BLAST PROTECTION OF INFRASTRUCTURE USING ADVANCED

COMPOSITES

by

Evan Brodsky

A thesis submitted to the Faculty of the University of Delaware in partial

fulfillment of the requirements for the degree of Master of Civil Engineering

Spring 2014

Copyright 2014 Evan Brodsky

All Rights Reserved

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BLAST PROTECTION OF INFRASTRUCTURE USING ADVANCED

COMPOSITES

by

Evan Brodsky

Approved: __________________________________________________________

John W. Gillespie, Jr., Ph.D.

Professor in charge of thesis on behalf of the Advisory Committee

Approved: __________________________________________________________

Harry W. Shenton III, Ph.D.

Chair of the Department of Civil and Environmental Engineering

Approved: __________________________________________________________

Babatunde A. Ogunnaike, Ph.D.

Dean of the College of Engineering

Approved: __________________________________________________________

James G. Richards, Ph.D.

Vice Provost for Graduate and Professional Education

iii

ACKNOWLEDGMENTS

Dedicated to my understanding and amazing wife Jennifer A. Cohen.

I would like to thank my advisor Dr. John W. Gillespie, Jr. for affording me

the opportunity to learn from his research experience. He bestowed guidance to me

with respect to the entire research and thesis process. I gained from him an important

understanding of the vast composites world, which will guide me through the rest of

my life. I look forward to continuing my relationship with him.

Dr. Bazle A. Gama was a member of my advisory committee, and I wish to

thank him for his patience and enlightenment in regards to the composites aspects of

my project. He was always willing to provide his support concerning the details of my

blast protection research.

Accordingly, I would like to thank Dr. Jennifer Righman McConnell for her

continued advice and guidance throughout the past few years. She generously

engaged in the blast protection research Bi-Weekly Graduate Student Meetings held

by Dr. John W. Gillespie, Jr.

I would like to express my gratitude towards Touy and Johnny Thiravong for

all of their help with the experimentation facets of my research. In addition, all of the

graduate students, especially Renee Cimo, with an office in the Center of Composite

Materials Graduate Student Office were greatly supportive when I required assistance.

iv

Conclusively, I would like to greatly acknowledge the Army Research Office

for funding my research and allowing me to contribute to the energy absorption

experimentations and investigations.

v

TABLE OF CONTENTS

LIST OF TABLES ................................................................................................... vii

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

ABSTRACT............................................................................................................. xv

Chapter

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

1.1 Explanation ............................................................................................ 1

1.2 Blast Overview ...................................................................................... 2

1.3 Materials Used in This Study ................................................................. 3

1.4 Blast Loading ....................................................................................... 18

1.5 Maximizing Energy Dissipation ........................................................... 30

1.6 Summary of Chapters........................................................................... 38

2 STATIC TESTING OF POLYISOCYANURATE FOAM ............................ 40

2.1 Introduction to Static Testing of Polyisocyanurate Foam ...................... 40

2.2 Description of Polyisocyanurate Foam Core ......................................... 40

2.3 Description of Polyisocyanurate Foam Tests ........................................ 44

2.4 Polyisocyanurate Foam Models ............................................................ 59

2.5 Conclusion of Polyisocyanurate Foam ................................................. 63

3 STATIC TESTING OF FIBERGLASS WEB ............................................... 64

3.1 Introduction to Static Testing of E-Glass Web ...................................... 64

3.2 Description of E-GlassWeb .................................................................. 64

3.3 Description of Web Buckling Tests ...................................................... 76

3.4 Web Buckling Results .......................................................................... 79

3.5 CMAP ................................................................................................111

3.6 Critical Beam Buckling Analysis ........................................................121

3.7 Southwell Plots ...................................................................................125

3.8 Web Compression Strength Tests ........................................................137

3.9 Conclusion of Fiberglass Web .............................................................153

4 STATIC TESTING OF WEB CORE ...........................................................155

4.1 Introduction to Static Testing of Web Core .........................................155

vi

4.2 Description of Web Core Experiments ................................................155

4.3 Discussion of Web Core Test Results ..................................................173

4.4 Conclusion of Web Core .....................................................................184

5 ENERGY ABSORPTION CAPABILITIES.................................................185

5.1 Introduction to Energy Absorption Capabilities ...................................185

5.2 Mine Blast Theory ..............................................................................185

5.3 Modeling Foam, Web, and Web Core Failure Modes ..........................194

5.4 Optimization and Design Improvement ...............................................202

5.5 Conclusion of Energy Absorption Capabilities ....................................211

6 CONCLUSIONS AND FUTURE WORK ...................................................212

6.1 Summary of Results for Each Chapter .................................................212

6.2 Future Work........................................................................................213

REFERENCES .......................................................................................................215

Appendix

REPRINT PERMISION LETTERS .............................................................221

vii

LIST OF TABLES

Table 1.1 DERAKANE 510A-40 Epoxy Vinyl Ester Resin Properties [1] ..................................12

Table 1.2 E-Glass/Epoxy Unidirectional Composite Properties [2] .............................................13

Table 1.3 E-Glass/Epoxy Biaxial Lamina Woven Fabric Properties [3] ......................................13

Table 2.1 Uniaxial Stress Polyiso Foam Dimensions ..................................................................46

Table 2.2 Uniaxial Strain Polyiso Foam Dimensions ..................................................................47

Table 2.3 Uniaxial Stress Mechanical Properties ........................................................................56

Table 2.4 Uniaxial Strain Mechanical Properties ........................................................................56

Table 2.5 Linear-Elastic Region Energy Absorption Values .......................................................63

Table 2.6 Plastic-Plateau Region Energy Absorption Values ......................................................63

Table 3.1 Load-Unload Specimen Dimensions ...........................................................................80

Table 3.2 Long-Length Web Buckling Specimen Dimensions ....................................................83

Table 3.3 Small-Length Web Buckling Specimen Dimensions ...................................................84

Table 3.4 Experimental Long-Length Applied Load, Stress, and Modulus Mechanical Results . 103

Table 3.5 Experimental Long-Length Displacement, Deflection, and Strain Mechanical

Results ..................................................................................................................... 104

Table 3.6 Experimental Small-Length Applied Load, Stress, and Modulus Mechanical Results 105

Table 3.7 Experimental Small-Length Displacement, Deflection, and Strain Mechanical Results ..................................................................................................................... 106

Table 3.8 Long-Length Percent Bending Calculations .............................................................. 108

Table 3.9 Small-Length Percent Bending Calculations ............................................................. 109

Table 3.10 E-Glass Fiber Properties [4] ..................................................................................... 112

Table 3.11 E-Glass – Vinyl Ester Resin Composite Lamina Properties ....................................... 112

Table 3.12 Encrusted Polymer (EP) Isotropic Lamina Properties [1]........................................... 112

viii

Table 3.13 Dimensions of Fiber Volume Fraction Coupons ........................................................ 113

Table 3.14 Summary of Fiber Volume Fraction Experiment ....................................................... 113

Table 3.15 Long-Length Web Laminates’ Input in CMAP ......................................................... 115

Table 3.16 Small-Length Web Laminates’ Input in CMAP ........................................................ 116

Table 3.17 Effective Long-Length Web Laminate Mechanical Properties ................................... 117

Table 3.18 Effective Small-Length Web Laminate Mechanical Properties .................................. 117

Table 3.19 Long-Length Elastic Moduli Comparison ................................................................. 118

Table 3.20 Small-Length Elastic Moduli Comparison ................................................................ 119

Table 3.21 Stiffness Matrix Values ............................................................................................ 120

Table 3.22 Long-Length Web Buckling Loads ........................................................................... 122

Table 3.23 Small-Length Web Buckling Loads .......................................................................... 122

Table 3.24 Long-Length and Small-Length Differences between Experimental and Calculated

Loads ....................................................................................................................... 124

Table 3.25 Long-Length Southwell Plots Comparison ................................................................ 135

Table 3.26 Small-Length Southwell Plots Comparison ............................................................... 136

Table 3.27 Web Compression Strength Coupon Dimensions ...................................................... 140

Table 3.28 Web Compression Strength Failure and Area ............................................................ 141

Table 3.29 WCS Acceptable Coupon Thicknesses (in) ............................................................... 141

Table 3.30 WCS Experimental Results ...................................................................................... 148

Table 3.31 Compression Load of Long-Length Webs................................................................. 149

Table 3.32 Compression Load of Small-Length Webs ................................................................ 150

Table 3.33 Small-Length Buckled Energy Absorption Values .................................................... 152

Table 4.1 WFC Dimensions ..................................................................................................... 160

Table 4.2 WFC Web and Encrusted Polymer Thicknesses ........................................................ 161

Table 4.3 Foam Crushing in WFC Samples .............................................................................. 174

Table 4.4 WFC Experimental Results in Web Only .................................................................. 176

ix

Table 4.5 WFC CMAP Laminate Values for Web .................................................................... 177

Table 4.6 WFC CMAP Matrix Stiffness Values for Web .......................................................... 179

Table 4.7 WFC Theoretical Buckling and Maximum Compression Loads for Web Only .......... 180

Table 4.8 WFC Dimensions for Acceptable Samples................................................................ 183

Table 4.9 WFC Experimental Mechanical Properties Web Only for Acceptable Samples .......... 183

Table 5.1 Mechanical Properties of DIAB Divinycell H-Grade Foam [5].................................. 202

Table 5.2 Divinycell H-Grade Foam Model Values .................................................................. 203

Table 5.3 Constant Values for Equation 5.2 ............................................................................. 206

Table 5.4 Normalized Energy Absorption Value from Equation 5.2.......................................... 207

x

LIST OF FIGURES

Figure 1.1 Web Core Panel Cross-Section with Vertical Webs Spaced 1.5”Apart .......................... 4

Figure 1.2 Polyiso Foam Quasi-Static Specimen .......................................................................... 5

Figure 1.3 Uniaxial Stress Polyiso Foam Specimen during Loading .............................................. 7

Figure 1.4 Uniaxial Strain Polyiso Foam Specimen during Loading .............................................. 8

Figure 1.5 (a) Uniaxial Stress and (b) Uniaxial Strain Loading Methods for Foam [6] ................... 9

