DEVELOPMENT, CHARACTERIZATION, AND MODELING OF BALLISTIC

IMPACT ON COMPOSITE LAMINATES UNDER COMPRESSIVE PRE-STRESS

by

ERIC KERR-ANDERSON

SELVUM PILLAY, COMMITTEE CHAIR

UDAY VAIDYA

ALAN EBERHARDT

SHANE CATLEDGE

GREGORY THOMPSON

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

2012

Copyright by

ERIC KERR-ANDERSON

2012

iii

DEVELOPMENT, CHARACTERIZATION, AND MODELING OF BALLISTICALLY

IMPACTED COMPOSITE LAMINATES UNDER COMPRESSIVE PRE-STRESS

ERIC KERR-ANDERSON

MATERIALS SCIENCE AND ENGINEERING

ABSTRACT

Structural composite laminates were ballistically impacted while under in-plane com-

pressive pre-stress. Residual properties, damage characterization, and energy absorption

were compared to determine synergistic effects of in-plane compressive pre-stress and

impact velocity. A fixture was developed to apply in-plane compressive loads up to 30

tons to structural composites during an impact event using a single-stage light-gas gun.

Observed failure modes included typical conical delamination, the development of an

impact initiated shear crack (IISC), and the shear failure of a pre-stressed composite due

to impact. It was observed that the compressive failure threshold quadratically decreased

in relation to the impact velocity up to velocities that caused partial penetration. For all

laminates impacted at velocities causing partial or full penetration up to 350 ms-1

, the

failure threshold was consistent and used as an experimental normalization. Samples im-

pacted below 65% of the failure threshold witnessed no significant change in damage

morphology or residual properties when compared to typical conical delamination. Sam-

ples impacted above 65% of the failure threshold witnessed additional damage in the

form of a shear crack extending perpendicular to the applied load from the point of im-

pact. The presence of an IISC reduced the residual properties and even caused failure

upon impact at extreme combinations. Four failure envelopes have been established as:

transient failure, steady state failure, impact initiated shear crack, and conical damage.

Boundaries and empirically based equations for residual compressive strength have been

iv

developed for each envelope with relation to two E-glass/vinyl ester laminate systems.

Many aspects of pre-stressed impact have been individually examined, but there have

been no comprehensive examinations of pre-stressed impact. This research has resulted in

the exploration and characterization of compressively pre-stressed damage for impact

velocities resulting in reflection, partial penetration, and penetration at pre-stress levels

resulting in conical damage, shear cracking, and failure.

Keywords: composite, impact, compression, pre-stress.

v

DEDICATION

To my wife, father, mother, and sister for their constant support and guidance.

vi

ACKNOWLEDGMENTS

This work would not have been possible without the generous support, advice, and

guidance from both Dr. Pillay and Dr. Vaidya. The composites research group at the

University of Alabama at Birmingham has truly become an extended family over the last

four years and will be missed. Thank you to Dr. Foley for her immeasurable help with

understanding photography and image processing. Thank you to Dr. Ning, Dr. That-

taiparthasarthy, and Andy Grabany for their help in equipment training and troubleshoot-

ing. Thank you to Pete Barfknecht, Benjamin Willis, Danila Kaliberov, John Smith, and

Dhruv Bansal for being my sounding board and critiquing this work. Thank you to the

rest of the labmates, staff, and faculty in the Materials Science and Engineering Depart-

ment at the University of Alabama at Birmingham for creating an enjoyable working en-

vironment. And thank you to the work itself, without which I would not have met and

married the love of my life.

vii

TABLE OF CONTENTS

Page

ABSTRACT ....................................................................................................................... iii

DEDICATION .....................................................................................................................v

ACKNOWLEDGMENTS ................................................................................................. vi

LIST OF TABLES ............................................................................................................. ix

LIST OF FIGURES .............................................................................................................x

LIST OF ABBREVIATIONS .......................................................................................... xiii

1. INTRODUCTION ...........................................................................................................1

1.1. In-plane compression of composite laminates ......................................................2

1.2. Impact of woven composite laminates ..................................................................3 1.3. Compression after impact of composite laminates ...............................................5 1.4. Pre-stressed impact of composite laminates .........................................................7

1.5. Objectives ...........................................................................................................11

1.5.1. Aim 1: Design, develop, and implement a novel test fixture and

method to conduct impact studies on composite structures under in-

plane compressive pre-stress. ..................................................................11

1.5.2. Aim 2: Characterize the damage and determine the residual

properties associated with compressively pre-stressed impact of

composite laminates. ...............................................................................11 1.5.3. Aim 3: Define boundaries for failure thresholds and develop a model

for the residual strength based on experimental data obtained with

compressively pre-stressed impact for composite laminates. .................11

2. EXPERIMENTAL APPROACH ..................................................................................12

2.1. Manufacture of samples ......................................................................................12

2.1.1. Materials ...................................................................................................12

2.1.2. Manufacture .............................................................................................12

2.2. Testing .................................................................................................................13

2.2.1. Gas gun testing .........................................................................................13 2.2.2. Compression during impact testing ..........................................................14 2.2.3. Compression after impact testing .............................................................15

2.3. Characterization and analysis..............................................................................15

2.3.1. Tap Testing ..............................................................................................15

viii

2.3.2. Back-lit Photography ...............................................................................15

3. ORGANIZATION OF WORK ......................................................................................17

4. COMPRESSIVELY PRE-STRESSED NAVY RELEVANT LAMINATED AND

SANDWICH COMPOSITES SUBJECTED TO BALLISTIC IMPACT ....................18

4.1. Abstract ...............................................................................................................19 4.2. Introduction .........................................................................................................20 4.3. Impact of Laminated Composites .......................................................................26 4.4. Residual Strength of Laminated Composites ......................................................28 4.5. Strain Rate Sensitivity .........................................................................................30

4.6. Impact Under Pre-Load .......................................................................................31 4.7. CDI Fixture Design .............................................................................................37 4.8. Procedure and Material .......................................................................................39

4.9. Results and Discussion .......................................................................................40 4.10. Conclusion ........................................................................................................51

5. DESIGN AND DEVELOPMENT OF A TEST FIXTURE AND METHOD FOR

INVESTIGATION OF IMPACT DURING PRE-STRESSED COMPRESSION .......59

5.1. Abstract ...............................................................................................................60

5.2. Introduction .........................................................................................................61 5.3. Design of the Compression During Impact Fixture ............................................64 5.4. Materials .............................................................................................................69

5.5. Procedure ............................................................................................................69 5.6. Validation and Discussion ..................................................................................71

5.7. Summary .............................................................................................................79

6. MODELING THE RESIDUAL STRENGTH OF BALLISTICALLY IMPACTED

E-GLASS/VINYL ESTER LAMINATES DURING IN-PLANE COMPRESSIVE

PRE-STRESS ................................................................................................................83

6.1. Abstract ...............................................................................................................84 6.2. Introduction .........................................................................................................85 6.3. Materials .............................................................................................................89

6.4. Procedure ............................................................................................................90 6.5. Results and Discussion .......................................................................................91 6.6. Summary ...........................................................................................................103

7. GLOBAL SUMMARY ................................................................................................108

8. FUTURE WORK .........................................................................................................110

GENERAL REFERENCES .............................................................................................111

ix

LIST OF TABLES

Table Page

MODELING THE RESIDUAL STRENGTH OF BALLISTICALLY IMPACTED E-

GLASS/VINYL ESTER LAMINATES DURING IN-PLANE COMPRESSIVE PRE-

STRESS

1 Experimentally determined boundaries and residual strengths associated

with compressively pre-stressed impact failure envelopes for both 5.4 mm

and 6.0 mm laminates ....................................................................................................95

x

LIST OF FIGURES

Figure Page

COMPRESSIVELY PRE-STRESSED NAVY RELEVANT LAMINATED AND

SANDWICH COMPOSITES SUBJECTED TO BALLISTIC IMPACT

1 Energy Absorbing Failure Modes of Ballistic Impact on Woven

Laminated Composite Structures. ........................................................................21

2 Standard compression after impact (CAI) test; (a, b) sample is impacted,

and (c) impacted sample is compressed to failure. ...............................................24

3 Pre-stressed compression during impact (CDI) test method – (a) pre-

stress is applied; (b) pre-stressed sample is impacted, and (c) impacted

sample is compressed to failure. ...........................................................................25

4&5 Pre-Stressed Impact Damage Area of Experimental (Left) Compared with

the Finite Element Analysis (Right). ....................................................................31

6&7 Gas Gun (a) and Capture Chamber (b). ................................................................37

8 CDI Fixture. A: Vertical Support Bars B: Hydraulic Cylinder C: Load

Transfer Block D: Sample E: Front and Back Support Plates F: Top and

Bottom Support Bars. ...........................................................................................38

9 Side view of CDI fixture - C: load transfer block D: sample, E: front and

back support plates, F: bottom support bar, and G: inner slip-fit support

plates. ....................................................................................................................39

10 Effect of compressive pre-stress on residual strength after impact. .....................40

11 Effect of pre-stress on residual strength after an impact (regression line

comparison). .........................................................................................................42

12&13 Development of a front face crack due to high pre-stress. (Left) displays a

typical conical delamination zone; (Right) shows a developing conical

delamination zone with the addition of an IISC on the Front Face. .....................43

14 Evolution of damage from increased compressive pre-stress during

ballistic impact......................................................................................................44

xi

15 Effect of front face IISC length on residual strength. ..........................................45

16 Effect of compression and impact on failure mode type. .....................................46

17 Failure threshold envelopes for safe design. ........................................................46

18 Synergistic effect of compression and impact on the residual compressive

strength of damaged GFRP. .................................................................................47

19 Penetration chart for 100 mm x 150 mm (4” x 6”) samples based on pre-

stress and impact velocity. ....................................................................................48

20 Comparison of the failure threshold envelopes for various laminate

configurations. ......................................................................................................49

21 Damage evolution effect of laminate configuration. ............................................50

DESIGN AND DEVELOPMENT OF A TEST FIXTURE AND METHOD FOR

INVESTIGATION OF IMPACT DURING PRE-STRESSED COMPRESSION

1&2 Gas Gun (a) and Capture Chamber (b). ................................................................65

3&4 Pro-E Model of CDI Fixture (Left). A: Vertical Support Bars B:

Hydraulic Cylinder C: Load Transfer Block D: Sample E: Front and Back

Support Plates F: Top and Bottom Support Bars. Actual Fixture (Right)............66

5 Internal Side view of CDI fixture - C: Load Transfer Block, D: Sample,

E: Front and Back Support Plates, F: Bottom Support Bar, and G: Internal

Support Plates. ......................................................................................................67

6 Bottom Bar Assembly - D: Sample, F: Bottom Support Bar, H: Contact

Plate, I: Barrel Pins. ..............................................................................................68

7&8 Typical Conical Deformation (Left) and IISC (Right) Caused by

Compressively Pre-Stressed Impact. ....................................................................71

9 Example of Damage Resulting from Partial Edge Loading – Damage

Indicates Significant Flexure in Bottom Support Bar or Non-square

Sample Dimensions. .............................................................................................72

10 Damage Evolution Resulting from the Synergistic Effect of Pre-Stress

and Impact Velocity. ............................................................................................73

11 Transducer Load Data during the CDI Test and Comparison of Damage

Evolution. The point of impact is denoted by a star for each load path. ..............75

xii

12 Failure Thresholds for 5.4 mm Thick EGVE Woven Laminates Impacted

During Compressive Pre-Stress. ...........................................................................76

13 Penetration Thresholds for 5.4 mm thick glass/vinyl ester Woven

Laminates Impacted During Compressive Pre-Stress. .........................................77

14 The Residual Compressive Strength using CAI Fixture for 5.4 mm thick

glass/vinyl ester Woven Laminates Impacted Under Compressive Pre-

Stress.....................................................................................................................78

MODELING THE RESIDUAL STRENGTH OF BALLISTICALLY IMPACTED E-

GLASS/VINYL ESTER LAMINATES DURING IN-PLANE COMPRESSIVE PRE-

STRESS

1&2 Failure threshold and ballistic limit for 5.4 mm glass/vinyl ester laminate. ........91

3 Normalized failure modes for both 5.4 mm and 6.0 mm laminates. ....................92

4 Failure/penetration thresholds for 5.4 mm laminate. ............................................93

5 Reduced failure envelopes for 5.4 mm thick laminate .........................................94

6 Formulation of the failure threshold boundary for both 5.4 mm and 6.0

mm thick laminates...............................................................................................96

7 Pressure transducer loading paths for 5.4 mm thick laminates comparing

load drop due to impact (denoted by star) and failure mode. ...............................97

8 Exponential relationship between the normalized residual strength and

the normalized change of pre-stressed energy factor. ..........................................98

9 Comparison of normalized kinetic energy and the change in normalized

pre-stressed energy factor in terms of the normalized compressive pre-

stress. ....................................................................................................................99

10 Comparison of the slopes of the linear regressions determined in Figure 9

with each respective average normalized compressive pre-stress. .....................100

11 Correlation of predictive model to experimental residual strength for both

5.4 mm and 6.0 mm laminates. ...........................................................................101

12 Conical damage comparison of residual compressive strength and

normalized kinetic energy for each laminate thickness. .....................................102

xiii

LIST OF ABBREVIATIONS

CAI Compression After Impact

CDI Compression During Impact

CFRP Carbon Fiber Reinforced Polymer

CLC Combined Loaded Compression

FAI Flexural After Impact

FEA Finite Element Analysis

FRP Fiber Reinforced Polymer

GFRP Glass Fiber Reinforced Polymer

HPI Hypervelocity Impact

HVI High Velocity Impact

IISC Impact Initiated Shear Crack

IVI Intermediate Velocity Impact

LVI Low Velocity Impact

PVC Polyvinyl Chloride

TAI Tension After Impact

UCS Ultimate Compression Strength

VARTM Vacuum Assisted Resin Transfer Molding

VE Vinyl Ester

1

1. INTRODUCTION

Composite structures continue to replace steel structures on naval vessels in order

to create lighter and often, more cost effective structures. Fiberglass offers operational

accessibility that steel and aluminum cannot compete against, due to the near elimination

of maintenance costs. Steel naval vessels must undergo extensive inspection and mainte-

nance regiments each year while in a corrosive marine environment. Attempts have been

made to reduce the weight of some steel naval vessels by replacing steel components with

aluminum, which resulted in costly maintenance and replacement. The high cyclical

swaying loading provided by ocean waves caused severe stress corrosion to develop in

the aluminum structures [1]. Large cracks formed over short periods of time which re-

sulted in fracture. An additional drawback of aluminum has been the drastic loss of struc-

tural strength during fires. Fiberglass naval vessels have been widely used as mine coun-

termeasure vessels in which typical construction methods included the use of a framed

single skin design, an unframed monocoque design, and a sandwich hull utilizing a thick

polyvinyl chloride (PVC) foam core. The 73 m long Visby class corvette was the first

naval ship to incorporate large amounts of carbon fiber into its hull which is comprised of

a hybrid carbon and glass fiber polymer laminate covering a PVC foam core [1]. Some

designs range in weight savings between 20% - 60%. The reduction of weight allows for

better performance in the form of speed or reduced fuel consumption. The reduction of

weight also provides additional cargo or payload capacity. Other benefits include radar

and magnetic transparency, yielding stealthier ships less susceptible to prevalent magnet-

2

ic mine attacks [1]. A comprehensive understanding is required to establish optimal

weight savings in terms of damage caused by blast waves, ballistic impact, and fire. This

study examined the synergistic effect of compressive pre-stress and impact to determine

the effect of impact on load bearing structures.

1.1. In-plane compression of composite laminates

The in-plane compression of composite materials has been thoroughly researched

[2-8] , but simple predictive models have yet to be found. Current models for predicting

the compressive strength of composites either over predict compressive strength or re-

quire difficult to attain properties such as initial fiber waviness or interface properties [2-

7]. There is a general consensus of failure modes observed for in-plane compressive

strength being: Euler buckling, bifurcation, and shear cracking [2, 6-9]. Euler buckling

results when the second moment of inertia is too low for the applied in-plane compressive

load and the critical buckling curvature is exceeded, resulting in failure. Euler buckling is

applicable for all materials. Bifurcation is unique to composite laminates because it is

caused when the bonding strength between layers is exceeded prior to global buckling

and shear cracking. Bifurcation typically occurs near the central plane of the laminate and

is associated with laminates greater than 25 mm thick, sandwich composites, or low vol-

ume fraction (< 20%) unidirectional composites [9]. The shear cracking witnessed in

compressive failure is primarily due to the polymer matrix which binds fibers together

and transfers load from one fiber to another. As the fibers are axially loaded, they begin

to buckle at wavelengths associated with their modulus and diameter. Fiber buckling does

not actually occur until the out-of-axis load transferred from fiber to the supporting ma-

trix exceeds the matrix yield strength. Fibers are forced past the buckling curvature and

3

fracture when the matrix begins to yield. The fiber diameter variance associated with

production causes larger fibers to fail under less curvature than smaller fibers. The load,

which was supported by the fractured fibers, is transferred to the remaining fibers. The

fiber failure process continues as more load is applied until a critical point is reached

where the remaining fibers in the laminate are insufficient to support the applied load.

