Bartus Dissertation Final

SIMULTANEOUS AND SEQUENTIAL MULTI-SITE IMPACT RESPONSE OF
COMPOSITE LAMINATES
by
SHANE D. BARTUS
UDAY K. VAIDYA, COMMITTEE CHAIR
JAMES S. DAVIDSON
DERRICK R. DEAN
GREGG M. JANOWSKI
MARK L. WEAVER
A DISSERTATION
Submitted to the graduate faculty of the University of Alabama at Birmingham,
In partial fulfillment of the requirements for the degree of
Doctor of Philosophy
Birmingham, Alabama
2006

ii
Copyright by
Shane D. Bartus
2006

iii
SIMULTANEOUS AND SEQUENTIAL MULTI-SITE IMPACT RESPONSE OF
COMPOSITE LAMINATES
SHANE D. BARTUS
ABSTRACT
The unique feature in this study was the investigation of the response of polymer
composite material to impact by multiple high velocity projectiles. Energy absorption,
new surface creation, and failure mechanisms from both sequential and near-
simultaneous multi-site, high velocity impact were compared to assess synergistic and
cumulative effects. A single-stage light-gas gun capable of launching three projectiles
with controlled impact location and velocity in both near-simultaneous and sequential
impact modes was developed to study these effects. Two test programs were conducted
to evaluate these impact scenarios on thin S-2 glass/epoxy laminates. In the first pro-
gram, the effect of laminate thickness was investigated using .30 caliber steel spherical
projectiles. The material response near and above the ballistic limit at constant incident
velocity was studied with respect to two and three projectile impacts. It was found that
specimens subjected to sequential impact absorbed 10.1 % more impact energy and ex-
hibited increases of 23.0 % (two projectile) and 10.5 % (three projectile) in delamination
damage over specimens subjected to simultaneous impact. The second test program in-
volved a study assessing projectile mass effects for .50 caliber spherical Al2O3 (3.94 g),
steel (8.38 g), and tungsten carbide (16.08 g) projectiles at constant incident energy. A
factor of four increase in projectile mass corresponded to 22.4 % (sequential impact) and
12.8 % (simultaneous impact) increases in delamination damage. Energy absorption in-
creased 11.9 % (sequential impact) and 8.7 % simultaneous impact for laminates sub-

iv
jected to tungsten carbide projectiles over Al2O3 projectiles. Energy absorption in lami-
nates subjected to sequential impact was 20.0 % higher (average) than those impacted
simultaneously. In contrast to the .30 caliber impact study, delamination damage in-
creased 14.6 % (average) for specimens subjected to simultaneous impact. In both stud-
ies, impact energy absorption increased with increasing cumulative damage. Finite ele-
ment modeling (LS-DYNA 3D) was pursued to gain insight into failure methods, energy
absorption, and damage prediction. New surface creation did not play a significant role
as an energy absorption mechanism. However, its influence on compliance dominated
the target response.

v
ACKNOWLEDGEMENTS
It is difficult to overstate my eternal gratitude to my advisor, Professor Uday K.
Vaidya, who encouraged my research while I worked for him as an undergraduate at my
alma mater and then granted me the opportunity to continue working under him, first as a
Master’s student and then supported me as a doctoral student. He has gone far beyond
what is required of an advisor and been a friend, as well. Dr. Vaidya’s ardent interest in
the advancement of composite materials motivates our entire group. His patience and
advice have been unfaltering since I first began work with him almost seven years ago.
This work reflects the contributions of many individuals. I thank my esteemed
committee members, Drs. Derrick R. Dean, James S. Davidson, Gregg M. Janowski, and
Mark L. Weaver for their valuable time and effort. Their input and guidance provided
invaluable contributions to the quality research. In addition, I thank the current and for-
mer colleagues in our research group whom I’ve had the opportunity to work closely
with.
Finally, I thank my family and friends for their encouragement and support during
this time. Their understanding and acceptance allowed me the freedom to pursue this re-
search, which would not have been possible without them.

vi
TABLE OF CONTENTS
ABSTRACT.......................................................................................................................iii
ACKNOWLEDGEMENTS................................................................................................ v
TABLE OF CONTENTS................................................................................................... vi
LIST OF FIGURES ............................................................................................................ x
LIST OF TABLES.........................................................................................................xviii
INTRODUCTION .............................................................................................................. 1
OBJECTIVES..................................................................................................................... 5
LITERATURE REVIEW ....................................................................................... 6
Failure Mechanisms and Energy Absorption in Traditional
Materials .......................................................................................................... 6
Impact Response of Composite Materials....................................................... 7
Failure Mechanisms and Energy Absorption under High
Velocity Impact ............................................................................................... 8
Energy Absorption in Flexible, High Strength Fabric
Targets...................................................................................................... 8
Energy Absorption in Composite Laminates ........................................... 9
Analytical Models for Impact Energy Absorption .......................................... 9
Analytical Framework for Laminate Impact Energy
Absorption ..................................................................................................... 11
Energy Absorbed due to Shear Plugging................................................ 11
Energy Absorption Due to Cone Formation........................................... 12
Energy Absorbed Through Elastic Deformation of the
Secondary Yarns..................................................................................... 14
Energy Absorbed in Tensile Failure of the Primary Yarns .................... 14
Kinetic Energy of the Cone .................................................................... 15
Energy Absorbed due to Matrix Cracking and
Delamination .......................................................................................... 15
Energy Absorption Based on Laminate Parameters............................... 17
Energy Absorbed due to Fiber-Matrix Debonding and
Pullout..................................................................................................... 18
Stress and Shock Wave Effects ..................................................................... 19
Dynamic Elasticity ................................................................................. 20
Stress Wave Effects................................................................................ 22
Stress Wave Interaction.......................................................................... 24

vii
TABLE OF CONTENTS (Continued)
Page
Dynamic Crack Propagation................................................................... 25
Spall Fracturing ...................................................................................... 27
Finite Element Modeling of Impact on Composite Structures...................... 28
Mechanical Effects of Impact Damage.......................................................... 30
Impact Damage Mitigation............................................................................ 31
Multiple Impact ............................................................................................. 33
Multiple Impact Test Methods ............................................................... 34
Multiple Impact Test Standards.............................................................. 34
Non-Standard Multiple Impact Test Methods........................................ 35
Multiple Impact on Concrete Structures................................................. 37
Multiple Impact of Metallic Structures .................................................. 38
Multiple Impact of Composite Structures...................................................... 40
Low Velocity Impact.............................................................................. 40
Multiple High Velocity Impact .............................................................. 42
Multiple High Velocity Projectile Impact .............................................. 44
Literature Review Summary.......................................................................... 45
EXPERIMENTAL APPROACH.......................................................................... 59
Materials Selection ........................................................................................ 59
Reinforcement ........................................................................................ 60
Matrix ..................................................................................................... 60
Materials Processing...................................................................................... 61
Impact Test Apparatus Development ............................................................ 64
Fragment Cluster Powder Gun Development......................................... 64
Single Projectile Apparatus Development.............................................. 67
Capture Chamber.................................................................................... 71
Firing Valve and Actuator...................................................................... 73
Fire Control ............................................................................................ 75
Pressure Vessels and Flow Control ........................................................ 75
Instrumentation....................................................................................... 78
Preliminary Results........................................................................................ 79
Materials................................................................................................. 79
Single Projectile Results......................................................................... 80
Multi-Site Simultaneous Results............................................................ 81
Multi-Site Impact Apparatus for Controlled Impact
Location.................................................................................................. 82
Non Destructive Evaluation........................................................................... 84
Impact Test Matrix ........................................................................................ 86
FINITE ELEMENT MODELING APPROACH ............................................... 119
Impact Modeling Using LS-DYNA3D........................................................ 119

viii
Page
Tensile/Shear Fiber Mode .................................................................... 121
Fiber Compression Failure Modes ....................................................... 122
Fiber Crush Mode................................................................................. 122
In-Plane Matrix Shear Mode ................................................................ 123
Delamination Failure Mode.................................................................. 123
Finite Element Model .................................................................................. 125
RESULTS AND DISCUSSION......................................................................... 129
.30 Caliber Projectile Impact Results on Three Layer
Laminates..................................................................................................... 129
Single Projectile Impact Results........................................................... 130
Two Projectile Impact Results.............................................................. 130
Two projectile impact results near ballistic limit.........................130
Two projectile impact results above ballistic limit......................131
Three Projectile Impact Results............................................................ 131
Sequential three projectile impact results above
ballistic limit ................................................................................131
Simultaneous three projectile impact results above
ballistic limit ................................................................................132
.30 Caliber Impact Results on Four Layer Laminates.......................... 133
Two projectile sequential impact near ballistic limit...................134
Two projectile simultaneous impact near ballistic
limit..............................................................................................134
Two projectile sequential impact above ballistic
limit..............................................................................................134
Two projectile simultaneous impact above ballistic
limit..............................................................................................135
Three projectile sequential impact above ballistic
limit..............................................................................................136
FEA Modeling Results for .30 Caliber Projectile Impact............................ 136
Sequential Impact Results .................................................................... 136
Simultaneous Impact Results ............................................................... 138
.30 Caliber Impact Discussion..................................................................... 139
Impact Velocity Regime....................................................................... 139
Damage Evaluation...................................................................................... 140
Three Layer Laminates................................................................................ 141
Sequential Impact ................................................................................. 141
Simultaneous Impact ............................................................................ 144
Simultaneous Impact vs. Sequential Impact......................................... 145
Four Layer Laminates.................................................................................. 147

