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one should rst understand the impact behavior of itsconstruction units such as single layer fabric, single yarn,and single ber. During the past several decades, a lot of experiments and theoretical work have been conducted tounderstand the transverse impact behavior of single yarnsand single layer fabrics [3–11]. Smith et al. [3], Roylance [4],

Morrison [5], and Field and Sun [6] studied the response of yarns to high-speed transverse impact while Wilde et al.[7,8], Briscoe and Motamedi [9], Shim et al. [10], andShockey et al. [11] investigated the transverse impactbehavior of single layer fabrics.

In this paper, a nite element analysis (FEA) model iscreated using LS-DYNA to simulate the transverse impactof a right circular cylinder (RCC) on a single layer plain-woven Kevlar fabric. The model allows for denition of contact between yarns and therefore takes into account thephysical interaction between yarns. It more realisticallydescribes the woven fabric structure than those computa-tional models in which yarn crossovers are described aslinks, joints or bulk continuum.

2. Transverse impact on yarns

2.1. Existing theory on transverse impact on a long straight yarn

As stated previously, the yarn in a ballistic fabric iscomposed of hundreds of high-strength bers. It is a verycomplex structure. For simplicity in analysis, the interac-tion between bers in a yarn is generally ignored and theyarn is assumed to be an elastic continuum. Fig. 1 shows aheavy wedge-tipped projectile transversely impacting on along straight yarn. The yarn tensile elastic modulus is E and volumetric density is r . The impact velocity is v and itis not high enough to cause the yarn to break. According toRefs. [3,4], two mechanical waves are generated by theimpact. One is a longitudinal wave, which propagates awayfrom the impact point at the sound speed of the yarnmaterial. The longitudinal wave speed c is given by

c ¼ ffiffiffiffiE rs . (1)

Ahead of the longitudinal wave front, yarn material strainis zero; behind, a constant tensile strain is developed. Thetensile strain, denoted as , is determined by the yarn tensileelastic modulus E , volumetric density r , and the impactvelocity v. It is implicitly given by

2 ffiffiffiffiffiffiffiffiffið1 þ Þp 2

¼r v2

E . (2)

The other mechanical wave generated by the impact is atransverse one, which propagates away from the impactpoint at a relatively lower speed. The transverse wave speedu is given by

u ¼ c ffiffiffiffiffiffiffiffiffi1 þr . (3)Across the transverse wave front, the strain of yarnmaterial does not change; however, the motion of yarnmaterial experiences an abrupt change. Ahead of thetransverse wave front but behind the longitudinal wavefront, yarn material moves longitudinally toward theimpact point. Behind the transverse wave front, yarnmaterial moves transversely in the impact direction. It canbe seen from Eq. (3) that the transverse wave speedpositively correlates with the yarn tensile strain. It is largerwith a larger tensile strain, and vice versa. When the yarntensile strain is zero, the transverse wave speed is also zero.

The yarn kinetic energy E k and the yarn strain energy E sduring the impact can be obtained from Eqs. (4) and (5),respectively.

E k ¼ At 2

ffiffiffiffiffiffiE 3

r

s 3 2

ffiffiffiffiffiffi1 þr , (4)

E s ¼ At 2 ffiffiffiffiffiffiE 3rs , (5)where, A is the yarn cross-section area and t is the timeafter impact. The two formulas may be obtained from theabove analysis of wave propagations in yarn material.

2.2. Comparison of FEA modeling results and predictions from the existing theory

Consider an impact case: a heavy wedge-tipped projectiletransversely impacts on a long straight Kevlar yarn thathas a tensile elastic modulus E of 74 GPa, a volumetricdensity r of 1,440 kg/m 3 , and a cross-section area A of 5:83 10 8 m 2 . The impact velocity v is 200 m/s. The yarntensile strain generated by the impact, , can be obtainedfrom Eq. (2) by using iteration method. Substitute thevalues of E ; r ; A, and into Eqs. (4) and (5), the yarnkinetic energy and the yarn strain energy at any time t canbe obtained.

A 3D FEA model is created using LS-DYNA to simulatethe impact. Fig. 2 shows the FEA model for the straightKevlar yarn. The yarn is modeled as a continuum and theyarn cross-section is dened by a pair of symmetric arcs.

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v

time = 0

v

time = t

Fig. 1. A wedge-tipped projectile transversely impacts on a long straightyarn at a constant velocity of v.