When this critical point is reached, compressive failure of the laminate results in the form

of a shear band. Mixed failure modes can occur depending on the strengths of each re-

spective failure mode. Some of the test methods used to characterize compressive

strength of composite materials have included ring compression, tube compression, com-

bined loaded compression (CLC) [10], Celanese compression, and IITRI compression [6,

7]. The failure strengths and failure modes are highly dependent on the constraints used

for testing. Span-to-thickness ratios have been used as comparison methods for buckling

strength [11, 12]. Dow and Rosen [2] created the first models to predict the compressive

strength of unidirectional composites using a beam on an elastic foundation. Lo and Chim

[7] improved on the original models by including the shear modulus. Dharan and Lin [5]

further improved the models by incorporating the interphase and modeling the unidirec-

tional composite as a three-part system. Lamina Theory and Timoshenko Plate Theory

have been used to predict the compressive strength of woven laminated composites [9].

Compressive strengths are typically normalized with respect to the critical buckling load

as a means of comparison between material type and constraint scenario [13-19].

1.2. Impact of woven composite laminates

The study of impact on composite materials is a very broad and complicated field.

The well-defined impact regimes for laminated composites are low velocity impact

4

(LVI), intermediate velocity impact (IVI), high velocity impact (HVI), and hyper velocity

impact (HPI) [20-22]. LVI covers the broadest forms of impact usually involving a large

mass impacting at relatively low velocities (<10 ms-1

). LVI events represent accidental

tool drops, cargo falling, or other non-static loading scenario. IVI events typically occur

between 10-100 ms-1

which range from rock debris to lower energy fragments. HVI or

ballistic impact typically involves small mass projectiles traveling at high velocities

(>100 ms-1

). HVI events include ballistic, fragment, shrapnel, and debris impact [23].

HPI represents small mass meteorites impacting at velocities in excess of 2000 ms-1

. This

paper focuses on the IVI and HVI regimes for an orthotropic woven laminate impacted

with a 7.62 mm diameter steel sphere weighing 2 g.

Transverse impact of woven laminated orthotropic composites is a strain rate de-

pendent event. When subjected to transverse loads at low strain rates, fibers will flex and

absorb energy; but at high strain rates, fibers will shear [24]. Cantwell and Morton [24]

demonstrated that low velocity impact caused surface damage at the point of impact

which increased radially as an effect of impact energy until perforation. Perforation re-

sulted in the formation of a 45° frustum-shaped fracture zone. Naik et al [25] suggested

that the energy absorption modes may include the kinetic energy of the displaced frus-

tum, secondary yarn deformation, tensile failure, delamination, and matrix cracking. Ha-

zell et al [26] showed that there is no significant difference in damage area when impact-

ed at velocities above the penetration threshold (up to 1875 ms-1

). Testing has indicated

that there exists a low velocity impact threshold which causes no damage followed by a

radially increasing damage area with additional impact energy up to the point of perfora-

tion after which minimal changes in damage area occur [26-28]. The consistency of the

5

damage area in terms of impact energy across many material types shows that damage

area results could be normalized in terms of the ballistic velocity.

1.3. Compression after impact of composite laminates

The residual strength after impact damage is of great interest to design engineers.

Prior studies have investigated tension after impact, compression after impact (CAI), and

flexure after impact for various composite systems [9, 20]. Impact damage has been

found to have the most dramatic effect for CAI testing due to crack initiation and reduc-

tion in cross-sectional area. Several fixtures and test methods have been developed by

NASA [29], Boeing [30], and Airbus [31] to characterize the CAI strength. The initial

test method and fixture designed by NASA to characterize the effect of LVI damage from

tool drops requires 6.35 mm thick samples 178 mm wide by 254-318 mm long. Samples

are trimmed to a 127 mm width after impact and compressed to failure using a fixture

which simply supports all sample edges while maintaining in-plane compression. Boeing

created a smaller fixture which requires a sample size of only 102 mm wide by 152 mm

long and a variable thickness of 4-6 mm. The Boeing fixture and test method have been

adopted as ASTM D7137 [30] and is one of the most common fixtures for CAI testing.

The design of the ASTM fixture allows for a wide range of flexibility to accommodate

many sample sizes and is relatively easy to remove/install samples. In addition to the

ASTM standardized fixture, Boeing has developed additional fixtures to accommodate

larger samples of up to 267 mm x 267 mm and also with longer dimensions, as much as

102 mm wide by 432 mm long to examine multiple buckling waves. The Airbus CAI

fixture [31] was developed to determine CAI strength with the clamped condition on top

6

and bottom of the damaged laminate. The Airbus CAI fixture also accounts for fixture

alignment but does not accommodate samples other than 152 mm x 102 mm x 4 mm.

There have been numerous studies on the residual compressive strength after im-

pact of composite laminates, because impact damage can reduce the residual compressive

strength to as low as one-tenth the ultimate strength for carbon/epoxy and one-third for E-

glass/epoxy laminates. Several authors have shown that decrease in compressive strength

is directly correlated to the impact damage area. Since the impact damage area is highest

at the ballistic limit, the compressive strength decreases as a function of impact velocity,

and reaches an asymptotic value at the ballistic limit. CAI samples are first impacted

which forms the frustum shaped damage area associated with non-pre-stressed impact.

The impact damage causes a stress concentration to form with the applied compressive

load at the edge of the delaminated area perpendicular to the applied load. It has been

shown that a linear elastic fracture mechanics approach can be used to determine limiting

loads that cause crack growth [20, 32]. Shear cracks propagate outward from the point of

impact quickly to the edge of the delaminated area, then slowly continue to propagate

until catastrophic failure occurs. Gillespie Jr. et al [33] showed that stitching of sandwich

panels and cross-ply laminates created marginal improvements in the CAI strength. Zhou

et al [34, 35] examined preconditioned laminates with embedded films to replicate de-

lamination damage. Oval, rectangular, and circular delaminations were created at multi-

ple locations through the thickness of the laminate. Comparisons were made between

open hole, impact damaged and preconditioned residual compressive strengths.

Several authors have researched the CAI strength of sandwich composites, where

several additional failure modes occur associated with the core. Williams et al [36] used a

7

modified CAI fixture and CFRP laminates containing hollow glass fibers filled with un-

cured resin. Samples were impacted, subjected to a curing cycle to heal the damaged ar-

ea, and residual strengths were obtained using a CAI test. The study concluded that an

impacted laminate could retain a majority of its original strength via this method. Aoki et

al [37] showed that hygrothermal conditions can drastically affect the CAI strength. The

wet samples had a lower Tg than dry samples, and when CAI was conducted above the Tg

of the matrix, compressive properties dramatically decreased. This study indicated that

the yield strength of the matrix has a dominant effect on the compressive strength of a

laminate.

1.4. Pre-stressed impact of composite laminates

Few studies have been conducted on the comparison of CAI results to compres-

sively pre-stressed impact [14, 17, 38-42]. Most of these studies utilized a compression

fixture similar to the ASTM CAI test in which the top and bottom of the sample were

clamped while the sides were simply supported on both sides with a knife edge. Herzl

Chai [38] used Devcon™ adhesive to fix both top and bottom for both the smaller 203

mm x 102 mm x 6 mm and larger 254 mm x 152 mm x 6 mm graphite/epoxy samples

which were tested. The compressive load was applied using a hydraulic testing machine.

McGowan and Ambur [39] examined both dropped weight and air gun impact of com-

pressively pre-stressed 127 mm x 254 mm x 16 mm sandwich composites made from

AS4/8552 graphite/epoxy pre-impregnated tape and cloth with a Korex™ honeycomb

core. All sandwich panels were potted to ensure minimal fiber brooming and loaded us-

ing a hydraulic testing machine. Zhang et al [14] applied in-plane compressive loads to

T800/924 carbon/epoxy laminates with a hydraulic jack. Samples were pre-stressed prior

8

to LVI testing. Herszberg and Weller [17] compressively pre-stressed both stitched and

unstitched T300 carbon/epoxy laminates with dimensions of 145 mm x 145 mm x 2 mm

and impacted the buckled samples on the convex and concave faces with a gas gun.

Wiedenman and Dharan [40] manufactured woven G10/epoxy fiberglass samples of 102

mm x 152 mm and thickness ranging from 1.6 - 6.4 mm. Samples were compressively

pre-stressed using a Boeing CAI fixture with a portable hydraulic press, and a civilian

M4 carbine was used to fire standard 5.56 mm ammunition. Heimbs et al [41] investigat-

ed three layups of tabbed carbon/epoxy laminates in which the 400 mm x 150 mm x 3

mm samples were pre-stressed in compression and impacted with a drop tower. Pickett et

al [42] compressively pre-stressed 600 mm x 200 mm x 4.2 mm tabbed carbon/epoxy

laminates prior to drop tower impact. Pickett et al did not use a knife edge support on

both longitudinal sides of the laminates, instead they opted to use a sample lateral back

face support.

Pre-stressed impact testing and analysis has shown that impact response is highly

dependent on the direction and magnitude of in-plane pre-stress. Tensile pre-stress results

in a higher peak stress and a shorter contact duration, while compressive pre-stress results

in lower peak stress and a longer contact duration [16, 43-48]. Experimental results have

shown that impact on composite laminates at high compressive or tensile pre-stress re-

sulted in failure perpendicular to the applied load while low levels of pre-stress caused no

discernible difference from CAI test damage [14, 16, 17, 27, 38-43, 49-52]. Herszberg

and Weller [17] showed that there was little to no effect on the ballistic limit for com-

pressively pre-stressed impact on both the concave and convex faces. Herszberg and

Weller [17] and Chai [38] both examined the ballistic impact of compressively pre-

9

stressed laminates and observed a transient failure threshold. Chai [38] and McGowan

and Ambur [39] observed the reduction of residual strength when pre-stressed with sig-

nificant compression.

The constitutive analysis of pre-stressed impact has been approached from several

directions. Sun and Chattopadhyay [47] used a normalized contact force and plate theory

to numerically analyze the pre-stressed condition. Zhou [35] and Zhou and Rivera [34]

preconditioned laminates with embedded shapes to replicate the residual strength of de-

lamination or open hole damage using fracture mechanic methods. Mikkor et al [28] uti-

lized PAM-CRASH finite element analysis to examine pre-stressed impact. Rossikhin

and Shitikova [45, 46] analyzed the behavior of the transient waves generated due to

shock impact for a pre-stressed circular plate and rod impact on a pre-stressed rectangular

plates which propagate along the median surfaces as diverging circles. Khalili et al [53]

used Sveklo’s elastic contact theory for anisotropic bodies to analyze the pre-stressed

impact of unidirectional graphite/epoxy composites in tension for both longitudinal and

transverse directions. Zheng and Bienda [48] analyzed the impact response using a Fouri-

er series expansion and Laplace transform technique by incorporating shear deformation

and permanent deformation for pre-stressed impact. Choi [15] and Choi et al [43] used a

modified displacement field based to create a finite element modeling code to determine

the impact response on pre-stressed laminates. Heimbs et al [41] utilized LS-DYNA’s

‘stacked shell’ model which allows for the definition of delamination energy release rates

to account for the impact damage caused in a pre-stressed condition. Ghelli and Minak

[16] utilized a Fortran program to simulate the LVI response of pre-stressed laminates in

terms of span-to-thickness ratios. Loktev [44] used Uflyand – Mindlin equations and a

10

series expansion based on a Legendre polynomial and Laurent series to examine the ten-

sile pre-stressed impact of composite laminates. Chai [38] utilized moire interferometry

and a high-speed camera to experimentally measure the damage growth rates of compres-

sively pre-stressed impact for carbon / epoxy laminates. Measurements were used to de-

fine the energy release rates for the defined empirical model.

This study expands on the fields examined by previous researchers, defines ob-

served failure thresholds, and outlines empirical formulas derived from experimental da-

ta. It is of critical importance to design composite vehicles and infrastructure that will

safely support a designated load after an impact event. Experimentally based models have

been developed to characterize the residual compressive strength of a laminate subjected

to pre-stressed impact as a means to safely design load bearing composite structures.

11

1.5. Objectives

1.5.1. Aim 1: Design, develop, and implement a novel test fixture and method to conduct

impact studies on composite structures under in-plane compressive pre-stress.

1.5.2. Aim 2: Characterize the damage and determine the residual properties associated

with compressively pre-stressed impact of composite laminates.

1.5.3. Aim 3: Define boundaries for failure thresholds and develop a model for the re-

sidual strength based on experimental data obtained with compressively pre-

stressed impact for composite laminates.

12

2. EXPERIMENTAL APPROACH

2.1. Manufacture of samples

2.1.1. Materials

Economical E-glass fabric has become the industry standard. A 24 oz/yd2 Compo-

sitesOne fabric with fiber diameter of 16µm and a 24k tow, Fiber Glass Industries (FGI)

Rovcloth® 3273, and Rovcloth® 2454 basket woven E-glass fabrics were used in this

research. Derakane 510A-40 vinyl ester resin was used to manufacture all laminates. The

catalyst was Trigonox, the inhibitor was CoNapthalate, and the accelerant was Acetyl

Acetone. A HP 130 divinyl cell foam core was utilized for the sandwich panels. Samples

tested included 6.0 mm thick woven orthotropic E-glass/VE laminates, 5.4 mm thick wo-

ven orthotropic E-glass/VE laminates, 4.2 mm thick woven orthotropic E-glass/VE lami-

nates, 6.2 mm thick quasi-isotropic E-glass/VE laminates, sandwich panels made of 3.1

mm thick quasi-isotropic E-glass/VE face sheets with a 50.8 mm thick, and 3.4 mm thick

orthotropic carbon fiber/VE laminates.

2.1.2. Manufacture

Samples were made via a vacuum assisted resin transfer molding (VARTM) pro-

cess. The VARTM process utilizes a vacuum to compress the fabric to a desired tool

shape, draw resin thru the fabric, and maintain pressure on the part while the resin cures.

13

It is a cost effective method to create complex geometry composites with one tool surface

and high fiber volume fractions.

VARTM panels were cut and machined to 4” x 6” rectangular plates for CDI test-

ing. The top and bottom surfaces were milled perpendicular to the warp fibers in the

length direction. The top and bottom surfaces were milled parallel and square to reduce

the amount of misalignment stress concentrations.

2.2. Testing

2.2.1. Gas gun testing

The single-stage light-gas gun testing apparatus at the University of Alabama at

Birmingham (UAB) utilizes a capture chamber with dimensions of 2.18 m long, 0.30 m

wide, and 0.36 m tall to house samples between 127 x127 mm to 254 x 254 mm in fully

clamped edge conditions. The projectile velocity is measured by a set of Oehler Model 35

proof chronographs before and after impact. Measurements from the chronographs are

obstructed if a fixture assembly thicker than 100 mm is used. Deflection plates and pro-

jectile capturing media is used to contain the projectile after impact. Pressurized helium is

released to propel a projectile seated in a foam sabot down a 4.6 m barrel striking the

sabot stripper. The sabot stripper is a steel plate with a centrally located hole large

enough for the projectile to pass through the plate when the foam sabot strikes the plate

and is broken up [54].

14

2.2.2. Compression during impact testing

The CDI fixture is mounted in the capture chamber between the sets of chrono-

graphs. The front internal support of the CDI fixture is initially set based on the sample

thickness to provide a vertical support for the centered sample. The sample is centered in

the fixture along the width direction and the back internal support is tightened to contact

the sample surface. A properly secured sample has a slip fit, in which it is constrained

out-of-plane but still allowed to easily move in-plane with the applied load. A slip fit is

important because if the sample is clamped in place, compression will only be applied to

the top most part of the sample, causing an invalid test. A strain gage should be mounted

on each sample, central to the width of the sample and at the bottom of the unconstrained

sample area, to verify pre-stress level and any concave/convex curvature.

After the sample is properly secured, the transfer block is inserted into the guide

rails and placed on top of the sample. Similar to the CAI test, the clamping plates on the

transfer block are butted up against the sample and tightened in place to prevent end

brooming during compression. Top shields are placed and secured, and the hydraulic

head is slid into position to apply in-plane compression to the sample.