ix
Page
Comparison of the Three and Four Layer Laminate
Impact Response................................................................................... 149
.50 Caliber Projectile Impact Results .......................................................... 150
Sequential impact results for the alumina projectile....................151
Simultaneous impact results for the alumina
projectile ......................................................................................152
Sequential impact results for the steel projectile .........................152
Simultaneous impact results for the steel projectile ....................153
Sequential impact results for the WC projectile ..........................153
Simultaneous impact results for the WC projectile .....................154
.50 Caliber Impact Discussion..................................................................... 154
Damage Evaluation .............................................................................. 155
Sequential Impact ................................................................................. 156
Simultaneous Impact ............................................................................ 159
Simultaneous vs. Sequential Impact............................................................ 161
SUMMARY AND CONCLUSIONS ................................................................. 229
FUTURE WORK AND RECOMMENDATIONS ............................................ 233
Experimental/Instrumentation Recommendations....................................... 233
Alternative Materials/Laminate Schedules.................................................. 234
Experimental Variations.............................................................................. 234
REFERENCES ............................................................................................................... 235

x
LIST OF FIGURES
Figure Page
1 Impact response of target plates subjected to (a) very short impact
times with dilatational wave dominated response, (b) short impact
times with flexural and shear wave dominated response, and (c)
long impact times with quasi-static response, adapted from Olsson
(2000).....................................................................................................................50
2 Cone formation on the distal side of a woven composite during
high velocity impact...............................................................................................51
3 Illustration showing shock wave formation. As the speed of sound
increases with increasing pressure, the front of the wave slows and
slope increases until it results in a discontinuous disturbance or
shock. .....................................................................................................................52
4 Shock wave conditions occur along the Rayleigh line (b) while the
release wave follows the Hugoniot curve (a).........................................................53
5 Illustration of a) longitudinal wave in which at any given time the
wave looks like a series of expansions and compressions and b) a
shear wave in which planes orthogonal to the wave vector glide
with respect to one another and their mutual separations remain
constant. .................................................................................................................54
6 Compressive elastic wave propagation through a bimaterial
interface showing the (a) incident wave and the (b)
reflected/transmitted wave components.................................................................55
7 Illustration showing the response of composites under low and
high velocity impact scenarios as a function of energy.........................................56
8 Schematic illustrating the principle of superposition of two saw
tooth compressive waves interacting. ....................................................................57
9 Illustration of the VARTM process showing the single sided
tooling, dry fiber preform, and processing consumables (sealant
tape, infusion/extraction lines, high permeability layer, and
vacuum bag)...........................................................................................................87

xi
LIST OF FIGURES (Continued)
Figure Page
10 VARTM lay-up used to process the samples shown before
infusion. Each panel produced was approximately 66 cm by 127
cm...........................................................................................................................88
11 Universal receiver outfitted with a 60.1 cm 12-gauge barrel
chambered for a 69.9 mm (2 3/4 in.) shell. ...........................................................89
12 Schematic of a 12 gauge shot shell cross-section for fragment
cluster tests (not shown to scale). ..........................................................................90
13 i. MEC Sizemaster 12-gauge hand loading press, ii. Denver
Instrument Company (model: A-160) scale, iii. RCBS powder
trickler, Frankfort Arsenal powder meter. .............................................................91
14 Velocity vs. propellant weight calibration curve for four 7.94 mm
diameter spherical projectiles fired from the 12-gauge shotgun
barrel. .....................................................................................................................92
15 Projectile spacing vs. distance to the target for a 2 ¾............................................93
16 (a) Pro-Engineer drawing of the high-velocity test fixture (b) i.
Oehler Skyscreen III for residual velocity measurement, ii. Oehler
Model 57 infrared sky screens (not shown is the Oehler 35 and
Oehler 35P chronographs). ....................................................................................94
17 Illustration showing the main components fo the gas gun including
the pressure vessels, firing valve and actuator, barrel and capture
chamber..................................................................................................................96
18 (a) Pro/E drawing of the gas gun, (b) Pro/E drawing of the entire
assembly.................................................................................................................96
19 (a) Image of the gas gun (b) Image showing the major components
of the gas gun assembly ........................................................................................97
20 High density polyurethane foam sabots: i. virgin sabot blank, ii.
machined and notched sabot, iii. 7.94 mm Φ steel spherical
projectile, iv. sabot after being stripped at 120 m s-1
, v. sabot after
being stripped at 256 m s-1
.....................................................................................98
21 Gas gun calibration plot of pressure vs. velocity for a 10.7 g
sabot/projectile launch package using N2. .............................................................99

xii
Figure Page
22 Image of the capture chamber showing the specimen location in
relation to the barrel muzzle, the velocity acquisition windows, and
the projectile recovery..........................................................................................100
23 i. solenoid , ii. modified Hytork-221 pneumatic actuator, iii. 63.5
mm (2 1/2 in.) Milwaukee butterfly firing valve.................................................101
24 Illustration of a double acting pneumatic actuator showing the
pistons, which are attached to the rack, the pinion and the
pneumatic circuit..................................................................................................102
25 Gas gun capture chamber shown with the 1.22 x 2.44 m2
, 12.7 mm
thick polycarbonate fragment barrier...................................................................103
26 Illustration of the fragment cloud impact test configuration. ..............................106
27 Inter-projectile spacing from the 12-gauge shot shells loaded with
four 7.94 mm diameter projectiles with a 4.318 m standoff................................107
28 Typical back-face damage for perforating and non-perforating FCI
is shown in (a) and (b), respectively....................................................................108
29 Energy absorbed (J) vs. number of plies for single projectile and
normalized Fragment Cluster Impact (FCI).........................................................109
30 Pro/E drawing showing the design of the tri-fire gas gun barrel
configuration........................................................................................................110
31 (a) Image of the tri-fire assembly and an illustration showing the
dimensions, configuration, and firing order of the tri-fire gas gun
barrels, (b) Image showing the tri-fire breach and lock ......................................111
32 Representative Image-Pro Plus delamination measurements for a
two projectile sequential impact of a three layered S-2 glass/SC-15
laminates, imaged from the (a) front and (b).......................................................112
33 An ultrasonic C-scan of a S-2 glass/SC-15 three layer laminate
impacted simultaneously with three projectiles. The signal
amplitude (a) and time-of-flight (b) are shown using a 1 MHz
transducer.............................................................................................................113
34 Three layer, .30 caliber test matrix with the 2.04 g, 7.94 mm
diameter spherical projectiles at a constant incident velocity of
approximately 223.2 m.
s-1
(standard deviation = 11.1 m.
s-1
)...............................114

xiii
Figure Page
35 Three layer, .30 caliber test matrix with the 2.04 g, 7.94 mm
s-1
s-1
).................................115
36 Four layer, .30 caliber test matrix with the 2.04 g, 7.94 mm
s-1
s-1
).................................116
37 Four layer, .30 caliber test matrix with the 2.04 g, 7.94 mm
s-1
s-1
).................................117
38 Three layer, .50 caliber test matrix with the 12.70 mm diameter
spherical projectiles at a constant incident energy of approximately
202.4 J (standard deviation = 16.7 J)...................................................................118
39 (a) illustration showing the effect of the material softening
parameter, m, and (b) the mesh used in all the simulations showing
the mesh refinement in the impact zone ..............................................................127
40 Illustration showing the test configuration (A, B, C) listed in the
tables. ...................................................................................................................165
41 Typical damage progression in three layer laminate (08.19.05-3-2)
subjected to a .30 caliber, three projectile sequential impact at
constant incident velocity (~220 m.
s-1
)................................................................173
42 Typical damage progression in three layer laminates subjected to a
three projectile, sequential (07.13.05-3-4) and simultaneous
(07.19.05-3-8) .30 caliber impact with an incident velocity of
approximately 220 m.
s-1
.......................................................................................174
43 Residual velocity for a three .30 caliber projectile sequential
impact series on three layer laminates with constant incident
velocity (227.0 m.
s-1
with a standard deviation of 4.0 m.
s-1
)
showing a decrease in residual velocity with increasing damage........................175
44 Impact energy absorption for a three .30 caliber projectile
sequential impact series on three layer laminates with constant
incident velocity (227.0 m.
s-1
with a standard deviation of 4.0
m.
s-1
) showing an increase in energy absorption with increasing
damage. The error bars indicate standard deviation. ..........................................176

xiv
Figure Page
45 New surface creation for 1, 2, and 3 .30 caliber (2.04 g) projectile
impact on three layer laminates at constant incident velocity (~220
m.
s-1
).....................................................................................................................177
46 Energy absorption for sequential and simultaneous, three .30
caliber projectile impact on three layer laminates at constant
incident velocity (average incident velocities of 227.0 m.
s-1
and
214.7 m.
s-1
for the sequential and simultaneous impacts,
respectively). The error bars indicate standard deviation...................................178
47 Typical damage progression in four layer laminates subjected to a
two projectile, sequential (07.13.05-4-9) and simultaneous
(07.13.05-4-16) .30 caliber impact with an incident velocity of
approximately 250 m.
s-1
.......................................................................................179
48 New surface creation vs. number of laminates for a two .30 caliber
projectile simultaneous impact series at constant incident velocity
(227.7 m.
s-1
and 238.9 m.
s-1
for the three and four layer laminates,
respectively).........................................................................................................180
49 Impact energy absorption vs. number of laminates for a two
simultaneous .30 caliber projectile impact series at constant
incident velocity (227.7 m.
s-1
and 238.9 m.s-1
for the three and four
layer laminates, respectively)...............................................................................181
50 New surface creation vs. number of laminates for a three .30
caliber projectile sequential impact series at constant incident
velocity (227.0 m.
s-1
and 249.9 m.
s-1
for the three and four layer
laminates, respectively)........................................................................................182
51 Impact energy absorption vs. number of laminates for a sequential
three .30 caliber projectile impact series at constant incident
velocity (227.0 m.
s-1
and 249.9 m.
s-1
for the three and four layer
laminates, respectively)........................................................................................183
52 Modeling results showing the three layer laminate response to
sequential and simultaneous impact (kinetic energy transfer) for
three .30 caliber projectiles..................................................................................184
53 30 caliber sequential impact series (3 layer laminate) comparing
the experimental results to the FEA prediction....................................................185