Figure 1.6 Compression Stress-Strain Response for an Elastomeric Foam [7] ..............................11

Figure 1.7 ±45° Unsymmetrically-Stacked Unidirectional E-glass Fibers without Resin froWeb ..12

Figure 1.8 Example of a Web Core [8] ........................................................................................14

Figure 1.9 Web Core Construction [8].........................................................................................14

Figure 1.10 G18 TYCOR® Plan View prior to Resin Infusion.......................................................15

Figure 1.11 G18 TYCOR® Side View Prior to Resin Infusion ......................................................15

Figure 1.12 TYCOR® Representation VARTM Process [9] ..........................................................16

Figure 1.13 Web Core Small-Length Unit Cell Dimensions (Depth is 2 inches into page, Width

is 1.5 inches, and Height is 1 inch) .............................................................................17

Figure 1.14 Blast from Spherical Charge [10] ...............................................................................18

Figure 1.15 Idealized Pressure-Time Curve [10]............................................................................19

Figure 1.16 Pressure vs. Time of Blast Wave on Panel Representation...........................................20

Figure 1.17 Nomenclature of Westine Equation 1.3 [11] ...............................................................21

Figure 1.18 Charge Mass Influence on Impulse .............................................................................23

Figure 1.19 Stand-Off Distance Influence on Impulse ...................................................................23

Figure 1.20 Web Core Experiment (a) After Quasi-Static Loading [12] and (b) After Dynamic

Loading [13] ..............................................................................................................25

Figure 1.21 Foam Core Sandwich Panel from Schubel Journal Article [14] ...................................26

xi

Figure 1.22 Representation of Impact vs. Quasi-Static Loading [14] ..............................................27

Figure 1.23 Web Core with Uniform Displacement and Average Pressure .....................................29

Figure 1.24 Side View of 3TEX-6 Sandwich Panel Subjected to Blast Loading [15] ......................31

Figure 1.25 Cross-Section of 3TEX-6 Sandwich Panel Subjected to Blast Loading [16] .................32

Figure 1.26 Maximum Dynamic Deflection vs. Areal-Density of 3TEX Panel [15] ........................33

Figure 1.27 Load vs. Displacement Foam Plastic-Semi-Plateau Model Energy Absorption ............34

Figure 1.28 Force vs. Axial Displacement E-Glass Web Plastic-Plateau Model Energy

Absorption .................................................................................................................35

Figure 1.29 Foam Experiment Illustrations of (a) Linear-Elastic Region (b) Plastic-Semi-Plateau

Crushing Region ........................................................................................................35

Figure 1.30 Example of a Buckled E-Glass Web (Foam Removed) in the Plastic-Plateau Region ...36

Figure 1.31 Models of Web Buckling, Foam Crushing, and Web + Foam Buckling and Crushing ..37

Figure 2.1 Polyisocyanurate Foam Specimen ..............................................................................41

Figure 2.2 Average Quasi-Static Stress-Strain Graph of Uniaxial Polyiso Foam Specimens .........42

Figure 2.3 Compressive Quasi-Static Stress-Density Graph of Uniaxial Polyiso Foam

Specimens..................................................................................................................42

Figure 2.4 Experimental Foam Uniaxial Stress Setup ..................................................................45

Figure 2.5 (a) Experimental Uniaxial Strain Setup Prior to Foam Placement (b) Experimental

Uniaxial Strain Setup after Foam Placement ...............................................................45

Figure 2.6 All Uniaxial Strain Specimens ....................................................................................48

Figure 2.7 All Uniaxial Stress Specimens ....................................................................................48

Figure 2.8 Uniaxial Stress Specimen 1 (a) at Commencement of Loading and (b) during

Densification..............................................................................................................49

Figure 2.9 Uniaxial Stress Specimen 2 at during Loading ............................................................49

Figure 2.10 Uniaxial Stress Specimen 3 during Loading ................................................................49

Figure 2.11 Uniaxial Stress Specimen 4 (a) at Commencement of Loading and (b) during

Densification..............................................................................................................50

Figure 2.12 Uniaxial Stress Specimen 5 during Loading ................................................................50

xii

Figure 2.13 Uniaxial Stress Specimen 6 (a) at Commencement of Loading and (b) during

Densification..............................................................................................................50

Figure 2.14 Uniaxial Stress – Load vs. Displacement using 100 LB Load Cell ...............................51

Figure 2.15 Uniaxial Stress – Stress vs. Axial Strain using 100 LB Load Cell ................................52

Figure 2.16 Uniaxial Strain – Load vs. Axial Displacement using 100 LB Load Cell .....................54

Figure 2.17 Uniaxial Strain – Stress vs. Axial Strain using 100 LB Load Cell ................................55

Figure 2.18 Average of Uniaxial Stress and Strain Specimens - Load vs. Axial Displacement ........58

Figure 2.19 Average of Uniaxial Stress and Strain Specimens - Stress vs. Axial Strain ..................58

Figure 2.20 Uniaxial Stress – Stress vs. Axial Strain EPPR Model.................................................61

Figure 2.21 Uniaxial Strain – Stress vs. Strain Foam EPPR Model ................................................61

Figure 3.1 Web Laminate (a) Before and (b) After Resin Removal ..............................................65

Figure 3.2 Panel Infusion Illustration [17] ...................................................................................65

Figure 3.3 Web Coordinate System .............................................................................................66

Figure 3.4 Fiberglass Web Deforming Out-Of-Plane with Axial Load .........................................68

Figure 3.5 Load vs. Axial Displacement of an Ideal Column .......................................................69

Figure 3.6 Load vs. Axial Displacement Graph of Long-Length Specimen IWB26JF ...................71

Figure 3.7 Load vs. Axial Displacement of Compression Strength Specimen WCS10 Using Side-Supported ASTM D 695 Fixture .........................................................................73

Figure 3.8 Web Core Variable Depiction, the Depth of the Web dw is into the Page .....................75

Figure 3.9 Web Buckling Fixture Schematics ..............................................................................77

Figure 3.10 Complete View of Actual Web Buckling Test Setup ...................................................78

Figure 3.11 Loading Block Dimensions ........................................................................................78

Figure 3.12 (a) IWB44JF Specimen Prior to Buckling (b) IWB44JF Specimen during Loading......79

Figure 3.13 Load vs. Axial Displacement of Load-Unload Specimens ...........................................81

Figure 3.14 Encrusted Polymer Representation of IWB42EP .........................................................85

Figure 3.15 Load vs. Axial Displacement Long-Length Web Buckling Specimens.........................86

xiii

Figure 3.16 Force vs. Lateral Deflection from LVDT Long-Length Buckling Specimens ...............88

Figure 3.17 Stress vs. Strain from Strain Gages of Long-Length Buckling Specimens ....................91

Figure 3.18 Load vs. Axial Displacement Small-Length Web Buckling Specimens ........................95

Figure 3.19 Force vs. Lateral Deflection from LVDT Small-Length Web Buckling Specimens ......97

Figure 3.20 Stress vs. Strain from Strain Gages Small-Length Web Buckling Specimens ...............99

Figure 3.21 Web Core Preform Prior to VARTM ........................................................................ 114

Figure 3.22 Southwell Plot [18] .................................................................................................. 126

Figure 3.23 Long-Length Southwell Plots ................................................................................... 128

Figure 3.24 Small-Length Southwell Plots .................................................................................. 132

Figure 3.25 ASTM D 695 Fixture ............................................................................................... 138

Figure 3.26 Example of Web Compression Strength Coupon ....................................................... 138

Figure 3.27 WCS5EP Shear Failure (a) Top View and (b) Side View .......................................... 142

Figure 3.28 WCS9EP Shear Failure (a) Top View and (b) Side View .......................................... 143

Figure 3.29 WCS10JF Shear Failure (a) Top View and (b) Side View ......................................... 143

Figure 3.30 WCS12HEP Shear Failure (a) Top View and (b) Side View...................................... 144

Figure 3.31 WCS Force vs. Axial Displacement from Instron ...................................................... 145

Figure 3.32 WCS Stress vs. Axial Strain from Instron ................................................................. 146

Figure 4.1 WFC Unit Cell ......................................................................................................... 156

Figure 4.2 View of Web Core Dimensions ................................................................................ 157

Figure 4.3 Web Core in Buckling Fixture .................................................................................. 157

Figure 4.4 Web Core Specimen WFC1 Prior to Loading............................................................ 158

Figure 4.5 Web Core Specimens after Bifurcation (a) WFC1, (b) WFC2, (c) WFC3, and (d)

WFC4 ...................................................................................................................... 159

Figure 4.6 WFC Force in Sample vs. Axial Displacement.......................................................... 163

Figure 4.7 WFC Stress in Sample vs. Axial Strain ..................................................................... 165

Figure 4.8 WFC Force in Web vs. Axial Displacement .............................................................. 168

xiv

Figure 4.9 WFC Stress in Web vs. Axial Strain ......................................................................... 170

Figure 5.1 Web Core Blast Panel Representation [17] ............................................................... 186

Figure 5.2 Web Core Blast Protection Panel Cross-Section [17] ................................................ 186

Figure 5.3 Web Core Plan View of Blast Protection Panel after Pressure Experiment [9] ........... 188

Figure 5.4 Web Core Section View of Blast Protection Panel after Pressure Experiment [9] ....... 188

Figure 5.5 Blast Representation 1 .............................................................................................. 190

Figure 5.6 Blast Representation 2 .............................................................................................. 191

Figure 5.7 Blast Representation 3 .............................................................................................. 191

Figure 5.8 Blast Representation 4 .............................................................................................. 192

Figure 5.9 Blast Representation 5 .............................................................................................. 192

Figure 5.10 Load vs. Strain Foam EPPR Model with Web Core Dimensions ............................... 195

Figure 5.11 Load vs. Strain Web Compression Failure Model using Unit Cell Dimensions .......... 197

Figure 5.12 Load vs. Strain Web Buckling Model using Unit Cell Dimensions ............................ 198

Figure 5.13 1) Web Buckles then Foam Crushes Regime ............................................................. 199

Figure 5.14 3) Web Fails then Foam Crushes Regime ................................................................. 200

Figure 5.15 H-Grade Foams in Unit Cell ..................................................................................... 204

Figure 5.16 Divinycell H-Grade Foams Normalized Energy Absorption vs. Foam Density .......... 208

Figure 5.17 Optimal Foam in Unit Cell Based on Regime Graph 1 .............................................. 210

xv

ABSTRACT

This research was a systematic investigation detailing the energy absorption

mechanisms of an E-glass web core composite sandwich panel subjected to an impulse

loading applied orthogonal to the facesheet. Key roles of the fiberglass and

polyisocyanurate foam material were identified, characterized, and analyzed. A quasi-

static test fixture was used to compressively load a unit cell web core specimen

machined from the sandwich panel. The web and foam both exhibited non-linear

stress-strain responses during axial compressive loading. Through several analyses,

the composite web situated in the web core had failed in axial compression.

