Normal projectile penetration and perforation of layered targets

Int. J. Impact Enong Vol. 7, No. 2, pp. 229-259, 1988 Printed in Great Britain

0734-743X/88 $3.00+0.00 © 1988 Pergamon Press plc

NORMAL PROJECTILE PENETRATION AND PERFORATION OF LAYERED TARGETS JOSEPH RADIN*'~ a n d WERNER GOLDSMITH + * Armament Research and Development Authority, Haifa, Israel and ~Department of Mechanical Engineering, University of California, Berkeley, CA 94720, U.S.A.

(Received 3 November 1987; and in revised form 22 February 1988) Summary~The response to normal impact of hard-steel blunt and conically-nosed projectiles on multi-layered plates of soft aluminum, both adjacent and spaced, as well as on adjacent disks of thin aluminum and polycarbonate, including sandwich arrangements, was studied experimentally in the subordnance velocity regime in the vicinity of the ballistic limit. A comparison of the penetration resistance of these targets with corresponding monolithic plates of aluminum or polycarbonate has been effected on the basis of aereal density. The ballistic resistance of the metallic monolithic target was found to be greater than that of several adjoining plates of the same thickness; this was considered to be due to the greater bending resistance of the former. On the other hand, a 15% greater ballistic resistance of the polycarbonate target was observed than for the corresponding aluminum disk. In several cases where an adjacent aluminum layer preceded the polymer, a terminal deflection of the aluminum plate in the direction opposite to that of the striker travel was observed, which was found to be due to the change in the penetration mode of the metal from petalling to extrusion. Elastic energy stored in the polycarbonate was returned to the metal cover, causing not only this rearward deflection, but also vibrations. When this occurred at the ballistic limit, the period of these oscillations was found to correspond closely to that of a plate with a distributed mass with the projectile mass concentrated at its center. Wave propagation effects were not considered in the analysis, but also contribute to this reversed deflection. The experimental ballistic limits for monolithic targets of the two materials were compared to predictions of other investigators for both the blunt and conically-tipped strikers, derived from simple models of the process. The expected ballistic limit for combined targets was calculated from an energy approach with the aid of relations for this parameter based on the above models for a single material. Satisfactory correspondence was obtained between the test results and calculated values.

NOTATION a b C d D E k K K* L m mat n P0 P R T T' T* v

crack length roB~PinT constant plug diameter projectile diameter energy, Young's modulus spring constant constant defined by equation (30) nptTa2/3mB length mass mass of striker and previous plugs upon impingement on a layer number of layers, n th layer constant perforation pressure central load projectile radius thickness thickness of frontal layer [ptnD 2 sin 2 0t/2mB]T velocity

tWork performed while the first author visited the Department of Mechanical Engineering, University of California, Berkeley. 229

230

J. R4DIN and W. G()LI)SMI-IH W

WCH :~ 6 0 v p cr o~

work second term in equation (18) half-cone angle of cylindro-conical projectile

deflection angular petal deflection Poisson's ratio density

engineering stress frequency

Subscripts A B BL c C

DH e E f F H L LT N o p r

R S SC t T UC US Y

aluminum projectile ballistic limit central compression deformation and heat equivalent experimental free bending homogeneous Lexan

layered target nose

initial plug residual rear plate shear targets supporting frontal plate target dishing failure in monolithic target ultimate compression ultimate shear yield

Superscripts E

1 T

experimental frontal layer theoretical INTRODUCTION

Shielding of equipment and personnel to prevent impact damage by strikers of various shapes travelling over a wide range of velocities is a major concern in both military and civilian applications. Performance and cost requirements indicate the need for minimum weight considerations which, in turn, suggests the use of multi-layered targets. A plethora of publications on penetration and perforation of homogeneous targets by projectiles including experimental, phenomenological and numerical modelling approaches has appeared. However, only limited results for multiple target materials exist in the literature [1-8], and the results obtained cannot easily be correlated since different target and projectile materials, nose shapes, impact geometries and striker speeds were used. Hence, additional information from a thorough study of the behavior of such targets for a selected number of materials and collision configurations is required to permit an examination of the unusual phenomena produced when penetration occurs in combined or spaced targets, and also to ascertain the ballistic limit (minimum perforation velocity) for these various combinations. In particular, this appears to be the first published work where one of the components of a combined target is a polymer. Recent research on layered steel targets [7, 8] confirmed that a single target is more effective in preventing penetration than a laminated one of equal thickness, a conclusion verified in [-1] and in the present tests, but contradicted by [3] and also by [4] when using aluminum. Plugging failure in aluminum alloy beams ensued upon impact by round-nosed

Penetration and perforation of layered targets

231

lead projectiles I-4], which was modelled by a modified energy balance due to [9] by adding a term for compressive work. The ballistic limit was obtained from a three-stage penetration model of normal impact of blunt projectiles on a homogeneous target [10,] using results for the permanent plastic deformation of clamped beams struck normally [11,]. Here, multilayered beams were found to be superior to single beams of equivalent thickness due to the structural deformation acting as a shear absorbing mechanism. The optimum number of equally-thick layers was three, but further optimization could be achieved by using layers varying in thickness. More recent tests on normal impact of multi-layered mild steel targets struck normally by hard-steel blunt projectiles [5-] indicated optimal use of a homogeneous layer below a critical value and a prescribed combination of layers above. A numerical analysis of monolithic, double layer and multiple layer targets of aluminum [-6-] based on the model of [-10-] showed that the ballistic limit of layered targets of equal thickness is always lower than that of a monolithic target of equivalent thickness. Twodimensional computer codes of hypervelocity impact into plastic layers backed by aluminum substrates have also been developed [-12,], based on petalling and plugging as failure modes. The criterion of perforation was chosen as the difference in the generalized plastic strain relative to a given criterion. In another investigation [4,], homogeneous and layered targets were found to provide greater penetration resistance than spaced units for the impact of two types of aluminum beam by round-nosed lead projectiles. In contrast, [8-] reported that two separated targets provided superior resistance, and [5-] indicated that there was no difference. Hence the question of the effectiveness of layering appears to be the subject of some controversy. Concurrently, analytical expressions for ballistic limits of homogeneous substances have been obtained in closed form for normal impact of blunt strikers when the effects of thermal action can be modelled in terms of an adiabatic shear zone [ 10,]. In the case of more general nose shapes, such as conical or ogival tips, an analytical determination of this parameter is more complicated [13,]. In general, the value obtained from either a phenomenological model or a numerical code will not agree with test results, in the former case because of the failure to incorporate all deformation mechanisms, and in the latter case because of inexactitudes in the delineation of the constitutive behavior and/or the failure criterion. Some of these mechanisms involve crack initiation and propagation, often in conjunction with petalling, brittle fracture, ductile hole growth, plugging and fragmentation, and-particularly in the case of thin plates~ishing; the latter process was found to absorb large amounts of energy [14, 15]. Friction is generally disregarded in penetration or perforation processes [16,]. Microstructural approaches that consider the coalescence and propagation of micro-cracks and voids have also been developed, leading to statistical descriptions of damage. In view of the disagreements described above, one of the objectives of the present work is to provide a larger database under controlled conditions for the performance of two types of material~2024-0 aluminum and polycarbonate (Lexan)--singly or in combinations, subjected to normal impact of undeformable strikers with two types of nose shape, blunt or 60 ° conically-tipped. Tests were conducted in the range from just below to just above the velocity where perforation of the target occurs. Specifically, ballistic limits, which, for a given projectile striking normally, represent a structural system property, were measured for various composite adjacent targets--this value was also predicted from a knowledge of the ballistic limits of the individual components--and for targets separated by a spacer. The difference between the penetrability of a target composed of a single homogeneous material and that of a layered target of the same total thickness was ascertained. Furthermore, the processes involved in the interaction of the components of adjacent layers of different materials during projectile perforation were investigated and compared to what occurs under the same conditions in corresponding homogeneous materials. Finally, the data were used to rank protective efficiencies of various barriers on the basis of areal density. Polycarbonate was selected as the polymeric component as it exhibits largely ductile response during perforation, in contrast to PMMA or nylon which shatter in brittle fashion during such an event.

232

J.

. ProJectlle

&

RADIN

and W.