Y. Duan et al. / International Journal of Mechanical Sciences 48 (2006) 33–4334

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Gasser et al. [12] have shown that an orthotropic elasticcontinuum has yarn behavior if its Poisson’s ratios are zeroand the shear moduli and transverse elastic moduli are verysmall with respect to the longitudinal elastic modulus. Inthe FEA model, the yarn has locally orthotropic elasticmaterial property. Table 1 lists the nine orthotropic elastic

material data. Each element in the model denes areferential coordinate whose three axes are determined bythe nodes of the element. The orthotropic elastic materialdata is dened in the local referential coordinates.

The yarn kinetic energy and the yarn strain energy as afunction of time are obtained from the FEA modeling.Fig. 3 shows a comparison of the modeling results and theanalytical results obtained from Eqs. (4) and (5). It can beseen from this gure that the FEA modeling results agreewell with the analytical results. The good agreementindicates that the FEA modeling approach and theorthotropic elastic material data listed in Table 1 describewell the transverse impact behavior of the Kevlar yarn.

2.3. Effect of yarn ends boundary condition

In the above analysis and modeling, the Kevlar yarn isassumed to be innitely long. Therefore, the effect of yarnends boundary condition is not taken into account. For areal impact situation, the stress/strain wave generated by

the impact soon arrives at the yarn ends. The yarn endsboundary condition inevitably plays a role in the yarnimpact behavior.

To explore the effect of yarn ends boundary condition,two cases are modeled where a heavy wedge-tippedprojectile transversely impacts at 200m/s onto the centerof a Kevlar yarn that has a length of 49 mm. In the rstcase, both the yarn ends are clamped, while in the secondcase both the yarn ends are left free. It can be seen fromTable 1 that the yarn longitudinal elastic modulus is muchlarger than its shear moduli and transverse elastic moduli.In this situation, the value of the maximum principal stressis very close to that of the tensile stress along berdirection. For convenient implementation in LS-DYNA, amaximum principal stress failure criterion is used in themodeling. When the maximum principal stress at amaterial point exceeds 2.3 GPa, the material fails and thecorresponding element is deleted automatically from themesh. The release wave resulted from deleting the elementis taken into account in subsequent deformation process.The maximum principal stress failure criterion is equivalentto a maximum tensile strain failure criterion with a failurestrain of 3.1%.

Fig. 4 shows the yarn deformation when both of its endsare clamped, while Fig. 5 shows the yarn deformation when

both of its ends are left free. It can be seen from the twogures that the yarn ends boundary condition signicantlyaffects the yarn deformation. The yarn is broken at theimpact point when its two ends are clamped while it is notbroken when its two ends are left free. The different yarnbehavior is a result of the different yarn ends boundarycondition. As stated previously, two mechanical waves aregenerated by the impact: a longitudinal one and atransverse one. The longitudinal wave propagates awayfrom the impact point at a very high speed while thetransverse wave propagates at a relatively lower speed.Behind the transverse wave front, yarn material movestransversely in the impact direction. Ahead of thetransverse wave front but behind the longitudinal wavefront, yarn material moves longitudinally toward theimpact point. When the longitudinal wave reaches theclamped ends, it is reected back and propagates towardthe impact point. Behind the reected wave front, yarnmaterial stops moving longitudinally and the tensile stressis doubled. The reected longitudinal waves meet at theimpact point where the tensile stress is superimposed oneach other. After three reections of the longitudinal wave,the stress at the impact point reaches the failure criterionand the yarn, as shown in Fig. 4 , is broken. Similarly, whenthe longitudinal wave reaches the free ends, it is alsoreected back and propagates toward the impact point.

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Fig. 2. The 3D FEA model for the straight Kevlar yarn.

0

0.01

0.02

0.03

0.04

0.05

0 2 4 6 8 10 12 14

Yarn kinetic energy; FEAYarn kinetic energy; analyticalYarn strain energy; FEAYarn strain energy; analytical

Time ( µ s)

E n e r g y

( J )

Fig. 3. A comparison of the FEA modeling results and the predictionsfrom theory.