Optimization studies were performed on the sandwich panel unit cell in order to

maximize the energy absorption capabilities of the web core. Ultimately, a sandwich

panel was designed to optimize the energy dissipation subjected to through-the-

thickness compressive loading.

1

Chapter 1

INTRODUCTION

1.1 Explanation

Numerous terrorist attacks have occurred in the past decade that have

generally been in the form of an explosion due to an incendiary device used to harm

the public and damage essential structures including bridges, buildings, and airports.

One very well-known devastating terrorist attack on the nation occurred on September

11, 2001 on the World Trade Towers in New York City. A terrorist group hijacked a

commercial jet and crashed into the World Trade Towers, which were demolished.

Unfortunately, many innocent civilians became casualties of a senseless act of

terrorism. This immediately fueled national security initiatives, which consequently

funded academic research aimed at increasing the protection of infrastructure. One of

the research goals of this thesis was to assess composite sandwich panels as an energy

absorbing blast protection system for bridges and buildings in order to upgrade the

nation’s infrastructure safety against terrorism.

2

1.2 Blast Overview

The three general methods of protecting against an explosion are to strengthen

the infrastructure, deflect the blast energy, and absorb the blast energy. Strengthening

the structure by using high performance materials can decrease the extent of damage

and prevent structural collapse caused by a terrorist attack. Deflection may be

achieved by geometrically shaping blast protection panels. Energy absorption can be

increased through the use of advanced materials. Due to a compressive force,

advanced composites – the primary focus of this research – absorb significant

amounts of energy per unit weight by crushing.

Composites are light-weight materials that offer high stiffness and strength,

while not considerably increasing the overall weight of the infrastructure system.

They typically consist of a reinforcing fiber embedded in a polymer matrix.

Composites are used extensively in various man-made structures: such as airplanes,

boats, space ships, cars, bridges and buildings. When designed appropriately,

composites can be efficiently used for blast protection due to their high specific

energy absorption characteristics. Since they are relatively new materials, composites

are more costly compared to other construction materials, such as steel, aluminum,

and concrete. Composite structures have directional properties that offer

opportunities to tailor properties in ways that are not possible with isotropic materials.

However, design methods for anisotropic materials can be more challenging. If the

most efficient mixture of composite materials is used, with the best geometry and

mechanical properties, one may create a light, stiff, strong, and high-energy-

absorption system.

3

1.3 Materials Used in This Study

For the blast protection panel, a sandwich structure was utilized. Sandwich

structures have been widely used for decades due to their robust nature. Sandwich

structures have top and bottom facesheets, and a middle layer(s), known as the core,

comprised generally of a foam or lattice system. In structural applications, the

facesheets carry the in-plane and bending loads providing stiffness and strength. The

core provides multiple functions. It “keeps the [facesheets] at their desired distance

and transmits the transverse normal and shear loads” [19]. In transverse impact and

impulse loading the core also provides a significant role in energy consumption

through transverse compression and shear deformation.

The blast protection panel used for this research was composed of E-glass

facesheets and a core with orthogonal rows of E-glass webs separated by

polyisocyanurate foam (i.e., Polyiso Foam). Figure 1.1 shows a cross-section of the

web core panel. The vertical layers of the web core appear similar to multiple series

of miniature I-beam columns, which distribute loads and provide superior mechanical

properties [20]. The web core is sturdier than the solitary foam core due to the webs

situated in-line with forces applied normal to the facesheet. A sandwich structure

blast protection panel unit cell was utilized in this research and is described at the end

of this section.

4

Figure 1.1 Web Core Panel Cross-Section with Vertical Webs Spaced

1.5” Apart

The following paragraphs describe the foam used in this research. Structural

foams are used for numerous applications. “Polymeric foams [are] used in everything

from disposable coffee cups to the crash padding of an aircraft cockpit” [7]. In

addition, present-day foams are used for insulation, cushioning, and absorbing an

impact [7].

To begin with, structural foams contain an internal geometry of cells. The

cells can have various sizes and wall thicknesses comprised of the constituent material

(i.e. polymers, metals or ceramics) [21]. As a result, foams are highly-compressible,

light-weight, and low-stiffness materials categorized as either closed or open-cell [7].

Foams are lightweight cellular materials that have extraordinary energy absorption

capabilities [21]. A closed-cell foam is comprised of cells that are completely

surrounded by membrane-like cell walls, while an open-cell foam contains

interconnected cells with cell walls interspersed throughout the foam [7].

Moreover, foams are mass-produced several different ways. One way is by

inserting gas particles by way of a blowing agent into a specific base material to form

the cellular foam structure [22]. The trapped gas dispersed throughout the foam

5

results in the aforementioned cellular structure. In turn, a foam’s mechanical

properties rely heavily on the amount of trapped gas it contains, defined as porosity.

A foam’s density is related to its porosity, shown in Equation 1.1.

(1.1) [23]

To specify, the maximum strain εmax equals unity minus the ratio of the foam density

and the original polymer density denoted as ρ0 and ρc, respectively.

Figure 1.2 Polyiso Foam Quasi-Static Specimen

The following explains the foam used in this research. To begin with, the

polymer polyisocyanate was reported to have densities of 60.6 pcf, 78.0 pcf, and

62.43 pcf in the Polymer Data Handbook, 2nd Edition as defined by authors

Chandima Kumudinie Jaysuriya, Jagath K. Premachandra, and Junzo Masamoto [24,

25]. As a result, the average polyisocyanate polymer density was 66.80 pcf ± 0.94

00 max 1

c

6

pcf. The Polyiso Foam – illustrated in the previous figure and derived from the

polymer polyisocyanate – had a density of 2.24 pcf. At the end of Section 2.2, these

two values will be inputted into Equation 1.1 producing the maximum strain value for

the Polyiso Foam.

Two different types of compression tests were performed on Polyiso Foam in

this study in order to determine its mechanical properties. These tests were Uniaxial

Stress and Strain experiments, which are categorized by their relationship to Poisson’s

Ratio defined in Equation 1.2 [26]. Uniaxial Stress and Strain specimens exhibited a

non-zero and zero Poisson’s Ratio, respectively. Specifically, Poisson’s Ratio for the

polyisocyanurate closed-cell foam is an average of 0.33 [7].

(1.2) [26]

For Uniaxial Stress, the unconfined cylindrical foam specimen is allowed to laterally

expand due to Poisson’s Ratio being non-zero [22].

In addition, the cross-sectional area of the Uniaxial Stress foam specimens was

no longer constant throughout the specimen [22]. A representation of the changing

cross-sectional area of a Uniaxial Stress foam specimen is illustrated in Figure 1.3.

7

Figure 1.3 Uniaxial Stress Polyiso Foam Specimen during Loading

The foam specimen axially compressed and laterally expanded, as a result of non-zero

Poisson’s Ratio, due to an applied compression load in the Uniaxial Stress

experiment. Lateral expansion at the platens is restricted due to friction giving rise to

the bulged shape shown in Figure 1.3.

To explain the second type of test performed on the foam, a Uniaxial Strain

experiment is executed by confining a cylindrical foam specimen inside a steel collar,

and then applying an axial load to the foam [27].The steel collar is orders of

magnitude stiffer than the foam [28].

8

Figure 1.4 Uniaxial Strain Polyiso Foam Specimen during Loading

Figure 1.4 shows a Uniaxial Strain experiment during loading, and Figure 1.5

illustrates both Uniaxial Stress and Strain tests. The steel collar was used to prevent

the foam specimen from radially expanding due to an applied load and hindered the

effect of Poisson’s Ratio [28]. As a result, radial strain remained zero and the

specimen’s cross-sectional area was kept constant.

The following describes the stress-strain response of foam. Figure 1.6

illustrates a typical compression stress-strain response for an Elastomeric Foam. To

begin with, the curve has a linear-elastic, plateau, and foam densification region [23].

First, the linear-elastic region incorporates the axial shortening or bending of the cell

walls [7].

9

Figure 1.5 (a) Uniaxial Stress and (b) Uniaxial Strain Loading Methods

for Foam [6]

Next, cell collapse due to buckling, yielding, or crushing of the cell walls

occurs at relatively constant stress in the plastic region [7]. In Figure 1.6 the curve

exhibited a relatively linear plateau region with an insignificant slope, which may be

assumed as a constant stress. Since stress is directly related to applied load, foam

absorbs a significant amount of energy in this region; energy absorption is related to

10

the area under a material’s load-displacement curve. This is explained in Section 1.5

Maximizing Energy Dissipation. Notably, the plateau stress in the second region is

directly proportional to the foam density and the applied strain rate [7]. Therefore, in

order to design a specific foam, one must decide on its density taking into account the

applied load velocity resulting in the specimen’s strain rate.

Finally, the foam experiences densification. The foam’s cell walls continually

buckle with little increase in stress, and as a result, the area under the curve

continually and efficiently increases until the foam begins to densify [29]. This was

illustrated in the curved region, at the interface of the plateau and densification region,

of the subsequent figure. During compressive loading and the densifying of the foam,

the cells almost completely collapse. This is defined as the densification region.

Effectively, the “opposing cell walls touch and further strain [compresses] the solid

itself” [7].

Conclusively, the foam cell walls elastically shorten, buckle, and finally the

cells densify in compression. Beneficially, the foam undergoes large deformation and

absorbs a significant amount of energy. The energy consumption capacity of the

foam in this research will be comprehensively described in Chapter 2.

