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This is to certify that the
thesis entitled

EFFECTS OF ARCH CAMBER AND BOUNDARY CONDITION ON
IMPACT-BASED ENERGY ABSORPTION

presented by

Peter John Schulz

has been accepted towards fulﬁllment
of the requirements for the

MS. degree in Mechanical Engineengg

 

 

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2105 p:IClRC/DateDue.indd-p.1

EFFECTS OF ARCH CAMBER AND BOUNDARY CONDITION ON IMPACT-
BASED ENERGY ABSORPTION

By

Peter John Schulz

A THESIS
Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of
MASTER OF SCIENCE

Department of Mechanical Engineering

2006

ABSTRACT

EFFECTS OF ARCH CAMBER AND BOUNDARY CONDITION ON IMPACT-
BASED ENERGY ABSORPTION

By

Peter John Schulz

Flat panels made of ﬁber composites have high energy absorption capability with low
density when subjected to low-velocity impact. This thesis research focused on studying
the effects of structural curvature on the composite’s energy absorption ability. Arched
composites with three curvatures were fabricated and centrally impacted at low
velocities. Experimental results showed that the contact duration, the maximum
deﬂection and the energy absorption increased as the arch camber increased while the
stiffness and the peak load decreased. It was also found that the boundary condition
played an important role in the energy absorption process. Three boundary conditions
termed bar-clamped, frame-clamped and bolted were investigated. Bar-clamped
specimens experienced the highest slippage with respect to the boundaries during central
impacts followed by the frame-clamped ones. Bolted specimens had the least slippage
and showed the most consistent results. The slippage of the boundaries in the specimens

produced additional energy absorption.

DEDICATION

This work is dedicated to my wife Lisa and my parents for supporting me during my time

in college.

iii

ACKNOWLEDGEMENTS

Many thanks to my advisor Dr. Dahsin Liu for his guidance and teaching me to think

creatively. I would also like to thank my committee members Dr. Alfred Loos and Dr.

Patrick Kwon.

iv

TABLE OF CONTENTS

LIST OF TABLES ........................................................................................................... viii
LIST OF FIGURES ............................................................................................................. x
1 . INTRODUCTION ....................................................................................................... 1
1.1 Literature Survey ................................................................................................. 2
1.2 Scope of Study ..................................................................................................... 6
1.2 Organization ........................................................................................................ 6

2. FABRICATION OF ARCHED SPECIMENS ............................................................ 8
2.1 Composite Material ............................................................................................. 8
2.2 Manufacturing Procedures ................................................................................... 8
2.3 Curing Process ................................................................................................... 10
2.4 Specimen Preparation ........................................................................................ 13

3. TESTING ................................................................................................................... 1 5
3.1 Testing Equipment ............................................................................................. 15
3.1.1 Low-velocity drop-weight impact test ....................................................... 15
3.1.2 Low-velocity impact data .......................................................................... 17

3 .2 Operating Procedure .......................................................................................... 18
3.2.1 Pre-impact test adjustments ....................................................................... 18
3.2.2 Impact test procedure ................................................................................ 19
3.2.3 Rebounding and perforation ...................................................................... 19

3 .2.3 Data Acquisition ....................................................................................... 19

4. DATA ANALYSIS ................................................................................................... 21
4.1 Load-Deﬂection Relation .................................................................................. 21
4.1.1 Extension Method ...................................................................................... 24
4.1.2 Impact Stiffness ......................................................................................... 25
4.1.3 Peak Load .................................................................................................. 26
4.1.4 Maximum Deﬂection ................................................................................. 26

4.2 Energy Proﬁle .................................................................................................... 27

5. FLAT PANEL BOUNDARY CONDITION STUDY .............................................. 29
5.1 Boundary conditions and specimens ................................................................. 29
5.2 Load-deﬂection curves for beam and plate ....................................................... 30
5.3 Energy proﬁle .................................................................................................... 31
5.4 Characteristics of impact response .................................................................... 32
5.5 Summary ............................................................................................................ 33

6. BOUNDARY CONDITIONS AND EFFECTS ........................................................ 34
6.1 Types of Boundary Conditions .......................................................................... 35
6.2 [0/90]3s Composite with Small Arch Curvature ................................................ 36
6.2.1 Load-deﬂection Curves ............................................................................. 36

6.2.2 Energy Proﬁle ........................................................................................... 40

6.2.3 Characteristics of Impact Response .......................................................... 41
6.2.4 The Damage Process ................................................................................. 42

6.3 [O/90]3s Composite with Medium Arch Curvature ........................................... 44
6.3.1 Load-deﬂection Curves ............................................................................. 44
6.3.3 Characteristics of Impact Response .......................................................... 47
6.3.4 The Damage Process ................................................................................. 48

6.4 [0/90]3s Composite with Large Arch Curvature ............................................... 48
6.4.1 Load-deﬂection Curves ............................................................................. 48
6.4.2 Energy Proﬁle ........................................................................................... 50
6.4.3 Characteristics of Impact Response .......................................................... 51
6.4.4 The Damage Process ................................................................................. 52

6.5 Summary of results ........................................................................................... 52

. CURVATURE AND EFFECTS ............................................................................... 54
7.1 Load-deﬂection Curves ..................................................................................... 54
7.2 Energy Proﬁles .................................................................................................. 56
7.3 Characteristics of Impact Response .................................................................. 57
7.4 Summary ........................................................................................................... 64
BUCKLING AND DAMAGE PROCESS ............................................................... 65

8.1 Buckling process literature review .................................................................... 65
8.2 Buckling Process ............................................................................................... 66
8.3 Damage Process for ﬂat panel composite ......................................................... 69
8.4 Damage process for arched composite ............................................................. 72
8.5 Summary ........................................................................................................... 74
CONCLUSIONS AND FUTURE STUDY .............................................................. 76

9.1 Conclusions ....................................................................................................... 76
9.2 Future Study ...................................................................................................... 78
APPENDICIES ................................................................................................................. 80
APPENDIX A ................................................................................................................... 81
MATLAB code for producing extension method line and calculating impact energy
and absorbed energy ..................................................................................................... 81
APPENDIX B ................................................................................................................... 84
Flat specimens with two sides frame clamped for plate versus beam impact study (hot
press cured) ................................................................................................................... 84
APPENDD( C ................................................................................................................... 89

Flat specimens with four sides frame clamped for plate versus beam impact study (hot
press cured) ................................................................................................................... 89

vi

APPENDIX D ................................................................................................................... 94

Flat specimens bolted (hot press cured) ........................................................................ 94
APPENDD( E ................................................................................................................... 98
Flat specimens frame clamped (autoclave cured) ......................................................... 98
APPENDD( F .................................................................................................................. 102
Small arch with bar clamped boundary condition ...................................................... 102
APPENDD( G ................................................................................................................. 105
Medium arch with bar clamped boundary condition .................................................. 105
APPENDD( H ................................................................................................................. 109
Large arch with bar clamped boundary condition ...................................................... 109
APPENDD( I .................................................................................................................. 112
Small arch with frame clamped boundary condition .................................................. 112
APPENDD( J .................................................................................................................. 116
Medium arch with frame clamped boundary condition .............................................. 116
APPENDD( K ................................................................................................................. 121
Large arch with frame clamped boundary condition .................................................. 121
APPENDD( L ................................................................................................................. 125
Small arch with bolted boundary condition ................................................................ 125
APPENDIX M ................................................................................................................ 129
Medium arch with bolted boundary condition ............................................................ 129
APPENDD( N ................................................................................................................. 134
Large arch with bolted boundary condition ................................................................ 134
REFERENCES ............................................................................................................... 139

vii

Table 1.1.1

Table 2.1.1

Table 5.4.1

Table 6.2.1

Table 6.3.1

Table 6.4.2

Table 7.2.1

Table 7.3.1

Table 7.3.2

Table 7.3.3

Table B.l

Table B.2

Table C]

Table C.2

Table D1

Table D2

Table E.1

Table E.2

Table F.1

Table F.2

Table G.1

LIST OF TABLES

Summary of literature on arched, cylindrical, or dome composites. ......... 5
Arch and mold dimensions ......................................................................... 9
Impact characteristics for plate and beam ................................................ 32
Characteristics of impact response for [0/90]3s with small arch. .............. 41
Characteristics of impact response for [0/90]3s medium arch. ................. 47
Characteristics of impact response for [0/90]3s with large arch. .............. 52
Bolted specimens mass and maxium absorbed energy. ............................ 57
Impact characteristics for bar clamped [0/90]3s ....................................... 62
Impact characteristics for frame clamped [0/90]3s specimens. ................ 62
Impact characteristics for bolted [0/90] 3,s specimens. ............................... 63
Flat panel (beam) data ................................................................................. 86
Flat panel (beam) Energy data. ................................................................... 86
Flat panel (plate) data ................................................................................... 91
Flat panel (plate) energy data. ...................................................................... 91
Bolted ﬂat panel data. ............................................................................... 96
Bolted ﬂat panel energy data. ................................................................... 96
Frame clamped ﬂat panel data. ................................................................... 100
Frame clamped flat panel energy data. ....................................................... 100
Bar clamped small arch energy data. .......................................................... 103
Bar clamped small arch data. ...................................................................... 103
Bar clamped medium arch energy data ................................................... 107

viii

Table G.2 Bar clamped medium arch data ............................................................... 107

Table H.1 Bar clamped large arch data .................................................................... 110
Table H.2 Bar clamped large arch energy data. ....................................................... 111
Table 1.1 Frame clamped small arch data ................................................................... 114
Table 1.2 Frame clamped small arch energy data ....................................................... 114
Table I .1 Frame clamped medium arch data. ............................................................. 117
Table I .1 Frame clamped medium arch data. ............................................................. 118
Table J .2 Frame clamped medium arch energy data. ................................................. 118
Table K.1 Frame clamped large arch data. .............................................................. 123
Table K.2 Frame clamped large arch data. .............................................................. 123
Table L.1 Bolted small arch data ................................................................................. 127
Table L.2 Bolted small arch energy data. .................................................................... 127
Table M.1 Bolted medium arch data. ....................................................................... 131
Table M.2 Bolted medium arch energy data. ........................................................... 131
Table N.1 Bolted large arch data. ............................................................................ 136
Table N.2 Bolted large arch energy data. ................................................................ 136

Figure 2.1.1

LIST OF FIGURES

(a) Schematic of end view of arched composite with dimensions, (b)

Schematic of arched composite showing the width ............................................................. 9
Figure 2.1.2 Steel mold schematic of pipe cut lengthwise on a plate. ........................... 10
Figure 2.1.3 Mold setup with composite strips and foot valve location. ....................... 11
Figure 2.1.4 Side view of bagging setup for autoclave curing. ..................................... 12
Figure 3.1.1 Side and front view schematic of impact testing. ...................................... 16
Figure 4.1.1 Load-deﬂection curves for frame clamped ﬂat panel and bolted medium
arch ................................................................................................................................ 22
Figure 4.1.3 Load-deﬂection curves of bolted medium arch. ........................................ 23
Figure 4.1.2 Load-deﬂection curves of bolted ﬂat panels. ............................................ 23
Figure 4.1.2 Load-deﬂection curve of frame clamped ﬂat panel ................................... 25
Figure 4.1.3 Load-deﬂection curve of bolted medium arch. ......................................... 25
Figure 4.2.1 Energy proﬁles for bolted ﬂat panel and bolted medium arch specimens.28
Figure 5.1.1 Flat panels (a) plate (b) beam. ................................................................... 30
Figure 5.2.1 Load-deﬂection curves for ﬂat plate with four frame clamped edges. ...... 30
Figure 5.2.2 Load—deﬂection curves for ﬂat beam with two ends frame clamped. ....... 31
Figure 5.3.1 Energy proﬁles for both plate and beam. .................................................. 32
Figure 6.1.1 Boundary conditions types:(a) bar clamped, (b) frame clamped and (c)
bolted.................. ......................................................................................................... 35
Figure 6.2.1 Bar clamped [0/90]3s with small arch. ....................................................... 37
Figure 6.2.2 Frame clamped [0/90]3s with small arch. .................................................. 37
Figure 6.2.3 Bolted [0/90]3s with small arch. ................................................................ 38

Figure 6.2.4

Typical load-deﬂection curves from the three types of boundary

conditions for [0/90]3s with small arch. ............................................................................ 39
Figure 6.2.5 Energy proﬁles for [0/90]3s with small arch for all three types of boundary
conditions ....................................................................................................................... 40
Figure 6.2.6 (a)Schematic diagram of tup and buckled arch composite and
(b)photograph of schematic in (a). .................................................................................... 43
Figure 6.3.1 Bar clamped [0/90]3s with medium arch ....................................................... 44
Figure 6.3.2 Frame clamped [0/90]3s with medium arch. ............................................. 45
Figure 6.3.3 Bolted [0/90135 with medium arch ............................................................. 46
Figure 6.4.1 Bar clamped [0/90]3s with large arch. ....................................................... 49
Figure 6.4.2 Frame clamped [0/90]3s with large arch .................................................... 49
Figure 6.4.3 Bolted [0/90]3s with large arch. ................................................................. 50
Figure 6.4.4 Energy proﬁle for [0/90]3s with large arch for all boundary conditions. ..51
Figure 6.5.1 Composite diagram of impact characteristics ............................................ 53
Figure 7.1.1 Typical load-deﬂection curves for bolted arches and ﬂat panel ................ 54
Figure 7.1.2 First maximum load and associated deﬂection .......................................... 55
Figure 7.1.3 Peak load and associated deﬂection. ......................................................... 56
Figure 7.2.1 Energy proﬁles for bolted small, medium and large arch, and ﬂat panel..57
Figure 7.3.1 Stiffness as a function of camber. .............................................................. 58
Figure 7.3.2 Peak load as a function of camber. ............................................................ 59
Figure 7.3.3 First peak load for bolted specimens. ........................................................ 60
Figure 7.3.4 Maximum deﬂection for each arch height. ................................................ 60
Figure 7.3.5 Contact duration for each arch height ........................................................ 61

Figure 8.2.1

(a) Common bolted small arch load-deﬂection curve (b) Schematic of

specimen buckling and deﬂection at critical points ........................................................... 67

xi

Figure 8.2.3 (a) Common bolted large arch load-deﬂection curve (b) Schematic of
specimen buckling and deﬂection at critical points. ......................................................... 67

Figure 8.2.2 (a) Common bolted medium arch load-deﬂection curve (b) Schematic of

specimen buckling and deﬂection at critical points. ......................................................... 67
Figure 8.2.4 Deﬂection of small, medium, and large arch peaks during impact. ......... 68
Figure 8.3.1 Bottom view of [0/90]3s of bolted ﬂat panel. ........................................... 69
Figure 8.3.2 Top view of [0/90]3s bolted ﬂat panel. ..................................................... 70
Figure 8.3.3 Bottom view of [0/90]35 frame clamped ﬂat panel. .................................. 71
Figure 8.3.4 Top view of [0/90]3s frame clamped ﬂat panel frame. ............................. 71
Figure 8.4.1 Side view of damaged bolted [0/90]3s large arch ..................................... 72
Figure 8.4.2 Top view of damaged bolted [0/90]3s large arch composite. ................... 73
Figure 8.4.3 Top view of delamination of [O/90]3s frame clamped medium arch
showing delamination pattern. .......................................................................................... 74
Figure B] Load-deﬂection curves for ﬂat beam with two sides frame clamped. ...... 85
Figure B.1 Flat panel (beam) damaged specimen photos. .......................................... 87
Figure B.2 Flat panel (beam) damaged specimen photos. .......................................... 88
Figure C.1 Load-deﬂection curves for ﬂat plate four sides frame clamped. .............. 90
Figure C .2 Flat panel (plate) damaged specimen photos. ........................................... 92
Figure C.3 Flat panel (beam) damaged specimen photos. .......................................... 93
Figure D.1 Load-deﬂection curves for bolted ﬂat specimens. .................................... 95
Figure D.2 Bolted ﬂat panel damaged specimen photos. ............................................ 97
Figure B] Frame clamped ﬂat panel load-deﬂection curves. .................................... 99
Figure E.2 Frame clamped ﬂat panel damaged specimen photos ............................. 101
Figure B] Bar clamped small arch load-deﬂection curves. ..................................... 103
Figure F2 Bar clamped small arch damaged specimen photos. .............................. 104

xii

Figure G.1
Figure G.2
Figure H.1
Figure H.2
Figure 1.1
Figure 1.2
Figure I .1
Figure J .2
Figure I .3
Figure K.1
Figure K.2
Figure L.1
Figure L.2
Figure M.1
Figure M.2
Figure M.2
Figure N.1
Figure N.2

Figure N.3

Bar clamped medium arch load-deﬂection curves .................................. 106
Bar clamped medium arch damaged specimen photos. .......................... 108
Bar clamped large arch load-deﬂection curves ....................................... 110
Bar clamped large arch damaged specimen photos. ............................... 111
Frame clamped small arch load-deﬂection curves .................................... 113
Frame clamped small arch damaged specimen photos. ............................ 115
Frame clamped medium arch load-deﬂection curves. ............................ 117
Frame clamped medium arch damaged specimen photos ....................... 119
Frame clamped medium arch damaged specimen photos ....................... 120
Frame clamped large arch load—deﬂection curves. ................................. 122
Frame clamped large arch damaged specimen photos. ........................... 124
Bolted small arch load-deﬂection curves. ............................................... 126
Bolted small arch damaged specimen photos. ........................................ 128
Bolted medium arch load-deﬂection curves. ......................................... 130
Bolted medium arch damaged specimen photos .................................... 132
Bolted medium arch damaged specimen photos. ................................... 133
Bolted large arch load-deﬂection curves. ............................................... 135
Bolted large arch damaged specimen photos. ......................................... 137
Bolted large arch damaged specimen photos. ......................................... 138

xiii

1. INTRODUCTION

Composite materials are a very effective form of vehicle armor due to their low
density and high strength. Work at the Armor Research Lab [I] sought to show the
effectiveness of glass-reinforced plastics compared to conventional steels. A ﬁber-
reinforced epoxy composite is less dense than a conventional steel, but has a larger
damage areas and less residual integrity. As a result armor systems with composites are
designed in a patterned cellular design such that damage to one cell does not affect
adjacent cells [2].

