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

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Copyright by Shane D. Bartus

2006

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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-

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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.

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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.

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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

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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

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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

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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

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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

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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

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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

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Figure Page

35 Three layer, .30 caliber test matrix with the 2.04 g, 7.94 mm diameter spherical projectiles at a constant incident velocity of approximately 201.3 m.s-1 (standard deviation = 3.8 m.s-1). ................................115

36 Four layer, .30 caliber test matrix with the 2.04 g, 7.94 mm diameter spherical projectiles at a constant incident velocity of approximately 249.8 m.s-1 (standard deviation = 8.8 m.s-1). ................................116

37 Four layer, .30 caliber test matrix with the 2.04 g, 7.94 mm diameter spherical projectiles at a constant incident velocity of approximately 225.1 m.s-1 (standard deviation = 8.8 m.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

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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

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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

59 Experimental vs. FEA prediction of the damage zone for a three (.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

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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

69 Typical damage progression in a three layer laminate (09.02.05-3-8) subjected to a .50 caliber sequential impact (steel, 8.38 g) at constant incident energy (~200 J). .......................................................................204

70 Typical damage progression in a three layer laminate (09.02.05-3-4) subjected to a .50 caliber sequential impact (WC, 16.08 g) at constant incident energy (~200 J). .......................................................................205

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

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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

81 Experimental vs. FEA prediction of the damage zone for a three projectile (3.91 g) sequential impact series..........................................................217

82 Experimental vs. FEA prediction of the damage zone for a three projectile (3.91 g) simultaneous impact series.....................................................218

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Figure Page

83 Experimental vs. FEA prediction of the damage zone for a three projectile (8.38 g) sequential impact series..........................................................219

84 Experimental vs. FEA prediction of the damage zone for a three projectile (8.38 g) simultaneous impact series.....................................................220

85 Experimental vs. FEA prediction of the damage zone for a three projectile (16.08 g) sequential impact series........................................................221

86 Experimental vs. FEA prediction of the damage zone for a three projectile (16.08 g) simultaneous impact series...................................................222

87 Modeling results showing the three layer laminate response to 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

88 Modeling results showing the three layer laminate response to 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

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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

121

)1()1()1()1()1()1(2

Cip

iFiMCiDLiTFiDiSPIpi Mm

EEEEEEVmV

++++++−

= −−−−−− (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 mpVI2,

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

nnSPiSP 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

εεσ

ρρσε ε

∫ ⎟⎠⎞

⎜⎝⎛−

+=

p

pP

tc0

ddd1)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) ⎟⎠⎞

⎜⎝⎛

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

−

−−++−+=

ab

b

rrrzdrdar

ptpit

i ip

iiii ln1

)())2/(()2/()/(

22

ε

(6) ( ) ( ){ } rrdrrhE itrd

isysysyiD 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 itiC2=

221

iiCiKE VME = (9)

(7) ( ) xAEax

obxTF dd)(

/

00 ∫∫= =

=

εεε 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(r2d(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

011

1

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−

−=

ρρρ

ppus

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

( )

( )dttLV

dttLV

cL

cL

cL

2

2

12

11

11

2

2

22

2

0

11

∫∫⎟⎠⎞

⎜⎝⎛=

⎟⎠⎞

⎜⎝⎛=

σρ

σρ (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-

34

val is several orders of magnitude greater, even at very high rates of fire (e.g. at 1200

rpm, the time hit interval is 0.05s).

Multiple Impact Test Methods

The threat of multiple impact can be defined several ways. It can be repeated im-

pacts over the same area until failure. Repeated impacts are most commonly conducted

using LVI (drop tower). Multi-site sequential impact is often the preferred method used

in existing impact standards. In this case, the spacing is known before impact and is typi-

cally in 2-5 locations. This method is employed to assess multiple impact behavior.

Multi-body collisions have also been a focus of study, but these are usually low velocity,

elastic collisions and have little relevance in the scope of this paper (Quinn and Bairava-

rasu, 2004; Quinn and Bairavarasu, 2006). Multi-site, near-simultaneous impact is usu-

ally conducted using a fragmentation devise with random impact locations. Very little

open literature addresses simultaneous impact with controlled impact location. Known

literature concerning multiple impacts is covered in this section. There appears to be a

lack of understanding is in the differences in material response under multi-site near-

simultaneous and multi-site sequential impact.

Multiple Impact Test Standards

There are several existing standard test methods for assessing multiple high veloc-

ity impact; ASTM F 1233, NIJ 0108.01, and UL-752. The test procedures imply sequen-

tial impact by a conventional powder gun and do not specify the target material being

tested. Metals, ceramics, and composites behave different under impact. The standards

35

call for 2-5 fair hits in predetermined locations (i.e. equilateral triangle with three im-

pacts).

Non-Standard Multiple Impact Test Methods

Lixin and coworkers (2002) used explosive fragment generators to emulate the

terminal effects of gimballed warheads. A fragment generator consists of a cylindrical

charge that drives the projectile(s) along the axial direction. The fragment hit density is

controlled by the angle of the explosive charge surface and the distance to the target

(Lixin et al., 2002). Reasonable prediction of fragment cluster spreading was obtained

using numerical methods.

Held (2001) also investigated hypervelocity impact by multiple projectiles in or-

der to study detonation characteristics of insensitive munitions. The fragments were mild

steel cubes with 12.7 mm sides impact with a velocity of 2530 m.s-1 ±90 m.s-1. MIL-

STD-2105 B requires impact by at least two fragments but no more than five fragments

(Held, 2001). In this case, two explosively formed projectiles charges were used to ac-

celerate two 16 g steel projectiles by simultaneously igniting the charges. The projectile

velocities were approximately 2500 m.s-1. Held (2001) was able to attain relatively accu-

rate impact location and terminal projectile velocities (±90 m.s-1). Held’s (2001) method

was a more controlled method than that used by Lixin et al. (2005); only two projectiles

were considered as opposed to 500.

Williams (1987) presented a technique of launching multiple projectiles (4-42) at

hypervelocity (2-5 km.s-1) using a two-stage light-gas gun. Their approach used a sabot

which contained multiple 6.35 mm spherical projectiles situated along the periphery of

the sabot axis. Upon striking a separator rod, the sabot deforms while the launch package

36

continues forward under its own momentum. The projectiles then separate out into a pat-

tern which has some degree of repeatability.

Yatteau and Dickinson (1993) impacted a shatter plate (mild steel) at high veloc-

ity (1.5-2.3 km.s-1) to generate a debris cloud. The debris cloud was then used as the

threat against a target. In this instance, the target was a witness plate used to evaluate the

debris cloud dispersion in addition to radiography, which was used to look at its shape.

The degree of dispersion could be controlled by varying the distance between the shatter

plate and the witness plate. The trajectory, size, shape, and mass of the debris cloud par-

ticles varied considerably (Yatteau and Dickinson, 1993).

A non-separable, multiple projectile launch package for hypervelocity impact was

proposed by Savveteev and coworkers (1999). In their work, a sabot (launch package)

held three rod shaped projectiles until impacting the target at which point the sabot breaks

apart. The sabot was machined from a low-density material (polyethylene) to minimize

interactions with the specimen. They placed the projectiles in an equilateral triangle with

15 mm sides. The targets were semi-infinite steel plates with a hardness of 19-22 RC.

Bartus and Vaidya (2004) utilized a 12-gauge powder gun to launch multiple 7.94

mm steel spherical projectiles against carbon-epoxy composite laminates. The impact

velocity range (~250-425 m.s-1) was much lower than the range investigated by the previ-

ous authors. The cartridges were hand loaded. As the projectiles exit the barrel, they

spread out into a pattern. The pattern density is dependant on the amount of restriction at

the end of the barrel (choke), the distance to the target, and the launch package velocity.

The velocity and spread of the projectiles at the target were determined experimentally

prior to testing. The projectile impact locations could not be controlled directly. A statis-

37

tical probability of obtaining an average inter-projectile spacing for a given test condition

defined the impact locations (Bartus and Vaidya, 2004; Vaidya and Bartus, 2004).

Holt and Mock (2004) used a reverse-ballistic technique for multiple-particle im-

pact using a gas gun. In the reverse-ballistic configuration, the target is accelerated to-

ward static penetrators, which in the case of Holt and Mock (2004), were supported by a

frangible assembly. The penetrators were steel spheres (6.35 mm φ) and the target mate-

rials were steel and aluminum (the technique is not limited to those geometries). Two

different projectile positions were investigated; side by side with a separation of 3.18 mm

and at the vertices of an equilateral triangle with a spacing of 3.18 mm. The specimen

size is a limited by the diameter of bore. In investigating multiple impact of composite

specimens, it is common for the damage to outgrow the bore size of most laboratory gas

guns.

Multiple Impact on Concrete Structures

Gomez and Shukla (2001) investigated repeated impact on semi-infinite concrete

specimens. In their work, a powder gun was used to fire ogive shaped projectiles with a

length to diameter ratio of ten. The impact location and velocity remained constant for

multiple impact loading. The crater depth and volume were measured after each shot.

The Forrestal model was used to predict penetration depth. The model is empirical and

was modified with a strength reduction factor in order to predict penetration depth for

repeated impact conditions (Gomez and Shulka, 2001).

Leppänen (2005) recently studied blast and fragment impacts on concrete. The

experimental work included explosively driven 4 mm diameter fragments with a velocity

38

of 1650 m.s-1, impacting semi-infinite concrete specimens. The depth of penetration var-

ied between 30 to 50 mm and the crater diameter varied 45 to 60 mm. The specimens

were sectioned and examined for macrocracking, which was attributed to reflections from

stress waves generated from impact and blast loading. The author did not address

whether additive effects were responsible for the variation in damage characteristics un-

der the multiple fragment loading (i.e. depth of penetration and crater diameter). The

blast loading and fragment impact event was also modeled using AUTODYN. The dam-

age predicted in the model matched qualitatively with the experimental results.

Multiple Impact of Metallic Structures

Qian et al. (2005) and Qian & Qu (2005) investigated FCI of thin metallic armor

plate based on explosive fragment generator experiments performed by Lixin et al.

(2002). The study by Qian et al. (2005) focused on an analytical model (based on the

empirical THOR formula) to distinguish between cumulative and additive effects on

specimens subjected to impact by an explosive fragment generator. Two important fac-

tors distinguishing additive and cumulative effects in their experimental results include

the rate of energy deposition on the target and the impact duration of the fragment cluster

(Qian et al., 2005). After adjusting the fragment density (number of fragments) and the

distance between the fragment generator and target, additive and cumulative effects were

identified.

Qian & Qu (2005) used a numerical approach (LS-DYNA 3D with the Johnson-

Cook material model) to study the time-hit interval effects and fragment density effects.

In the fragment density study, the fragments were modeled using four fragment rings

with uniform spacing in each ring. They found that the residual velocities of the center

39

fragments in the simultaneous model were substantially lower than the fragments in the

outer rings. Qian and Qu (2005) attributed this to higher fragment cluster densities at the

center of the plate, which resulted in an increase in plastic deformation. They failed to

address other synergistic mechanisms at play. According to Ball (2003), each of the im-

pacting fragments creates a stress wave that emanates from the impact point. When the

impact points are relatively close together, the stress waves overlap. Damage caused by

the multiple overlapping stress waves can be more severe than the damage caused by in-

dividual, widely separated fragment hits considered alone (Ball, 2003).

Qian and Qu (2005) varied the interval between hit intervals in the time-hit study.

As the time-hit interval increased, the damaged state (or amount of material punched out)

decreased. With a time interval of 50 μs, almost all of the material between the impact

locations remained intact; at short time-hit intervals, almost all of the material intercon-

necting the fragment-hit locations was sheared out.

Majzoobi et al. (2005) successfully implemented LS-DYNA 3D code to simulate

multiple impacts on metallic targets in order to study the cold working process in shot

peening. The Johnson-Cook material model was used for both the shot and target. Stress

wave effects were accounted for using the Gruneisen equation of state for a compressed

material. They reported results on a four projectile simultaneous impact and a nine pro-

jectile simultaneous/sequential impact with overlapping impact locations. The projectile

velocity for the simulations was between 50 and 100 m.s-1 with a shot radius of 0.4 mm.

The model predicted when the target material achieved a uniform state of residual stress.

In addition, they determined the critical impact velocity for the maximum residual stress

distribution (90 m.s-1), above which resulted in residual stress reductions.

40

Khorev et al. (1989) investigated two high-velocity steel projectiles in synchro-

nous contact with a steel plate using a simple two-dimensional finite element model.

Their analysis indicated two distinct stages of interaction. The first is the manifestation

of large negative pressure zone (which determines damage growth based on the failure

model used) as a result of stress wave interactions. The second, lasting considerably

longer, is the interaction of the plastic deformation zones. Findings indicate the interac-

tion is dependant on the inter-particle spacing. For small inter-particle spacing, the de-

formation of the particles retarded damage growth in the region of influence. For large

spacings, interaction was weak.

Multiple Impact of Composite Structures

Low Velocity Impact

Wu and coworkers (1994) developed an analytical model based on classical lami-

nation theory (the Rayleigh-Ritz method) to identify LVI forces at multiple locations on

composite laminates. Modal superposition was used to account for forces acting on mul-

tiple locations. Experimental verification was carried out using an instrumented impact

hammer. The multiple impact condition was simulated by adding the strain data from

several single impact events. In this case, the composite was not damaged as a result of

multiple impact.

Found and Howard (1995) conducted a low velocity repeated impact study of car-

bon-epoxy laminates. They found an impact energy threshold below which the contact

force between the indenter and specimen did not change (up to 100 impacts in the same

location). Above the threshold energy, substantial decreases in contact force and large

damaged areas were noted after the first few impacts.

41

Lam and Sathiyamoorthy (1999) presented a numerical method to analyze lami-

nated composite beams under LVI by multiple arbitrary spherical masses. Using a modi-

fied Hertzian contact law, their approach predicted contact force and beam deflection by

multiple (different) masses and varied initial velocities at arbitrary locations No experi-

mental verification of the model was provided. Their model does not account for failure

from penetrating impacts, nor does it predict delamination from non-penetrating impacts.

An experimental investigation into repeated LVI of stitched/unstitched S2-glass/SC-15

epoxy laminates was conducted by Hosur and coworkers (2003).

The specimens were impacted in the same location repeatedly and the damage

progression was monitored using ultrasonic C-scan, and the time-force and time-energy

curves recorded. They found that at low impact energy levels (≤ 30J), the peak load, and

energy absorption did not change significantly. At 40 and 50 J of impact energy, there

was a distinct drop in peak load and energy absorbed after several impacts. The speci-

mens with large grid spacing (25.4 mm) fared better than specimens with a small grid

spacing (12.7 mm). The damage area increased as number of impacts increased (pro-

jected area from C-scan) but reached a plateau after a certain number of impacts.

Chakraborty and Kumar (2005) and Chakraborty (2006) employed finite element

modeling to study delamination under multiple LVI loading. The code considers differ-

ences in velocity, location, time intervals, and location of impact from cylindrical masses

(Chakraborty and Kumar, 2005; Chakraborty, 2006). A stress based failure criterion for

delamination was used based on the criterion proposed by Choi and coworkers. Chak-

raborty and Kumar (2005) and Chakraborty (2006) reported several interesting conclu-

sions based on the studies. Contact forces at different points of impact were dependant

42

on the time interval between impacts, the impactor mass, and the velocity of the impac-

tors. Chakraborty (2006) found that the time interval between successive impacts, impac-

tor velocity, and the distance between impact locations determined whether two distinct,

remote delaminations will coalesce into a single delamination or remain separate. During

shorter intervals of time between successive impacts, the probability of remote delamina-

tions coalescing into one large delamination increased.

Greenhalgh and coworkers investigated impact damage in a carbon-epoxy wing-

box under load. They took a full-scale structure with a simulated flight load and used it

to determine the effects on structural response and damage from multiple impactors. The

structure was impacted, preloaded (tension/compression), and unloaded using a drop-

weight rig in 22 predetermined locations. Ultrasonic C-scan results indicated no damage

interaction between impact sites (with one exception). Tensile preloading promoted ex-

tension of damage parallel to the spars (matrix splitting) and compressive loading pro-

moted damage perpendicular to the spars (delamination).

Multiple High Velocity Impact

Malekzadeh and coworkers (2006) proposed an improved higher-order sandwich

plate theory to analyze multiple small mass impacts on sandwich composites. At the time

of their paper’s publication, they reported a lack of published experimental data for mul-

tiple impacts of sandwich composites. They validated their model indirectly by compar-

ing the results with the LVI response of two double small mass strikes and a single small

mass strike. The contact points were chosen such that there would be no wave interac-

tions with the boundaries or between projectiles based on Olsson’s (2000) criterion. By

this reasoning there would be little or no synergistic influence from adjacent projectiles.

43

Olsson (2000) states a criterion for small mass impact response occurs when the

impactor mass is 1/5 the mass of the impacted panel. Using the relation between density

and volume of materials (spherical impactor), the following relationship can be written

as, Eq. 15, where Ri and ρi are the radius and the material density of the ith impactor, re-

spectively (Olsson, 2002; Malekzadeh et al., 2006). The ith superscript denotes the ith

impact (i=1, 2,..., N), ρ and h are the target material density and thickness, respectively.

The minimum distance between two arbitrary impactors (ith and (i-1)th) can be calcu-

lated from Eq. 16: With Eq. 16 satisfied, the impact response of the structure will be lo-

calized and the nearly independent of contact locations. If the two projectiles are identi-

cal, Eq. 16 simplifies into Eq. 17:

Malekzadeh and coworkers (2006) found reasonable agreement between their

model with experimental results from single and double (simultaneous) 5 g and 10 g (10

mm diameter) impactors with a velocity of 3 m.s-1. The largest contribution in the work

would have been in the study of multiple projectiles impacting within the interaction dis-

tance defined by Olsson (2002). The validity of the model under such conditions was not

addressed directly. In addition, the impacts were elastic and damage criterion was not

implemented.

(15) hRRR

iiii

352

ρρ

≥

(16) hRR

hRRd

iii

iii

352

352

111

min ρρ

ρρ −−

−+≥

(17) hRRd

iii

351639.5min ρ

ρ≥

44

Multiple High Velocity Projectile Impact

Fixed wing and rotary wing aircraft have been a primary focus in the investigation

of multi-site damage because of vulnerability to fragmentation warheads. Because of

fixed wing aircraft’s high rate of speed, fragmentation warheads threats are often em-

ployed. These threats have a large weapon’s envelope, which is used to increase the

probability of a kill (Ball, 2003).

Jones (1994) investigated residual strength of carbon-epoxy with multiple impact

damage. In the preliminary study, single and double impact conditions were simulated

using quasi-static indentation. Jones (1994) reported that there was very little damage

interaction in the case of double perforations and that the two damage areas could be con-

sidered independent. Energy absorption under quasi-static loading also remained con-

stant. In the larger scope of the study, a repair strategy was implemented for two F/A-18

horizontal stabilizers damaged in service. One of the stabilizers was impacted by two

fragments from a tracer rocket; the other contained two zones of barely visible damage

(the source of damage was not disclosed). The stabilizer, which had been impacted by

the two fragments contained visible damage (delamination and fiber breakage) with in-

teraction; damage on the stabilizer that was barely visible (assumed to occur from LVI),

remained local. Both stabilizers were statically loaded with air bags before and after re-

pair, and strain measurements were taken. The repairs proved effective but the effect of

damage interaction under multi-site impact was not noted.

Riedel and coworkers (2002) conducted a limited study of a generic carbon-epoxy

box structure representative of an aircraft wing structure. The structure was subjected to

blast and impact from a fragmenting high explosive warhead. The warhead inflicted 126

perforations on the front skin with 52 of those fragments also perforating the back skin.

45

The spars provided some degree of shading, increasing the level of protection at the rear

skin.

Ultrasonic C-scan was used to determine the extent of damage. Large, intercon-

nected areas of damage were most prevalent in close proximity to the warhead. Isolated

perforations had more localized damage while other perforations in close proximity to the

damage zones combined. This produced an increased damage zone greater than a similar

impacts would have when isolated. Virgin skins and spars and those with extensive per-

forations where cut out (unconfined area of 711 cm2) to assess post impact compressive

structural response and determine strength/stiffness degradation. They found that 90% of

the local stiffness was retained with up to 13 perforations (182 impacts m-2). The load

carrying capacity decreased by more than 35% with only 14 impacts m-2 (50% reduction

with just three local perforations which damaged a very small area).

Riedel and coworkers also performed finite element analysis using the commer-

cial code AUTODYNTM. Although the model captured the extent of perforations, it un-

der-predicted the extent of damage. The model also failed to predict increases in the ex-

tent of damage from oblique projectiles.

Literature Review Summary

An overview on the impact response of polymer matrix composites has been pre-

sented, including some of the recent work building from past reviews by Cantwell and

Morton (1991), Abrate (1998), and Reid and Zhou (2000). A comprehensive overview of

impact damage, energy absorption mechanisms, and impact response of composite lami-

nates has been presented.

46

The first section of the review focused on damage and energy absorption in duc-

tile metallic and brittle materials. Ductile materials generally absorb energy through elas-

tic and plastic deformation while brittle materials absorb energy through fracture proc-

esses.

The second section focused on the impact response of composite laminates. The

three impact velocity regimes discussed in the paper were LVI, intermediate velocity im-

pact, and high velocity impact. The impact regime dictates the material response and can

affect the failure mode. LVI specimens generally absorb impact energy through elastic

strain. In high velocity impact, energy must be absorbed through faster mechanisms,

such as the creation of new surfaces.

The response of woven fabric and loosely bound fibers was briefly discussed in

order to provide insight into the differences between the compliant targets and hard tar-

gets. It is generally accepted that the matrix prevents fibers from moving when subjected

to impact allowing a greater number of fibers to carry the load, thus absorbing more en-

ergy.

The next section highlighted an analytical framework for a model predicting pre-

dominate energy absorption mechanisms for composite laminates subjected to high ve-

locity impact. The energy absorption mechanisms covered are shear plugging, kinetic

energy of the moving portion of the cone which forms during penetration, deformation of

the secondary yarns, failure of the primary yarns, and matrix cracking and delamination.

Recently, it has been shown that the momentum imparted to the cone by the impactor as a

major source of energy absorption, which was previously assumed negligible. Deforma-

tion of the secondary yarns is also a large contributor to the energy absorption process

47

followed by tensile failure in the primary yarns. According to the analytical model, ma-

trix cracking and delamination do not contribute significantly to the overall energy ab-

sorption. When very large areas of new surfaces are created, the contribution can be

greater.