GOLDSMITH

storage scope

post

veioaty

FIG. 1. Schematic EXPERIMENTAL

of the experimental

ARRANGEMENT

arrangement. AND

PROCEDURE

A few tests were executed by means of a powder gun* at speeds up to 360 m s- ’ ; however, the vast majority of experiments were performed by means of a pneumatic propulsion device using compressed nitrogen. This unit, which has been described frequently in the past (for example in [17]), accelerates the strikers placed in the breech through the 1.341 m long barrel upon the opening of a quick-acting valve. Two types of cylindrical strikers, both with diameters of 12.57 mm and lengths of 38.1 mm, with either blunt or 60” conical tips and corresponding masses of 35 and 29g, were projected at speeds of up to 210 m s-l. Their interruption of two light beams a fixed distance apart passing through two sets of slots cut into the barrel near the muzzle end provided the signals for the transit time and hence the velocity. The projectiles were composed of alloy steel with a hardness of R, 56-59; they did not deform in any of the tests. A schematic of the experimental arrangement is shown in Fig. 1. The residual velocity of the blunt strikers was determined from the time interval derived from the interruption of two laser beams placed in two parallel planes normal to the projectile path; the second ray formed a net by successive reflections from a set of mirrors. The technique employed, detailed in [18], is capable of identifying both the final projectile speed and that of a preceding plug. The timing data were recorded by means of Nicolet digital oscilloscopes with a minimum sampling rate of 5 MHz. The ballistic limit of the targets struck by conically-tipped projectiles was bracketed by the measurement of the additional striker penetration in a relatively thick aluminum witness plate positioned approximately 50mm behind the target for a series of initial velocities. Extrapolation of the data to zero depth provided a first-order approximation of this parameter that was refined by the conduct of additional tests around this velocity. An example of this procedure is shown in Fig. 2 for several classes of adjacent targets, with the extrapolation error compared to the measured speed for embedment indicated in the diagram. All tests were performed on 139.7 mm diameter plates sandwiched between a circular steel ring and a hard-steel circular frame, clamped together by a series of bolts on a 114.3mm diameter. The frame was rigidly fastened to a heavy steel table. Metal disks consisted of 20240 aluminum with hardnesses ranging from 42 to 52 Brine11and thicknesses of 1.6,3.2,4.8 and *These tests were performed

at the Naval

Weapons

Center,

China

Lake, California.

Penetration and perforation of layered targets

233

2,40 ~ /. - - ~

I 0I~5~/~

2OO

E ~

q60

U ~

11.7 mm lexen frontal plate 3.2 mm aluminum plate

~ f ~ - - ~ e ~ ' ~ ' ~ - ~ - - 2

~

-

X 3.2 mm aluminum adjacent ~ \

-1%

4 x 16 mm aluminum adjacent

~

120

plates ptates

2 x 3.2 mm lexon adjacent plates

40

o

~

,~

I

~

Depth of penetration in a witness plate ( m m )

FIG. 2. Approximate determination of the ballistic limit of a target by linear extrapolation of the penetration depth in a witness plate. 30C 28O 260 Aluminum

240 220 200 180 160 140 (/3

120 ~ = 10-3S -I

~00

Lexan

8O 60 4O 2O 0

/./J/

.~-"~

01020041

E,0.15 s

0106

0108

i 0 IO

all2

Strain

FIG. 3. Quasi-static compression curves of aluminum and polycarbonate.

6.4 mm. The polycarbonate used was Lexan,* with a density of 1.2 g cm- 3 and thicknesses of 3.2, 4.8, 5.7, 8.6 and l l . 7 c m . Quasistatic stress-strain curves for the aluminum 1-13-] and Lexan are presented in Fig. 3. Both strikers and plugs were extracted from a recovery box filled with celotex, permitting the evaluation of the plug mass and its terminal dimension to an accuracy of 0.025 mm. Both homogeneous aluminum and Lexan targets and combined targets consisting of adjacent layers of only aluminum or aluminum and Lexan were emplaced in the holder. Spaced targets were positioned on each side of a spacing ring with a central hole. For selected runs of a 1.6 mm thick aluminum plate prefacing a 11.7 mm thick disk of Lexan, a Photec IV intermediate-speed camerat with an operational range from 100 to 104 pps was used to obtain the deflection history of the target center. Owing to the clamped boundary condition, any separation between adjacent plates in the laterally unconstrained region could not be detected photographically. The data were recorded at 9700 frames s-1 on 400 ft rolls of Kodak 4-X reversal film with a sensitivity of ASA 400. The variable velocity of the film was determined from the exposure of dots produced by a 1000 Hz pulsed flash of a photodiode. Lighting was provided by a Pallite VIII lamp consisting of eight 300 W bulbs spaced in a circle around the camera lens tube. A delay unit in the camera triggered the gun after passage *General Electric Co. tPhotonic Systems, Sunnyvale, California.

234

J. RAI)INand W. GOLDSMJJH

of a specified footage of film. P o s i t i o n d a t a o n the film were o b t a i n e d by m e a n s of a V a n g u a r d m o t i o n a n a l y z e r e q u i p p e d with a c u r s o r a n d a digital r e a d o u t m e c h a n i s m . T h e m e a s u r e m e n t error in these d a t a is e s t i m a t e d to be n o larger t h a n _+5"~,, w h e r e a s the m a x i m u m e r r o r in the direct striker velocity d a t a does n o t exceed + 1%.

RESULTS A total of 150 p e n e t r a t i o n e x p e r i m e n t s were c o n d u c t e d o n the v a r i o u s targets at n o r m a l i n c i d e n c e , s u b d i v i d e d as follows: 19 tests each were p e r f o r m e d o n h o m o g e n e o u s a n d l a y e r e d a l u m i n u m a n d o n s i m i l a r targets of L e x a n with b l u n t - n o s e d projectiles; 36 shots o n single o r a d j a c e n t layers of a l u m i n u m were fired with c o n i c a l - t i p p e d strikers, i n c l u d i n g f o u r with the p o w d e r g u n ; 27 e x p e r i m e n t s w i t h this projectile were c a r r i e d o u t o n single o r l a y e r e d L e x a n plates; a n d 49 r u n s were m a d e w i t h the c o n i c a l projectile o n a d j a c e n t a l u m i n u m / L e x a n c o m b i n a t i o n s . F i g u r e s 4 - 6 show typical t e r m i n a l c o n f i g u r a t i o n s for ballistic limit shots o n a l u m i n u m , L e x a n a n d l a y e r e d a l u m i n u m / L e x a n c o m b i n a t i o n s . At a n d j u s t a b o v e the ballistic limit, the b l u n t projectile p r o d u c e s a c i r c u l a r p l u g in b o t h types of plate. T h e c o n i c a l projectile f o r m s p e t a l s in b o t h s u b s t a n c e s at these speeds u p o n piercing, with c o n s i d e r a b l e

(i)

(ii) (a) FIG. 4. Photographs of adjacent layered 2024-0 aluminum targets struck at the ballistic limit. (a) Two 1.6 mm layers, 60 ° conical projectile, vo = 95.1 m s - l : (i) side, (ii) front. (b) Four 1.6 mm layers, 60 ° conical projectile, vo = 157.2m s - 1: (i) side, (ii) front, (iii) rear. (c) 1.6 mm front, 3.2 mm rear layer, 60 ° conical projectile, Vo= 129.7m s 1: (i) side, (ii) front. (d) Two 3.2 mm layers, blunt projectile, Vo= 133.1 m s - l : (i) side, (ii) front.

Penetration and perforation of layered targets

235

(i)

(ii)

(iii) FIG. 4(b).

dishing in the metal, and to a lesser extent in the polymer. The final hole shape in the Lexan layers exhibits a much smaller diameter than that of the aluminum, showing substantial elastic recovery, and extrusion towards the distal side was frequently found in both materials on the impact side. Figure 7 shows the perforation phenomenon for a set of spaced aluminum plates. The central deflection histories of a 11.7 mm thick Lexan layer and a prefacing 1.6 mm aluminum sheet are presented in Figs 8 and 9 for the impact of a conically-tipped striker just above and at the ballistic limit, respectively; only the displacement of the metallic component was recorded in the second diagram. The ballistic limits of homogeneous aluminum and polycarbonate targets using blunt or

236

J. RADIN and W. GOLDSMITH

(i)

(ii) FIG. 4(c).

