-kela omposite tagets (np = 4) s. an AK-47 bullet Compaatie estimation of the stopping powe of these shields s the ply numbe an be seen in Fig. 7. Hee V es () = is the bullet esidual eloity afte pefoation of the pimay laye n p is the ply numbe in the pakage n * p is the numbe of pefoated plies es (b) (a) M - 6 -data(b) es (b) (a) AK - 47 n * p 5 n * p n p 4 8 n p Fig. 7 Shield stopping powe s. the numbe of plies

9 It an be seen that the stopping powe of the pliable fabis (b) poes bette than that of the igid one (a). Compaison of alulation esults with test data fo atual steel-kela shields podued by the Isaeli Militay Industies Co. shows good pedition ability of the tool. ACKNOWLEDGEMENTS: The authos ae indebted to D. A. Pido fo his onstant attention to the wok to D. N. Fabe and D. Y. Yeshuun fo the tehnial ollaboation and the oppotunity to use the test data. This eseah was suppoted by gants No fom the Ministy of Siene Isael and No fom the United States-Isael Binational Siene Foundation (BSF) Jeusalem Isael. REFERENCES. Ballisti Pefomane of Potetie Amo In: Composite Poduts fo Ballisti Potetion. Infomation Bulletin of the Roket Systems Diision. TAAS Isaeli Militay Industies Co. (99).. Wilkins M. L. (978) Mehanis of Penetation and Pefoation. Int. J. Engng. Si Wilkins M. L. (98) Compute Simulation of Penetation Phenomenon. In Ballisti Mateials and Penetation Mehani (R. C. Laible ed.). Elseie Andeson C. E. and Bodne S. R. (988) Ballisti Impat: The Status of Analytial and Numeial Modeling. Int. J. Impat Engng Zukas J. A. (ed.) (99) High Veloity Impat Dynamis Wiley N.-Y. 6. Cotes R. Naao C. Matinez M.A. Rodiguez J. and Sanhez-Galez V. (99) Numeial Modelling of Nomal Impat on Ceami Composite Amous. Int. J. Impat Engng Johnson G. R. and CookV.H. (99) Lagangian EPIC Code Computations fo Oblique Yawed-Rod Impat onto Thin-Plate and Spaed-Plate Tagets at Vaious Veloities. Int. J.Impat Engng Roylane D. Wilde A. and Toi G. (97) Ballisti Impat of Textile Stutues. Textile Res. J Cunniff P. M. (99) An Analysis of the System Effets in Woen Fabis unde Ballisti Impat. Textile Res. J Ting J. Roylane D. Chi C. H. and Chitangad B. (99) Numeial Modelling of Fabi Panel Response to Ballisti Impat. In: Po 5 th Int. SAMPE Tehn. Conf. Ot Vinson J. R. and Zukas J. A. (975) On the Ballisti Impat of Textile Body Amou. J. Appl. Meh Shim V. P. W. Tan V. B. C. and Tay T. E. (995) Modelling Defomation and Damage Chaateistis of Woen Fabi unde Small Poetile Impat. Int. J.Impat Engng Naao C. Rodigues J. and Cotes R. (994) Analytial Modelling of Composite Panels Subeted to Impat Loading. Colloque C8 J. Phys. IV 4 9 C8-55 C Cunniff P. M. (996) A Semiempiial Model fo the Ballisti Impat Pefomane of Textile-based Pesonnel Amou.. Textile Res. J

10 5. Choon-Benloulo I. S. Rodiguez J. and Sanhez-Galez V. (997) A Symple Analytial Model to Simulate Textile Fabi Ballisti Impat Behaio.Textile Res. J Choon-Benloulo I. S. Rodiguez J. and Sanhez-Galez V. (997) A Symple Analytial Model fo Ballisti Impat in Composites. Colloque C J. Phys IV 7 C-8 C Smith J. C. MkCakin F. L. and Shiefe F. H. (958) Stess-Stain Relationships in Theads Impated Tansesely.Textile Res. J Ayzenbeg-Stepanenko M. V. (98) Numeial Expeiment on Fatue Dynamis of a Layeed Composite. Mehanis of Composites Ayzenbeg-Stepanenko M. V. (99) Non-Stationay Wae Popagation in Composite Stutues. Po. 4 th Isael Conf. Meh. Engng. se Slepyan L. Ayzenbeg-Stepanenko M. Pido A. Shtemle Yu. and Vainbeg Ya. (995) Light Amo Penetation by Small Ams. The Institute fo Industial Mathematis and the Roket Systems Diision of TAAS. Repot July 995 Bee-Shea Isael.. Pido A. Slepyan L. Ayzenbeg-Stepanenko M. and Shtemle Yu. (998) Engineeing Poblems of Penetation: Adanements at the Institute fo Industial Mathematis Bee- Shea. Po.7 th Isael Conf. Meh. Eng Slepyan L. and Ayzenbeg-Stepanenko M. (997) Supeplasti Potetie Stutues. In Pogess in Industial Mathematis. B.G. Teubne Stuttgat 5-59.