Furthermore, foam specimens were tested to determine their mechanical

properties by the aforementioned uniaxial compression experiments. Figures 1.3 and

1.4 refer to these tests. These investigations are discussed in Chapter 2 – conducted to

understand the energy absorption mechanisms of the foam – in which foam samples

are quasi-statically loaded in compression.

11

Figure 1.6 Compression Stress-Strain Response for an Elastomeric

Foam [7]

Next, the E-glass-vinyl-ester-resin webs will be reviewed. The composite

webs were spaced at 1.5” apart comprised of four angle-ply lamina. The fibers in

these laminae were “alternately oriented at angles of +θ and –θ” [30]. In this

investigation the stacking sequence [45°/-45°/45°/-45°] was composed of

unsymmetrically-stacked E-glass sheets shown in Figure 1.7.

12

Figure 1.7 ±45° Unsymmetrically-Stacked Unidirectional E-Glass

Fibers without Resin from Web

The E-glass webs, which comprised the core and carries “the transverse shear force”

applied to the sandwich panel, were impregnated with a vinyl ester resin (see Table

1.1) [31]. Each ply measured 0.008 inches thick, with the E-glass webs equaling a

total 0.032 inches thick.

Table 1.1 DERAKANE 510A-40 Epoxy Vinyl Ester Resin Properties [1]

Table 1.2 shows typical mechanical properties of a unidirectional E-glass layer,

representative of the web layers in this study, with a fiber volume fraction of 0.29

taken from the Delaware Composite Design Guide Encyclopedia [2]. The web

buckling samples in this research are listed in the Web Buckling Results Section 3.4.

Density

(pci)

Flexural

Strength

(psi)

Flexural

Modulus

(psi)

Shear

Modulus

(psi)

Poisson’s

Ratio

Vinyl Ester

Resin 0.044 21,700 5.22E5 1.89E5 0.38

13

Moreover, the blast protection panel was also composed of ten E-glass cross-

ply woven facesheets [E-glass (9 oz)]10 infused with DERAKANE 510A-40 vinyl

ester resin situated above and below the sandwich structure to provide bending

stiffness to the panel. Table 1.3 lists E-glass/epoxy biaxial woven fabric facesheet

lamina properties. The facesheets react to the “bending moment as longitudinal

tensile and compressive forces and stresses” [31].

Table 1.2 E-Glass/Epoxy Unidirectional Composite Properties [2]

Density

(pci)

Compressive

Strength

(psi)

Young’s

Modulus

(psi)

Shear

Modulus

(psi)

Poisson’s

Ratio

Minimum 0.0578 52,210 5.076E6 2.103E6 0.05

Maximum 0.0705 127,600 6.527E6 2.698E6 0.04

Table 1.3 E-Glass/Epoxy Biaxial Lamina Woven Fabric Properties [3]

Density

(pci)

Compressive

Strength (psi)

Young’s

Modulus

(psi)

Shear

Modulus

(psi)

Poisson’s

Ratio

Fiber

Volume

Fraction

Minimum 0.06322 40,610 3.829E6 0.6396E6 0.14 43%

Maximum 0.07117 43,950 - 0.7687E6 0.17 48%

The web core sandwich structure used in this study will be explained. The

previously-described foam, E-glass-vinyl-ester-resin web, and E-glass composite

facesheets comprise the web core sandwich structure. Sandwich structures have been

used for numerous applications since the 1940s for aircraft due to their “high flexural

stiffness-to-weight ratio” [8]. Figures 1.8 and 1.9 show a sandwich structure

composed of a web core and the construction of a web core sandwich panel.

14

Figure 1.8 Example of a Web Core [8]

Figure 1.9 Web Core Construction [8]

Directly related to the reason for this research, the sandwich structure was

utilized for its energy absorption capabilities. Structural sandwich panels with

composite facesheets have excellent properties, for instance superior bending

stiffness, low weight, and efficient blast energy dissipation [20]. The bending

stiffness per unit weight is superior in a sandwich panel due to its larger moment of

inertia and depth compared to a solid plate [32]. In addition, sandwich panels are

considerably better at consuming blast energy than a solid plate of the same weight

[33]. This is due to their core. “Core compression constitutes a major contribution to

energy dissipation” [32].

15

Figure 1.10 G18 TYCOR® Plan View prior to Resin Infusion

Figure 1.11 G18 TYCOR® Side View Prior to Resin Infusion

16

The sandwich structure was G18 TYCOR® Webcore Technologies, Inc.

sections consisting of foam surrounding through-the-thickness plies. This core

material was chosen for its easy manufacturing and energy consumption abilities.

Previous research had been performed at the University of Delaware Center for

Composite Materials had determined this in the “Processing and Performance

Evaluation of Thick-Section Sandwich Composite Structures” papers. Figures 1.10

and 1.11 illustrate the G18 TYCOR® sections prior to resin infusion. In addition,

Figure 1.1 presents a G18 TYCOR® blast panel cross-section after resin infusion, but

prior to machining. Notably, the preceding figure shows the aforementioned cross-ply

E-glass composite web.

To specify, the entire blast protection panel was “made in one single operation

in which resin is injected [into the webs and facesheets] with assistance of vacuum”

[34] by a process defined as vacuum-assisted resin transfer molding (VARTM).

Figure 1.12 TYCOR® Representation VARTM Process [9]

17

Resin is infused at the Resin Infusion line and removed at locations on the left side of

the figure, denoted as the vacuum vents, allowing for resin impregnation of the

composite part shown in Figure 1.13. The E-glass facesheets and webs were infused

during this process with DERAKANE 510A-40 vinyl ester resin while under vacuum.

The 24-inch-by-26-inch VARTM-infused blast protection panels were

machined to produce test samples. The machining process employed to procure the

samples is comprehensively discussed in Section 3.2. The sandwich panels were cut

to samples an average plan area of 2 inches by 1.5 inches. The heights differed for the

long-length and small-length webs, which were approximately 1.5 inches and 1 inch,

respectively. A web core test sample is illustrated in the following figure, and the

specimens and dimensions utilized in compression tests are detailed in Chapter 4.

Figure 1.13 Web Core Small-Length Unit Cell Dimensions (Depth is 2

inches into page, Width is 1.5 inches, and Height is 1 inch)

The sandwich panel and aforementioned web buckling samples were designed

to absorb a blast loading. The next section explains the theoretically-applied blast

loading considered in this research. The reason for employing quasi-static

18

experiments on the web buckling samples will be explained at the end of the Blast

Loading Section.

1.4 Blast Loading

The dynamic blast loading imparted to the protection panel was modeled as a

blast pressure impulse loading, which varies in pressure versus time, from an

incendiary device. Figure 1.14 shows a blast from a spherical charge.

Figure 1.14 Blast from Spherical Charge [10]

An idealized pressure wave versus time of an applied blast, which begins at point A,

is depicted in Figure 1.15 [10]. Figure 1.15 shows the impulse pressure curve in

19

which point B is the “arrival time”, peaks at point C, and then exponentially-decreases

until it ends at point D where it is equal to zero [10].

Figure 1.15 Idealized Pressure-Time Curve [10]

As seen from a representation of a blast wave interacting with a panel in

Figure 1.16, overpressure – “the difference between the pressure generated by the

blast and the ambient atmospheric pressure” [10] – varies with respect to time. The

pressure wave from the subsequent figure initiates once the charge ignites, which

correlates to point A in Figure 1.15. The wave then expands outward eventually

contacting the panel at point B, noted as time tB, in Figure 1.16 [10]. The panel

observes “an immediate increase in the pressure from ambient air pressure at point B

to the peak pressure at point C” once the wave impacts the panel [10].

20

Figure 1.16 Pressure vs. Time of Blast Wave on Panel Representation

Pressure, time, and stand-off distance will be compared. Viewed in Figure

1.16 as time increases the pressure wave area increases, while the pressure intensity

decreases at point C. The pressure wave begins at a single point, the charge, and

spreads out over time. Pressure wave area and time are directly related, while

pressure intensity at the panel and time are inversely related. Charge stand-off

distance is defined as the distance from the center of the charge to the front face of the

panel. Illustrated in the varying pressure waves in Figure 1.16, pressure wave area

increases with increasing charge stand-off distance. In turn, as the charge stand-off

21

distance increases, the pressure intensity at point C decreases. Charge stand-off

distance is directly related to pressure wave area and inversely related to pressure

intensity at the panel.

Equation 1.3 from Westine et al. (1985) explains these interactions

analytically by defining an impulse loading (iz) distributed onto a plate from a blast

pressure wave exerted by a buried mine [11]. The variables are illustrated in Figure

1.17.

(1.3) [11]

Figure 1.17 Nomenclature of Westine Equation 1.3 [35]

2/3

8/34/5

2/1

2/12/125.3

2.2tanh

)(

9

71

)9589.0tanh(1352.0)(

s

dAs

rdrP

s

s

dW

P

Pri

Mine

S

Soil

S

SZ

22

In this figure charge stand-off distance s is on the vertical axis, while radius r

is on the horizontal axis. The previous equation can be tailored for a charge situated

in air by inputting the density of air 1.274 kg/m3 into ρsoil and forcing the plate stand-

off distance s from the mine equal to the mine burial depth d.

Once the equation was manipulated for a blast in air, a model of Equation 1.3

was utilized to determine the influence of the charge mass, stand-off distance, and

time parameters have on impulse. This representation was developed by Dr. Bazle

Gama in a Microsoft EXCEL Spreadsheet. Using this model, Figures 1.18 and 1.19

were created with impulse (iz) as the vertical axis and radius (r) as the horizontal axis

labeled in the preceding illustration. Figure 1.18 shows the relationship between

charge mass and impulse, in which ten different charge masses were graphed against

impulse. Charge mass is directly related to impulse; as the charge mass increases, the

maximum impulse value increases. Figure 1.19 illustrates the relationship between

stand-off distance and impulse. In this graph similar to Figure 1.18, ten different

stand-off distances were graphed against impulse. Stand-off distance varies inversely

with impulse, which is the opposite of the charge-mass-impulse relationship. As the

stand-off distance increases, the maximum impulse value decreases.