xv
Figure Page
54 30 caliber sequential impact simulation showing von Mises
stresses; (a) shows the stress wave propagation just after full
penetration of the first projectile (note the stress wave has passed
the location of the next projectile), (b) 2nd impact at 50 %
perforation, (c) 3rd
impact at the start of penetration. .........................................186
55 30 caliber sequential impact simulation showing projectile
penetration, time-hit interval, and cone formation; (a) 90 %
penetration of the first projectile at location B, 75 % penetration of
the second projectile at location A, and (c) full penetration at
location B.............................................................................................................187
56 Experimental vs. FEA prediction of the damage zone for a three
(.30 caliber) projectile sequential impact series...................................................188
57 30 caliber simultaneous impact simulation showing von Mises
stresses; (a) shows the stress wave propagation interaction along
the primary yarns at positions B and C, (b) peak stress wave
interaction, (c) destructive stress wave interference (d) just before
full penetration with wave propagation being interrupted by
delamination damage. ..........................................................................................189
58 .30 caliber simultaneous impact simulation penetration and cone
formation..............................................................................................................190
(.30 caliber) projectile simultaneous impact series..............................................191
60 .30 caliber (three projectile) simultaneous and sequential impact
results comparing the experimental values for damage to the FEA
prediction. ............................................................................................................192
61 30 caliber (three projectile) simultaneous and sequential impact
results comparing the experimental values for residual velocity to
the FEA prediction...............................................................................................193
62 Impact energy vs. new surface creation for three layer laminates
subjected to single, two, and three projectile simultaneous and
sequential impacts at constant incident velocity (~220 m.
s-1
). ............................194
63 Impact energy absorption vs. new surface creation for three layer
laminates subjected to single, two, and three projectile
simultaneous and sequential impacts at constant incident velocity.....................195

xvi
Figure Page
64 Normalized new surface creation/laminate vs. number of laminates
for a .30 caliber simultaneous two projectile impact series with
incident velocities of 227.7.9 m.
s-1
and 238.9 m.
s-1
for the three and
four layer laminates, respectively. .......................................................................196
65 Normalized energy absorption/laminate vs. number of laminates
for a .30 caliber simultaneous two projectile impact series with
incident velocities of 227.7.9 m.
s-1
and 238.9 m.
s-1
for the three and
four layer laminates, respectively. .......................................................................197
66 Normalized (new surface creation/laminate) vs. number of
laminates for a .30 caliber sequential three projectile impact series
at constant incident velocity (~220 m.
s-1
and 250 m.
s-1
for the three
and four layer laminates, respectively)................................................................198
67 Normalized impact energy absorption (J/laminate) vs. number of
laminates for a sequential three .30 caliber projectile impact series
at constant incident velocity (~220 m.
s-1
and 250 m.
s-1
for the three
and four layer laminates, respectively)................................................................200
68 Typical damage progression in a three layer laminate (09.02.05-3-
6) subjected to a .50 caliber sequential impact (alumina, 3.94 g) at
constant incident energy (~200 J)........................................................................203
8) subjected to a .50 caliber sequential impact (steel, 8.38 g) at
4) subjected to a .50 caliber sequential impact (WC, 16.08 g) at
71 Typical damage for sequential (left column) and simultaneous
(right column) three projectile impact of the alumina (3.9 g), steel
(8.4 g) and WC (16.1 g) .50 caliber projectiles at constant incident
energy (~200J). ....................................................................................................206
72 New surface creation vs. number of sequential impacts at constant
incident energy (200 J) for the alumina, steel, and WC .50 caliber
projectiles.............................................................................................................207

xvii
Figure Page
73 Residual velocity of a three projectile sequential impact series on
three layer laminates with constant incident energy (200 J)
showing an increase in energy absorption with increasing number
of impacts (increasing damage state)...................................................................208
74 Energy absorption (J) vs. new surface creation (cm2
) of a three
projectile sequential impact series on three layer laminates with
constant incident energy (200 J) showing an increase in energy
absorption with increasing damage state. ............................................................209
75 New surface creation for the three projectile sequential impact
series on three layer laminates with constant incident energy (200J)
comparing the experimental results with the FEA prediction for the
3.9, 8.4, and 16.1 g .50 caliber projectiles. ..........................................................210
76 50 caliber sequential impact series on three layer laminates
showing the experimental results and FEA prediction of residual
velocity with increasing number of impacts (damaged state)..............................211
77 .50 caliber simultaneous and sequential impact results comparing
energy absorption vs. projectile mass at constant incident energy
(~200 J)................................................................................................................212
78 .50 caliber simultaneous and sequential impact results comparing
energy absorption vs. projectile mass at constant incident energy
(~200 J)................................................................................................................214
79 New surface creation for the three projectile sequential impact
series on three layer laminates with constant incident energy (200
J) comparing the experimental results with the FEA prediction for
the alumina, steel, and WC .50 caliber projectiles...............................................215
80 Residual velocity of a three .50 caliber projectile simultaneous
impact series on three layer laminates with constant incident
energy (200J) comparing the experimental results with the FEA
prediction for the 3.9, 8.4, and 16.1 g .50 caliber projectiles. .............................216
projectile (3.91 g) sequential impact series..........................................................217
projectile (3.91 g) simultaneous impact series.....................................................218

xviii
Figure Page
projectile (8.38 g) sequential impact series..........................................................219
projectile (8.38 g) simultaneous impact series.....................................................220
projectile (16.08 g) sequential impact series........................................................221
projectile (16.08 g) simultaneous impact series...................................................222
sequential impact (kinetic energy transfer) for three .50 caliber
(3.94, 8.38, and 16.08 g) projectiles at constant incident energy
(~200 J)................................................................................................................223
simultaneous impact (kinetic energy transfer) for three .50 caliber
(3.94, 8.38, and 16.08 g) projectiles at constant incident energy
(~200 J)................................................................................................................224
89 Modeling results comparing the three layer laminate response to
.30 and .50 caliber (steel projectile) sequential impact with
approximately the same impact velocity, 220 m.
s-1
.............................................225
90 Modeling results comparing the three layer laminate response to
.30 and .50 caliber (steel projectile) simultaneous impact with
approximately the same impact velocity, 220 m.
s-1
.............................................226
91 Plot showing new surface creation for the first impact of a
sequential impact series and new surface creation for a three
projectile simultaneous impact normalized by the number of
projectiles.............................................................................................................227
92 Plot showing impact energy absorption for the first impact of a
sequential impact series and new surface creation for a three
projectile simultaneous impact normalized by the number of
projectiles.............................................................................................................228

xix
LIST OF TABLES
Table Page
1 Parameters for three generic warheads. .................................................................58
2 Single projectile imapct results............................................................................104
3 Multi-site simultaneous impact results. ...............................................................105
4 Material properties used in the simulation of plain weave S-2
glass/SC-15 epoxy composite..............................................................................128
5 Three layer laminate, .30 caliber single projectile impact results
above ballistic limit..............................................................................................166
6 Three layer laminate, .30 caliber simultaneous and sequential two
projectile impact near ballistic limit.. ..................................................................167
7 Three layer laminate, .30 caliber simultaneous two projectile
impact above ballistic limit..................................................................................168
8 Three layer laminate, .30 caliber simultaneous and sequential three
projectile impact above ballistic limit..................................................................169
9 Four layer laminate, .30 caliber simultaneous and sequential two
projectile impact near the ballistic limit...............................................................170
10 Four layer laminate, .30 caliber simultaneous and sequential two
projectile impact above ballistic limit..................................................................171
11 Four layer laminate, .30 caliber sequential three projectile impact
above ballistic limit..............................................................................................172
12 Simultaneous and sequential impact results for the alumina (3.94
g) .50 caliber projectile (3 layer laminate)...........................................................200
13 Simultaneous and sequential impact results for the steel (8.38 g)
.50 caliber projectile (3 layer laminate)...............................................................201
14 Simultaneous and sequential impact results for the WC (16.1 g) .50
caliber projectile (3 layer laminate).....................................................................202
15 Momentum of the various (.30 and .50 caliber) projecitles used in
the study at a constant incident energy of 200 J. .................................................213

1
INTRODUCTION
This work contributes to fields connected with high velocity impact of advanced
lightweight materials. Historically, the aerospace industry has been the biggest propo-
nent of composite materials because of performance gains associated with lightweight
primary load bearing structures and inherent radar absorption characteristics. Use of
these materials is well documented in fifth generation fighter aircraft such as the F-22
Raptor and F-35 Lightening II.
The role in the use of composite materials has been increasing rapidly in other
branches of the military worldwide due to increased performance, lower thermal signa-
ture (via reduced power plant size), stealth and electromagnetic characteristics, surviv-
ability, extended range, and increased deployability. The US Army’s well known Future
Combat Systems (FCS) program is placing an emphasis on weight reductions which will
allow transport of armored vehicles by C-17 and C-130 aircraft. The Swedish Navy’s
Visby Class Corvette demonstrated the first large use of composite materials in a surface
warship using a hull comprised of carbon fiber/vinyl ester facesheets with a PVC core.
Northrop Grumman is currently following suit with the DD(X) Destroyer, a littoral com-
bat ship. There is also significant interest in the impact response of composites in the ci-
vilian sector for turbine blade containment.
Impact response of advanced composite structures has received considerable at-
tention over the last four decades. These structures are frequently subjected to impact
loading by secondary blast debris, primary blast debris (shrapnel), and multiple bullet
impact. Laminated structures are susceptible to damage under both static and dynamic