Table 1Orthotropic elastic material data (GPa) for the Kevlar yarn

E11 E22 E33 G12 G13 G 23 n12 n13 n23

74 0.74 0.74 0.148 0.148 0.148 0 0 0

Y. Duan et al. / International Journal of Mechanical Sciences 48 (2006) 33–43 35

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However, behind the reected wave front, the yarn tensile

stress becomes zero and the velocity of the yarn materialmoving longitudinally toward the impact point is doubled.As can be seen from Fig. 5 , with reection of thelongitudinal wave the two ends of the yarn move long-itudinally toward the impact point. The transverse wavestops propagating when the reected longitudinal wavemeets the transverse one.

3. Modeling transverse impact on a ballistic fabric

Fig. 6 shows the initial geometry of an impact event: arigid RCC projectile transversely impacts onto the centerof a patch of plain-woven Kevlar fabric. The fabric is atand aligned with the x – z plane. It is composed of 39 yarnsin each of the warp direction (along the x-axis) and the weftdirection (along the z-axis). The fabric maximum thicknessis 0.23 mm, and both of its side length is 32.7 mm. Thefabric four edges are left free. The projectile diameter is8 mm, its mass is 2 g, and its impact velocity v is 200 m/s.During the impact, the rigid projectile can only move alongthe y-direction and the other ve degrees of freedom areconstrained.

A 3D FEA model is created using LS-DYNA to simulatethe aforementioned impact. The impact system hassymmetry with respect to both the x – y plane and the y – zplane, therefore only a quarter of the entire system needs to

be modeled. Fig. 7 shows a part of the 3D FEA model forthe plain-woven fabric. The fabric is modeled to yarn levelresolution and the yarns are modeled as continuum withlocally orthotropic elastic material property. The materialproperties of the Kevlar yarn have been given in the

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Fig. 4. Deformation of the straight Kevlar yarn at various instants of timewhen both of its ends are clamped; the arrows indicate the transverse wavefronts at 20 ms.

Fig. 5. Deformation of the straight Kevlar yarn at various instants of timewhen both of its ends are left free; the arrows indicate the transverse wavefronts at 20 ms.

f f f

z

x

yRCC projectile

Kevlar fabric

v

Fig. 6. A rigid RCC projectile transversely impacts onto the center of asquare patch of plain-woven Kevlar fabric; the impact velocity is v.


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previous section. The cross-section of the crimped yarn isthe same as that of the straight yarn shown in Fig. 2 . Thecrimped proles of the warp and the weft yarns areidentical and are dened by a series of connected arcs. The3D FEA model for the plain-woven fabric denesyarn–yarn contact and allows for relative motion betweenyarns. Simple Coulomb friction is introduced betweenyarns and between the projectile and the fabric. A frictioncoefcient of 0.3, which is obtained from experiments onKevlar fabrics, is used for both the types of friction [13].The inuence of interfacial friction on fabric impactbehavior will not be discussed in this paper. However, itis worth noting that the friction between projectile and

fabric, between yarn and yarn, and between bersthemselves might have signicant effects on the impactbehavior of ballistic fabrics, especially when the projectileis in spherical shape [9,14,15] .

In order to comparatively investigate the effect of fabricboundary condition, two additional cases are modeledwhere all the conditions described previously are main-tained except that different boundary conditions areapplied on the fabric. In one case, two opposite edges of the fabric are clamped and the other two edges are left free;in the other case, all the four edges of the fabric areclamped. Finally, to explore the effect of impact velocity onthe fabric ballistic performance, three cases are modeledwhere the impact velocity v is 400 m/s instead of 200 m/sand the three different types of boundary conditionsdescribed previously are applied on the fabric, respectively.

4. Results and discussion

4.1. Projectile-fabric interaction and energy transfer

Fig. 8 shows time history of the projectile velocity for thecase with four fabric edges left free and impact velocityv ¼ 200m/s. It can be seen from this gure that within avery short period of time ð0:3 msÞ, the projectile velocitydrops from 200 to 198.3 m/s. Afterwards, the projectile

gradually slows down and at 50 ms its velocity is 188m/s.Fig. 9 depicts contour maps of the fabric transversevelocity and transverse displacement at 0 :3 ms when theprojectile velocity is 198.3 m/s. It can be seen from thisgure that the local fabric that directly contacts the RCCprojectile abruptly moves with the transverse impact.The projectile momentum is transferred to the local fabric.The momentum transfer occurs so quickly that thefabric located out of the impact zone is not affected atall. At this moment, the fabric transverse displacementcoincides with the projectile-fabric contact zone and is in apie shape. The initial momentum transfer is responsible forthe abrupt drop of the projectile velocity from 200 to198.3 m/s.