23

Figure 1.18 Charge Mass Influence on Impulse

Figure 1.19 Stand-Off Distance Influence on Impulse

0

5

10

15

20

25

30

35

40

45

50

0 1 2 3 4 5 6 7

Weight 40 lbsWeight 36 lbsWeight 32 lbsWeight 28 lbsWeight 24 lbsWeight 20 lbsWeight 16 lbsWeight 12 lbsWeight 8 lbsWeight 4 lbs

Radius: r (ft)

Imp

uls

e:

iz (

psf-

s)

Stand-Off Distance = 3 (ft) Mass Chart: Impulse: iz (psf-s) vs. Radius: r (ft)

0

2

4

6

8

10

12

14

16

0 1 2 3 4 5 6 7

Stand-off Distance 30 ftStand-off Distance 27 ftStand-off Distance 24 ftStand-off Distance 21 ftStand-off Distance 18 ftStand-off Distance 15 ftStand-off Distance 12 ftStand-off Distance 9 ftStand-off Distance 6 ftStand-off Distance 3 ft

Radius: r (ft)

Imp

uls

e:

iz (

psf-

s)

Charge Mass = 4 (lbs) Stand-Off Chart: Impulse: iz (psf-s) vs. Radius: r (ft)

24

Dynamic blast loading, the foundation of this research, on a plate will be

reviewed. A dynamic blast load is applied as a pressure loading – the force acts upon

a specific area – and as an impulse. Since the load is administered over a period of

time, the blast load is defined as an impulse, shown in Equation 1.4.

(1.4)

To explain this equation, if the applied force does not vary with time, the force is

explicitly constant, and the simple impulse formula (p = force * time) is accurate. The

rightmost integration formula is, however, utilized when the force (F) varies with time

(t); i.e., a dynamic blast loading. This research study utilizes both impulse formulae.

Relating the Westine Equation 1.3 to the impulse formulae, if a flat plate were placed

in front of a blast, its blast wave would exert a non-uniform load on the plate with

respect to time. The difference between quasi-static and blast loadings is explained in

the following paragraphs.

Quasi-static and blast loading investigations vary significantly. The quasi-

static tests do not capture any dynamic or strain rate effects in the samples, as opposed

to blast loading studies. The subsequent pictures exemplify the different results

between quasi-static and dynamic loading.

Fdttimeforcepimpulse *

25

(a) (b)

Figure 1.20 Web Core Experiment (a) After Quasi-Static Loading [12]

and (b) After Dynamic Blast Loading [13]

Both samples in the previous photographs were comprised of web core. The quasi-

static compression loading was applied to the specimen by a horizontal platen, and the

dynamic blast loading was imparted to the sandwich panel by a 5-lb C4 charge at a

stand-off distance of 3 feet. More internal foam damage was evident in the second

dynamic blast loaded specimen. For the dynamically-loaded specimen, both the foam

and web in the composite core absorbed the impulse imparted to the sample.

The following interpreted a study in 2005 performed by Patrick M. Schubel

detailed in the journal article “Low velocity impact behavior of composite sandwich

panels.” This investigation, in which quasi-static and dynamic loadings were

examined, is related to this research. “Besides the localized effects caused by load

contact characteristics, the quasi-static and low velocity impact behavior of composite

sandwich panels composed of woven carbon fabric/epoxy facesheets and a PVC foam

core investigated in the [Schubel] study are quite similar” [14]. Figures 1.21 and 1.22

illustrated the foam core sandwich panel and load-compressive-strain curve from the

Schubel journal article. The latter figure was created from data points of a gage

located on the backside of the foam core panel with an applied loading normal to the

front face. Two different loading conditions were examined, an impact (with a

26

velocity of 3.6 to 11 mph) and a quasi-static loading [14]. In Figure 1.22, the line

represented the quasi-static examination, while the stars denoted the impact test

results [14].

Figure 1.21 Foam Core Sandwich Panel from Schubel Journal Article

[14]

With the gage situated away from the impact location, localized deformation

was insignificant and the impact and quasi-static loading conditions were compatible

as seen in the proceeding figure [14]. This illustrated the quasi-static tests’ ability at

ranking the energy-consuming PVC cores from the research paper [14].

In addition, Wolf Elber in 1983 published an article titled “Failure Mechanics

in Low-velocity Impacts on Thin Composite Plates,” which was also related to this

same quasi-static dynamic comparison. This article examined composite plates of

Thornel 300 graphite in Narmco 5208 epoxy resin [36]. Quasi-static and low-velocity

load-drop tests were compared [36]. In this article “8-ply graphite-epoxy plates with

27

a quasi-isotropic [0/45/-45/90]S stacking sequence” was impacted by a 1-inch-

diameter steel ball [36]. The impact velocities were a maximum of 16 mph [36].

“For the T300/5208 graphite-epoxy [laminate] the differences in damage mechanics

between static and impact tests are small” [36].

The data from Schubel’s and Elber’s article will be applied to this current

research comprehending the blast protection capacity of G18 TYCOR® web core.

Conclusively, an assumption will be made in this research that the quasi-static

experimental data will correlate with impact loading results; with the understanding

that this assumption may not be implemented for locally-applied loading conditions.

Figure 1.22 Representation of Impact vs. Quasi-Static Loading [14]

28

Moreover, sandwich structure unit cells will be detailed. The experiments in

this research were performed on blast protection panel unit cells; with dimensions

shown in Figure 1.13. The unit cell was studied in order to comprehend the entire

blast panel. Note that the size of the unit cell (a depth of approximately 2 inches) is

quite small compared to the stand-off distances and radii from the graph in Figure

1.19. This allows the pressure/force applied to the unit cell to be assumed uniform.

Consequently, this investigation of the web core unit cell’s energy absorption

capabilities was simplified.

To specify dimensions, a unit cell, which was a repeating geometry throughout

the blast panel, contained a single web surrounded by an average 0.6848-inch-thick

Polyiso Foam on both sides. The foam in the unit cell depicted in Figure 1.13

increased the web core energy consumption abilities by crushing. The webs measured

an average 0.1052 inches thick. The top and bottom unit cell facesheets were an

average 0.2298 inches thick by 1.5 inches wide by 2 inches deep.

Furthermore, the unit cell can be applied to the blast wave theory discussed at

the beginning of this section. The unit cell geometry was depicted in the blast wave

representation in Figure 1.16. The differential area of the blast panel labeled as

dPANEL in the illustration was accepted as the width of a unit cell.

29

Figure 1.23 Web Core with Uniform Displacement and Average

Pressure

Due to the unit cell’s small width relative to the blast panel’s size, the pressure

applied to the unit cell was assumed uniform. This is based on the conceptual blast

wave exemplified in Figures 1.14, 1.15, and 1.16. Figure 1.23 depicts a unit cell

specimen in the experimental fixture designed for this research with an applied

normal uniform pressure. The fixture will be divulged in Section 3.3 Description of

Web Buckling Tests.

Lastly, Equation 1.4 was modified for the uniform pressure imparted on the

unit cell. The impulse formula through algebraic manipulation was adjusted to relate

impulse to pressure. As previously stated, the blast wave may be represented as an

impulse and a pressure. By multiplying the right-side of Equation 1.4 by unity,

impulse equates to area (A) multiplied by the integral of pressure (P) with respect to

30

time shown as the third evaluation in Equation 1.5. The right-most formula in

Equation 1.5 is employed when pressure does not vary with time.

∫ ∫ (1.5)

With respect to the quasi-static unit cell discussions in this section, an impulse may be

computed for a uniform pressure. Using the right-side of the preceding formula, an

impulse may be figured by multiplying area (A) by the applied uniform pressure (P)

and time (t).

This section reviewed a blast loading imparted to a unit cell. The unit cell size

compared to the blast panel was detailed, and the loading conditions were discussed.

The next step given in the following section was to determine the amount of energy

absorption that could be achieved during crushing of the unit cell by an impulse

loading.

1.5 Maximizing Energy Dissipation

During a blast, a panel will be subjected to dynamic forces that will impart

kinetic energy to the system by accelerating the panel from rest. The panel will

deform and develop internal energy; consisting of elastic energy stored in the plate

from deformation and absorbed plastic dissipated energy as a result of material

damage. The mechanics of what occurs to the panel from an imparted blast will first

be developed. Then, the macroscopic through-the-thickness displacement effects of

the panel will be explained.

31

To begin, Figure 1.24 shows a side view of a 3TEX blast panel with through-

the-thickness fibers. This figure illustrates the panel after a five-pound C-4 spherical

charge was set off at 36-inches stand-off distance from the strike face center [15].

Using a “digital high speed camera,” the maximum dynamic deflection of 5.5 inches

was determined at approximately 10 msec [15]. Maximum dynamic deflection refers

to the greatest deflection viewed by the camera at high speeds, measured at the back

face of the panel. This panel measured “54 by 50 inches wide” by 2.5 inches thick

[15].

Figure 1.24 Side View of 3TEX-6 Sandwich Panel Subjected to Blast

Loading [15]

Max deflection of 5.5”

At ~10 msec

Max deflection of 5.5”

At ~10 msec

32

Figure 1.25 Cross-Section of 3TEX-6 Sandwich Panel Subjected to Blast

Loading [16]

Figure 1.25 gives a cross-section of the 3TEX blast panel with the aforementioned

fibers. As seen from Figure 1.25, this 3TEX blast panel’s through-the-thickness

structure was similar to the web core blast panel from this research.

A maximum dynamic deflection vs. areal density graph for the 3TEX panels is

illustrated in Figure 1.26. Areal density of a panel is defined as the weight per unit

plan area of the panel [8]. Therefore, areal density is directly related to its mass. The

thicknesses, multiplied by their respective densities, added together equal the panel’s

areal density [8]. The 3TEX-6 panel areal density and maximum deflection of 6.9 psf

and 5.5 inches, respectively, are shown as a data point in the following graph. The

other two data points were taken from the 2006 test report by J. Klein titled “Test

Summary for 3TEX Panels, 3TEX-2 through 3TEX-6 and Martin Marietta Composite

Panels MMC-1 through MMC-6”. “The graph trends with an exponential decay of

increased mass giving less net deflection” [15].Since the greater the mass the less

deflection, the capability of the panel depends on its material strength as well as its

inertial characteristics[15]. The panel strength for each material is determined in

Chapters 2, 3, and 4, while the inertial aspects, i.e., momentum and impulse of the

blast panel, are discussed in Chapter 5. The subsequent paragraphs discuss the

through-the-thickness displacement effects of the unit cell.