2
loading conditions. However; inertial and strain-rate effects differentiate the two phe-
nomena. Variations in the material response, impact induced stress and shock wave
propagation, strain rate effects, and dynamic crack/damage propagation make impulse
loading of laminates complex in contrast to quasi-static loading.
In the general case, impact response of composite materials is gauged in two
ways. One involves protective structures where the main concern is focused on impact
energy absorption and determination of the ballistic limit, VB (a statistically based veloc-
ity in which a given projectile has a 50% probability of perforating a target). The goal in
materials selection and design is to defeat projectiles, thus maintaining operation of the
vehicle while providing protection to the occupants. In order to provide adequate protec-
tion against a given threat, the component is structurally over designed. In this case, the
ability to withstand multiple impacts within an area containing damage is of greater im-
portance than post impact load carrying capability.
The other major assessment in the impact response of composites involves meas-
uring the amount of damage a target sustained from an impact event and reduced me-
chanical properties associated with that damage. Delamination is the most detrimental
failure mode in composites and is typically induced by impact. Degredation is most com-
monly measured using Compression After Impact (CAI) in which a laminate is subjected
to an axial compressive load after sustaining damage. While maintaining structural integ-
rity is important for ground based vehicles and naval ships, it is essential in fixed and ro-
tary winged air vehicles. In this case, the focus may not necessarily be on projectile de-
feat but rather maintaining a high degree of post impact strength since air vehicles typi-
cally have a very low factor of safety. Moreover, a fighter aircraft, for example, would

3
likely be in an evasive or escape maneuver after being hit by a fragmentation warhead,
both of which are high g maneuvers subjecting the vehicle to peak stresses. Knowledge
of damage evolution is key to understanding the survivability of a vehicle under such
conditions.
Although these composite structures are frequently subjected to multiple impact
loading, the vast majority of studies reported in open literature only address single point
projectile impact with little or no consideration given to the effect of multiple impacts.
This was the focus in the present work. Pertinent literature regarding this subject is given
in the Literature Review section which includes a background in impact response and en-
ergy absorption mechanisms in laminated composites and previous work in experimental
methods for multiple impact loading of structures.
The Experimental Approach section highlights the development of two impact
apparati for multiple impact testing. It also includes preliminary results from a powder
gun impact study which led to the development of an apparatus capable of controlled im-
pact velocity and location. The experimental development encompassed a considerable
portion in the overall scope of work. Justification of material selection is included along
with and processing and characterization details. The test matrix is also outlined.
A brief background into simulating the impact response of composites using LS-
DYNA 3D is provided in the Modeling Approach chapter. The pertinent equations re-
garding the five failure modes used in the laminate material model are provided. Details
of the material parameters, finite element mesh, and calibration of the model to experi-
mental results are described.

4
Findings from the study, both experimental and modeling, are shown in the Re-
sults and Discussion. For clarity, the results are presented in two parts, .30 caliber pro-
jectile impact and .50 caliber projectile impact. In the .30 caliber impact study, three and
four layer laminates were subjected to simultaneous and sequential impact, both near and
above ballistic limit. The .50 caliber projectile study focused on projectile mass effects.
Summary and Conclusions details the most significant results in the experimental
program for both studies. General conclusions specific to this study and described and
comparisons between the two impact scenarios are made. Suggestions for additional
studies are included in Future Work and Recommendations, including materials, experi-
mental parameters, and instrumentation.

5
OBJECTIVES
• Design, develop, and establish unique test methodologies for controlled single,
and multi-site high velocity impact(s) to laminated composite structures.
• Understand the phenomena of damage evolution and energy absorption in lami-
nated composites subjected to high velocity impact by multiple projectiles with
the aid of experiments and finite element modeling.
• Characterize damage states and mechanisms in composite laminates subjected to
multi-site sequential and near-simultaneous impact using quantitative non-
destructive evaluation techniques.

6
LITERATURE REVIEW
Failure Mechanisms and Energy Absorption in Traditional Materials
It is widely accepted that materials behave differently under high strain rate load-
ing versus quasi-static loading (Voyiadjis et al., 2002). Failure mechanisms in polymer
matrix composites subjected to impact are complex when compared to the same failure
scenario in ductile metallic targets. In the generic case, metallic targets absorb impact
energy through elastic and plastic strain (Zhou, 1996), phase changes, shear plugging,
and adiabatic shear band formation (Dikshit et al., 1995). Shear plugging is the ejection
of the target material (spall), roughly the size of the impactor.
Adiabatic shear band formation is observed in ductile materials loaded at very
high strain rates resulting in narrow regions of intense plastic deformation (Guduru et al.
2001). When shear bands are formed there is a rapid increase in local temperature. The
rise in local temperature is greater than the heat conduction rate to the surrounding mate-
rial, resulting in conditions that are approximately adiabatic. This occurs local to the
point of impact and generally does not result in significant loss of load carrying capacity
or a decrease in the ability to stop subsequent impacts if they do not overlap the previous
point of impact (Guduru et al., 2001).
Brittle materials, including ceramics, fracture through the propagation of a net-
work of discrete cracks (Voyiadjis et al., 2002). Composites exhibit a very limited ability
to undergo plastic deformation. As a result, energy is absorbed through the creation of
large areas of fracture, which are generally complex in nature and difficult to characterize
(Cantwell and Morton, 1991).

7
Impact Response of Composite Materials
The impact response of materials is generally categorized into low (large mass),
intermediate, high/ballistic (small mass) and hyper velocity regimes. Large mass, Low
Velocity Impact (LVI), results from conditions arising from tool drop, and typically occur
at velocities below 10 m.
s-1
. Testing for this condition is performed using a LVI appara-
tus such as a drop weight test rig. Secondary blast debris, hurricane and tornado debris,
and foreign object debris on roads and runways are categorized in the intermediate veloc-
ity impact regime, typically from 10 to 100 m.
s-1
(Bartus and Vaidya, 2005).
High velocity (ballistic) impact (>100 m.
s-1
) is usually a result of small arms fire
or explosive warhead fragments. In hyper velocity impact, projectiles are moving at very
high velocities (2-15 km.
s-1
), and the target materials behave like fluids (Naik and
Shrirao, 2004). This type of impact is studied to develop protection against micrometeor-
ites for objects and people in low earth orbit. The relevant impact regimes covered in this
paper are illustrated in Fig.1, which shows the response of targets subjected to (a) low,
(b) intermediate, and (c) high velocity impact (Olsson 2000). Under small mass, high
velocity impact, damage is more localized demonstrating that the impact duration plays a
significant role (Olsson, 2000).
The failure mode depends on the impact response. For LVI, the failure mode and
energy absorption is highly dependant on the specimen size, stiffness, and boundary con-
ditions (Cantwell and Morton, 19892
). The majority of the impact energy for a compliant
specimen subjected to LVI is absorbed by strain (Thaumaturgo and Da Costa, 1997). In-
termediate velocity, Fig. 1(b), and high velocity impact loading, Fig. 1(c), lead to a higher
degree of local loading resulting in a corresponding increase in damage for equivalent
impact energy in contrast to the loading condition shown in Fig. 1(c), with a quasi-static

8
impact response (Olsson, 2003). Cantwell and Morton (19892
) found small mass, high
velocity impact to be more detrimental to carbon fiber reinforced laminates than low ve-
locity drop tower impact. The material response in this case is wave controlled (Fig. 1)
making the load and deflection out of phase and independent of the plate size and bound-
ary conditions (Olsson, 2003).
There is some debate on classifying impact regimes in literature. It is common for
authors to mistakenly classify impact regimes based on impactor velocity. One of the
accepted definitions for high velocity impact regime states that the ratio between the im-
pactor velocity and the transverse compressive wave velocity is greater than the maxi-
mum strain to failure in that direction (Abrate, 1998). The high velocity impact response
is governed by wave propagation, not by the impactor velocity.
Failure Mechanisms and Energy Absorption under High Velocity Impact
Energy Absorption in Flexible, High Strength Fabric Targets
Failure and energy absorption in composite laminates differs from impact on high
strength textile laminates such as those used in soft (flexible) body armor. The matrix in
laminated composites inhibits yarn slippage allowing a greater number of primary yarns
to carry the load and absorb energy through strain (Lee et al., 2001). Lee and coworkers
(2001) also reported an influence on resin matrix properties for Spectra™ fiber reinforced
composites. They found that composites with a vinyl ester resin matrix had a higher bal-
listic limit than the same configuration using a polyurethane matrix at the same incident
velocity. Although the matrix generally contributes a small portion of the overall energy
absorption, the stiffer matrix inhibited fiber movement beneath the projectile and allowed
higher fiber strain energy absorption (Lee et al., 2001).