After the initial momentum transfer, the local fabric inthe impact zone moves together with the projectile. Due tothe sudden transverse motion of the local fabric, alongitudinal wave and a transverse wave are generated inthe principal yarns (those yarns that directly contact theprojectile). The longitudinal wave propagates away fromthe impact zone at a very high speed; behind the wavefront, yarn material is strained and moves longitudinallytoward the impact zone. The transverse wave propagatesaway from the impact zone at a relatively lower speed;behind the wave front, yarn material moves transversely inthe impact direction. Fig. 10 shows contour maps of thefabric resultant displacement at initial stages of the impact.It can be seen from this gure that at 0 :5 ms, mainly theprincipal yarns are affected. With propagation of themechanical waves, yarn–yarn interactions cause the sec-ondary yarns (those yarns that do not directly contact theprojectile) to move. At 1 :0 ms, the impact-affected zonetakes a square form, and with time going on it graduallyexpands outward. During the process, the fabric absorbsenergy from the projectile and the projectile graduallyslows down. At 3 :0 ms when most of the fabric has beenaffected by the impact, the projectile velocity is 197.9 m/s.The projectile velocity is reduced by 1.7m/s during theinitial 0 :3 ms while it is only reduced by 0.4 m/s during theperiod from 0.3 to 3 ms.

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Fig. 7. The 3D FEA model for the plain-woven Kevlar fabric.

185

188

191

194

197

200

0 10 20 30 40 50

Time ( µ s)

P r o

j e c t i l e v e

l o c i

t y ( m / s )

Fig. 8. Time history of the projectile velocity for the case with four fabricedges left free and v ¼ 200 m/s. The arrow on the projectile velocity versustime curve indicates the stage of deformation shown in Fig. 9 .


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Deformed congurations of the fabric at various instantsof time are illustrated in Fig. 11 for the case with fourfabric edges left free and impact velocity v ¼ 200 m/s. It canbe seen from this gure that during the impact, the fabric atthe impact zone conforms to the at round nose of theRCC projectile. Lim et al [16] have observed by using high-speed camera the conformation of fabric to the nose shapeof a at-nosed projectile during transverse impact. It isfound from the deformed congurations of the fabric thattwo warp yarns and one weft yarn are broken during theimpact. Except for the three yarns, no other yarns inthe fabric are broken. It can be seen from Fig. 11 that thefabric transverse displacement is in the form of a conicalfrustum at 10 ms. At that instant of time, the four fabricedges slightly bow toward the impact zone but most of thefabric is not affected by the transverse wave yet. Bowingsof the fabric edges indicate that the longitudinal wave hasbeen reected back from the fabric edges. With time goingon, the four fabric edges gradually bow toward the impact

zone and the fabric transverse wave gradually propagatesoutward. It is noted that the fabric transverse wave frontevolves during the impact. It is in the form of a circle at10 ms while it is in the form of a round-lleted square at30 ms. The corresponding projectile velocity for each of the deformed congurations of the fabric can be found inFig. 8 .

There is no external force acting on the system during theimpact. The energy in the system is therefore conserved.The lost projectile kinetic energy is completely absorbed bythe fabric. Fig. 12 shows time history of the energy transferbetween the projectile and the fabric. It can be seen that atthe initial momentum transfer, the projectile loses 0.68 J of kinetic energy, of which 80% is absorbed by the fabric inthe form of yarn kinetic energy, 19% is absorbed by thefabric in the form of yarn strain energy, and the remaining1% is dissipated as heat through friction between theprojectile and the fabric and between yarns themselves. It isevident that yarn kinetic energy is the dominant energy

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Fig. 9. The fabric deformation at 0 :3 ms. (a) Contour map of the fabric transverse velocity ð 103 m/s). (b) Contour map of the fabric transversedisplacement (mm).

Fig. 10. Contour maps of the fabric resultant displacement (mm) at the initial stage of the impact ( v ¼ 200 m/s, four fabric edges left free).


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absorption mechanism during the impact. At 50 ms, around67% of the lost projectile kinetic energy is absorbed by thefabric in the form of yarn kinetic energy, while 25% in the

form of yarn strain energy and 8% in the form of frictiondissipated energy.