With the increasing demand for improved armor new designs must be tested.
Typically laminated composites are reinforced in the z-direction to improve interlaminar
strength [3]. Finding the most effective arrangement of the composite materials for
energy absorption and weight reduction are desirable. Finding the most effective
geometry and ﬁber angles for energy absorption are the goal. The arch is a common
structural feature, which supports a structure, yet leaves space for an entryway into a
building or decreases the amount of material needed in a bridge. It is unique in that
stresses are distributed in plane. With the topological design of the arch and ﬁber angles
a unique energy absorbing structure can be designed.

When designing a composite that absorbs the energy from an impact several
parameters are typically considered. The strength to weight ratio is a measure of the
composite strength compared to how much it weighs. Where the stiffness to weight ratio
is a measures of the stress to strain ratio to the weight. The lightweight, high strength and

stiffness are what make composites so lucrative compared to steals and other metals.

Some study has been done on arched laminated composites, but typically for
measuring the impact response, characterize the damage, stress distribution, and buckling
[4-18]. Work focusing on the energy absorption, curvature effects, and boundary
conditions have not been widely studied. Damage characterization and buckling have
been a focus of study, but give only some insight into what curvature and boundary
conditions are best for armor.

1.1 Literature Survey

Understanding the failure phenomena of composite materials provides the key to
energy absorption. Work by Kistler and Waas [12-14] has been done to characterize the
response of arched composite panels due to impact. They showed that as the thickness
decreases the curvature effects become more important. They concluded that ﬂat panels
respond to impacts with larger peak forces than the arched panels. Where the ﬂat panel
has a smaller maximum displacement. Kim, Irn, and Yang [11] in a similar study
mentioned that as the radius of curvature increases the contact force decreases. They also
showed that a composite design with the smallest radius of curvature and the most
interlaminar surfaces has the least amount of damage. As the panel becomes ﬂat the
impact force increases. Finite element work done by Zafer, et a1. [16] shows this same
trend, but he also mentions that with increasing curvature the maximum contact load will
converge to a constant.

Work by Ambur, et a1. [20] on the scaling effects of adjusting the ply-level or the sub-
laminate in both ﬂat and arched panels for non-linear impact response showed that the
arched composites dissipate energy due to structural deformation and retain higher

residual stiffness than a ﬂat panel. In other work by Ambur, et al. [4] the contact force

initially increases as the radius of curvature becomes large. Eventually the contact force
decreases as the radius of curvature continues to increase.

Baucom, Zikry, and Rajendran [22] said that in ﬂat panels the main modes of energy
dissipation are through delamination and matrix cracking, a stitched 3D woven fabric
absorbs more energy than a 2D woven. Cheeseman and Bogettie [23] mentioned that the
effects of wave propagation in a fabric during impact are an area of study. Woven fabrics
are typically used to catch the projectile and spread the damage. A ﬂat panel goes
through a stiffening phase during impact. This is when the ﬁbers are pulled taunt as the
specimen bends. Kirkwood, et a1. [24] mentions one of the energy modes is ﬁber pullout.

Eventually the layers will delarninate and many times ﬁber breakage will occur, both
causing energy dissipation. Shenoi and Wang [18] studied the through-thickness stresses
of arched composite laminates. Their work shows the maximum stress is on the inner
side of the mid-plane. It would be deduced that failure would likely happen near the mid-
plane ﬁrst. The projectile geometry is also of signiﬁcance where a blunt projectile shears
the ﬁbers. In most paper reviews a hemispherical design is used. In work by Hersberg
and Weller [8] composite laminates with stitching were post-buckled and impacted. The
critical load ﬁom the projectile decreased with increasing preloading. Stitching reduced
the damage area caused by impact, whereas specimens in tensile load with stitching
showed no change in the damage area.

Work by Short, Guild, and Pavier [19] on impact on arched composites showed a
linear trend of damage area with increasing impact energy for a ﬂat panel and two

different radii. Ging, et al. [7] showed that low-speed drop impact tests in the transverse

direction of cylinders with ﬁbers angles at i 55° there was a non-linear trend overall in

the damage area with increasing impact energy after a certain energy level. The trend
initially had a very sharp slope and after approximately 6.1 of energy the slope decreased
dramatically.

Chun and Lam [5] worked on the modeling of three types of loading on arched panels,
where the loading types are step, triangular, and explosive. They concluded analytically
that the transverse deﬂection is mainly due to the impulses of the external loading, not to
the peak of the load.

For an armor system a combination of ceramics and polymer matrix composites
(PMC) would form a sandwich composite for ideal armor design [25-26]. Arched PMC
would take the place or be added to conventional ﬂat panel designs. A review of
literature did not show arched composites in an armor system.

In summary of the literature mentioned on arched, cylindrical, and dome composites
Table 1.1.1 was formed. It covers the testing type, analyses type, specimen geometry,
radius of curvature, camber, length, thickness and the ﬁber angles. The analysis types
ranged from low-velocity to quasi-static, with one studying using pressures at various
frequencies. The analysis types were experimental and ﬁnite element modeling (FEM).
The majority of the studies were done on ached composites. The boundary conditions
were clamped for most of the studies, but some were clamped on the arched sides and

others on the ends of the arches.

Summary of literature on arched, cylindrical, or dome

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1.2 Scope of Study

The scope of this study was two fold. One was to investigate the relationship between
laminated composite curvature and energy absorption for low-velocity impact and the
other to identify the effect of boundary condition on energy absorption. All specimens
were made of the same pre-impregnated (prepreg) tape material and a cross-ply stacking
sequence of [0l90]3s such that a comparison can be made between tests. Analysis of the
load-deﬂection relation, the energy proﬁle and the damage process were of primary
interest as they provide the insight into the impact behavior of composites, such as peak
load, deﬂection at the peak load, specimen stiffness, maximum specimen deﬂection,
contact duration, energy absorption and damage modes.
1.2 Organization

The thesis is organized into nine chapters. Chapter 1 is an introduction of composite
armor design and arched composites. Chapter 2 gives the details on the fabrication
process, which consists of lamination of the prepreg tape, curing, and specimen
preparation. Chapter 3 covers the equipment for testing, operating procedure, and data
acquisition. Chapter 4 gives the details on the data analysis of the results obtained from
the test procedure. Chapter 5 discusses the results from impact tests for specimens ﬁxed
on four sides versus two sides (plate vs. beam problem). The purpose was to show the
boundary condition change from conventional clamping on four sides to only two sides
clamped for ﬂat panels. Chapter 6 is the analysis of the boundary condition and its
effects on the impact on ﬂat and arched composites clamped on two ends. Chapter 7 is
the analysis of the effects of curvature on the energy absorption and impact behavior.

Chapter 8 focuses on the buckling process of the arched composites. Additionally the

damage process for both the ﬂat panel and arched composites are covered. Chapter 9 is

the conclusions of this research study and recommendations for the future.

2. FABRICATION OF ARCHED SPECIMEN S

The fabrication process consisted of layering prepreg (pm-impregnated) tape, molding
the arched specimens, and curing the arched laminates in an autoclaving process. All
arched specimens were fabricated from a glass/epoxy prepreg tape. They were twelve
plies with a symmetric conﬁguration to avoid any warpage due to unsymmetric thermal
contraction after curing. To obtain the arched specimens, the composites were wrapped
onto arched molds and cured in an autoclave. The other ﬂat panels were cured in the
autoclave as well as a hot press and are labeled in the appendecies.
2.1 Composite Material

The glass/epoxy prepreg tape is a product of Cymat [27] with an item number
CY COM 1003/W-490, but was formally a 3MTM product under the name Scotchply. The
prepreg tape is a non-woven, unidirectional tape with continuous glass ﬁbers along the
length of the tape. The tape is in 30.48cm (12”) wide rolls at 65 .8m (72 yards) per roll.
The glass is an electrical grade, i.e. E-glass. The tape was sealed inside a large ZiplocTM
bag and stored in a freezer. It was removed from the freezer approximately 45-60 minutes
prior to use to prevent condensate buildup on the tape, to allow ﬂexibility, and to prevent
it ﬁ'om un-sticking from the wax paper backing before stacking with the other layers.
2.2 Manufacturing Procedures

A conventional stacking sequence of [0/90]3s was chosen for this study. In
manufacturing, the prepreg tape was ﬁrst cut into 30.48cmx30.48cm (12”x12”) layers.
For ﬂat panels, twelve layers of tape were stacked into a 30.48cmx30.48cm (12”x12”)
laminate. For arched specimens, the uncured laminate was further cut into 6.99cm

(2.75”) wide strips. The strips were then trimmed to desired lengths such that they could

be wrapped onto molds without any excess. For the small arch, the strip length was
12.7cm (5.0”), the medium arch 13.34cm (5.25”), and the large arch 13.97cm (5.5”).
Figure 2.1.1 shows the dimensions of each arch. It can be seen in Figure 2.1.1(a) that the
span of each arch is maintained at 7.62cm (3.0”). The thickness is also maintained at
0.249cm (0.098”). The “wings” on either side are maintained at 2.54cm (1.0”). The
width dimensions of the specimens can be seen in Figure 2.1.1(b), where it is maintained
at 6.99cm (2.75”). The other dimensions of the arches, camber (y) or arch height, radius
of curvature (r), curvature (l/r) or inverse of the radius, and arc length can be seen in
Table 2.1.1. The arc length does not include the “wing” portions, just the curvature. The
composite strips are cut with an extra 50.8mcm (2.0”) added to the arch length to account

of the winged portion.

 

 

(a) (b)

Figure 2.1.1 (a) Schematic of end view of arched composite with dimensions,
(b) Schematic of arched composite showing the width.

Arc
Camber (y), Radius (r), Curvature (1Ir), Length (5),
mm mm mm mm

 

The molds were fabricated out of steel pipe cut lengthwise and welded to a steel plate.
Figure 2.1.2 shows a schematic one of the three steel molds. A typical mold could hold
up to three composite strips. Each composite strip was wrapped onto the arched portion
and onto the ﬂat portion such that each arched specimen had 2.54cm (1”) “wings” on
either side. The composite wings were taped to the mold with masking tape to prevent

them from sliding during autoclaving.

 

Figure 2.1.2 Steel mold schematic of pipe cut lengthwise on a plate.

The arched portions of the molds varied in length from 22.86cm to 27.98cm (9” to
11”). The steel pipes were cut parallel to the axis such that the maximum span of the
curvature was maintained at 7.62cm (3.0”). The steel plates dimensions were
30.48cmx12.7cmx0.6350m (12”x5”x0.25”). Table 2.1.1 shows the major dimensions of
the composite strips made from these molds.

2.3 Curing Process
The composite laminates and strips were cut to size prior to curing, sealed inside

ZiplocTM bags and kept in the freezer. Prior to autoclaving, the bagged laminated

prepreg strips were removed from the freezer and given 30-45minutes to warm up. The
molds were previously wrapped with non-stick release ﬁlms and the support plate for the
seven molds was covered in two layers of bleeder cloth (details given below). Once the
composites were warmed up, they were pressed onto the molds and further wrapped with
non-stick release materials.

Figure 2. 1 .2 shows seven molds without any of the release materials, bleeder cloth or
vacuum bag. The diagram shows the location of the molds, composite strips, and the foot
valve for pulling vacuum. The foot valve was located in the valley of two specimens.
Each mold was covered individually with release materials and all seven molds covered

on top and bottom with bleeder cloth.

   
 
 

Steel Mold

Foot Valve

   

Composite Strip

Support Plate

   

Figure 2.1.3 Mold setup with composite strips and foot valve location.
A end view diagram of the bagging materials used for the molding setup can be seen
in Figure 2.1.3, To preventing sticking, each steel mold was covered in non-porous
Teﬂon sheets. A pours layer was then laid to aid in release of the specimens aﬂer curing.

Next, the uncured composite strip was pressed onto the mold and the wing ends taped to

prevent movement. The composite strips were then covered in a layer of porous Teﬂon
and a layer of non-porous Telfon. Two layers of bleeder cloth were laid underneath all
the molds on the support plate and two layers of bleeder cloth were placed on top of all
the wrapped molds. An extra thick piece of bleeder was inserted directly below the foot
valve to prevent epoxy from being sucked into the valve and to provide a cushion

between the valve and the composite below.

Foot valve for vacuum

1 ‘// Extra thick bleeder cloth

Vacuum bag

ﬂ Bleeder cloth
A: Non-porous Teﬂon

 

 

 

Porous Teﬂon

Porous Teﬂon
" Non-porous Teﬂon

Steel mold

 

 

Tacky tape
seal Bleeder cloth

Support plate

 

 

Figure 2.1.4 Side view of bagging setup for autoclave curing.

The process procedures for curing the composites in the autoclave are as follows:
1) Check vacuum bag seal.

2) Close autoclave and pressurize to 551kPa (80psi).

3) Temperature begins ramping from ambient to 160°C (320°F) at a rate of SOC/min
(IOOF/minute).

4) When the temperature reaches 121°C (250°F), the vacuum is shut off and the

vacuum vent opens. The pressure of 551kPa (80psi) is maintained.

12

5) Once the 160°C (320°F) temperature is reached, it is maintained for 45 minutes.
6) The last stage is cooling where the temperature decreases at a rate of SOC/min

(1 OoF/minute) to 267C (80°F), at which time the pressure is released.

Note: The ﬂat panels cured in the hot press underwent the same pressures and

temperature cycles.

After the composite arches were cured, the bagging, Teﬂon, and bleeder cloth were
removed along with the cured composites. Sometimes the epoxy bridged the specimens,
bonding them together. The specimens were cut to separate the specimens. The
specimens were then numbered and the centers were marked.

2.4 Specimen Preparation

The impact location at the peak of the arch was identiﬁed by tracing the specimen
curvature onto graph paper. The peak of the trace on paper was found by sweeping two
arcs with centers at the ends of the “wings” with a compass. The arch peak was located
by the intersection of these arcs. The arched composite was then laid back onto the trace
and the peak was marked on the specimen. Then the middle of the specimen was found
by measuring half of the axial length of the specimen.

Each specimen was labeled according to the curvature, the ﬁber angles, and a
specimen number or letter. For example, there were three curvatures named small,
medium, and large, where the ﬁrst letter S, M, or L designated the curvature. The ﬁber
angles being [O/90]3s, thus the name would include 090. An example specimen name
would be M090-A. This would represent the ﬁrst specimen in a series of medium arches

with [0/90]3s stacking sequence.

13

Three boundary conditions named bar clamped, frame clamped and bolted were
involved in the study. The specimens with the bolted boundary condition required an
extra step in preparation. The holes are drilled slightly larger than 6.35mm (0.25”) at
3.8lcm (1.5”) apart and centered on the wing. Each specimen was set underneath the

clamping frame and a drill press was used to drill holes into the specimen through the

holes in the frame.