60 ° conically-tipped strikers are presented in Fig. 10 as a function of areal density; there is somewhat less data scatter in the case of the pointed projectile. It is evident that Lexan exhibits a 15~o greater perforation resistance than aluminum. Figure 11 presents comparisons of the ballistic limit of homogeneous and adjacent targets with up to four layers and of the same total thickness, composed of aluminum, when struck by both types of penetrators, whereas Fig. 12 also includes similar data for layers spaced 6.4 mm apart when struck by the conical bullet. Clearly, the resistance of the layered targets drops relative to that of monolithic blocks of the same thickness, amounting to 15 ~o when a 6.4 mm plate is replaced by four 1.6 mm adjacent disks; spaced targets are even less effective. Finally, Fig. 13 depicts the variation in the ballistic limit of targets composed of combinations of the two materials as a function of areal density upon perforation by a conically-headed striker. The resistance increases linearly with this density, and it can be noted that combinations of materials generally exhibit a higher ballistic limit than for a corresponding homogeneous aluminum, but less than that for the comparable monolithic polymer block. Different ordering of layers can change the limit of targets composed of both materials. For aluminum layers of 3.2 mm thickness and Lexan layers of 8.6 and 11.7 mm thickness, a higher ballistic resistance was encountered when the Lexan layer was used as the backing material. For convenience, the data of Figs 10-13 are reproduced in Tables 1-4. Post-impact examination of monolithic aluminum targets indicated the well known result of the shearing of a plug by the blunt projectile and plate dishing and petal formation when perforation was accomplished by the conically-headed striker. Flat-nosed strikers generated the same effect in polycarbonate; however, the conical bullet produced only petalling without any dishing in this material. In combined targets where the aluminum layer was first struck by such a bullet with the Lexan as the back-up, the metal was occasionally perforated

Penetration and perforation of layered targets

237

(i)

(ii) FIG. 4(d).

in an extrusion mode---as found when such bullets were fired at the center of predrilled holes with diameters less than 1/3 that of the striker [13J--rather than by petalling, and the deflection of the aluminum plate occurred in a direction opposite to the projectile velocity. MODELLING CONSIDERATIONS

Phenomenological models of normal monolithic plate perforation abound, as exemplified for the impact of blunt projectiles by the well-known contribution of [-9] (which requires prior knowledge of the ballistic limit), and gives the residual velocity vr in terms of initial velocity Vo, the ballistic limit VBLand the mass of projectile ma and plug mp by the equation Dr [-mB/(mB+ mp)](Vo2 -- V~L) =

(1)

and the analyses of [-18-21], from which a ballistic limit can also be calculated. Corresponding models exist for normal perforation of conically-tipped strikers [ 13, 22-26-] that also permit the determination of a zero residual striker velocity in closed form. (a) Ballistic limits and work of perforation for normal blunt-nosed impact on adjacent targets of the same material The ballistic limit of multi-layered targets composed of the same material struck at right angles by a blunt-nosed nondeformable bullet can be estimated from an energy balance that

238

J. RADIN a n d W . GOLDSMITH

(i)

(ii) FIG. 5(a).

(i) F m . 5(b). FIG. 5. P h o t o g r a p h s o f a h o m o g e n e o u s L e x a n t a r g e t at t h e b a l l i s t i c limit. (a) 3.2 m m t h i c k , 60 ° c o n i c a l p r o j e c t i l e , Vo = 62.9 m s - ' : (i) side, (ii) front. (b) 4.8 m m t h i c k , 60 ° c o n i c a l p r o j e c t i l e , vo = 82.1 m s - 1 : (i) front. (c) 6.35 m m t h i c k , 60 ° c o n i c a l p r o j e c t i l e , Vo = 93.89 m s ' : (i) side, (ii) front. (d) 11.7 m m t h i c k , 60 ° c o n i c a l p r o j e c t i l e , Vo = 161.5 m s - 1 : (i) side, (ii) front. (e) 3.2 m m t h i c k , b l u n t projectile, t'o = 65 m s - , : (i) side.

Penetration and perforation of layered targets

239

(i)

(ii) FIG. 5(c).

neglects the interaction term between layers. The work required to perforate such a structure, WLT, is the sum of the work required to pass through each plate, Wi:

WLT= Y, W~, i=l

(2)

where n is the number of layers. The work required to penetrate the rear plate, WR, is determined experimentally at the corresponding ballistic limit from an expression that describes the arrest of the projectile in this component, given by

WR = (1/2)mB(vEL) 2.

(3)

The energy consumed to penetrate the frontal plate should include the work performed on the supporting layers during plugging, Wsc. When the energy balance cited in [9] is modified to account for this term, the result is:

(1/2)m.TV2o = EDH + Wsc + (1/2)(mBT + mp)V~,

(4)

where mBT is the total mass of the striker prior to impact on a current layer and EDH is the energy required to deform the target and account for heat effects. The term EDn is the difference between the initial and final kinetic energy, given by EDH = (1/2 )(mpf/[mBT + mpf])msT v2 ,

(5)

where mpfis the free mass of the plug. At the ballistic limit Vo= VBL,where vr = 0, equations (4)

240

J. RADIN and W. O()LDgMll,'t

(ii) FIG. 5(d).

(i) FIG. 5(e).

Penetration and perforation of layered targets

241

(i)

(ii) (a) FlG. 6. Photographs of the penetration of adjacent layers of different materials. (a) 4.8 mm thick frontal Lexan layer, 3.2 mm thick rear aluminum layer, conical projectile, vo = 140.9 m s - l , partial perforation: (i) front, (ii) rear. (b) 11.7 mm thick frontal Lexan layer, 3.2 mm thick rear aluminum layer, conical projectile, vo = 197 m s- 1, producing petals: (i) side, (ii) front. (c) Same configuration as (b), % = 203 m s- 1: (i) front, (ii) rear. (d) Two 1,6 mm aluminum plates sandwiching a 11.7 mm thick Lexan plate, conical projectile, vo = 203.7 m s - 1, producing extrusion on the frontal aluminum layer and petalling on the others: (i) side, (ii) front, (iii) exploded. a n d (5) p r o v i d e the e x p r e s s i o n for the w o r k r e q u i r e d to o v e r c o m e the r e s i s t a n c e d u e to the p r e s e n c e of the s h e a r z o n e a n d c o m p r e s s i o n of the s u p p o r t i n g l a y e r s [-4] :

Wsc = (1/2)(mBT/[mBT + mpf])m~T(V~L) 2,

(6)

w h e r e Vie is the ballistic limit for a f r o n t a l l a y e r w h i c h , h o w e v e r , c a n n o t b e c a l c u l a t e d directly. H o w e v e r , Wsc c a n b e e v a l u a t e d as the e n e r g y t r a n s m i t t e d to the c u r r e n t l a y e r t h r o u g h the p e r i p h e r a l s h e a r z o n e Ws a n d t h a t t r a n s m i t t e d to the s u p p o r t i n g l a y e r s b y c o m p r e s s i o n Wc:

Wsc = ws + we.

(7)

T h e q u a n t i t y Wc p r o d u c e d b y the c o m p r e s s i v e stress d u r i n g p l u g g i n g is

Wc = ¼(aucrcdZT'),

(8)

w h e r e U C d e n o t e s u l t i m a t e c o m p r e s s i v e s t r e n g t h , d is the p l u g d i a m e t e r a n d T' is the t h i c k n e s s of the f r o n t a l layer.

242

J. RADIN and W. GOLDSMIIH

(i)

(ii) FIG. 6(b).

Reference [4] assumed that the energy transmitted to the present layer in a multi-layered system by peripheral shear effects is the same as that for an isolated layer. Thus, Ws is obtained from the energy balance of such a layer when vr = 0 as

Ws = (1/2)(msT/[msT + mp])mBTV2L,

(9)

where VSLis the ballistic limit of this isolated layer. Substitution of equations (8) and (9) into the energy balance, equation (4), yields Ur =

(msv/[mBT + mp])(Voz -- ,rvtsLj-]211/2! ,

(10)

where the ballistic limit of the current layer is given by U/L

=

[ ,~2 -~- (aucztd2T'[msT

~t~BL

+ mp])/2m2T} '/2.