9
Energy Absorption in Composite Laminates
The high velocity impact performance of laminated polymer matrix composites is
dependant on the mechanical properties of the reinforcement and matrix, the laminate
stacking sequence, reinforcement architecture, and the initial physical conditions and me-
chanical properties of the impactor. The predominant energy absorption mechanisms of
laminates under high velocity, small mass impact are; kinetic energy imparted to the
specimen (namely cone formation on the distal side of the laminate and/or spall forma-
tion), energy absorption as a result of shear plugging, tensile fiber failure of the primary
yarns, fiber debonding, fiber pull-out, elastic deformation of the secondary yarns, matrix
cracking (intralaminar), interlaminar delamination, and frictional energy absorbed during
interaction of the penetrator and laminate (Goldsmith et al., 1995; Sun and Potti, 1996;
Morye et al., 2000; Cheng et al., 2003; Naik and Shrirao, 2004; Nunes et al., 2004; da
Silva et al., 2004).
Energy is also absorbed in elastic and plastic deformation of the impactor, heat
generation in the laminate and impactor, and vibration and sound energy. The energy
created by heat and vibration contributes a very small amount of energy absorption with
respect to other mechanisms (Morye et al. 2000; Gu, 2003).
Analytical Models for Impact Energy Absorption
There are currently several analytical models available for predicting the ballistic
limit, energy absorption, or damage mechanisms in composite materials. These models
take into account some form of the laminate mechanical and physical properties, and
penetrator size and shape. The two main approaches use a static punch curve of load
versus displacement for a given penetrator (Goldsmith et al., 1995; Sun and Potti, 1996;

10
Potti and Sun, 1997; Wen, 2000; Wen 2001; Ulven et al. 2003; Bartus and Vaidya, 2004)
or using dynamic material response data (Morye et al., 2000; Naik and Shrirao, 2004;
Naik et al., 2005). Most of the models are semi-empirical or semi-numerical requiring at
least limited experimental data.
Morye and coworkers used high speed photography to measure the velocity of
deformed region in thin thermoplastic (nylon, aramid, and polyethylene) fiber composite
laminates. They reported that inertia transferred to a target via high velocity impactor is a
major mode of energy absorption. Naik and Shrirao (2004) and Naik et al. (2005) also
incorporated energy absorption due to cone formation in their analytical models. The
analytical framework described in Naik and Shrirao (2004) was also used in an extended
study in Naik and coworkers (2005), which considered thickness of the target, and mass
and diameter of the projectile.
The analytical model used by Morye and coworkers (2000) incorporated three
components contributing to energy lost by a projectile during high velocity impact: en-
ergy absorbed in tensile fiber failure of the primary yarns, energy absorbed in elastic de-
formation of the secondary yarns, and inertial energy transferred to the moving portion of
the composite. The model described by Naik and Shrirao (2004) and Naik and coworkers
(2005) was expanded to include energy absorbed by shear plugging of the target by the
projectile, matrix cracking and delamination, and frictional energy between the target and
projectile. An important feature of the model described by Naik and Shrirao (2004) is
that it predicts the size of the moving portion of the cone based on propagation of the
transverse stress wave, negating the need to determine it experimentally.

11
{ }
)(2
1
2
1
)1()1()1()1()1()1(
2
Cip
iFiMCiDLiTFiDiSPIp
i
Mm
EEEEEEVm
V
+
+++++−
= −−−−−−
(1)
Analytical Framework for Laminate Impact Energy Absorption
The following analytical formulation follows that described by Naik and cowork-
ers (2004, 2005, 2006). At the instant of impact, the incident kinetic energy of the pro-
jectile begins dissipating through; kinetic energy of the moving cones at time ti, EKEi, en-
ergy absorbed by shear plugging until time ti, ESPi, energy absorbed by deformation of the
secondary yarns until time ti, EDi, energy absorbed by tensile failure of the primary yarns
until time ti, ETFi, energy absorbed by delamination until time ti, EDLi, energy absorbed by
matrix cracking until time ti, EMCi, and energy absorbed by friction between the target and
projectile until time ti, EFi. The incident kinetic energy of a projectile is: KEpo= ½ mpVI
2
,
where mp is the projectile mass and VI is the incident velocity. The kinetic energy of the
projectile at a given time step is given by KEpi. The mass of the cone, MCi, is dependent
on the time step; it gains mass as the impact duration increases as the projectile transfers
maximum momentum to the target. The projectile velocity at a given time step is given
by Eq. 1. If the projectile velocity at the end of the impact event is zero, then the projec-
tile is considered to be at or below the ballistic limit.
Energy Absorbed due to Shear Plugging
Upon contact with a target, the shear stresses along the periphery of the projectile
can exceed the shear plugging strength of the laminate and result in the ejection of a plug
of target material. This is most prevalent in carbon-epoxy type laminates, which exhibit
low strain to failure. It is less common in laminates containing relatively extensible fi-

12
bers (Cantwell and Morton, 1990). The shear plugging strength is typically measured
using quasi-static loading using the same penetrator geometry and diameter as used in the
experimental impact conditions (Sun and Potti, 1996). The energy absorbed by shear
plugging, ESPi, over the ith interval is equal to the product of the shear plugging strength,
SSP, the number of layers, N, (distance) sheared, the laminate thickness, hl, and the area of
the penetrator, Eq. 2. The total energy absorbed by shear plugging is given by the sum-
mation of each ith intervals, Eq. 3.
Energy Absorption Due to Cone Formation
Energy absorption as a result of kinetic energy imparted to the specimen has been
described in detail by Morye and coworkers (2000), Gellert and coworkers (2000), Naik
and Shrirao (2004), and Naik and coworkers (2005). As the projectile decelerates upon
contact with the target, some of the momentum is transferred to the region surrounding
the point of impact. The kinetic energy of the moving portion of the cone surrounding
the point of impact was identified as a large contributor to energy absorption.
Figure 2 represents cone formation in a 0o
/90o
laminate, in which two features are
represented: the deformation of the primary and secondary yarns. The area of deforma-
tion on the distal side of the laminate is defined by the radius, r, the distance traveled by
the projectile at time i, Zi, the laminate thickness, h, the projectile diameter, d, and the
projectile velocity at time interval i, Vi. The velocity of the cone is assumed to be the
same as the projectile velocity at any giving point while they are in contact. Loading and
(3)∑Δ=
=
=
in
n
nSPiSP EE
0
(2)hSNhE SPlnSP dπ=Δ

13
deformation of the primary and secondary yarns are also shown in Fig. 2. The primary
yarns, assuming normal incidence, are the fibers in direct contact with the projectile dur-
ing the penetration process and undergo elastic and plastic deformation along the fiber
axis.
Strain is greatest in the region directly under the projectile, and the fibers in this
region fail when the dynamic strain exceeds the maximum strain-to-failure in the effected
region at the corresponding strain rate. The strain is greater in the incident layers (first
layers in contact with the projectile) for the through-the-thickness direction because of
the additional flexure stiffness provided by the distal layers. As the projectile penetrates,
the distal layers of the laminate undergo more bending,which also explains the fiber-
crushing phenomenon noted by Gellert et al. (2000) in the first stage of the penetration
process.
The secondary yarns in the remainder of the conical region undergo elastic de-
formation as a result of cone displacement. The cone formation is considered an artifact
of transverse wave propagation from the ballistic impact event. The extent to which the
wave propagates defines the radius of the cone formation. The degree of energy absorp-
tion depends on the strain distribution within the conical region and varies with position,
fiber orientation and distance from the point of impact.
The extent of cone formation depends on the transverse wave propagation, which
is given by Eq. 4, where εp denotes the region of plastic strain at high strain rate. Plain
weave laminates with fibers in a 0o
/90o
configuration produce a quasi-lemniscate (four
ε
ε
σ
ρρ
σε ε
∫ ⎟
⎠
⎞
⎜
⎝
⎛
−
+
=
p
pP
t
c
0
d
d
d1)1(
(4)

14
leaf clover) shape due to variations in the in-plane elastic properties. Stress waves at-
tenuate as they emanate from the point of impact due to impedance mismatch at the fiber-
matrix interface, reflections/transmission at the free surfaces and boundaries, interaction
with voids and inclusions, and the viscoelastic behavior of polymers.
The strain in the yarn is calculated along the entire conical region for each ith
in-
terval, as given by Eq. 5, where a is the yarn size and b is the transmitted component of
the stress wave and is a constant less than one. The magnitude of strain will vary with
distance from the point of impact to where the stress wave has propagated.
Energy Absorbed Through Elastic Deformation of the Secondary Yarns
Strain in the secondary yarns is equal to the strain in the primary yarns, εpy, in the
areas where they intersect, Fig. 2. The energy absorbed through deformation of the sec-
ondary yarns is then obtained through integration of Eq. 6. The derivation for Eqn. 6 is
detailed in Naik and coworkers (2006).
Energy Absorbed in Tensile Failure of the Primary Yarns
As the primary yarns, Fig. 2, reach their strain limit for a given loading rate, they
will fail progressively in tension. The area under the stress-strain curve (at high strain
rate) for a yarn with cross-sectional area A determines the energy absorbed, Eqn. 7. The
(5)⎟
⎠
⎞
⎜
⎝
⎛
⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
−
−−++−+
=
a
b
b
rrrzdrd
ar
ptpit
i ip
iiii ln
1
)())2/(()2/(
)/(
22
ε
(6)( ) ( ){ } rrdrrhE itr
d
isy
sysyiD
d2sin82)d( 1
2/ 0 sy
−
−∫ ∫= πεεσε

15
ultimate strain limit, εo, determines failure. When multiple fibers or yarns fail simul-
taneously, Eq. 7, which gives the energy absorption for a single yarn, is multiplied by the
number failing, N.
Kinetic Energy of the Cone
The cone formed at the distal side of the laminate has been shown to absorb a
considerable amount of the impact energy, Morye et al. 2000; Naik and Shiraro, 2004;
Naik et al., 2005; Naik et al., 2006. The time dependent mass of the cone is calculated
using Eq. 8, where h is the laminate thickness and ρ is the composite density. The en-
ergy absorbed can be determined from Eq. 9, where the cone velocity, Vi is equal to the
projectile velocity at time, ti, calculated using Eq. 1.
Energy Absorbed due to Matrix Cracking and Delamination
Delamination and matrix cracking greatly diminish the load carrying capability of
composite structures (Abrate, 1998; 2003). They are also responsible for a portion of the
energy absorption. Although the energy absorption capability of thermoset polymers is
small compared to the high strength fibers, large amounts of new surface creation can
contribute significantly to the overall energy absorption process. The change in energy
absorption until time, ti, is primarily a function of the mode II strain energy release rate
and the elastic modulus for delamination and matrix cracking, respectively, Eqs. 10 and
(8)ρπ hrM itiC
2
=
2
2
1
iiCiKE
VME = (9)
(7)( ) xAE
ax
obx
TF
dd)(
/
00 ∫∫=
=
=
εε
ε
εεσ