14

3. TESTING

All specimens were tested using a modiﬁed low-velocity instrumented drop-weight
impact system from Dynatup [28]. The impact results produced the impact velocity and
the load history in terms of voltage. The histories of impact load (in terms of N or lbs),
deﬂection, velocity, and absorbed energy were obtained subsequently with the use of a
computer program based on Newton’s second law and mathematical integration.
Calculation was also done to determine the impact energy so that a comparison could be
made with the absorbed energy. Each test was run under the same conditions and setup
to eliminate additional variables beyond adjusting the impact energy. The following
sections will give details on the equipment and standard operating procedures.
3.1 Testing Equipment
3.1.1 Low-velocity drop-weight impact test

A schematic for discussion purposes of the low-velocity impact test setup can be seen
in Figure 1.1.1. Starting at the top, there are several important features to note. First,
there is the crosshead, which has a load cell tup and two ﬂags. It is attached to a rail
clamp. The load cell has a 22241N (SOOOlbf) capacity and a 12.7mm (0.5”) hardened
steel hemispherical tip for impacting the specimen. Assumed to be perfectly rigid, the
load cell measures the load during impact. The two ﬂags run through the infrared
detector right before impact to record the impact velocity at the moment of contact
between the specimen and tup tip. The velocity obtained by dividing the distance
between the ﬂags with the time it takes the ﬂags to run through the detector. The rail
clamp allows adjustment of the height of the crosshead on the guide rails. The latch is

pressed to release the crosshead from the rail clamp.

15

 

    
   

  
    
 
   

I Clamping Rail Clamp for
/ Knob _ . height adjustment
F.— LatCh u S“ aft .. ‘L
. ,. /Crosshead
Trip T
Flag
Roller lever Bouom
/ switch \ Flag
Guide
Toggle / Rail
switch Specimen

   

Detector/
Emitter

/

 

  

 

 

 

 

Cylinder I

Figure 3.1.1 Side and front view schematic of impact testing.

The specimen is clamped at the base of the equipment such that the tup tip impacts the
center of the specimen. If the impact energy is low enough, the crosshead/mp will
rebound several times, ﬁrrther damaging the specimen. To prevent this, a rebounding
system is in place. The crosshead will cause the toggle switch to go from an off (central
position) to an on (downward) state at impact. Since the distance between the switches is
greater than that of the crosshead height, the roller lever switch will remain off (outward)
during impact. If the crosshead rebounds away from the specimen, it will leave the
toggle switch in an on (downward) position and depress the roller lever switch into an on
(inward) state. The roller lever switch is a momentary spring loaded switch such that it is
naturally in an oﬁ‘ state unless the top or bottom of the crosshead is pressing the lever to

an on mode. The switches are in series, thus if both are in the on position, a solenoid

l6

valve will activate the air cylinder upwards which prevents the tup from touching the
specimen again.

To control the amount of impact energy, either deadweight can be added to the
crosshead or the crosshead height can be changed. This allows duplication of the tests.
The crosshead height is determined by measuring the distance from the tup tip to the
impact location on the specimen. The total impact weight (crosshead, tup, ﬂags and
deadweight) is recorded so that accurate impact energies can be calculated.

3.1.2 Low-velocity impact data
When impact takes place, the load cell records the tup load, F (t). To ﬁnd the
acceleration, Equation (3.1) is used, where the tup load is divided by the the total impact
mass, m. The data is recorded every 25 ,us.
a(t)=F(t)/m. (3.1)

From the acceleration calculation in Equation (3.1), the velocity of the tup can be
determined. Equation (3.2) is the numerical integration of the acceleration over time.
Since the tup is decelerating during the impact, the integration is multiplied by —1. The
initial velocity v,- is determined by the infrared detector and is added to this integration.

t
v(t) = —j a(t)dt + v,- (3.2)
0

Equation (3.3) shows the ﬁnal calculation to determine the deﬂection of the specimen
during impact. The velocity is integrated over time from zero to the ﬁnal time of the

impact.

17

t
5(t) = jv(t)dt (3.3)
O

The data acquisition program also calculated the absorbed energy. However, due to
important subtleties in calculating the absorbed energy by the specimen, the calculations
will be covered in the chapter on data analysis.
3.2 Operating Procedure
3.2.1 Pre-impact test adjustments

Before running the ﬁrst test, several adjustments were made to the impact testing
machine. Initially, the specimens were prepared by marking the centers and drilling
holes in the ends if they were bolted instead of clamped. A specimen was then ﬁxed into
the clamping system such that it was centered. Any weights in the crosshead were
removed and the crosshead lowered by hand until the tup tip touched the impact location
of the specimen. While the tup tip was resting on the specimen, the infrared sensor was
adjusted up or down such that the second leading edge of the bottom ﬂag is about 3.2mm
(0.125”) beyond the centerline of the plastic insert in the detector block. This adjustment
assured that the velocity at impact was recorded. The toggle switch was adjusted such
that the crosshead pushed it from its originally off (central) position to an on (downward)
position just before impact. The distance between the toggle switch and roller lever
switch was checked so that the roller lever switch was not being depressed to its on
(inward) at the same instant the toggle switch was being pushed into an on (downward)

position, thus prematurely activating the rebounding system at impact.

18

3. 2.2 Impact test procedure

Once the pre-impact adjustments were done testing could begin. The specimen was
centered on the clamping ﬁxture and clamped (or bolted). Weights were added to the
crosshead if needed and the crosshead height adjusted. The computer was set to retrieve
the data from the load cell and infrared sensor. A personnel protection shield was set in
place and the latch pressed to release the crosshead tup, allowing gravity to accelerate it
toward the specimen.

3. 2.3 Rebounding and perforation

For convenience it was desirable to ﬁnd a particular weight to run all tests and only
adjust the height when changing the impact energy. For this reason, a particular weight
that caused both perforation and rebounding at different heights was determined in the
ﬁrst couple of tests. To accomplish this, several weights were loaded into the crosshead,
typically in 2.27kg(51bm) increments. The crosshead was adjusted to the maximum
height to determine if perforation was possible at this maximum height. If perforation
was reached, the height was decreased until rebounding occurred for following
specimens.

Each new test involved a new undamaged specimen. Specimens were never impacted
twice. However, occasionally multiple impacts occurred due to the rebounding system
not activating. Specimens with multiple impacts are noted in the appendices.

3. 2.3 Data Acquisition

The voltage signals from the load cell and infrared sensor are sent to a computer data

acquisition unit. The computer obtains the load and impact velocity. The results are

obtained at a rate of 25us up to IOOms. The computer outputs the load, deﬂection,

19

velocity, and absorbed energy for each time step. This data is sent to a print ﬁle for

conversion to an ExcelTM spreadsheet.

20

4. DATA ANALYSIS

The most ﬁmdamental data from the impact experiments performed in this thesis
research was impact force recorded in voltage. The experiments resembled impact forces
due to a projectile, shock wave, crash or combination of them. The ﬁmdamental data
could be converted into force (N or lbf), acceleration, velocity, displacement, and energy
histories. To protect against the impact force, armor composites must absorb the
associated impact energy so that it is not transferred to the combat personnel and vehicle
equipment. In understanding how energy is absorbed, the load-deﬂection relation and the
energy proﬁle play are important keys.

4.1 Load-Deﬂection Relation

The load-deﬂection relation is the most fundamental way to describe behavior of
composites during impact. A load-deﬂection relation can be established by plotting the
force against the corresponding displacement throughout the entire impact event. It
provides the majority of data for impact analysis. This relation can also give insight to
how a composite damages. Most important, it shows how the composite absorbs the
impact energy throughout the impact process.

There are two general types of load-deﬂection curves based on whether or not the tup
tip penetrates the specimen or rebounds. Figure 4.1.1 shows these two types of curves for
a frame clamped ﬂat panel and a bolted medium arched panel, where the closed curves
are rebounding and the open curves are penetration. For the closed curves, notice how
the load increases to a peak load and loops back to the start such that the load decreases
as the deﬂection also decreases. This looping back of the curve is due to the

crosshead/tup rebounding upwards, which causes the load to decrease and as the

21

specimen deﬂects back. Penetration takes place as the tip embeds into the specimen.
Once penetration is reached, there is no rebounding of crosshead and tup, resulting in an
open curve. When the tup tip punches through the specimen, it is deﬁned to be
perforation. Once perforation is reached, there is still a small load due to the tup tip
rubbing on the specimen. Since the specimen has been perforated, this small load is not

considered in the energy absorption calculation.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

9000
Bolted
8000 Medium
7000 Arch
6000 Frame “3%:
Clamped ' a
z, 5000 Flat Panel T
3 4000 r; -
0 i
-'| 3000 r‘
Q
2000 A“ ‘ 0 b
ﬁg ‘ i;
1000 3 y i“,
O V I Tl '
_1 000 1 20 30 40 5p

 

Deﬂection, mm

Figure 4.1.1 Load-deﬂection curves for frame clamped ﬂat panel and
bolted medium arch.

The load-deﬂection curves for different impact energies for a particular design are
typically plotted on one chart. Figure 4.1.2 shows such a chart for a ﬂat panel with the
ends bolted to the testing ﬁxture. Notice that the curves follow a pattern for the rise in
load, which reaches a maximum near 6,800N. The maximum deﬂections are on average

about 15m. There are three closed curves and three open curves.

22

7000

:2 1h
._,, , MM
H/ u

 

 

 

 

 

 

3 3000

2000 W ff\\&
1000 /’
0 A”. r 1

0 10 20
Deﬂection, mm

~ “WM

 

 

 

 

Figure 4.1.2 Load-deﬂection curves of bolted ﬂat panels.

7000

 

6000

 

 

5000

'0
z ,0, I W

 

 

 

 

    
   

 

 

 

   

 

ﬁ'm
2000 . i in"? Aut'f': 10:“ :1 xi". “vi“:
1000 i izi-i‘il' “ﬁnal-7110i! \

ﬂ'

0 10 20 30 40 50
Deﬂection, mm

Figure 4.1.3 Load-deﬂection curves of bolted medium arch.

In comparison, the load-deﬂection relation for bolted medium arched specimens can
be seen in Figure 4.1.3. The shape of the curves has changed dramatically. There are

two peaks and a much larger maximum deﬂection. The maximum loads are

23

approximately just over 6,000N and the maximum deﬂection around 40-47mm. There
are four closed curves and four open curves.

The energy absorbed by the composite during impact is calculated via Equations
(4.1 . 1) and (4.1.2). It is simply the determination of the area bounded by the load-
deﬂection curves. The load f( a) deﬁned in Equation (4.1.1) is integrated over the
deﬂection 6. The upper limit d is taken as the ﬁnal deﬂection for closed curves. For the
open curves, the limit a is determined by the extension method, which is explained in the

next section.

F = f(§) (4.1.1)
5t

Ea = I f (5M5 (4.1.2)
0

4.1.1 Extension Method

Determining the area for integration on the open load-deﬂection curves is critical for
determining accurate energy absorption. Figures 4.1.4 is for a ﬂame clamped ﬂat panel
and Figure 4.1.5 for a bolted medium arch. They show plots with open curves where
perforation takes place. A line is extended to the abscissa at the same slope as the
descent of the load during the penetration process. This line is the extension of the load-
deﬂection curve to eliminate the effects of the friction due to the rubbing of the tup with
the specimen after perforation. The location where the extension intersects the abscissa is

the upper bound, 6; in Equation (4.1.2).

24

8000

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7000 ._____._ Second —— __
stiffness
°°‘””‘“ y l “
5000 -
'3 Point
3 3000
Bum -
2000 _ P . Extensron
Initial line\
1000 — stiffness
0 line r . -
0 5 10 15 20
-1000

 

 

Deﬂection, mm

Figure 4.1.1 Load-deﬂection curve of frame clamped ﬂat panel

 

 

 

 

 

 

 

 

 

 

 

 

 

7000
0000 A
5000
4000 -
Z Bump
'3 3000
3
10(1) Stiffne\ss AV - Extension“
0 line T . line \‘V
0 10 20 30 40
-1000 $
Deﬂection, nm

Figure 4.1.31 Load-deﬂection curve of bolted medium arch.

4.1.2 Impact Stiﬂness
The stiffness can be divided into two parts for a ﬂat panel. The initial stiffness is

determined by obtaining the slope during the initial major rise a load-deﬂection curve as

25

seen in Figure 4.1.4 and Figure 4.1.5. There is a bump in the load in both plots. This
small bump is not included in the determination of the stiffness (slope). For the arched
composites, this bump in the load-deﬂection curve is much more pronounced, as shown
in Figure 4.1.5 and again is not included in the structural stiffness. Also notice how the
slope of the initial stiffness changes for the ﬂat panels into the second stiffness at a
deﬂection around 5.0mm in Figure 4.1.4. The critical point in this stiffness change is (3
believed to be the onset of delamination. This stiffness change is not as apparent for the
arched composites.
4.1.3 Peak Load

The peak impact load changes based on specimen curvature and clamping boundary
condition. A ﬂat panel produces a single peak load, where the load increases sharply and
then dr0ps sharply with a relatively small deﬂection. An arched composite, however,
produces different peak loads depending on the clamping boundary condition. If the
specimen is clamped, there will be a single peak load amongst many oscillations. An
arched specimen that is bolted will produce two peak loads, where the initial peak load is
much smaller than the second peak load. The second peak load for arched composites is
comparable to the single peak of the ﬂat panel.
4.1.4 Maximum Deﬂection

The maximum deﬂection of the specimens changes greatly based on the curvature of
the specimen. The higher the camber of the specimen, the greater the deﬂection it
experiences during impact. Thus, the specimen with higher curvature has a larger camber

resulting in a larger maximum deﬂection.

26

4.2 Energy Profile

The equations for determining the impact energy are given below in Equation (4.2. 1)
and Equation (4.2.2). The impact velocity is determined by two factors. The ﬁrst is the
energy due to kinetic energy, which is the ﬁrst term of Equation (4.2.1). The variable m
is the mass of the crosshead/mp. The initial velocity v,- is determined by Equation (4.2.2),
which is also the impact velocity measured by the infrared sensor/emitter. The second
component of the impact energy is the potential energy generated by the deﬂection of the
specimen during impact. The additional variables of Equation (4.2.1) is g the
acceleration of gravity and h ’ the maximum deﬂection of the specimen. The maximum
deﬂection is determined by ﬁnding the deﬂection where the extension line intersects the
abscissa for open curves. For closed curves, it is the maximum deﬂection the specimen

ever experiences.

2

Bi = émvi + mgh'= mgh + mgh' (4.2.1)

Vi = W/2gh (4.2.2)

The energy proﬁle is the key to characterizing the energy absorption of the composite.
The energy proﬁles shown in Figure 4.2.1 are for a bolted ﬂat panel and bolted medium
arch. The impact energy (E,) is plotted on the abscissa and the absorbed energy (Ea) on
the ordinate. The scales for both axes are intentionally the same such that a line can be
drawn at a 45 °angle, which is the equal energy line. Any data point that lies on this line
means for that given impact energy the specimen absorbed all of that energy. At the
upper end of the energy proﬁle, the absorbed energy is very close to the impact energy.

Once perforation or complete breakdown of the specimen is reached, the specimen has

27

absorbed the maximum amount of energy. As a result, the data points move away from
the equal energy line for increasing impact energies. In this particular case, the
perforation energy or the maximum absorbed energy is 91] for the medium arched

specimen and 501 for the ﬂat panel.

160.00

 

Equal Energy

140-00 ‘ —‘ m ‘*m —' Line /
120.00 -- \

i—ﬁ Maximum
Absorbed
100.00 --——— Energy \ _.

80.00 9
\ /, o Bolted Medium
60.00 —~ A Bolted Flat
— %- — —L .—
40.00
/
20.00 A

A

 

 

 

 

 

 

 

Absorbed Energy (J)

 

 

 

 

0.00

 

0 20 40 60 80 100 120 140 160
Impact Energy (J)

Figure 4.2.1 Energy proﬁles for bolted ﬂat panel and bolted medium arch
specimens.

28

5. FLAT PANEL BOUNDARY CONDITION STUDY

Studying the effects of the boundary conditions on a conventional ﬂat panel gives
insight into the effects the boundary has on energy absorption. A composite beam is
ﬁxed on two sides, but a composite plate on four. For the [0/90]35 composite beams the
ﬁbers in the transverse direction (90°-p1ies) do not contributed to the impact resistance as
much as those in the axial direction, i.e. the 0°-plies. However, the ﬁbers in both the 0°-
plies and 90°-plies contribute to the impact resistance in the [0/90]33 composite plates.
Correlating the results ﬂom these two studies provides some insight into how the energy
is absorbed.
5.1 Boundary conditions and specimens

The boundary effects study of a plate versus a beam for ﬂat panels with [0/90]3s
stacking sequence are given below. The beam problem has the same frame clamped
boundary condition as the arched composites. The plate problem is ﬂame clamped on all
four sides instead of the two ends for the beam problem. Figure 5.1.1 shows schematics
of the specimen geometry with the hatched regions showing the clamped areas. The ﬁrst
diagram, Figure 5.0.1(a), is a 102mmx102mm (4”x4”) plate with 12.7mm (0.5”) clamped
on all four sides. Figure 5,0.1(b) is the beam with dimension of 127mmx76.2mm (5”x3”)

where 25.4mm (1”) on either end are clamped.