4.2. Effect of fabric boundary condition

Two additional cases with different fabric boundaryconditions (two opposite edges clamped; four edgesclamped) are modeled to comparatively study the effectof fabric boundary condition. Fig. 13 shows the projectilevelocity as a function of time for the three cases that havethe same impact velocity v of 200m/s but different fabricboundary conditions. It can be seen from this gure thatwithin the initial 5 ms, the projectile velocity is the same forall the three cases. This result indicates that the fabricboundary conditions do not play a role in decelerating theprojectile during that period of time. After 5 ms, the fabricboundary conditions take effect and the projectile velocitybecomes different for the three cases; the projectile velocitydrops most slowly when all the four fabric edges are leftfree while it drops most quickly when all of the four fabricedges are clamped. It can be seen that at 10 ms, theprojectile velocity is 197.0 m/s for the case with four fabricedges left free while it is 196.1 m/s for the case with twoopposite fabric edges clamped and 195.1m/s for the casewith four fabric edges clamped. Though the fabric mostquickly decelerates the projectile when its four edges are

clamped, it loses function at the earliest time; the projectilepunches through the fabric at 12 ms and moves away at aconstant velocity of 194.4 m/s. When two opposite edges of the fabric are clamped, the projectile gradually slows downuntil 45 ms when the fabric is punched through and loses itscapability to decelerate the projectile. As can be seen, thefabric most effectively slows down the projectile when all of its four edges are left free; at 50 ms, the projectile velocity is188.0m/s when the four fabric edges are left free while it is193.1 m/s when two opposite edges of the fabric areclamped and 194.4 m/s when all of the four fabric edgesare clamped.

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Fig. 11. Top and side view of the fabric deformation at various instants of time ( v ¼ 200 m/s, four fabric edges left free).

0

1

2

3

4

5

6

0 10 20 30 40 50

Loss of projectile kinetic energyYarn kinetic energyYarn strain energyFriction dissipated energy

Time ( µ s)

E n e r g y

( J )

Fig. 12. Time history of energy transfer between the projectile and thefabric ( v ¼ 200 m/s, four fabric edges left free).


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Fig. 14 shows the maximum principal stress distributionin the fabric at 8 ms for the three impact cases. It can beseen that the maximum principal stress mainly distributesin the clamped principal yarns and it is very small in theunclamped principal yarns or in the secondary yarns. Thefabric boundary condition signicantly affects the stress

distribution pattern in the fabric. Fig. 15 shows contourmaps of the fabric transverse displacement at 10 ms for thethree cases. As can be seen, the transverse wave front is inthe form of a circle when all the four fabric edges are leftfree, while it is in the form of an ellipse with the long axis

along the clamped yarns when two opposite fabric edgesare clamped and a lleted square when all the four fabricedges are clamped. The different stress distributions andthe different transverse displacements are due to thedifferent fabric boundary conditions. As stated previously,with the transverse impact, two mechanical waves originate

in the impact zone. The longitudinal wave propagates awayfrom the impact zone at a very high speed while thetransverse wave propagates at a lower speed. Behind thelongitudinal wave front, yarn material is tensioned andmoves longitudinally toward the impact zone, while behindthe transverse wave front, yarn material moves transver-sely. When the longitudinal wave arrives at the free fabricedges, it is reected back and propagates toward the impactzone. Behind the reected wave front, the yarn tensile stressfades away and the velocity of the yarn material movingtoward the impact zone is doubled; the interactionsbetween yarns gradually produce bowings along the freefabric edges. When the longitudinal wave arrives at theclamped edges, it is also reected back and propagatestoward the impact zone. However, behind the reectedwave front, the yarn tensile stress is doubled and the yarnmaterial stops moving longitudinally toward the impactzone. At 8 ms, the longitudinal wave has been reected bythe fabric edges and propagated back to the impact zone.Therefore, the stress in the clamped principal yarns is muchlarger than the stress in the unclamped principal yarns andthe secondary yarns. As shown by Eq. (3), the transversewave speed in a yarn is determined by the sound speed of

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Fig. 14. Distribution of maximum principal stress ( 103 GPa) in the fabric at 8 ms for the three cases that have the same impact velocity of 200 m/s butdifferent boundary conditions. (a) Four fabric edges left free. (b) Two opposite fabric edges clamped. (c) Four fabric edges clamped.