16
11. The area of matrix cracking and delamination considered by Naik and coworkers
(2004, 2005, 2006), is termed quasi-lemniscate and is given by: Aql= π(r2
d(i+1)-r2
di). The
percent of delamination and matrix cracking is Pd and Pm, respectively. The total energy
absorbed is then the summation of the changes in energy absorption at each time step,
Eqs. 10 and 11.
The dominant energy absorption mechanism(s) depends on the constituent mate-
rial properties of the laminate, strength of the fiber-matrix interface, interlaminar fracture
toughness, laminate compliance and areal density, stacking sequence, weave architecture,
and impact velocity. In addition, laminate response is dependant on projectile density,
shape, material properties, and velocity. For example, compare a brittle, low strain-to-
failure reinforcement such as carbon fiber to more compliant fibers such as S-2 glass™,
Spectra™, or aramid. The low shear strength and low strain to failure of carbon fiber
laminates tends to result in a high degree of shear plugging (ejection of spall roughly the
same size as the projected shape of the impactor).
Morye and coworkers (2000) noted past work in which authors investigating car-
bon fiber composites found tensile fiber failure contributed little to the overall energy ab-
sorption, whereas extensible thermoplastic fiber composites absorbed considerable en-
ergy through tensile fiber failure. In addition, fibers such as E glass and S-2 glass™ have
a high degree of strain rate sensitivity when compared to carbon. They also absorb more
energy as the strain rate increases (Cantwell and Morton, 1991; Nemes et al., 1998; Lee
et al., 2000; Hammond et al., 2004).
(10)IIcdqldiiddiDL GArrPE )( 22
)1( −=Δ +π
(11)mmtqldiidmiMC VhEArrPE )( 22
)1( −=Δ +π

17
Energy Absorption Based on Laminate Parameters
The stacking sequence of woven laminates has been shown to have little influence
on the transverse high velocity impact response and energy absorption because energy
absorption is not dominated by strain as in LVI (Cantwell and Morton, 1991). However,
unidirectional laminates show an increase in macroscopic damage (longitudinal splitting)
with very low energy absorption under impact (Nemes et al., 1998; Hammond et al.,
2004). Will and coworkers (2002) conducted a study on the effect of stacking sequence
of filament wound carbon/epoxy tubes subjected to high velocity impact in which a [-
35/+35/903/-35/+35/903/-35/+35] winding exhibited a 36% decrease in ballistic limit ve-
locity in contrast to a [906/(-35/+35)3] winding. However, the experimental data was lim-
ited, and conclusions concerning possible mechanisms (damage) behind the difference in
energy absorption were not all together clear.
Weave architecture has been shown to influence impact response where satin and
twill weaves tend to absorb more energy than plain weave. The increase in energy ab-
sorption is attributed to a decrease in fiber crimp angle. Hosur et al. (2004) reported up
to a 38% increase in ballistic limit for 8-harness satin weave carbon-epoxy specimens as
opposed to the same system in a plain weave configuration. It is well accepted that de-
creased fiber crimp angle increases in-plane properties due to a decrease in stress concen-
tration. As the distal side fibers undergo tensile failure, an increase in energy absorption
is expected.
The most significant laminate parameter pertaining to energy absorption is the
laminate thickness or areal density. Gellert and coworkers (2000) studied the effect of
laminate thickness for plain weave E-glass/vinyl ester composites subjected to high ve-
locity impact by various shape and mass steel penetrators. They found a transition in en-

18
ergy absorption for each of the penetrators examined in which the plot of energy ab-
sorbed as a function of specimen thickness behaved in a bilinear manner (Gellert et al.,
2000). This behavior was attributed to a change in perforation mechanisms. For thin tar-
gets the penetration mechanism was postulated as dishing or cone formation. Thick tar-
gets underwent indentation, or fiber crushing, in addition to cone formation (Gellert et al.,
2000). Gellert and coworkers identified the indentation phase as a significant energy ab-
sorber, indicating that thicker targets are more ballistically efficient.
Energy Absorbed due to Fiber-Matrix Debonding and Pullout
The fiber-matrix interface plays a critical role in impact energy absorption, dam-
age tolerance, and structural performance (Tanoglu et al, 2001). It is generally accepted
that a weak interface can promote energy absorption (Park and Jang, 1998). A weak in-
terface also decreases structural performance and damage tolerance (Jensen and
McKnight, 2006). Composites designed with weak adhesion at the fiber-matrix inter-
phase typically display large areas of damage due to extensive fiber-matrix debonding,
pull-out, and delamination. Fiber breakage dominates in composites with a strong fiber-
matrix interphase (Park and Jang, 1998; Jensen and McKnight, 2006). Some authors
have reported that fiber-matrix debonding and frictional sliding are more significant en-
ergy absorption mechanisms than delamination or matrix cracking (Tanoglu et al., 2001).
Generally, there is a compromise between structural performance and ballistic
protection. Jensen and McKnight (2006) recently reported a balanced approach in E-
glass/epoxy composites. Using a hybrid silane (organic/inorganic) sizing to promote
compromised fiber-matrix adhesion, they improved post-impact properties by controlling
fiber surface roughness. This resulted in enhanced fiber-matrix friction. Little of the

19
known work has addressed interface failure mechanisms with incipient damage. Preex-
isting matrix cracks and delaminations could affect the energy absorption characteristics
of fiber-matrix debonding and frictional sliding. Gama et al. (20041
) and Gama et al.
(20042
) conducted a limited study on the effect of pre-existing damage on penetration
(quasi-static punch and ballistic, respectively). They found the primary failure mode
changed from compression-shear to tension-shear for specimens with incipient delamina-
tion.
Stress and Shock Wave Effects
In the high velocity regime where forces are applied for very short periods of
time, stress and shock wave propagation must be considered in order to understand dam-
age mechanisms. When local stresses surpass the Hugoniot Elastic Limit (HEL), the ma-
terial behavior falls into the elastic-plastic regime. Above the HEL, the material response
is in the shock regime (Chen and Chandra, 2004). Shock wave behavior is a material
property based on the relation between the speed of sound in the material and pressure.
As the pressure in a material increases, speed of sound also increases. Fig. 3 illustrates
the wave behavior when jumping to a shocked state. When the pressure is high enough,
the front of the wave slows and propagates as a discontinuous disturbance or shock (Kno-
bel, 2000). Shock results in pressure, density, particle velocity, and energy increases.
Conditions for shock formation are illustrated in Fig. 4. A shock will form when the
equation of state, p=p(ρ,e), satisfies the thermodynamic quantities; density, pressure, and
energy. The equation of state can be used to eliminate energy in order to describe a
unique relationship between pressure and compression. Equation 12 describes shock

20
conditions where us is the shock speed, p is pressure, ρ is density, and the subscript 0 in-
dicates the state ahead of the shock (Hallquist, 2000): Shock conditions take place along
the Rayleigh line, while unloading follows the Hugoniot curve, Fig. 4. In the elastic-
plastic and shock regime, laminated materials have insufficient time to absorb the shock
wave energy as strain, hence the majority of the energy is absorbed through faster
mechanisms such as the creation of new surfaces.
Dynamic Elasticity
Inertia effects in solids have motivated research on wave propagation in various
fields ranging from seismology to hypervelocity impact (Rinehart, 1975; Wang, 2003).
When an elastic body is displaced by an impulse load, a certain period of time elapses
before the rest of the body is affected by the initial displacement. Inertial and elastic ma-
terial properties control the velocity of the advancing disturbance (Rinehart, 1975). The
study of stress wave propagation in a single isotropic medium subjected to shock loading
has reached a fair degree of maturity (Wang et al., 2002), whereas the study of wave
propagation in heterogeneous, layered materials is still being actively pursued (Ma and
Huang, 1995).
A large number of waves can be excited depending upon the impulse loading and
propagation conditions. Longitudinal (compressive) waves and transverse (shear) waves
are the two most common types of waves, Fig. 5. Longitudinal waves are characterized
(12)
21
0
01
0
11
1
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
−
−
=
ρρ
ρ
pp
us

21
by particle displacement parallel to the direction of propagation. A longitudinal wave
creates a variation in the distances between parallel planes normal to the direction of
propagation, compressing and expanding like an accordion, such that volume is not con-
stant. Shear waves displace perpendicular to the direction of propagation and result in no
volume variation.
In the absence of phase transitions, stress/shock waves in homogeneous materials
are known to have a one-wave structure (pure shear or pure longitudinal wave). Layered
heterogeneous materials, however, have a two-wave structure because of impedance mis-
match, geometric mismatch and nonlinearities arising from material inelasticity and fail-
ure (Tsai and Prakash, 2005). The two-wave (complex) structure obtained in layered het-
erogeneous materials consists of a leading shock front followed by a complex wave pat-
tern, which varies as a function of time (Wang, 2003). Complex wave patterns are attrib-
uted to nonlinearities arising from the wave characteristics, loading conditions, and mate-
rial heterogeneity (Chen et al., 2004). Nonlinear wave characteristics are a result of im-
pedance and geometric mismatch inherent in composite laminates.
The effect of impedance mismatch is illustrated in Fig. 6, which shows (a) an ide-
alized triangular compressive wave propagating through the interface of two materials,
and (b) the reflected/transmitted components. The original wave was a simple compres-
sive wave; the reflected component is tensile in nature, or a rarefaction wave. Nonlineari-
ties from preexisting voids, void nucleation and growth, microcracking, and delamination
are considered material heterogeneity effects (Chen et al., 2004). Strong shock waves
generated under high velocity impact can also introduce nonlinear effects in the deforma-
tion and fracture behavior (Chen et al., 2004). The amplitude and period of the initial