Data acquisition was initiated at two readings per second for the hydraulic trans-

ducer, and the sample is compressed to the desired gauge pressure. The samples were

allowed to relax for at least 60 seconds before impact testing to allow for sample relaxa-

tion and a uniform stress field to develop. The additional relaxation time more closely

simulates service loading conditions for structural composites. The gas gun is used to

impact samples with a 7.6 mm spherical stainless steel impactor at a velocity range of 50

- 350 ms-1

. After impact, hydraulic pressure is released and data acquisition is terminated.

15

2.2.3. Compression after impact testing

A SATEC model TC-55 load frame was used to compress impacted plates to fail-

ure in a CAI fixture [30]. The CAI fixture provides a clamped end condition on the top

and bottom of the sample to prevent fiber brooming. The sample sides are simply sup-

ported with a knife-edge to allow uniform compression and bending to develop.

2.3. Characterization and analysis

2.3.1. Tap Testing

Samples were initially measured to ensure that the top and bottom surfaces were

flat, square, and parallel. A WichiTechTM

Digital Tap Hammer was utilized to ensure

consistent machined sample quality. Tap testing is a nondestructive evaluation method

which measures the response of the material tapped with the hammer. Sensors mounted

in the head of the hammer measures the time for the pressure wave from impact to reflect

back to the hammer [9]. A fast response time indicates no damage, and a slow response

time indicates damage.

2.3.2. Back-lit Photography

With the correct exposure time, back lit photography [54] is a method which can

be used to determine internal damage in translucent media such as the glass/vinyl ester

laminate used in this study. Light transferred through the laminate is impeded by dam-

aged areas and is observed as a darker region. As more damage is witnessed through the

thickness, the resulting area will become darker. Diffuse, high-intensity lighting is used

in both thru-transmission and back-scatter modes to capture the delamination and surface

16

damage of both sides of the fiberglass samples. Front face delamination area, back face

delamination area, and the IISC length are measured and recorded. All photographic

analysis was conducted using the ImagePro Plus 6.0 software package. This method of

non-destructive evaluation was used before impact to ensure tow alignment and sample

quality, and after impact to characterize damage.

17

3. ORGANIZATION OF WORK

The focus of this study was to ascertain the effect of impact on a composite lami-

nate under in-plane pre-stressed compression. The experimental and analytical results

accompanied by discussions for each objective of the study are organized into three inter-

connected manuscripts; each one builds from the other and is consistent with the objec-

tives of the entire study. Manuscript 1 provides a thorough literature review of the subject

of pre-stressed impact and shows how material response changes due to laminate thick-

ness, material type, and material construction. Manuscript 2 outlines the compression

during impact (CDI) fixture design and test procedure, which provides a standard method

for future comparison. Maunscript 3 explores the experimental modeling of residual

compressive strength after impact for the four distinct failure zones.

18

COMPRESSIVELY PRE-STRESSED NAVY RELEVANT LAMINATED AND

SANDWICH COMPOSITES SUBJECTED TO BALLISTIC IMPACT

by

Eric Kerr-Anderson

Dr. Uday Vaidya

Dr. Selvum Pillay

Dr. Basir Shafiq

Submitted to Dynamic Failure of Composites and Sandwich Structures

ONR Special Issue Book Chapter

Copyright

2012

by

Elsevier

Format adapted for dissertation

19

4. COMPRESSIVELY PRE-STRESSED NAVY RELEVANT LAMINATED AND

SANDWICH COMPOSITES SUBJECTED TO BALLISTIC IMPACT

4.1. Abstract

Assembled structures such as ship decks, walls, and masts are oftentimes under

different degrees of pre-stress or confinement. Structural composite integrity can be com-

promised when subjected to impacts from events such as wave slamming, tool drops,

cargo handling, and ballistic fragments/projectiles. It has been shown by several re-

searchers that when a highly pre-stressed structure is subjected to impact, the damaged

area and impact response changes. The main focus of this study was the impact of com-

pressively pre-stressed structures which can also be considered as compression-during-

impact. The results showed that for various laminate configurations, there was a com-

pressive pre-stress threshold above which impact damage caused more damage than wit-

nessed in typical compression after impact (CAI) tests. Both fiberglass and carbon lami-

nates pre-stressed to higher than 30% of ultimate compressive strength, failed from im-

pact at 300 ms-1

; but the carbon laminates developed shear cracks above 10% of the ulti-

mate compressive strength. The work is of benefit to naval and other composite designers

to be able to account for failure envelopes under complex dynamic loading states, i.e.

pre-stress and impact for various composite configurations.

20

4.2. Introduction

Composite structures continue to replace steel structures on naval vessels in order

to create lighter and often more cost-effective structures. Fiberglass offers operational

accessibility that steel and aluminum cannot compete with due to the near elimination of

maintenance costs. Steel naval vessels must undergo extensive inspection and mainte-

nance regiments each year while in a corrosive marine environment. Attempts have been

made to reduce the weight of some steel naval vessels by replacing steel components with

aluminum, which resulted in costly maintenance and replacement. The high cyclical

swaying loading provided by ocean waves caused severe stress corrosion to develop in

the aluminum structures. Large cracks formed over short periods of time which resulted

in fracture. An additional drawback of aluminum has been the drastic structural strength

loss during fires. Fiberglass naval vessels have been widely used as mine countermeasure

vessels in which typical construction methods included the use of a framed single skin

design, an unframed monocoque design, and a sandwich hull utilizing a thick polyvinyl

chloride (PVC) foam core. The 73 m long Visby class corvette was the first naval ship to

incorporate large amounts of carbon fiber into its hull which is comprised of a hybrid

carbon and glass fiber polymer laminate covering a PVC foam core. Some designs range

in weight savings between 20% - 60%. The reduction of weight allows for better perfor-

mance in the form of speed or reduced fuel consumption. The reduction of weight also

provides additional cargo or payload capacity. Other benefits include radar and magnetic

transparency, yielding stealthier ships less susceptible to prevalent magnetic mine attacks

[1]. A comprehensive understanding is required to establish optimal weight savings in

terms of damage caused by blast waves, ballistic impact, and fire. This study examined

21

the synergistic effect of compressive pre-stress and impact to determine if load-bearing

structures would be able to withstand ballistic impact.

Laminated and sandwich composites are susceptible to impact damage from

events such as tool drops, wave impacts, bullets/fragments, and log debris strikes to name

a few [1-3]. The impact damage typically follows a conical profile illustrated in Figure 1

primarily in the form of matrix cracking, fiber breakage and delamination in a laminated

composite.

Figure 1. Energy Absorbing Failure Modes of Ballistic Impact on Woven Laminated

Composite Structures.

The well-defined impact regimes for laminated composites are low velocity im-

pact (LVI), intermediate velocity impact (IVI), high velocity impact (HVI), and hyper

velocity impact (HPI) [2-4]. LVI covers the broadest forms of impact usually involving a

large mass (1-10kg) impacting at relatively low velocities (<10 ms-1

). LVI events repre-

sent accidental tool drops, cargo falling, or other non-static loading scenario. IVI events

typically occur between 10-100 ms-1

which range from rock debris to lower energy frag-

ments. HVI or ballistic impact typically involves small mass projectiles, such as a 2g 7.62

mm diameter steel sphere, traveling at high velocities (>100 ms-1

). HVI events include

22

ballistic impacts, fragment, shrapnel, and debris impact [5]. HPI represents small mass

meteorites impacting at velocities in excess of 2000 ms-1

. The differences between the

four classes are based on impact velocity, mass, and contact area which translates into

imparted strain and momentum exchange deformation.

For a normal impact event with constant mass and contact area, the impact force,

damage evolution, resultant strains and stresses of the target laminate are highly depend-

ent on the impactor velocity. LVI to a laminate may cause out-of-plane deflection, but

minimal fiber breakage. Most damage in this mode is in the form of matrix shearing be-

tween lamina, i.e. delamination. As the impact velocity increases, the delaminated area

extends outward in a conical shape from the point of impact through the thickness to the

distal face and fiber breakage may be more prevalent. The lowest velocity at which the

entire thickness delaminates and the projectile penetrates the laminate is called the ballis-

tic limit or V50. As the velocity is increased further, the initial layers of material begin to

shear and delamination begins afterwards, which in effect shifts the conically shaped de-

lamination zone to an inverse funnel. If the laminate is sufficiently rigid, a high enough

impact velocity causes a shear plug, leaving a relatively clean hole with little or no de-

lamination [2-4]. It has also been observed that the conical delamination angle for a glob-

ally rigid laminate is much less than that of a somewhat flexible laminate.

Compression-after-Impact (CAI) is one of the standard test methods to determine

residual strength after impact [6-8]. It is a means to determine the compressive strength

after an impact event. There have been three main CAI fixtures developed by NASA,

Boeing, and Airbus. The NASA CAI test utilizes a sample with dimensions 10-12.5 in x

7 in x 0.25 in for low velocity impact after which the sample is trimmed to 10-12.5 in x 5

23

in x 0.25 in for compression testing [6]. The NASA fixture has no accommodation for

thickness variation and uses a large amount of material. The Boeing fixture, which has

been adopted as ASTM D 7137 [7], requires test samples 6 in long by 4 in wide and a

thickness between 4-6 mm. The Boeing test fixture allows the most sample dimension

flexibility as the thickness can be adjusted, but it provides only a simply supported con-

tact on all edges. The side supports have a knife edge support to allow bending while the

top and bottom clamps are square to prevent brooming. The top and bottom supports are

not clamped but press fit at best. The Airbus CAI fixture utilizes a sample with dimen-

sions 6 in x 4 in x 4 mm and allows for a fully clamped top and bottom while providing a

simply supported side constraint. There is no accommodation for thickness variation, but

the Airbus fixture does incorporate the top support into the main fixture to force align-

ment, which is not accounted for with the Boeing CAI fixture. Additionally, there have

been some scaled up versions of the Boeing CAI test fixture to accommodate samples up

to 10.5 x 10.5 in and with longer aspect ratios as much as 17 x 4 in [8]. All CAI data in

this study was obtained using a CAI fixture consistent with ASTM D 7137 specifications.

The samples are large enough to account for the damage area caused by the impact event,

the sides of the sample are simply supported, and the ends are supported to prevent

brooming. Figure 2 below illustrates the process of obtaining a CAI test result.

24

Figure 2. Standard compression after impact (CAI) test; (a, b) sample is impacted, and (c)

impacted sample is compressed to failure.

With the CAI test method, samples are impacted (Figure 2a & b) and compressed

to failure in a CAI fixture (Figure 2c). Since no in-plane load is applied until after the

impact event, no synergistic effects between impact and compression can be extrapolated

from the CAI test. However, structural components are under pre-load during an impact

event, which is the reason for observation of pre-stress effects during impact.

Assembled structures such as ship decks and walls are oftentimes under different

degrees of compression pre-stress or confinement [9]. When a pre-stressed structure is

subjected to impact, this condition can be considered as compression-during-impact

(CDI). Although this is a more complex test to conduct, the results are more representa-

tive of in-field condition. Figure 3 shows the difference between CAI and CDI.

25

Figure 3. Pre-stressed compression during impact (CDI) test method – (a) pre-stress is

applied; (b) pre-stressed sample is impacted, and (c) impacted sample is compressed to

failure.

CDI testing involves compressing a sample prior to impact (Figure 3a), impacting

the sample (Figure 3b), and compressing the damaged sample to failure in the CAI fix-

ture (Figure 3c). For both methods, step (c) is the same.

Since structural composite materials are susceptible to impact events, it is im-

portant for design purposes to characterize the extent of damage caused by impact. Naval

designers must be able to account for failure envelopes under a complex loading state.

Several researchers have examined the residual strength after impact event to accommo-

date the loss in structural properties due to any anticipated impact from service use. The

methods used to obtain design allowables have included residual flexural strength after

impact (FAI), tensile strength after impact (TAI), compression strength after impact

(CAI), strain energy density calculations, and impact under pre-stressed conditions.

Testing of impact under pre-stressed conditions requires 5x more samples than

CAI testing and requires an additional 20 minutes per sample for installation and pre-

stressing. It is preferable to have experiments replicate service conditions as close as pos-

26

sible to ascertain synergistic effects of loading and impact, which can be otherwise

missed from post-testing an impacted sample under tension, compression, or flexure.

Lamination theory is adequate to predict failure in tension and flexure for most

laminated systems [10, 11]. However, compressive strength for composite laminates has

been more difficult to characterize, because models are idealized and require difficult to

attain properties. For example, it has been reported that in-plane compressive strength of

a composite material can be less than a tenth of the in-plane tensile strength [11-13].

Most fiber reinforcements have a small fiber diameter (8 to 22 µm) to obtain enhanced

tensile, bending, and torsional properties. Smaller diameters are detrimental to compres-

sive loading. Since classical Euler buckling is directly related to the second moment of

inertia, each small diameter fiber has a very low buckling strength when compared to its

tensile strength. When loaded in compression, the fibers begin to buckle and compress

the matrix. The fibers begin to fail when the matrix yields and a critical buckling radius is

reached.

4.3. Impact of Laminated Composites

There have been numerous studies of impact on composite structures. Several

models have been implemented based on analytical methods [14-27]. Naik et al [5] ex-

plored the shift in energy absorbing mechanisms when altering the impact velocity of a

projectile. They confirmed that the highest amount of energy is absorbed at the ballistic

limit and proposed a momentum exchange model. Hazell et al [24] reported that even at

very high velocities (1825 ms-1

), there appeared to be an asymptotic maximum delamina-

tion area threshold. Several studies have reported the impact face distortion caused at the

27

impact contact area. In some cases, this distortion affects through the thickness profile [5,

16, 22-27].

In a pre-stress composite laminate, the momentary geometrical distortion caused

by a point impact can cause it to behave differently due to the local strains causing geo-

metrical distortion. The compressive buckling load is lower due to the increased out of

plane deflection. Several approaches used to enhance compression performance under

impact include increasing interfacial strength, increasing matrix yield strength, or de-

creasing the global deflection with ribbing or other reinforcing methods.

One of the main methods used to determine laminate properties after an impact

event is to use a standard tensile, compression, or flexural test on impacted samples. Tru-

del-Boucher et al [28] examined the effects of LVI damage on the residual flexural and

tensile strengths of 3.5 mm thick cross-ply glass fiber/polypropylene composites. They

observed that damage progressively increased as the impact energy increased; and at the

highest impact energy of 9 J, plastic deformation resulted in residual curvature. They also

reported that both the normalized flexural strength and modulus decreased linearly with

respect to the impact energy. Applying flexure on the non-impacted side resulted in high-

er flexural strength, but resulted in a pronounced drop in flexural modulus. This indicated

that compression was a limiting factor for flexural strength.

Trudel-Boucher et al [28] also showed that the normalized tensile strength was

not affected until an impact energy greater than 5 J was reached, after which it decreased.

The tensile modulus was not affected by the level of impact damage. O’Higgins et al [29]

suggested that insight into the damage evolution for impacted tensile specimens can be

obtained from investigating the crack initiation and growth in an open hole tension test. It

28

was seen that cracks propagated transversely from the hole until failure. It was also seen

that the stress concentration decreased as higher levels of damage were attained, which

resulted in higher open hole tensile strength. Craven et al [30] modeled a carbon/epoxy

multi-directional laminate with pre-existing damage patterns under tensile loading and

observed its effect on the tensile stiffness. It was found that both delamination and fiber

fracture cracks must be taken into account to determine residual tensile properties. Cui et

al [31] modeled a T300/BMP-316 laminate in which tensile specimens were subjected to

LVI prior to applying tensile load to capture the effect of actual damage instead of crack

concentrations. The transverse crack forms at the boundaries of the delaminated zone and

then propagates outward until failure. The error associated with this method for both

damage area and residual tensile strength was less than 10%.

4.4. Residual Strength of Laminated Composites

There have been numerous studies on the residual compressive strength after im-

pact of composite laminates, because impact damage can reduce the residual compressive

strength to as low as one-tenth the ultimate strength for carbon/epoxy and one-third for E-

glass/epoxy laminates. Several authors have shown that decrease in compressive strength

is directly correlated to the impact damage area. Since the impact damage area is highest

at the ballistic limit, the compressive strength decreases as a function of impact velocity

and reaches an asymptotic value at the ballistic limit. CAI samples are first impacted

which forms the frustum-shaped damage area associated with non-pre-stressed impact

shown in Figure 1. The impact damage causes a stress concentration to form with the

applied compressive load at the edge of the delaminated area perpendicular to the applied

29

load. It has been shown that a linear elastic fracture mechanics approach can be used to

determine limiting loads that cause crack growth [2, 32]. Shear cracks propagate outward

from the point of impact quickly to the edge of the delaminated area, then slowly contin-

ue to propagate until catastrophic failure occurs. Gillespie Jr. et al [33] showed that

stitching of sandwich panels and cross-ply laminates created marginal improvements in

the CAI strength. Zhou et al [34, 35] examined preconditioned laminates with embedded

films to replicate delamination damage. Oval, rectangular, and circular delaminations

were created at multiple locations through the thickness of the laminate. Comparisons

were made between open hole, impact damaged and preconditioned residual compressive

strengths.