(11)

This ballistic limit of the frontal layer accounts for the effects of structural motion by inclusion of a peripheral shear energy term which is transformed into kinetic energy of the layer. It is necessary to consider the effective mass of the projectile, mBT, which takes into account the material added from previous layers. The work required to penetrate the frontal plate, Wv, can thus be calculated from equations (10) and (11) when equation (11) has been evaluated previously to obtain the ballistic limit of an isolated layer from the experimentally determined ballistic limit of a homogeneous target of identical thickness and from the measured dimensions of the plug from the frontal plate. The impact velocity on the rear plate is equal to the residual velocity

Penetration and perforation of layered targets

243

(i)

(ii) FIG. 6(c).

after penetrating the adjacent frontal plate, as shown in Fig. 14, with W~ = f(Vo, Vr, VBL).

(12)

Hence the impact velocity Voon the rear plate, i.e. the residual velocity after penetrating the n - 1 adjacent frontal layers, equals its experimental ballistic limit only when the initial striking speed on the system is equal to the ballistic limit of the combination: (t~r)n- 1 ~---(/)o)n = (/)BL)n"

(13)

The same procedure can be used to calculate the impact velocity for the n - 1 adjacent frontal layers, so that, finally, the required impact velocity on the first layer to provide the ballistic limit for the system can be calculated. Furthermore, for a known residual velocity of each layer of a composite adjacent target, the work required to penetrate each layer is Wi = f[(Vo)i, (Vr)i, (t~BL)I]

(14)

and the work required to perforate the remaining layers can be similarly calculated. (b) Ballistic limits and perforation work for normal impact of conically-tipped projectiles on adjacent layers of the same material The same approach in tracing the velocity drop through a succession of adjacent layers as

244

J. RADIN and W. GOLDSMITH

t,~ ~0

(i)

(ii)

(iii) FIG. 6(d).

°~

Penetration and perforation of layered targets

245

i¸/iil ! i¸¸

(i)

(ii) FIG. 7. Photographs of two 3.2 mm thick 2024-0 aluminum layers with a 6.4 mm spacing perforated by the conical projectile with vo = 153.4 m s - 1 : (i) side, (ii) rear.

Lexon

ALuminum

\

/

vo =206m/s~

Penetration

=i

vr=738m/s

g E

-I

v

-

-

~

-

-

--

"

8 =6 - 2

I ~ I

8

T

~

Time (msec) t

I ~ . ~I ' - i-

2

~

3

4

t~.--.~-"---J

. . . . .

--

I "~J

ALuminum Lexon

. . . . . .

FIG. 8. Deflection history of an adjacent layered target composed of a 1.6 mm thick frontal aluminum plate and a 11.7 mm thick rear Lexan plate struck by the conical projectile at the ballistic limit of 1 9 1 m s -1.

246

J. RAD1N a n d W. GOLDSMITH ALurninum

Penetration

Le×on

i)

BaLListic Limit

E ~

-4.

/~ V

A

A

v

v

2

4

3

5

Time ( m s e c ) ~)

2

FIG. 9. Deflection history for the configuration of Fig. 8 perforated by a conical projectile at a velocity of 206 m s '.

/

2oo

~/.

180L

~ ;60 _~ ,4o

/"

o

/~/V

-~_ 120

E_

I00

+

o 60 ~13 40i

L

20L

•

~

~

;

BLunt projectile

----

ConicaL-nosed projectile

--'--~

v (A) [k)

(A)

l

Areal density (kg/m

]

FIG. 10. Ballistic limit of homogeneous 2024-0 aluminum and polycarbonate targets for bluntfaced and 60 ° cylindro-conical projectiles as a function of areal density.

20o

/

2 80 )

MonoLithic,bLunt

"

20 ; 0

L a y e r e d , conical. I

2

3

4

5

6

7

8

9-

Thickness(ram) FIG. 11. Ballistic limits of monolithic and layered aluminum plates as a function of target thickness for blunt and conical-nosed strikers.

Penetration and perforation of layered targets

247

200 180

/ •

160

-I

thick

140

E t20 E

io0

o

80

/ . ~ /

(adjacent)

/f

:

--

6c

v Two Layers with spacing 6 4 mm

4C 20

o

i

~

~

~

~

~

~

~

Thickness (mm)

FIG. 12. Ballistic limit of two layers of 2024-0 aluminum targets, adjacent or spaced, 6.4 mm apart, struck by conically-tipped projectiles.

24oI

220I 200[ "~ ~8o~ ~" 160F

~ 2oh '-2- kO0 _~

-6 m

80 6O 40 20

/,>2"// onoL,th,c Lexon

/.~/~/ /~)~'/ ~//'

Double-Layered Lexan Monolithic aLuminum Double Layered a l u m i n u m -

--

& Peta/ling of aluminum and Lexan layers, and deflection of layers in direction of impact x Extrusion of aluminum frontal layer, and deflection of aluminum plate opposite to impact

4 ~ ,~ ~ 2'0 2'~ 2~ Areal density ( kg / m 2 } 1. 11.7 mm sandwiched Lexan (LE), 2 x 1.6 mm aluminum (AL) 2. 11.7 mm LE, 1 x 3.2 mm AL (front) 3. 11.7 mm LE, 1 x 1.6 mm AL (front) 4. 3.2 mm sandwiched LE, 2 x 1.6 mm AL 5.4.8 mm LE, 1 x 1.6 mm AL (front) 6.5.7 mm LE, 1 × 1.6 mm AL (front) 7.3.2 mm LE, 1 x 1.6 mm AL (front) 8.5.7 mm sandwiched LE, 2 x 1.6 mm Al 9.4.8 mm LE, I x 3.2 mm AL (front) 10. 3.2 mm LE, 1 x 3.2 mm AL (front) 11.3.2 mm LE, 1 x 4.8 mm AL (front) 12. 11.7 mm LE, 1 x 3.2 mm AL (rear) 13.8.6 mm LE, 1 x 3.2 mm AL (front) 14.8.6 mm LE, 1 x 3.2 mm AL (rear)

FIG. 13. Ballistic limit of various combinations of adjacent multi-layered plates of aluminum and Lexan struck by a conical projectile as a function of areal density. in (a), a l s o s h o w n i n F i g . 14, c a n b e u s e d i n t h i s c a s e , w i t h t h e m o d i f i c a t i o n t h a t t h e r e s i d u a l velocity must be adapted to the different tip shape. The model homogeneous target yields

+ K* 2 + K- )2 Vo

ltaT2(02

-

-

01)O'Yq

J

of [13] for any single

1/2

(15)

J. RADIN a n d W. GOLDSMITH

248

T A B L E 1. B A L L I S T I C LIMITS O F M O N O L I T H I C 2 0 2 4 - 0 A L U M I N U M AND L E X A N AS A l- U N C T I O N OI- AEREAL DENSITY V~HEN STRUCK BY 12.7 m m

(FIG. 10)

D I A M E T E R B L U N T AND 6 0 c C O N I C A L L Y - T I P P E D HARD-STEEL PROJECTILES

Ballistic limit of projectiles

Target

{ms

1)

Thickness Material Aluminum

Lexan

(ram)

Blunt

1.66

Conically-nosed

61.9

52.8

3.2 4.8 6.4

93.0 135 142.4

95.2 144 184.4

3.2 4.8 5.7 11.7

65.0 92.4 99.8 147

62.8 82.0 93.9 161.6

TABLE 2. BALLISTIC LIMITS OF HOMOGENEOUS AND ADJACENT LAYERED 2 0 2 4 - 0 ALUMINUM TARGETS WHEN STRUCK BY 12.7 m m aLUNT AND 60 ° CONICALLY-NOSED HARD STEEL PROJECTILES AS A FUNCTION OF NUMBER OF LAYERS AND LAYER THICKNESS (FIG. l l)

Ballistic limits of projectiles

(ms -~) Layers and thickness (mm)

Blunt

Conically-nosed

1 × 1.6

61.9

52.8

2 x 1.6 3 x 1.6 4 × 1.6

90 113.6 137

93.2 124 157.7

TABLE 3. BALLISTIC LIMITS OF HOMOGENEOUS, ADJACENT LAYERED AND SPACED LAYERED ALUMINUM TARGETS AS A FUNCTION OF TOTAL THICKNESS WHEN STRUCK BY THE 60 ° CONICALLY-NOSED PROJECTILE (FIG. 12)