22
pulse are determined by the intensity and duration of the impact. In the general case for
an unbounded anisotropic medium, three waves are excited upon contact of the projectile
with the target: a compressive wave, shear wave, and a Rayleigh wave (Rinehart, 1975;
Dieulesaint and Royer, 1980).
Stress Wave Effects
When a laminate is subjected to a high velocity impact, stress waves propagate in
the transverse direction at the speed of sound, c=(E/ρ)1/2
, where E is Young’s modulus
and ρ is density. As compressive strain reaches values in the approximate range 0.5-1%
of V/c, where V is the projectile velocity, damage initiates (Abrate, 1998). For carbon-
epoxy, with c equal to 2000 m s-1
(transverse), the expected V/c ratio would occur at ap-
proximately 20 m s-1
. Experimental and analytical studies have shown that stress wave
effects begin to dominate at impact velocities as low as 20 m s-1
(Davies and Zhang,
1994; Olsson, 2000; Dwivedi and Espinosa, 2003). Other authors contend that stress
waves are not generated until impact velocities are greater than 100 m s-1
(Tanabe et al.,
2003). In general, for impact durations on the order of the transition time for through-
the-thickness waves, Czarnecki (1992) found experimentally that the sudden transition
from shear plugging to delamination occurs when the projectile interacts with the return-
ing impact-generated tensile wave. Bahei-El-Din and Zikry (2003) also concluded from
finite element analysis of a micromechanical model that the transverse compressive stress
wave reflected between the free surfaces several times before fiber failure initiated. They
also concluded this was a major mechanism leading to penetration. This phenomenon is
shown in Fig. 7 (Thaumaturgo and Da Costa, 1997).

23
Numerous investigators have studied the stress/shock wave propagation in lami-
nated composites. These stress waves are thought to be responsible for the creation of
delamination during high velocity impact (Nishiwaki et al., 1995; Lahtinen and Pramila,
1996; Thaumaturgo and Da Costa, 1997; Tong, 1997; Rogerson, 1998; Abrate, 1998;
Parga-Landa et al., 1999; Olsson, 2000; Artan and Altan, 2002; Wang et al., 2002; Bahei-
El-Din and Zikry, 2003; Dwivedi and Espinosa, 2003; Mahapatra and Gopalakrishnan,
2003; Zhaung et al., 2003; Chen and Chandra, 2004; Mines, 2004). Delaminations result
in substantial mechanical property degradation by reducing the stability of the plies, re-
sulting in premature failure through buckling. (Ramkumar, 1982; Bathias and Laksimi,
1983; O’Brien, 1983; Abrate, 1998; Ried and Zhou, 2000). Cantwell and Morton (1991)
reported a 50% reduction in compression-after-impact properties for composite lami-
nates, illustrating how impact induced stress waves are likely the most detrimental dam-
age producing mechanism in composite laminates.
Parga-Landa et al. (1999) and Mines (2004) applied classical one-dimensional
stress wave theory to study wave propagation in laminates. However, analysis of two and
three-dimensional wave propagation in an orthotropic medium can take on far more com-
plicated behavior. Spatial variations, preexisting damage, reflected waves from free sur-
faces, and boundary/structural interactions increase the complexity of the analysis. Chen
and Chandra (2004) analytically examined elastic and shock wave scattering due to dif-
ferent heterogeneity factors using Representative Volume Elements (RVE). Bahei-El-
Din and Zikry (2003) found that wave propagation was highly affected by material ani-
sotropy. Zhuang et al. (2003) investigated shock wave scattering due to inter-
face/microstructure of dissimilar homogeneous layered materials via flyer-anvil impact

24
experiments. They concluded that interface scattering effects reduce the shock wave ve-
locity also increasing the shock-front-rise time. Artan and Altan (2002) found that
nonlocal effects arising from voids, micro-cracks, etc. become important during the
propagation of high frequency waves. The complexity of studying wave propagation in
composite laminates is well appreciated from the experimental, analytical, and numerical
studies discussed above. LSDYNA 3D finite element modeling can be used to gain a
greater understanding of stress wave propagation in laminates subjected to FCI and aid in
predicting what areas will be more susceptible to an increase in the damaged state.
Stress Wave Interaction
Two common scenarios of wave interference arise in Hookean elastic solids. The
first is a single elastic wave reflecting or changing upon interacting with a boundary. If
the wave encounters a different material, as in Fig. 6, part of the wave is transmitted and
part is reflected. This can lead to complex interactions in multiple layered materials such
as in laminated composites. The other scenario, relevant to this present work is interfer-
ence between simultaneous or near simultaneous loading at different locations. The prin-
ciple of superposition of elastic waves was first suggested by Lord Rayleigh (Rinehart,
1975). It can be applied to Hookean solids by the vector sum of the disturbances pro-
duced by transient forces. This is illustrated in Fig. 8 which shows two saw tooth com-
pressive waves moving toward one another (a) and (b) and then away from one another
(c) and (d). What is interesting to note is that in Fig. 8, the magnitude (b) and duration
(c) of the interacting stress waves is greater than either wave by itself, which suggests
that the material response and subsequent damage could differ for simultaneous loading.
Also note that the final shape of the waves, Fig. 8 (d), remains unaltered.

25
Dynamic Crack Propagation
One of the first failure mechanisms initiated during an impact event is matrix
cracking and delamination. Understanding the behavior of cracks during such loading is
important since the rate at which the impact energy is dissipated is likely to depend on the
mode of crack opening and its velocity (Cantwell et al., 1989). Impact damage usually
follows very complex distributions in plane and through the laminate thickness. High
local stresses around the impact point initiate cracks, propagate delaminations, and lead
to the final damaged state. As a matrix crack reaches the interface of two adjacent plies,
stress redistribution takes place creating four possible sites for delamination (Abrate,
1998).
Interlaminar normal and shear stresses play a significant role in determining dam-
age initiation and propagation, and are usually determined using first-order shear defor-
mation plate theory (Abrate, 1998). Stresses in the vicinity of the crack tip propagate the
delamination. The rate and extent to which a delamination will propagate depends on the
mixed-mode (mode I and II) strain energy release rates. The mode I and II strain energy
release rates around an interlaminar crack tip are not well defined since the stresses are
oscillatory in nature; however, the total energy release rate is always well defined
(Abrate, 1998). When considering multi-site impact with impact locations in close prox-
imity, damage interaction through the thickness must be considered since it is major en-
ergy dissipation mechanism.
Cantwell and coworkers (1989) measured dynamic crack velocity in carbon and
glass fiber composites subjected to low velocity (Charpy impact) loading. They found
that interlaminar cracks could propagate at velocities in excess of 100 m.
s-1
, while cracks
propagating across fibers extend at velocities equivalent to the impactor (Cantwell et al.,

26
1989). However, crack behavior under the wave dominated regime differs from cracks
initiated from low velocity impact. Dwivedi and Espinosa (2003) investigated dynamic
mode I and mode II crack propagation velocity in laminated composites. They found that
crack velocity and mode of propagation were dependent not only on the imparted impact
energy, but also on the velocity of the impactor.
At impact velocities below 20 m s-1
, the crack propagated in primarily in mode I
at sub-sonic speed, e.g. below the shear wave speed. However, at higher impact veloci-
ties, the crack propagated under predominately mode II at intersonic velocities. The
steady state crack speed for 20 - 40 m s-1
impact velocities was found to be as high as 3.9
times the shear wave speed and 0.83 times the longitudinal wave speed of the material.
Cracks propagating in this velocity range are termed intersonic. This demonstrates that
dynamic crack propagation is tied to stress wave propagation in the case of impact load-
ing. Hao et al. (2004) reported modeling results that indicated the quasi-constant crack
propagation velocity was around the dilatational wave speed, oscillating between a lower
bound of the shear wave speed to an upper bound of approximately √ 2 times the shear
wave speed.
The unifying conclusion from the various studies discussed is that inertia, strain
rate, and stress wave effects are interrelated (Wang 2003). It is also clear that there is a
lack of studies addressing multiple impacts to composite structures. Experimental and
numerical modeling studies would aid in providing insight into the complicated phe-
nomenon of impact to composite structures.