The ability of a composite laminate to absorb impact energy is dependant on a

large number of variables. General trends where there is wide agreement are summa-

rized. The largest factor of energy absorption is laminate thickness or areal density.

Thick targets tend to absorb more energy in the first stage of penetration, fiber crushing.

Tough, high strain to failure fibers (S2-glass, aramid, polyethylene) are better energy ab-

sorbers than high strength fibers like carbon, which have a low strain to failure. Al-

though matrix cracking and delamination are not the largest contributors to energy ab-

sorption, post impact mechanical properties are very heavily influenced by the damage

tolerance of the matrix. While rubber toughened epoxies and thermoplastic matrices de-

crease delamination, strength and stiffness are usually sacrificed. An increase in the fiber

matrix bond strength increases the composite strength, but also decreases energy absorp-

tion by limiting energy dissipation via fiber-matrix debonding and frictional sliding.

Woven fabric laminates with a low fiber crimp angle (undulation) result in increases in-

plane properties and energy absorption.

Understanding shock and stress wave response of composites is essential to char-

acterizing impact resistance under impact conditions. Shock and stress wave propagation

is relevant to the impact response regimes of intermediate velocity and greater. Split

Hopkinson pressure bar and flyer plate impact are the two most prevalent techniques for

measuring shock response. Understanding material behavior under high strain rates

48

(equation of state) is essential for accurate modeling of impact behavior under such con-

ditions. In the shock regime, composites are not able to absorb energy as strain so they

absorb it via faster mechanisms such as the creation of new surfaces. Stress and shock

wave propagation is thought to be responsible for delamination initiation and propaga-

tion. Delamination is considered the most important damage mode as it results in the

largest decrease in mechanical properties, particularly compression.

Impact damage mitigation methods were discussed. The most common are inter-

leaving, toughened matrices, the addition of short fibers (interlaminar and translaminar),

and z-stitching. There are drawbacks to all methods. Many techniques result in signifi-

cant increases in processing costs and limit the available processing routes. Interleaving

is effective in mitigating damage. CAI strength often suffers due to a lack of support for

the fibers. Mechanical properties and the glass transition temperature are also reduced.

While toughened matrices do not require additional processing steps, they reduce me-

chanical properties and glass transition temperature. Interlaminar reinforcement (in-plane

and out of plane) can be effective in reducing delamination while increasing CAI

strength, but reductions in CAI are commonly reported. Z-stitching is very effective for

increasing interlaminar fracture toughness, but results in a significant reduction for in-

plane properties.

Previous work shows that materials respond differently under multiple impact

conditions. The vast majority of open literature addresses single point, non-repeated im-

pact. A review of current non-standard test procedures for multiple impact scenarios was

presented, along with relevant supporting numerical studies. The review is pertinent to

understanding material response in light of realistic conditions, such as on the battlefield,

49

where the threat of fragmentation devices (e.g. Improvised Explosive Devises (IEDs) and

fragmentation warheads) is of concern.

Multiple impact can be defined several ways. It has been discussed from the

standpoint of sequential and simultaneous/near-simultaneous impacts. An impact series

is considered sequential when the time-hit interval is sufficiently long, such that synergis-

tic effects arising from stress and shock wave interaction is avoided. Sequential impact

has been studied as a repeated impact series in which the specimen is impacted in the

same area and as multi-hit impact, affecting different locations. Sequential impact is of-

ten carried out to qualify whether a target can withstand multiple impacts without damage

accumulation.

Simultaneous/near-simultaneous impact is more difficult to reproduce in a con-

trolled manner and studies available in open literature are limited. Single and two-stage

light gas guns using specially designed sabots to carry multiple projectiles offer a greater

degree of experimental control in contrast to explosive fragment generators and bursting

munitions. Multiple barrels have also implemented a gas gun in order to control impact

location and velocity for sequential and near-simultaneous testing. This was done to gain

insight between the two scenarios. Synergistic mechanisms in simultaneous impact and

the effect of cumulative damage under sequential impact are not well understood.

50

Fig. 1. Impact response of target plates subjected to (a) very short impact times with di-latational 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).

a b c

51

Vi

h

Zi

d

r

Primary yarns

Secondary yarns

Fig. 2. Cone formation on the distal side of a woven composite during high velocity impact. Adapted from Naik & Shrirao 2004.

52

Fig. 3. Illustration showing shock wave formation. As the speed of sound in-creases with increasing pressure, the front of the wave slows and slope increases until it results in a discontinuous disturbance or shock.

σ

x

(b) (a)

53

ε

σ

(a)

P1

0

1ρ

1

1ρ

P0

Rayleigh line Hugoniot

(b)

Fig. 4. Shock wave conditions occur along the Rayleigh line (b) while the release wave follows the Hugoniot curve (a). The area in the cross hatched region, (b), represents the difference between the internal energy behind the shock and the in-ternal lost on release.

54

λ

Propagation

a

λ

Propagation

b

Fig. 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 an-other and their mutual separations remain constant.

55

Fig. 6. Compressive elastic wave propagation through a bimaterial interface showing the (a) incident wave and the (b) reflected/transmitted wave components.

c1 c2 c1

Pmax

Period

Material 1 (E1, ρ1) Material 1 (E1 , ρ1) Material 2 (E2, ρ2) Material 2 (E2, ρ2)

a b

56

Fig. 7. Illustration showing the response of composites under low and high veloc-ity impact scenarios as a function of energy.

(Energy absorbed via creation of new surfaces)

Energy absorption mechanisms

(Energy absorbed via strain)

Fiber fracture matrix cracking interface failure

Low velocity impact

High velocity impact

Impa

ct e

nerg

y

Delamination

Stress wave propagation

Shock wave propagation

57

σo

(a)

(b)

(c)

(d)

Fig. 8. Schematic illustrating the principle of superposition of two saw tooth compressive waves interacting.

58

Parameter Small warhead Medium warhead Large warheadFragment weight (grams) 2.59 6.48 5.18Number of fragments 2600 3200 8300Fragment velocity (m.s-1) 1524 1829 2743

Table 1.Parameters for three generic warheads

59

EXPERIMENTAL APPROACH

The experimental approach section is developed as follows: (1) materials, proc-

essing, and characterization, (2) preliminary experimental approach, (3) final experimen-

tal approach, (4) non-destructive damage characterization technique. In the first section,

materials and processing methods used in the study are discussed. In the following sec-

tion, experimental development of the powder gun impact apparatus for multi-fragment

testing is discussed along with some of the preliminary results. The results will point out

several of the limitations with that particular experimental approach, which ultimately

lead to the development of a new apparatus. The final approach employed a single-stage

light-gas gun equipped with multiple barrels which allow it to fire up to three projectiles

near-simultaneous or sequential with controlled velocity and impact locations. In the last

section, the damage characterization and analysis technique employed are discussed.

Materials Selection

The goal in this study was not to develop a materials system which will better

withstand multiple impact, rather to investigate the impact response of a well known sys-

tem under multiple impact. A laminated composite that has received considerable atten-

tion in regard to high strain rate behavior is S-2 glass/SC-15 epoxy (Song et al., 2003;

Hosur et al., 2003; Ren et al., 2004; Gamma et al., 2004, Pan et al., 2005, Hosur et al.,

2005, Bartus et al., 2006). The material properties, in particular high strain-rate proper-

ties, have been characterized and published in previous studies (Deka et al., 2006). S-2

60

glass has been used extensively in light weight armor applications because of its excep-

tional energy absorbing capability while the rubber toughened SC-15 epoxy affords in-

creased damage tolerance.

Reinforcement

A plain weave, 24K tow S-2 glass with 933 sizing (manufacturer: Owens-

Corning) was chosen for the reinforcement. The areal density is 0.81 kg.m-2 (24 oz.

yd.-2). While 90% of all glass fiber produced is E glass, S-2 glass or high silica glass, of-

fers better mechanical properties (Chawla, 1998). The main difference lies in the chemi-

cal composition. S-2 glass typically has approximately 15% more SiO2, 54% more MgO,

and 68% more Al2O3 (Chawla, 1998). Typically E glass has a tensile strength between

1.7-3.5 GPa with Young’s modulus is between 69-72 GPa. The tensile strength of S

glass is between 2.0-4.5 GPa with a Young’s modulus of 85 GPa (Chawla, 1998). In ad-

dition, S-2 glass has a higher strain to failure (4.8% vs. 5.7%), which allows it to absorb

more energy (Agarwal and Broutman, 1990).

Matrix

SC-15 (manufacturer: Applied Poleramic Inc.) is a low-viscosity two phase, two

component epoxy resin system consisting of part A (deglycidylether of bisphenol-A, ali-

phatic diglycidylether epoxy toughner) and part B (cycloaphatic amine and polyoxylal-

kylamine) (Pervin et al., 2005). The second phase rubber particles afford increased dam-

age tolerance, in particular against impact induced delamination when compared to poly-

ester, vinyl ester, and conventional epoxy systems, without sacrificing properties signifi-

61

cantly. Young’s modulus and tensile strength of the neat resin were reported by Pervin

and coworkers (2005) as 2.20 ±0.12 GPa and 85.1±4.3 MPa, respectively.

Materials Processing

There are several methods commonly employed for processing laminated com-

posites with thermoset resin systems. Some of the most prevalent include hand lay-up,

autoclave molding of prepregs, resin film infusion, Resin Transfer Molding (RTM), and

vacuum infusion molding. Vacuum infusion is a cost effective, single sided tooling proc-

ess in which liquid resin is drawn into a dry fabric preform under atmospheric pressure

with the aid of a high permeability layer and kept under vacuum until the component

cures. The advantages are in low cost tooling, relatively high fiber volume fractions, low

void content, low Volatile Organic Compound (VOC) emissions, and the ability to pro-

duce large structures. The first liquid molding vacuum infusion patent was Seemann

Composite Resin Infusion Molding Process (SCRIMP) (1990). A significant number of

variations have been implemented since. One of the more common variations is Vacuum

Assisted Resin Transfer/Infusion Molding (VARTM/VARIM) (Pike et al. 1994). The

VARTM process was chosen for the study because it is commonly used in conjunction

with the resin and reinforcement.

An illustration of the VARTM process is shown in Fig. 9, and the actual lay-up

prior to infusion is shown in Fig. 10. A 19 mm thick glass table (91x183 cm2) was used

for the tool. The surface was prepped by first cleaning it with a razor and acetone and

then applying three coats of NC-700 Freekote® (manufacturer: LOCTITE) mold release.

A hot air gun was used to preheat the mold surface to approximately 60oC to drive off

excess moisture and to decrease the time required for the mold release to dry. Masking

62

tape was placed 50 mm away from the preform periphery in order to keep the mold re-

lease off the area where the sealant tape was placed. The mold release discourages the

resin from bonding to the tool by increasing the surface free energy (decreased wetabil-

ity) and by providing a slippery surface to decrease mechanical bonding. The masking

tape along the periphery of the preform was then removed, and the sealant tape was

placed. The infusion and extraction lines were placed next to the preform as shown in

Figs. 9 and 10. Release film (woven nylon) was cut slightly larger than the preform. It

serves to keep the high permeability layer from adhering to the composite once the resin

cures. The high permeability layer was cut to the length of the preform but was left 25

mm short from the resin extraction line in order to slow the resin flow through the media

and allow it to wet out the preform through the thickness.

The vacuum bag was then matted to the sealant tape and vacuum was applied. If

any leaks were found they were stopped and the preform was debulked for 20 minutes.

While the preform debulked, the part A and part B of resin was measured by weight and

carefully mixed for 5 minutes using a stirring stick. The amount of resin mixed was de-

termined by weighing the preform and multiplying that weight by 55%. That weight of

resin provided a close approximation to the amount of resin needed to wet-out the pre-

form, including resin lost in the infusion/extraction lines, the release film, and high per-

meability layer.

The samples were left to cure at room temperature for 24-28 hours under vacuum.

Once cured, the samples were debagged and left to further cure at room temperature for

160-170 hours. They were then cut into 20.3 x 20.3 cm2 specimens, labeled with an ad-

hesive specimen tag, and post cured at 82oC for five hours in a convection oven. The

63

specimen designation was as follows: (date processed)-(number of plies)-(specimen

number), e.g. 03.13.05-3-1 would be a specimen processed on March 13, 2005, with three

plies, and is the first specimen from the sample. The stacking sequence was [0/90]3,

[0/90]4, and [0/90]5 in which 86, 18, and 12 specimens were processed, respectively.

The average specimen thickness for the three layer laminates was 2 mm ± 0.05

mm, measured using a digital caliper. The average specimen thickness for the four layer

laminates was 2.51 mm ± 0.05 mm. The fiber volume fraction was determined using the

immersion density technique. The immersion density method is based on Archimedes’

principle which states that a body immersed in a fluid is buoyed by a force equal to the

weight of the displaced fluid. Density was calculated using the following relationship,

Eq. 19:

where mdry is the mass of the section dry, mwet is the mass of the section when immersed,

and OH2ρ is the density of water at the test temperature. Sections, roughly 25.4 x 25.4

mm2 were cut from the panels and the edges were polished. The sections were then

cleaned in an acetone bath and dried in a convection oven for 30 minutes at 82oC. The

sections were first weighed on a balance dry. Then they were immersed in a dilute solu-

tion of soap and water, rinsed and placed in a distilled water bath and weighed. The di-

lute solution of soap and water helps deter bubbles from nucleating on the specimen

while taking the mass measurement. Once the composite density is known, the fiber vol-

ume fraction can then be determined using Eq. 20:

(19) OHwetdry

dry

mmm

2ρρ ⋅

−=

64

where compositeρ is the composite density measured using Eq. 19, matrixρ is the density of the

matrix, also determined using immersion density, and fiberρ is the fiber density which was

obtained from Chawla (1998). The density was determined from twelve sections taken

from six panels. The fiber volume fraction calculated was 52.4% ± 2.7% for both the

three and four layer laminates.

Impact Test Apparatus Development

Fragment Cluster Powder Gun Development

The first impact apparatus implemented for near-simultaneous multi-site impact

was the universal receiver powder gun (manufacture: H-S Precision Inc.), Fig. 11. Dif-

ferent caliber barrels can be interchanged in the universal receiver, facilitating different

test conditions. Three different caliber barrels have been procured; 2 ¾” 12-gauge, .300

Winchester Magnum, and .50 caliber Browning Machine Gun (BMG). The velocity

range is approximately 180 m.s-1 (12-gauge, 4 fragments) to ca. 1500 m.s-1 (.50 BMG, .50

caliber FSP). For multi-site simultaneous impact, the universal receiver powder gun was

equipped with a 60.1 cm long, full choke 12-gauge barrel and a custom fixture allowing

the gun to articulate to adjust for windage and elevation, Fig. 11. The articulating fixture

allows the user to aim powder gun at the desired impact location. It was designed and

fabricated using surplus materials and an x-y translation table. The test rig can be

clamped to a firing bench to absorb the recoil. All testing was conducted at the Fraternal

Order of Police (F.O.P.) firing range in Pleasant Grove, AL.

100(%)fraction meFiber volu ⋅−−

=matrixfiber

matrixcomposite

ρρρρ

(20)

65

The 12-gauge round was chosen for the ability to load multiple projectiles into the

hull (shell). The shell, illustrated in Fig. 12, consists of a hull, primer, wad, and projec-

tiles. The primer ignites the propellant. When the propellant ignites, it produces a sub-

sonic deflagration wave that rapidly expands producing a pressure gradient across the sa-

bot/projectiles, accelerating them down the barrel. Smokeless propellant consists of ni-

trocellulose (single base) often combined with up to 20% nitroglycerin (double base)

(Jones, 1998). Since smokeless propellants only burn at the surfaces of the granules, the

shape and size of the granules affects the burn rate. In addition, flame-deterrent coatings

are often used to retard the burn rate such that a more or less constant pressure is exerted

on the projectile but yet burn at a sufficient rate to fully combust while the launch pack-

age is in the barrel.

Several propellants (Hodgson Clays Universal and Hodgson HS-6) were tested in

order to determine the most suitable for the desired impact conditions. Both propellants

are single-base and the granules are flake shaped. The Clays Universal propellant had a

faster burn rate and proved more consistent than the HS-6 propellant, so it was chosen for

testing. Loads were produced by hand loading the shells using a commercially available

reloading press (manufacture: MEC, model: Sizemaster), Fig. 13. The components cho-

sen for reloading were a primed Fiocci 2 3/4 in. hull, a BPI multi-metal 2 3/4 in. 12-

gauge wad, and Ballistic Products Inc. Shot Buffer (used to take up excess space in the

hull and provide more consistent impact spacing). The projectiles used in the study were

AISI 52100 7.94 mm diameter (~ .30 caliber), grade 25, alloyed steel ball bearings with a

hardness of 63 to 67 Rockwell C, and a mass of 2.039 g. Four projectiles were used in

the powder gun to emulate fragment cluster impact conditions. The total mass of the pro-

66

jectiles (8.15 g) used in the impact testing was 1/3 the mass of typical 12-gauge shell, so

published loading data was not available. Propellant weight was varied, and a calibration

curve for velocity vs. propellant weight was established, Fig. 14. Deviating from pub-

lished loading data can be extremely dangerous so extra care was taken to insure exces-

sive chamber pressures were not encountered. Flattened and pierced primers indicate ex-

cessive chamber pressure, but excessive pressures can be encountered without these indi-

cations present (Jones, 1998).

Another parameter that has to be established prior to testing is the inter-projectile

spacing. As the projectiles travel down range, they spread out in a pattern, Fig. 15. The

amount of spread can be controlled by the choke (restriction) at the end of the barrel and

by the distance from the target. A full choke will provide a tighter, more controlled pat-

tern. The exact pattern will differ with the projectile velocity, and the number, size, and

mass of the projectiles. The desired pattern density was determined experimentally prior

to testing.

A fixture was designed and fabricated in-house to hold the specimen and align it

with the universal receiver and velocity screens. The boundary conditions were clamped

on four sides. The clamped area was 218 cm2 with an exposed area of 712 cm2 (26.7 x

26.7 cm2). Clamping is considered to provide a boundary condition between simply sup-

ported and fully clamped (Czarnecki, 1998). The velocity screen spacing was set at 1.22

m. The fixture elevates the sample to the bore line of the universal receiver so that the

impact occurs normal to the specimen and houses the infrared sky screens. The specimen

fixture can also be rotated to allow for oblique impacts up to 45o from the normal. The

fixture was designed using Pro/Engineer 2000i2 (Pro/E) and is shown in Fig. 16 (a), and

67

the fabricated assembly is shown in Fig. 16 (b). It can be fully disassembled for easy

transport and handling since the entire assembly weights approximately 140 kg.

A fixture was also made to support a 0.5 mm thick 2024-T3/T4 aluminum witness

plate with normal orientation, 20.3 cm behind the specimen. Witness plates are common

in ‘go/no go’ impact testing. If the witness plate is held up to a 60 W light bulb and no

light passes through after fully penetrating impact, the projectile is considered defeated.

A chronograph can also be placed behind the specimen on a standard camera tripod to

measure residual velocity, Fig. 16 (a).

Single Projectile Apparatus Development

Single-stage, light gas guns (which will be referred to simply as a gas gun for the

remainder of the document), are the most common form of laboratory scale high velocity

impact apparatus. Velocities up to 1500 m.s-1 have been reported for single–stage gas

guns (Bourne, 2004), however large gas guns achieve velocities around 1000 m.s-1

(Coppa et al., 1979; Bourne et al., 1995). In order to reach even higher velocities, a far

more complicated and expensive impact apparatus is needed (Pavarin and Francesconi,

2003). The most common is the two-stage light gas gun, which utilizes an explosively

driven (gun powder, methane gas or high explosive) piston which compresses a light gas

(He or H2) in the pump stage. Once the desired pressure is reached, either a fast acting

valve or burst diaphragm releases the pressure to the second stage which accelerates the

launch package to hyper velocities, which can reach in excess of 8 km.s-1 (Pavarin and

Francesconi, 2003).

Due to the complexity, expense, maintenance, and safety concerns associated with

two-stage light-gas guns, it was decided that a single-stage, high shot frequency, light-gas

68

gun would best suit our current research needs. It was designed, fabricated, and assem-

bled in-house. The design was carried out using Pro/E, and supported with ANSYS 7.0

and analytical calculations, primarily for the pressure vessel design. The gas gun consists

of a pressure vessel (19,750 cm3 volume), 457 cm long barrel (38.1 mm φ, 5,210 cm3

volume), a modified pneumatic actuator for the firing valve, and linear bearings to allow

translation for the breach loading mechanism. The ratio between pressure vessel volume

and barrel volume is approximately 4:1. This insures quasi-constant pressure acting on

the launch package while being accelerated down the barrel.

Figure 17 shows the main components of the gas gun while Figs. 18 and 19 show

the Pro/E design and final assembly, respectively. The working fluids are N2 for the ac-

tuator, and He or N2 for projectile acceleration. The firing pressure range is 34 kPa to

1724 kPa, which gives a velocity range of 40 m s-1 (N2) to 435 m s-1 (He) depending on

the launch package mass. The sabot is made from high-density polyurethane foam and is

stripped off at the end of the barrel, Fig. 20. A calibration plot of pressure vs. velocity for

a 10.4 g launch package using N2 and He for the firing fluid is shown in Fig. 21. The

pressure is shown in SAE units because of the pressure instrumentation on the gas gun is

SAE. From the regression analysis, the firing pressure for a given launch package and

working fluid can be calculated to achieve a given velocity ± 3.2 m.s-1.

The limiting factors on achievable velocities for a gas gun or powder gun are the

speed of sound in the working fluid (e.g. air, N2, or combustion products), launch pack-

age mass, barrel length, and firing pressure. Work is required to accelerate the launch

package and the firing fluid itself. Lighter gas requires less work to accelerate. In addi-

tion, the pressure wave cannot propagate faster than the speed of sound in the medium.

69

The speed of sound in He is about three times the speed of sound in air. The speed of

sound in an ideal gas is only a function of temperature with no dependence on pressure.