Ballistic limit Layers and position

(m s - ~ )

2 x 1.6 m m 2 x 1.6 m m with spacing 1.6 m m f r o n t , 3.2 m m r e a r 2 × 3.2 m m 2 x 3.2 m m with spacing

93.2 90.6 129.9 160.4 153.4

where K* = nPt Ta2/3mB, Pt is the target density, a is the length of the crack generated by the conical tip frequently approximated for thin aluminum plates by 80 ~o of the diameter of the projectile whose mass is mB---and T is the target thickness. Quantity av is the yield stress of the perfectly-plastic target plate, and 0 t and 02 are the petal rotation angles at the point of crack arrest and projectile perforation, respectively. The former is assumed to be 2 ° on the basis of extensive previous experiments and the latter is calculable from the crack length and the triangular shape of the petal. Equation (15), which can be expanded to include the dishing effect, provides the best fit for Lexan in the present tests. On the other hand, the model of [25], which ignores bending outside the crater region, gives reasonable correlation for aluminum. The residual velocity for this analysis is vr2 = e - T * (t,o2 -

[gpo/pt sin 2 ct] [ e T•

--

1]),

(16)

Penetration and perforation of layered targets

249

TABLE 4. BALLISTIC LIMITS AS A FUNCTION OF AEREALDENSITY FOR ADJACENT LAYEREDTARGETSCOMPOSED OF DIFFERENT MATERIALSAS SHOWN BY VARIOUSPOINTS IN FIG. 13

Point in Fig. 13 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Target layers LE = Lexan; AL = 2024-0 a l u m i n u m 11.7 m m 11.7 m m 11.7 m m 3.2 m m 4.8 m m 5.7 m m 3.2 m m 5.7 m m 4.8 m m 3.2 m m 3.2 m m 11.7 m m 8.6mm 8.6 m m

thick thick thick thick thick thick thick thick thick thick thick thick thick thick

LE LE LE LE LE LE LE LE LE LE LE LE LE LE

sandwiched between two 1.6 m m thick AL plates prefaced by 3 . 2 m m thick AL prefaced by 1.6 m m thick AL sandwiched between two 1.6 m m thick AL plates prefaced by 1.6 m m thick AL prefaced by 1.6 m m thick AL prefaced by 1.6 m m thick AL sandwiched between two 1.6 m m thick AL plates prefaced by 3.2 m m thick AL prefaced by 3.2 m m thick AL prefaced by 4.8 m m thick AL with a 3.2 m m thick AL rear plate prefaced by 3.2 m m thick AL with a 3.2 m m thick AL rear plate

Ballistic limit (m s - 1) 201.3 213 195.5 127.5 111.3 122.0 95.8 152.8 143.4 125.7 175.4 190.6 186.7 171.4

123

Vo=(vB~).~~ _~

v~=0 =--

Layeredtarget--

~:~' //~BrLoUjntctihtee adedorconicatLytipped

(Vo)3:(ve~)3~

(v~)z=O 2

(vo)2

H

(Vr)2= (Vo)5

I

V°=(V°)I = (VBL)LTIIL

(V,)~

= (Vo) 2

FIG. 14. Definitions of velocities for energy modelling for targets composed of various adjacent layers.

where T* = [ptnD 2 sin 2 ~/2mB] T, D is the bullet diameter, which is frequently approximated as the diameter of the plug, the half-cone angle is given by ~ and Po is an assumed constant perforation pressure, which is equal to or related to the yield stress. The ballistic limit is determined from the value of Voin the previous residual velocity relations when vr is set equal to zero. Such a result using an energy approach [24] yields VBL= (try{2 + [L~ tan 4 ct/b]}/2ptb)l/2(LN tan ~),

(17)

where LN is the nose length and b = ma/prt. An analogous procedure can be applied when the layers are composed of different materials. In the present investigation, the number of layers is limited to three.

250

J. RADIN and W. GOLDSMIHt

(c) Effect on penetrability of doublin 9 the plate thickness (i) Resistance of two adjacent layers of the same material and thickness to normal impact of a conical-tipped striker based on a known ballistic limit of a homogeneous target of equal aereal density. Reference 1-26] has derived an expression for the work required, WT, to produce dishing failure in a monolithic plate based on bending, plastic deformation and ductile hole enlargement by combining previous models; it is given by Wv = (n/2)RTav(R + [n/2]T) + 1.42ay T(T/1.81) z.

(18)

For a target composed of a frontal layer of thickness 7"1 and a rear layer of thickness T2, and neglecting the interaction term between the two segments, the total work WT for this system can be obtained by replacement of T by T 1 + 7"2. When the layers have equal thickness (1/2)T, this becomes WH = WLT +¼n2Ray[T2/2] + 2.13navT[T/1.81] z.

(19)

Hence, equation (19) provides the ballistic limit of homogeneous targets as (UBL) 2 ~--- (UBL)L2T 7!- (WF)H/FnB) "~- 1.5(WcH)H/m,),

(20)

where (VBL)LTis the ballistic limit of two adjacent targets of the same material and thickness. The ballistic limit of two adjacent targets of the same material with two layers, each of thickness (1/2)T, relative to that of a homogeneous target of thickness T is obtained as (UBL)LT = [(UBL) 2 - - { ( W F ) H / m . }

-- 1.5{(WcH)r~}/mB] l/z,

(21)

where (Wcn)n is the second term of equation (18) and represents the transition from dishing to ductile hole formation failure as the thickness of the plate is increased. (WF)H is the work of bending of a homogeneous target [27]. Equation (21) shows that (VBL)LTis always less than (VBL)n for the same material and total target thickness. (ii) Penetrability of an adjacent two-layer aluminum/Lexan target, each with a thickness twice that of a similar system arranged in the same order struck by a conically-tipped projectile. For a frontal aluminum layer of thickness T 1 and an adjacent Lexan backing of thickness T2, the ballistic limit of the combination for the normal impact of a conically-tipped striker may also be obtained upon neglect of interaction by using energy considerations. The ballistic limit of the Lexan plate is obtained from a modification of the value obtained from equation (15) by setting/)r = 0, by neglecting 01 and setting 0 z equal to (n/2) and relating the crack length to the projectile radius (D/2). This limit is equal to the residual velocity of the front aluminum layer, and the ballistic limit for the system equals the striking velocity of the first layer, which is represented by equation (16). From experiments on Lexan targets, it was found that the crack length a could be expressed by the empirical relation a = (D/2)[1 + e x p ( - Vo/VBL)2].

(22)

When Vo~> VBL,then a ~ (D/2), and when Vo = VBL,then a]BL = 1.37(D/2).

(23)

Substituting equations (22) and (23) and the approximation 02 = (n/2) into equation (15) and using the value of VBL derived therefrom, the following expressions are obtained, respectively: vr = (Vo212+ K*]/2[1 + K*] 2 - {[nZT2avD/4m,][1 + exp(--Uo/I)BL)2]})1/2

(24)

VBL= 0.83nT(1 + K*)[Day/mB(2 + K*)] U2.

(25)

and

From the last relation, the ballistic limit of the rear Lexan layer (equal to the residual velocity of the frontal aluminum layer) of thickness T 2 is (VBL)2 = (0.83nT2[1 + K*])2[DayL/mB(2 + K*)].

(26)

Penetration and perforation of layered targets

251

Substitution into equation (16) for Vo the ballistic limit of the combined target, (VBL)LT,and equating the result to equation (26) yield z T, + T2 = (0.83rtT2[1 + K*])Z[D(trv)r exp T*]/(m.[2 + K*]) [(V.L)LT] + [oa~L/p, sin 2 a] [e r" -- 1].