27
Spall Fracturing
Hopkinson was the first to document the phenomenon of spall formation in 1914
(Rinehart, 1975). Spalling results from high intensity compressive stress wave reflects
off a targets free surface as a tensile wave. The tensile wave is never as high in magni-
tude because the compressive wave, being geometric in shape (e.g. square, triangular
etc.), interacts with the first part of the tensile wave reflecting off the free surface. Its
magnitude can be determined from the principle of superposition (Rinehart, 1975). Fac-
tors which determine whether spalling occurs include the resistance of the material to
fracture, magnitude of the stress wave, and the shape of the stress wave. The shape of the
stress wave determines the location in which the superimposed stress wave becomes ten-
sile in nature. This is to say, waves with flat top portions will become tensile further
from the free surface because the flat compressive portion will cancel out the tensile
wave until they move past one another.
Spall formation is a common occurrence in high velocity/hypervelocity impact of
composite laminates. In the case of layered materials with weak interfaces (normal to the
stress wave), as the tensile wave reflects from the free surface, the interface between plies
is fails and the layers peal off.
If the amount of spall formation (including shear plug formation) is significant,
the kinetic energy of the ejected material must be taken into account as an energy absorp-
tion mechanism. The velocity of the spall is linearly related to the stress intensity, so the
higher the stress, the greater the spall velocity. Spall velocity can be approximated from
Eqs. 13 and 14, where V1 and V2 are the first and second spall velocities, respectively. Ln
is the thickness of the spall, ρ is the material density, σ(t) is the transient stress at time t,

28
and c1 is the dilatational stress wave velocity and c2 is the shear wave velocity (Rienhart,
1975). The same treatment can be used for subsequent spall formation.
Finite Element Modeling of Impact on Composite Structures
Finite Element Modeling (FEM) has been implemented steadily as a tool for pre-
diction, design, and analysis of impact on composite structures over the last several dec-
ades. Failure modes and mechanisms which can be difficult to observe during quasi-
static testing can be nearly impossible to determine in high velocity impact given the ex-
tremely short time scales, which limit measurements and instrumentation. In the present
work, the physical phenomenon which occur during both near-simultaneous and sequen-
tial impact were investigated using explicit finite element modeling. However, there are
limitations to modeling, and one must realize that it is merely a simplified representation
of a physical component. For instance, woven fabrics are often represented as unidirec-
tional fibers in two directions in order to simplify the model. Voids and defects are typi-
cally also neglected. In addition, a large number of experimental parameters and material
properties (quasi-static and strain rate dependant) are required for the model itself. All
these things must be considered when interpreting modeling results.
In the present work, the finite element modeling considered is based off contin-
uum mechanics. In order to formulate a continuum mechanics problem, you first need a
description of: motion and deformation, stress, the physical and thermodynamic laws
( )
( )dtt
L
V
dtt
L
V
cL
cL
cL
2
2
12
11
11
2
2
2
2
2
0
1
1
∫
∫
⎟
⎠
⎞
⎜
⎝
⎛
=
⎟
⎠
⎞
⎜
⎝
⎛
=
σ
ρ
σ
ρ
(13)
(14)

29
governing the body, and a relation between motion/deformation and stress. The relation
between motion/deformation and stress is referred to as the constitutive relation.
Classical continuum mechanics is used to describe the dynamics of continuous
media, based off a set of differential equations, which apply principles of conservation of
mass, momentum, and energy. Transient behavior of material is described by the Equa-
tion Of State (EOS), which relates the density (or volume) and internal energy (or tem-
perature) of the material as they vary with pressure. The material response is determined
by the constitutive relation which relates the deformation (strain) and internal force
(stress). In the general case, any appropriate constitutive relation can be used as long as it
does not violate any laws of thermodynamics.
The length scale is also important to define. Structural length scales (0.1mm-
100m) are typically associated with continuum mechanics; however they can be applied
to micron (0.1μm-0.1mm), and nano (1nm-100nm) length scales. Atomic length scales
(0.1nm) are not considered in the context of continuum mechanics. As the length scale
decreases, the complexity of the model increases significantly. Only structural scale is
considered in the present work.
There are two basic ways in which kinematic deformation of continuous media
can be described: the Lagrangian (material) and Eulerian (spatial). In the Lagrangian de-
scription, the deformed body is referenced to an undeformed state. The Lagrangian for-
mulation represents interfaces accurately but does not handle large deformations well be-
cause of severe mesh distortion resulting in numerical instabilities. The Eulerian formula-
tion avoids severe distortion of the discretization because it is fixed in space and does not
move with the material during time stepping. Because the Eulerian formulation has im-

30
precise boundaries and the discretiztion does not deform with the material. In cases
where large deformations occur, an adaptive mesh approach known as Arbitrary Lagran-
gian-Eulerian (ALE) can be used. Both ALE and Lagrangian formulations can be used in
LS-DYNA, however the Lagrangian formulation was used in the present work because it
is suitable for modeling impact of solid materials since the surfaces of the bodies in con-
tact will always coincide with the discretization.
Mechanical Effects of Impact Damage
The susceptibility to impact damage has been a major limitation in implementa-
tion of composites as primary load bearing structures (Zhou, 1996). Although matrix
cracks are typically the first damage mode to initiate during impact, it is widely recog-
nized that their effect on the mechanical properties is minimal (Potti and Sun, 1997). It is
also well known that matrix cracks trigger delaminations which are detrimental to the
load carrying capability of a structure, particularly during bending and compression. In-
ternal delamination damage is detrimental to primary load bearing structures because it is
difficult to detect. This is commonly referred to as BVI (Barely Visible Damage) and is
found using advanced NDE (non-destructive evaluation) techniques.
The low interlaminar shear strength unique to laminated composites results in
significant strength reduction when subjected to compressive loading (Zhou, 1996). A
popular method of assessing the effects of impact damage is the Compression After Im-
pact (CAI) test. There are several variations in the actual test method, including Boeing,
Airbus Industries and NIST. In typical CAI testing, the damaged specimen is secured in
a load frame, and the load is introduced through the ends which are potted in a thermoset
resin to avoid end-brooming. The sides of the specimen are restricted from out-of-plane

31
deformation using an anti-buckling guide. At present, the conservative, damage-tolerant
design calls for allowable strain of less than one-third the basic material value (Zhou,
1996). In a review paper, Cantwell and Morton (1991) reported up to a 50% reduction in
CAI strength. However, more recently Guédra-Degeorges (2006) reported up to a 70%
reduction in compressive strength for specimens without visible damage.
Impact Damage Mitigation
Several strategies have been investigated to improve delamination resistance un-
der impact conditions. The majority of the work has focused on LVI testing in order to
characterize the effectiveness of various damage mitigation schemes. Research efforts
have mainly focused on interleaving, implementing tougher matrices, the addition of
short fibers, and stitching (Walker et al., 2002).
Interleaving involves inserting thin, tough polymer layers (interleaves) between
the plies. This has been shown to improve LVI resistance and damage tolerance (Duarte
et al., 1999). Toughened resins and interleaving rely on crack limitation imparted by
their inherent elasticity. Duarte and coworkers (1999) reported an increase in damage
tolerance using low modulus olefin interleaves. However there was a reduction in CAI
strength due to a lack of lateral support of the fibers. Sohn et al. (2000) reported low val-
ues for CAI strength for interleaved laminates (41% reduction) even though the damaged
area was significantly reduced (69% decrease over non-interleaved laminate). The disad-
vantage of interleaving and toughened resin systems is reduced stiffness, reduced glass
transition temperatures, and poor tolerance to adverse environments (Walker et al., 2002).
The addition of short fibers between the lamina (usually less than 5 wt. % of the
continuous reinforcement) provides a fiber-bridging mechanism (Walker et al., 2002).

32
There are two different methods of interface reinforcement; translaminar reinforcement
and short fiber reinforcement. Fibers are parallel to the ply surface while short fibers are
oriented through-the-thickness (also call z-fiber reinforcement) in translaminar rein-
forcement. Interlaminar reinforcement reduces delamination and energy absorption by
fiber pullout or fiber breakage. Short fiber interlayer has little effect on the laminate
stiffness and no effect on the glass transition temperature. Sohn et al. (2000) reported
increases in CAI strength for KevlarTM
and ZylonTM
translaminar reinforcement with a
significant reduction in damaged area. Zhang and coworkers (2006) reported a 19-64%
decrease in damaged area and 45% increase in CAI for carbon/BMI z-fiber reinforcement
(2% areal density). The main disadvantage of interlaminar and translaminar reinforce-
ment is the increased cost associated with manufacturing and the limitation on processing
routes.
Through-the-thickness stitching (z-stitching) has also proven effective in mitigat-
ing impact damage. Z-stitching typically employs a continuous high strength fiber (often
KevlarTM
) which is stitched in a grid using a lock or chain stitch. Hosur et al. (2004) re-
ported that high velocity impact damage (carbon/epoxy) was well contained within the
stitched grid (aramid cord) but the ballistic limit decreased. Larsson (1997) reported in-
creases of 44% and 50% for CAI strength, for specimens subjected to LVI and high ve-
locity impact, respectively. However, stitching reduces in-plane properties by 10-25%
(Larsson, 1997; Hosur et al., 2003). In addition, manufacturing costs are increased sig-
nificantly.

33
Multiple Impact
Protection against multiple impacts on lightweight future combat vehicles has
been recognized as a key issue in survivability (de Rosset, 2003). Multiple impact sce-
narios arise from the fragmentation of a metallic case containing a high explosive charge
(bursting munition), improvised explosive device, or automatic weapons fire. In the case
of high explosive charges (warheads) and improvised explosive devices, immobilization
is achieved through the blast wave and the ejection of high velocity projectiles from the
charge. The most damaging result is typically from high velocity fragments, which in-
crease the probability of a kill by damaging a structural component or critical system
(Ball, 2003). These projectiles are termed primary blast debris or shrapnel. The number,
mass, velocity, and spatial extent of the fragment spray zone are dependant on the type
and mass of the metallic case and the type of material used. Steel, tungsten, and alumi-
num are typical warhead case materials.
The two most common types of cases are natural fragmentation cases and con-
trolled fragmentation cases. The difference is that controlled fragmentation cases use
geometric stress concentrators to gain greater predictability in the fragment size and
shape. Table 1 gives the generic parameters for small, medium, and large warheads
(Ball, 2003). The highest occurrence of fragments is in a mass range of 2.07-2.59 g. The
question of whether there are synergistic effects in simultaneous impact or cumulative
effects in sequential impact is still an area of open research. If there are differences be-
tween the two scenarios, what time-hit interval dictates whether the impact event would
be treated as simultaneous or sequential? In the case of bursting munitions, the time hit
interval is within micro or nano seconds. For automatic weapons fire, the time-hit inter-

Bartus Dissertation Final

Recommended

Recommended

More Related Content

Similar to Bartus Dissertation Final

Similar to Bartus Dissertation Final (20)

Bartus Dissertation Final