The final pressure after expansion in the barrel can be estimated as an isothermal process

from Eq. 21:

where p1 and p2 are the initial and final pressures, respectively, V1 and V2 are the initial

and final volumes respectively, and n is the path dependant polytropic constant (Moran

and Shapiro, 1995). For an initial pressure of 1371 kPa, the final pressure at the end of

the muzzle is about 971 kPa, a 29% decrease. The total available work from the gas ex-

pansion can then be estimated from Eq. 22:

where W is work and the remaining variables are the same as in Eq. 21. With a poly-

tropic constant equal to 1.5 (for a cylinder/piston expansion), the maximum theoretical

available work for the gas gun is approximately 6.02 kJ. This does not account for pres-

sure losses through the valve, in the pressure vessel and down the barrel. It also does not

account for the work required to accelerate the firing fluid and launch package, the pres-

sure rise of ambient air in front of the launch package, frictional effects, or reflections of

rarefaction waves in the gas reservoir. The maximum kinetic energy obtained to date is

2.8 kJ for a 38.1 mm diameter, 100 g projectile (247 m.s-1). This equates to an efficiency

of 46.5 %. For light launch packages (10.25 g), the efficiency decreases significantly to

(22) nVpVpW

−−

=1

1122

(21) n

VVpp ⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅=

2

112

70

16.1 % (435 m.s-1) due to supersonic wave rarefactions and the high pressure in front of

the launch package.

In order to sustain a high shot frequency in the current design, it was decided to

not evacuate the ambient air from the barrel and capture chamber. Designing the capture

chamber and barrel to operate under vacuum conditions (~1 mbar) would significantly

increase the cost and complexity of the system (Bourne et al., 1995). The experimental

apparatus footprint would also be increased because of the need for expansion tanks

which allow the firing gas to expand once they exit the muzzle (Bourne et al., 1995;

Bourne, 2004). Firing under vacuum conditions would also decrease the shot frequency

by having to wait for the system to pump down in addition to the added maintenance as-

sociated with vacuum systems.

Firing in ambient conditions limits achievable velocities because the air has to be

displaced by the launch package as it progresses down the barrel causing a pressure front

to build as it accelerates. The ambient air in front of the projectile is a large contributor

to the non-linear behavior seen in pressure vs. velocity curve, Fig. 21. An analytical

theoretical dynamic gas model was given by Coppa et al. (1979) to predict gas gun per-

formance. A similar approach was taken by Brown and coworkers (1989), but they also

included the effects of pressure buildup of ambient air in front of the launch package and

the rarefaction waves in the pressure vessel. Analytical models were not employed in the

design because of physical size (barrel length) limitations, allowable operating pressures,

and bore size were already known.

71

Capture Chamber

The sample was housed in a 31.75 x 31.75 x 184 cm3 capture chamber with opti-

cal polycarbonate windows for incident and residual velocity acquisition. The chamber

can be accessed via a hinged door which opens vertically, running the full length of the

chamber itself, Fig. 22. The capture chamber was constructed out of 6.35 mm thick mild

steel which has a ballistic limit far above an impact by a 12.7 mm (.50 caliber) Fragment

Simulating Projectile (FSP) at maximum firing pressure (381 m.s-1) with normal inci-

dence (determined experimentally). A normal incidence impact is not possible given the

geometry of the capture chamber so the actual ballistic limit would be much higher in the

case of an oblique impact. A kinetic energy deflector (projectile trap) was placed oppo-

site the barrel in order to catch penetrating projectiles. The projectile trap consists of

three 12.7 mm thick, cold rolled 1040 steel plates which were welded together at angles

represented in Fig. 17. Its purpose is to provide an extra margin of safety against pene-

trating projectiles and to serve as a mechanism to keep them from ricocheting around in

the capture chamber. A soft recovery trap can also be placed within the projectile trap

allowing the post impact deformation of projectiles to be examined and save projectiles

from deformation so they can be reused. A blast screen with a 15 mm aperture was place

25.4 cm in front of the muzzle to reduce pressure loading effects from the firing gas and

ambient air in front of the projectile on the target.

Three specimen fixtures have been constructed to account for various specimen

sizes, boundary conditions, and for examining oblique impact. The boundary conditions

in the study were fully clamped on four sides with the supports 20.32 cm apart. The

boundary conditions used in the single projectile study differed slightly from those used

in the preliminary powder gun study, which used supports 30.48 cm apart. In the final

72

gas gun study, the boundary conditions were maintained as fully clamped with the sup-

ports 20.32 cm apart. However, it was assumed that the influence of the boundary condi-

tions was negligible for the velocity range used in this study. This assumption is sup-

ported by the work of Potti and Sun (1997) who found that for impact velocities greater

than 100 m s-1, extent of damage was controlled by the impact velocity and not the size of

the specimen.

A frame was constructed out of 76.2 x 101.6 mm2 steel tubing with 6.35 mm wall

thickness, Fig. 22. The open design allows access to the six, 1780 N clamping force,

toggle clamps. There are four leveling mounts which adjust up to 50.8 mm to level the

capture chamber and allow the barrel to mate up with it.

A Drawn Over Mandrel (DOM), 38.1 mm x 4.57 m long (6.35 mm wall thick-

ness) barrel was chosen because of the high dimensional tolerances associated with that

processing method. Machining would have been far too expensive and would have a

large lead time. The large caliber was chosen so a wide array of projectile threats can be

evaluated. Large caliber threats (>20mm) are secondary blast debris, tornado and hurri-

cane debris, runway kick-up, and road debris (Bartus, 2003). Also, high velocities can be

achieved using sabots for smaller caliber projectiles since the pressure is acting over a

greater area (e.g. a 38.1 mm diameter barrel has a factor of 24.5 times greater cross sec-

tional area vs. a .30 caliber projectile).

The barrel is supported by a stand with four, 127 mm rings, Fig. 18 (b), and Fig.

19 (b). The rings are drilled and tapped 120o apart with knurled thumb screws to fix and

center the barrel. The 3.3 m long wide flange, 127 mm web I-beam provides a stable

73

platform and absorbs recoil. The I-beam is supported by 76.2 x 101.6 mm2 steel box

beams with leveling mounts.

Firing Valve and Actuator

The most crucial component in the consistent and efficient operation of a high

shot frequency gas gun is the firing valve. The valve must have a very fast response in

order to release the firing pressure uniformly. In addition, in order to provide the maxi-

mum precision, it must repeatedly open at the same rate otherwise inconsistencies in the

launch package velocity will arise. Diaphragm valves are commonly employed as the

firing valve in which the diaphragm is clamped between two mounting blocks at the

breach between the pressure vessel and launch package (Coppa et al., 1979). They are

typically made from a metal or polymer plate that is either scored such that it will fail at a

predetermined pressure or utilize a conductive wire across the polymer face (Bourne,

2003). In the case of the later, an electrical current heats the conductive wire, causing the

diaphragm to fail. Although a straight forward method for abrupt release of firing pres-

sure, there can be deviations in velocity because of uncertainty in failure of scored dia-

phragms and prepping can be tedious and time consuming for conductive wire initiated

failures.

A soft seat, fast acting valve was chosen for releasing firing pressure because of

good repeatability and ease of operation, Fig. 23 (iii). The valve chosen is a heavy duty

ductile iron, 50.8 mm Milwaukee butterfly valve with a compressible gas pressure rating

of 1380 kPa. Butterfly valves are durable, need little maintenance, and require a minimal

amount of torque for actuation.

74

While the firing valve was off the shelf, the actuator had to be modified signifi-

cantly in order to open the valve fast enough. A double acting, Hytork XL221DA pneu-

matic actuator was chosen as the starting point, Fig. 23. (ii). The electric solenoid actua-

tors investigated were too slow and spring return (single acting) actuators are not as fast

as double acting actuators because the force of the spring has to be overcome upon open-

ing the valve. At maximum pressure, the actuator provides 298 N.m of torque to the

valve. The actuator was first tested using line pressure (8 bars), but it opened far too

slow. An illustration of the actuator operation is shown in Fig. 24. As pressure is applied

to the pistons which are connected to the racks, they move toward each other, causing the

pinion to turn. The valve opens as the pinion rotates. Since 8 bars is the maximum oper-

ating pressure, it was decided that the best way to increase the opening speed was to in-

crease the flow.

The factory internal passageways for the valve opening pneumatic circuit were

plugged with a press fit pieces of aluminum. The actuator end caps, Fig. 23 (i), were re-

placed with machined billet aluminum caps so that a soft manifold could be run directly

to the end cap itself, bypassing the factory internal manifold, allowing much larger 1/2”

NPT fittings to be installed. The valve closing pneumatic circuit was increased to 3/8”

NPT. After modification, the flow to the actuator was increased 513% over the factory

design based on the increase in manifold cross sectional area.

Flow to the actuator is controlled by a 6500 series, three position MAC, electri-

cally actuated (120 V/60 Hz) solenoid valve, Fig. 23 (i). The flow through the valve is

5.0 Cv at the maximum operating pressure of 1034 kPa. The energize time is 9-14 ms. A

large 19.05 mm diameter line feeds the actuator, providing sufficient flow to the firing

75

actuator. Currently, the firing valve has been cycled over 600 times without requiring

any maintenance.

Fire Control

An Omron H5CR, 1/16 DIN, multifunctional digital timer was used for fire con-

trol, Fig. 19 (a). The output is a Single Pull, Double Throw (SPDT) normally open

switch that sends power to the solenoid at the end of a user defined duration, currently set

up in count down mode (10 s). The duration of the one-shot output signal is also user

defined (3 s). The count down can be used for remotely firing of the gas gun. It can also

be hooked to a PC allowing it to be fired from a remote network location. A keyed Sin-

gle Pull, Single Throw (SPST) switch sends power to the timer, at which the gas gun is in

a ‘hot’ condition. Once the gas gun is ‘hot’, a red strobe light flashes to indicate no one

is allowed ahead of the breach. An auditable alarm is manually activated once the timer

begins the count down sequence after pressing a normally open momentary switch, send-

ing a signal to the timer. The double redundant firing sequence prevents accidental fir-

ing, while the strobe and auditable alarm indicate when the gas gun is hot, and when the

firing sequence has begun, respectively. The keyed switch prevents unauthorized persons

from operating the gas gun.

Pressure Vessels and Flow Control

Two pressure vessels are required for the gas gun to function; one powers the

pneumatic actuator which opens the firing valve and the other is the firing pressure ves-

sel. A pressure vessel for the pneumatic actuator was necessary because the flow rate

from the two-stage high pressure slave regulator (Fisher Scientific Inc., 0-820 kPa) was

76

insufficient to open the firing valve fast enough. A Wilkerson R28 regulator acts in se-

ries with the slave high pressure regulator which is connected to the pressure vessel using

a 12.7 mm diameter line. A large 19.05 mm inside diameter line connects the pressure

vessel to the actuator solenoid. This provides a very high flow rate enabling the actuator

to open the firing valve very quickly. A normally closed momentary valve is connected

to the actuator pressure vessel for emergency evacuation from the fire control panel. The

emergency valve works in conjunction with a 1034 kPa ASTM high flow pressure safety

valve. The pressure vessel is rated from the factory for a maximum pressure of 1034 kPa.

The firing pressure, either N2 or He, first goes through a Prest-o-lite two-stage

regulator (0-3000 kPa), and then to a high precision R40 Norgren regulator (0-1724 kPa).

The pressure vessel was designed for a maximum operating pressure of 1724 kPa with a

minimum factor of safety of four. The pressure vessel is made from seamless cold rolled

1040 steel with an inside diameter of 25.4 cm with a length of 45.72 cm and wall thick-

ness of 6.35 mm. The yield strength is 490 MPa (Shigley and Mischke, 1989). The tan-

gential, radial, and longitudinal principle stresses for a thick walled pressure vessel were

calculated from Eqs. 23, 24, and 25, respectively (Shigley and Mischke, 1989):

where r = ri is the inside radius, ro is the outside radius, and pi is the internal pressure.

Based on the given dimensions, with an internal pressure of 1724 kPa, the tangential

(23)

(24)

22

2

2

2

22

2

2

2

22

2

1

1

io

iil

o

io

iir

o

io

iit

rrpr

rr

rrpr

rr

rrpr

−=

⎟⎟⎠

⎞⎜⎜⎝

⎛−

−=

⎟⎟⎠

⎞⎜⎜⎝

⎛+

−=

σ

σ

σ

(25)

77

stress is 35.36 MPa, the radial stress is -1.73 MPa, and longitudinal stress is 16.82 MPa.

This gives a factor of safety of 13.8 based on yield strength.

A bolted design was chosen to eliminate welds and the difficulties associated with

them in pressure vessel design. Eight, 22.23 mm diameter, cold rolled 1018 steel (yield

stress = 370 MPa) tensioners were used to bolt the 38.1 mm thick 6061-T6 aluminum end

caps on (Shigley and Mischke, 1989). The weakest point is where the ½ in. x 13, grade

8, socket head cap screws are bolted threaded into the tensioners. The force in the ten-

sioners is equal to the axial force exerted on the end caps as a result of the internal pres-

sure, divided by the number of tensioners. Stress at the weakest point is 83.58 MPa,

which results in a factor of safety of 4.42, based on yield strength. A normally closed

momentary valve is on the fire control panel, connected to the firing pressure vessel for

emergency pressure evacuation. An ASTM 1724 kPa, high flow safety valve is on the

end cap of the pressure vessel in case the maximum working pressure is exceeded.

Because of the danger of catastrophic rupture, both vessels must be inspected at

annual intervals using a suitable Non-Destructive Evaluation technique. Corrosion is the

main concern so the inside of the firing pressure vessel was painted using a rust resistant

paint (Rustoleum paint and primer). A seamless cylinder was chosen so there were no

welds requiring inspection. Dye penetrant or magnetic particle combined with visual in-

spection of the disassembled firing pressure vessel would be adequate. The actuator

pressure vessel has two welds which require inspection. The inside of the actuator pres-

sure vessel cannot be easily inspected visually so X-ray would be recommended for fu-

ture inspections. Laboratory N2 was chosen for the working fluid in the actuator and N2

and He for firing pressure to minimize corrosion issues due to water in compressed air.

78

Instrumentation

The key measurements required to operate a laboratory gas gun are firing pres-

sure, and incident/residual projectile velocity. The actuator pressure is held constant at

827 kPa, and is monitored using a liquid filed US Gauge, Bourdon tube, 0-1034 kPa, 114

mm pressure gauge (accuracy ±0.5% of span). Firing pressure (high range) is monitored

using the same gauge except with a range of 0-2068 kPa. For low range measurements

(0-1034 kPa), where small changes in pressure result in large differences in velocity, a

high precision 2088 Rosemount digital pressure transmitter was chosen (accuracy ±0.2%

of the calibrated span).

There are several means of measuring projectile velocity, and all methods utilize

some form of detection (e.g. photoelectric, break screen, magnetic) in which two or more

detectors are placed a known distance apart. The time between detections is recorded,

and the velocity is the known distance divided by time. The most common form of ve-

locity measurement is the photoelectric chronograph. They are widely used because of a

number of manufactures have off the shelf units readily available which are accurate, re-

liable, simple to use, and cost effective. The only requirement is light from the sun, infra-

red Light Emitting Diode (LED), or incandescent light bulb. Note that florescent lights

cannot be used because they pulse at 60 Hz causing errors in readings. Operation begins

with the photodetector sensing a break in the light. At that point, a chronograph which

uses a crystal oscillator is used to measure the time until the second photodetector senses

a break. Most of the chronographs automatically calculate the velocity based on the dis-

tance between the sensors, where it can be read on a (Liquid Crystal Display) LCD.

The photoelectric chronographs chosen for the gas gun are the Oehler Model 35 Proof

Chronograph with the Oehler Skyscreen III photodetectors. One was placed fore and one

79

aft of the specimen fixture for incident and residual velocity measurement, respectively,

Fig. 23. The chronographs use a 4.0 MHz crystal oscillator which results in a 0.25 mi-

crosecond time resolution. The powder gun uses the Oehler Model 35P chronograph

with the Model 57 infrared sky screens for incident measurement and the Oehler Model

35 Proof Chronograph with the Oehler Skyscreen III photodetectors for residual velocity

measurement, Fig. 16.

Preliminary Results

The preliminary results will be discussed briefly. They are included in the Ex-

perimental Approach chapter because the shortcomings of the test method developed for

the powder gun led to the development multi-site impact gas gun apparatus. Some of the

experimental procedure in the multi-site simultaneous impact powder gun has been high-

lighted. The key features from the study will be presented followed by the progression to

the final experimental approach.

Materials

The fabric chosen in the preliminary study was a non-crimped 45o double bias

carbon fiber (Vectorply CB-X 1200-512K) with an areal density of 400.1 g m-2. The pre-

form uses Toray T700 pan carbon fibers with a density of 1.8 g cm-3, tensile strength of

4,900 MPa, tensile modulus of 230 GPa, and a tensile strain to failure of 2.1%. The fi-

bers were sized for epoxy. SC-15 rubber toughened epoxy was used for the matrix for its

impact properties and low viscosity to allow for ease in processing. Three different panel

ply counts were investigated with [±45]6, [±45]12, and [±45]16 lay-ups with an average

thicknesses of 2.56 mm, 5.75 mm, and 6.86 mm, respectively. The average fiber volume

80

fractions of the 12, 24, and 32 ply specimens was found to be 44.2%, 39.1%, and 39.9%,

determined from immersion density. After curing at room temperature, the panels were

sectioned to yield 30.5 cm x 30.5 cm specimens, which were then post cured at 82oC for

five hours. The specimen nomenclature is FCI (number of plies)-(sample number) e.g.

FCI 12-02 is 12-ply specimen number 2.

Single Projectile Results

The projectiles used in the study were 7.94 mm diameter (~ .30 caliber), grade 25,

alloyed steel ball bearings with a hardness of 63 to 67 Rockwell C, and a mass of 2.039 g.

Four projectiles were used in the powder gun to emulate fragment cloud impact condi-

tions and the same projectiles were used in the single projectile gas gun study.

The single projectile impact results from the single projectile gas gun study are

given in Table 2. The impact energy was calculated from the kinetic energy, KE, ab-

sorbed during the impact was calculated from KE = 1/2 m (Vi2-Vr

2), where m is the mass

which was 2.039 x 10-3 kg, Vi (m.s-1) is the incident velocity and Vr (m.s-1) is the residual

velocity. The effect of kinetic energy imparted to the spall was neglected due to the large

mass retention (~99.98 %) of samples FCI 24-01d and FCI 32-09 from the single projec-

tile study, in which the projectile had a high residual velocity after impact. Mass reten-

tion for the FCI specimens could not be measured since the plate mass was beyond the

range of the balance able to resolve the mass loss. A “no reading” or a false reading oc-

curred several times in measuring the exit velocity. This is attributed to a low residual

velocity (< 30 m.s-1), spall, or a skewed projectile, determined from previous work (Bar-

tus, 2003). An undetectable residual velocity was assumed to have occurred for speci-

81

mens FCI 12-05a and FCI 12-05b. Other errors in residual velocity measurement were

omitted from calculations for the VB and energy absorption.

Multi-Site Simultaneous Results

The multi-site simultaneous impact results are given in Table 3. An illustration of

the experimental setup is shown in Fig. 26 and the resulting inter-projectile spacing from

the preliminary study is shown in Fig. 27. The number of measurements between all pro-

jectiles is equal to (n-1)!, so in the case of four projectiles there were six measurements.

The average projectile spacing was 30.2 mm with a standard deviation of 15.2 mm. Rep-

resentative distal side impact damage is shown in Fig. 28. In some cases, multiple pro-

jectiles impacted the same approximate location, Figs. 28 (c) and (f). For FCI 32-05 and

FCI 32-07, two projectiles impacted the same location and as a result, perforated the

specimen while the other two projectiles remained embedded. The same phenomenon

occurred with specimen FCI 32-06 except three projectiles impacted the same location

while one, in a remote location, remained embedded, Fig. 28 (f). This may have contrib-

uted to the high residual velocity measurement. In other instances, two or three projec-

tiles perforated the specimen while the remaining projectiles embedded. Two projectiles

in specimen FCI 32-07 impacted an area in line with the back face delaminations. The

back-face damage was similar to that shown in Fig. 28 (b). These projectiles perforated

the specimen while the remaining two, without visible interaction of the damaged area,

were embedded. Perforation in this case is attributed to visible damage interaction.

The most notable result is shown in Fig. 29, showing impact energy absorbed vs.

number of plies for the single projectile and FCI results. A linear fit though both data

sets give a nearly identical slope but the results are offset by approximately 32 J. There

82

are several possible explanations for this. One obvious possibility is that interactions be-

tween damage mechanisms, evident in the visible damage, and internal damage allowed a

greater dissipation of energy through an increased number of nucleation sites. Another

possible explanation is the energy dissipation due to kinetic energy transfer to the target

by the projectiles, which was the dominate energy absorbing mechanism reported by

Morye and coworkers (2000). This would explain disparity in ballistic limit for 12-ply

samples subjected to FCI (12% increase in VB) in contrast to the 24 and 32-ply laminates

where the V50 only increased 9% and 4%, respectively. In addition, stress wave and

shock wave interactions could have played a role in the perforation mechanics described

by Bahei-El-Din and Zikry (2003) and Czarnecki (1992).

While the multi-site simultaneous impact study was representative of random im-

pact locations from fragmentation device, from a fundamental standpoint, it is difficult to

examine cumulative and synergistic mechanisms that might occur under such conditions.

An experimental apparatus which could control impact velocity and location under both

near-simultaneous and sequential conditions is highly desirable.

Multi-Site Impact Apparatus for Controlled Impact Location

A design for an experimental apparatus for multi-site impact with controlled im-

pact location was undertaken using Pro/E, Fig. 30. While the design of the gas gun was

conventional with respect to other projectile launchers of this type, the unique capability

of this gun lies in its ability to launch up to three projectiles near-simultaneously or se-

quentially with controlled impact locations. The gas gun has three barrels, equally

spaced 120o apart on a 20 mm radius (approximately), Fig. 31.

83

The equilateral triangle configuration for the impact locations was chosen such

that interactions along the primary yarns and secondary yarns could be investigated. The

effect of stress wave interaction also warranted investigation so the impact locations had

to be close. The wave amplitude decays rapidly from the point of impact. Olsson (2002)

developed an analytical criterion for estimating the region of stress wave influence, Eqn.

24. The exception is that Olsson wanted to insure multiple projectiles impacted outside

the region of influence. In the present work, the opposite is desired so the inter-projectile

should be smaller than dmin. The radius of influence was calculated as 56.8 mm with; Ri =

3.97x10-3 m, ρi = 7860 kg.m-3, ρ = 1850 kg.m-3 and h = 2x10-3 m. Thus, the impact loca-

tions (38 mm) are within the region of stress wave influence.

The 25.4 mm ID, DOM barrels are breach loaded and connected to a single 63.5

mm diameter butterfly valve with a common 200 mm ID manifold. This ensures that the

sabot assisted projectiles will be subjected to the same firing pressure, while the mass and

dimensional tolerances of the sabots are maintained to very high standards to ensure near-

simultaneous impact condition. Three 3600 N toggle clamps couple the breach which is

sealed with an o-ring, Fig. 31 (b).