29

ﬁr

101.6mm 127mm

 

 

'4
V

 

101.6mm

 

(a)
Figure 5.1.1 Flat panels (a) plate (b) beam.
5.2 Load-deﬂection curves for beam and plate
The load-deﬂection curves for the two structures, i.e. beam and plate, can be seen
below. Figure 5.2.1 is the load-deﬂection curves for the plate with the four ﬂame

clamped edges. The average peak load is 6947N. The maximum deﬂection is 11.9mm

8000

 

7000 .

 

 

 

 

     

 

 

o 5 1o 15 20 25
Deﬂection, mm

Figure 5.2.1 Load-deﬂection curves for ﬂat plate with four frame

clamped edges.

30

for the open curves where perforation is achieved. The initial stiffness of the structure is
813 N/mm while the second stiffness is 1,333N/mm.

The load-deﬂection curves for the beam are given in Figure 5.2.2. The average peak
load is 6161N. The maximum deﬂection for the open curves ranges ﬂom 15 .6m to
20.9mm. Notice that two of the closed curves have maximum deﬂection greater than the
three open curves. The maximum deﬂections of these two closed curves are 20.9mm to
23.6mm. The explanation for the large deﬂections without perforation is that slippage
occurred in the clamping system in the beam problem. The beam stiffness is 62 N/mm
for the initial stage and for the second stage 584N/mm. The lower stiffness in the second

stage is due to the ﬁbers in the transverse direction not being utilized.

 

 

 

 

 

 

 

 

2.... // //l l i
m, ////V

0 I . N {All .0; 1:0; N
0 5 10 15 20 25
Deﬂection, mm

Figure 5.2.2 Load-deﬂection curves for ﬂat beam with two ends
frame clamped.

 

 

 

 

 

 

 

 

5.3 Energy profile
The energy proﬁles for both the beam and plate are given in Figure 5.3.1. The
diamonds are for the plate data points and the squares are for the beam. The plate has a

clear maximum absorbed energy at 40] of energy. The beam on the other hand continues

31

to absorb energy, even at 831. The beam does not absorb all of the impact energy even
for low impact energies, but the plate performs slightly better for the impact energies

below 40.1.

 

100.00
90.00
80.00 1
70.00 1 ~

 

 

 

60.00 ‘

 

50.00

 

 

0 Plate
40.00

 

 

I800!!!

 

 

 

 

 

30.00 1

 

Absorbed Energy, J

20.00 1

 

10.00 —— —,—

0.00
0.00

 

 

 

 

40.00 60.00 80.00

Impact Energy, J

20.00 100.00

Figure 5.3.1 Energy profiles for both plate and beam.

5.4 Characteristics of impact response
The impact characteristics give a picture of the behavior of each boundary condition
and their contribution to energy absorption. The characteristics are stiffness, peak load,
deﬂection at the peak load, maximum deﬂection, and absorbed energy. Table 5.4.1
contains the averages for each characteristic in bold with its standard deviation next to it.
The plate has the higher stiffness of 834N/mm and 1,333N/mm in both the initial and
second stiffness. The plate also has the higher peak load. Taking into account the

standard deviation for the peak load, there is a difference. For the plate, there are two

 

 

 

Table 5.4.] Impact characteristics for plate and beam.
Deﬂection @ Max Absorbed
Stiffness 1 Stiffness 2 Peak Load peak load Deﬂection Energy
(Nlmm) (Nlmm) (N) (mm) (mm) (J)
Plate 834/108 133/116 6947/548 7.3/0.27 113/0.19 40
Beam 576744 W5— 7 . 1.5 . . 83

 

 

 

 

 

 

 

 

 

 

32

 

results that push the standard deviation ﬂom 159N to its current 548N. It is also clear that
the deﬂection at the peak load is lower for the plate than for the beam.

Since the plate is ﬁxed on four sides, it is stiffer and produces a larger peak load with a
smaller deﬂection. Because of the plate’s high stifﬂress and small deﬂection, it produces
load-deﬂection curves that are triangular like shape, which have less area under them.
The larger loads will produce ﬁber breakage for the same plate that would not cause ﬁber
breakage in the beam.

5.5 Summary

In terms of energy absorption, the beam clearly absorbs more energy without
breaking. The trade off is that lower stiffness and larger deﬂection. The beam is 25.6%
less stiff than the plate, but absorbs nearly 50% more energy without as much damage.
The deﬂection is the main contribution of the energy absorption because the maximum
deﬂection is almost twice in the beam for the doubling of energy absorption. This is only
the case because the peak load is slightly lower in the beam case. It is likely that the
ﬂiction forces around the clamped boundaries decrease deﬂection of the specimen, but
increase the peak loads. The clamping boundary forces are critical to prevent slippage,
which would allow for increase energy absorption. But the beams can deﬂect more than

the plate due to the ﬂee boundary on the two sides.

33

6. BOUNDARY CONDITIONS AND EFFECTS

The arched composite specimens investigated in this study were of rectangular shape
ﬂom the top view. Along the longitudinal direction, there was a designated curvature in
the middle section and ﬂat wings at the end sections. For impact tests, the composite
specimens were clamped to the base plate of the specimen holder of the impact tester by
steel bars at the end wings. The specimens were found to pull out of the bars signiﬁcantly
when the impact energy was high, resulting in signiﬁcant energy absorption due to the
friction between the composite specimens and the specimen holder rather than purely due
to the damage of the composite specimens.

In order to reduce the ﬂiction-induced energy absorption, the composite specimens
were clamped by a square ﬂame at the end wings. The ﬂame functioned similarly to the
bars except that the two clamping end members were not ﬂee to move with respect to
each other due to the constraint ﬂom two side members. Composite specimens clamped
by the frame still showed pullout up to some extent. In order to completely eliminate the
pullout phenomenon, four holes, two at each clamping end member, were introduced to
the square ﬂame. The composite specimens were then bolted in between the ﬂame and
the base plate of the specimen holder before being clamped.

The three methods of holding the composite specimens were titled bar clamped, ﬂame
clamped, and bolted boundary conditions. This chapter gave insight into the effects of
these boundary conditions on the performance of the arched composites. It covered the
load-deﬂection curve, energy proﬁle, characteristics of impact response and the damage
process of individual composites. A thorough understanding of the boundary effects may

lead to more effective armor designs.

34

6.1 Types of Boundary Conditions

There are three clamping boundary conditions in these experiments. Figure 6.1.1
shows all three boundary conditions. Each specimen sits on a ﬂame with a
76.2mmx76.2mm (3”x3”) opening and the winged portions rest on either side of the
opening. Toggle clamps are used to secure the specimen, where the locations of the feet

are given in the diagrams.

Toggle

Clamp Foot Arched Bolt Holes
Composite

é’é"

(c )
Figure 6. (1. )1 Boundary condition:b types: (a) bar clamped, (b) frame clamped and
(c) bolted.

     

The bar clamped design can be seen in Figure 6.1.l(a). The arched composite sits on
the base plate of the specimen holding ﬁxture of the impact tester. Two steel bars
25.4mm (1.0”) wide by 12.7mm (0.5”) thick clamp the arched composite at the two
wings with four toggle clamps. The force of the toggle clamps provides the clamping
force that secures the specimen.

Figure 6.1.1(b) shows the ﬂame clamped design. It is very similar to the bar clamped
design. The only difference is that the two end members are secured to each other by the
two side members, preventing a relative motion between them ﬂom occurring. The

pullout can take place when the arched composite collapses during impact.

35

To completely secure the composite to the base plate, the composite is bolted and
clamped between two ﬂames. The diagram of this setup can be seen in Figure 6.1.1(c).
Two 6.3 5mm (0.25”) bolts are used to secure each wing of the arch composite. With this
third boundary condition, the effects of the ﬂiction forces between the specimen and the
specimen holder are eliminated, allowing analysis of the energy absorption based on the
composite damage.

6.2 [0I90]3, Composite with Small Arch Curvature

To analyze the effects of the boundary conditions on the impact response of arched
composites, [0/90135 composite with a small curvature was investigated. The
investigations included load-deﬂection curve, energy proﬁle, impact characteristics and
the damage process. The results could give insight to the energy absorption of the arch
composite. The small arch has a radius of curvature of 84.14mm (3.31”) and a camber of
7.95mm (0.313”).

6. 2.1 Load-deﬂection Curves

Figure 6.2.1 shows the load-deﬂection curves for the small arched composites with the
bar clamped boundary condition. There is a sharp rise in load with the peak between
3,000N and 4,000N at a deﬂection ranging ﬂom 8.2mm to 9.6mm. The load decreases
signiﬁcantly, and then remains relatively constant before decreasing to failure gradually.
Failure is difﬁcult to deﬁne because the specimen slips in the clamps. The maximum

deﬂection is on average 55mm.

36

 

 

 

 

 

 

 

 

 

 

 

 

 

0 10 20 30 40 50 60 7o
Deﬂection, mm
Figure 6.2.1 Bar clamped [0/90]3, with small arch.

For the ﬂame clamped boundary condition, the load-deﬂection curves can be seen
in Figure 6.2.2. Once again, there is a sharp rise in load before it levels off with large
oscillations. Because of the oscillations, it is difﬁcult to deﬁne the peak load without
averaging out the oscillations. The maximum loads right after the initial rise ranges ﬂom

2,000N to 4,300N at a deﬂection of 13.6mm. The maximum deﬂection is at 60mm, but

 

 

 

 

 

 

11"“ f

I

 

 

 

 

 

 

Deﬂection, mm
Figure 6.2.2 Frame clamped [0/90]3, with small arch.

37

failure also occurs at 48mm and 54mm of deﬂection.

For the third boundary condition where the specimens are bolted in place, the load-
deﬂection curves are shown in Figure 6.2.3. Again, there is a sharp rise in load, then
decreases sharply. Once the local minimum is reached the load again increases to a peak
range ﬂom 5,990N to 6,760N at deﬂections 21mm to 23mm. The deﬂection at failure

ranges ﬂom 29mm to 34mm.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 10 20 30 40 50 60 70
Deﬂection, mm

Figure 6.2.3 Bolted [0I90]3, with small arch.

As the boundary conditions become more constrained, the results become more
consistent. Because of the large forces generated during impact, bolting the specimen in
place was the only guaranteed way to assure a ﬁxed boundary condition. The slippage
decreased the peak load ﬂom approximately 7,000N to 4,000N while increasing the
maximum displacement ﬂom 34mm to 60mm. The load-deﬂection curves changed ﬂom
a ﬂat plateau for the clamped design to a double-peak mountain shape.

To make a comparison among the load-deﬂection curves ﬂom all three types of

boundary conditions, they are plotted on the same graph. Figure 6.2.4 shows a typical

38

curve representing each type of boundary condition for the [0/90]3s composite with a
small arch. Notice how the bolted design reaches the ﬁrst peak load at about 6mm of
deﬂection, but the other two boundary conditions allow the load to peak at a larger load
at 10-15mm. The bolted however peaks at 6000N at about 22m, whereas the other two
boundary conditions have had a decrease in load to an approximate average of 2,500N.
The bolted design fails at a much lower deﬂection. The bar clamped does decrease the

load at a faster rate than the ﬂame clamped.

 

 

 

 

 

 

 

 

7000 Bolted
6000 in // Frame
500° Clamped *
i. 4000 - / Bar
g 3000 . V ___ Clamped
2000 ~ /
1000 / N

 

 

 

 

 

 

0 10 20 30 40 50 60 70
Deflection, mm

Figure 6.2.4 Typical load-deﬂection curves from the three
types of boundary conditions for [0/90]3, with small arch.

From a design perspective, a semi—ﬁxed boundary condition may be ideal as the
objective is to increase the area under the curves. Purely ﬁxed, such as bolted, increases
the load but limits the deﬂection of the specimen whereas too much slippage allows just
the opposite. Therefore, a semi-ﬁxed clamping system would potentially provide the

most desirable load-deﬂection curves. An energy analysis may help to verify the claim.

39

6.2.2 Energy Proﬁle

Figure 6.2.5 shows the energy proﬁles for the load-deﬂection curves ﬂom Figures
6.2.2, 6.2.3, and 6.2.4. The diamond data points are ﬂom the bar clamped, the squares
are ﬂom the ﬂame clamped and lastly the triangles are ﬂom the bolted design. The plot
shows that the impact energy approaches the absorbed energy as it increases, i.e. the
impact is almost completely absorbed by the composite in each case. For both the bar and
ﬂame clamped, however, it is difﬁcult to distinguish a perforation point. This is due to
the specimen being pulled out of the clamping system, instead of being damaged by
perforation. At Ea=82J the bolted specimens has the closest value between the impact
and absorbed energy implying the penetration energy point is near. The bar clamped has
a higher maximum absorbed energy around 95 Joules due likely to the slippery boundary
condition. The ﬂame clamped is absorbing nearly all 140] of impact energy ﬂom the
highest impact energy test conducted. The reason for this performance could be that the

clamping was improved, but it was not so ﬁrm that slippage could be avoided. It is

160.0

 

140.0 1 -

l

 

 

 

 

I

1

1
5.
l

OBarClamped

‘I ‘ I lFrameClamped
Q . ABolted

 

 

 

a a:
o o
o o

I

Absorbed Energy (J)

1
1

 

 

.0
o

 

r

20.0 40.0 60.0 80.0 100.0 120.0 140.0 150.0
Impact Energy (J)

.0
c

Figure 6.2.5 Energy profiles for [0I90]35 with small arch for all
three types of boundary conditions.

40

believed that the slippage and larger associated deﬂection of the specimen are what
allowed this higher energy absorption. Besides, it should be pointed out that regardless
of the type of boundary condition, the maximum absorbed energies of the arched
composites are much higher than that of ﬂat counterpart, implying that an arch is an
efﬁcient design to improve the energy absorption capability. Moreover, with an
adequate slippage in the boundary, the highest maximum absorbed energy can be further
increased.
6. 2. 3 Characteristics of Impact Response

The characteristics of the impact response of composites are the stiffness, the peak
load, the maximum deﬂection, contact duration, and energy absorption. Table 6.2.1
shows averaged results for the three boundary conditions for the composites with small
arch. The slope of the initial rise in the load is the stiffness. The ﬂame clamped has a
slightly lower stiffness than the bar clamped. The bolted specimen a stiffness that is

middle of the range, where there is overlap in the results.

Table 6.2.1 Characteristics of impact response for [0/9019, with small arch.

 

 

 

 

 

 

 

 

 

 

 

 

Deﬂection @ Max Contact Absorbed
Boundary Stiffness Peak Load peak load Deﬂection Duration Energy
Condition (Nlmm) (N) (mm) (mm) (ms) (J)
Bar 285 3802 15.9 49.0 33.2 93
Frame 262 4119 18.4 54.3 28.5 136.4
Bolt 276 6294 21.9 31.3 10.8 83.0

 

 

The bolted design has the largest peak load, 6,294N, which was after the ﬁrst peak
load. The deﬂection at the peak load for the bolted design occurred at 21 .9mm of
deﬂection. The ﬂame clamped has the peak force right after the initial rise in loading

except one curve with large oscillations causing the peak load late in the damage process

41

(see Figure 6.2.2). The peak load of the bar clamped is slightly smaller than that of the
ﬂame clamped.

The ﬂame clamped has the largest maximum deﬂection at 54.3mm, which is 9.8%
larger than the bar clamped at 49mm. The bolted specimens had a maximum deﬂection
of 3 1 .3mm. This matches with the fact that they were not allowed to deﬂect as much due
to the bolting.

The contact durations for the bar and the ﬂame clamped boundary conditions are very
similar. The bolted design has a much lower contact duration around 10.8ms. The result
ﬂom the contact duration seems to match with that ﬂom the maximum deﬂection.

The energy absorption is the perforation or maximum absorbed energy by the
specimens. The ﬂame clamped absorbs the most energy at 136.4] with the bolted
absorbing the least at 83.0J . It is evident that the clamping boundary conditions absorb
energy.

6. 2.4 The Damage Process

The damage process for the arched composite was much different than ﬂat panels.
The arched specimens went through a large deﬂection process due to buckling and
bending. The arches had much greater delamination and ended in an inverted state when
damaged. The composite was damaged by initial indentation, ﬁber breakage, and
delamination. If the specimen is bolted, it will buckle, causing the initial peak and load
drop in the load-deﬂection curves. The bar and ﬂame clamped load-deﬂection curves are
much different in that there are not noticeable peaks. The slippage at the boundary

condition reduced the buckling effects causing the change in the load-deﬂection relation.