Several authors have researched the CAI strength of sandwich composites, where

several additional failure modes occur associated with the core. Williams et al [36] used a

modified CAI fixture and CFRP laminates containing hollow glass fibers filled with un-

cured resin. Samples were impacted, subjected to a curing cycle to heal the damaged ar-

ea, and residual strengths were obtained using a CAI test. The study concluded that an

impacted laminate could retain a majority of its original strength via this method. Aoki et

al [37] showed that hygrothermal conditions can drastically affect the CAI strength. The

wet samples had a lower Tg than dry samples, and when CAI was conducted above the Tg

of the matrix, compressive properties dramatically decreased. This study indicated that

the yield strength of the matrix has a dominant effect on the compressive strength of a

laminate.

30

4.5. Strain Rate Sensitivity

When characterizing damage caused by an impact event, the determination of

strain rate sensitivity for a material is critical. Daniel et al [38], Xiao et al [39], and

Brown et al [40] have conducted strain rate sensitivity studies on composite laminates

and observed that, as the strain rate increases, the modulus and strength increase but the

strain to failure decreases. LS-DYNA’s MAT 162 [41] utilizes strain rate sensitive

strength and modulus functions as given by:

{ } { } ( { }

) (1)

{ } { } ( { }

) (2)

where the rate coefficient is a user-defined input used to fit data regressions. Based on the

work done by Matzenmiller et al [42], this method is important for pre-stressed materials,

because although the initial loading is quasi-static, the impact event and initial failure

upon impact is a dynamic event. As discussed by Abrate [2], the shear, compressive, and

tensile waves produced at an impact site repeatedly travel back and forth through the lam-

inate, prior to any distortion. When failure takes place, the recoil force causes damage at

a higher strain rate than the loading rate. The result of which is a laminate failing at a

lower strength than anticipated from standard residual strength test methods. Preliminary

studies by the authors have shown that the strain sensitivity functions of MAT 162 can be

used to effectively model the impact under compression damage as shown below in Fig-

ures 4 and 5.

31

Figures 4 and 5. Pre-Stressed Impact Damage Area of Experimental (Left) Compared

with the Finite Element Analysis (Right).

The resultant front face damage area of a fiberglass laminate pre-stressed to 190 MPa

impacted by a 2g 7.62 mm diameter steel sphere at 120ms-1

had an 8.8% error between

the experiment and model, for the front face crack length.

4.6. Impact Under Pre-Load

Several researchers examined impact while under a pre-load. These investigations

include analytical models, FEA, biaxial loading under impact, compression under impact,

torsion/shear under impact, flexure under impact, and tension under impact. Sun and

Chattopadhyay [43] studied central impact of a mass on a simply supported plate. They

analytically determined that the contributions of pre-stressed tension on an impacted

composite reduced the deflection, bending stress, shear force, and energy absorption due

to impact. Rossikhin and Shitikova [44] used a ray series approximation and linearized

32

Hertzian contact deformation to analytically determine the effect of in-plane compressive

pre-stressed orthotropic circular plates under normal low velocity impact. It was analyti-

cally shown that a compressive pre-stress will soften the impact response and cause

greater out-of-plane deflection. It was shown that shear locking occurs at the compressive

critical magnitude, which attenuates the transverse shear wave similar to Landau attenua-

tion witnessed in highly compressed gases. Zheng and Binienda [45] analyzed laminated

plates which were simply supported and impacted using a linearized elastoplastic contact

law and shear deformable plate theory. The contact force history was not affected by pre-

stress, but it was found that pre-stress significantly affected the out-of-plane deflection.

Pre-tension reduced the deflection and pre-compression increased deflection. Rossikhan

and Shitikova [46] went on to determine the impact response generalized non-

dimensional equations for transversely isotropic plates with compressive pre-stress. It

was found that as the compressive force increased due to impact, the shear wave was

attenuated. The concentrated absorbed energy was closer to the impact site which caused

more damage. The studies showed that additional compressive pre-stress caused more

deflection and less contact force.

Schoeppner and Abrate [22] examined the Air Force Research Laboratory

(AFRL) database and found that for AS4/3501-6 graphite/epoxy laminates subjected to a

tensile pre-load up to 2400 µε and impacted up to 4.2 ms-1

caused no significant differ-

ence in the delamination threshold limit. Khalili et al [47] used Sveklo’s elastic contact

theory to determine analytical results for an impact under both uniaxial and biaxial tensile

pre-stress. It was determined that the maximum impact force increased and central de-

flection increased as the tensile pre-load increased. For the unidirectional carbon fiber

33

laminate analyzed, the transverse pre-stress caused more of the aforementioned effects

than the longitudinal pre-stress. Biaxial pre-stress resulted in the most impact force in-

crease and central deflection decrease. Garcia-Castillo et al [48] conducted a study in

which the ballistic limit of 1.5 mm thick aluminum samples was determined in the un-

loaded and 38% pre-loaded tensile state. There was no discernible difference in the ballis-

tic limit, but it was witnessed that the pre-loaded samples catastrophically failed upon

impact while the unloaded samples did not fail.

Minak et al [49, 50] investigated carbon fiber epoxy cylinders which were pre-

stressed in torsion prior to LVI. They reported that the torsional pre-load did not change

the delamination initiation though it aids in the delamination propagation. High torsional

pre-load resulted in more delamination propagation, lower critical buckling loads, and

lower residual torsional strength. Catastrophic failure resulted in some cases. Mizukawa

et al [51] created a fixture which allowed torsion and bending to be applied to thin-walled

tubes while being impacted by a drop tower. They found that there was a synergistic ef-

fect between the apparent torsional stress and apparent bending stress when under impact.

Kepler and Bull [52] conducted tests on sandwich panels subjected to global bending

while ballistically impacted. They found that under applied bending loads, the impact

caused catastrophic shear cracking that was non-existent without the applied bending.

Kulkarni et al [53] conducted a drop tower study on plain woven fiberglass samples

which were pre-stressed by pressurizing the distal side of the laminate up to 0.9 MPa. No

discernible difference was witnessed in the range of pre-stress tested.

Robb et al [54] conducted drop tower studies on biaxially pre-loaded chopped E-

glass polyester laminates. It was found that the most damage, least contact force, and

34

least contact duration were caused in a biaxially loaded tension/compression state. Ten-

sile pre-stress caused stiffening while compressive pre-stress caused softening. Whitting-

ham et al [55] tested carbon fiber epoxy laminates under realistic biaxial pre-stressed

loads witnessed in the field. It was found that within the realistic biaxial pre-stressed

state, no discernible difference was witnessed. Mitrevski et al [56] examined the effect of

impactor shape on the biaxially pre-stressed impact of E-glass / polyester laminates. As

the contact surface of the impactor shifts from cylindrical to spherical to conical, the

maximum deflection and absorbed energy increased. At the levels of pre-tensioned biaxi-

al impact tested, no discernible differences of damaged area were observed. Garcia-

Castillo et al [57] conducted studies on woven glass/polyester laminates subjected to high

velocity normal impact under both uniaxial and biaxial tensile pre-stress. It was deter-

mined that the biaxially preloaded samples had a slightly higher ballistic limit, but for the

range of preload tested there were no discernible differences in the energy absorbing

terms of primary yarn, secondary yarn, kinetic energy cone, delamination, and matrix

cracking. Loktev [58] studied spherical impact on a pre-stressed orthotropic Uflyand-

Mindlin plate using a Legendre polynomial and Laurent series expansion. It was deter-

mined that pre-tensioned samples had a higher contact force and duration, while the pre-

compressed laminates had a lower contact force and duration. A positive pre-stressed

moment caused a stiffening response and dramatically reduced the contact duration.

Finite element model (FEM) analysis has been conducted on the impact response

on pre-stressed laminates. Mikkor et al [59] used PAM-CRASH to analyze ballistic fail-

ure of pre-stressed laminates. Their findings show that at higher tensile pre-stress, failure

occurs higher than a critical impact velocity. Choi et al [60, 61] examined in-plane pre-

35

stress with the FEM method and experimental results to determine that tensile pre-

stressed caused a faster impact response while compressive pre-stress induced a slower

response. Ghelli and Minak [62] studied the effect of membrane pre-loads through FEA.

It was shown that tensile pre-load increased the peak stress while the compressive pre-

load reduced the peak impact stress.

Herzl Chai [63] conducted LVI testing on stiffened carbon/epoxy panels pre-

stressed in compression. A 0.5” diameter aluminum sphere impacted the pre-stressed

laminates up to 400 fps. It was determined that shear cracks leading to catastrophic fail-

ure developed at 30% of the ultimate compressive strength. Equations were derived based

on a strain energy density analysis which accurately modeled the failure phenomenon of

impact under compression. McGowen and Ambur [64] conducted compressive pre-

stressed impact on graphite/epoxy sandwich panels with honeycomb cores. Similar re-

sults were achieved as Chai in which pre-stressed samples caused failure upon impact at

high levels of pre-stress. Zhang et al [65] also compressed laminates prior to impact and

found that failure can result if the compressive pre-stress is too high during impact. Vary-

ing buckling shapes at impact were compared. Herszberg and Weller [66] conducted

studies for impact under compressive pre-loads on stitched and unstitched carbon/epoxy

laminates. Catastrophic failure was also found at high pre-stress levels when impacted.

Stitching was found to dramatically reduce the impact damage area, though it had no ef-

fect on the penetration velocity or catastrophic failure thresholds. Heimbs et al [67] im-

pacted compressively pre-stressed carbon / epoxy laminates and observed catastrophic

failure witnessed by the aforementioned researchers. The quasi-isotropic laminates exhib-

ited damage reshaping as pre-stressed conditions increased. Additionally, LS-DYNA was

36

used to corroborate the results. Pickett et al [68] conducted a study using a significantly

longer sample to apply in-plane compressive pre-stress during drop tower impact. The

carbon/epoxy laminates exhibited transverse cracks when impacted at high pre-stress.

PAM-CRASH was used to validate the witnessed failure modes.

Wiedenman and Dharan [69] investigated samples of G10 glass of varying thick-

nesses compressed to different levels and penetrated with a 5.56 mm projectile with the

equivalent of an M4 carbine. A CAI fixture and portable MTS load frame were used to

apply in-plane compressive load. It was found that the combination of impact and com-

pressive strain was much more detrimental than that of impact alone. They also observed

a delamination reshaping to damage more of the structure perpendicular to loading and

shear kink band formation due to impact. There was no account for the increased deflec-

tion which would be present in thinner samples. The authors found good agreement when

using the model presented by Starnes et al [70].

The database for complex loading of polymer matrix composites is sparse. Predic-

tive models have been implemented with some success to help fill the gap for the lack of

test data; but to truly understand the failure strength of a laminate configuration, a large

amount of exploratory testing must be conducted. Testing conducted closest to the ser-

vice loading witnessed at failure would yield more accurate failure thresholds and allow

existing models to be supplemented. The work done on pre-stressed composites by the

authors provides additional insight into failure modes that could be witnessed by structur-

al composites subjected to an impact event. By understanding the failure mechanisms and

failure thresholds, improved predictive models can be developed for use by naval design-

ers. The value to naval designers would be the reduction of required safety factors by

37

removing some of the uncertainty associated with complex loading. A reduced safety

factor would allow for an optimized structure, which by further reducing vessel weight,

would result in increased naval vessel performance.

4.7. CDI Fixture Design

For the purpose of evaluating realistic residual strength after impact, studies were

conducted by the authors to characterize the synergistic effect of impact under pre-

stressed in-plane compression for woven glass/vinyl ester (VE) composite laminates. The

ballistic impact equipment used was a custom built gas gun allowing for spherical ball

rounds up to 12.7 mm (0.5”) diameter to be fired up to 350 m/s. The equipment illustrat-

ed in Figures 6 and 7 uses compressed helium to propel a machined foam sabot housing a

projectile down the barrel [71]. The sabot breaks apart when it strikes the stripper plate

and the projectile continues to propel to the sample. Velocity measurements were attained

from two sets of Oehler Model 35 proof chronographs with the Oehler Skyscreen III pho-

to detectors.

Figures 6 and 7. Gas Gun (a) and Capture Chamber (b).

38

The compression during impact (CDI) fixture used to conduct pre-stressed testing

was designed, machined, and manufactured in-house, see Figure 8. The CDI fixture fits

inside the capture chamber dimensions of 304 mm x 292 mm x 100 mm (12” x 11.5” x

4”). It is completely replaceable when required, and effectively applies uniform, in-plane

compressive loads of up to 300 kN. Load is applied with a 30-ton low-clearance hydrau-

lic cylinder as shown in Figure 8 and 9. The hydraulic cylinder used was a manually op-

erated unit retrofitted with both a psi gage and a pressure transducer which allowed moni-

toring of the applied load before and after impact.

Figure 8. CDI Fixture. A: Vertical Support Bars B: Hydraulic Cylinder C: Load Transfer

Block D: Sample E: Front and Back Support Plates F: Top and Bottom Support Bars.

All of the components of the CDI fixture are attached with bolts. The fixture was

designed so that the hydraulic cylinder was placed outside the capture chamber, and a

load transfer block is used to both apply load to the sample and mimic the clamped end

condition used in the CAI test fixture. The samples are constrained in-plane by two ad-

39

justable ½” plates shown in Figure 9, which allowed a slip-fit to be achieved. The bottom

and top support bars are made from 2” square steel bars, and an exchangeable contact

plate is used to provide for testing flexibility.

Figure 9. Side view of CDI fixture - C: load transfer block D: sample, E: front and back

support plates, F: bottom support bar, and G: inner slip-fit support plates.

4.8. Procedure and Material

Samples were made via a VARTM process and machined to 4” x 6” rectangular

samples for CDI testing. Samples were installed in the CDI fixture and a load was ap-

plied. The sample was given at least 30 seconds to relax prior to impact. All samples in

this study were impacted with a 0.3” steel sphere weighing 2g at velocities ranging from

75 to 350 ms-1

. After impact, the load was released, back-lit photography was adopted,

and samples were compressed to failure in an ASTM CAI fixture. Samples tested includ-

ed 6 mm thick woven orthotropic E-glass/VE laminates, 4.2 mm thick woven orthotropic

E-glass/VE laminates, 6.2 mm thick quasi-isotropic E-glass/VE laminates, sandwich pan-

els made of 3.1 mm thick quasi-isotropic E-glass/VE face sheets with a 50.8 mm thick

HP 130 divinyl cell foam core, and 3.4 mm thick orthotropic carbon fiber/VE laminates.

40

4.9. Results and Discussion

The effect of compressive pre-stress on the residual strength of a 6 mm thick E-

glass/VE composite laminate is shown in Figure 10 [72]. Each series represents the level

of in-plane compressive pre-stress the laminate was subjected to when impacted. Five

samples tested in accordance with the Combined Loading Compression (CLC) ASTM

D6641 [73] yielded an ultimate compressive strength, σUCS

, of 377 (± 40) MPa.

Figure 10. Effect of compressive pre-stress on residual strength after impact.

At higher loading levels (31.2%, 33.5%, 37.0%, and 42.7% σUCS

), samples failed

compressively when impacted at velocities higher than 225 ms-1

. These samples are dis-

played along the x-axis of Figure 10, since their residual strength was zero. These sam-

ples failed because the impact event damaged enough material where the remaining

cross-sectional area was unable to sustain the applied load. The effect of changing the

geometrical loading of compression due to the instantaneous out-of-plane distortion

caused by the impact event causes this failure. The point at 0 m/s was determined from

41

baseline compression tests of unimpacted samples using the CAI fixture. The baseline

compressive strength found using the CAI fixture was 280 MPa, which was much less

than the ultimate compressive strength obtained from CLC testing. The CLC fixture [73]

utilizes a much shorter span length of 12.7 mm and larger grip lengths of 64 mm in com-

parison to the CAI fixture [7] which has a span length of roughly 137 mm and grip

lengths of 8 mm. The CAI fixture does not adequately constrain samples to be used for

determining ultimate compressive strength.