Either one or two of the barrels can be plugged allowing a two projectile or single

projectile test condition, respectively. The plugs can be rotated for a sequential impact

series or the plugs can be removed for a near-simultaneous impact series. This way, cu-

mulative and synergistic effects from those impact scenarios can be contrasted by main-

taining constant impact locations.

Pressure vs. velocity studies were conducted prior to testing in order to obtain

calibration curves for single, two, and three projectile test conditions. The sabots were

84

carefully machined and individually weighed. The sabot mass was maintained between

3.70 g and 3.73 g with an average of 3.714 g (standard deviation = 0.013 g and 98 % con-

fidence interval = 0.00003). In addition, the projectile velocity through each barrel (sin-

gle projectile) was found to be extremely consistent for a given pressure indicating that

assumption of a near-simultaneous impact condition is valid.

This was measured by normalizing the projectile velocity (m.s-1) by the firing

pressure (psi), for each barrel (A,B,C) in the single projectile configuration. The normal-

ized velocity (m.s-1/psi) at quasi-constant firing pressure (~40 psi/275.9 kPa) was 5.626

(standard deviation = 0.0602, 95 % confidence interval = 0.00017), 5.583 (standard de-

viation = 0.1335, 95 % confidence interval = 0.00037), and 5.594 (standard deviation =

0.0265, 95 % confidence interval = 0.00007) for barrels A, B, and C, respectively. The

values for barrels A and B are within 0.569 % and 0.765 % of the value found for barrel

C, respectively.

One limitation of the test method in the current configuration is in the velocity

acquisition. The photoelectric chronographs only record the first projectile to break the

beam. While the near-simultaneous impact condition seems valid based on previous test-

ing, the residual velocity measurement is questionable. Previous modeling studies indi-

cated that residual velocities varied for both near-simultaneous and sequential impact

(Bartus et al., 2006). Future work will include high speed photography to verify the near-

simultaneous impact condition and measure residual velocity.

Non Destructive Evaluation

An accurate understanding of the material response under multiple impact, a

method to characterize damage in a large number of specimens quickly had to be devised.

85

Delamination damage was characterized using digital image analysis. A similar approach

was taken by da Silva and coworkers (2004b) and Nunes and coworkers (2004) where

surface damage was measured. In the present case, through-the-thickness delaminations

were investigated. The S-2 glass/epoxy specimens are translucent and when damaged,

present very distinct delaminations which can be seen visually. In order to better visual-

ize the delamination area, a light box was constructed. It consists of specimen supports, a

reflective tunnel to provide for even illumination, a 25.4 mm scale and a 150 W halogen

light source. Digital images were taken normal to the back lit specimen with the scale

placed within view. The images were then post processed using Image-Pro Plus (Media

Cybernetics Inc.). The same software was then used to trace and measure the delami-

nated areas, in which case the number of delaminations is equal to the number of plies

minus one. Once the delaminated area is traced, the software calculates the encircled

area based on the calibration with respect to the scale.

Figure 32 shows representative 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) back. The delamination furthest from the backlight (nearest to the image surface)

is more distinct and provides better contrast for measurements. The contrast, gamma, and

brightness are adjusted using Image-Pro Plus to increase the accuracy of the measure-

ment. The software allows for automatic measurements but the trace must be moved

manually when there is insufficient contrast. The projectile impact locations are noted by

the dark region.

Ultrasonic C-scan was also performed on a limited number of specimens. Testing

was conducted at Tuskegee University Center for Advanced Materials, Tuskegee, AL

86

using a custom Sonix ultrasonic C-scan machine. The results were presented in both sig-

nal time-of-flight and amplitude formats. C-scans from a specimen subjected to three

projectile simultaneous impact is shown in Fig. 33. The digital image technique proved

faster, more cost effective and more accurate for the thin, translucent specimens so the C-

scan technique was abandoned.

Impact Test Matrix

The objective in experimental design was to evaluate the response of thin S-2

glass laminates under a wide variety of loading conditions and characterize damage evo-

lution and impact energy absorption. In all cases, simultaneous and sequential impact

loading was investigated for the .30 and .50 caliber impact studies. Flow charts provided

in Figures 34-38 illustrate the test matrix for the .30 caliber impact study, which investi-

gated the effect of laminate thickness (three and four layer laminates), number of impacts

(one, two or three), and damage evolution near and above the ballistic limit at constant

impact velocity.

In the .50 caliber impact study, three layer laminates were used for the study pro-

jectile mass effects at constant impact energy (~200 J). Three different projectile densi-

ties were used to investigate mass effects for projectiles with the same geometric dimen-

sions, 12.7 mm diameter spheres. Figure 38 shows the parameters investigated in the

mass effect study. Al2O3 (alumina), steel, and Tungsten Carbide (WC) were used with

masses of 3.91 g, 8.38 g, and 16.08 g, respectively. Give that the factor of mass differ-

ence is on the order of four (alumina and WC), which results in a velocity difference of

about a factor of two in order to maintain incident energy (Kinetic Energy (J) = ½ m.V 2,

where m is mass (kg) and V is the projectile velocity (m.s-1).

87

Vacuum bag Resin infusion Resin extraction

Resin flow

Single sided tooling

Sealant tape High permeability layer

Release film

Fig. 9. Illustration of the VARTM process showing the single sided tooling, dry fiber preform, and processing consumables (sealant tape, infusion/extraction lines, high per-meability layer, and vacuum bag).

88

Fig. 10. VARTM lay-up used to process the samples shown before infusion. Each panel produced was approximately 66 cm by 127 cm.

Center injection

Resin extraction

89

Fig. 11. Universal receiver outfitted with a 60.1 cm 12-gauge barrel chambered for a 69.9 mm (2 3/4 in.) shell.

Barrel

Elevation adjustment Universal

receiver

Articulating fixture

Windage adjustment

90

Fig. 12. Schematic of a 12 gauge shot shell cross-section for fragment cluster tests (not shown to scale).

Propellant

Primer

Sabot (wad)

Hull

.30 caliber (7.94 mm) projectiles

Base

91

iii.

ii

i.

iv.

Fig. 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.

92

Velocity (m/s) = 287 [propellant wt. (g)] - 58.8R2 = 0.95

100

150

200

250

300

350

400

450

500

0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9Propellant wt. (g)

Vel

ocity

(m/s

)

4 Fragments(8.156 g)

Fig. 14. Velocity vs. propellant weight calibration curve for four 7.94 mm di-ameter spherical projectiles fired from the 12-gauge shotgun barrel.

93

0

50

100

150

200

250

300

5 7 9 11 13 15 17 19 21 23 25

Distance to target (m)

Proj

ectil

e sp

acin

g (m

m)

Fig. 15. Projectile spacing vs. distance to the target for a 2 ¾” 12-gauge shot-shell loaded with OOO buck.

94

Fig. 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 chrono-graphs).

a

b

I

ii. ii.

i.

95

Fig. 17. Illustration showing the main components of the gas gun including the pressure vessels, firing valve and actuator, bar-rel and capture chamber.

95

96

(b)

Fig. 18. (a) Pro/E drawing of the gas gun, (b) Pro/E drawing of the entire as-sembly

(a)

97

Fig. 19. (a) Image of the gas gun (b) Image showing the major components of the gas gun assembly.

98

Fig. 20. High density polyurethane foam sabots: i. virgin sabot blank, ii. ma-chined 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.

i. v. ii. iii.

iv.

99

Fig. 21. Gas gun calibration plot of pressure vs. velocity for a 10.7 g sa-bot/projectile launch package using N2.

Velocity = 53.15 * Ln(Pressure) + 1.7R2 = 0.99

Velocity = 1.20*(pressure) + 191

0

50

100

150

200

250

300

350

400

450

500

0 25 50 75 100 125 150 175 200 225Pressure (psig)

Vel

ocity

(m/s

)

N2

He

100

Fig. 22. Image of the capture chamber showing the specimen location in relation to the barrel muzzle, the velocity acquisition windows, and the projectile recovery.

Projectile recovery

Specimen fixture

Muzzle

101

Fig. 23. i. solenoid , ii. modified Hytork-221 pneumatic actuator, iii. 63.5 mm (2 1/2 in.) Milwaukee butterfly firing valve.

i.

iii.

ii.

New end caps

102

Piston

Piston

Rack

Rack

Pinion

Valve closing pneumatic circuit

Valve opening pneumatic circuit

Fig. 24. Illustration of a double acting pneumatic actuator showing the pistons, which are attached to the rack, the pinion and the pneumatic circuit. When pressure is applied to the valve opening circuit, the pistons are pushed toward one another, driving the rack against the pinion causing it to rotate. The valve is attached to the pinion and it opens as the pinion rotates.

103

Fig. 25. Gas gun capture chamber shown with the 1.22 x 2.44 m2, 12.7 mm thick polycarbonate fragment barrier.

104

Table 2.

105

Table 3.

106

Velocity screens

Sample holder

12-gauge barrel

4.32 m 1.22 m

Fig. 26. Illustration of the fragment cloud impact test configuration.

107

Fig. 27. Inter-projectile spacing from the 12-gauge shot shells loaded with four 7.94 mm diameter projectiles with a 4.318 m standoff.

0102030405060708090

100110120

0 1 2 3 4 5 6 7 8 9 10 11 12 13

Test number

Mea

n pr

ojec

tile

spac

ing

(mm

)

108

a b

d c

f e

Fig. 28: Typical back-face damage for perforating and non-perforating FCI is shown in (a) and (b), respectively. Similar visible damage occurred in samples subjected to impact by a single projectile. Figures (c), (d), (e), and (f) show impact-face damage in which the circled region indicates an em-bedded projectile.

109

Energy = 3.98 * (# of plies) - 23.2R2 = 0.90

Energy = 3.91 * (# of plies) - 9.2R2 = 0.98

0

20

40

60

80

100

120

140

8 12 16 20 24 28 32 36Number of plies

Ener

gy a

bsor

bed

(J)

Single projectileNormallized FCI

Fig. 29. Energy absorbed (J) vs. number of plies for single projectile and nor-malized Fragment Cluster Impact (FCI).

110

Fig. 30. Pro/E drawing showing the design of the tri-fire gas gun barrel configuration.

111

38 mm 25.4 mm

c a

b

Fig. 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

(b)

(a)

112

(b)

(a)

Fig. 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) back. The delamination furthest from the backlight (nearest to the image surface) is more distinct and is best for measurements. The total new surface creation is 147.7 cm2.

25.4 mm

25.4 mm

113

(a)

(b)

Fig. 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.

114

Fig. 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).

.30 caliber test matrix, above ballistic limit

Three layer laminate

Sequential impact Simultaneous impact

Single projectile

Two projectile

Three projectile

Two projectile

Three projectile

115

.30 caliber test matrix, near ballistic limit



Two projectile

Two projectile

Fig. 35. Three layer, .30 caliber test matrix with the 2.04 g, 7.94 mm diameter spherical projectiles at a constant incident velocity of approximately 201.3 m.s-1


Single projectile

116


Four layer laminate


Two projectile

Three projectile

Two projectile

Fig. 36. Four layer, .30 caliber test matrix with the 2.04 g, 7.94 mm diameter spherical projectile at a constant incident velocity of approximately 249.8 m.s-1


Single projectile

117

.30 caliber test matrix, near ballistic limit

Four layer laminate


Two projectile

Two projectile

Fig. 37. Four layer, .30 caliber test matrix with the 2.04 g, 7.94 mm diameter spherical projectile at a constant incident velocity of approximately 225.1 m.s-1


Single projectile

118



Sequential impact

Single projectile

Two projectile

Three projectile

Three projectile

Alumina (3.91 g)

Steel (8.38 g)

WC (16.08 g)

Simultaneous impact

Alumina (3.91 g)

Steel (8.38 g)

WC (16.08 g)

Fig. 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).

119

FINITE ELEMENT MODELING APPROACH

Impact Modeling Using LS-DYNA3D

LS-DYNA3D 790 (LS-DYNA) was used for analysis of single and multi-site im-

pact response of the S-2 glass/epoxy laminates. LS-DYNA is a finite element code for

analyzing large deformations of structures subjected to dynamic loading. The dynamic

loading analysis is performed by seeking a solution to the momentum equation, which

satisfies the boundary conditions, while integrating the energy equation to be used as a

balance for global energy (Chan et al., 2005). The solutions are based on explicit time

integration. Explicit finite element methods are less computationally intensive that im-

plicit methods because they avoid having to solve large sets of non-linear equations. Ex-

plicit methods also avoid the cost of inverting the mass matrix by using a diagonal,

lumped mass matrix (Hallquist, 2000).

Dynamic modeling requires definition of the contact between the penetrator and

target. The LS-DYNA code offers three different methods for this: kinematic constraint,

penalty, and distributed parameter methods. The first approach is only used for tied inter-

faces (Hallquist, 2000). The penalty method implements normal interface springs be-

tween all the penetrating nodes and the contact surface. The interface stiffness is propor-

tional to the stiffness of the element (Chan et al., 2005). The method has the advantage

of minimizing hourglassing (mesh stability) because of the symmetry of the approach.

No special treatment is required for intersecting interfaces as in the kinematic constraint

method. The distributed parameter method takes half the mass of the slave element in

120

contact and distributes it to the covered master surface area and was developed for mod-

eling blast loading on structures using the sliding option (Halquist, 2000).

The segment based penalty method

(CONTACT_ERODING_SINGLE_SURFACE, SOFT=2) was chosen to define contact

between the projectile and target. It is one of the most prevalent methods in LS-DYNA

for defining contact between the penetrator and composite laminate (Deka et al., 2006,

Chan et al., 2005, Deka et al., 2006). The penalty method is less computationally inten-

sive than the kinematic constraint method with little or no reported loss in the results ac-

curacy (Chan et al., 2005). The contact algorithm checks segment versus segment pene-

tration and does not use the shooting node logic parameter because it ignores the initial

penetrations. When segment penetration occurs, penalty forces are applied normal to the

penetrating segment. These penalty forces are proportional to the excess penetration

depth given by Eq. 26:

where penaltyf is penalty force, K is penalty stiffness, currentd is the current penetration

depth and initiald is the initial penetration depth. High pressure generation at the contact

interfaces can result in unacceptable penetration. This can be avoided by scaling up the

stiffness (SLSFAC) or scaling down the time step size (Halquist, 2000). In high velocity

impact problems, the effect of frictional forces at the interfaces is negligible. As the static

friction (FS) should be greater than the dynamic friction (FD), FD was taken as 0.1 while

FS at 0.3.

The failure criterion used in the material model plays an essential role in the ef-

fectiveness of the numeric model. LS-DYNA incorporates several well known failure

( )initialcurrentpenalty ddKf −= * (26)

121

criteria for composite material models based off Chang-Chang (Hao et al., 2000), Tsai-

Wu (Iannucci and Ankersen, 2006), and modified Hashin (1980) failure criterion, respec-

tively. The Chang-Chang and Hashin failure criterion use a progressive damage ap-

proach. Material models 161/162 were developed independently by the Materials Sci-

ence Corporation, Horsham, PA. Both employ the progressive damage approach based

on Hashin’s failure criterion. They are among the most advanced commercially available

material models for composite structures. Both implement five failure modes, tensile and

compressive fiber failure, fiber crushing, and tensile and compressive matrix failure, Eqs.

27-33.

The damage mechanics approach incorporates progressive failure and material

softening after damage initiation. MAT 162 is an extension of MAT 161 (Yen, 2003),

both of which are progressive failure models based off a modified (to account for off axis

plies) Hashin (1980) criterion. Both material models can model damage without physi-

cally modeling the interface using contact interfaces. However, MAT 162 incorporates

material softening with damage accumulation based on the damage mechanics approach

taken by Matzenmiller and coworkers (1995). A brief overview of the damage modes is

given here. Further details can be found in Yen (2003), Sriram (2005), Xiao et al. (2005),

and Chan et al. (2005).

Tensile/Shear Fiber Mode

The fill and warp tensile/shear fiber damage is given by the quadratic interaction

between axial and through-the-thickness shear strains, Eqs. 27 and 28:

122

where a and b indicate the in-plane fill and warp directions, respectively, and c the out-

of-plane direction. E and G are the tensile and shear moduli, respectively, SAT and SBT are

the tensile strength in the fill and warp directions, SAFS and SBFS are the fiber shear

strengths in the fill and warp directions, εa and εb are the tensile strains in their respective

directions, and εac and εbc are the shear strains in the a-c and b-c planes and r1 and r2 are

the damage thresholds.

Fiber Compression Failure Modes

In-plane compressive damage is assumed to follow the maximum strain criterion,

Eqs. 29 and 30:

where SAC and SBC are the in-plane compressive strengths.

Fiber Crush Mode

Fiber crushing occurs when a concentrated load is applied to the laminate in the

transverse direction and commonly occurs in high velocity impact. Through thickness

compressive pressure is modeled with the following Equation (31):

(27)

(28) direction)-b(in 0

direction)-a(in 0

22

22

21

22

=−⎟⎟⎠

⎞⎜⎜⎝

⎛ ⋅+⎟⎟

⎠

⎞⎜⎜⎝

⎛ ⋅

=−⎟⎟⎠

⎞⎜⎜⎝

⎛ ⋅+⎟⎟

⎠

⎞⎜⎜⎝

⎛ ⋅

rS

GS

E

rS

GS

E

BFS

bcbc

BT

bb

AFS

acac

AT

aa

εε

εε

(29)

(30) direction)-b(in ,0

direction)-a(in ,0

24

2

23

2

b

ccbb

BC

bb

a

ccaa

AC

aa

EEr

SE

EEr

SE

εεεε

εεεε

−−=′=−⎟⎟⎠

⎞⎜⎜⎝

⎛ ′⋅

−−=′=−⎟⎟⎠

⎞⎜⎜⎝

⎛ ′⋅

123

where SFC is the fiber crush strength.

In-Plane Matrix Shear Mode

` The in-plane matrix shear mode, which is independent of fiber failure, is given by

Eq. 32:

where SAB is the interlaminar shear strength of the matrix.

Delamination Failure Mode

Equation 33 accounts for delamination which is very important in terms of predic-

tion of post-impact mechanical behavior:

where SCT is through-thickness tensile strength, SBC0, and SAC0, are interlaminar shear

strengths in the a-c and b-c planes, respectively. The delamination parameter, S, which is

an input in the LS-DYNA deck, has been reported to take into account delamination

growth dependence stress concentration (Xiao et al., 2005). However, it appears to be an

empirical factor used to gain a greater correlation with experimental data (Yen, 2003).

The compliance matrix, [C], is given by Eqn. 34. The stiffness matrix can be de-

termined by inverting the compliance matrix, [D] = [C]-1. The compliance matrix is tied

027

2

0

2

0

2

2 =−⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛+⋅

+⎟⎟⎠

⎞⎜⎜⎝

⎛+⋅

+⎟⎟⎠

⎞⎜⎜⎝

⎛ ⋅ rSS

GSS

GS

ESSRAC

caca

SRBC

bcbc

CT

cc εεε (33)

(32) 026

2

=−⎟⎟⎠

⎞⎜⎜⎝

⎛ ⋅ rS

G

AB

abab ε

025

2

=−⎟⎟⎠

⎞⎜⎜⎝

⎛ ⋅ rS

E

FC

cc ε (31)

124

to damage accumulation by the damage variable, ϖi, where i = 1,...,6,. The damage vari-

able for a given failure mode, j, can be found using Eqns. 35 and 36:

The amount the stiffness is reduced is dependent on the material softening pa-

rameter, mi, the damage threshold, rj, and the damage variable, ϖi. The stiffness reduc-

tion is then given by Eq. 37. As damage accumulates the laminate stiffness decreases as

a function of the damaged state. If the damage threshold is set to 1, the material model

reduces to MAT 161. The effect of the material softening parameter is shown in Fig. 39

(a).

(34)

(36) { }5,...,1 , max == jq jiji φϖ

1 ,11)1( ≥−=

−−

jmr

i remjφ (35)

10 ,)1( ,)1( 00 ≤≤−=−= iiiiiii GGEE ϖϖϖ (37)

125

Finite Element Model

Altair Hypermesh v7.0 and Finite Element Model Builder (Eta/FEMB-PC version

28.0) were used for pre-processing. A series of mesh refinement schemes were carried

out as part of a convergence test to determine an acceptable mesh size and integration

time step. The final mesh chosen is graded such that the area containing the impact loca-

tions is made up with the smallest element sizes. The final mesh near the impact region

is shown in Fig. 39 (b).

The mesh is progressively larger as it approaches the plate boundaries to increase

computational efficiency but was kept as fine as reasonably possible because delamina-

tion growth is sensitive to mesh size. Each lamina (three) had the same dimensions of the

plates in used in the experiments, 20.3 x 20.3 cm2, each comprised of 18,304 elements.

The brick elements had 8 nodes with a single integration point. Single point integration

elements are more robust than fully integrated elements. The boundary conditions used

were the same as those in the experimental program, fully clamped on four edges. Sym-

metry could not be used in the case of multiple projectiles so the full plate was modeled

in all cases. The spherical projectiles were also modeled using brick elements with MAT

3 (MAT_PLASTIC_KINEMATIC). The .30 caliber projectiles had 3,847 elements each

while the .50 caliber projectiles had 15,850 elements. Table 4 gives the material proper-

ties for the laminate and projectiles used in the model (Xiao et al., 2005, Deka et al.,

2006).

MAT 162 was used to model the laminate in all simulations. Published material

properties were available for S-2 glass/SC-15 epoxy however the material softening, m,

and delamination, S, parameters had to be adjusted to match the experimental results.

The model was calibrated to the single projectile, .30 caliber impact results for energy

126

absorption and new surface creation. The softening, m, and delamination, S, parameters

that provided the best correlation to experimental data were 3.5 and 2.7, respectively, Ta-

ble 4. With exception to projectile size, mass and velocity which were taken from the

respective experimental details, all parameters were kept constant for all simulations.

For the .30 caliber impact study (three layer laminate), simultaneous and sequen-

tial impact simulations were run. In the case of sequential impact, the projectiles were

staggered 50 mm normal to the laminate to provide a sufficient time-hit interval that

would minimize synergistic artifacts from adjacent projectile interaction. It was a com-

promise between computation time (as the time-hit interval increases, computation time

also increases) and having the target completely at rest before the next projectile im-

pacted. The primary stress wave had passed before the next projectile impacted in all the

simulations (shown in Fig. 50). Simultaneous and sequential models were run for the all

test cases in the .50 caliber impact study.

The FEA results were compared to the experimental results for new surface crea-

tion and energy absorption (or residual velocity prediction) in all cases examined. The

models were also used to provide insight into target response and perforation behavior.