(27)

Replacement of 7"1, T2, T* and K* by twice their values in equation (27) yields an expression for a combined layered target of double thickness with the same order of layering. (d) Vibrations of perforated plates The central deflection 8c of a plate clamped on a radius r c due to a central load P is denoted by the relation [27] (28)

6 = [PS/16nDe],

where De, the equivalent plate stiffness for two adjacent materials 1 and 2 with thickness T, Young's modulus E and Poisson's ratio v, is given by [28] (29)

De = [Ex T(/12(1 - v~)]K,

and where K = 1 -+

E2 T S ( 1 - v21) E1Ta(1-v22)

3(1- v~)1+

1 + -f-+-]

q

(30) ( l + E 2E~2//-(vl+v2~2T2]E1Tl~ 1Tl~ 2"

A simple structure, such as a plate, can be idealized by its representation as a single degreeof-freedom system with an equivalent mass m~q and spring constant k. With the assumption that the adjacent layers vibrate as a single unit without separation, the equivalent spring constant k for elastic vibrations is deduced from equation (28) as k = P/6c = 16~zDffr 2 ,

(31)

with D e obtained from equation (29). The frequency of vibration, co, is given by = (k/mq) 1/2

(32)

and the equivalent mass is me = rff(Tlpl + T2P2).

(33)

(e) Effect of lateral constraint The effect of lateral constraint on the indentation process has been considered both under quasi-static and dynamic conditions [29-31]. It was found that the stress required to initiate perforation of a plate exceeded that in uniaxial compression by factors ranging from 1.4 to 3.2 depending on strain, strain rate and thickness to diameter ratio of the specimens. In consequence, a yield stress three times greater than that found in uniaxial compression was employed in evaluating the analytical expression. COMPARISON OF EXPERIMENTAL AND PREDICTED RESULTS AND DISCUSSION Figure 15 depicts the velocity drop in 3.2 mm thick Lexan targets as a function of initial velocity perforated by a blunt-nosed striker and the corresponding predictions of equation (1); the results are in excellent correspondence. Measured quantities for these tests are listed in Table 5. The values of the ballistic limit determined here support the estimate that the variation in this parameter both for homogeneous and layered targets due to experimental error, material property variations and small projectiles obliquities amounts to about + 3 ~o. Similar agreement was obtained with the data for thin aluminum disks obtained from [18]. Variations of the ballistic limit of the present aluminum targets with thickness are shown in Fig. 16 and compared with the data from [5] derived from corresponding tests on

252

J. RADIN and W. GOLDSMITH

i n,x',~

6° J

~ 4C

~"

Eq (I)

~>' 30

o

L

2'o

4'0

#o

8'o

,oo

,~o

Impact vetocity (m/s)

FIG. 15. V e l o c i t y drop as a function of impact velocity for a L e x a n target of 3.2 m m thickness perforated by a blunt-faced projectile.

TABLE 5. COMPARISON BETWEEN THE EXPERIMENTALBALLISTICLIMIT V~L AND THE VALUE OBTAINED EROM EQUATION(1) FOR 3.2 m m THICK LEXANTARGETSPENETRATEDNORMALLYBY BLUNTPROJECTILES(FIG. 15)

Impact velocity (m s - 1)

Residual velocity (m s l )

Plug diameter (mm)

Plug mass, mp (g)

Ballistic limit from eq. (1) (m s- 1)

71.4 65.0 67.1 76.9 85.1 93.6

23.8 0 2.8 29.0 48.5 61.0

13.79 15.24 14.76 14.91 14.76 14.76

0.389 -0.430 0.451 0.420 0.433

67.7 65.0 67.0 7 i. 1 69.2 70.2

Fit to relation V,L= 5 4 7 9 T(mm) (5) 200

~. ~ ~

180

Exp.

160 From (51 ALuminum el.toy

.~ 140

E

,/

~ 120

( 2 % CU, 1.6% Mg, 1.2% Ni, 1.2% Fe 9 4 % ALl cr = 4 6 0 MPa

E IO0 ~. / , ~

~ 80 o 60 rn 40

20

/ 2

3 4 5 6 Thickness ( mm )

7

8

9

FIG. 16. Experimental ballistic limit for different aluminum alloy targets perforated by blunt-faced projectiles as a function of target thickness. an a l u m i n u m a l l o y w i t h a yield strength try = 4 6 0 M P a . T h e present results are linear, w h e r e a s [5] reports a bilinear curve w i t h a k i n k at T ~ 4 m m ; the d i a g r a m also indicates the empirical relation p r o p o s e d by [-5] for the range of small target thicknesses. T h e a p p a r e n t l o w e r ballistic resistance o f the a l u m i n u m a l l o y relative to 2 0 2 4 - 0 A1 for plate t h i c k n e s s e s in excess of 6 m m was e x p l a i n e d to be d u e to a c h a n g e of the p r e d o m i n a n t energy a b s o r p t i o n

Penetration and perforation of layered targets

253

240

/

220 2OO

/

180 E ~60 .~a140 E t2o k~ .~ ioo 8o

./

//

6O 4O 20

~,. ~ . ~ ' . ~ e r

imental o Eq. (17) •

0

4

6

8 IO Thickness (m m )

Eq 12

(25)

'4

FIG. 17. Comparisonof experimentaland predictedballistic limits for a Lexan target perforatedby a 60° conically-tipped projectile as a function of target thickness.

2OOF 180k

~

~

~60I

~ t40

.EE_too

. . ~ / / . o 7 ~ ..~.~~'" m ~ 60 40 20 0

~ ~ /..../ /6 II

2

f

3i

4i

Thickness

o Experimental

5 (mm)

• Fromeq.(16) . . . . o Fromeq (15) __.__ + Eq (17) ~0 7 8L

FIG. 18. Comparison of experimental and predicted ballistic limits for an aluminum target perforated by a 60° conically-tipped projectile as a function of target thickness. from plastic plate deformation, with only a small fraction transformed into plugging, to a shearing mechanism which requires a lower force to deform the target [5]. From an energy and m o m e n t u m balance which ignores effects outside the plug region, the ballistic limit of a uniform target may be estimated by equating the change of kinetic energy of the projectile during perforation to the work done in overcoming shear strength aus to remove a plug of diameter d from the target of thickness T. For a projectile of radius R, length L and density Ps, /)BL Do for vr = 0 and d = 2R becomes =

VSL = T ( 2 x R t r u s / m s ) 1/2 = C T .

(34)

The values of C are smaller by a factor of about 2 compared to those calculated from the curves of Fig. 10; this is attributed to the neglect of other energy absorption mechanisms such as bending, dishing and lateral constraint. With such a neglect, VSLwill be proportional to the square root of the strength. Thus the slope expected from the empirical equation of [5] for 2024-0 aluminum would be 26.7 m s -1 m m -~ compared to a value of 21 m s -~ mm -~ determined from Fig. 10. The variation of the ballistic limit with thickness is indicated in Fig. 17 for Lexan and in Fig. 18 for 2024-0 aluminum upon employment of conically-tipped strikers. In the former case, the experimental results are in much better agreement with the predictions of equation (25) than with those of equation (17), because the model corresponding to the latter neglects significant physical effects. Similar conclusions are reached in the case of aluminum targets, except that the correspondence is less satisfactory and becomes increasingly more