33

Figure 1.26 Maximum Dynamic Deflection vs. Areal-Density of 3TEX

Panel [15]

As detailed in Section 1.4, the unit cell is a small representation of a blast

protection panel. This research focuses on the unit cell response subjected to a

pressure loading that undergoes through-the-thickness displacement resulting from

elastic storage and dissipated energy. The energy absorbed by a unit cell is defined by

the area under the compression load-axial-displacement curve.

Figures 1.27 and 1.28 define the symbols for the subsequent equations. These

graphs are conceptual examples of load-displacement curves for Polyiso Foam and E-

glass composite web specimens undergoing axial compression and buckling,

respectively, taken from examinations explained later in this research. The regions

34

are also labeled in these figures. In the case of an elastic response, the maximum

energy (Ee) stored from displacement is given at the point of maximum force (F) and

displacement (δe) shown in the following formula.

(1.6)

Regarding Equation 1.6, the stored elastic energy is released upon unloading with no

energy absorbed by material damage. In the case of purely plastic dissipation, the

energy (Ea) is consumed by the material during loading and displacement (δa); a force-

displacement curve gives the energy absorbed by material damage. Equation 1.7

equates the purely-plastic dissipated energy.

(1.7)

Figure 1.27 Load vs. Displacement Foam Plastic-Semi-Plateau Model

Energy Absorption

e

DENSIFICATION

PLASTIC-SEMI-PLATEAU

LINEAR

F2

a

F, F1

Displacement,

Lo

ad

, P

Energy_Semi-Plateau_Computation: Load, P vs. Displacement,

35

Figure 1.28 Force vs. Axial Displacement E-Glass Web Plastic-Plateau

Model Energy Absorption

Foam specimens with an applied load situated in the (a) linear-elastic and (b)

plastic-plateau regions were illustrated in Figure 1.29, while Figure 1.30 shows an

experimentally buckled E-glass web in the plastic-plateau region. These pictures

correspond to their previous curves.

(a) (b)

Figure 1.29 Foam Experiment Illustrations of (a) Linear-Elastic Region

(b) Plastic-Semi-Plateau Crushing Region

PLASTIC-PLATEAU

LINEAR

a

e

F

Axial Displacement,

Fo

rce

, F

Energy_Plateau_Computation: Force, F vs. Axial Displacement,

36

Figure 1.30 Example of a Buckled E-Glass Web (Foam Removed) in the

Plastic-Plateau Region

Both the foam specimen and E-glass composite web stored elastic energy through

displacement remaining in the load-axial-displacement curves’ linear-elastic regions.

In the plastic-plateau regions, the foam dissipated energy by crushing, and in turn, the

E-glass web absorbed energy through buckling. Piece-wise linear models of these

materials were considered in the following paragraphs.

The following graph shows piece-wise linear models of the foam, web, and

web and foam combination used in this research. The regions from Figures 1.27 and

1.28 were incorporated into Figure 1.31. The red, blue, and black lines denoted the

foam, web, and combination web and foam failure mechanisms. Ideal responses are

shown of the web buckling and then foam crushing models illustrated in the preceding

figure, taken from Chapter 5. The polyisocyanurate foam crushing experiments will

be explained in Chapter 2, the E-glass vinyl ester resin web buckling tests will be

described in Chapter 3, and the combination of web and foam compression

investigations will be analyzed in Chapter 4.

37

Figure 1.31 Models of Web Buckling, Foam Crushing, and Web + Foam

Buckling and Crushing

Accordingly, the energy consumption of these samples with respect to their

load-axial-displacement curves and piece-wise linear models from Figure 1.28 may be

enhanced in several different ways. The foam model may be augmented by

increasing the crushing strength, decreasing the crushing displacement, and/or

increasing the displacement value at which the plastic-semi-plateau region essentially

ends. The crushing strength, crushing displacement, and displacement value at which

the plastic-semi-plateau region ends are depicted in Figure 1.27 as F1, δe, and δe+δa,

respectively. These techniques would increase the area under the curve in the plastic-

semi-plateau region. The E-glass web capabilities may be upgraded by three

methods; by increasing the buckling load, reducing the buckling displacement value,

and extending the value at which the plastic-plateau region ends. The E-glass web

variables F, δe, and δe + δa from Figure 1.28 signify the buckling load, buckling

WEB + FOAMFOAMWEB

FOAM CRUSHINGIN PLASTIC-PLATEAUREGION

WEB BUCKLING INPLASTIC-PLATEAUREGION

FOAM LINEAR-ELASTICREGION

WEB LINEAR-ELASTIC REGION

Axial Displacement,

Lo

ad

, P

Web Buckles then Foam Crushes: Load, P vs. Axial Displacement,

38

displacement, and value at which the plastic-plateau region ends, respectively. All of

the foam and web optimization techniques would augment the unit cell’s energy

consumption abilities. These theoretical concepts are the foundation of this research;

a complete description of energy consumption will be discussed in Chapter 5 Energy

Absorption Capabilities.

1.6 Summary of Chapters

Chapter 2 focuses on Polyiso Foam characterization. Descriptions of the foam

and details of the quasi-static foam experimental tests are in this chapter. Uniaxial

Stress and Strain test data was examined, and the polyisocyanurate foam’s energy

absorption capabilities were computed.

The four-ply E-glass vinyl ester resin web is investigated in Chapter 3. A

description of the composite web, theoretical beam buckling calculations, graphical

Southwell Plot analysis, and web compression strength tests are studied in this

chapter. In addition, the computer program CMAP, which facilitated the beam

buckling calculations, is explained. At the conclusion of this chapter, the web

compression test mechanical results are compared to the beam buckling values.

In Chapter 4, web core specimens based on blast panel unit cells are described.

The experiments are detailed and the data is compiled. Similar to Chapter 3, the

theoretical beam buckling values are calculated for the web core E-glass webs. Then,

the web core experiments in this chapter are compared to theoretical web buckling

and maximum compression loads.

39

The energy consumption capabilities of the G18 TYCOR® from Webcore

Technologies, Inc. are incorporated into a model sandwich structure model for blast

mitigation in Chapter 5. Mine blast theories were first discussed. Next, the role of the

polyisocyanurate foam and four-ply E-glass composite web in the G18 TYCOR®

were investigated and optimized to maximize energy absorption. Subsequently, linear

graphical analyses were executed on the foam and web mechanical failure modes.

Finally the web core system was optimized for energy dissipation.

40

Chapter 2

STATIC TESTING OF POLYISOCYANURATE FOAM

2.1 Introduction to Static Testing of Polyisocyanurate Foam

A description of the polyisocyanurate foam and quasi-static compression tests

are detailed in this chapter. The foam provides opportunity to increase energy

dissipation of the sandwich structure. Quasi-static experiments were conducted on the

foam to quantify the stress-strain behavior of the material; essential to understanding

the absorption capabilities of the web core.

2.2 Description of Polyisocyanurate Foam Core

The polyisocyanurate foam mentioned in Chapter 1 Introduction will be

further described in this section. Figure 2.1 shows a polyisocyanurate foam specimen

used in the experiments described in Section 2.3 Description of Polyisocyanurate

Foam Tests. The dimensions of the foam specimens are located in Tables 2.1 and 2.2,

and the mechanical data measured in the experiments is listed at the end of Section

2.3.

41

Figure 2.1 Polyisocyanurate Foam Specimen

Figures 2.2 and 2.3 represented the exemplary Uniaxial Stress and Strain

experimental data described in Section 2.3 Description of Polyisocyanurate Foam

Tests. The experimental curves from Specimens 3 and 5 were displayed. To explain

these quasi-static stress-strain and stress-density graphs, the initial slope of the stress-

strain curve denoted as the foam’s compressive modulus Ec depended solely on the

change in stress and strain of the foam in the elastic region. The crushing strength σcr

and strain εcr are located at the intersection of the elastic and semi-plateau regions’

tangents on the stress-strain plot of Figure 2.2 [23]. Figure 2.2 was related to Figure

1.6 in which the curve rose linearly, at a slope equal to its compressive modulus,

plateaued until the foam began to densify, and then increased rapidly until the foam

was fully compressed. The area under the following curve is proportional to the

energy absorption potential of the foam. This was discussed in Sections 1.3 and 1.5.

42

Figure 2.2 Average Quasi-Static Stress-Strain Graph of Uniaxial

Polyiso Foam Specimens

Figure 2.3 Compressive Quasi-Static Stress-Density Graph of Uniaxial

Polyiso Foam Specimens

0

20

40

60

80

100

120

140

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Uniaxial Strain Replica Specimen 5Uniaxial Stress Replica Specimen 3

max

Ec

(cr

, cr

)

Strain, (in/in)

Str

ess, (

psi)

100 LB Polyiso Foam: Stress, (psi) vs. Strain, (in/in)

0

20

40

60

80

100

120

140

0 0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.24 0.27

Uniaxial Strain Replica Specimen 5Uniaxial Stress Replica Specimen 3

Density, (pcf)

Str

ess, (

psi)

100LB Polyiso Foam: Stress, (psi) vs. Density, (pcf)

43

Figure 2.3 emphasized the foam’s compressive stress-density relationship; as

the stress increased, the foam specimen decreased in size and rose in density. To start

with, the graphs in Figures 2.2 and 2.3 were comparable. The left-side of the two

specimens’ stress-density curves correlated with the linear-elastic region of the stress-

strain curves. These regions for both sets of curves were relatable due to the foam

specimens’ miniscule changes in density. The slopes of the stress-density curves in

the linear-elastic region in Figure 2.3 were affected by the minute density changes;

resulting in nearly infinite, vertical slopes. In addition, Equation 2.1 detailed the

relationship between the elastic modulus (E), the density (ρ), and the stress (σ) of the

foam samples’ linear-elastic regions. This formula may be utilized to quantitatively

compare the two different graphs. This formula showed that the stress-strain curve’s

elastic modulus (E) is directly proportional to the instantaneous foam density (ρ) and

equal to the slope (Δσ/Δρ) of the foam stress-density curve [37]. Figure 2.3 also

depicted the interface of the stress-strain curves’ linear-elastic and plastic-semi-

plateau regions. The quasi-static stress-density curves of specimens 3 and 5

illustrated the moment that cell collapse commenced; at the point the slopes changed

from nearly vertical to relatively steep [37].