This was an important aspect in the study since high speed photography was not available

to examine individual projectile velocities and real time failure mechanisms.

127

Fig. 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.

Decreasing softening parameterσ

ε

Decreasing softening parameterσ

ε

10 mm

(a)

(b)

128

Table 4.

Density (Kg.m-3 ) ρ 1850E 11 27.5E 22 27.5E 33 11.8G 21 2.9G 31 2.14G 32 2.14υ 21 0.11

Poisson’s ratio υ 31 0.18υ 32 0.18X T 0.604Y T 0.604Z T 0.58X C 0.291T C 0.291

Matrix mode shear strength (GPa) S 12 0.075S 23 0.058S 31 0.058

Fiber shear strength (GPa) S FS 0.85Fiber crush strength (GPa) S FC 0.3Erosion elastic limit 4Delamination factor S 2.7Friction angle ϕ 20Strain rate coefficient C1 0.1Tensile fiber damage parameter AM 3.6Material softening parameter m 3.5

Density (Kg.m-3 ) ρ 7860Poisson’s ratio υ 21 0.28Yield strength (GPa) σ y 1.08Young’s Modulus (GPa) E 210

Material properties for the steel projectile

Tensile strength (GPa)

Compressive strength (GPa)

Material properties used in the simulation of plain weave S-2 glass /SC-15 epoxy composite

Young’s modulus (GPa)

Shear modulus (GPa)

129

RESULTS AND DISCUSSION

The results will be discussed in order according to the test matrix in Figures 34-39

and will be broken down into two categories; .30 caliber and .50 caliber impacts with the

FEA modeling results given with each. In the overall test program, including the pre-

liminary study, 99 specimens were impacted with a total of 248 projectiles. Seventy

eight specimens are included in the results and discussion section, Tables 5-14. Several

specimens, indicated in Tables 5-14, may have had processing defects and were not in-

cluded in the analysis.

The results are discussed primarily in terms of energy absorption and new surface

creation. Energy absorption provides an indication of ballistic efficiency which is the

energy absorption or ballistic limit velocity as a function of areal density. New surface

creation, such as delamination is considered because it is the most detrimental damage

mode in composites for post impact performance.

.30 Caliber Projectile Impact Results on Three Layer Laminates

The goal in the .30 caliber projectile impact study was to establish laminate thick-

ness effects using three and four layer laminates and to investigate the effect of number

of impacts. In the assessment of the number of impacts, single, two and three projectile

simultaneous and sequential impacts were carried out on both the three and four layer

laminates. The impact velocity was kept constant for two impact conditions for the three

and four layer laminates. The two impact conditions were near the ballistic limit and

above the ballistic limit of the three and four layer laminates.

130

Single Projectile Impact Results

The single projectile impact study was conducted on three layer laminates in order

to establish a benchmark for the multiple impact study. The impact velocity was held

constant at 226.8 m.s-1 (standard deviation = 19.1 m.s-1), which is above the ballistic limit.

The average energy absorption was 43.9 J with a standard deviation of 3.4 J, Table 5.

The average new surface creation was 73.7 cm2 with a standard deviation of 8.5 cm2.

Typical delamination damage is shown in first image in Fig. 41.

Two Projectile Impact Results

The two projectile impact positions indicated in Tables 6-14 are shown in Fig. 40.

The two projectile simultaneous and sequential impacts, Tables 6 and 7 were at the A and

C positions, along the primary yarns. These positions were chosen because the highest

wave speed is along the primary yarns and to examine damage interaction along the pri-

mary yarns. Two different velocities were investigated in both the three (~200 m.s-1 and

220 m.s-1) and four layer laminates (~225 m.s-1 and 250 m.s-1). These velocities resulted

in impact conditions near the ballistic limit (below the threshold velocity for complete

penetration) and above the ballistic limit. The impact velocity for the two projectile im-

pact was 201.2 m.s-1 (standard deviation = 4.2 m.s-1) for sequential impact and 201.9 m.s-1

(standard deviation = 1.9 m.s-1) for near-simultaneous impact (will be referred to as si-

multaneous impact throughout the document), Table 6. This velocity was closer to the

single projectile ballistic limit for the three layer laminate.

Two projectile impact results near ballistic limit. The experimental results for

simultaneous and sequential two projectile impact near the ballistic limit for three layer

131

laminates are given in Table 6. For the two projectile sequential impact experiments, po-

sition A was the first to be impacted, followed by position C. The average impact energy

per projectile was 41.3 J (standard deviation = 1.71 J) and 41.6 J (standard deviation =

0.80 J) for simultaneous and sequential two projectile impact, respectively. This corre-

sponded to an average new surface creation of 107.9 cm2 (standard deviation = 13.9 9

cm2) and 140.2 9 cm2 (standard deviation = 6.7 9 cm2) for simultaneous and sequential

impacts, respectively. Although the average impact energy for the simultaneous and se-

quential two projectile impacts was within 0.7 % of one another, sequential impact re-

sulted in a 23 % increase in new surface creation.

Two projectile impact results above ballistic limit. Two projectile simultaneous

impact above ballistic limit was conducted at ca. 227.7 m.s-1 (standard deviation = 6.2

m.s-1), Table 7. The average energy absorption was ca. 82.4 J with a standard deviation

of 6.4 J. This resulted in a new surface creation of 118.6 cm2 with a standard deviation of

17.7 cm2. This test configuration was conducted to compare energy absorption in four

layer laminates.

Three Projectile Impact Results

Sequential three projectile impact results above ballistic limit. The sequential .30

caliber, three projectile impact results are given in Table 8. The impact positions and or-

der were kept constant; positions B (1st), C (2nd), and A (3rd), respectively, Fig. 40. The

average impact velocity was 227.0 m.s-1 with a standard deviation of 4.0 m.s-1. The total

energy absorption (summation of the three projectile energies) was 134.8 J with a stan-

dard deviation of 4.0 J and the new surface creation was 177.3 cm2 with a standard devia-

132

tion of 19.6 cm2. Note that the standard deviation for sequential impact energy is taken

before the individual projectile energies were summed. The average energy absorption

for the first, second and third impact was 42.4 J (standard deviation = 4.0 J), 44.7 J (stan-

dard deviation = 2.9 J), and 47.7 J (standard deviation = 3.6 J), respectively. For speci-

mens 07.13.05-3-1 and 07.13.05-3-4, the third projectile did not fully penetrate.

A single specimen sequential delamination damage study was conducted on speci-

mens 08.29.05-3-1 and 08.29.05-3-2 where the specimen was removed, imaged and re-

placed between impacts in order to gain an understanding of delamination progression.

The average new surface creation for the first, second and third impacts was 54.7 cm2

(standard deviation = 8.5 cm2), 113.1 cm2 (standard deviation = 7.2 cm2) and 151.7 cm2

(standard deviation = 4.2 cm2), respectively. Delamination progression is shown in Fig.

41 for a three projectile sequential impact series and the comparison of sequential and

simultaneous delamination appearance is shown in Fig. 42. The residual velocity as a

function of number of impacts is shown in Fig. 43. Energy absorption as a function of

number impacts is shown in Fig. 44. Figure 45 shows the delamination damage reported

in Table 6.

Simultaneous three projectile impact results above ballistic limit. The simultane-

ous impact results above ballistic limit for three layer laminates are given in Table 6. The

incident velocity was ca. 214.7 m.s-1 with a standard deviation of 12.2 m.s-1. Impact en-

ergy absorption and new surface creation was ca. 121.2 J (standard deviation = 8.0 J) and

158.6 cm2 (standard deviation = 10.0 cm2), respectively. Typical delamination damage is

shown in Fig. 42. The comparison between simultaneous and sequential impact is shown

133

in Fig. 45, which evaluates new surface creation as a function of number of projectile im-

pacts at quasi-constant impact energy.

As noted in the sequential impact study, some of the projectiles failed to fully

penetrate although the impact velocity was above the ballistic limit. There was partial

penetration at position B (07.13.05-3-6), position A (07.13.05-3-7), positions B and C

(07.13.05-3-8), position C (07.13.05-3-9) and position A (07.13.05-3-10). The residual

velocity of the other penetrating projectiles was assumed to be the same and the energy

absorption at the non-penetrating location(s) was taken as the incident energy.

Sequential impact resulted in a 23.0% and 14.2% increase in delamination dam-

age over simultaneous impact for two and three projectile impacts, respectively. Figure

46 compares energy absorption for sequential and simultaneous three projectile impacts.

Specimens subjected to sequential impact exhibited 10.1 % greater energy absorption

than specimens impacted simultaneously. However, this must be considered carefully

given instrumentation limitations discussed in Experimental Approach and is discussed in

greater detail later in this section.

.30 Caliber Impact Results on Four Layer Laminates

The results for the impact study on four layer laminates are given in Tables 9-11.

The impact velocity for the four layer laminate study was held quasi-constant at ap-

proximately 225 m.s-1 near the ballistic limit, and 250 m.s-1 above the ballistic limit. This

was done in order to compare results with the three layer laminates which were subjected

to the same impact conditions.

134

Two projectile sequential impact near ballistic limit. The incident velocity for

two projectile sequential impact near the ballistic limit was 221.3 m.s-1 with a standard

deviation of 6.5 m.s-1, Table 9. The impact energy was the same as the energy absorption

(no perforations) with an average of 99.9 J with a standard deviation of 3.0 J. The new

surface creation was 342.0 cm2 with a standard deviation of 14.8 cm2. The new surface

creation in this case was similar to that in the three projectile sequential impact study

above ballistic limit.

Two projectile simultaneous impact near ballistic limit. The two projectile simul-

taneous impact results near the ballistic limit are given with the sequential impact results

in Table 9. The incident velocity was ca. 230.2 m.s-1 with a standard deviation of 10.2

m.s-1. The energy absorption was ca. 103.6 J with a standard deviation of 1.9 J. Three

specimens were tested and a projectile penetrated at position C for specimen 07.13.05-4-

2. There were no other penetrations in the other specimens which were impacted at a

lower velocity. New surface creation was not measured because the edges of the delami-

nations were not discernable for an accurate measurement. These results will not be in-

cluded in the discussion as the main interest was in comparing delamination behavior

with three layer laminates subjected to two projectile impact near the ballistic limit.

Two projectile sequential impact above ballistic limit. The results for both se-

quential and simultaneous impacts are shown in Table 10. The impact velocity for the

four layer laminates subjected to two projectile sequential impact was 254.4 m.s-1 with a

standard deviation of 3.5 m.s-1. The energy absorption was 109.3 J with a standard devia-

135

tion of 6.5 J and new surface creation of 231.8 cm2 (standard deviation = 38.0 cm2).

There was no penetration for the second impact at position C for specimen 07.13.05-4-9.

The large number of data acquisition errors, particularly with the second impact may

have been a result of the projectile being just above the ballistic limit, which is difficult

for the photoelectric chronographs to detect. Typical delamination damage is shown in

Fig. 47.

Two projectile simultaneous impact above ballistic limit. Five specimens were

subjected to two projectile simultaneous impact at an average incident velocity of ca.

238.9 m.s-1 with a standard deviation of 5.5 m.s-1. The energy absorption was ca. 109.7 J

with a standard deviation of 1.1 J. This resulted in a new surface creation of 235.4 cm2

with a standard deviation of 37.1 cm2. Typical delamination damage is shown in Fig. 47.

Several specimens subjected to these impact conditions did not result in full penetration

by both/either projectiles. Specimen 07.13.05-4-15 did not have penetration at position A

and position C was at ballistic limit. There was no penetration at position A for specimen

07.13.05-4-16 and position A was at ballistic limit for specimen 07.13.05-4-17. This may

have been a result of a lower incident velocity than what was used for the sequential im-

pact tests (ca. 6.1 % lower).

Figure 48 shows the comparison of the delamination in the three and four layer

laminates subjected to two projectile impact above the respective ballistic limit of each

laminate. The four layer laminate exhibited a 218 % increase in delamination damage

compared to the three layer laminate. Energy absorption in three and four layer laminates

136

is compared in Fig. 49, in which the three layer laminate exhibited a 24.9 % decrease in

energy absorption.

Three projectile sequential impact above ballistic limit. Two specimens were im-

pacted by three sequential projectiles at a velocity of 249.9 m.s-1 (standard deviation = 5.5

m.s-1). The energy absorption was 166.6 J with a standard deviation of 4.5 J and new sur-

face creation was 342.0 cm2 with a standard deviation of 14.8 cm2. The delamination

damage in three and four layer laminates subjected to three projectile impact above bal-

listic limit is compared in Fig. 50. The same comparison is made with impact energy ab-

sorption in Fig. 51 where the four layer laminate absorbed 19.1 % more energy than the

three layer laminate.

FEA Modeling Results for .30 Caliber Projectile Impact

The FEA modeling of three layer laminates subjected to .30 caliber simultaneous

and sequential impact was carried out with the commercially available code LS-DYNA

3D using material model MAT 162. The specimen dimensions, boundary conditions and

impact locations, and impact sequence (sequential) were the same used in the experimen-

tal approach. The impact velocity for all cases was held constant at 220 m.s-1. The model

predictions are compared with the experimental results in Figs. 52-61.

Sequential Impact Results

As described previously, the three projectile simultaneous impact model had all

three projectiles impact at the same time while the projectiles were staggered 50 mm

apart (z-direction) in the sequential impact simulation. This projectile staggering was

137

sufficient to allow the primary stress wave to pass the location of the next impact before

the next projectile impacted, Fig. 54. Although there was interaction with stress wave

reflections from the boundaries, the stresses were at least two orders of magnitude lower

than the primary stress wave based on the predicted von Mises stress shown in Fig. 54.

Another point to note is that in the sequential model, the target plate never came

to complete rest, e.g. zero kinetic energy, before the next projectile impacted. The plate

kinetic energy as a function of time for simultaneous and sequential impact is shown in

Fig. 52. Each of the three laminates had nearly identical responses in both simultaneous

and sequential impact, so they were summed. The kinetic energy decreased about 46 %

before the second projectile struck and 34 % before the third impact. Increasing the time

hit interval until the plate is completely at rest would be computationally costly.

Figure 53 shows residual velocity data from the experimental results and the FEA

prediction for a .30 caliber, three projectile sequential impact. The experimental results

are linear with a slope of -24.8 m.s-1/impact (e.g. increasing energy absorption with in-

creasing damage) with an R2 value of 0.9975. The residual velocity for the first impact

was under predicted by 4.5 %. The preliminary single projectile model prediction was

closer than 4.5 %. This is attributed to a difference in incident velocities between what

was used in the FEA model and sequential impact results. The model was based off data

for a projectile with an incident velocity of 220 m.s-1 and not the experimental value of

227 m.s-1, which results in a 6.5 % difference in impact energy. The subsequent residual

velocity predictions, however, deviated considerably from the experimental results. The

residual velocity prediction for the second sequential impact was over predicted by 41.2

% and the third impact by 113.1 %. The prediction was non-linear and the change in re-

138

sidual velocity prediction decreased with increasing number of impacts. There was a

15.7 % increase in residual velocity prediction between impacts one and two and only a 1

% increase between impacts two and three. On an average, the model over predicted re-

sidual velocity by 37.6 %, Fig. 60. The large scatter in the sequential impact data in Fig.

61 is because the average was taken for all residual velocities and the standard deviation

was large because residual velocity was dependant on the damage state.

The delamination damage prediction is compared with what was typically found

experimentally in Fig. 56. The inner delamination area was over predicted by 2 % while

the outer delamination area was under predicted by 34.1 %. The overall comparison be-

tween the experimental results and the FEA prediction is shown in Fig. 60, where the

model under predicted delamination damage by 15.2 %. The model predicts a decrease

in impact energy absorption with increasing damage, whereas the experimental results

show an increase in energy absorption.

Simultaneous Impact Results

As with the sequential impact simulations, the incident velocity was chosen as

220 m.s-1 whereas the average experimental velocity was 214.7 m.s-1. This results in a 4.9

% increase in impact energy. Since individual projectile velocities could not be measured

experimentally, the average results of the three projectiles are compared. New surface

creation, Fig. 60, was under predicted by 6.6 %. The damage prediction is compared

with typical damage in a simultaneous three projectile impact in Fig. 59. The inner de-

lamination area was over predicted by 3 percent and the outer area was under predicted

by 14.7 %.

139

The simultaneous impact model provided better agreement in the average residual

velocity prediction than the sequential model. Residual velocity was over predicted by

11.4 %. In the case of sequential impact, the residual velocity was over predicted by 37.6

%. In either case, energy absorption was under predicted. As with the sequential impact

simulation, all the projectiles exited the target with different velocities. The residual ve-

locities were 88.7 m.s-1, 110.4 m.s-1, and 104.0 m.s-1 in the A, B and C positions, respec-

tively. This equates to energy absorption of 40.5 J, 36.1 J, and 37.5 J at those respective

positions.

.30 Caliber Impact Discussion

Impact Velocity Regime

Different velocity regimes, above and near ballistic limit, were investigated for

two reasons. The first is to examine damage progression below the threshold velocity for

penetration and second, because of instrumentation limitations. As discussed in the Ex-

perimental Approach section, the photoelectric chronographs will only measure the ve-

locity of the first projectile to break the beam (for the near simultaneous impact experi-

ments). This could lead to an underestimate of the impact energy absorption. Measuring

sequential impact incident and residual velocities was not a problem. The chronographs

did exhibit some recording errors, particularly for small diameter, slow moving (< 40

m.s-1) projectiles. This was often the case for residual velocity measurements in which

instrumentation errors occurred 25 % of the time as opposed to 9.2 % of the time for in-

cident velocity measurements, Tables 5-11.

The simultaneous impact modeling results suggested that there were differences

in the residual velocity of the projectiles. Based on the velocity variation in each barrel

140

discussed in the Experimental Approach chapter, it appears that it is far more likely that

the projectiles are arriving at the target at approximately the same time than for them to

have the same exit velocities. Thus, there is a higher degree of confidence in the incident

velocity measurement. If the projectile strikes the target below the threshold velocity and

does not perforate, new surface creation as a function impact energy is likely to be more

reliable. This was the rationale for performing impact experiments near the ballistic

limit. In the general case however, the greatest amount of delamination occurred from

impacts above ballistic limit so the majority of testing for the .30 caliber experiments and

all of the .50 caliber experiments was performed above ballistic limit. In addition, energy

absorption characteristics must be evaluated at or above ballistic limit.

Damage Evaluation

All the specimens exhibited a characteristic conical shaped delamination zone

with the delamination closest to the impinging projectile being the smallest, and getting

progressively larger toward the distal side of the laminate (Cantwell and Morton, 1989).

Shear-punch failure was not noted in any of the specimens. This is commonly seen in

thick laminates impacted at high velocity but was not present in the thin laminates in the

velocity regime investigated (Sun and Potti, 1996). For both simultaneous and sequential

impact specimens, there was damage interaction along the primary yarns between impact

locations A and C. This was manifested as an increase in matrix cracking and fiber pull-

out. Similar damage was found along the primary yarns surrounding impact location B,

but it was not as pronounced as the damage along the primary yarns between impact loca-

tions A and C and did not appear to interact significantly with those locations either.

There were no quantifiable differences between the damaged state in either simultaneous

141

or sequential impact aside from delamination damage. In some cases, the damage in

specimens subjected to sequential impact exhibited delamination damage bias away from

the initial delamination as seen in Fig. 47.

The FEA predictions of delamination damage compared favorably in simultane-

ous impact (6.6 % under prediction) and reasonably for the sequential model (15.2 % un-

der prediction). There was only a 1.4 % difference between the simultaneous and se-

quential impact damage predictions indicating that damage prediction was not very sensi-

tive in the two different impact scenarios. Although the overall damage prediction was

reasonably good, the model had difficulty capturing through the thickness damage. The

inner and outer delaminations were almost identical in shape and area. This is likely be-

cause thin laminates are particularly difficult to model (Yen, 2006). Although the overall

shape of the delaminations predicted were consistent with the experimental results, Figs.

56 and 59, the projected area of damage was under predicted because the inner and outer

delamination was almost the same. The projected area of damage (largest delamination)

is the most critical to predict because it encompasses the entire damaged region which

would have to be repaired or replaced in a real world application. FEA predictions in

previous work using MAT 162 on thick laminates were able to capture both the size and

shape of through the thickness damage (Deka et al., 2006).

Three Layer Laminates

Sequential Impact

There was a very distinct difference in energy absorption for specimens subjected

to sequential impact as the amount of damage increased. As the number of impacts,

hence damage accumulation increased, energy absorption increased linearly, Fig. 44.

142

The energy absorption increased 12.5 % between the first and third impact. The average

increase in new surface creation for sequential impact above ballistic limit was 73.7 cm2

(Table 5), 118.6 cm2 (Table 7), and 177.3 cm2 (Table 8), which is an increase of 60.0 %

from the first to second and 49.5 % from the second to third impact. From the first to the

third impact, new surface creation increased 140.6 %.

The FEA residual velocity prediction did not follow the same trend seen in the

experimental results. In fact, the trend was opposite in that energy absorption decreased

with increasing damage. By the third impact the model over predicted residual velocity

by 113.1 %. This can be explained by the MLT theory of continuum damage mechanics.

As damage accumulates, as dictated by Eqn. 36 (Modeling Approach), the material stiff-

ness is reduced by the damage variable, ωi. The amount the damage variable is reduced

is dependent on the material softening parameter and the damage threshold variable. The

stiffness reduction is then given by Eqn. 37. As damage accumulates the laminate stiff-

ness decreases as a function of the damaged state. Since resistance to penetration is di-

rectly tied to the stiffness, reductions in stiffness will in turn decrease energy absorption.

There is no known way to alleviate this issue using the existing code.

New surface creation increased far more significantly than energy absorption,

however, the increase in energy absorption is not likely due to delamination. Energy dis-

sipation through new surface creation is usually small in comparison to other mechanisms

such as primary yarn failure and secondary yarn deformation because of the low strength

and strain to failure of the matrix (Naik et al., 2005). However, it is surmised that the

delaminations contribute to energy absorption via a change in the material response. As

damage accumulates, the specimen becomes more compliant. This is particularly rele-

143

vant in a thin laminates. As the specimen becomes more compliant, increasing the con-

tact duration resulting in a decrease in contact stresses and an increase in elastic bending.

This is likely more evident at impact velocities near the ballistic limit with large

contact times in contrast to incident velocities far in excess ballistic limit when the

specimen may not have adequate time to respond to the loading. With increased contact

duration, the fibers directly in contact with the projectile witnesses peak stress at a later

stage in the penetration process because Hertzian contact stress (localized stress) will not

develop as rapidly. Hertzian contact stress initiates fiber failure at the contact location,

which is the beginning of the penetration process.