184

188

192

196

200

0 10 20 30 40 50

Four fabric edges left freeTwo opposite fabric edges clampedFour fabric edges clamped

Time ( µ s)

P r o

j e c

t i l e v e

l o c

i t y ( m / s )

Fig. 13. The projectile velocity as a function of time for the three casesthat have the same impact velocity of 200m/s but different boundaryconditions.

Fig. 15. Contour maps of the fabric transverse displacement (mm) at 10 ms for the three cases that have the same impact velocity of 200m/s but differentboundary conditions. (a) Four fabric edges left free. (b) Two opposite fabric edges clamped. (c) Four fabric edges clamped.


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the yarn material and the tensile strain in the yarn. It ishigher with a larger strain and lower with a smaller strain.Due to reection of the longitudinal wave from the fabricedges, the transverse wave propagates much quicker alongthe clamped yarns than along the free yarns. Therefore, forthe case with two opposite fabric edges clamped, thetransverse wave front is in the form of an ellipse, with itslong axis along the clamped yarns and its short axis alongthe free yarns.

Fig. 16 illustrates the deformed congurations of thefabric at 40 ms for the three cases. It can be seen from thisgure that the fabric boundary condition signicantlyaffects the fabric deformation at later stage of the impact.For the case with four fabric edges left free, large bowingsare produced along the four edges; the integrity of thefabric is maintained well and only a few yarns are brokenalong the periphery of the impact zone. For the case with

two opposite fabric edges clamped, bowings are producedalong the two free edges; most of the clamped yarns arebroken. For the case with four fabric edges clamped, all theprincipal yarns are broken at the impact zone. As Fig. 13shows, the fabric most effectively slows down the projectilewhen all its four edges are left free. The reason for the highperformance of the fabric is that only few yarns are brokenduring the impact when all the four fabric edges are leftfree. Due to the local failure at the impact zone, the fabricloses capability to decelerate the projectile at later stages of the impact when two or four of its edges are clamped.

4.3. Effect of impact velocity

Three cases with an impact velocity of 400 m/s anddifferent boundary conditions (four fabric edges left free;two opposite fabric edges clamped; four fabric edgesclamped) are modeled to comparatively study the effectof impact velocity. Fig. 17 shows time history of theprojectile velocity while Fig. 18 shows the fabric deformedcongurations at various instants of time for the case withfour fabric edges left free. It can be seen that the projectileis decelerated very quickly at initial stage of the impact.Within 0 :3 ms, the projectile velocity drops from 400 to396.7m/s. The abrupt drop of the projectile velocity is dueto the initial momentum transfer from the projectile to the

local fabric at the impact zone. The projectile velocitydrops by 0.5 m/s during the period from 0.3 to 4 ms whenthe fabric completely loses capability to decelerate theprojectile. The fabric fails along the periphery of the impactzone. The local fabric at the impact zone is punched outwhile most of the fabric does not move transversely. Thefabric deformation is very different from that with animpact velocity of 200 m/s (see Fig. 11 ). The energy transferbetween the projectile and the fabric is illustrated in Fig. 19for the case with v ¼ 400 m/s and four fabric edges left free.It can be seen that yarn kinetic energy is the dominantenergy absorption mechanism; it accounts for around 63%of the total absorbed energy.

Fig. 20 shows the projectile velocity as a function of timefor the three cases with the same impact velocity of 400 m/sbut different boundary conditions, while Fig. 21 depictscontour maps of the fabric transverse displacement at10 ms. It can be seen that the time history of the projectilevelocity is the same for all the three cases and the fabricdeformed congurations show little difference for the threedifferent boundary conditions. The fabric boundary con-dition does not take any effect when the impact velocity is400 m/s. The phenomena are very different from those withan impact velocity of 200 m/s (see Figs. 13 and 16). Thefabric energy absorption as a function of time is shown inFig. 22 for the six cases that have different impact velocities

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Fig. 16. The fabric deformation at 40 ms for the three cases that have the same impact velocity of 200 m/s but different boundary conditions. (a) Fourfabric edges left free. (b) Two opposite fabric edges clamped. (c) Four fabric edges clamped.