(2.1) [37]

Furthermore, density was less for the unconfined Uniaxial Stress sample than

the Uniaxial Strain specimen. Figure 2.3 emphasized this. This notion was discussed

when relating the Uniaxial Stress and Strain samples in Section 1.3. For the Uniaxial

Strain experiment, the entire load caused the foam specimen to densify. While in the

Uniaxial Stress test, the load imparted to the foam sample was divided between

densifying and bulging, due to Poisson’s Ratio being non-zero. In addition, the steel

44

collar confining the Uniaxial Strain foam specimen augmented its mechanical results.

The confinement increased the crushing stress – one of the most important values in

determining the web core unit cell mechanical properties – and compression modulus

compared to the unconfined Uniaxial Stress specimens. The individual curves,

dimensions, and experimental results for each foam specimen will be shown in the

next section.

Moreover, Equation 1.1 was utilized to determine the Polyiso Foam’s porosity.

Since from Section 1.3 the average polymer polyisocyanate and Polyiso Foam

densities were66.8 pcf and 2.24 pcf, respectively, the foam porosity equated to 0.97.

The final strain εmax seen in Figure 2.2 is the maximum theoretical strain at which the

foam was fully compressed equal to the foam porosity as seen in Equation 1.1 [23].As

a result, the final strain from this formula equated to 0.97 in/in, or 97%.

2.3 Description of Polyisocyanurate Foam Tests

To begin, cylindrically-shaped foam specimens were machined from a foam

preform comprised of the same material and density as the foam situated in the

TYCOR® web core sandwich panel depicted in Section 1.3.

45

Figure 2.4 Experimental Foam Uniaxial Stress Setup

(a) (b)

Figure 2.5 (a) Experimental Uniaxial Strain Setup Prior to Foam

Placement (b) Experimental Uniaxial Strain Setup after

Foam Placement

46

The foam specimens were core-drilled using a wet drill with a diamond-tipped core,

ensuring similarly-shaped specimens. The quasi-static Uniaxial Stress and Strain

experiments, shown in Section 1.3 Materials Used in This Study, were executed at a

cross-head rate of 0.05 in/min using a 5567 Instron machine with a 100-pound load

cell. Twelve Polyiso Foam specimens measuring an average 1.0777incheslong and

0.9513inches in diameter were tested. Figures 2.4, 2.5(a), and 2.5(b) show the

Experimental Foam Uniaxial Stress setup, the Experimental Foam Uniaxial Strain

system prior to placing the foam specimen inside the steel collar, and the

Experimental Foam Uniaxial Strain setup after the foam specimen was placed inside

the steel collar, respectively. The force from the Instron 5567 was applied by the

small circular platen located above the specimens in the previous figures. Two

methods were executed prior to testing to ensure satisfactory foam specimen tests.

Table 2.1 Uniaxial Stress Polyiso Foam Dimensions

Specimen Length (in) Diameter (in) Weight (lb) Cross-Sectional

Area (in2)

Density (pci)

1 1.0997 0.9521 1.0e-3 0.7120 1.3e-3

2 1.0811 0.9612 1.0e-3 0.7256 1.3e-3

3 1.0869 0.9592 1.0e-3 0.7226 1.3e-3

4 1.0901 0.9509 1.0e-3 0.7102 1.3e-3

5 1.0981 0.9523 1.0e-3 0.7123 1.3e-3

6 1.0737 0.9473 1.0e-3 0.7048 1.4e-3

Average 1.0883 0.9538 1.0E-3 0.7146 1.3E-3

Standard

Deviation 0.0100 0.0053 9.0E-6 0.0079 2.5E-5

Coefficient of

Variation 0.0092 0.0055 8.7E-3 0.0111 1.9E-2

47

Table 2.2 Uniaxial Strain Polyiso Foam Dimensions

Specimen Length (in) Diameter

(in) Weight (lb)

Cross-Sectional

Area (in2)

Density (pci)

1 1.0829 0.9475 1.0E-3 0.7051 1.4E-3

2 1.0667 0.9563 9.7E-4 0.7183 1.3E-3

3 1.0654 0.9494 9.7E-4 0.7079 1.3E-3

4 1.0637 0.9465 1.1E-3 0.7036 1.4E-3

5 1.0723 0.9448 1.0E-3 0.7011 1.3E-3

6 1.0520 0.9484 1.0E-3 0.7064 1.4E-3

Average 1.0681 0.9502 9.8E-4 0.7091 1.3E-3

Standard

Deviation 3.667E-3 0.0058 1.7E-5 0.0086 4.3E-5

Coefficient of

Variation 3.433E-3 0.0061 1.8E-2 0.0122 3.3E-2

First, the large circular platen, on which the foam specimen rested, was leveled using

feeler gages to ensure the load was applied perpendicular to the specimen. Second,

WD-40 lubricant was sprayed inside the steel collar for the Uniaxial Strain

examination to reduce friction between the foam and steel. The previous Tables 2.1

and 2.2 list the complete foam sample dimensions. The averages, standard deviations,

and coefficient variations are given. The following Figures 2.6 to 2.13 were

photographs taken prior and during the experiments. The Uniaxial Strain specimens

were not photographed during the experiment since they were situated in a steel

collar. As seen from most of the pictures, the foam specimen in the Uniaxial Stress

tests laterally expanded as a result of Poisson’s Ratio being non-zero during loading.

48

Figure 2.6 All Uniaxial Strain Specimens

Figure 2.7 All Uniaxial Stress Specimens

49

(a) (b)

Figure 2.8 Uniaxial Stress Specimen 1 (a) at Commencement of

Loading and (b) during Densification

Figure 2.9 Uniaxial Stress Specimen 2 during Loading

Figure 2.10 Uniaxial Stress Specimen 3 during Loading

50

(a) (b)

Figure 2.11 Uniaxial Stress Specimen 4 (a) at Commencement of

Loading and (b) during Densification

Figure 2.12 Uniaxial Stress Specimen 5 during Loading

(a) (b)

Figure 2.13 Uniaxial Stress Specimen 6 (a) at Commencement of

Loading and (b) during Densification

51

Figure 2.14 Uniaxial Stress – Load vs. Displacement using 100 LB Load

Cell

0

10

20

30

40

50

60

70

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

UStress1_100LB

cr

= 0.05 in/in

cr

= 21 psi

Ec = 420 psi

Displacement, (in)

Lo

ad

, P

(lb

)

100LB Polyiso Foam - UStress 1: Load, P (lb) vs. Displacement, (in)

0

10

20

30

40

50

60

70

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

UStress2_100LB

cr

= 0.04 in/in

cr

= 23 psi

Ec = 570 psi

Displacement, (in)

Lo

ad

, P

(lb

)

100LB Polyiso Foam - UStress 2: Load, P (lb) vs. Displacement, (in)

0

10

20

30

40

50

60

70

80

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

UStress3_100LB

cr

= 0.05 in/in

cr

= 22 psi

Ec = 440 psi

isplacement, (in)

Lo

ad

, P

(lb

)

100LB Polyiso Foam - UStress 3: Load, P (lb) vs. Displacement, (in)

0

10

20

30

40

50

60

70

80

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

UStress4_100LB

cr

= 0.05 in/in

cr

= 22 psi

Ec = 440 psi

Displacement, (in)

Lo

ad

, P

(lb

)

100LB Polyiso Foam - UStress 4: Load, P (lb) vs. Displacement, (in)

0

10

20

30

40

50

60

70

80

90

100

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

UStress5_100LB

cr

= 0.06 in/in

cr

= 24 psi

Ec = 390 psi

Displacement, (in)

Lo

ad

, P

(lb

)

100LB Polyiso Foam - UStress 5: Load, P (lb) vs. Displacement, (in)

0

10

20

30

40

50

60

70

80

90

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

UStress6_100LB

cr

= 0.06 in/in

cr

= 24 psi

Ec = 410 psi

Displacement, (in)

Lo

ad

, P

(lb

)

100LB Polyiso Foam - UStress 6: Load, P (lb) vs. Displacement, (in)

52

Figure 2.15 Uniaxial Stress – Stress vs. Axial Strain using 100 LB Load

Cell

Figures 2.14, 2.15, 2.16, and 2.17 show the experimental results of the

Uniaxial Stress and Strain tests. Figure 1.27, which was a general representation of a

0

10

20

30

40

50

60

70

80

90

100

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

UStress1Cin_100LB

Ecr

= 420 psi

(cr

, cr

)=(0.05 in/in, 21 psi)

Axial Strain, (in/in)

Str

ess, (

psi)

100LB Polyiso Foam - UStress 1: Stress, (psi) vs. Axial Strain, (in/in)

0

10

20

30

40

50

60

70

80

90

100

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

UStress2Cin_100LB

Ecr

= 570 psi

(cr

, cr

)=(0.04 in/in, 23 psi)

Axial Strain, (in/in)

Str

ess, (

psi)

100LB Polyiso Foam - UStress 2: Stress, (psi) vs. Axial Strain, (in/in)

0

20

40

60

80

100

120

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

UStress3Cin_100LB

Ecr

= 440 psi

(cr

, cr

)=(0.05 in/in, 22 psi)

Axial Strain, (in/in)

Str

ess, (

psi)

100LB Polyiso Foam - UStress 3: Stress, (psi) vs. Axial Strain, (in/in)

0

20

40

60

80

100

120

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

UStress4Cin_100LB

Ecr

= 440 psi

(cr

, cr

)=(0.05 in/in, 22 psi)

Axial Strain, (in/in)

Str

ess, (

psi)

100LB Polyiso Foam - UStress 4: Stress, (psi) vs. Axial Strain, (in/in)

0

20

40

60

80

100

120

140

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

UStress5Cin_100LB

Ecr

= 390 psi

(cr

, cr

)=(0.06 in/in, 24 psi)

Axial Strain, (in/in)

Str

ess, (

psi)

100LB Polyiso Foam - UStress 5: Stress, (psi) vs. Axial Strain, (in/in)

0

20

40

60

80

100

120

140

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

UStress6Cin_100LB

Ecr

= 410 psi

(cr

, cr

)=(0.06 in/in, 24 psi)

Axial Strain, (in/in)

Str

ess, (

psi)

100LB Polyiso Foam - UStress 6: Stress, (psi) vs. Axial Strain, (in/in)

53

foam’s load-displacement curve with the delineated regions, is congruent with Figures

2.14 and 2.15. “The [crushing] stress was evaluated as the intersection of the two

lines interpolating the first part (elastic) and the second part (plastic) of the

experimental stress-strain curve”[38]. The Compression Modulus was determined by

dividing the crushing stress by the crushing strain. The mechanical results are listed

in Tables 2.3 and 2.4. The data in the subsequent tables was graphically analyzed

from the foam experimental curves.