Morye and coworkers (2000), and Naik and coworkers (2004, 2005) reported that

the kinetic energy transferred to the conical region surrounding the point of impact was a

significant energy absorbing mechanism for thin laminates. Since the area of cone for-

mation is dependant on the stiffness of the laminate, it would follow that a laminate with

increased compliance would form a larger cone with subsequent impacts. This is quite

evident in Fig. 52 showing the kinetic energy transfer of the projectile to the laminate.

The kinetic energy transfer to the laminate increases with increasing damage accumula-

tion. After the first impact, the peak kinetic energy of the plate was 11.1 J while it in-

creased to 15.7 J after the second impact (48.6 % increase) and 20.3 J after the third im-

pact (29.3 % increase). The increase in the laminate compliance can be seen in the model

shown in Fig. 55. Secondary yarn deformation increased after each impact as the damage

accumulates.

144

Simultaneous Impact

Based on the .30 caliber simultaneous impact modeling prediction, the impact en-

ergy absorption was 40.5 J, 37.5 J and 36.1 J at locations A, B, and C respectively. The

residual velocity prediction varied by up to 24.5 % between locations C and A, which

results in a difference in energy absorption of 12.2 %. Since verification of individual

projectile velocities could not be measured directly in the simultaneous impact experi-

ments, the FEA model was examined to determine what type of measurement error could

be expected. The highest residual velocity predicted was 110.4 m.s-1 at location C. As-

suming that 110.4 m.s-1 was the residual velocity for all penetrating projectiles, as the ex-

perimental results were interpreted, the energy absorbed would be 110.7 J. The energy

absorption predicted by the model was 114.1 J, so assuming all projectiles had the same

velocity as the highest velocity projectile only leads to a 3.0 % under estimation of en-

ergy absorption according to model prediction. This helps confirm that, although there

may be differences in the residual velocity of penetrating projectiles, the overall estimate

of energy absorbed in simultaneous impact can still be compared with sequential impact

results.

Stress wave propagation showing von Mises stresses is shown in Fig. 57. The

stress wave velocity was calculated from the simulation by measuring the time for the

wave to travel from the point of impact to the specimen boundary. The velocity was

3820.4 m.s-1. The stress wave velocity from the model was compared to the calculated

stress wave velocity (sonic velocity) using c=(E/ρ)1/2, where E11 = E22 = 27 GPa and

ρ = 1850 kg.m-3. The calculated sonic velocity was 3820.3 m.s-1, which was in excellent

agreement with the model. Partial penetration occurred at positions A and B at approxi-

145

mately 0.022 ms and at position C at 0.027 ms. Full penetration occurred after approxi-

mately 0.091 ms with all the projectiles exiting the laminate after 0.126 ms. The stages

of penetration correlate with the kinetic energy of the plate. Penetration began at the

peak kinetic energy of the plate, indicated in Fig. 52 while perforation occurred just after

the kinetic energy plateaus.

Stress wave interaction along the primary yarns is shown in Fig. 57 (a). The

stress wave propagates preferentially along the fiber axis (0/90o), and would first be ex-

pected to interact in the region between positions A and C. Figure 57 (b) shows peak

stress wave interaction between all three projectiles where Fig. 57 (c) shows a combina-

tion of damage interaction (damage accumulation disrupts stress wave communication)

and destructive wave interference. Figure 57 (d) illustrates damage interaction evidenced

by the region of low stress in the center which correlates with the delamination damage

shown in Fig. 59. Cone formation is shown in Fig. 58 with maximum out of plane de-

formation occurring at 0.047 ms, which coincides with the peak kinetic energy of the

plate.

Simultaneous Impact vs. Sequential Impact

The only complete data set for experiments conducted above ballistic limit was

the three projectile impact series. The comparison between the two projectile simultane-

ous and sequential impact was performed near the ballistic limit, henceenergy absorption

could not be compared. The two projectile simultaneous impact experiments above bal-

listic limit were performed to compare energy absorption and damage characteristics in

four layer laminates under the same impact conditions.

146

The decrease in energy absorption for the three projectile, .30 caliber sequential

(134.8 J, standard deviation = 4.0 J) and simultaneous (121.2 J, standard deviation = 8.0

J) impact experimental results was 10.1 %. These values fall outside the standard devia-

tion within each data set. If the experimental simultaneous impact energy absorption was

3.0 % less due to instrumentation limitations as predicted by the model, the energy ab-

sorption would be 124.9 J, which is still less than the sequential impact value including

experimental variation. Hence there is an increase in energy absorption for three layer

laminates subjected to sequential impact in contrast to simultaneous impact. Figures 62

and 63 summarizes the experimental results with Fig. 62 showing impact energy vs. new

surface creation and Fig. 63 showing impact energy absorption vs. new surface creation.

Both indicate that sequential impact results in greater new surface creation. Only the

three projectile impact results, Fig. 63, show an increase in energy absorption for sequen-

tial impact because the two projectile impact results (Fig. 62 and Fig. 63) were near the

ballistic limit.

While the experimental results show an increase in energy absorption for sequen-

tial impact, the FEA model predicts an 8.9 % decrease in energy absorption. This dispar-

ity is attributed to the difficulty mentioned previously in modeling sequential impact. In

the simultaneous impact model, a considerable amount of the penetration process occurs

before the damage zones interact, reducing laminate stiffness. Damage had already ac-

cumulated after the first impact in the sequential simulation and directly affected the sub-

sequent energy absorption.

The kinetic energy transfer to the target was 2.96 times greater in the simultane-

ous impact model at the onset of penetration as would be expected, Fig. 52. The linear

147

portion of the plate kinetic energy slopes during loading was also different. For sequen-

tial impact, the slopes for the first, second, and third impacts were 528.1 J/ms, 475.0

J/ms, and 530.6 J/ms, respectively. The slope for simultaneous impact plate loading was

1454 J/ms, which was 2.84 times greater than the average sequential impact slope. Inter-

estingly, the model predicted full penetration of all the simultaneous impact projectiles

(t = 0.091 ms) before full perforation of first projectile in sequential impact (t = 0.10 ms).

The unloading response post penetration was also different. The kinetic energy of

the plate in the sequential impact model reached a plateau just after penetration of each

projectile while the plate in the simultaneous impact model reached an initial plateau af-

ter penetration and then the kinetic energy decreased after 0.154 ms and reached another

plateau at 0.170 ms, Fig. 52. The most prominent feature of the sequential impact was

the increase in plate kinetic energy with increasing damage. This could also account for

some of the increase in energy absorption with increasing damage.

There were distinct differences in the target response, some of which was ex-

pected such as the peak kinetic energy and slope of the loading curve being about three

times greater for simultaneous vs. sequential impact. Some of the target responses were

not expected, e.g. the increase in kinetic energy of the plate as damage increased and that

all the simultaneous impact projectiles perforated the target before the first sequential im-

pact projectile.

Four Layer Laminates

There are two experimental data sets comparing simultaneous and sequential im-

pact of the four layer laminates; .30 caliber, two projectile impact series near the ballistic

limit (Table 9) and .30 caliber, two projectile impact series above the ballistic limit (Ta-

148

ble 10). However, a comparison between new surface creation was not available for the

.30 caliber, two projectile impact series near the ballistic limit and energy absorption is

unavailable since the impact velocity was below ballistic limit. Therefore, only the .30

caliber, two projectile impact series above the ballistic limit data set will be compared.

FEA was not conducted on the four layer laminates.

The impact energy absorption and new surface creation for the .30 caliber, two

projectile impact series above the ballistic limit for simultaneous and sequential impact

were quite close. Energy absorption and new surface creation increased 0.4 % and 1.6 %

for specimens subjected to sequential vs. simultaneous impact. These results are slightly

misleading though. The impact velocity was not very far above ballistic limit, particu-

larly in the case of simultaneous impact and as a result, five projectiles failed to penetrate

or were at ballistic limit. In addition, there were an unusually high number of data acqui-

sition errors leaving incomplete data sets for six out of eleven specimens. The standard

deviation was small even though there were only two data points per test condition avail-

able but additional testing would be required to fully assess differences.

In the two sequential impact specimens with complete data sets, the same trend

noted in the three layer laminate sequential impact data was seen for the four layer

specimens; energy absorption increases as damage increases. The average energy ab-

sorption for the available data in Table 10 was 52.2 J and 61.0 J for the first and second

sequential impacts, respectively. This was a 16.8 % increase in energy absorption. This

is believed to occur for the same reasons as well; namely a change in contact stiffness,

increase in specimen compliance resulting in increased contact duration and an increase

and plate kinetic energy with increasing damage.

149

Comparison of the Three and Four Layer Laminate Impact Response

The impact response of three and four layer laminates subjected to sequential and

simultaneous impact was compared. All the laminates were impacted above their ballis-

tic limits so that new surface creation and energy absorption characterizes can be exam-

ined. In order to compare results objectively, the data must be normalized. This is typi-

cally done on an areal density, laminate thickness, or number of laminates basis. Nor-

malizing based on areal density is typically done when comparing different materials

whereas normalizing based on laminate thickness or number of laminates is usually done

when comparing the same material with different laminate schedules. In the present case,

it was decided to normalize based on number of laminates so that new surface creation

could be directly compared since the number of delaminations is equal to the number of

laminates, n, minus one (n-1).

The results for two projectile simultaneous impact on three and four layer lami-

nates are shown in Figs. 48 and 49 which show new surface creation and energy absorp-

tion as a function of number of laminates, respectively. The normalized graphs are

shown in Figs. 64 and 65. The normalized new surface creation, Fig. 64, shows an in-

crease of 117 % for the four layer laminate over the three layer laminate which was about

the same as shown in Fig. 48 (118 %). The normalized energy absorption, Fig. 65, shows

a 1.1 % decrease in energy absorption for the four layer laminate.

The three projectile sequential impact results on three and four layer laminates is

shown in Figs. 50 and 51 (new surface creation and energy absorption, respectively).

The normalized values for those results and given in Figs. 66 and 67. The normalized

new surface creation, Fig. 66, shows a 46.9 % increase for the four layer laminate com-

pared to the 92 % increase shown in the raw data. As with the two projectile simultane-

150

ous impact study comparing laminate thickness effects, there was not a large difference in

the normalized impact energy absorption, a 7.1 % decrease for the four layer laminate.

Both results in the laminate thickness study indicated that new surface creation

increased substantially as the number of laminates increased but the normalized energy

absorption did not change significantly (energy absorption per laminate was constant) for

the laminate configurations considered. This reinforces the idea that delamination is a

not likely a large contributor to energy absorption. For both the three and four layer

laminate studies, the change in energy absorption seemed to be dominated by the target

response. Gellert and coworkers (2000) reported similar results. It was noted in sequen-

tial impact, that energy absorption increased with increasing damage state and the change

in perforation mechanisms for a specimen subjected to simultaneous impact where pene-

tration occurred at an earlier time step than for the first penetration seen in the sequential

impact model.

.50 Caliber Projectile Impact Results

The incident impact energy was held constant at 200 J (within experimental error)

in the mass effect study. The projectiles included in the test matrix, Fig. 38, were all 12.7

mm diameter spheres with three different densities resulting in projectile masses of 3.94 g

(alumina), 8.38 g (steel), and 16.08 g (WC). The projectile masses will be described by

their constituent materials or their mass in the results. In order to have constant impact

energy with different mass projectiles (about a factor of four difference in mass), the in-

cident velocity must be adjusted. The theoretical velocities for an impact energy of 200 J

were 318.6 m.s-1 (alumina), 218.5 m.s-1 (steel), and 157.7 m.s-1 (WC). This results in a

velocity range factor of 2.02 which should establish if there were strain rate or material

151

response effects. The laminate schedule was the same for the specimens, which were

constructed of three layer laminates.

The results from the mass effect study are given in Tables 12-14 and in Figures

68-92. A minimum of three specimens were tested for each configuration with the ex-

ception of the WC simultaneous impact series which only includes two specimens be-

cause two of the WC projectiles fractured during recovery. The simultaneous and se-

quential steel projectile impact study incorporated more specimens. There were process-

ing issues, again believed to be contamination of the preform, with specimens 09.07.05-

3-1, 09.07.05-3-2, and 09.07.05-3-3. These specimens were not included in the study and

are indicated in Table 14.

The same impact location and order were maintained from the three projectile, .30

caliber impact study; positions B, C, and A, respectively. For the sequential impact se-

ries, progressive damage was measured for all specimens. Reference marks were made

so the specimen could be placed back in the fixture in its original location. After the

specimen was impacted, it was removed from the fixture, imaged from the front and

back, and replaced back in its original position in the fixture before impacting it in the

next location. This was only done for two specimens in the .30 caliber impact study.

Sequential impact results for the alumina projectile. The average incident veloc-

ity was slightly higher than the theoretical 318.6 m.s-1 resulting in impact energy of 215.0

J on average with a standard deviation of 21.7 J, Table 12. The energy absorption for the

first, second and third impacts were 100.9 J (standard deviation = 6.0 J), 99.7 J (standard

deviation = 2.4 J) and 113.1 J (standard deviation = 113.1 J) for an average total of 313.6

152

J. Energy absorption decreased 1.2 % for the second impact and increased 13.4 % for the

third impact. The new surface creation was 119.3 cm2 (standard deviation = cm2) for the

first impact, 172.1 cm2 (standard deviation = 33.9 cm2) for the second, and 233.6 cm2

(standard deviation = 26.4 cm2) for the third impact. New surface creation increased 44.3

% after the second impact and 34.7 % after the third impact. Typical damage for this im-

pact condition is shown in Fig. 68.

Simultaneous impact results for the alumina projectile. The average incident en-

ergy was ca. 214.8 J with a standard deviation of 21.3 J for the simultaneous impact using

the alumina projectile, Table 12. The energy absorption was ca. 300.7 J with a standard

deviation of 20.3 J. This was a 4.1 % decrease in energy absorption compared to the se-

quential impact results for the alumina projectile. However, new surface creation was

35.5 % higher for simultaneous impact with an average of 316.5 cm2 with a standard de-

viation of 38.1 cm2. Typical damage for this impact condition is shown in Fig. 71.

Sequential impact results for the steel projectile. The average energy absorption

was 90.3 J (standard deviation = 9.0 J) for the first impact, 113.3 J (standard deviation =

9.1 J) for the second and 120.2 J (standard deviation = 6.2) for the third impact with an

average incident energy of 204.5 J (standard deviation = 14.9 J). The total energy ab-

sorption was 323.7 J. Energy absorption increased 25.5 % for the second impact and 6.1

% for the third impact. The resulting new surface creation after the first impact was

170.3 cm2 with a standard deviation of 18.3 cm2, 285.7 cm2 for the second impact with a

standard deviation of 20.5 cm2 (67.8 % increase), and 347.9 cm2 with a standard devia-

153

tion of 11.4 cm2 (21.8 % increase) for the third impact. Results for two of the specimens

were not included in the study due to inherent processing defects; specimens 09.07.05-3-

1 and 09.07.05-3-2. Typical delamination damage for specimens subjected to sequential

impact by the steel projectiles is shown in Fig. 69.

Simultaneous impact results for the steel projectile. The incident impact energy

was ca. 195.1 J with a standard deviation of 20.9 J in the simultaneous impact results for

the steel projectile. The energy absorption was 296.0 J (standard deviation = 29.9 J)

which new surface creation of 336.7 cm2 (standard deviation = 128.1 cm2). Energy ab-

sorption decreased 21.0 % and new surface creation decreased 3.2 % in contrast to the

sequential impact data.

There was a significant number of data acquisition errors in this data set along

with processing defects in specimen 09.07.05-3-3, which was excluded from the data

analysis in Table 13. Because of this, a larger sample population was taken to account

for the disparities. Despite testing 14 specimens, the standard deviation for new surface

creation was still exceedingly large, reducing confidence in this data set. Typical damage

is shown in Fig. 71.

Sequential impact results for the WC projectile. Impact energy absorption was

102.2 J (standard deviation = 8.5 J), 119.5 J (standard deviation = 8.6 J), and 129.4 J

(standard deviation = 9.5 J) for the first, second, and third impacts, respectively (Table

14). This gave average energy absorption of 351.0 J for the three projectiles combined.

Energy absorption increased 16.9 % for the second impact and for the third impact, 8.3

154

%. The incident energy was 197.4 J with a standard deviation of 5.6 J. New surface

creation was 120.3 cm2 (standard deviation = 33.7 cm2) for the first impact, 216.6 cm2

with a standard deviation of 40.8 cm2 (80.0 % increase) for the second impact and the

third impact resulted in new surface creation of 285.9 cm2 (32.0 % increase) with a stan-

dard deviation of 42.0 cm2. Figure 70 shows typical delamination damage for this data

set.

Simultaneous impact results for the WC projectile. The results for simultaneous

impact are shown in Table 14. Although there were only two data sets available for this

test configuration, impact energy and energy absorption were consistent. The delamina-

tion, however, exhibited a fairly large standard deviation. The incident energy was 197.0

J with a standard deviation of 0.5 J. Energy absorption was 326.8 J with a standard de-

viation of 1.6 J. New surface creation was 357 cm2 on average with a standard deviation

of 73.2 cm2. This resulted in an increase of 6.9 % decrease in energy absorption and a

24.9 % increase in new surface creation compared to the sequential impact data. Typical

delamination damage is shown in Fig. 71.

.50 Caliber Impact Discussion

Much of the discussion from the .30 caliber impact results applies to the .50 cali-

ber impact results. However; there were some distinct differences between the two in

terms of amount of new surface creation and impact response. With the wide range of

impact velocities explored in the .50 caliber study, differences were also noted within the

study itself. Because of the similarities between the .30 and .50 caliber studies, the FEA

155

results will be given at the same time as discussion to supplement understanding of the

target response.

Damage Evaluation

Damage progression was far more extensive in the .50 caliber impact study than

was seen in the .30 caliber impact study. In many cases, damage grew to the boundaries

after the second or third impact in the sequential impact study and almost always grew to

the boundaries in the three projectile simultaneous impact studies. Since the specimens

were fully clamped, the constraint pressure limited delamination growth making an accu-

rate assessment of damage difficult. The clamped area is indicated in Figs. 68-71 by a

dashed line. In addition, there were apparent edge effects, particularly in specimens im-

pacted simultaneously with steel and WC projectiles and for specimens impacted sequen-

tially with WC projectiles, Fig. 71. This indicates that the specimens subjected to impact

by massive projectiles were undergoing a substantial amount of bending in order to cause

delaminations at the clamped edges. A larger fixture and specimen would elevate both of

these issues but this was not available at the time of the study. Fairly clear trends were

still seen in the new surface creation measurements and will still be reported despite some

of the limitations noted.

Damage followed the same classic conical progression seen in the .30 caliber im-

pact study with in the inner, closest to the point of impact, delamination being smaller in

area than the outer delamination nearest the distal side of the laminate. In the general

case, as projectile mass increased, the severity of damage increased. This was noted in

both the simultaneous and sequential impact studies. In addition to delamination damage,

there was significant damage along the primary yarns. There was significant fiber

156

debonding and pullout with a high degree of interaction along impact positions A and C

and to a smaller extent, interaction of position B with the region between A and C. This

damage was much greater than what was seen in the .30 caliber impact study but like the

.30 caliber impact study, no evidence of shear-plugging was found, even with the higher

velocity alumina projectiles.

Sequential Impact

As damage accumulated, the energy absorption increased significantly as noted in

the previous studies. Figure 72 shows the damage progression (average) for the alumina,

steel, and WC projectiles as a function of number of impacts. The trend was highly linear

with R2 values ranging from 0.97 to 0.99. The steel projectiles produced the greatest de-

gree of damage followed the WC and alumina projectiles. The slopes of the steel and

WC projectiles were quite close (88.8 and 82.8 cm2/impact, respectively). The slope of

the alumina projectile was not as steep, 57.2 cm2/impact. This indicates that lighter

weight sequential impact projectiles are not as damaging as heavy projectiles. However;

the steel projectile shows a higher degree of damage than the heavier WC projectile. It is

not entirely clear whether the steel projectile data not fitting within the trend is an actual

result, if there were specimen variations (specimens from four different panels were

tested and specimens 09.07.05-3-1 and 09.07.05-3-2 were discarded), or if there was a

large influence form clamping effects affecting delamination growth.

Figure 73 shows energy absorption as a function of number of impacts. This fig-

ure shows a significant dependence of energy absorption on projectile mass. The stan-

dard deviation was low and there is a high degree of confidence in this data set. Again a

linear relationship is seen, as the number of impacts increases, energy absorption in-

157

creases. The linear trend was not as strong as was in new surface creation but respectable

with R2 values of 0.52, 0.71, and 0.69 for the alumina, steel, and WC projectiles, respec-

tively. The heaviest projectiles exhibited the highest degree of energy absorption with

the smallest mass having the least amount of energy absorption with the exception of the

first impact by the alumina projectile. The degree energy absorption increase with in-

creasing number of impacts was highest for the steel projectile (slope = 14.9 J/impact),

followed closely by the WC projectile (slope = 13.6 J/impact). The slope was considera-

bly lower for the alumina projectile with a 6.1 J/impact increase in energy absorption.

Energy absorption as a function of new surface creation is shown in Fig. 74. This

shows a combination of the results in Figs. 72 and 73. A strong linear trend was also ap-

parent with R2 values of 0.72, 0.98, 0.996 for the alumina, steel and WC projectiles re-

spectively. In this case, the steel projectile exhibited the lowest increase in energy ab-

sorption as a function of damage. The WC projectiles exhibited the highest energy ab-

sorption followed by alumina. As seen in the previous graphs, the steel and WC projec-

tiles had similar slopes (the same in this case both having slopes of 0.17 J/cm2) and the

alumina projectiles had a slope of 0.11 J/cm2. The increase in energy absorption is not

attributed to energy absorbed via delamination damage. As was surmised in the .30 cali-

ber impact study, the increase in energy absorption is attributed to a change in specimen

compliance as damage accumulates. More evidence of this will be given in the discus-

sion of the FEA results showing kinetic energy transfer to the target by the projectiles.

Sequential impact damage was predicted poorly in the FEA model. Figure 75

compares the experimental results and the numeric prediction for delamination damage

where the model under predicted new surface creation for sequential impact by the alu-

158

mina, steel, and WC projectiles by 48.1 %, 15.0 %, and 57.5 %, respectively. The predic-

tion was better in the .30 caliber sequential impact model. The large deviation in the .50

caliber projectile impact prediction is likely due to an increase in the damaged state re-

sulting in material softening. The sequential steel projectile damage prediction was better

only under predicting damage by 15 %. Experimental delamination damage is compared

with the FEA prediction in Figs. 75 and 79. The model in all cases, predicts the delami-

nation damage area is almost the same through the thickness. The comparison between

the FEA damage prediction and experimental results are shown in Figs. 81, 83, and 85.