254

J. RAD[Nand W. GOLDSMITH

unsatisfactory with increased plate thickness; better correlation is obtained by use of equation (16). However, all ballistic limit predictions for conically-tipped strikers are lower than experimental data except for extremely thin targets, because of the neglect of some energy-absorbing processes during perforation. Within the range of variables investigated here, monolithic targets struck normally exhibit a resistance up to 15 ~o greater than layered plates of identical total thickness for both types of projectiles, as predicted by equation (21). As shown in Fig. 12, spaced plates are less effective, but the most significant drop in resistance, 12,5~iout of a total of 16 ~i~, is due to the presence of layers. Corresponding results have been obtained by other investigators with different target materials; however, this diversity prevents a direct quantitative comparison. Reference [4] fired lead projectiles against two types of heat-treated aluminum alloy beams at speeds of 380 m s- 1, producing failure by plugging. The ballistic resistance decreased in the order: adjacent targets, a uniform target of equivalent weight, separated targets of equal weight. The maximum ballistic resistance was obtained with three adjacent laminations of equal thickness. Thin mild steel targets were struck by lead-core cupronickel bullets in another test sequence at speeds of 790 m s i [8]; adjacent plates exhibited a lower ballistic resistance than a monolithic block of equal thickness. The ballistic limit for a number of single plates varying in thickness from 2 to 10 mm was also compared with that of two spaced plates, each half of the thickness of the monolithic block, spaced either 66 or 200 mm apart. Here, the latter arrangement exhibited a higher ballistic limit than the monolith, attributed to the generation of yaw by the first plate that results in greater resistance when encountering a second target due to the increased presented area. As indicated earlier, projectiles at velocities of 250 m s-1 [5] provided no increase in resistance for multi-layered units below a critical value; adjacent layers provided a higher ballistic limit than that obtained when these layers were separated by 12 mm. A comparison was also effected for the perforation by blunt hard-steel projectiles of mild steel plates varying from 1 to 9.5 mm in thickness and multilayered adjacent disks of the same total thickness at velocities up to 500 m s- l. The very thin laminated unit exhibited less resistance than the equivalent single plate, but as the shield thickness increases, the multiple sheets became relatively more effective [1], an effect attributed to an increase in the amount of energy absorbed in bulging of the second layer. Equal effectiveness of the two types of target was found for a ratio of thickness to projectile diameter of about 1/4, associated with a target thickness of 2.4 mm. The present investigation utilized an aluminum target with half the diameter employed in [1] and generated a plug of the same diameter as the projectile, whereas this diameter was larger in the tests of [1]. Thus, the effect of increasing the contact area while striking the second layer does not exist in the current research, and the ballistic limit did not increase upon replacement of the monolithic target by a layered system. It is suspected that, for higher striker velocities, the diameter of the plug reported in [1] would decrease to that of the projectile and a monolithic target would then have again a larger ballistic resistance. These results are in accord with the findings of [4] and [5] for adjoining layers. Whenever the presented area of the plug-penetrator system is increased, the ballistic resistance is also increased; when this does not occur, the dominant parameter influencing the decrease in the ballistic resistance of the layered system relative to the solid target is the lower stiffness. Thus, there is a diversity in the information pertaining to ballistic resistance as affected by layering; the results are highly dependent on target and projectile material and geometry, as well as the impact velocity. A comparison between the experimental and the semi-empirical value of the ballistic limit of adjacent multi-layered targets of 2024-0 aluminum and Lexan by conically-tipped cylindrical strikers is shown in Fig. 19. Predicted values were found from an energy approach, equation (2), with equation (16) or (25) used depending on whether the frontal plate was 2024-0 aluminum (with cry = 2 7 0 M P a ) or Lexan (with cry= 172MPa), respectively. There is reasonably good agreement between calculated and measured results for this normal impact, but the predicted resistance is lower than that observed because the interaction term between and the dishing of the layers was neglected in the energy equation.

Penetration and perforation of layered targets

255

240

'~200

~

160

•

x •

TT

~ L20

o

÷÷•

N -~ 8e ~_ 40 40

80

i 20

tC~O

200

240

Experimental baLListic Limit { m / s )

+ 1 6 mm Thick 2 0 2 4 - 0 aluminum frontal plate, Lexan Layer / several thicknesses) •

5 2 r n m Thick 2 0 2 4 - 0 aluminum frontal plate, Lexan Layer (severaLthicknesses) o 4 8 r a m Thick 2 0 2 4 - 0 aluminum frontal Layer, 3 2 mm thick texan Layer z~ 1 6 m m

Thick 2 0 2 4 - O a L u m i n u m front and rear Layers, texan sandwiched (several thicknesses ) • II 7mm Thick Lexan frontal Layer, 3 2 mm thick 2 0 2 4 - 0 aluminum rear Layer x 8 6 m m Thick Lexan frontal Layer, 5 2 mm +.hick 2 0 2 4 - 0 aluminum

FIG. 19. Correlation of predicted and measured ballistic limits for several adjacent layers of kexan and aluminum perforated by the 60° conical tipped projectile. TABLE6.

COMPARISONBETWEENEXPERIMENTALBALLISTICLIMITSANDTHOSECOMPUTEDFROME Q U A T I O N i 2 7 ) W I T H

APPROPRIATE SUBSTITUTION OF THE THICKNESS VALUES FOR COMBINED MULTI-LAYERED ADJACENT TARGETS OF ALUMINUM AND LEXAN PENETRATED BY 6 0 ° CONICALLY-TIPPED PROJECTILES

Material and ordering of combined multi-layered target R = rear layer F = front layer

Experimental ballistic limit of target, VE (m s- 1)

Calculated limit of combined layered target from known limit of half thickness of each component, vc (m s- 1)

[(vc -- VE)/#E] X 100 (percent)

Aluminum: Lexan:

3.2ram iF) 6.4 mm (R)

161"

171.9

6.7

Aluminum: Lexan:

3.2 mm iF) 9.6 mm JR)

195.2"

206.7

5.9

Aluminum: Lexan:

3.2mm (F) 11.7 mm (R)

213"

231.1

8.5

*Obtained by extrapolation.

In all cases, the Lexan layer exhibited petalling u p o n perforation and the a l u m i n u m experienced extrusion when frontal, but petalling when located at the back. A target consisting of two 1.6 m m thick outer a l u m i n u m plates sandwiching a 3.2 m m thick Lexan disk manifested petalling of all three layers when perforated. Table 6 provides a c o m p a r i s o n of the experimental and the quasi-empirical ballistic limits predicted by equation (27) with the indicated thicknesses replaced by twice their values for targets c o m p o s e d of a frontal a l u m i n u m layer of 3.2 m m thickness and adjacent Lexan layers of variable thickness when struck by a conically-tipped projectile. The c o m p u t e d value of this limit is based on the existing experimental d a t a for the same target arrangement, but half

256

J. RADIN and W. GOLDSMITH

the thickness of each layer. The correspondence between the two magnitudes is very satisfactory. The ballistic limit of composite adjacent targets is expected to be bounded by the ballistic limits of equivalent homogeneous plates of the two materials; this was actually found for most materials, as shown in Fig. 13 for conical strikers, with the lines for two adjacent singlematerial layers representing plates of equal thickness. When there is considerable disparity in the layer thicknesses, the above conditions may be violated; the layering then exerts a dominant influence on this limit. In some cases, where the first layer is a thin aluminum plate and the adjacent backing is substantially thicker polycarbonate, the aluminum was pierced by the pointed projectile in an extrusion mode rather than petalling, giving rise to a backward deflection whenever the thickness ratio of the frontal to rear plate was less than 1/3. This type of reverse deflection involves the absorption of a large amount of projectile energy, but even this phenomenon does not compensate for the reduced ballistic limit in layered targets. To explore the nature of this unexpected phenomenon, some tests were conducted with a 1.6 mm thick frontal aluminum plate with a predrilled central 22 mm diameter hole backed by a 11.7 mm thick Lexan disk struck by a conical-headed projectile passing through this hole at 175ms-~. Although the projectile did not touch the aluminum, this material exhibited a large backward deflection, as illustrated in Fig. 20. When a similar test was conducted with two adjacent Lexan plates, each 16mm thick, as backing, the first Lexan layer was not perforated, as expected, a~d the rearward deflection of the aluminum was quite small. The central deflection of the same layered target due to conical-nosed impact slightly above and at the ballistic limit was photographed at framing rates of about 9500 pps with the results shown in Figs 8 and 9. The first diagram shows that both layers are bent forward during penetration, and, after perforation of the Lexan, it vibrates and exhibits a permanent rearward deflection. In the perforation case, the Lexan plate is bent forward during penetration and its elastic energy is subsequently partly returned to the aluminum cover producing therein both a permanent rearward deflection and vibrations. The experimental frequencies exhibited in these diagrams are compared to those calculated from equation (32) in Table 7, with reasonable agreement. At the ballistic limit, the equivalent stiffness was computed from equation (29) and the equivalent mass from equation (33) with the addition of projectile mass mu. Above this limit, the value olD for each plate was taken as the standard flexural plate stiffness and the equivalent masses for the two layers as corresponding to the plate volume for a clamping radius of 50.8 mm. The Young's moduli and Poisson ratios for the aluminum and Lexan were taken as 72 G P a and 2.2 GPa, and 0.33 and 0.35, respectively. The photographic records indicate that the rearward deflection is due to two effects. One arises from the first increase of the deformation, where material is pushed aside, while the second results from the elastic rebound of the polycarbonate plate, manifested by the second peak of the polycarbonate deformation in Fig. 9. The first effect describes the major mechanism of perforation in thick targets, where axial flow also occurs to form lips on the' free surfaces that were also observed here. Wave propagation has been neglected in the present analysis, but its effects enhance the opposite directions of the permanent deformations exhibited by many multi-component adjacent layered targets. The most distal layer bulges in the direction of projectile travel, while the impact surface is deformed rearward. Perforation in thin plates ensues as the result of petalling for a conical-nosed projectile striking at normal incidence. When the thickness is increased, the major part of the energy is consumed in cratering, with the remainder still generating petalling. In the present tests, perforation occurred primarily in cratering for thicknesses above 12ram (about one projectile diameter) and the height of the lip does not increase further. The elastic rebound effect was documented by the tests involving predrilled holes in the aluminum cover. An estimate of the elastic energy stored can be obtained by assuming that the plate deforms with a constant stiffness until plastic collapse occurs [5]. The total energy is 0.SP~m& with P~,n = 4gMo as the elastic limit load, Mo as the plastic yield moment and a as the elastic

Penetration and perforation of layered targets

(i)

(ii)

(iii) FIG. 20. Photograph of a target composed of a 1.6 mm aluminum frontal plate with an initial central 22 mm diameter hole and an adjacent 11.7 mm thick Lexan plate perforated by a 60 ° conically-tipped projectile at a velocity of 176 m s - 1: (i) back, combined target, (ii) side and rear, exploded, (iii) side, aluminum cover.