42

Tup

. .1 Buckled
. / Composite

Frame
/ Clamping

R111

:‘1
.111»
‘ 1':
. 1
1i“,

1

   

Buckled Composite

(8) (b)

Figure 6.2.6 (a)Schematic diagram of tup and buckled arch composite and
(b)photograph of schematic in (a).

The arched composites went through a stage when the sides bend until the composite
was in an inverted state. Figure 6.2.6 shows the tup and inverted composite interaction.
Figure 6.2.6(a) is a schematic and Figure 6.2.6(b) is an actual top view of their
interaction. Notice how the tup rubs against the composite and is slightly wedged. This
ﬂictional interact can be another mode of energy absorption.

When perforation happened, sometimes the tip left a hole at the center of the specimen
and other times there were enough delamination, matrix cracking and ﬁber breakage
across the width of the specimen to cause the composite to break into two pieces. More
commonly, the specimen would pull out of the clamps before being perforated. The
bolted design eliminated the pullout and increased the amount of damage in the
specimen.

The boundary condition affects the damage process and the energy absorption of

composite. The damage process is similar for all boundary conditions up to some extent.

43

Once enough force is transferred to the boundary, the bar clamped or the ﬂame clamped
composite can slip. When a composite slips, instead of being damaged, some of its
structural integrity is maintained. On the contrary, the bolted design increases the impact
load and decreases the deﬂection of the composite. A semi-ﬁxed boundary condition
allows larger slippage, reducing the buckling effects.
6.3 [0190]“ Composite with Medium Arch Curvature

To present all of the data in regards to the effects of the boundary conditions, the
results ﬂom the composites with medium arch are given in this section. The medium
arch has a larger camber and curvature than the small arch. The medium arch has a radius
of curvature of 57.15mm (2.25”) and a camber of 15.88mm (0.625”). That is, the radius
of curvature for the medium arch is smaller than that for small arch. The curvature
effects will be mentioned in chapter 7.
6. 3.1 Load-deﬂection Curves

Figure 6.3.1 shows the load-deﬂection curves for the bar clamped boundary condition

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Deflection, mn
Figure 6.3.1 Bar clamped [0I90]3s with medium arch.
44

of the medium arched composites with a stacking sequence of [0/90135. The peak loads
range ﬂom 4423N to 3936N at deﬂections of 25.3mm and 29.4mm, respectively. The
maximum deﬂections range ﬂom 39.4mm to 42.9mm. Notice that the load has an initial
maximum about 8.6mm of deﬂection, then drops off and ﬁnally increases to the peak

loads before reducing.

8000

 

7000

 

6000

 

 

 

 

 

 

 

 

 

 

 

 

1000 /

o I I I U l J I k I
0 10 20 30 40 50 60 70
Deﬂection, mm

 

Figure 6.3.2 Frame clamped [0/90]3, with medium arch.

The results for the ﬂame clamped boundary condition can be seen in Figure 6.3.2.
The peak load ranges ﬂom 23 82N to 3376N and the deﬂection at the peak load ranges
ﬂom 9.4mm to 49.8mm. The maximum deﬂections range ﬂom 34.9mm to 51.7mm. It
can be seen ﬂom the diagram that this boundary condition has a saddle-like region, but
the peak load is maintained for a deﬂection of approximately 20mm.

The load-deﬂection results for the bolted specimens can be seen in Figure 6.3.3. In
comparison to the small arch, the load-deﬂection curves look very similar. There is the
initial increase in load, then a sharp decline followed by another increase to the peak

load. The peak load ranges ﬂom 5123N to 6869N and the deﬂections at the peak load

45

8000

 

7000 *

 

6000-

 

 

 

 

 

 

 

 

 

 

 

 

 

0 10 20 30 40 50 60 70
Deﬂection, mm

Figure 6.3.3 Bolted [0/90]3. with medium arch.

ranges ﬂom 31.1mm to 34.3mm. The maximum deﬂection reaches a range ﬂom 41mm

to 46.5mm.
6.3.2 Energy Proﬁle

The energy results ﬂom the calculated impact and absorbed energies can be seen in

160.0

 

 

—h .8
8 8
'o b

100.0 d,,___ ,_____ ____ _ /

(r A A 0 Bar Clamped
80'0 ii ‘ IFrame Clamped
[ e , ABolted

60.0 ._____, — a

40.0

 

 

 

 

 

 

 

 

Absorbed Energy (J)

 

20.0

 

 

 

0.0 r T I U I T I
0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0

Impact Energy (J)

 

Figure 6.3.4 Energy profiles for medium arch curvature [0/90]3,
for all three boundary condition types.

46

Figure 6.3.4, where all three boundary conditions are included. The diamonds are for the
bar clamped, the squares for the ﬂame clamped, and the triangles for the bolted. The data

points located on the diagonal line mean that the specimens absorb all of the impact
energy. Beyond Ei=70 Joules, the specimens can no longer absorb the energy efﬁciently.

The ﬂame clamped shows nearly complete energy absorption at all impact energies up to
114 Joules, which is the highest impact energy performed. For the bolted boundary
condition the most energy the specimen can absorb is 91 Joules.

Similar to the small arched composites, the medium arched composites absorbed the
highest energy among the three types of boundary conditions, due likely to the most
effectiveness of the ﬂame clamped boundary condition. They could absorb much of the
energy at lower impact energies and almost all energy at higher impact energies. The
clamping force seemed to be around an ideal level.

6.3.3 Characteristics of Impact Response

Characteristics of the impact response of the composites with medium arch are
summarized in Table 6.3.1 where all of the results are based on average. The stiffness is
lowest for the ﬂame clamped and more than doubles for the bolted specimens. The peak
load is also much greater for the bolted specimens. However, being different ﬂom that of
small arch, the peak force for the ﬂame clamped is smaller than that for the bar clamped

in the medium arched composites. Another difference occurs in the maximum

Table 6.3.1 Characteristics of im act response for [0190133 medium arch.

 

 

 

 

 

 

 

 

 

 

 

Deﬂection @ Max Contact Absorbed
Boundary Stiffness Peak Load peak load Deﬂection Duration Energy
Condition (Nlmm) (N) (mm) (mm) (ms) (J)
"'"Bar 427 4236 27.1 41.1 19.5 €4—
iame 236 2884 30.8 44.4 29.1 1 13.6
Bolt 576 5984 32.4 40.6 13.5 91.3

 

47

 

deﬂections. They are very close for all boundary conditions. However, it should be
pointed out that both the bar clamped and the ﬂame clamped specimens tested did not
reach the maximum capacity of the composites as can be seen in Figures 6.3.1 and 6.3.2,
i.e. the load-deﬂection curves do not decrease to zero gradually as those shown in Figures
6.2.1 and 6.2.2 for small arched composites. Although the maximum deﬂections are
similar among the different boundary conditions, the contact durations for open curves
are not. The shortest contact duration is the bolted specimen at 13.5ms and the ﬂame
clamped with the longest contact duration at 29.1ms.
6. 3 .4 The Damage Process

The damage process for the medium arch follows similar process to the small arch.
The largest difference is that the medium arch has to travel more distance before the arch
collapses. This distance can be seen in Figure 6.3.2 where the transition ﬂom the ﬁrst
peak load to the second peak load is longer for the bolted specimens. The bar and ﬂame
clamped boundary conditions allow slippage of the specimen so there is not deﬁnite
second peak load when the arch inverts as seen in Figures 6.3.1 and 6.3.2.
6.4 [0/90]3. Composite with Large Arch Curvature

The results for the large arch composites are given in this section. The radius of
curvature is 44.45mm (1.75”) with a camber of 20.65mm (0.813”) at the peak. Because
this design has the smallest radius of curvature, the sides of the arch are more vertical
than the other two designs and the camber is the greatest.
6. 4.1 Load-deﬂection Curves

The load-deﬂection curves for the bar clamped boundary condition are shown in

Figure 6.4.1. The peak load ranges ﬂom 237N to 3754N at deﬂections 6.6mm and

48

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 10 20 30 40 50 60 70
Deﬂection, mm
Figure 6.4.1 Bar clamped [0/90]3. with large arch.
37.0mm, respectively. The maximum deﬂections are at 44.0mm and 55.6mm. It can be
seen that the peak loads seem to occur in the later part of the curves.
Figure 6.4.2 shows the load-deﬂection curves for the ﬂame clamped boundary
condition for the large arch. The peak load ranges ﬂom 2815N to 4649N with their

deﬂections ranging ﬂom 34.0mm to 43.4mm. The maximum deﬂections for the two ﬁnal

curves are 59.8mm and 69.2mm. In this case the larger deﬂection is due to higher impact

 

 

 

 

 

 

 

 

 

 

 

 

 

8000
7000
6000«—--
25000-»—— A ___.
'6‘ 000.2
E4
3000 i: » -
2000~ ,1}, 4 1: .fl'ﬁ $1,“? 1‘ "1‘
, ’ 1 M .‘ {1 J
1..., 15 r . .11 nit/11.11..
0 J J ‘
0 10 20 30 40 50 60 70

Deﬂection, mm
Figure 6.4.2 Frame clamped [0/90]3, with large arch.

49

energies promoting slippage of the specimen. The larger the impact energy, the more the
specimen pulls out of the clamping system, which allows it to deﬂect more. Hence, care
should be exercised in the comparison of energy absorption capability.

The results for the bolted specimens are shown below in Figure 6.4.3. The general
trend of these load-deﬂection curves is similar to the results ﬂom the small and medium
arches. The major difference, however, is the large saddle after the ﬁrst peak. The
average load in this saddle region is about 1,500-2,000N and increases to the second peak
at about 30mm of deﬂection. The second peak load ranges ﬂom 3,374N to 6,470N with a
corresponding deﬂection ranging ﬂom 50.0mm to 61 .9mm. The second peak loads are
actually slightly lower than the initial peak load for some cases. Also, there is some

variation in the location of the peak load.

8000

 

7000

 

5000 ‘

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 10 20 30 40 50 60 70
Deﬂection, mm

Figure 6.4.3 Bolted [0/90]3s with large arch.
6. 4.2 Energy Proﬁle
The energy proﬁles for all three boundary conditions for the large arch can be seen in

Figure 6.4.4. The diamond data points are for the bar clamped specimens, the squares for

50

the ﬂame clamped, and the triangles for the bolted. The bar clamped data points appear
to have a “perforation” point at 100 Joules. The ﬂame clamped specimens appear to
absorb most of the impact energy up to 113 Joules. The bolted specimens absorb a
maximum energy of 107 Joules. All three designs seem to absorb about the same amount

of energy for the impact energies tested.

160.0
140.0

120.0

   
 
     

a
.8
O

  

0 Bar Cl-nped
I Franc Clamped
A Bolted
60.0

Absorbed Energy (J)
8
O

40.0
20.0

0.0
0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0 160.0

Impact Energy (J)

Figure 6.4.4 Energy proﬁle for [0/90]3, with large arch for all
boundary conditions.

6. 4.3 Characteristics of Impact Response

The characteristics of the impact response for the large arch specimens are
summarized in Table 6.4.1, where all the values are averages. Again the stifﬂiess is
much larger for the bolted specimens than for the bar or ﬂame clamped because slippage
cannot occur in the bolted specimen. The peak load for the bolted specimens is the
largest, with the bar clamped having the smallest peak load. The ﬂame clamped
however, had the largest maximum deﬂection. The bolted specimens have the lowest

contact duration with the bar clamped specimens with the largest contact time. The result

51

of the contact duration is not consistent with the result of the maximum deﬂection as that

occurs in the small arch specimens.

Table 6.4.2 Characteristics of impact response for [OIQObs with large arch.

 

 

 

 

Deﬂection @ Max Contact Absorbed
Boundary Stiffness Peak Load peak load Deﬂection Duration Energy
Condition (Nlmm) (N) (mm) (mm) (ms) (J)
—§ar 327 2918 29.0 49.9 48.4 101.2
Frame 280 3444 37.2 64.5 30.5 93.5
Bolt 570 4702 47.4 56.6 20.5 107.8

 

 

 

 

 

 

 

 

 

6. 4.4 The Damage Process
The damage process for the large arch again is most similar to the medium arch.

The major difference is that more deﬂection must take place to initiate the peak load for
the bolted specimens. This deﬂection will cause more delamination as the sides buckle
inwards to the inverted state.
6.5 Summary of results

Each boundary condition produces different results with energy absorption being the
primary focus. A composite diagram of the results seen in this chapter are summarized in
Figure 6.5.1. The data is organized such that each arch and boundary condition is labels
on the x-axis where the abbreviations are: small bar clamped (SBC), small ﬂame clamped
(SFC), small bolted (SB), medium bar clamped (MBC), medium ﬂame clamped (MFC),
medium bolted (MB), large bar clamped (LBC), large ﬂame clamped (LPG), and large
bolted (LB). The stiffness numbers have been divided by 10 and peak loads (FL) by 100
for sealing purposes.

The most noticeable feature is that the bolted specimens have the largest peak load.
The small arch has the largest peak load with the large arch with the smallest peak load.
The ﬂame clamped boundary condition has the largest maximtun deﬂection for each arch

size. This large deﬂection is one of the contributing factors to energy absorption.

52

Further details on the curvature effects on energy absorption will be covered in the

 

 

 

 

 

 

 

 

 

 

 

 

following chapter.
_ 70
A E 0 .
2 g 601—— —I
8 -. ' .
r. 3 g '
_| 1.3 v 50 ~ "—1. 1 -
D. D g . OStIffness
’8‘ i 3 4o _. ' l e
E g E I : lPeakLoad
:
2 ézo 30 g X + f x e ‘ ADeﬂectionQ
a O X load
2 E o A Q . . .mDOﬂOCWI
says 0
3 at g 20 ~~- x ‘ x
O o ‘
C d x
E o 10 «~ X
*' c
‘0 o
D
o T I I I

 

 

 

SBC,SFC,SB, MBC,MFC,MB, LBC,LFC,LB

Figure 6.5.1 Composite diagram of impact characteristics.

53

7. CURVATURE AND EFFECTS

The effects of the arch curvature on the load-deﬂection relation should provide insight
to an even more effective design for energy absorption. An ideal armor is one that stops
ballistic projectile or blast wave through absorbing all impact energy. With the increase
of curvature, a composite specimen has more material aligned along the impact direction,
the impact resistance should be increased accordingly. However, the gross mass of the
specimen is also increased. An optimal curvature may be identiﬁed.
7.1 Load-deﬂection Curves

Figure 7.1.1 shows a typical load-deﬂection curve ﬂom each of the three types of arch
composites with bolted boundary condition as well as a bolted ﬂat composite (zero arch).
The ﬂat panel is 69.85mm (2.75”) wide like the arches and is 127mm (5”) long so that

only 25.4m (1”) on each end is clamped like the arches. Several important features

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Flat Small .
7000 - Panel —— Arch —— Med1um
/ Arch
6000 — Large
Arch
5000 - I
z. 4000
0
g 3 o J r j
u. 00
2000 - — ——
1000 .
ll \lF‘W
0 I I T I T I T
0 10 20 30 40 50 60 70

Deﬂection, mm

Figure 7.1.1 Typical load-deﬂection curves for bolted arches and flat panel.

54

should be noted. There are two main maximum loads

in the arched composites, the ﬁrst, i.e. the initial maximum load, occurs about 6mm of
deﬂection and the second, i.e. the peak load, is located at different deﬂection value
depending on the arch size. The ﬂat panel has no initial maximum load and its stiffness
is similar to those of the arches. For the arch composites, the region between the two
maximum loads looks like a saddle shape and tends to increase as the curvature of the
composite increases. The ﬂat panel has zero curvature and there is only one peak load
and no saddle region.

Measuring the two maximum loads and associated deﬂections and plotting their
relation will help to sort out the curvature effects. Figure 7.1.2 shows a plot for the ﬁrst
peak load and the corresponding deﬂections for the three arch sizes. The load
measurements are taken ﬂom individual tests. The diamonds are the data points for the
small arches, which have the lowest initial maximum force, followed by the medium

arch, and the large arch has the highest initial maximum force. It can be concluded ﬂom

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6000
A
5000 1 A a ”A
A A 3
Z_ 4000 U
'0
a If
3 0305'
O

x 3000 ° ,9 0 Small
“ 0
a 0 Medium
B 2000 -~—- - - A Large
E

1000 ..

o T I l I
0 2 4 6 8 10

Deﬂection, mm

Figure 7.1.2 First maximum load and associated deﬂection.

55

this diagram that the initial maximum load increases as the curvature increases. This
result is likely due to the fact that more material is aligned along the impact direction
when the curvature increases.

The results for the second peak load and corresponding deﬂections can be seen below
in Figure 7.1.3. The general trend is that the peak load decreases as the curvature
increases, while the corresponding deﬂection increases. The increase in the deﬂection is
due to the height of the arch, which allows the composite to deﬂect more before being
perforated. The decrease in the peak load may be due to the ﬁbers not being as stiff

because they are not pulled as taunt as a ﬂat panel or small arch.