Statgraphics [69] was utilized to determine empirical best-fit regression. The cor-

relation was found to fit the form:

√( ) (3)

The model indicates that the residual compressive strength can be derived by subtracting

from the compressive ultimate strength, B, times the square root of the impact velocity.

The coefficient B which is unique to each loading level is derived from the constituents

of the sample and the amount of pre-stress. Each regression passed an ANOVA analysis

with a 95% confidence level. The comparison of these regressions, as seen in Figure 11,

indicated that there is little statistical difference in the first four loading levels. Residual

strength decreased as the loading increased in the range of 31% up to 37%, which implied

that there was an increase in transverse cross-sectional damage.

42

Figure 11. Effect of pre-stress on residual strength after an impact (regression line com-

parison).

Regressions were only plotted up to 225 ms-1

due to the failure witnessed at high-

er impact velocities. The pre-stress level of 42.7% was not plotted, because all samples

failed due to impact. This drop in residual strength was observed to be due to an impact

induced shear crack (IISC) on the front face of the laminate. The IISC was similarly seen

in studies by Kepler et al, Chai, and Wiedenman et al [48,59,65]. The length of the IISC

increased with increase in impact velocity as illustrated in Figures 12 and 13. It was also

observed that as the IISC increased in length, the delamination area increased. With in-

crease in IISC, an additional conical delamination zone develops whose base is in the

front face of the composite. This base is elliptical in nature following the profile of the

IISC. For nominally thick laminates – such as 4 mm or greater for woven glass/VE, the

total delamination area resembles a distorted yo-yo or an hour glass on its side.

43

Figures 12 and 13. Development of a front face crack due to high pre-stress. (Left) dis-

plays a typical conical delamination zone; (Right) shows a developing conical delamina-

tion zone with the addition of an IISC on the Front Face.

The damage evolution resulting in a set of glass/VE laminates from increasing the

impact velocity and compressive pre-stress is shown in Figure 14. The lighter images are

back-lit samples showing the delamination damage. The darker images are front-lit sam-

ples showing the formed IISC. All pictures are at the same magnification. Impact velocity

increases from top to bottom, and compressive pre-stress increases from left to right in

the figure.

44

Figure 14. Evolution of damage from increased compressive pre-stress during ballistic

impact.

The formation of an IISC is clearly visible for the higher pre-stressed samples, and failure

can be seen at high compressive pre-stress and at higher loading combinations.

By plotting the residual strength as a function of the length of the compression

initiated crack in Figure 15, a strong correlation is obtained linking the front face crack

length to a decrease in the residual strength (i.e. cross-sectional area). A further ANOVA

analysis validated the correlation. When the crack length becomes too large, the sample

fails in compression.

45

Figure 15. Effect of front face IISC length on residual strength.

Since the crack length directly correlates with the residual strength, it is inferred

that a front face crack denotes damage throughout the thickness of the composite. Figure

16 shows the samples failed due to impact. Failure was caused by a compressive pre-

stress, but it was also observed that the synergistic effect of pre-stress and impact was

more detrimental. Failure mode envelopes are observed in which typical conical damage

occurs, an IISC is formed, and that IISC extends far enough to cause failure. The data

from Figure 16 is used to create failure threshold envelopes shown in Figure 17.

46

Figure 16. Effect of compression and impact on failure mode type.

Figure 17. Failure threshold envelopes for safe design.

These envelopes can be used to determine when it is safe to use predictive models for

conical delamination, when additional safety factors may be needed, and when failure

will occur.

Figure 18 is a contour plot displaying the combined effect of compression and

impact on the residual compressive strength attained from CAI testing. Combined with

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

0 100 200 300 400

Co

mp

ress

ive

Pre

-Str

ess

(%)

Impact Velocity (ms-1)

Failure

IISC

Conical

47

the results from Figures 11-16, it is seen that more transverse damage in the form of an

IISC is created as a laminate is impacted under higher compressive pre-stress. For an

impact velocity of 100 ms-1

, Figure 18 displays that at low levels of compression there is

very little change in the residual strength; but as the pre-stress is increased the residual

strength reduces. Correlating these results with Figure 17, it can be seen that the reduc-

tion in residual strength is directly linked with the formation of an IISC. The impact ve-

locity also has a strong effect on the length of such a shear crack and the residual strength

of the GFRP laminate.

Figure 18. Synergistic effect of compression and impact on the residual compressive

strength of damaged GFRP.

Likewise, the penetration chart below in Figure 19 designates the observed penetration of

the compressed laminates. It was observed that for the samples tested thus far, none of

the samples were fully penetrated at the tested impact velocities.

48

Figure 19. Penetration chart for 100 mm x 150 mm (4” x 6”) samples based on pre-stress

and impact velocity.

It may be noted that partial penetration only occurred at higher velocities. Based

on the initial results, penetration does not seem to be effected by the synergistic effect of

compression and impact indicating that the IISC formation occurs prior to penetration.

Naik et al have shown that the friction force between projectile and laminate absorbs a

significant amount of energy [5]. If the IISC had formed after penetration, more energy

would be absorbed from the increased friction forces when pre-stress was applied and the

ballistic limit decreases.

Similar studies have been conducted for other data sets including a 4.2 mm thick

woven orthotropic E-glass/VE laminates, 6.2 mm thick quasi-isotropic E-glass/VE lami-

nates, sandwich panels made of 3.1 mm thick quasi-isotropic E-glass/VE face sheets with

a 50.8 mm thick HP 130 divinyl cell foam core, and 3.4 mm thick orthotropic carbon

fiber/VE laminates [70]. The failure threshold envelopes associated with each of these

data sets are shown below in Figure 20.

49

Figure 20. Comparison of the failure threshold envelopes for various laminate configura-

tions.

The failure threshold envelopes remain relatively the same for E-glass / vinyl es-

ter laminates. The carbon fiber data set showed a significant reduction in relative failure

strength when compared to the E-glass fiber data set, which can be attributed to strain

rate sensitivity associated with carbon fibers. Figure 21 shows the difference in damage

evolution for the various data sets.

50

Figure 21. Damage evolution effect of laminate configuration.

There was little difference between damage resulting in 7 and 10 layer orthotropic con-

figurations. The ±45° contribution in the quasi-isotropic laminate displays damage bias-

ing in both the delamination and IISC. The quasi-isotropic sandwich panel showed a

more unique failure mode showing biased delamination and a thicker IISC.

Since the compressive modulus of the laminate facesheets and foam core differ

and they are bound by a weaker interface, some barreling or tendency towards barreling

occurs during loading. When the front laminate is impacted and penetrated, it is ade-

quately supported by the core and associated impact deformation/delamination is re-

duced. The load carried by the delaminated front face is transferred to the surrounding

undamaged material and the back laminate. The projectile is also significantly slowed

down from penetrating the front facesheet. When the back facesheet is impacted, the pro-

jectile is moving slower which produces more damage if slightly less than the ballistic

limit. The back facesheet is under a locally higher pre-stress due to the loss of structural

51

integrity of the front facesheet. The back facesheet is also not supported by anything oth-

er than the interface and is essentially a 5 layer thick laminate with a much lower buck-

ling load than the sandwich panel. All of these conditions lead to large delamination on

the back facesheet. The structural failure associated with the back face damage is then

passed back to the front which will force shear cracks to propagate if the stress concentra-

tion is too high. Sandwich panels offer some of the most beneficial aspects for structural

composites, but the addition of a foam core has many unintended consequences that must

be accounted for during design.

It should be noted that many factors affect both compression and impact of com-

posite structures to cause uncertainty. The information presented is intended as a guide to

designers of what to expect to see when a structure is loaded too high and impacted. Con-

siderable additional testing is required to be able to use such a threshold diagram for de-

sign purposes. The general trends have been established and presented by this and other

works. Various factors have to be taken into account, such as percent strain, some span to

thickness ratio, and percent ultimate stress to establish standard design guidelines for

laminates impacted during compression.

4.10. Conclusion

This study provided some insights into the failure modes and safety thresholds of

navy relevant composites in regards to ballistic impact when subjected to different de-

grees of in-plane compressive pre-stress. It was observed that beyond a threshold combi-

nation of impact velocity and degree of pre-stress, the shape of the damage changes from

circular to elliptical leading to catastrophic damage. Failure was witnessed using the im-

pact under compression test method which was not accounted for by standard CAI test

52

methods. Failure envelopes for the combined effects of pre-stress and impact have been

developed for orthotropic glass/vinyl ester laminates, quasi-isotropic glass/vinyl ester

laminates, quasi-isotropic glass/vinyl ester sandwich composites, and carbon/vinyl ester

laminates. Although the testing of the CFRP system was sparse, it indicated that a GFRP

system would be better suited to structural application in compression, subject to ballistic

impact. Since the ultimate compressive strength of a composite system is dependent on

thickness, boundary conditions, and lay-up, it is difficult to pin point a safety threshold;

but in this case, the safety threshold for the orthotropic GFRP was 30% σUCS, quasi-

isotropic GFRP was 40% σUCS, quasi-isotropic GFRP sandwich panel was 40% σUCS, and

the orthotropic CFRP was 15% σUCS. Based on these results, the weight savings would

not justify the use of the more expensive CFRP system for structural composites in an

environment of ballistic threat. A significant amount of work is left to be done in this

field relating to effectively modeling the residual strengths of pre-stressed impact for

composite structures. A framework has been established to conduct such testing; but at

present, a constitutive model is yet to be developed.

Acknowledgement

We are grateful to support from the ONR Solid Mechanics program managed by

Dr. Yapa D. Rajapakse, Office of Naval Research. Some aspects of the compression fix-

ture for crashworthiness studies were funded through the Department of Energy, Gradu-

ate Automotive Technology Education (GATE) program; and we gratefully acknowledge

this support.

53

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59

DESIGN AND DEVELOPMENT OF A TEST FIXTURE AND METHOD FOR

INVESTIGATION OF IMPACT DURING PRE-STRESSED COMPRESSION

by

Eric Kerr-Anderson

Benjamin Geiger-Willis

Selvum Pillay

Uday Vaidya

In preparation for ASTM Journal of Testing and Evaluation

Format adapted for dissertation

60

5. DESIGN AND DEVELOPMENT OF A TEST FIXTURE AND METHOD FOR

INVESTIGATION OF IMPACT DURING PRE-STRESSED COMPRESSION

5.1. Abstract

As composites become more integrated into large structures and vehicles, there is

a need to design for laminate failure associated with realistic combined loading scenarios.

Since a structural composite is typically brittle, impact damage has been extensively stud-

ied and residual strength has been evaluated post-impact damage. Few studies have been

conducted to determine the effects of pre-stressing a composite during impact. In the case

of in-plane compression during impact, it has been found that there is a synergistic effect

which causes more damage than occurs with a standard compression-after-impact (CAI)

test. When compressive pre-stress greater than 70 MPa was applied to 150 mm x 100 mm

x 5.4 mm glass fiber/vinyl ester laminates, an impact initiated shear crack (IISC) devel-

oped perpendicular to the applied load leading to failure. To accommodate designers

concerned with compressively loaded composite structures that may endure an impact

event, a test method has been established to conduct compression during impact (CDI)

testing. This paper reports the design, construction and implementation of an innovative

test fixture that enables investigation of failure mechanisms in the CDI test mode.

Keywords: Pre-stress, Ballistic impact, Composite, Compression, Fixture

61

5.2. Introduction

The high specific strength and minimal maintenance costs have made composite

materials extremely attractive to structural designers for vehicles, planes, and ships. The

brittle composite materials best suited to structural loading have shown to incur damage

due to impact from events such as tool drops, striking posts, blast impact, runway debris,

and ballistic impact [1-4]. A large body of knowledge has been developed studying the

damage evolution developed from the impact of composite structures. Several good re-

views on the subject of composite impact have been written by Goldsmith [5], Cantwell

[3], and Abrate [1].

An impact event typically falls into one of four classes: low velocity impact

(LVI), intermediate velocity impact (IVI), high velocity impact (HVI), and hyper velocity

impact (HPI) [1, 6, 7]. LVI usually involves a large mass of 1-10 kg impacting at veloci-

ties less than 10 ms-1

. IVI events represent smaller masses less than 1 kg such as rock

debris or lower energy fragments traveling at a velocity of 10-100 ms-1

. HVI is typically

associated with projectiles, fragments, shrapnel, or debris weighing less than 10 g impact-

ing at a velocity of 100-2000 ms-1

. HPI is characterized by small mass meteorites, flyer

plates, and shaped charges impacting at velocities in excess of 2000 ms-1

.

The in-plane compression of composite materials has also been thoroughly re-

searched [8-14] , but simple predictive models have yet to be found. Current models for

predicting the compressive strength of composites either over predict compressive

strength or require difficult to attain properties such as initial fiber waviness or interface

properties [8-13]. There is a general consensus of failure modes observed for in-plane

compressive strength: Euler buckling, bifurcation, and shear cracking [4, 8, 12-14]. Euler

62

buckling results when the second moment of inertia is too low for the applied in-plane

compressive load and the critical buckling curvature is exceeded, resulting in failure.

Euler buckling is applicable for all materials. Bifurcation is unique to composite lami-

nates because it is caused when the bonding strength between layers is exceeded prior to

global buckling and shear cracking. Bifurcation typically occurs near the central plane of

the laminate and is associated with laminates greater than 25 mm thick, sandwich compo-

sites, or low volume fraction (< 20%) unidirectional composites [4]. The shear cracking

witnessed in compressive failure is primarily due to the polymer matrix which binds fi-

bers together and transfers load from one fiber to another. As the fibers are axially load-

ed, they begin to buckle at wavelengths associated with their modulus and diameter. Fi-

ber buckling does not actually occur until the out-of-axis load transferred from fiber to

the supporting matrix exceeds the matrix yield strength. Fibers are forced past the buck-

ling curvature and fracture when the matrix begins to yield. The fiber diameter variance

associated with production causes larger fibers to fail under less curvature than smaller

fibers. Load which was supported by the fractured fibers is transferred to the remaining

fibers. The fiber failure process continues as more load is applied until a critical point is

reached where the remaining fibers in the laminate are insufficient to support the applied

load. When this critical point is reached, compressive failure of the laminate results in the

form of a shear band.

The residual strength after impact damage is of great interest to design engineers.

Prior studies have investigated tension after impact, compression after impact (CAI), and

flexure after impact for various composite systems [1, 4]. Impact damage has been found

to have the most dramatic effect for CAI testing due to crack initiation and reduction in

63

cross-sectional area. Several fixtures and test methods have been developed by NASA

[15], Boeing [16], and Airbus [17] to characterize the CAI strength. The initial test meth-

od and fixture designed by NASA to characterize the effect of LVI damage from tool

drops requires 6.35 mm thick samples 178 mm wide by 254-318 mm long. Samples are

trimmed to a 127 mm width after impact and compressed to failure using a fixture which

simply supports all sample edges while maintaining in-plane compression. Boeing creat-

ed a smaller fixture which requires a sample size of only 102 mm wide by 152 mm long

and a variable thickness of 4-6 mm. The Boeing fixture and test method have been adopt-

ed as ASTM D7137 [16] and is one of the most common fixtures for CAI testing. The

design of the ASTM fixture allows for a wide range of flexibility to accommodate many

sample sizes and is relatively easy to remove/install samples. In addition to the ASTM

standardized fixture, Boeing has developed additional fixtures to accommodate larger

samples of up to 267 mm x 267 mm and also with longer dimensions, as much as 102

mm wide by 432 mm long to examine multiple buckling waves. The Airbus CAI fixture

[17] was developed to determine CAI strength with the clamped condition on top and

bottom of the damaged laminate. The Airbus CAI fixture also accounts for fixture align-

ment but does not accommodate samples other than 152 mm x 102 mm x 4 mm.

Few studies have been conducted on the comparison of CAI results to compres-

sively pre-stressed impact [18-24]. Most of these studies utilized a compression fixture

similar to the ASTM CAI test in which the top and bottom of the sample were clamped

while the sides were simply supported on both sides with a knife edge. Herzl Chai [18]

used Devcon™ adhesive to fix both top and bottom for both the smaller 203 mm x 102

mm x 6 mm and larger 254 mm x 152 mm x 6 mm graphite/epoxy samples which were

64

tested. Load was applied using a hydraulic testing machine. McGowan and Ambur [19]

examined both dropped weight and air gun impact of compressively pre-stressed 127 mm

x 254 mm x 16 mm sandwich composites made from AS4/8552 graphite/epoxy pre-

impregnated tape and cloth with a Korex™ honeycomb core. All sandwich panels were

potted to ensure minimal fiber brooming and loaded using a hydraulic testing machine.