257

258

J. RADIN and W. GOLDSMITH

TABLE 7. COMPARISON BETWEEN EXPERIMENTAL AND THEORETICAL FREQUENCIES FOR ADJACENT LAYERS OF DIFFERENT MATERIALSSTRUCK BY A 60 ° CONICALLY-TIPPEDPROJECTILE Velocity (m s - 1)

Equivalent mass meq

Impact

Residual

(g)

t~o

IJr

178

198.0

Frequency, 10 '*s-

0

114 206 35

(0} T - - O.}E)/(.O E

(percent)

Commenl

t'T

VE

1.24

1.05

0.76

0.9

- 16

Vibration of a Lexan layer

0.42

0.55

-24

Vibration of an aluminum layer

18

meq includes equivalent mass of both layers and projectile

73.8

displacement. The elastic stiffness is obtained from equation (31) with De replaced by lET3~12(1 - v2)] and the stored elastic energy is then equal to (3~r~T [1 - v2]a2)/8E. Thus, the energy which can be stored in a polycarbonate plate is about twenty times greater than that which can be stored in a 2024-0 aluminum plate of the same thickness. In fact, owing to its high yield strain, a large amount of the kinetic energy of the projectile is absorbed elastically, and the Lexan plates exhibit almost no permanent deflection after perforation, as indicated in Fig. 8. Ordinarily, for metal targets, this energy will be absorbed plastically and will produce a permanent deformation. CONCLUSION

An investigation of the ballistic resistance of monolithic and adjacent layered targets composed of either 2024-0 aluminum or polycarbonate, or a combination of these materials, was conducted with both blunt and 60 ° conically-nosed projectiles striking at normal incidence in the velocity range 50-210m s - 1. The results were primarily gaged on the basis of areal density; thus, the ballistic resistance of Lexan was found to be about 15 % greater than that of aluminum. The observed ballistic limits of monolithic targets were compared with the predictions of various simplified models and found to be in fair agreement for bluntnosed strikers and in good agreement for pointed projectiles. The ballistic resistance of adjacent layers of equal depth was found to be less than that of the equivalent monolithic target, as was also predicted from simple analytical considerations. Spaced targets were found to be less effective than layered targets in contact, but the most significant resistance drop was due to layering. The ballistic limit for combined layered targets was compared to predictions based on an energy approach. Whenever layers were formed from a combination of materials, the ballistic limit of the system was even less than the lower ballistic limit of the monolithic target of the same thickness. When a thin aluminum plate was backed by an adjacent, relatively thick polycarbonate plate, the former was unexpectedly deflected opposite to the direction of impact, and the ballistic limit of this configuration was found to be about 10 % higher than when the layers were inverted. Two effects were found to be responsible for this rearward deflection: the dominant mechanism is the elastic rebound of the Lexan plate, and the secondary one is due to the change of the penetration mode of the aluminum cover from petalling to cratering. The elastic energy release in the Lexan also generated vibrations whose period corresponded well with the predictions of a simple lumped-parameter model. Acknowledoements---Thisinvestigation was performed at the University of California, Berkeley, and sponsored by the Army Research Office under Contract No. DAAG29-84-K-0021. The authors would like to express their utmost appreciation to Prof. Sol Bodner for his extensive efforts in the acceptance of this work as an M.Sc. thesis of the first author in the Department of Mechanical Engineering at the Technion, Haifa, Israel, as well as for many valuable

Penetration and perforation of layered targets

259

suggestions and discussions. The authors are also grateful to Dr Meir Mayseless for his help and to Mr Stephen Virostek for his generous assistance in the experimental phase of the program.

REFERENCES 1. A. I. ZAID and F. W. TRAVIS, Inst. Physics Conf. Ser. No. 21,417-428 (1974). 2. J. AWERBUCH,Israel J. Tech. 8, 375-383 (1970). 3. R.E. FLAHERTY,A study of low-velocity impacts into thin-sheet aluminum and nylon cloth. NASA TN-6324 (1964). 4. I. MAROM and S. BODNER, Int. J. Mech. Sci. 21,489-504 (1979). 5. R. S. CORRAN, P. J. SHADBOLT and C. RUIZ, Int. J. Impact Engng l, 3-22 (1983). 6. K. NIXDOREE, Trans. CSME 8, 16-20 (1984). 7, S.J. ARISAKA, Coll. Eng. Univ. Tokyo 7, 231 (1916). 8, T. HONDA, G. TAKEMAEand T. WATANABE,Sci. Rep, Tokohu Imp. Univ. 69 (1930). 9. R. F. RECHT and T. W. IPSON, J. appl. Mech. Trans. ASME E30, 384-390 (1963). 10, J. AWERBUCHand S. R. BODNER, Int. J. Solids Struct. 10, 671-684 (1974). ll. E. W. PARKES, Proc. R. Soc. A288, 462-476 (1955). 12. K. N. KREYENHAGEN, M. H. WAGNER, J. J. PIECHOCKI and R. L. BJORK, AIAA J. 8, 2147-2151 (1970). 13. B. LANDKOF and W. GOLDSMITH, Int. J. Solids Struct. 21,245-266 (1985). 14. R. L. WOODWARD, Int. J. Impact Engng 2, 121-129 (1984). 15. C. A. CALDER, J. M. KELLY and W. GOLDSMITH, Int. J. Solids Struct. 79, 1143-1152 (1971). 16. J. M. KRAFFT, J. appl. Phys. 26, 1248-1253 (1955). 17. W. GOLDSMITH,T. W, LUI and S. CHULAY,Exp. Mech. 5, 1 20 (1965). 18. J. Llss and W. GOLDSMITH,Int. J. Impact Engno 2, 37-64 (1984). 19. J. AWERBUCHand S. R. BODNER, Exp. Mech. 17, 147-153 (1977). 20. J. LISS, W. GOLDSMITH and J. M. KELLY, Int. J. Impact Engng 1,321-341 (1983). 21. M. RAVID and S. R. BODNER, Int. J. Engng Sci. 21,577-591 (1983). 22. M. ZAID and B. PAUL, J. Franklin Inst. 268, 24-45 (1959). 23. W. T. THOMSON, J. appl. Phys. 26, 80-83 (1955). 24. M. S. SODHA and V. K. JAIN, J. appl. Phys. 29, 1769-1771 (1958). 25. J. NISHIWAKI, J. Phys. Soc. Japan 6, 374-378 (1951), 26. R. L. WOODWARD, Int. J. Mech. Sci. 20, 599-608 (1978). 27. R. SZILARD,Theory and Analysis of Plates, Classical and Numerical Methods. Prentice-Hall, New Jersey (1974). 28. R.J. ROARg and W. C. YOUNG, Formula for Stress and Strain, 5th edition. McGraw-Hill, New York (1975). 29. J. LIss, W. GOLDSMITH and F. E. HAUSER, J. appl. Mech. 50, 694-698 (1983). 30. W. JOHNSON, Impact Strength of Materials. Edward Arnold, London (1972). 31. D. TABOR, The Hardness of Metals. Clarendon Press, Oxford (1951).