8000

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7000 o 0
0° C] A

z 6000 <><>° B—

e“ :1

§ 5000 D A

x A 0 Small

3 4000 El Medlum

a A A Large

1:

1: 30001 _

§

en 2000 A

1000
0 . . , , .
0 10 20 30 40 50 60

Deﬂection, mm

Figure 7.1.3 Peak load and associated deﬂection.

7.2 Energy Proﬁles

The energy proﬁle provides some details of the energy absorption process. Figure
7.2.1 shows the impact energy versus the absorbed energy proﬁles for the ﬂat panel,
small, medium, and large arches with bolted boundary condition. There is a clear trend

that as the curvature increases the maximum energy absorption increases.

56

160.00

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

140.00 - — /
3120.00 ,, —-—mr_¥ _,,,
>1 I
910000 ~»— -—— — —— .3
e emu-861m
.5 ° .
'3 . eMediurn-Bolted
'9 60.00
3 ‘ lLarge-Bolted
‘ A
.n o
< 40.00 -» ~—
0 AFlat-Bolted
20.00 ~~
A
0.00 I T r j I T T
0 20 40 60 80 100 120 140 160
Impact Energy (J)

Figure 7.2.] Energy profiles for bolted small, medium and
large arch, and ﬂat panel.

Table 7.2.1 shows the mass, maximum absorbed energy, and the ratio of them. The
ratio gives an indicator of the trade-off of weight to energy absorption. The data shows
that the weight increases with increasing curvature. The absorbed energy of the ﬂat panel
is about 71 Joules, the small arch 83 Joules, the medium arch 91 Joules, and the large
arch 108 Joules. Looking at the ratio of the maximum absorbed energy (AE) to the

mass, it can be seen that the large arch has the best energy absorption to weight ratio.

Table 7.2.1 Bolted specimens mass and maxium

 

 

 

 

 

absorbed energ.
Max. Absorbed Max. AEIMass
Mass (9) Energy (J) (J19)
Flat Panel 42.2 50 1.19
Small 43.1 83 1.93
Medium 44.6 91 2.04
Large 47.6 108 2.27

 

 

 

 

 

 

7.3 Characteristics of Impact Response
Figure 7.3.1 shows a plot of the stiffness for the camber of the arches for all three

boundary conditions. As expected, the ﬂat panel has the highest stiffness. Despite some

57

scatter in the data the small arch has the lowest average stiffness for the bolted
specimens. For the frame and bolted specimens the large and medium arches have
overlapping ranges of stifﬁiess, which suggest that they have similar stiffness. However,
the bar clamped boundary conditions show that the medium arch has a slightly larger
range of stifﬁiess than the large arch. Since, the results from the bolted boundary
condition can be considered to be most consistent it can be concluded that the ﬂat panel
has the largest stiffness, the medium and large arches have similar stiffness and the small

arch the least.

 

 

 

D

 

 

§

 

[mm
D» ID- ll»

oBarClamped

0 Frame Clamped
A Bolted

 

N
§

 

 

 

 

Stiffness,

 

é
um CID [CI Dd) 09(1) 0' [>
0 CDC! 1000

§

N
8

 

9
I

 

 

 

O

0 5 110 115 2'0 25
Camber, mm
Figure 7.3.1 Stiffness as a function of camber.
Figure 7.3.2 shows a plot of camber of the arches in comparison to the peak loads.
The trend are roughly linear with some scatter in the data, with the ﬂat panel having the

largest peak load, followed by the small arch, with the large arch having the smallest

peak load on average. This is also noticeable in Figure 7.1.1, where the ﬂat panel has the

58

largest peak force, followed by the small arch, and medium arch, and then large arch.
Even though the ranges show some overlap, there is a noticeable trend in that the small

arch has a higher peak load than the large arch.

9000

 

8000

 

m FIJL}

 

7000 E

 

I?»

6000

 

 

 

()Bar

Ch
DFramg'M

A SL135“

5000 J

 

4000

 

 

(mum

Peak Load, N

 

 

 

3000

 

[11] [III] 0‘!» DD DDDJ

(DUDMO D D D

2000

 

1000

 

 

 

 

0 5 10 15 20 25
Camber, mm
Figure 7.3.2 Peak load as a function of camber.
It is desired to study the effects curvature has on the ﬁrst peak load for the bolted
specimens. Figure 7.3.3 shows the ﬁrst peak load compared to the arch cambers. The

initial peak load decreases with decreasing curvature. From an energy and armor design

standpoint the large arch would be ﬁrst choice because overall it absorbs the most energy.

59

 

6000

5000 —

 

 

 

 

 

 

 

 

 

 

 

 

 

 

z
.5 4000
N
O
.l
g 3000 a A Bolted
n.
E 2000 4H”_ - ’PO'Y- (WM)
i: y = 13.9%):2 - 260.41x + 4090.2
R2 = 0.9022
1000
0 Y I l r
0 5 10 15 20 25

Camber, mm

Figure 7 .3.3 First peak load for bolted specimens.

Because deﬂection is one of the major contributors to energy absorption, the trends
of the maximum deﬂection are plotted for each design in Figure 7.3.4. The large arch

traveled the longest distance, followed by the medium, and small arches. As expected the

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

80

70 L]
E
E —— a 9*

- H
c o
,2 50 g :1 ’9
en E] U u
0 I
a I ,g o 0 Bar Clamped
0 Q I)" a El Frame Clamped
2 A I , I 6 A Bolted
:3 30 ~ ———-——--,g’ * - -Llnear (Bolted)
E , ’ ’
'5 20 4_. __,7,._{___ --4—— --—H——
E I z y = 1 .9242): + 13.861
2 _
10 f__ u R - 0.9277
0 . . . .
O 5 10 15 20 25

Camber, mm

Figure 7.3.4 Maximum deﬂection for each arch height.

60

ﬂat panel has the smallest maximum deﬂection. A trend line has been plotted for the
bolted specimens to enhance the trend due to the camber.

The contact duration is plotted in Figure 7.3.5. The contact duration is measured
only for open curves. The bar and frame clamped contact durations have a lot of scatter.

The bolted specimens have less scatter in the contact time and show a linear trend with

 

 

 

 

 

 

 

 

 

 

 

 

 

the camber.
60
O

50 O
U) 0
E 40 D
0' E]
E B a 0 Bar Clamped
'- 30 o 0 Frame Clamped
‘5 D 6 A Bolted
g B 3 — Linear (Bolted)
o 20
U /§//§

.0 :—

y = 0.7071x + 4.4375
0 R2 = 0.8303
0 5 10 15 20 25

Camber, mm

Figure 7.3.5 Contact duration for each arch height.

Table 7.3.1 below summarizes all characteristics of impact response for the bar
clamped specimens with averages. The values are all averages and shown in bold font.
They are followed by the standard deviations in regular font. The medium arch has the
largest stiffness, with the small arch having the lowest. The medium arch has the largest
peak load of 423 6N, followed by the small arch with 3802N. The large arch has the
lowest peak load of 291 SN. The large and small aches have similar maximum

deﬂections. The maximum deﬂections however, are very similar for the small and large

61

arch, but surprisingly the medium arch has a lower maximum deﬂection. The large arch

has the longest contact duration. The medium arch has the shortest contact time with the

small arch having a longer contact time. The large arch has the most absorbed energy,

but is followed by the small arch. The medium arch specimen has the lowest absorbed

energy.

Table 7.3.1 Impact characteristics for bar clamped [0I90]£

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

D e on (ﬁntact Absoi'bed
Stiffness Peak Load peak load Max Deﬂection Duration Energy
Arch Size (Nlmm) (N) (mm) (mm) (ms) (J)
Small 285/27 3802/265 15.9/7 .5 49.0/73 33.2/14.1 93
Medium 427/96 4236/263 27.1/2.1 41.1/2.5 19.6/2.6 67.4
‘ __£rge . . .0 4K4/0.4 101,2

 

 

Table 7.3.2 shows the response characteristics for the arched composites and the ﬂat
panel for the frame clamped boundary condition. Again the initial stiffness of each arch
is similar and statistically the same. The large and small arches have peak loads of
3444N and 4119N, respectively. Taking into account the large standard deviations, there
is a large overlapin the data. The deﬂections for these peak loads do show the same
trend as the bar clamped, except that there is a larger standard deviation. The maximum
deﬂections of the specimen show a trend, except when looking at the standard deviations,

which show some overlap in the results. Due to the pulling out of the clamping system

the maximum deﬂection has large standard deviations. The contact duration is

statistically the same due to the standard deviations. The small and medium arches

Table 7.3.2 Impact characteristics for frame clamped [0/90]3, specimens.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Deﬂection @ Contact Absorbed
Stiffness Peak Load peak load Max Deﬂection Duration Energy
Arch Size (Nlmm) (N) (mm) (mm) (ms) (J)
Flat 671/65 6662/88? 10.0/1.37 12.66/0.38 4.98/0.98 50.8
Small 262/40.1 4119/312 18.4/5.1 54.3/5.6 28.5/5.0 136.4
Medium 236/62 2884/466 30.8/12.6 44.4/6.7 29.1/6.5 113.6
La . . . . L‘55/83 93,5

 

62

 

absorbed the most impact energy, followed by the large arch. The ﬂat panel absorbs the
least amount of energy.

Table 7.3.3 shows the results for the bolted boundary condition, which eliminates
large slippage. The results include a ﬂat panel with bolted boundary conditions. It can
be seen that the standard deviations are much smaller for the bolted boundary condition
results than the other two boundary conditions. The large arch, however, had a large
amount of variance for the second peak load. It was found that the second peak was
actually smaller than the initial peak load for the large arch. It was observed that the
load-deﬂection plots for the bolted were more consistent and these small standard
deviations prove that. The stiffest arch was the large arch, but with the standard
deviation the medium and large arches have similar stiffness. The second peak loads
were all very close to that of the ﬂat panel, except for the large arch. Again, with the
large standard deviations there is statistically no difference. The deﬂection at the peak
loads has very small standard deviations, where the large arch has a peak load at 47.4mm
on average. The medium arch has its peak load at 32.4mm and the small at 21 .9mm.
That is nearly a 10mm difference for each arch design. The maximum deﬂections show a
similar trend. The contact duration shows this trend where contact time increases with
curvature. The energy absorption increases with increasing curvature, where the energy

absorption increase from 50.5] for the ﬂat panel to 107.8J for the large arched composite.

Table 7.3.3 characteristics for bolted 0/90

     

Stiffness Peak Load Peak Load Deﬂection @ Deﬂection Duratlon Energy
Arch Size (Nlmm) (N) (N) max load (mm) (mm) ) (J)

50 .9/1.1 5 .7
.1 .8

63

7.4 Summary

By adding various curvatures together or choosing an optimum curvature the most
energy can be absorbed. The large curvature absorbs the most energy and ﬂom the load
deﬂection relation it is apparent that it is the large deﬂection. When looking at the bolted
boundary condition the medium and large arches have similar stiffness, but the small arch
has the lowest stiffness. In regards to the peak load and its deﬂection the less curvature
the higher the load and the less deﬂection. There ispa linear relation between curvature
and maximum deﬂection. With the larger deﬂection comes a slightly longer contact
time.

For energy absorption the best boundary condition is the ﬂame clamped. The ﬂame
clamped specimens have some slippage, which allows increased energy absorption. The
down side with the ﬂame clamped boundary condition is inconsistence results. The
bolted specimens have low standard deviations and predicable results. The bolted results

show the trends in impact results for each curvature.

64

8. BUCKLIN G AND DAMAGE PROCESS
8.1 Buckling process literature review

The damage and buckling processes for arched composites was complex and can
easily be the focus of a research project. The buckling process and damage have been
studied by Wardle [2 8] in his work on composites shells (arches). His work on
bifurcation buckling provided a deﬁnition of buckling for bolted arched composites. He
focused on quasi-static loading and modal analysis after damage to deﬁne buckling. He
deﬁned limit-point buckling to be the point on a load-deﬂection curve where the tangent
stifﬂiess slope goes to zero. /This is when the load peaks and then drops off. A
characteristic of bifurcation buckling is when there is a discontinuity in the tangent
stifﬂiess slope, but is usually identiﬁed by the tangent stiffness slope becoming negative.
He said that buckling is the process of compressive membrane strain energy transferring
to bending strain energy. In work by Ciu, et a1. [4] for quasi-static loading of dome
composite shells, deﬁned bifurcation buckling when the center deﬂection buckled away
ﬂom the platen surface. The dome initially formed a ﬂat surface with the platen surface,
and after more loading it formed a dimple or inverted the center away ﬂom the platen
surface. Buckling was at the point when this dimple was formed. This happened when
there was a decrease in the loading per platen deﬂection. This agrees with Wardle [28]
where he later stated that bifurcation buckling in pressure loaded spherical caps is found
by a change in the tangent stiffness slope, but the slope remained positive. Analytical
work has shown that positive Gaussian curvatures (arches) are shear buckling resistant
apposed to shells with negative (peaks & valleys in the arch) or zero (ﬂat plat) Gaussian

curvature [17].

65

In the damage process work by Huang et a1. [9] on static contact crushing of arched
composites showed the buckling and damage phenomena. It was observed that cracking
near the peak of the arch almost split the specimen into two pieces. Other work by
Johnson and Holzapfel [3 0] showed the extensive delamination damage and transverse
cracking of an arched composite impacted at speeds of 107.5 rn/s. The delamination area
was large, extending ﬂom the impact location and partially down the sides and to the A.
edges near the peak.

8.2 Buckling Process

The damage process is a very complex phenomenon, which can be roughly
represented by the schematics shown in Figures 8.2.1, 8.2.2, 8.2.3. Each ﬁgure shows a
single load-deﬂection curve that is representative of a damaged specimen. The energy-
deﬂection relation is also plotted. The curve is marked by six critical points in the
process, lettered A through F. Next to each load-deﬂection curve is a scaled schematic
showing the buckling and bending of the specimen during the impact process. Each
schematic begins with the initially undamaged specimen, followed by the damaged
specimen at deﬂection points B-F, where the deﬂection of the center of the specimen is
the only known point. The deformed proﬁles were created with resemblance to Wardle’s
quasi-static loading results. Initially, each specimen is in its original undamaged state
point A. Then the composite is impacted and the load rises to point B. The load then
drops ﬂom point B to point C with very little deﬂection. The critical buckling load or
onset of buckling is at point B. The specimen then deﬂects to the point where it ends up
in an inverted state, which occurs at point D. The peak of this load is at point B where

the specimen is either in a completely inverted

66

120 A
C amber=7.95mm

100 ~

 

TAB.“
503 L,
3__/V\__
sag C
403 V D
203 b

i’

 

F

i

8 l

0 10 20 30 40 50
Deﬂection, mm

Figure 8.2.1 (a) Common bolted small arch load-deﬂection curve (b) Schematic
of specimen buckling and deﬂection at critical points.

12° WA
100 L
AB

80

60

 

Absorbed Energy. J

 

Deﬂection. mm

Figure 8.2.2 (a) Common bolted medium arch load-deﬂection curve (b)
Schematic of specimen buckling and deﬂection at critical points.

1 20
Camben=20£5mm A
i

7000
6000 100

5... .. AB
34000 so _/_V_\_C
" VD

  

Absorbed Energy, J

c
0 ‘2° F
0 10 20 30 4o 50 60
Deﬂection. mm

Figure 8.2.3 (a) Common bolted large arch load-deﬂection curve (b) Schematic of
specimen buckling and deﬂection at critical points.

67

state (twice the original height of the arch) or in a hyper-inverted (more than twice the
original height of the arch). At point P, all specimens will be in a hyper-inverted state
because enough delamination and ﬁber breakage has taken place allowing the specimen
to deﬂection beyond twice the original height of the arch.

During the impact process, the tip of the tup did not typically penetrate the specimen.
Perforation would take place when the arch had collapsed and inverted. When perforation
did take place, the tup tip left a hole at the center of the specimen or enough
delamination, matrix cracking, and ﬁber breakage across the width of the specimen
caused the composite to break into two pieces.‘ More commonly, the specimen would
pull out of the clamps before perforation; however, the bolted design eliminated the
pullout and increased the amount of damage in the specimen.

To compare the deﬂection of the arch peak during the impact process, the values ﬂom

the critical values on the plots in Figures 8.2.1, 8.2.2, and 8.2.3 are plotted in a single

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

30
E 20 A L
A I
E- , n i
'05 0 B-L ' OSmall-Bolted
:6 C I lMedlum-Bolted
E _ D . ALarge-Bolted
8 '10“? D
E 0 A
"6 E D
a .20.
S
9 F O F I
o E
I -30 F .L
-40

 

 

 

Small Medium Large

Figure 8.2.4 Deﬂection of small, medium, and large arch peaks during
impact.