The inability of the model to capture the size and shape of the delaminations in-plane and

through the thickness is could be due to the difficulties associated with modeling thin

laminates (Yen, 2006).

The correlation was closer because the softening and S (delamination) parameters

were calibrated from the .30 caliber impact data which had almost the same velocity as

the .50 caliber steel projectile (227.0 m.s-1 and 220.8 m.s-1, respectively) indicating there

is a sensitivity to impact velocity. This was done intentionally so that the .30 and .50

caliber steel projectile data could be compared. However, it was decided this comparison

would not be made due to large differences in the impact response. Since the material

model is sensitive to strain rate, vastly different impact velocities (factor of two differ-

ence) may have influenced energy absorption in the model. The delamination and mate-

rial softening parameters could be adjusted to provide a better correlation to the experi-

mental data but was not done in this work.

The FEA model for .50 caliber sequential impact provided a closer prediction of

residual velocity than seen in the case of the .30 caliber projectile impact, Fig. 76. The

159

results were in fact, quite different than what was seen in .30 caliber projectile impact

model. In this case, residual velocity (a function of energy absorption) did not decrease

significantly with increasing damage. The slopes are actually close to zero, but all

slightly positive, e.g. a small decrease in energy absorption as a function of number of

impacts. The FEA results were closest for the steel projectile, under predicted for the

alumina projectile and over predicted for the WC projectile. This is believed to occur

because of the same reasons mentioned above. Both the softening parameter and the de-

lamination parameter mentioned above would have to be adjusted to provide better corre-

lation to the experimental data when comparing different projectile masses and velocities.

Simultaneous Impact

Figure 77 compares new surface creation for simultaneous and sequential impact

for the three different projectiles. Delamination increased with increasing mass for the

.50 caliber simultaneous impact experiments. These results are in contrast to the work by

Cantwell and Morton (19891) who reported that small mass, high velocity projectiles

were more damaging than large mass projectiles. However, their study was also limited

to carbon/epoxy targets at higher velocities and may not be directly comparable to these

findings. Steel projectiles resulted in a 9.9 % increase in damage compared to alumina

projectiles and with WC, damage increased 2.6 % over the steel projectiles. There was

more deviation in the WC simultaneous impact data in which there was overlap with the

standard deviation in the steel projectile impact data. It appears that there was greater

contrast in the results between the steel and alumina projectiles. One notable difference

in damage was in fiber debonding and pullout along the primary yarns and elastic bend-

ing artifacts at the specimen boundaries. As projectile mass increased, the amount of

160

debonding and pullout along the primary yarns surrounding the points of impact in-

creased significantly from a qualitative standpoint. The increase in damage may have

played a role in energy absorption.

The momentum equation uses the same variables, mass (m) and velocity (V), as

the kinetic energy equation but is a measure of inertia or resistance to change in velocity,

p = m.V. The increase in damage with increasing projectile mass is attributed to the in-

crease in momentum of the projectiles, Table 15. An increase in momentum results in

the laminate undergoing an increase in displacement. The maximum displacement pre-

dicted by the FEA model was 3.82 mm, 4.38 mm, and 4.42 mm for specimens subjected

to impact by the alumina, steel, and WC projectiles. This increase in displacement, 14.7

% increase for steel over aluminum, and 0.9 % increase for WC in contrast to steel,

which is roughly proportionate to the increases in damage seen in the experimental data.

The increase in displacement is associated with an increase in strain which may account

for the differences in damage.

The FEA study was much closer in the prediction of new surface creation for si-

multaneous impact, Fig. 79. Like the sequential impact model, the simultaneous impact

model also under predicted delamination damage. In this case, it was only by 7.3 %, 5.8

%, and 32.5 % for the alumina, steel and WC projectiles, respectively. The improved

correlation could arise from the fact that damage did not fully progress until the projec-

tiles had almost completed penetration. In the case of the WC projectile, penetration took

the longest and which may have influenced the delamination growth. The comparison

between typical delamination damage and the FEA prediction is shown in Figs. 82, 84,

and 86. Again, as mentioned previously, the model failed to capture through the thick-

161

ness damage. Also, the FEA prediction shows significant tearing when the laminates are

subjected to simultaneous impact. This tearing occurred when the projectiles had almost

completed penetration and the delamination prediction was almost complete. Increasing

the erosion elastic limit in the model would decrease the tearing which was not seen in

the experimental results.

With the exception of the steel projectile, simultaneous impact data in which there

were some difficulties obtaining accurate data, energy absorption increased with increas-

ing projectile mass, Fig. 78. The increase in energy absorption can also be attributed to

the increase in elastic deformation with increasing projectile mass and an increase in pri-

mary yarn damage described in the previous section. Naik and coworkers (2006) re-

ported that based on their analytical model, deformation of the primary yarns was the

dominate energy absorption mechanism in thin E-glass/epoxy laminates followed by the

kinetic energy of cone formation and then tensile fiber failure. They reported that matrix

cracking and delamination contributed little to the overall energy absorption.

The FEA model predicts the same trend for residual velocity seen experimentally,

Fig. 80. There was very good agreement in the residual velocity prediction for the steel

and WC projectiles (0.6 % decrease and 7.9 % increase, respectively). Residual velocity

for the alumina projectile was under predicted by 23.2 %. This disparity could likely be

attributed to strain rate effects and better correlation could be achieved by varying the

material softening parameter.

Simultaneous vs. Sequential Impact

Figures 77 and 78 compare new surface creation and energy absorption for the three pro-

jectiles in the study under simultaneous and sequential impact conditions. In contrast to

162

the .30 caliber projectile impact results, where sequential impact resulted in a greater de-

gree of damage (Fig. 63), the general trend for the .50 caliber impact results shows that

simultaneous impact resulted in the greatest damage. Specimens subjected to impact by

the steel projectiles did not follow this trend but there were numerous problems with that

data set which remain unresolved. Making a comparison between projectile size was dif-

ficult. Aside from having lower incident energy (148 J vs. 600 J for three .30 and .50

caliber projectiles, respectively), .50 caliber projectiles have a 256 % increase in pro-

jected area (49.5 mm2 vs. 126.7 mm2). This means a greater number of yarns will be sub-

jected to loading, affecting both the primary and secondary yarn deformation.

The laminate response was very different because of this. Figure 89 shows the

kinetic energy of target plates subjected to impact by steel .30 and .50 caliber projectiles

by sequential impact. The predicted target response (impulse loading) for .30 caliber se-

quential impact was 0.108 ms for the first projectile, 0.105 ms (2.8 % decrease) for the

second projectile and for the third projectile, 0.0847 ms (19.3 % decrease). In the .50

caliber sequential impact simulation, the target responded to the first projectile for 0.167

ms, the second 0.188 ms (12.6 % increase), and 0.164 ms (13.0 % decrease) for the third

projectile. The predicted target interaction time was substantially greater in the case of

the .50 caliber projectiles in contrast to the .30 caliber projectiles (54.6 % increase for the

first impact, 79.0 % increase for the second and 93.2 % increase for the third). Since

there was an increase in contact duration, an increase in primary and secondary yarn de-

formation would be expected.

The same trend is shown in Fig. 90 where the target interaction time for simulta-

neous impact was 0.091 ms (.30 caliber) and ca. 0.389 ms (.50 caliber). In this case how-

163

ever, there was an increase in target interaction time of 163.1 % (.30 vs. .50 caliber si-

multaneous) compared to an average increase of 57.5 % (.30 vs. .50 caliber sequential).

This change in target response could be responsible for the transition in damage for

specimens subjected to .30 and .50 caliber simultaneous and sequential impact.

The increase in damage for simultaneous impact was hypothesized at the begin-

ning of this work but for different reasons. It was originally thought that constructive

stress wave interactions would result in a higher degree of damage in specimens sub-

jected to simultaneous impact. The FEA models were not able to show this definitively

and further analysis would be required to confirm such affects. Target response was ini-

tially given less consideration with the exception of kinetic energy of the cone which

forms around the point of impact and secondary yarn deformation. Upon examining the

results, in particular the target plate deformation using the modeling results, energy ab-

sorbed in flexure and kinetic energy transfer to the target appears to have a direct rela-

tionship to damage evolution and energy absorption.

In all cases, impact energy absorption was greater for sequential impact, in which

energy absorption increased with increasing damage. As damage accumulates, the com-

pliance of the specimen increases. This changes the contact between the target and pro-

jectile and alters the laminate response. The modeling results show an increase in the ki-

netic energy of the plate with increasing number of impacts. Although the models were

unable to capture the increase in energy absorption with respect to cumulative damage

because of reduced stiffness, they do show an increase in kinetic energy transfer to the

target plate with increasing damage.

164

A significant relationship was found when comparing energy absorption and new

surface creation from the first impact in a sequential impact series to simultaneous impact

normalized by the number of projectiles. It appears that the normalized simultaneous im-

pact response was very comparable to the laminate response from the first impact of a

sequential impact series. New surface creation is shown in Fig. 91. All comparisons are

quite close with the exception of the .50 caliber steel projectile which had a large stan-

dard deviation (128.1 cm2). Figure 92 shows energy absorption which had an even better

correlation.

These results indicate that cumulative damage sustained in sequential impact

plays a greater role in the overall target response of thin S-2 glass/epoxy laminates than

synergistic events such as stress wave interaction, kinetic energy transfer to the target

plate, increase in elastic deformation of the secondary yarns, and damage along the pri-

mary yarns. This is believed to occur because in near-simultaneous impact, the impact

event occurs over such a short time span that there is not significant time for synergistic

events to culminate into a change in the target response much like table wear does not

change positions when the table cloth is rapidly pulled from under them.

165

38 mm

25.4 mm

B

C

Fig. 40. Illustration showing the test configuration (A, B, C) listed in the tables.

A

166

Specimen ID Test configuration

Incident velocity (m.s-1)

Residual velocity (m.s-1)

Impact energy

(J)

Energy absorption

(J)

New surface creation

(cm2)

06.25.05-3-1 Center impact NR NR NA NA NA06.25.05-3-2 Center impact 215.1 0.0 47.2 47.2 73.206.25.05-3-3 Center impact 224.6 63.3 51.4 47.3 82.306.25.05-3-4 Center impact 213.0 0.0 46.3 46.3 59.806.25.05-3-5 Center impact 221.8 95.9 50.2 40.8 77.706.25.05-3-6 Center impact 264.7 174.4 71.5 40.5 68.606.25.05-3-7 Center impact 221.5 92.5 50.0 41.3 80.706.25.05-3-8 Center impact NR NR NA NA NA06.25.05-3-9 Center impact NR NR NA NA NA

Three layer laminate, single projectile impact results above the ballistic limit

NR = No Reading, NA = Not Available

Table 5.

167

Table 6.


(A,B,C)



Impact energy

(J)

Energy absorption

(J)

New surface creation (cm2)

A 193.2 0.0 38.1 38.1 NAC 198.7 0.0 40.3 40.3A 203.9 0.0 42.4 42.4 147.7C 203.0 0.0 42.0 42.0A 207.5 0.0 43.9 NA 137.8C 199.9 0.0 40.7 40.7A 201.1 0.0 41.2 NA 135.1C 202.1 0.0 41.6 41.6

07.13.05-3-20 A,C 200.5 0.0 82.0 82.0 98.107.13.05-3-21 A,C 203.3 0.0 84.2 84.2 117.7

Sequential impact

Simultaneous impact

Three layer laminate, .30 caliber simultaneous and sequential two projectile impact results near the ballistic limit


07.13.05-3-16

07.13.05-3-17

07.13.05-3-18

07.13.05-3-19

168

Table 7.


(A,B,C)



Impact energy

(J)

Energy absorption

(J)


07.13.05-3-11 A,C 232.2 101.0 110.0 89.1 138.907.13.05-3-12 A,C 230.2 113.5 108.0 81.8 109.507.13.05-3-13 A,C 220.6 105.9 99.2 76.4 107.3

Simultaneous impact

Three layer laminate, .30 caliber simultaneous two projectile impact results above the ballistic limit


169

Table 8.


(A,B,C)



Impact energy

(J)

Energy absorption

(J)


B 231.3 82.5 54.5 47.6C 221.5 37.7 50.0 48.6A 225.2 0.0 51.7 51.7B 226.4 97.1 52.3 42.6C 227.3 98.0 52.7 42.9A 225.8 74.9 52.0 46.3B 224.9 99.5 51.6 41.5C 225.8 100.7 52.0 41.6A 223.7 83.7 51.0 43.9B 222.1 NR 50.3 NAC 222.7 82.8 50.6 43.6A 227.0 0.0 52.5 52.5B 226.4 79.7 52.3 45.8C 223.7 NR 51.0 NAA 229.4 89.5 53.7 45.5B 238.9 146.4 58.2 36.3C 228.5 NR 53.2 NAA 226.9 NR 52.5 NAB 231.9 118.4 54.8 40.5C 231.3 87.3 54.5 46.8A 226.7 78.5 52.4 46.1

07.13.05-3-6 A,B,C 213.9 73.0 140.1 123.7 NA07.13.05-3-7 A,B,C 215.1 98.0 141.6 112.2 169.407.13.05-3-8 A,B,C 195.4 NR 116.7 NA 164.007.13.05-3-9 A,B,C 221.1 NR 149.4 NA 153.7

07.13.05-3-10 A,B,C 227.9 101.0 159.0 127.7 147.3

Sequential impact

Simultaneous impact

07.13.05-3-4

197.0

172.9

184.0

185.1

199.0

07.13.05-3-1

07.13.05-3-2

154.6

07.13.05-3-5

148.7

Three layer laminate, .30 caliber simultaneous and sequential three projectile impact results above the ballistic limit


07.13.05-3-3

08.29.05-3-2

08.29.05-3-1

170

Table 9.


(A,B,C)



Impact energy

(J)

Energy Absorption

(J)


07.13.05-4-5 A 229.7 0.0 53.8 53.8C 215.7 0.0 47.5 47.5

07.13.05-4-6 A 216.7 0.0 47.9 47.9C 223.1 0.0 50.7 50.7

07.13.05-4-2 A,C 241.9 81.6 119.4 105.8 NA07.13.05-4-3 A,C 223.7 0.0 102.0 102.0 NA07.13.05-4-4 A,C 224.9 0.0 103.1 103.1 NA

Simultaneous impact

352.4

Sequential impact

Four layer laminate, .30 caliber simultaneous and sequential two projectile impact near the ballistic limit


331.6

171

Table 10.


(A,B,C)



Impact energy

(J)

Energy absorption

(J)


A 248.9 85.8 63.2 55.7 287.6C 247.7 0.0 62.6 62.6A 252.3 82.8 64.9 57.9 243.3C 256.5 NR 67.1 NAA 256.5 NR 67.1 NA 198.6C 255.9 NR 66.8 NAA 251.7 111.1 64.6 52.0 194.1C 254.4 80.9 66.0 59.3A 256.2 117.2 66.9 52.9 235.2C 257.1 NR 67.4 NAA 257.1 156.7 67.4 42.4 NAC 258.4 NR 68.0 NA

07.13.05-4-15 A,C 232.5 0.0 110.2 110.2 293.407.13.05-4-16 A,C 237.6 NR 115.0 NA 219.007.13.05-4-17 A,C 235.2 NR 112.8 NA 217.907.13.05-4-18 A,C 243.7 79.1 121.2 108.4 248.607.13.05-4-19 A,C 245.3 77.3 122.6 110.5 198.2

Sequential impact

Four layer laminate, .30 caliber simultaneous and sequential two projectile impact above ballistic limit

Simultaneous impact

07.13.05-4-11


07.13.05-4-13

07.13.05-4-12

07.13.05-4-9

07.13.05-4-10

07.13.05-4-14

172

Table 11.


(A,B,C)



Impact energy

(J)

Energy absorption

(J)

New surface creation

(cm2)

B 239.5 92.5 58.5 49.7 331.6C 251.7 75.5 64.6 58.8A 249.5 NR 63.5 NAB 254.7 115.0 66.1 52.6 352.4C 250.4 89.8 63.9 55.7A 253.6 68.5 65.6 60.8

Sequential impact

Four layer laminate, .30 caliber sequential three projectile impact above ballistic limit

07.13.05-4-7

07.13.05-4-8


173

25.4 mm

Fig. 41. Typical damage progression in a 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).

174

Fig. 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.

Sequential impact

Simultaneous impact

1st

2nd

25.4 mm

25.4 mm

3rd

175

Residual velocity = -24.8*(# of impacts) + 129.3R2 = 0.333

0

20

40

60

80

100

120

140

160

0 1 2 3 4Number of impacts at constant incident velocity

Res

idua

l vel

ocity

(m s-1

)

Fig. 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.

176

42.4

44.7

47.7

25

30

35

40

45

50

Number of impacts1 2 3

Impa

ct e

nerg

y ab

sorp

tion

(J)

Fig. 44. Impact energy absorption for a three .30 caliber projectile sequential impact se-ries 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.

5.4%

6.7%

177

Fig. 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). The error bars indi-cate standard deviation.

73.7

140.2

107.9

177.3

158.6

0

40

80

120

160

200

1Number of impacts

Sequential

Simultaneous

New

surf

ace

crea

tion

(cm

2 )

1 2 3

23.0%

10.5%

178

Fig. 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.

134.8121.2

0

20

40

60

80

100

120

140

160

Impa

ct e

nerg

y ab

sorp

tion

(J)

30 caliber, 3 projectile sequential 30 caliber, 3 projecitle simultaneous

10.1%

179

Fig. 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.

Sequential impact

Simultaneous impact

1st 2nd

25.4 mm

25.4 mm

180

Fig. 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). The error bars indicate standard deviation.

107.9

235.4

0

50

100

150

200

250

300

1Number of laminates

New

surf

ace

crea

tion

(cm

2 )

3 layer, 2 projectile simultaneous


3 4

118%

181

Fig. 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). The error bars indicate standard deviation.

82.4

109.7

0

25

50

75

100

125

150




33.1%

3 4

Ener

gy a

bsor

ptio

n (J

)

182

Fig. 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). The error bars indicate standard deviation.

177.3

342.0

0

75

150

225

300

375


New

surf

ace

crea

tion

(cm

2 )

3 layer, 3 projecitle sequential

4 layer, 3 projectile sequential

92% increase

3 4

183

Fig. 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). The error bars indicate standard deviation.

134.8

166.6

0

25

50

75

100

125

150

175

200


Ener

gy a

bsor

ptio

n (J

)

3 layer, 3 projectile sequential4 layer, 3 projectile sequential

23.6%

3 4

184

Fig. 52. Modeling results showing the three layer laminate response to sequential and simultaneous impact (kinetic energy transfer) for three .30 caliber projectiles.

0

5

10

15

20

25

30

35

0 0.1 0.2 0.3 0.4 0.5 0.6Time (ms)

Kin

etic

ene

rgy

(J)

30 caliber simultaneous

30 caliber sequential

Full penetration

Start of penetration

185

Fig. 53. .30 caliber sequential impact series (3 layer laminate) comparing the experimental results to the FEA prediction.

y = -24.8*x + 129.4R2 = 0.9975

0

20

40

60

80

100

120

140

0 1 2 3 4

Number of impacts

Res

idua

l vel

ocity

(m. s-1

)

30 caliber sequential FEA

30 caliber sequential experimental

4.5%

41.2% 113.1%

186

Fig. 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.

(a) MPa

MPa

(b)

(c)

MPa

t = 0.210 ms

t = 0.245 ms

t = 0.490 ms

187

t = 0.07 ms

t = 0.28 ms

t = 0.56 ms

Fig. 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.

Vincident = 220 m.s-1(a)

(b)

(c)

188

Fig. 56. Experimental vs. FEA prediction of the damage zone for a three (.30 caliber) pro-jectile sequential impact series.

Inner delamination

Outer delamination

200 mm

200 mm

25.4 mm

189

Fig. 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.

t = 0.025 ms

t = 0.010 ms t = 0.020 ms

t = 0.080 ms

MPa

MPa MPa

MPa

(a) (b)

(c) (d)

190

Fig. 58. .30 caliber simultaneous impact simulation penetration and cone forma-tion.

t = 0.20 ms

t = 0.103 ms

t = 0.047 ms

Vincident = 220 m.s-1

191

Fig. 59. Experimental vs. FEA prediction of the damage zone for a three (.30 caliber) pro-jectile simultaneous impact series.

Inner delamination

Outer delamination

200 mm

200 mm

25.4 mm

192

Fig. 60. .30 caliber (three projectile) simultaneous and sequential impact results compar-ing the experimental values for damage to the FEA prediction. The error bars in the ex-perimental data series represent standard deviation.

158.6 148.2177.3

150.3

0

40

80

120

160

200

1

New

surf

ace

crea

tion

(cm

2 )

30 caliber simultaneous experimental 30 caliber simultaneous FEA30 caliber sequential experimental 30 caliber sequential FEA

6.6%15.2%

193

Fig. 61. .30 caliber (three projectile) simultaneous and sequential impact results compar-ing the experimental values for residual velocity to the FEA prediction. The error bars in the experimental data series represent standard deviation.

90.7

101.0

79.9

110.0

0

20

40

60

80

100

120

140

1

Res

idua

l vel

ocity

(m. s-1

)

30 caliber simultaneous experimental 30 caliber simultaneous FEA30 caliber sequential experimental 30 caliber sequential FEA

11.4%

37.6%

194

20

40

60

80

100

120

140

160

50 70 90 110 130 150 170 190 210


Impa

ct e

nerg

y (J

)

Single projectile

2 projectile simultaneous

2 projectile sequential


3 projectile sequential

Fig. 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). Note: the 2 projectile simultaneous and sequential impacts were near the ballistic limit while all others reported are above ballistic limit. The error bars indicate standard deviation.

195

Fig. 63. Impact energy absorption vs. new surface creation for three layer laminates sub-jected to single, two, and three projectile simultaneous and sequential impacts at constant incident velocity. Note: the 2 projectile simultaneous and sequential impacts were near the ballistic limit while all others reported are above ballistic limit. The error bars indicate stan-dard deviation.

20

40

60

80

100

120

140

160

50 70 90 110 130 150 170 190 210


Impa

ct e

nerg

y ab

sorp

tion

(J)

Single projectile(above VB)


(near VB)

2 projectile sequential (near VB)


(above VB)

3 projectile sequential (above VB)

196

Fig. 64. Normalized new surface creation/laminate vs. number of laminates for a .30 cali-ber 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.