Zhang et al [20] applied in-plane compressive loads to T800/924 carbon/epoxy laminates

with a manual hydraulic system. Samples were pre-stressed prior to LVI testing. Her-

szberg and Weller [22] compressively pre-stressed both stitched and unstitched T300

carbon/epoxy laminates with dimensions of 145 mm x 145 mm x 2 mm and impacted the

buckled samples on the convex and concave faces with a gas gun. Wiedenman and

Dharan [21] manufactured woven G10/epoxy fiberglass samples of 102 mm x 152 mm

and thickness ranging from 1.6 - 6.4 mm. Samples were compressively pre-stressed using

a Boeing CAI fixture with a portable hydraulic press, and a civilian M4 carbine was used

to fire standard 5.56 mm ammunition. Heimbs et al [23] investigated three layups of

tabbed carbon/epoxy laminates in which the 400 mm x 150 mm x 3 mm samples were

pre-stressed in compression and impacted with a drop tower. Pickett et al [24] compres-

sively pre-stressed 600 mm x 200 mm x 4.2 mm tabbed carbon/epoxy laminates prior to

drop tower impact. Pickett et al did not use a knife edge support on both longitudinal

sides of the laminates, instead they opted to use a sample lateral back face support.

5.3. Design of the Compression During Impact Fixture

The gas gun testing apparatus, shown below in Figures 1 and 2, at the University

of Alabama at Birmingham (UAB) utilizes a capture chamber with dimensions of 2.18 m

long, 0.30 m wide, and 0.36 m tall to house samples between 127 x127 mm to 254 x 254

65

mm in fully clamped-edge conditions. The projectile velocity is measured by two sets of

Oehler Model 35 proof chronographs before and after impact. Measurements from the

chronographs are obstructed if a fixture assembly thicker than 100 mm is used. Deflec-

tion plates and projectile capturing media is used to contain the projectile after impact.

Pressurized helium is released to propel a projectile seated in a foam sabot down a 4.6 m

barrel striking the sabot stripper. The sabot stripper is a steel plate with a centrally located

hole large enough for the projectile to pass through the plate when the foam sabot strikes

the plate and is broken up [25].

Figures 1 and 2: Gas Gun (a) and Capture Chamber (b).

The goal for the CDI fixture design was to retrofit the gas gun capture chamber to

apply in-plane compressive load to a laminate sample. For the purposes of post-impact

residual strength analysis, the sample size used was to be consistent with ASTM D7137

[16] at 102 mm wide and 152 mm tall with the option of wider samples and variable

thicknesses of up to 50.8 mm. It was necessary to make the CDI fixture less than 40 kg,

compact in the thickness direction, and maximize the width and height utilization inside

the capture chamber to avoid elaborate system modifications. A 30-ton RAM-PAC low

clearance hydraulic cylinder was selected to establish pre-stress conditions in the compo-

site samples.

66

Early in the design process, four critical design aspects were identified. The bot-

tom support bar could not deflect more than 0.05 mm under a 270 kN force; otherwise,

non-uniform loading would occur across the sample width. Fixture alignment was para-

mount to ensure in-plane compressive loading, and the entire fixture needed to be sym-

metric to avoid non-uniform deflection due to loading. Practical operation required a

simple means of sample placement and extraction. Due to the size limitations and the

necessity of centering samples in the capture chamber, a load frame shown in Figures 3-5

was developed to extend above the top of the capture chamber.

Figures 3 and 4: Pro-E Model of CDI Fixture (Left). A: Vertical Support Bars B: Hydrau-

lic Cylinder C: Load Transfer Block D: Sample E: Front and Back Support Plates F: Top

and Bottom Support Bars. Actual Fixture (Right).

By having the top portion of the load frame extending outside of the capture

chamber, the hydraulic system is protected from impact damage and an easy means of

sample installation/extraction through the top is available. A double shear load bearing

vertical support was used on both sides of the fixture designed with a safety factor of 2.

67

The top and bottom support bars were machined from 50.8 mm square steel bar, and the

bottom bar was further reinforced with bolts across the span to meet deflection design

requirements. The 32.7 kg fixture was mechanically fastened together using grade 8 bolts

to allow adaptability to new test constraints, ease of damaged part replacement, and the

ability to redesign existing components. The 30-ton hydraulic hand jack was outfitted

with an Enerpac 10 ksi needle gage for visual monitoring, and an OMEGA PX4100-

6KGV pressure transducer was used with a data acquisition (DAQ) system to monitor

load during the CDI test. The internal assembly of the CDI fixture is shown below in

Figure 5.

Figure 5: Internal Side view of CDI fixture - C: Load Transfer Block, D: Sample, E:

Front and Back Support Plates, F: Bottom Support Bar, and G: Internal Support Plates.

The front and back plates were bolted to the side and bottom support bars, and

were used to provide mounting points for the internal support plates as well as provide

structural rigidity to the fixture. The internal support plates were fixed in place using

threaded rods tapered to accommodate snap rings. A key was made to rotate the threaded

68

rods on the outside of the structure which translated the internal plates inward and out-

ward allowing for adaptability to a wide range of sample thicknesses. The use of internal

support plates and threaded rods allowed a slip fit pseudo-clamped condition to be creat-

ed completely around the sample test area while maintaining a fixture thickness profile

under 100 mm. The sample test area was 76.2 mm wide by 101.6 mm tall, which left 12.7

mm of pseudo-clamped support on both sides and the top. The bottom support length was

25.4 mm. Figure 6 shows the use of an exchangeable contact plate on the bottom support

bar.

Figure 6: Bottom Bar Assembly - D: Sample, F: Bottom Support Bar, H: Contact Plate, I:

Barrel Pins.

The contact plate was held in place with four compression barrel pins fixed in the

bottom support bar. The benefits of using a contact plate include the elimination of dam-

age to the bottom support bar, ability to change the contact geometry for partial edge

loading, and the flexibility of changing the support width for thicker composites. Another

benefit would be the ability to use harder materials to eliminate indentation that may re-

sult from the compression of stiffer composite structures.

69

5.4. Materials

Glass fiber/vinyl ester resin samples were processed using vacuum-assisted resin

transfer molding (VARTM) method. Six layers of plain woven Fiber Glass Industries

(FGI) Rovcloth® 3273 were used to make a composite laminated panel with an average

thickness of 5.4 mm. Derakane 510A-40 vinyl ester resin was used as the matrix. Sam-

ples were machined to dimensions of 158 mm x 103 mm x 5.4 mm to accommodate test-

ing in the CAI fixture used in ASTM D7137M – 05 [16]. Samples were machined square

and parallel with the warp fibers in the length direction and weft fibers in the width direc-

tion.

5.5. Procedure

Samples were initially measured to ensure that the top and bottom surfaces were

flat, square, and parallel. A WichiTechTM Digital Tap Hammer was utilized to ensure

consistent machined sample quality. Tap testing is a nondestructive evaluation method

which measures the response of the material tapped with the hammer [4]. With the cor-

rect exposure time, back lit photography [25] is a method which can be used to determine

internal damage in transparent media such as the glass/vinyl ester laminate used in this

study. Light transferred through the laminate is impeded by damaged areas and is ob-

served as a darker region. As more damage is witnessed through the thickness, the result-

ing area will become darker. All photographic analysis was conducted using the Image-

Pro Plus 6.0 software package. The front internal support is initially set based on the

sample thickness to provide a vertical support for the centered sample. The sample is

centered in the fixture along the width direction and the back internal support is tightened

to contact the sample surface. A properly secured sample has a slip fit, in which it is con-

70

strained out-of-plane, but still allowed to easily move in-plane with the applied load. A

slip fit is important because if the sample is clamped in place, compression will only be

applied to the top most part of the sample, causing an invalid test. A strain gage should be

mounted on each sample central to the width of the sample and at the bottom of the un-

constrained sample area to verify pre-stress level and any concave/convex curvature.

After the sample is properly secured, the transfer block is inserted into the guide

rails and placed on top of the sample. Similar to the CAI test, the clamping plates on the

transfer block are butted up against the sample and tightened in place to prevent end

brooming during compression. Top shields are placed and secured, and the hydraulic

head is slid into position to apply in-plane compression to the sample.

Data acquisition is initiated at two readings per second for the hydraulic transduc-

er and the sample is compressed to the desired gauge pressure. The samples are allowed

to relax for at least 60 seconds before impact testing to allow for sample relaxation and a

uniform stress field to develop. The additional relaxation time more closely simulates

service loading conditions for structural composites. The gas gun is used to impact sam-

ples with 7.6 mm spherical stainless steel impactor at a velocity range from 50 - 350 ms-1

.

After impact, hydraulic pressure is released and data acquisition is terminated.

Post-impact back-lit photography is taken to allow damage characterization with

the use of ImagePro Plus 6.0. Diffuse, high-intensity lighting is used in both through-

transmission and back-scatter modes to capture the delamination and surface damage of

both sides of the fiberglass samples. Front face delamination area, back face delamination

area, and the IISC length are measured and recorded. After photography, the impacted

laminates are compressed to failure in the CAI fixture [16]. The compressive strength and

71

modulus attained are the residual compressive strength and residual compressive modulus

at the impact velocity and pre-stress of the respective sample.

5.6. Validation and Discussion

One of the key differences witnessed in compressively pre-stressed impact in-

volved the shift in failure mode resulting in more damage propagating perpendicular to

the pre-stressed load due to impact. This failure mode formed on the impact face of the

laminate and has been identified in previous work [26], Chai [18], McGowan and Ambur

[19], Zhang et al [20], Herszberg and Weller [22], Wiedenman and Dharan [21], Heimbs

et al [23], and Pickett et al [24]. An example of the typical conical impact damage wit-

nessed in woven orthotropic thermoset laminates is shown below in Figure 7, and an ex-

ample of pre-stressed impact damage forming an IISC is shown in Figure 8.

Figures 7 and 8: Typical Conical Deformation (Left) and IISC (Right) Caused by Com-

pressively Pre-Stressed Impact.

72

It was observed that even at a pre-stress of 64 MPa, conical impact damage was

witnessed. It is shown in Figures 7 and 8 that if an IISC formed, laminates impacted at

lower velocities (141 ms-1

) under higher pre-stress (119 MPa) exhibited damaged cross

sectional areas similar to laminates impacted at higher velocities (226 ms-1

) under lower

pre-stress (64 MPa).

Preliminary studies have shown that extreme care must be taken when machining

samples and designing a compression fixture. The misalignment of 0.05 mm would result

in a stress concentration of 1.8 MPa for the sample set used in this study. If the combina-

tion of the misalignment stress and the applied pre-stress exceeds the crush strength of a

sample, damage will result at the edges as shown below in Figure 9.

Figure 9: Example of Damage Resulting from Partial Edge Loading – Damage Indicates

Significant Flexure in Bottom Support Bar or Non-square Sample Dimensions.

73

If damage develops at the corners during testing, the alignment and deflection of

the compression plates must be examined as well as the sample dimensions. Since devel-

oping the fixture outlined in this paper, no partial edge compression damage has oc-

curred. This result has provided some validation that a uniform stress field has been suc-

cessfully developed.

The damage evolution as a function of impact velocity and compressive pre-stress

is shown below in Figure 10.

Figure 10: Damage Evolution Resulting from the Synergistic Effect of Pre-Stress and

Impact Velocity.

74

It is quite clear that the damage area is strongly dependent on the impact velocity, but it

can also be seen that the front face damage increases at higher levels of pre-stress for all

impact velocities. There exists a pre-stress threshold above which failure occurs upon

impact. At low velocity, the pre-stress required to cause catastrophic failure due to impact

was much higher than required at velocities nearing or exceeding the ballistic limit. The

fact that stable compression levels nearing the compressive strength of the sample mate-

rial and the presence of IISC reinforce that uniform in-plane compression has been at-

tained and tested using the presented fixture.

To accurately measure the compressive pre-stress applied to the laminate, a pres-

sure transducer was incorporated into the hydraulic assembly. The pressure transducer

allowed the measurement of real time load data during the CDI test. Examples of trans-

ducer data for samples witnessing conical damage, IISC cracks, and failure are shown

below in Figure 11.

75

Figure 11: Transducer Load Data during the CDI Test and Comparison of Damage Evo-

lution. The point of impact is denoted by a star for each load path.

The point of impact is indicated by the star and the drop in compressive pre-

stress. Based on the load paths shown in Figure 11, it is apparent that the loading rate was

consistent and the relaxation time was adequate to provide a stabilized state of compres-

sion. The pressure drop is associated with the hydraulic cylinder translating downward.

As the damage inside the laminate is increased, there is less remaining strength, and the

overall deflection of the laminate increased. Samples resulting in conical damage exhib-

ited a drop in pre-stress ranging from 0.2 – 4.96 MPa which correlated to a deflection of

0.002 -0.135 mm. Samples resulting in IISC damage exhibited a drop in pre-stress rang-

ing from 0.37 – 13.17 MPa which correlated to a deflection of 0.008 – 0.25 mm. Samples

resulting in failure exhibited a drop in pre-stress ranging from 49 – 135 MPa, and the

associated deflection was indeterminable due to failure. For each failure mode, the mag-

76

nitude of the drop in pressure was directly related to the extent of laminate cross-sectional

damage.

The results of such a pre-stress study could be best presented as shown below in

Figures 12-14. As shown in Figure 12, a failure threshold diagram could be quite useful

to the designer.

Figure 12: Failure Thresholds for 5.4 mm Thick EGVE Woven Laminates Impacted Dur-

ing Compressive Pre-Stress.

A failure threshold diagram can be used to determine what stress levels would be appro-

priate to use traditional CAI data, and which levels should be avoided or have considera-

tions for additional reinforcement [16]. The penetration thresholds are shown in Figure

13.

77

Figure 13: Penetration Thresholds for 5.4 mm thick glass/vinyl ester Woven Laminates

Impacted During Compressive Pre-Stress.

Based on the data presented in this and previous studies [26], pre-stress does not

appear to have an effect on the penetration for woven fiberglass laminates. This would

indicate that IISC damage and failure occurs prior to penetration as the additional friction

force due to pre-stress would otherwise have absorbed more energy and increased the

ballistic limit at higher pre-stress.

Figure 14 shows the residual compressive strength tested in the CAI fixture result-

ing from damage caused by impact under compressive pre-stress.

78

Figure 14: The Residual Compressive Strength using CAI Fixture for 5.4 mm thick

glass/vinyl ester Woven Laminates Impacted Under Compressive Pre-Stress.

The samples plotted on the vertical axis which failed had no damage and were com-

pressed to failure in the CAI fixture to give a baseline compressive strength. However,

the CAI fixture is inappropriate to use for testing ultimate compressive strength for lami-

nates due to the large unconstrained lengths, minimal support length, and pseudo-

clamped end condition. There was a significant amount of data scatter at higher velocities

due to the minimal number of samples tested in this study. It can be seen that, in general,

the residual strength of the conically damaged samples correlated with the failure thresh-

old for its respective impact velocity. An additional observation is that some samples near

the failure threshold were pre-stressed above the residual strength. This observation

means that in a realistic load-controlled system, failure during impact would result at less

pre-stress than shown in Figure 14. There were samples that had less residual strength

79

than the respective conically damaged samples, yet were impacted at a pre-stress value

lower than the residual strength. Simply stated, more damage is caused at higher levels of

pre-stress than predicted by standard conical delamination models. Increased impact ve-

locity had a much stronger effect on reducing the residual strength than the effect of in-

creased pre-stress.

5.7. Summary

1) An innovative fixture has been successfully designed and utilized to characterize

the synergistic effect of in-plane compressive pre-stress loading and ballistic im-

pact loading.

2) Using the developed fixture, a test method for investigating in-plane compression

during impact has been proposed, in conjunction with test data, testing protocol

and validation methods. For example, it has been determined that impact damage

for a 5 mm nominally thick glass/vinyl ester woven orthotropic laminates pre-

stressed under in-plane compression exceeding 70 MPa, exhibit additional dam-

age extending perpendicular to the applied load and less residual strength than de-

termined using the ASTM D7137M – 05 [16] CAI test impacting under no pre-

stress.

3) Characteristic failure modes witnessed during CDI testing have been character-

ized.

4) This paper provides the framework for what could become a more widely accept-

ed test for evaluating complex interacting loading conditions. The test method can

be useful to designers to generate failure envelopes and damage mode transitions

for any given percentage of pre-stress versus impact velocity. This would further

80

allow designers to determine survivability of structures for complex loading con-

ditions.

Acknowledgements

We are grateful to support from the ONR Solid Mechanics program managed by

Dr. Yapa D. Rajapakse, Office of Naval Research. Some aspects of the compression fix-

ture for crashworthiness studies were funded through the Department of Energy, Gradu-

ate Automotive Technology Education (GATE) program; and we gratefully acknowledge

this support.