68

chart. Figure 8.2.4 shows this plot where the arch sizes are plotted on the abscissa and
the height of the center of the arch is plotted on the ordinate. The data points labeled A
are the initial height of each arch before damage. The other ﬁve points are the critical
deﬂection points B through F. It can be seen that the initial maximum load at deﬂection
B occurs at roughly the same amount of deﬂection. The onset of buckling takes place at
point B. At point C each specimen goes through a large deﬂection with low loading.
This deﬂection difference ﬂom C to D increases with the arch camber. It can be seen that
the large arch has the largest overall deﬂection and inverts to over —30mm and the
medium to —24 and the small to -—22mm. Clearly, the deﬂection aﬂer onset of buckling to
point D is a main contributor to energy absorption because of the specimen’s distance
traveled. This can be seen in by the energy-deﬂection relation plotted in Figures 8.2.1,
8.2.2, 8.2.3.
8.3 Damage Process for ﬂat panel composite

The damage process is much different for a conventional ﬂat panel than a arched
composite. In particular, the ﬁnal damage is much different. Figure 8.3.1 shows a

bottom view of a bolted ﬂat panel on a light table, where perforation was reached. Local

    

Figure 8.3.1 Bottom viewuof [0/9015. of bolted ﬂat panel. -

69

.\J

delamination can be seen near the impact point. There is also ﬁber breakage and some
ﬁber pullout and strips of delamination on the backside. The main cause for the
(ﬂamination is the ﬁber angle difference between adjacent layers causing interlaminar
shear stresses.

The top view of this specimen can be seen in Figure 8.3.2. Again, it is on a light table,
but due to the protruding damage on the backside it cannot lay directly on the table,
which causes the darker colors. The most noticeable damage is that the ﬁbers have been
pushed ﬂom the top layers through the hole. Once again, it can be seen that the damage

is local to the hole and that there is less damage on the impact side.

 

Figure 8.3.2 Top view of [0/90]3s bolted ﬂat panel.

The ﬂame clamped ﬂat panels produced some expected results. The main difference
between the ﬂame clamped and bolted boundary conditions was that there was increased
bending of the specimen for the ﬂame clamped. This bending allowed more ﬁber
breakage along the transverse direction. Figure 8.3.3 shows a bottom view of a ﬂame
clamped ﬂat panel on a light table. The damage near the impact location is now
elongated in the. transverse direction due to the bending of the specimen. Fibers now

break not just due to the localized loads at the impact point, but also in regards to the

70

bending of the specimens. This bending also causes the ﬁbers on the bottom side to be
pulled in tension and break. There is some localized delamination around the parameter

of the broken ﬁbers and some more wide spread delamination on the upper left side.

 

Figure 8.3.3 Bottom view of [0,90133 frame clamped ﬂat panel.

A top view can be seen in Figure 8.3.4 for the ﬂame clamped specimen. The
delamination area looks even smaller than the bottom view. Again the hole where the tup
tip perforated the specimen can be seen with the transverse elongation of damage. The

damage does not spread along the axial direction as much as the transverse.

    

Figure 8’3'4 TOP View Of [0,901.35 frame clamped ﬂat‘panel frame

71

8.4 Damage process for arched composite

Fiber breakage and delamination traveled the top of each specimen in the transverse
(90°-direction) direction. The ﬁber breakage was visible at the initial stages of damage,
where it began at the ﬂee edges and propagated towards the center. The ﬁber breakage
began at the top surface and worsened as the delamination became more pronounced.
Figure 8.4.1 shows an oblique side view of a damaged composite. The delamination and
ﬁber breakage near the top surface can be easily seen. Notice how the top layers are

completely ﬂactured along the width of the specimen.

Fiber
breakage

    

Figure 8.4:] Side View of damaged bolted [0/90]3slarge arch

composite.

Figure 8.4.2 shows a top view of the specimen in Figure 8.4.1. Faint changes in the
shades of the color show the delamination patterns on the top of the specimen. The ﬁber
breakage along the transverse direction can be seen. The side view shows more of the

extensive damage.

72

 

Figure 8.4.2 Top view of damaged bolted [0/90]3, large arch
composite.

A top view of a damaged ﬂame clamped specimen can be seen in Figure 8.4.3. It is
on a light table, which shows the delamination patterns. The delamination is in oval
patterns with the major axes along the axial direction (0°-direction). If the impact energy
is great enough, the delamination will spread to the clamped wings. There is also
rectangular shaped delamination at the center of the arch, which extends to the edges at
an oblique angle to the axis of the arch. This rectangular delamination is able to take
place due to the extensive ﬁber breakage. Notice the rectangular shaped delamination
area near the transition ﬂom the arch to the winged sections. This delamination takes
place due to the bending of the sides. For the bolted specimens the delamination near the
top center and ﬂom the bending of the sides meets causing complete delamination of the
layers. As the specimen buckles the damage progressively increased by delamination and

ﬁber breakage in the layers at the peak of the arch.

73

Oblique

Delamination Oval

Pattern

     
   

Rectangular
Delamination

Figure 8.4.3 Top view of delamination of [0/90]3, frame
clamped medium arch showing delamination pattern.

8.5 Summary

In order to understand how the energy is absorbed the buckling and damage process
must be studied. Buckling typically increases the complexity and instability of the
damage process creating less predictability and difﬁculty in characterizing the damage.
If buckling is reduced more control over the specimen damage process will allow precise
damage control, which in turn will allow control in energy absorption. In our work, it
was believed that buckling occurred more apparently in the specimens with the bolted
boundary condition due to the specimen being unable to slip. Frame clamping would
allow the specimen to smoothly bend during impact. The slipping of the specimen at the
clamping boundaries allowed the specimen to bend and deﬂect downward, without large
drops in load, which are associated with buckling. By bolting the specimen, the
boundaries were ﬁxed, forcing the specimen to suddenly fail, which is apparent by

sudden load drops. The peak load before this sudden load drop is the onset of buckling.

74

Bolting the specimen increased the visible delamination and ﬁber breakage and several

times the specimen actually broke into two pieces because of the high impact energy.

75

9. CONCLUSIONS AND FUTURE STUDY
9.1 Conclusions

The main goal of this study was to determine the effects of curvature on energy
absorption. The trend was clearest for the bolted boundary condition. As the curvature
increased the maximum absorbed energy increased. From the load-deﬂection relation it
became apparent that the large deﬂection of the specimens contributed to the energy
absorption. With increasing curvature came increasing camber and ultimately larger
deﬂection of the specimen.

In the beam and plate problem, the beam clearly absorbs more energy without
breaking. The trade off is that it has lower stifﬁiess and larger deﬂection. The beam is
25 .6% less stiff than the plate, but absorbs nearly 50% more energy without as much
damage. The deﬂection is the main contribution of the energy absorption because the
maximum deﬂection is ahnost twice in the beam for the doubling of energy absorption.
This is only the case because the peak load is slightly lower in the beam case. It is likely
that the ﬂiction forces around the clamped boundaries decrease deﬂection of the
specimen, but increases the peak loads. The clamping boundary forces are critical to
prevent slippage, which would allow for increased energy absorption. But the beams can
deﬂect more than the plate due to the ﬂee boundary on the two sides.

For the boundary condition effects for the arched specimens, the most noticeable
feature is that the bolted arched specimens have the largest peak load. The small arch has
the largest peak load with the large arch with the smallest peak load. The ﬂame clamped
boundary condition has the largest maximum deﬂection for each arch size. This large

deﬂection is one of the contributing factors to energy absorption.

76

The large curvature absorbs the most energy and ﬂom the load deﬂection relation it is
apparent that it has the largest deﬂection. When looking at the bolted boundary condition
the medium and large arches have similar stifﬂress, but the small arch has the lowest
stifﬂiess. In regards to the peak load and its deﬂection the less curvature the higher the
load and the less deﬂection. There is a linear relation between curvature and maximum
deﬂection. With the larger deﬂection comes a slightly longer contact time.

For energy absorption the best boundary condition is the ﬂame clamped. The ﬂame
clamped specimens have some slippage, which allows increased energy absorption. The
down side with the ﬂame clamped boundary condition is inconsistence results. The
bolted specimens have low standard deviations and predicable results. The bolted results
show the trends in impact results for each curvature.

In order to understand how the energy is absorbed the buckling and damage process
was be studied. Buckling typically increased the complexity and instability of the
damage process creating less predictability and difﬁculty in characterizing the buckling.
If buckling is reduced more control over the specimen damage process will allow precise
damage control, which in turn will allow control in energy absorption. It is believed that
buckling occurred in the specimens with the bolted boundary condition due to the
specimen being unable to slip. Slippage would have allowed the specimen to smoothly
bend during impact. The slipping of the specimen at the boundaries allows the specimen
to bend and deﬂect downward, without large drops in load. By bolting the specimen, the
boundaries were ﬁxed, forcing the specimen to suddenly fail, which is apparent by

sudden load drops. This sudden load drop is the onset of buckling. Bolting the specimen

77

increased the visible delamination and ﬁber breakage and several times the specimen
actually broke into two pieces because of the high impact energy.

In a book by Ashby, et a1. [32] on metals foams it is apparent that the load-deﬂection
relation for these foams is similar to the relation for arched composites. There is an
initial peak load, similar to the ﬂame clamped initial peak. The load then dips slightly
and remains constant while the foam collapses. As near the end of the densiﬁcation of
the foam the impact load increases sharply. This sharp increase is similar to the bolted
specimens in the inverted state. An arched polymer matrix composite could be a
replacement for metal foams.

Photos of the damaged specimens are in the appendix. The photos are given in two
columns with the top view on the leﬁ and bottom view on the right. The damage type of
each specimen in listed in corresponding tables. If a specimen is perforated it is
designated with a P, non-perforated with NP, and broken in two pieces with BITP.

9.2 Future Study

The literature review and this study consisted of impacts on the arch peaks and normal
to the surface. A thorough study of the effects of oblique and off peak impacts will
provide a complete analysis of the curvature effects on impact characteristics. This study
will show the usefulness of arched composites in armor design, where direct impacts are
not always the case. The main variable in this study was the camber, which was varied
by changing the radius of curvature and maintaining the span of the arch at 7.62cm
(3.0”). In studying curvature the effects of span of the arch and the length of the arch are

important. It may be desirable to maintain a constant camber, by changing the radius of

78

curvature and allow the arch span to vary. This study will be very insightful because the
camber appears to be a major contributor to energy absorption.

Low speed impact tests have been conducted, but ballistic and blast tests produce
different results in polymer matrix composites. A couple ballistic tests on the arched
composites in a shock tube showed large delamination. It is believed that an arched

composite will absorb more ballistic energy than a ﬂat panel due to the spread of damage.

79

APPENDICIES

80

APPENDIX A

MATLAB code for producing extension method line and calculating impact energy

and absorbed energy

81

clear all

clc
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This program is written for English units (ft, lb, 5) %

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Import EXCEL with xlsread('File_Name.xls','XLS_Worksheet')
data = xlsread('Dynatup Data.xls', 'Raw_Data');

%Organizes EXCEL data into MATLAB vectors
Point_Number = data(:,l);

Time = data(:,2)/1000;

Load = data(:,3);

Deflection = data(:,4)/12;

Velocity = data(:,S);

Energy = data(:,6);

%Asks user to specify whether or not the particular impact
%test was a REBOUND curve or an open PENETRATION curve.
r=input('Rebound enter 1 OR Penetration enter 0');

%Input the weights of the crosshead, tup, tup bolt, and additional
weights
weight=27.07; %lbs

Mass = weight/32.1740;

%Finds the velocity at initial impact.
1:0;
for(i=1:length(Time));
if(Time(i)==0);
l=l+1;
zero_velocity(l) = Velocity(i);
end
end

if r==l

h=max(Deflection); %Finds h' for rebounding results
%Calculates the extension and adds additional data points
%to the existing vectors to create the extension.
elseif r==0
u=10; %No. of data points to generate trendline from.
a=lengthtDeflection);
c=Deflection(a-u:a);
d=Load(a-u:a);
p = polyfit(c,d,l); %Fits a trendline through data to determine
%extension slope.

xmax=-p(2)/p(l); %Determines where the extension intersects the x—
axis.

del=(xmax-Deflection(a))/10; %The delta increments from the first
extension

82

%data point to the data point on the x-axis. There are 10 points in
this
%range.

%Adds the extended data points to the Load & Deflection vectors.
for i=1:10

Deflection(a+i)=Deflection(a)+(del*i);
Load(a+i)=Deflection(a+i)*p(1)+p(2);

end

h=xmax;

end

Impact_Energy = .5*Mass*zero_velocity.“2 + Mass*32.l74*h
Absorbed_Energy_polyarea=polyarea(Deflection,Load)
Energies=[Impact_Energy Absorbed_Energy_polyarea]

figure (5)
plot(Deflection, Load)

83

APPENDIX B

Flat specimens with two sides frame clamped for plate versus beam impact study

(hot press cured)

84

8000

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7000

6000 ._ — “—
25000 J 2 _ ‘/ 18 7
'8 4000 . l - /
3 3000 -4 //6/ 9

2000 - ‘1: // 10

1000 ~ 1’: 5

0 . r .
0 10 20 30 40 50 60 70

Deflection (mm)
Figure B.l Load-deﬂection curves for ﬂat beam with two sides frame clamped.

85

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table B.l Flat panel (beam) data.
Stiffness Stiffness Deflection Max Contact
Specimen 1 2 Peak Load @ peak Deflection Duration
# (Nlmm) (Nlmm) (N) load (mm) (mm) (ms)
1 579 461 5925 12.0
2 564 610 5639 10.2
3 610 544 6552 11.6
4 564 543 5734 13.7
5 655 572 6629 1 0.5 18.0 6.6
6 647 551 6051 10.5
7 651 749 5600 8.3
8 591 634 5978 9.4
9 690 590 6929 9.9 20.8 7.1
10 649 585 6571 1 1 .5 15.4 4.6
Average 620 584 6161 10.8 18.1 6.1
Std. Dev. 44 75 472 1.52 2.70 1.31
Table B.2 Flat panel (beam) Energy data. .
Impact Absorbed
Specimen Energy Energy
# (J) (J) Damage
1 48.6 31.5 NP
2 29.8 1 4.0 NP
3 44.6 26.7 NP
4 58.5 42.2 NP
5 78.5 71.5 P
6 62.4 49.0 NP
7 78.9 65.4 NP
8 90.4 79.2 NP
9 87.4 61 .1 P
10 95.1 82.8 P

 

 

 

 

 

 

86

 

#1
48.57.]

#2
29.8J

#3
44.6J

58.5J

#5
78.5J

#6
62.4J

78.9J

#8
90.4.1

 

Figure B] Flat panel (beam) damaged specimen photos.

Note: Specimen #1 had multiple hits.

#9
87.5J

#10
95.”

 

Figure B.2 Flat panel (beam) damaged specimen photos.

88

APPENDIX C

Flat specimens with four sides frame clamped for plate versus beam impact study

(hot press cured)

89

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 10 20 30 40 50 60
Deflection, mm

Figure C.1 Load-deﬂection curves for ﬂat plate four sides frame clamped.

9O

70

Table C.l Flat panel (plate) data.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Stiffness Stiffness Peak Deflection Max Contact
Specimen 1 2 Load @ peak Deflection Duration
# (Nlmm) (Nlmm) (N) load (mm) (mm) (ms)
1 968 1386 7227 7.37 1 1 .82 5.00
2 723 1 194 7224 7.52
3 921 1469 7496 7.25
4 834 1219 6218 7.81 11.98 4.57
5 914 1415 7294 7.08 11.60 3.70
6 799 1 370 7035 7.47
7 645 1 182 5966 6.91
8 864 1431 7113 7.33 12.03 4.10
Avera e 834 1333 6947 7.3 11.9 4.3
Std. Dev. 108 116 548 0.27 0.19 0.56
Table C.2 Flat panel We) eneEgy data.
Impact Absorbed
Specimen Energy Energy
# (J) (J) Damage
1 42.6 39.6 P
2 29.7 22.2 NP
3 42.0 38.7 NP
4 44.3 38.5 P
5 65.1 39.8 P
6 37.3 33.0 NP
7 17.7 8.2 NP
8 49.2 39.4 P

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

91

 

 

#1
42.7.]

#2
29.75J

 

#3
42.0.1

44.3J

 

Figure C.2 Flat panel (plate) damaged specimen photos.

#5
65.12.}

37.3J

 

#7
17.731

#8
49.21

 

Figure C.3 Flat panel (beam) damaged specimen photos.