39.5

85.5

0

20

40

60

80

100


Normalized 3 layer, 2 projectilesimultaneousNormalized 4 layer, 2 projectilesimultaneous

117% increase

3 4

Nor

mai

lized

new

surf

ace

crea

tion

(cm

2 )/lam

inat

e

197

Figure 65. Normalized energy absorption/laminate vs. number of laminates for a .30 cali-ber 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.

27.727.4

0

5

10

15

20

25

30

35

40


Normalized 3 layer, 2 projectile simultaneous

Normalized 4 layer, 2 projectile simultaneous

1.1%

3 4

Nor

mai

lized

ene

rgy

abso

rptio

n (J

)/lam

inat

e

198

Fig. 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).

59.1

85.5

0

25

50

75

100


Normailized 3 layer, 3projecitle sequentialNormalized 4 layer, 3projectile sequential

46.9% increase

3 4

Nor

mai

lized

new

surf

ace

crea

tion

(cm

2 )/lam

inat

e

199

Fig. 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).

44.9 41.7

0

10

20

30

40

50

60


Normalized 3 layer, 3 projectile sequential

Normalized 4 layer, 3 projectile sequential

7.1% decrease

3 4

Nor

mai

lized

ene

rgy

abso

rptio

n (J

)/lam

inat

e

200

Table 12.

Specimen ID Impact location (A,B,C)

Total projectile mass (g)

Incident velocity (m s-1)

Incident kinetic

energy (J)

Residual velocity (m s-1)

Energy absorbed

(J)


09.02.05-3-1 B 3.94 356.0 249.5 280.6 94.6 89.6C 3.94 307.6 186.3 209.7 99.8 172.1A 3.94 318.6 199.8 213.3 110.2 206.9

09.02.05-3-3 B 3.94 353.3 245.7 266.0 106.5 131.4C 3.94 323.2 205.6 234.6 97.2 138.2A 3.94 315.3 195.6 204.8 113.1 234.2

09.02.05-3-6 B 3.94 333.8 219.4 244.7 101.5 136.9C 3.94 336.9 223.4 248.3 102.0 205.9A 3.94 326.2 209.5 217.9 116.0 259.7

08.22.05-3-3 A,B,C 11.82 325.3 208.3 234.0 301.5 343.108.22.05-3-4 A,B,C 11.82 348.1 238.6 258.7 320.6 272.808.24.05-3-1 A,B,C 11.82 316.8 197.5 230.1 280.1 333.6NR=No Reading, NA=Not Available**=Not used (process/specimen issue), *=Not used (testing/data acquisition issue)

Simultaneous and sequential impact results for the alumina (3.94 g) .50 caliber projectile (3 layer laminate)

Simultaneous impact

Sequential impact

201

Table 13.




Incident kinetic

energy (J)


Energy absorbed

(J)


09.02.05-3-8 B 8.38 219.7 202.3 164.9 88.3 160.6C 8.38 236.4 234.2 168.6 115.2 278.6A 8.38 221.5 205.6 146.4 115.9 341.3

09.07.05-3-1** B 8.38 229.4 220.6 150.9 125.1 NAC 8.38 225.8 213.6 115.3 157.9 NAA 8.38 217.0 197.2 106.2 150.0 NA

09.07.05-3-2** B 8.38 221.5 205.6 149.4 112.1 NAC 8.38 NR NA 111.1 NA NAA 8.38 208.1 181.5 0.0 181.5 NA

08.19.05-3-8 B 8.38 222.1 206.8 172.2 82.5 158.8C 8.38 222.7 207.9 157.9 103.4 269.7A 8.38 212.1 188.5 130.2 117.4 341.2

08.24.05-3-3 B 8.38 230.1 221.7 170.4 100.1 191.3C 8.38 210.0 184.7 122.9 121.4 308.8A 8.38 214.8 193.4 125.7 127.2 361.1

08.19.05-3-3* A,B,C 25.14 308.0 397.4 268.1 288.6 NA08.19.05-3-4* A,B,C 25.14 292.1 357.6 252.9 268.9 NA08.19.05-3-5 A,B,C 25.14 222.1 206.8 160.7 295.8 270.608.19.05-3-6* A,B,C 25.14 224.0 210.2 154.9 329.1 NA08.19.05-3-7 A,B,C 25.14 NR NA NR NA 583.408.19.05-3-9 A,B,C 25.14 222.1 206.8 172.2 247.4 NA08.24.05.3-2 A,B,C 25.14 203.0 172.6 129.9 305.6 309.708.24.05-3-4 A,B,C 25.14 203.0 172.6 125.7 253.1 418.008.29.05-3-1 A,B,C 25.14 203.0 172.6 130.8 302.6 194.008.31.05-3-5* A,B,C 25.14 206.6 178.9 134.8 308.2 NA09.07.05-3-3** A,B,C 25.14 235.5 232.4 167.7 343.8 NA08.24.05-3-5 A,B,C 25.14 221.5 205.6 161.0 291.2 265.608.31.05-3-1* A,B,C 25.14 224.6 211.3 NR NA NA08.31.05-3-4 A,B,C 25.14 205.4 176.8 140.3 283.0 315.4NR=No Reading, NA=Not Available

Simultaneous and sequential impact results for the steel (8.38 g) .50 caliber projectile (3 layer laminate)

**=Not used (process/specimen problem), *=Not used (testing/data acquisition error)

Simultaneous impact

Sequential impact

202

Table 14.




Incident kinetic

energy (J)


Energy absorbed

(J)


09.02.05-3-2 B 16.08 154.9 192.8 102.9 107.8 122.5C 16.08 160.4 206.7 102.5 122.2 213.2A 16.08 155.8 195.1 84.3 138.0 283.5

09.02.05-3-4 B 16.08 157.0 198.2 114.7 92.4 85.5C 16.08 158.5 202.0 107.1 109.8 177.6A 16.08 154.6 192.1 95.2 119.2 245.1

09.02.05-3-5 B 16.08 158.2 201.2 108.6 106.4 152.8C 16.08 153.4 189.1 88.2 126.5 258.9A 16.08 157.6 199.7 92.5 130.9 329.0

08.22.05-3-1 A,B,C 48.24 156.4 196.6 104.7 325.7 408.808.22.05-3-2 A,B,C 48.24 156.7 197.4 104.7 328.0 305.3NR=No Reading, NA=Not Available**=Not used (process/specimen problem), *=Not used (testing/data acquisition error)

Sequential impact

Simultaneous impact

Simultaneous and sequential impact results for the WC (16.1 g) .50 caliber projectile (3 layer laminate)

203

Fig. 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). The dashed lines indicate the specimen boundary and the scale is the same in all images (25.4 mm).

25.4 mm

204

Fig. 69. Typical damage progression in a three layer laminate (09.02.05-3-8) subjected to a .50 caliber sequential impact (steel, 8.38 g) at constant incident energy (~200 J). The dashed lines indicate the specimen boundary and the scale is the same in all im-ages (25.4 mm).

25.4 mm

205

Fig. 70. Typical damage progression in a three layer laminate (09.02.05-3-4) subjected to a .50 caliber sequential impact (WC, 16.08 g) at constant incident energy (~200 J). The dashed lines indicate the specimen boundary and the scale is the same in all im-ages (25.4 mm).

25.4 mm

206

Fig.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 (~200 J). The dashed lines indicate the specimen boundary and the scale is the same in all images (25.4 mm).

Sequential Simultaneous

25.4 mm

Alumina Alumina

Steel Steel

WC WC

207

Fig. 72. New surface creation vs. number of sequential impacts at constant incident energy (200 J) for the alumina, steel, and WC .50 caliber projectiles.

y = 88.8*x + 90.4R2 = 0.97

y = 82.8*x + 42.0R2 = 0.99

y = 57.2*x + 60.7R2 = 0.99

0

50

100

150

200

250

300

350

400

0 1 2 3 4Number of impacts

New

surf

ace

crea

tion

(cm

2 )

Steel

WC

Alumina

208

Fig. 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 absorp-tion with increasing number of impacts (increasing damage state).

y = 13.6*x + 89.8R2 = 0.69

y = 6.1*x + 92.3R2 = 0.52

y = 14.9*x + 78.0R2 = 0.71

80

90

100

110

120

130

140

150


Ener

gy a

bsor

ptio

n (J

)

.50 caliber WC

.50 caliber steel

.50 caliber alumina

209

y = 0.17*x + 82.8R2 = 0.996

y = 0.17*x + 61.8R2 = 0.98

y = 0.11*x + 85.2R2 = 0.72

80

90

100

110

120

130

140

100 150 200 250 300 350 400


Ener

gy a

bsor

ptio

n (J

)

.50 caliber WC

.50 caliber steel

.50 caliber alumina

Fig. 74. Energy absorption (J) vs. new surface creation (cm2) of a three projectile se-quential impact series on three layer laminates with constant incident energy (200 J) showing an increase in energy absorption with increasing damage state.

210

Fig. 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. The error bars in the ex-perimental data series indicate standard deviation.

233.6

135.9

347.9

295.6285.9

121.4

0

50

100

150

200

250

300

350

400

1

New

surf

ace

crea

tion

(cm

2 )

Alumina sequential experimental Alumina sequential FEASteel sequential experimental Steel sequential FEAWC sequential experimental WC sequential FEA

41.8 %

15.0 %

57.5 %

211

Fig. 76. .50 caliber sequential impact series on three layer laminates showing the experi-mental results and FEA prediction of residual velocity with increasing number of impacts (damaged state).

0

50

100

150

200

250

300


Res

idua

l vel

ocity

(m/s

)

50 caliber alumina experimental 50 caliber alumina FEA50 caliber steel experimental 50 calibersteel FEA50 caliber WC experimenal 50 caliber WC FEA

212

Fig. 77. .50 caliber simultaneous and sequential impact results comparing energy absorption vs. projectile mass at constant incident energy (~200 J). The error bars indicate standard deviation.

316.5

233.6320.8

347.9357.0

285.9

0

50

100

150

200

250

300

350

400

450

1

New

surf

ace

crea

tion

(cm

2 )

Alumina (simultaneous) Alumina (sequential)Steel (simultaneous) Steel (sequential)WC (simultaneous) WC (sequential)

213

Projectile type

Velocity (m.s-1)

Diameter (mm)

Mass (g)

Kinetic energy

(J)

Number of

projecitles

Total energy

(J)

Total momentum (Kg.m.s-1)

Factor increase in momentum (baseline .30

caliber steel projectile)

Steel 442.9 7.92 2.04 200 3 600 2709.3 0.0Alumina 318.6 12.7 3.94 200 3 600 3766.2 1.4

Steel 218.5 12.7 8.38 200 3 600 5492.5 2.0WC 157.7 12.7 16.08 200 3 600 7608.4 2.8

Momentum of the various (.30 and .50 caliber) projeciltes used in the study at a constant incident energy of 200JTable 15.

214

313.6

300.7

323.7

285.9

351

326.8

200

230

260

290

320

350

380

1

Ener

gy a

bsor

ptio

n (J

)

Sequential

Simultaneous

3.94 g 8.38 g 16.08 gFig. 78. .50 caliber simultaneous and sequential impact results comparing energy absorption vs. projectile mass at constant incident energy (~200 J). The error bars indicate standard deviation.

4.1 % 11.7 %

6.9 %

215

Fig. 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. The error bars in the experimental data series indicate standard deviation.

316.5 293.5320.8

302.3357.0

240.8

0

75

150

225

300

375

450

0

New

surf

ace

crea

tion

(cm

2 )

Alumina simultaneous experimental Alumina simultaneous FEASteel simultaneous experimental Steel simultaneous FEAWC simultaneous experimental WC simultaneous FEA

7.3% 32.5%5.8%

216

Fig. 80. Residual velocity of a three .50 caliber projectile simultaneous impact series on three layer laminates with constant incident energy (200 J) comparing the experimental results with the FEA prediction for the 3.9, 8.4, and 16.1 g .50 caliber projectiles. The error bars in the experimental data series indicate standard deviation.

240.9

184.9

139.2 138.4

104.7 112.9

0

50

100

150

200

250

300

1

Res

idua

l vel

ocity

(m. s.1

)

50 caliber alumina simultaneous50 caliber alumina simultaneous FEA50 caliber steel simultaneous50 caliber steel simultaneous FEA50 caliber WC simultaneous50 caliber WC simultaneous FEA

23.2%

0.6%

7.8%

Alumina Steel WC

217

Fig. 81. Experimental vs. FEA prediction of the damage zone for a three projectile (3.91 g) sequential impact series.

Inner delamination

Outer delamination

200 mm

200 mm

25.4 mm

218

Fig. 82. Experimental vs. FEA prediction of the damage zone for a three projectile (3.91 g) simultaneous impact series.

Inner delamination

Outer delamination

200 mm

200 mm

25.4 mm

219


Inner delamination

Outer delamination

200 mm

200 mm

25.4 mm

220


Inner delamination

Outer delamination

200 mm

200 mm

25.4 mm

221


Inner delamination

Outer delamination Outer delamination

200 mm

200 mm

25.4 mm

222


Inner delamination

Outer delamination

200 mm

200 mm

25.4 mm

223

Fig. 87. Modeling results showing the three layer laminate response to sequential impact (kinetic energy transfer) for three .50 caliber (3.94, 8.38, and 16.08 g) projectiles at con-stant incident energy (~200 J).

0

10

20

30

40

50

60

70

80

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Time (ms)

Kin

etic

ene

rgy

(J)

Sequential aluminaSequential steelSequential WC

224

Fig. 88. Modeling results showing the three layer laminate response to simultaneous im-pact (kinetic energy transfer) for three .50 caliber (3.94, 8.38, and 16.08 g) projectiles at constant incident energy (~200 J).

0

20

40

60

80

100

120

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Time (ms)

Kin

etic

ene

rgy

(J)

Simultaneous aluminaSimultaneous steelSimultaneous WC

225

0

20

40

60

80

100

120

0 0.2 0.4 0.6 0.8 1 1.2 1.4Time (ms)

Kin

etic

ene

rgy

(J)

.30 caliber steel sequential

.50 caliber steel sequential

Fig. 89. Modeling results comparing the three layer laminate response to .30 and .50 cali-ber (steel projectile) sequential impact with approximately the same impact velocity, 220 m.s-1.

226

Fig. 90. Modeling results comparing the three layer laminate response to .30 and .50 cali-ber (steel projectile) simultaneous impact with approximately the same impact velocity, 220 m.s-1.

0

20

40

60

80

100

120

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4Time (ms)

Kin

etic

ene

rgy

(J)

.30 caliber steel simultaneous

.50 caliber steel simultaneous

227

54.7

119.3

170.3

120.3 119

52.9

105.5112.3

0

40

80

120

160

200

New

surf

ace

crea

tion

(cm

2 )

Single impactNormalized simultaneous impact

.30 caliber steel

.50 caliber alumina

.50 caliber steel

.50 caliber WC

Fig. 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 num-ber of projectiles.

228

38.4 40.4

100.9 100.290.3

98.7 102.2108.9

0

30

60

90

120

150

Impa

ct e

nerg

y ab

sorb

ed (J

)

Single impactNormalized simultaneous impact

.30 caliber steel

.50 caliber alumina

.50 caliber steel

.50 caliber WC

Fig. 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.

229

SUMMARY AND CONCLUSIONS

A new test apparatus for assessing near-simultaneous and sequential impact with

controlled impact location and velocity was devised using a single-stage light-gas gun.

The barrel configuration was in the shape of an equilateral triangle on a radius of ap-

proximately 20 mm. This allowed the study of primary and secondary yarn interaction

with an impeding projectile.

In the preliminary study, it was found that a difference in energy absorption ex-

isted for carbon/epoxy panels subjected to single projectile impact and near-simultaneous

impact without controlled impact location. In the extended study, S-2 glass/epoxy

specimens were subjected to simultaneous and sequential impact with controlled impact

location and velocity. In the extended study, a total of 78 three and four layer laminates

were subjected to impact by a total of 191 projectiles. The study examined the behavior

of these laminates in terms of new surface creation and impact energy absorption. Impact

experiments were carried out near and above the ballistic limit at constant impact velocity

for the three and four layer laminates with .30 caliber, spherical steel projectiles which

had a mass of 2.04 g. A mass effect study was conducted at constant incident energy of

200 J with .50 caliber, spherical projectiles comprised of alumina, steel, and WC which

had masses of 3.94 g, 8.38 g, and 16.08 g, respectively.

FEA was performed for three projectile, .30 caliber simultaneous and sequential

impact on three layer laminates and for three projectile, .50 caliber simultaneous and se-

quential impact and three layer laminates with alumina, steel, and WC projectiles. The

results compared favorably for the simultaneous impact simulations (new surface creation

230

and energy absorption) but modeling sequential impact proved more difficult. As de-

lamination damage accumulated in the prediction, the material stiffness was reduced and

the laminate offered less resistance to penetration. This is also believed to have affected

the prediction of delamination damage.

All the specimens exhibited a characteristic conical shaped delamination zone

with the delamination closest to the impinging projectile being the smallest and getting

progressively larger toward the distal side of the laminate. Shear-punch failure was not

noted in any of the specimens. For both simultaneous and sequential impact specimens,

there was damage interaction along the primary yarns. This was manifested as an in-

crease in matrix cracking, fiber debonding and fiber pull-out. Similar damage was found

along the primary yarns surrounding the projectile acting along the secondary yarns but

was not as pronounced as the damage along the primary yarns and did not appear to in-

teract significantly with those locations either. There were no quantifiable differences

between the damaged state in either simultaneous or sequential impact aside from degree

of delamination damage in the .30 caliber impact study. An increase in primary yarn

damage and bending artifacts at the clamped edges were seen in the .50 caliber impact

study, particularly for the steel and WC projectiles.

Three .30 caliber projectile sequential impact resulted in an increase in new sur-

face creation and energy absorption compared to three projectile simultaneous impact.

The difference in new surface creation was much more significant than the increase in

energy absorption. Energy dissipation through new surface creation is usually small in

comparison to other mechanisms and is not attributed to the increase in energy absorp-

tion. It is surmised that the delaminations contribute to energy absorption via a change in

231

the material response. As damage accumulates, the specimen becomes more compliant.

This is particularly relevant in a thin laminates. As the specimen becomes more compli-

ant, increasing the contact duration resulting in a decrease in contact stresses and an in-

crease in elastic bending. In the case of simultaneous impact, the impacts appeared to

have acted independently of one another and did not result in significant increases in en-

ergy absorption or new surface creation.

The laminate thickness study indicated that the normalized new surface creation

increased substantially as the number of laminates increased but energy absorption per

laminate was constant for the laminate configurations considered. This reinforces the

idea that delamination is a not likely a large contributor to energy absorption. For both

the three and four layer laminate studies, the change in energy absorption seems to be

dominated by the target response. This was noted in evaluating sequential impact, with

increasing energy absorption with increasing damage state and the change in perforation

mechanisms for a specimen subjected to simultaneous impact where penetration occurred

at an earlier time step than for the first penetration seen in the sequential impact model.

In the .50 caliber mass effect study, the general trends were an increase in delami-

nation damage and energy absorption with increasing projectile mass. The steel projec-

tile results did not always follow the same trends seen in the alumina and WC projectile

studies which correlated well with one another.

The .50 caliber impact study reinforced what was seen in the .30 caliber impact

study; an increase in energy absorption for sequential impact over simultaneous impact.

However, new surface creation was greater for simultaneous impact in the .50 caliber

projectile study; opposite of what occurred in the .30 caliber impact study. This differ-

232

ence is attributed to substantial increases in impact energy, momentum, and the number

of yarns affected by the larger, heavier projectiles imposing greater strain in the speci-

men.

The results indicate that cumulative damage sustained in sequential impact plays a

greater role in the overall target response of thin S-2 glass/epoxy laminates than synergis-

tic events such as stress wave interaction, kinetic energy transfer to the target plate, in-

crease in elastic deformation of the secondary yarns, and damage along the primary

yarns. In near-simultaneous impact, the impact event occurs over such a short time span

that there is not significant time for synergistic events to culminate into a change in the

target response.

233

FUTURE WORK AND RECOMMENDATIONS

Experimental/Instrumentation Recommendations

A new experimental approach was presented which yielded some interesting re-

sults. The most important contribution to the significance of this work would be in data

acquisition. A data acquisition board with a high enough sampling rate and enough

channels to measure individual velocities was not available during the study but would

have been very beneficial in providing insight into material response and energy absorp-

tion characteristics. A minimum of six channels (start/stop) for three projectile velocity

measurements would be required for incident or residual velocity. Since the event occurs

on the order of milliseconds, a sufficient sampling rate is required in order to provide

adequate resolution.

In this experimental program, velocity was measured using photoelectric chrono-

graphs. While they work well for single projectile measurements, they would not be the

best choice for multiple projectile velocity measurements. Multiple projectile velocity

could be measured a number of other ways though. Break wire, passive or active elec-

tromagnetic detectors, or isolated laser beam detectors would work well. Doppler radar

systems have the ability to track multiple projectiles but one would not be able to discern

which projectiles were being tracked. In addition, Doppler radar systems are quite ex-

pensive but they can continuously measure velocity during penetration.

The single most beneficial instrument would be a high speed camera. Like with

the other systems mentioned this was prohibitively expensive in this program but would

have provided valuable insight into failure mechanisms and target response in addition to

234

measuring multiple projectile velocities. The one major limitation in high speed photog-

raphy is providing adequate light on the target or projectiles and limited field of view. As

the frame rate is increased, the shutter speed increases and more light is required to obtain

a clear image. The field of view also decreases significantly as the frame rate is in-

creased. A wide angle lens would have been needed for this study to visualize all the

projectiles in one field.

Alternative Materials/Laminate Schedules

This particular study was limited to thin S-2 glass laminates. Because an optical

NDE technique that was fast, relatively easy, and very inexpensive was used, a very large

amount of data was generated. The thin laminates are of little practical use in terms of

ballistic protection but new insights were gained because of the study. Future work will

include thicker S-2 glass laminates which will be characterized using ultrasonic C-scan.

Also, the response of alternate materials should be investigated, such as carbon, as they

are often subjected to multiple impact loading but fragmentation warheads.

Experimental Variations

One of the major advantages to the experimental setup is that since the projectiles

are sabot assisted, a wide range of sizes and shapes can be accommodated. Moreover, the

projectiles are stable in flight so different projectile shapes can be examined e.g. right

cylinder, ogive, fragment simulating projectile, etc. This is beneficial since actual frag-

ments are rarely an idealized shape such as a sphere, which was used in the present study.

235

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