81

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space structural applications. 1965, Washington, DC: National Aeronautics and Space

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ence and Manufacturing, 2008. 39(1): p. 19-28.

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plastics. Composites Science and Technology Composites Science and Technology,

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11. Dharan, C.K.H. and C.L. Lin, Longitudinal compressive strength of continuous fiber

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imental studies. Progress in aerospace sciences, 1996. 32(1): p. 43-78.

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nal of Reinforced Plastics and Composites, 1992. 11:8: p. 838-896.

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82

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posites, 2007. Nov: p. 4-6.

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California Institute of Technology: Pasadena, CA, PhD Dissertation.

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impacted with and without compression loading. Journal of Aircraft, 1999. 36(3): p.

596-602.

20. Zhang, X., G.A.O. Davies, and D. Hitchings, Impact damage with compressive pre-

load and post-impact compression of carbon composite plates. International Journal

of Impact Engineering, 1999. 22: p. 485-509.

21. Wiedenman, N., Ballistic penetration of compressively loaded composite plates.

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els. Composite Structures, 2006. 73(2): p. 130-137.

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e-glass/vinyl ester composites, in Proceedings Mechanics of Composite Materi-

als2010. p. College Park, MD.

83

MODELING THE RESIDUAL STRENGTH OF BALLISTICALLY IMPACTED E-

GLASS/VINYL ESTER LAMINATES DURING IN-PLANE COMPRESSIVE PRE-

STRESS

by

Eric Kerr-Anderson

Dr. Selvum Pillay

Dr. Uday Vaidya

In preparation for Composites: Part B

Format adapted for dissertation

84

6. MODELING THE RESIDUAL STRENGTH OF BALLISTICALLY IMPACTED E-

GLASS/VINYL ESTER LAMINATES DURING IN-PLANE COMPRESSIVE PRE-

STRESS

6.1. Abstract

Composite structures used in ships, ground vehicles, aerospace, and infrastructure

applications are typically designed to support static compressive loads during service.

Such structures can also witness ballistic loading during operation and are attributed a

higher safety factor than would be required if the failure mechanisms were better under-

stood. Residual strength characterization for laminates sustaining impact damage is de-

termined by compression after impact (CAI) testing. CAI testing neglects the effect of the

static load structural composite witness during the impact event. Analysis was conducted

on 5.4 mm and 6.0 mm thick E-glass/vinyl ester laminates with dimensions of 156 mm x

103 mm to determine empirical failure thresholds and models for residual compressive

strength. The empirical model derived to predict the residual compressive strength of

impacted laminates under in-plane compressive pre-stress showed agreement with the

experimental results.

Keywords: ballistic impact, compression, laminate, FRP, pre-stress

85

6.2. Introduction

Composite materials have seen increased use in aerospace, automotive, and ma-

rine industries as structural replacements for steel or aluminum. The reduced weight and

maintenance resulting from the use of composite materials can create savings by reducing

operational costs or increasing performance of ships, planes, and cars. Structural compo-

sites are typically quite brittle and witness significant damage due to impact. Mouritz et

al [1] outlined that the knowledge base must be extended on the effects of ballistic im-

pact, air blast, water blast, and fire on the residual properties of composite structures.

Current test methods utilize a compression after impact (CAI) test to obtain the residual

compressive strength of a structure which has witnessed impact damage [49]. This paper

examines the residual compressive strength of fiberglass laminates subjected to impact

while under an in-plane compressive pre-stress.

The three widely accepted modes of in-plane compressive failure for laminated

composite materials are global buckling, bifurcation, and shear kink band failure [2-6].

Global buckling failure is entirely dependent on the Euler buckling failure associated

with the compression of long, slender components of any material type. Bifurcation or

delamination results when the global buckling strength exceeds the inter-ply bonding

strength. Failure results near the centerline of the thickness of a laminate and each half-

laminate buckling outward from the centerline. Shear kink band formation results from

the Euler buckling of individual fibers. If both the global buckling strength and the inter-

ply bonding strength exceed the fiber critical buckling strength, loaded fibers will exceed

the critical buckling curvature and fail. Failure occurs as a shear kink band thru the thick-

ness of the laminate perpendicular to the applied load [2-6]. Mixed failure modes can

86

occur depending on the strengths of each respective failure mode. Some of the test meth-

ods used to characterize the compressive strength of composite materials have included

ring compression, tube compression, combined loaded compression (CLC) [7], Celanese

compression, and IITRI compression [5, 6]. The failure strengths and failure modes are

highly dependent on the constraints used for testing. Span to thickness ratios have been

used as comparison methods for buckling strength [8, 9]. Dow and Rosen [4] created the

first models to predict the compressive strength of unidirectional composites using a

beam on an elastic foundation. Lo and Chim [5] improved on the original models by in-

cluding the shear modulus. Dharan and Lin [10] further improved the models by incorpo-

rating the interphase and modeling the unidirectional composite as a three part system.

Lamina Theory and Timoshenko’s Plate Theory have been used to predict the compres-

sive strength of woven laminated composites [3]. Compressive strengths are typically

normalized with respect to the critical buckling load as a means of comparison between

material type and constraint scenario [11-17].

The study of impact on composite materials is a very broad and complicated field.

The well-defined impact regimes for laminated composites are low velocity impact

(LVI), intermediate velocity impact (IVI), high velocity impact (HVI), and hyper velocity

impact (HPI) [18-20]. LVI covers the broadest forms of impact usually involving a large

mass impacting at relatively low velocities (<10 ms-1

). LVI events represent accidental

tool drops, cargo falling, or other non-static loading scenario. IVI events typically occur

between 10-100 ms-1

which range from rock debris to lower energy fragments. HVI or

ballistic impact typically involves projectiles of small mass traveling at high velocities

(>100 ms-1

). HVI events include ballistic impacts, fragment, shrapnel, and debris impact

87

[21]. HPI represents small mass meteorites impacting at velocities in excess of 2000 ms-1

.

This paper focuses on the IVI and HVI regimes for an orthotropic woven laminate im-

pacted with a steel sphere of 2 g mass.

Transverse impact of woven laminated orthotropic composites is a strain rate de-

pendent event. When subjected to a transverse load at low strain rates, fibers will flex and

absorb energy, but at high strain rates fibers will shear [22]. Cantwell and Morton [22]

demonstrated that low velocity impact caused surface damage at the point of impact

which increased radially as an effect of impact energy until perforation. Perforation re-

sulted in the formation of a 45° frustum-shaped fracture zone. Naik et al [23] suggested

that the energy absorption modes may include the kinetic energy of the displaced frus-

tum, secondary yarn deformation, tensile failure, delamination, and matrix cracking. Ha-

zell et al [24] showed that there is no significant difference in damage area when impact-

ed at velocities above the penetration threshold (up to 1875 ms-1

). Testing has indicated

that there exists a low velocity impact threshold which causes no damage followed by a

radially increasing damage area with additional impact energy up to the point of perfora-

tion after which minimal changes in damage area occur [24-26]. The consistency of the

damage area in terms of impact energy across many material types shows that damage

area results could be normalized in terms of the ballistic velocity. CAI testing has been

used as a method to determine the damage created due to impact energy [9, 17, 27-30].

CAI testing is a post-impact compression test which does not account for any synergistic

effects that would be witnessed if a structure was impacted under pre-stressed conditions.

Pre-stressed impact testing and analysis has shown that impact response is highly

dependent on the direction and magnitude of in-plane pre-stress. Tensile pre-stress results

88

in higher peak stress and a shorter contact duration, while compressive pre-stress results

in lower peak stress and a longer contact duration [14, 31-36]. Experimental results have

shown that impact on composite laminates at high compressive or tensile pre-stress re-

sulted in failure perpendicular to the applied load while low levels of pre-stress caused no

discernible difference from CAI test damage [12, 14, 15, 25, 31, 37-45]. Herszberg and

Weller [15] showed that there was little to no effect on the ballistic limit for compressive-

ly pre-stressed impact on both the concave and convex faces. Herszberg and Weller [15]

and Chai [45] both examined the ballistic impact of compressively pre-stressed laminates

and observed a transient failure threshold. Chai [45] and McGowan and Ambur [39] ob-

served the reduction of residual strength when pre-stressed with significant compression.

The constitutive analysis of pre-stressed impact has been approached from several

directions. Sun and Chattopadhyay [35] used a normalized contact force and plate theory

to numerically analyze the pre-stressed condition. Zhou [46] and Zhou and Rivera [47]

preconditioned laminates with embedded shapes to replicate the residual strength of de-

lamination or open hole damage using fracture mechanic methods. Mikkor et al [26] uti-

lized PAM-CRASH finite element analysis to examine pre-stressed impact. Rossikhin

and Shitikova [33, 34] analyzed the behavior of the transient waves generated due to

shock impact for a pre-stressed circular plate and rod impact on a pre-stressed rectangular

plate which propagate along the median surfaces as diverging circles. Khalili et al [48]

used Sveklo’s elastic contact theory for anisotropic bodies to analyze the pre-stressed

impact of unidirectional graphite/epoxy composites in tension for both longitudinal and

transverse directions. Zheng and Bienda [36] analyzed the impact response using a Fouri-

er series expansion and Laplace transform technique by incorporating shear deformation

89

and permanent deformation for pre-stressed impact. Choi [13] and Choi et al [31] used a

modified displacement field to create a finite element modeling code to determine the

impact response on pre-stressed laminates. Heimbs et al [37] utilized LS-DYNA’s

‘stacked shell’ model which allows for the definition of delamination energy release rates

to account for the impact damage caused in a pre-stressed condition. Ghelli and Minak

[14] utilized a Fortran program to simulate the LVI response of pre-stressed laminates in

terms of span-to-thickness ratios. Loktev [32] used Uflyand – Mindlin equations and a

series expansion based on a Legendre polynomial and Laurent series to examine the ten-

sile pre-stressed impact of composite laminates. Chai [45] utilized moire interferometry

and a high speed camera to experimentally measure the damage growth rates of compres-

sively pre-stressed impact for carbon/epoxy laminates. Measurements were used to define

the energy release rates for the defined empirical model. This study expands on the fields

examined by previous researchers, defines observed failure thresholds, and outlines em-

pirical formulas derived from experimental data.

6.3. Materials

Two material data sets were used in this study; a 5.4 mm thick glass/vinyl ester

laminate and a 6.0 mm thick glass/vinyl ester laminate. The 5.4 mm thick laminate was

manufactured using vacuum-assisted resin transfer molding (VARTM) with six layers of

Fiber Glass Industries (FGI) Rovcloth® 3273 and Derakane 510A-40 vinyl ester resin.

Samples had average dimensions of 156 mm x 103 mm x 5.4 mm. The 6.0 mm thick lam-

inate was manufactured using VARTM with 10 layers of FGI Rovcloth® 2454 and De-

rakane 510A-40 vinyl ester resin. Samples were machined to dimensions of 156 mm x

103 mm x 6.0 mm to accommodate testing in the CAI fixture used in ASTM D7137M –

90

05 [49]. Samples were machined square and parallel with the warp fibers in the length

direction and weft fibers in the width direction. A 7.6 mm diameter stainless steel sphere

was used to impact the samples. A single-stage light-gas gun was used to propel foam

sabots down the 4.6 m barrel. Sabots house the projectiles and strike a sabot stripper at

the end of the barrel which breaks apart the sabot and allows the projectile to proceed

unhindered.

6.4. Procedure

Laminates were manufactured using a VARTM method. Samples of dimensions

of 156 mm x 103 mm were machined flat, square, and parallel. Samples were tap tested

utilizing a WichiTechTM Digital Tap Hammer and photographed with a backlight to

ensure sample quality. Samples were compressed in the Compression During Impact

(CDI) fixture using a low clearance hydraulic cylinder. A hydraulic transducer was used

to obtain real-time compressive loads and loaded samples were allowed to relax for at

least 60 seconds prior to impact. Compressed laminates were impacted with a spherical

projectile at velocities ranging from 50 ms-1

to 375 ms-1

using a single-stage light-gas gun

[50]. The samples were again photographed post-impact with a backlight to determine

delamination area. The samples were then compressed to failure in a CAI fixture to as-

sess the residual compressive strength after pre-stressed impact. The CAI fixture utilized

a clamped top and bottom condition to prevent brooming and a simply supported knife-

edge side support to allow uniform compression [49].

91

6.5. Results and Discussion

For the purposes of modeling relationships for both 5.4 mm and 6.0 mm lami-

nates, data was experimentally normalized using the failure threshold and ballistic limit

as shown below in Figures 1 and 2.

Figures 1 and 2: Failure threshold and ballistic limit for 5.4 mm glass/vinyl ester lami-

nate.

It was observed that the failure threshold decreased asymptotically as the impact

velocity increased to the ballistic limit. The value of the asymptote, shown in Figure 1, is

referred to in this paper as the failure threshold. The failure threshold was used as a

means to experimentally normalize data sets for preliminary regression analysis neglect-

ing the stiffness and residual strength of the laminate. Likewise, the ballistic limit was

utilized to experimentally normalize the impact velocity. Figure 3 shows the normalized

data of both 5.4 mm and 6.0 mm laminates.

92

Figure 3: Normalized failure modes for both 5.4 mm and 6.0 mm laminates.

It can be observed that comparison of failure envelopes for different laminates by

means of normalization is effective. Some data scatter was observed for the transition

from conical damage to the formation of an IISC, but the failure threshold transition was

very consistent. For the purposes of modeling, the normalized failure modes were addi-

tionally segmented into their respective penetration thresholds as shown in Figure 4.

93

Figure 4: Failure/penetration thresholds for 5.4 mm laminate.

It was observed that while the projectile reflected off the laminate, the compres-

sive pre-stress failure threshold changed according to the impact velocity. When the pro-

jectile was caught by or penetrated the laminates, the failure threshold was observed to

have no discernible change according to impact velocity. Based on these observations the

failure thresholds were reduced as shown in Figure 5 to include the transient failure enve-

lope (A), the steady state failure envelope (B), the IISC envelope (C), and the Conical

Damage Envelope (D).

94

Figure 5: Reduced failure envelopes for 5.4 mm thick laminate

The significant changes in failure that take place for different failure thresholds

require a piecemeal analysis for each failure envelope. The experimentally obtained

boundaries and residual strengths are given below in Table 1. The formulation of each

boundary condition and residual strength follows.

95

Table 1: Experimentally determined boundaries and residual strengths associated with

compressively pre-stressed impact failure envelopes for both 5.4 mm and 6.0 mm lami-

nates.

Normalized Impact Veloci-ty Boundary

Normalized Compressive Pre-Stress Boundary

Residual Compressive Strength (MPa)

A – Transi-ent Failure Envelope

0.2 > v/v50 > 0.8

σPS/σFT > 2.9 × ( v/v50)2 – 4.4 × ( v/v50) + 2.7

σRCS = 0

B – Steady State Fail-ure Enve-lope

v/v50 > 0.8 σPS/σFT > 1 σRCS = 0

C – IISC Envelope

0.2 > v/v50 > 0.8 v/v50 > 0.8

2.9 × ( v/v50)2 – 4.4 × ( v/v50) + 2.7 > σPS/σFT > 0.65 1 > σPS/σFT > 0.65

σRCS = 0.96 × σPS + 1.51 × σFT

1.44 × σPS-0.44 × ((vi

2-vo

2)/v502)-0.2 + 0.33 × σFT

× (vi2-vo

2)/v502 – 202

σRCS = 0.96 × σPS + 1.51 × σFT

1.44 × σPS-0.44 × ((vi

2-vo

2)/v502)-0.2 + 0.33 × σFT

× (vi2-vo

2)/v502 – 202

D – Conical Damage Envelope

0.2 > v/v50 > 0.8 v/v50 > 0.8

0.65 > σPS/σFT

0.65 > σPS/σFT

σRCS = 0.89 × σFT × ((vi2-

vo2)/v50

2)-0.25 σRCS = σFT

96

The transient failure envelope was experimentally curve fit using a polynomial

regression as shown below in Figure 6.

Figure 6: Formulation of the failure threshold boundary for both 5.4 mm and 6.0 mm

thick laminates.