93

APPENDIX D

Flat specimens bolted (hot press cured)

94

8000

 

 

 

 

 

 

 

 

 

 

 

7000
6000i = 1
I- : / 6

z 5000 4 ‘
a ‘1 3
a 4000 a
3 5

3000 2

2000 - 1 4

1000 -

0 l I l T
0 10 20

30 40 5O

60
Deflection, mm

Figure D.1 Load-deﬂection curves for bolted ﬂat specimens.

95

 

70

Table D.1 Bolted ﬂat panel data.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Stiffness Stiffness Peak Deflection Max Contact
Specimen 1 2 Load @ peak Deflection Time
it (Nlmm) (Nlmm) (N) load (mm) (mm) (msec)
1 732 852 6260 10.13 13.7 5.2
2 684 706 6722 8.354
3 758 863 6536.92 10.832 14.09 4.9
4 776 924 6498.46 7.66
5 665 580 5139.5 7.3
6 754 944 6694.73 9.904 13.7 3.95
Average 728.17 811.50 6308.60 9.03 13.83 4.68
Std. Dev. 44.27 140.87 596.21 1.45 0.23 0.65
Table D.2 Bolted ﬂat panel may data.
Impact Absorbed
Specimen Energy Energy
# (J) (J) Damaa
1 53.1 47.1 P
2 28.6 21.2 NP
3 58.0 50.4 P
4 38.8 35.7 NP
5 17.6 12.6 NP
6 78.6 48.6 P

 

 

 

 

 

 

96

#3
58.0.1

#6
78.6.1

 

Figure D.2 Bolted ﬂat panel damaged specimen photos.

97

APPENDIX E

Flat specimens frame clamped (autoclave cured)

98

 

 

 
 

 

 

 

  

 

 
  

 

 

 

 

 

8000 t‘/ 3

7000 -—— A

6000 . “

5000 - 2
z I ‘/
15‘ 4000 - I, ‘f

5

3 3000 ‘7
" II I 1

 

 

2000

   

rill/1‘ . 4

1000

 

 

     
 

 

  
   

 

"1'
V T I x...»
20 30 40 50

'l///‘ _

.
0 ' I,

-1000

60

 

Deflection, mm

Figure E.l Frame clamped ﬂat panel load-deﬂection curves.

99

 

Table E.l Frame clamped ﬂat panel data.

 

 

 

 

 

 

 

 

 

 

 

 

Stiffness Stiffness Peak D—E'f'lection Max Contact
Specimen 1 2 Load @ peak Deflection Time
# (Nlmm) (Nlmm) (N) load (mm) (mm) (msec)
1 570 648 6323 1 1.57
2 705 683 6509 1 0.86
3 736 1 037 7744 9.49 1 2.73 4.00
4 737 851 7087 9.24 1 3.00 5.00
5 690 1290 6764 9.00
6 655 804 7243 1 1.51 12.25 5.95
7 601 724 4963 8.00
Average 671 863 6662 9.95 1 2.66 4.98
Std. Dev. 65 229 887 1.37 0.38 0.98

 

 

 

 

 

 

 

Table E.2 Frame clamped ﬂat panel energy data.

 

 

 

 

 

 

 

 

 

Impact Absorbed
Specimen Energy Energy

# (J) (J) Damag£_
1 43.1 25.7 NP

2 63.3 41 .5 NP

3 61 .5 50.8 P

4 61 .5 50.8 P

5 34.6 19.6 NP

6 46.9 46.7 P

7 19.3 7.9 NP

 

 

 

 

 

100

 

#1
43.1.]

 

 

#3
61.5.1

61.5.1

#5
34.6.1

46.9.1

#7
19.3J

 

Figure E.2 Frame clamped ﬂat panel damaged specimen photos.

101

APPENDIX F

Small arch with bar clamped boundary condition

102

 

8000

 

7000

 

 

 

 

 

 

Deflection, mm

Figure F.1 Bar clamped small arch load-deﬂection curves.

 

 

 

 

 

Table F.1 Bar clamm small arch energy data.
Impact Absorbed
Specimen Energy Energy

# (J) (J) Damage
1 44.7 32.1 P

2 74.9 65.5 P

3 109.8 64.4 P

4 96.7 93.0 NP

5 85.5 85.2 NP

 

 

 

 

 

 

Deflection @ Max. Contact
Specimen Stiffness Peak peak load Deflection Tlme
# Load

 

103

 

Figure F.2 Bar clamped small arch damaged specimen photos.

APPENDIX G

Medium arch with bar clamped boundary condition

105

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

O 10 20 30 4O 50

Figure G.1 Bar clamped medium arch load-deﬂection curves.

106

 

70

Table G.2 Bar clamped medium arch data.

 

 

 

 

 

 

 

 

 

Peak Deflection @ Max. Contact
Specimen Stiffness Load peak load Deflection Time
# (Nlmm) (N) (mm) (mm) (msec)
1 341 4423 25.33 39.40 1 7.78
2 387 4350 26.69
3 370 3936 29.40 42.89 21 .45
4 580
5 459
Average 427 4236 27.14 41 .1 5 19.62
Std. Dev. 96 262 2.07 2.47 2.60

 

 

 

 

 

 

 

Table 0.] Bar clamped medium arch energy data.

 

 

 

 

 

 

 

Absorbed
Specimen Impact Energy

# Energy (J) (J) Damage
1 1 08.3 64.7 P

2 74.1 55.9 NP

3 93.3 67.4 P

4 44.9 42.3 NP

5 62.4 50.7 NP

 

 

 

 

 

 

107

 

Figure G.2 Bar clamped medium arch damaged specimen photos.

108

APPENDIX H

Large arch with bar clamped boundary condition

109

8000

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7000
6000
2 5000
g 4000 .
o
-' 3000
2000 -
3
1000 W 3
0 i i l I I I I
0 10 20 30 40 50 60 70
Deflection, mm
Figure H.l Bar clamped large arch load-deﬂection curves.
Table H.1 Bar clamped large arch data.
Peak Deflection Max. Contact
Specimen Stiffness Load @ peak load Deflection Time
# (Nlmm) (N) (mm) (mm) (msec)
1 352 3754 37.0 44.3 48.1
2 396 2357 6.6
3 1 87 2499 36.6 55.6 48.65
4 372 3062 35.9
Average 327 291 8 29.03 49.93 48.38
Std. Dev. 95 635 14.93 7.95 0.39

 

 

 

 

 

 

 

110

 

 

Table H.2 Bar clamped large arch enerﬂ data.

 

 

 

 

 

 

 

Impact Absorbed
Specimen Energy Energy
# (J) (J) Damage
1 94.5 81 .3 P
2 44.6 37.5 NP
3 103.1 1 01 .2 P
4 80.5 71 .7 NP

 

 

 

 

 

Figure H.2 Bar clamped large arch damaged specimen photos.

Note: Specimen #2 had multiple hits.

111

APPENDIX I

Small arch with frame clamped boundary condition

112

8000

 

7000

 

6000

 

 

5000
'P 4000 -
3000 ~

2000..

WY
ii... Mir 1’]

 

1000 *-

 

  

 

 

   

(‘Flf' [WW

 

 

 

   

 

   

 

Figure 1.1

 

I

 

111.1 III
14 ",1

Frame clamped small arch load-deﬂection curves.

113

 

70

Table [.1 Frame clamped small arch data.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DETEction @ Max. Contact
Specimen Stiffness Peak peak load Deflection Time
# (Nlmm) Load (N) (mm) (mm) (msec)
1 329 41 02 1 9.36
2 230 4051 15.98 60.12 31.00
3 291 3673 13.31 48.97 22.78
4 243 3976 21 .56
5 227 4588 26.50
6 255 4322 13.53 53.80 31 .83
Average 262 41 19 1 8.37 54.30 28.54
Std. Dev. 40 312 5.14 5.59 5.00

 

Table 1.2 Frame clamped small arch energy data.

 

 

 

 

 

 

 

 

 

 

Impact Absorbed
Specimen Energy Energy

# (J) (J) Damage_
1 81 .5 74.1 NP

2 139.0 136.4 P

3 1 12.4 107.7 P

4 74.0 66.9 NP

5 93.2 87.9 NP

6 1 30.5 130.2 P

 

 

 

114

 

#1
81.5]

 

Figure [.2 Frame clamped small arch damaged specimen photos.

115

APPENDIX J

Medium arch with frame clamped boundary condition

116

 

8000

 

 

 

 

 

 

 

 

 

    

 

 

7000 n_______ﬁ__,, ﬂ
6000
z 5000 “mm—g—
£4000 «—- —~ ‘
g \
3000 " 1 M“; 'Sw‘ gt";~ . ‘ 8
2000 r j.‘ {w :ir.:éj ‘;€|Z4u 'ww' a." 1‘ 3

 

1000

 

 

 

 

0 10 20 30 40 50 60
Deflection, mm

Figure J .1 Frame clamped medium arch load-deﬂection curves.

ll7

 

7O

Table J .1 Frame clamped medium arch data.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Peak ”ﬁt-ﬁction @ Max.
Specimen Stiffness Load peak load Deflection Contact
# (Nlmm) (N) (mm) (mm) Time (msec)
1 194 2382 41 .60 44.59 38.53
2 171 321 1 32.51
3 1 85 2458 9.44 49.67 23.55
4 260 3372 31 .85 34.92 32.98
5 194 3308 36.63 41.1 1 26.78
6 342 2489 22.35
7 303 2480 22.49
8 236 3376 49.79 51 .70 23.85
Average 236 2884 30.83 44.40 29.14
Std. Dev. 62 466 12.60 6.74 6.47

 

Table J .2 Frame clamped medium arch energy data.

 

 

 

 

 

 

 

 

Impact Absorbed
Specimen Energy Energy

# (J) (J) DamagL.
1 71 .3 70.4 P
2 61 .6 55.2 N
3 83.7 78.9 P
4 68.1 64.3 P
5 95.9 95.8 P
6 54.4 50.5 NP
7 38.3 30.6 NP
8 1 13.9 1 13.6 P

 

 

 

 

 

 

 

118

 

#1
7133J

  
 
 

#2
61.62J

#3
837]
#4
as 11

Figure J. 2 Frame clamped medium arch damaged specimen photos.

 

119

96.01

54.4.1

#7
87. BJ

#8
ll3..9J

 

Figure J .3 Frame clamped medium arch damaged specimen photos.

120

APPENDIX K

Large arch with frame clamped boundary condition

121

 

8000

 

7000

 

6000

 

5000

 

154000 4 A

 

 

 

3000 ‘ 9'7"1|’

 

 

 

ii: '1. - 11 Will/m. 1

 

 

O .13 -
O 10 20 30 40 50 60

Figure K.1 Frame clamped large arch load-deflection curves.

122

 

Table K.l Frame clamped large arch data.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

123

Peak Wection Max. W ‘
Specimen Stiffness Load @ peak load Deflection Time
# (Nlmm) (N) (mm) (mm) (msec)
1 260 3304 33.96 69.22 24.60
2 348 3037 43.42 59.75 36.40
3 258 2815 31.97
4 239 4649 37.66
5 296 3417 39.03
Average 280 3444 37.21 64.49 30.50
Std. Dev. 43 713 4.48 6.70 8.34
Table K.2 Frame clamped large arch data.
Impact Absorbed
Specimen Energy Energy
# (J) (J) Damage
1 136.3 112.8 P
2 96.8 93.5 P
3 64.3 58.0 NP
4 80.1 66.2 NP
5 87.3 84.6 NP

 

#1
136.3J

#2
96.8.1

#3
64.31.]

  

 

Figure K.2 Frame clamped large arch damaged specimen photos.

124

APPENDIX L

Small arch with bolted boundary condition

125

8000

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7000 ~»—— w “ﬁgs —
6000
Z 5000 h“
15‘
a 4000 A l
3111 it 2
3000 a; -, :1"! ’ ' /
'1 A . ., .Ils/
2000 5‘1;

  

 

  

1000

  
 

“’m.‘ 4....“

0 10 20 30 4'0 50 60
Deflection, mm

Figure L.l Bolted small arch load-deflection curves.

126

 

70

 

Table L.l Bolted small arch data.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Def-lection @ Max. ﬁContact
Specimen Stiffness Flrst Second peak load Deﬂection Time
ff (Nlmm) Peak Load (N) Peak Load (N) (mm) (mm) (msec)
1 299.7 3059 6033 23.3
2 203 2733 6457 23.1 33.66 1 1 .9
3 251.5 2701 6535 21.5 31.09 11.6
4 327.4 2831 6760 21 .0
5 253.6 2831 5991 20.6 28.6 8.75
6 322.5 2887 5990 22.0
Average 276.27 2840 6294.30 21 .9 31 .12 10.75
Std. Dev. 49 127 332.80 1.1 2.53 1.74

 

Table L.2 Bolted small arch energy data.

 

 

 

 

 

 

 

 

 

 

Impact Absorbed
Specimen Energy Energy

ff (J) (J) Damage_
1 77.8 72.7 NP

2 1 18.5 1 05.0 P

3 94.4 79.8 P

4 85.3 83.0 NP

5 109.2 78.4 P

6 63.2 58.0 NP

 

 

 

127

 

 

Figure L.2 Bolted small arch damaged specimen photos.

128

APPENDIX M

Medium arch with bolted boundary condition

129

 

8000

 

 

 

 

 

 

 

 

 

7ooo -__- / 1
6000 5\
z 5000
'3 4000 e
3 7
3000 ~ - /

 

 

 

 

 

5
3
2000 v F](/’
1000 4
6 W
0 I T

O 10 20 3O 2 4O 50 60 70

Deflection, mm

 

 

Figure M.1 Bolted medium arch load-deflection curves.

130

 

Table M.1 Bolted medium arch data.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DeTiecﬁon (3) Max. Contact
Specimen Stiffness First Second peak load Deflection Time
it (Nlmm) Peak Load (N) Peak Load (N) (mm) (mm) (msec)
1 487.2 3217 6495 32.95 40.74 1 1 .4
2 527 3235 5901 32.23 36.54 1 5.5
3 586.3 3499 5416 31 .90
4 504 3924 6105 32.19
5 595 3470 6869 31 .07 39.25 12.85
6 749 3378
7 518 3626 5123 34.30 45.89 14.2
8 640.81 3514
Avera e 575.91 3483 5985 32.44 40.61 13.49
Std. Dev. 87.37 227 653 1.09 3.93 1.76

 

Table M.2 Bolted medium arch energy data.

 

 

 

 

 

 

 

 

 

 

impact Absorbed

Specimen Energy Energy

if (J) (J) Damage—

1 130.3 79.5 P

2 86.7 81 .2 BITP

3 79.6 71 .4 NP

4 94.7 91 .3 NP

5 1 10.5 87.9 P

6 36.0 28.2 NP

7 123.0 87.4 P

8 49.1 45.1 NP

 

 

 

 

 

131

 

#1
130.3]

#2
86 .7}

#3
79.6.1

94.7.1

#5
1105.1

#6
36.01

 

Figure M.2 Bolted medium arch damaged specimen photos.

132

    

Figure M.2 Bolted medium arch damaged specimen photos.

Note: Specimen #3 had multiple hits.

133

APPENDIX N

Large arch with bolted boundary condition

134

8000

 

 

7000

6000

 

 

5000

'3 4000

 

 

 

 

-' 3000

 

 

 

2000

1000

0 10

 

 

 

T l

20 30 4o 50 60
Deflection, mm

 

Figure N.l Bolted large arch load-deflection curves.

135

 

70

 

Table N.1 Bolted large arch data.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Deflection @ Max. Contact
Specimen Stiffness First Second peak load Deﬂection Time
it (Nlmm) Peak Load (N) Peak Load (N) (mm) (mm) (msec)
1 560.5 4886 6469.1 47.1
2 500.27 4425 5208.7 44.1 52.76 19.0
3 554.67 4377
4 544.47 4457 3373.6 48.0 61 .94 25.8
5 607.2 4949
6 601.2 5211 4229 48.9 59.13 19.9
7 619.5 4454 4229 48.9 49.99 17.4
Average 569.69 4680 4701.89 47.38 55.96 20.51
Std. Dev. 42.12 330 1 182.30 1.99 5.53 3.67
Table N.2 Bolted large arch energy data.
Impact Absorbed
Specimen Energy Energy
# (J) (J) Damage__
1 11 1.6 107.8 NP
2 120.5 108.3 P
3 47.6 38.9 NP
4 1 16.1 105.0 P
5 80.4 72.8 NP
6 134.5 106.7 P
7 1 11.7 98.5 BITP

 

 

 

 

 

136

 

 

Figure N.2 Bolted large arch damaged specimen photos.

137

#7
“1.8.1

 

Figure N.3 Bolted large arch damaged specimen photos.

138

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139

 

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142

 

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