395

396

397

398

399

400

0 2 4 6 8 10

Time ( µ s)

P r o

j e c t

i l e v e

l o c i

t y ( m / s )

Fig. 17. Time history of the projectile velocity for the case with four fabricedges left free and v ¼ 400m/s.


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and different fabric boundary conditions. It can be seenfrom this gure that the fabric responses under 200 and400 m/s are very different. When the impact velocity is200 m/s, the fabric boundary condition signicantly affectsthe fabric energy absorption. However, when the impactvelocity is 400 m/s, the fabric boundary condition does nothave any effect on the fabric energy absorption. Furthermodeling work shows that the transition takes place ataround 300 m/s. The results indicate that fabric boundarycondition plays an important role only when the impactvelocity is low. When the impact velocity is high enough to

cause yarns to break instantaneously, the fabric deforma-tion is localized at the impact region and the fabric far eldboundary condition does not take any effects.

5. Conclusions

A 3D FEA model is created using LS-DYNA to simulatethe transverse impact of a rigid RCC projectile on a singlelayer plain-woven Kevlar fabric. The fabric is modeled toyarn level resolution and relative motion between yarns isallowed. A frictional contact is dened between yarns and

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Fig. 18. Top and side view of the fabric deformation at various instants of time ( v ¼ 400 m/s, four fabric edges left free).

0

1

2

3

4

5

6

0 2 4 6 8 10

Loss of projectile kinetic energyYarn kinetic energy

Yarn strain energyFriction dissipated energy

Time ( µ s)

E n e r g y

( J )

Fig. 19. Time history of energy transfer between the projectile and thefabric ( v ¼ 400 m/s, four fabric edges left free).

395

396

397

398

399

400

0 2 4 6 8 10

Four fabric edges left freeTwo opposite fabric edges clamped

Four fabric edges clamped

Time ( µ s)

P r o

j e c t

i l e v e

l o c i

t y ( m

/ s )

Fig. 20. The projectile velocity as a function of time for the three casesthat have the same impact velocity of 400m/s but different boundaryconditions.


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between the fabric and the projectile. Three boundaryconditions are applied on the fabric: four edges left free;two opposite edges clamped; four edges clamped. Modelingresults show that during initial stage of the impact, theprojectile velocity drops very quickly. There exists anabrupt momentum transfer from the projectile to the localfabric at the impact zone. When the impact velocity is low,the fabric boundary condition plays an important role. Itsignicantly affects the fabric deformation, stress distribu-tion, energy absorption, and failure modes. The fabricmost effectively slows down the projectile when all its fouredges are left free. The reason for the high performance of the fabric is that only few yarns are broken during theimpact when all the four fabric edges are left free. When theimpact velocity is high and causes yarns to breakinstantaneously, the fabric deformation is localized at theimpact region and the fabric far eld boundary conditiondoes not take any effects on the fabric ballistic perfor-mance.

Acknowledgements

The support of the US Army Research Laboratory atAberdeen Proving Ground and the Center for CompositeMaterials at University of Delaware (UD-CCM) duringthis research is gratefully acknowledged.

References

[1] Phoenix SL, Porwal PK. A new membrane model for theballistic impact response and v 50 performance of multi-ply broussystem. International Journal of Solids Structure 2003;40(24):6723–65.

[2] Jacobs MJN, Van Dingenen JLJ. Ballistic protection mechanismsin personal armour. Journal of Materials Science 2001;36(13):3137–42.

[3] Smith JC, Blandford JM, Schiefer HF. Stress-strain relationships inyarns subjected to rapid impact loading. Part VI: velocities of strainwaves resulting from impact. Text Research Journal 1960;30:752–60.

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ARTICLE IN PRESS

Fig. 21. Contour maps of the fabric transverse displacement (mm) at 10 ms for the three cases that have the same impact velocity of 400 m/s but differentboundary conditions. (a) Four fabric edges left free. (b) Two opposite fabric edges clamped. (c) Four fabric edges clamped.

0

1

2

3

4

5

6

7

0 10 20 30 40 50

v=200 m/s, four fabric edges left freev=200 m/s, two fabric edges clampedv=200 m/s, four fabric edges clampedv=400 m/s, all boundary conditions

Time ( µ s)

E n e r g y a

b s o r b e

d b y

f a b r i c

( J )

Fig. 22. Time history of the fabric energy absorption for the six cases withdifferent impact velocities and boundary conditions.


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