It can be seen that the quadratic boundary used adequately describes the boundary for the

woven orthotropic E-glass/vinyl ester laminates examined. The limit of the transient fail-

ure boundary was found to be consistent with partial penetration of the laminate. Lami-

nates witnessing partial or full penetration exhibited a consistent failure threshold for the

range of impact velocities examined. Compressive strength is highly dependent on the

support geometry and unconstrained sample length of the test fixture. The CAI fixture

used in this study to determine failure strength of an undamaged laminate, as shown on

the vertical axis of Figure 6, was much lower than compressive strengths attained using

the CLC test method. CLC strength measurements correlated to a normalized compres-

97

sive pre-stress of 2.7, which correlated with the failure threshold boundary. For design

purposes, the residual compressive strength of the failed laminate is assumed to be zero.

The boundaries of the IISC envelope were defined by the failure threshold and the

conical damage threshold. Modeling the residual compressive strength in the IISC enve-

lope required a relationship in the form of

( ) ( ) ( ) (1)

where the residual compressive strength, , is related to the compressive pre-stress,

, and the kinetic energy, KE, of the projectile must be established. The constants α, β,

γ, and δ would need to be determined as well. In order to compare the compressive pre-

stress and the impact velocity, both terms were transformed into energy. The compressive

pre-stress was transformed into a pre-stressed energy factor in the laminate prior to and

after the impact event. The normalized pre-stressed energy factor was determined using

the load paths from the pressure transducer as shown in Figure 7.

Figure 7: Pressure transducer loading paths for 5.4 mm thick laminates comparing load

drop due to impact (denoted by star) and failure mode.

98

By comparing the pre-stressed energy factor before impact with the pre-stressed

energy factor after impact, the change in pre-stressed energy factor can be attained as

( )

, (2)

where the difference between the normalized pre-impact pre-stressed energy factor,

, and the normalized post-impact pre-stressed energy factor, , was found

using the difference of the stress before and after impact divided by the failure threshold

stress, . The volume, V, cancels out when normalized.

The change in the normalized pre-stressed energy factor is exponentially related

to the damaged area and residual strength as shown in Figure 8.

Figure 8: Exponential relationship between the normalized residual strength and the nor-

malized change of pre-stressed energy factor.

Figure 8 yields the first fundamental relationship of

( ) ( ). (3)

99

The impact velocity was transformed into kinetic energy and normalized using the kinetic

energy of the ballistic limit. Figure 9 displays the result of comparing the normalized

kinetic energy with the normalized change of pre-stressed energy factor in terms of the

normalized compressive pre-stress.

Figure 9: Comparison of normalized kinetic energy and the change in normalized pre-

stressed energy factor in terms of the normalized compressive pre-stress.

In order to account for some data scatter and the lack of enough data points for

every pre-stress band, linear regression lines were forced to a zero intercept. The second

fundamental relationship is shown in Figure 9 to be

( ) , (4)

where the normalized kinetic energy, , is equal to A multiplied by the normalized

change in pre-stressed energy factor. A is a function relating the slope of the linear re-

gression in Figure 9 to its associated pre-stress. By comparing the slope of each regres-

100

sion line with its respective average pre-stress, an exponential relationship can be found

as shown in Figure 10.

Figure 10: Comparison of the slopes of the linear regressions determined in Figure 9 with

each respective average normalized compressive pre-stress.

Figure 10 yields the desired relationship between the regression slope of Figure 9 and the

normalized pre-stress to be

( ) ( ). (5)

By substituting Equation (5) into Equation (4) and solving for the change in normalized

pre-stressed energy factor, it can be found that

( )

. (6)

Substitution of Equation (6) into Equation (3) yields

( )

( )

, (7)

which can be simplified into the synergistic effect term of

( ) ( ) ( ). (8)

101

Since the variables altered in this study were pre-stress and impact velocity, the remain-

ing normalized terms from Equation (1) used were

( ) (9)

and

( ) √ (10)

Reassembling Equation (1) with the normalized terms shown in Equations (8), (9), and

(10) provides a normalized model in the form of

( ) ( ) √ . (11)

Multiplying both sides by the failure threshold yields the dimensionally stable model of

( )

( ) ( ) √ . (12)

Statgraphics 6.0 was used to analyze and optimize Equation (12). The model passed the

ANOVA analysis with a 95% certainty in the form of

( )

( ) ( ) √ . (13)

It can be seen in Figure 11 that high correlation was achieved between the optimized

model and the experimental results for both 5.4 mm and 6.0 mm laminates.

Figure 11: Correlation of predictive model to experimental residual strength for both 5.4

mm and 6.0 mm laminates.

102

Higher correlation can be attained by modeling laminate sets individually, but an inade-

quate number of samples were tested to ensure repeatability.

The Conical Damage Envelope was found to exist at normalized pre-stress values

lower than 0.65 and exhibited typical frustum-shaped impact damage. Figure 12 shows

the relationship between the residual compressive strength and the normalized kinetic

energy.

Figure 12: Conical damage comparison of residual compressive strength and normalized

kinetic energy for each laminate thickness.

Laminates impacted with a normalized kinetic energy higher than 0.64 exhibited

partial or full penetration. Penetrated laminates exhibited residual compressive strengths

consistent with the failure threshold. Laminates impacted with a normalized kinetic ener-

gy less than 0.64 resulted in no penetration. The equation used to describe the residual

compressive strength was created using the failure threshold which would be unique to a

laminate and the fourth root of the normalized kinetic energy is directly related to the

width of conical delamination. The coefficient was optimized.

103

6.6. Summary

The effect of in-plane compression during transverse ballistic impact of ortho-

tropic woven E-glass/vinyl ester laminates of 5.4 mm and 6.0 mm thicknesses has been

analyzed and several observations have been made.

1) A method for normalization of multiple material data sets was provided, though a

comparison of fiber types was not examined.

2) Failure thresholds including the transient failure envelope (A), the steady state

failure envelope (B), the IISC envelope (C), and the Conical Damage Envelope

(D) were defined for analysis and design purposes.

3) Threshold boundaries for the failure and conical damage envelopes were deter-

mined based on experimental data.

4) An empirical model was derived to predict the residual strength of laminates im-

pacted in the IISC envelope. Very good agreement was found, though additional

testing would be required to determine a constitutive equation to determine the re-

sidual strength of compressively pre-stressed impacted laminates.

Acknowledgements

We are grateful to support from the ONR Solid Mechanics program managed by

Dr. Yapa D. Rajapakse, Office of Naval Research. Some aspects of the compression fix-

ture for crashworthiness studies were funded through the Department of Energy, Gradu-

ate Automotive Technology Education (GATE) program; and we gratefully acknowledge

this support.

104

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19. Vaidya, U.K., Impact response of laminated and sandwich composites. Courses and

Lectures-International Centre for Mechanical Sciences, 2011(526): p. 97-192.

20. Bartus, S.D. and U.K. Vaidya, Performance of long fiber reinforced thermoplastics

subjected to transverse intermediate velocity blunt object impact. Composite Struc-

tures, 2005. 67(3): p. 263-277.

21. Naik, N.K. and P. Shrirao, Composite structures under ballistic impact. Composite

Structures, 2004. 66(1-4): p. 579-590.

22. Cantwell, J. and J. Morton, A comparison of the low and high velocity impact re-

sponce of cfrp. Composites Composites, 1989. 20(6): p. 514-514.

23. Naik, N.K., P. Shrirao, and B.C.K. Reddy, Ballistic impact behaviour of woven fabric

composites: Formulation. International Journal of Impact Engineering, 2006. 32(9): p.

1521-1552.

24. Hazell, P.J., et al., Penetration of a woven cfrp laminate by a high velocity steel

sphere impacting at velocities of up to 1875m/s. International Journal of Impact En-

gineering, 2009. 36(9): p. 1136-1142.

25. Nettles, A., A. Hodge, and J. Jackson, An examination of the compressive cyclic

loading aspects of damage tolerance for polymer matrix launch vehicle hardware.

Journal of Composite Materials, 2010. 45(4): p. 437-458.

26. Mikkor, K.M., et al., Finite element modelling of impact on preloaded composite

panels. Composite Structures, 2006. 75(1-4): p. 501-513.

27. Kinsey, A., D.E.J. Saunders, and C. Soutis, Post-impact compressive behaviour of

low temperature curing woven cfrp laminates. Composites Composites, 1995. 26(9):

p. 661-667.

106

28. Habib, F.A., A new method for evaluating the residual compression strength of com-

posites after impact. Composite Structures Composite Structures, 2001. 53(3): p. 309-

316.

29. Gillespie, J.W., A.M. Monib, and L.A. Carlsson, Damage tolerance of thick-section s-

2 glass fabric composites subjected to ballistic impact loading. Journal of Composite

Materials, 2003. 37(23): p. 2131-2147.

30. Aoki, Y., K. Yamada, and T. Ishikawa, Effect of hygrothermal condition on compres-

sion after impact strength of cfrp laminates. Composites Science and Technology,

2008. 68(6): p. 1376-1383.

31. Choi, I.-H., et al., Analytical and experimental studies on the low-velocity impact

response and damage of composite laminates under in-plane loads with structural

damping effects. Composites Science and Technology, 2010. 70(10): p. 1513-1522.

32. Loktev, A.A., Dynamic contact of a spherical indenter and a prestressed orthotropic

uflyand–mindlin plate. Acta Mechanica, 2011. 222(1-2): p. 17-25.

33. Rossikhin, Y.A. and M.V. Shitikova, Dynamic response of a pre-stressed transversely

isotropic plate to impact by an elastic rod. Journal of Vibration and Control, 2009.

15(1): p. 25-51.

34. Rossikhin, Y.A. and M.V. Shitikova, Dynamic stability of a circular pre-stressed elas-

tic orthotropic plate subjected to shock excitation. Shock and Vibration, 2006. 13(3):

p. 197-214.

35. Sun, C.T. and S. Chattopadhyay, Dynamic response of anisotropic laminated plates

under initial stress to impact of a mass. J. Appl. Mech. Journal of Applied Mechanics,

1975. 42(3): p. 693.

36. Zheng, D. and W.K. Binienda, Analysis of impact response of composite laminates

under prestress. J Aerosp Eng Journal of Aerospace Engineering, 2008. 21(4): p. 197-

205.

37. Heimbs, S., et al., Low velocity impact on cfrp plates with compressive preload: Test

and modelling. International Journal of Impact Engineering, 2009. 36(10-11): p.

1182-1193.

38. Kulkarni, M.D., R. Goel, and N.K. Naik, Effect of back pressure on impact and com-

pression-after-impact characteristics of composites. Composite Structures, 2011.

93(2): p. 944-951.

39. McGowan, D.M. and D.R. Ambur, Structural response of composite sandwich panels

impacted with and without compression loading. Journal of Aircraft, 1999. 36(3): p.

596-602.

107

40. Mitrevski, T., et al., Low-velocity impacts on preloaded gfrp specimens with various

impactor shapes. Composite Structures, 2006. 76(3): p. 209-217.

41. Pickett, A.K., M.R.C. Fouinneteau, and P. Middendorf, Test and modelling of impact

on pre-loaded composite panels. Applied Composite Materials, 2009. 16(4): p. 225-

244.

42. Robb, M.D., W.S. Arnold, and I.H. Marshall, The damage tolerance of grp laminates

under biaxial prestress. Composite structures., 1995. 32(1-4): p. 141.

43. Whittingham, B., et al., The response of composite structures with pre-stress subject

to low velocity impact damage. Composite Structures, 2004. 66(1-4): p. 685-698.

44. Wiedenman, N., Ballistic penetration of compressively loaded composite plates.

Journal of Composite Materials, 2006. 40(12): p. 1041-1061.

45. Chai, H., The growth of impact damage in compressively loaded laminates, 1982,

California Institute of Technology: Pasadena, CA, PhD Dissertation.

46. Zhou, G., Investigation for the reduction of in-plane compressive strength in precon-

ditioned thin composite panels. Journal of Composite Materials, 2005. 39(5): p. 391-

422.

47. Zhou, G. and L.A. Rivera, Investigation on the reduction of in-plane compressive

strength in thick preconditioned composite panels. Journal of Composite Materials,

2007. 41(16): p. 1961-1994.

48. Khalili, S.M.R., R.K. Mittal, and N. Mohammad Panah, Analysis of fiber reinforced

composite plates subjected to transverse impact in the presence of initial stresses.

Composite Structures, 2007. 77(2): p. 263-268.

49. ASTM D 7137, Standard test method for compressive residual strength properties of

damaged polymer matrix composite plates. 2005, West Conshohocken, PA: American

Society for Testing and Materials.

50. Bartus, S.D., Simultaneous and sequential multi-site impact response of composite

laminates, 2006, University of Alabama at Birmingham: Birmingham, AL, PhD Dis-

sertation.

108

7. GLOBAL SUMMARY

This study provided some insights into the failure modes and safety thresholds of

navy relevant composites in regards to ballistic impact when subjected to different de-

grees of in-plane compressive pre-stress.

1) A test fixture was designed and munfactured to conduct CDI testing. A test pro-

cedure was established to obtain repeatable, accurate results.

2) It was observed that beyond a threshold combination of impact velocity and de-

gree of pre-stress, the shape of the damage changes from circular to elliptical

leading to catastrophic damage.

3) Failure was witnessed using the impact under compression test method which was

not accounted for by standard CAI test methods.

4) Failure envelopes for the combined effects of pre-stress and impact have been de-

veloped for orthotropic glass/vinyl ester laminates, quasi-isotropic glass/vinyl es-

ter laminates, quasi-isotropic glass/vinyl ester sandwich composites, and car-

bon/vinyl ester laminates.

5) Although the testing of the CFRP system was sparse, it indicated that a GFRP

system would be better suited to structural application in compression, subject to

ballistic impact.

6) Since the ultimate compressive strength of a composite system is dependent on

thickness, boundary conditions, and lay-up, it is difficult to pin point a safety

109

threshold; but in this case, the safety threshold for the orthotropic GFRP was 30%

σUCS

, quasi-isotropic GFRP was 40% σUCS

, quasi-isotropic GFRP sandwich panel

was 40% σUCS

, and the orthotropic CFRP was 15% σUCS

.

7) Threshold boundaries for the failure and conical damage envelopes were deter-

mined based on experimental data.

8) An empirical model was derived to predict the residual strength of laminates im-

pacted in the IISC envelope. Very good agreement was found, though additional

testing would be required to determine a constitutive equation to determine the re-

sidual strength of compressively pre-stressed impacted laminates.

110

8. FUTURE WORK

With the groundwork laid for the testing of composite materials under compres-

sively pre-stressed impact, there are many avenues of future research.

1) Additional studies characterizing the residual strength of materials with varying

modulus, strain to failure, and strain rate sensitivity in conjunction with FEA mod-

eling could lead to a constituatively based equation for residual strength under

compressively pre-stressed impact.

2) Studies on partial-edge compression during impact could be used to characterize

the effects resulting from inherent misalignment during manufacturing.

3) Multi-strike compression during impact studies would examine the effect of ma-

chine gun fire on a pre-stressed laminate. The study would also result in the exper-

imental determination of delamination overlap.

4) The effect of sample size, clamped/unclamped sample dimension, impactor

size/shape on the residual compressive strength of laminates needs to be analyzed.

111

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Journal of Composite Materials, 2010. 45(4): p. 437-458.

113

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elastic orthotropic plate subjected to shock excitation. Shock and Vibration, 2006.

13(3): p. 197-214.

47. Sun, C.T. and S. Chattopadhyay, Dynamic response of anisotropic laminated

plates under initial stress to impact of a mass. J. Appl. Mech. Journal of Applied

Mechanics, 1975. 42(3): p. 693.

48. Zheng, D. and W.K. Binienda, Analysis of impact response of composite

laminates under prestress. J Aerosp Eng Journal of Aerospace Engineering, 2008.

21(4): p. 197-205.

49. Kulkarni, M.D., R. Goel, and N.K. Naik, Effect of back pressure on impact and

compression-after-impact characteristics of composites. Composite Structures,

2011. 93(2): p. 944-951.

50. Mitrevski, T., et al., Low-velocity impacts on preloaded gfrp specimens with

various impactor shapes. Composite Structures, 2006. 76(3): p. 209-217.

51. Robb, M.D., W.S. Arnold, and I.H. Marshall, The damage tolerance of grp

laminates under biaxial prestress. Composite structures., 1995. 32(1-4): p. 141.

52. Whittingham, B., et al., The response of composite structures with pre-stress

subject to low velocity impact damage. Composite Structures, 2004. 66(1-4): p.

685-698.

115

53. Khalili, S.M.R., R.K. Mittal, and N. Mohammad Panah, Analysis of fiber

reinforced composite plates subjected to transverse impact in the presence of

initial stresses. Composite Structures, 2007. 77(2): p. 263-268.

54. Bartus, S.D., Simultaneous and sequential multi-site impact response of

composite laminates, 2006, University of Alabama at Birmingham: Birmingham,

AL, PhD Dissertation.