The standard deviations and coefficients of variation in Tables 2.3 and 2.4

were reasonable; both the standard deviations and coefficients of variation were

relatively small. This signified that the foam examinations were compatible. The

largest coefficient of variation was 0.3 for the Uniaxial Strain crushing strain due to

the outlier specimen 6 exhibiting a relatively high crushing strain. Otherwise, the data

in the Tables 2.3 and 2.4 had not varied significantly.

As mentioned in the preceding section, the Uniaxial Strain average crushing

stress was greater than the Uniaxial Stress value; resulting in approximately a 15%

increase. In addition, there was approximately a 20% difference between the Uniaxial

Strain and Stress average crushing strains.

54

Figure 2.16 Uniaxial Strain – Load vs. Axial Displacement using 100 LB

Load Cell

0

10

20

30

40

50

60

70

80

90

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

UStrain1Cin_100LB

Axial Displacement, (in)

Lo

ad

, P

(lb

)

100LB Polyiso Foam - UStrain 1: Load, P (lb) vs. Axial Displacement, (in)

0

10

20

30

40

50

60

70

80

90

100

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

UStrain2Cin_100LB

Axial Displacement, (in)

Lo

ad

, P

(lb

)

100LB Polyiso Foam - UStrain 2: Load, P (lb) vs. Axial Displacement, (in)

0

10

20

30

40

50

60

70

80

90

100

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

UStrain3Cin_100LB

Axial Displacement, (in)

Lo

ad

, P

(lb

)

100LB Polyiso Foam - UStrain 3: Load, P (lb) vs. Axial Displacement, (in)

0

10

20

30

40

50

60

70

80

90

100

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

UStrain4Cin_100LB

Axial Displacement, (in)

Lo

ad

, P

(lb

)

100LB Polyiso Foam - UStrain 4: Load, P (lb) vs. Axial Displacement, (in)

0

10

20

30

40

50

60

70

80

90

100

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

UStrain5Cin_100LB

Axial Displacement, (in)

Lo

ad

, P

(lb

)

100LB Polyiso Foam - UStrain 5: Load, P (lb) vs. Axial Displacement, (in)

0

10

20

30

40

50

60

70

80

90

100

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

UStrain6Cin_100LB

Axial Displacement, (in)

Lo

ad

, P

(lb

)

100LB Polyiso Foam - UStrain 6: Load, P (lb) vs. Axial Displacement, (in)

55

Figure 2.17 Uniaxial Strain – Stress vs. Axial Strain using 100 LB Load

Cell

0

20

40

60

80

100

120

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

UStrain1Cin_100LB

Ecr

=440 psi

(cr

, cr

)=(0.05 in/in, 22 psi)

Axial Strain, (in/in)

Str

ess, (

psi)

100LB Polyiso Foam - UStrain 1: Stress, (psi) vs. Axial Strain, (in/in)

0

20

40

60

80

100

120

140

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

UStrain2Cin_100LB

Ecr

=530 psi

(cr

, cr

)=(0.05 in/in, 26 psi)

Axial Strain, (in/in)

Str

ess, (

psi)

100LB Polyiso Foam - UStrain 2: Stress, (psi) vs. Axial Strain, (in/in)

0

20

40

60

80

100

120

140

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

UStrain3Cin_100LB

Ecr

=460 psi

(cr

, cr

)=(0.06 in/in, 28 psi)

Axial Strain, (in/in)

Str

ess, (

psi)

100LB Polyiso Foam - UStrain 3: Stress, (psi) vs. Axial Strain, (in/in)

0

20

40

60

80

100

120

140

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

UStrain4Cin_100LB

Ecr

= 360 psi

(cr

, cr

)=(0.08 in/in, 29 psi)

Axial Strain, (in/in)S

tre

ss, (

psi)

100LB Polyiso Foam - UStrain 4: Stress, (psi) vs. Axial Strain, (in/in)

0

20

40

60

80

100

120

140

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

UStrain5Cin_100LB

Ecr

= 510 psi

(cr

, cr

)=(0.05 in/in, 25 psi)

Axial Strain, (in/in)

Str

ess, (

kP

a)

100LB Polyiso Foam - UStrain 5: Stress, (psi) vs. Axial Strain, (in/in)

0

20

40

60

80

100

120

140

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

UStrain6Cin_100LB

Ecr

= 340 psi

(cr

, cr

)=(0.09 in/in, 31 psi)

Axial Strain, (in/in)

Str

ess, (

psi)

100LB Polyiso Foam - UStrain 6: Stress, (psi) vs. Axial Strain, (in/in)

56

Table 2.3 Uniaxial Stress Mechanical Properties

Table 2.4 Uniaxial Strain Mechanical Properties

Specimen Crushing Strain:

εcr (in/in)

Crushing Stress:

σcr (psi)

Compression

Modulus: Ec (psi)

1 0.05 21 420

2 0.04 23 570

3 0.05 22 440

4 0.05 22 440

5 0.06 24 390

6 0.06 24 410

Average 0.05 23 450

Standard

Deviation 0.01 1.2 65

Coefficient of

Variation 0.15 0.051 0.14

Specimens Crushing Strain:

εcr (in/in)

Crushing Stress:

σcr (psi)

Compression

Modulus: Ec (psi)

1 0.05 22 440

2 0.05 26 530

3 0.06 28 460

4 0.08 29 360

5 0.05 25 510

6 0.09 31 340

Average 0.06 27 440

Standard

Deviation 0.02 3.0 75

Coefficient of

Variation 0.3 0.11 0.17

57

Due to both percentages being similar, the compression moduli were comparable.

This is in agreement with the samples being comprised of the same material.

Figure 2.18 depicted the average Uniaxial Stress and Strain load-displacement

results comparable to Figure 2.2. The average stress-strain curves were shown in

Figure 2.19; the integral values stated in this graph will be utilized in Section 2.4. As

seen in Figure 2.18, the linear-elastic regions were similar for the Uniaxial Stress and

Strain foam specimens because Poisson’s Ratio had no distinctive effect in this

region.

Conversely, the plastic-semi-plateau and densification regions were dissimilar

for both specimen types seen in the following figures. The average Uniaxial Stress

plastic-semi-plateau region ended at approximately 0.5 in, while the average Uniaxial

Strain plastic-semi-plateau region terminated at approximately 0.7 in. The Uniaxial

Strain specimens exhibited larger stresses, in both the plastic-plateau and densification

regions, than the Uniaxial Stress samples [39, 40]. Consequently, the crushing

strength was greater when Poisson’s Ratio equaled zero since the “lateral deformation

was restricted” in the steel collar and the instantaneous foam density continually

increased [40, 41]. This phenomenon was most likely due to the Uniaxial Stress

specimen expanding laterally at the commencement of crushing, “indicating the

specimen lost its load-bearing capacity” [40].

58

Figure 2.18 Average of Uniaxial Stress and Strain Specimens - Load vs.

Axial Displacement

Figure 2.19 Average of Uniaxial Stress and Strain Specimens - Stress vs.

Axial Strain

0

10

20

30

40

50

60

70

80

90

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

UStress_AVG_100LBUStrain_AVG_100LB

Axial Displacement, (in)

Lo

ad

, P

(lb

)

100LB Polyiso Foam - Averages: Load, P (lb) vs. Axial Displacement, (in)

0

10

20

30

40

50

60

70

80

90

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Uniaxial Stress AverageUniaxial Strain Average

Uniaxial Stress Integral = 15 psi-in/inUniaxial Strain Integral = 29 psi-in/in

Strain, (in/in)

Str

ess, (

psi)

100LB Polyiso Foam - ALL: Stress, (psi) vs. Strain, (in/in)

59

Additionally, the densification regions were different. These incongruent

regions were explicitly shown in the previous graphs. The average Uniaxial Stress

and Strain curves’ densification regions were approximately 0.1 in/in wide and 0.3

in/in wide, respectively. Due to research time constraints, the reason for the

densification regions being incongruent was not determined.

These polyisocyanurate foam tests were completed to obtain the crushing

strength, compressive modulus, crushing strain, maximum strain, and density of the

foam. The next section forms analogs for both foam specimen types.

2.4 Polyisocyanurate Foam Models

This section involves creating foam models and then computing their energy

absorption capabilities. Both the Uniaxial Stress and Strain replicas were created.

The values from Tables 2.3 and 2.4 along with the stress-strain graph from Figure

2.19 were used to design Elastic-Perfectly-Plastic-Rigid (EPPR) Models [23]. The

foam crushing EPPR models were created by applying the experimental curves’

critical values to simple piece-wise linear curves similar to the procedure executed in

“Modeling the Progressive Collapse Behavior of Metal Foams” by Sergey L.

Lopatnikov. EPPR foam replicas were formed, instead of an Elastic-Plastic-Rigid

(EPR) model, due to their simplicity [23].

To explain the EPPR model formation, the crushing stress σcr, critical strain

εcr, and final strain εmax were the three values required to construct EPPR stress-axial-

strain foam curves. The EPPR crushing strains were set to 0.05 in/in and 0.06 in/in

for Uniaxial Stress and Uniaxial Strain models, respectively. These numbers were

60

taken from Tables 2.3 and 2.4. For both specimen representations, the EPPR final

strains were set to 0.97 in/in discussed at the end of Section 2.2. Equation 2.2 is a

linear formula used to compute the EPPR foam models’ crushing stresses σcr. The

area under a curve, or its integral, is equal to its energy consumption as mentioned in

Section 1.5. Due to this fact, Equation 2.2 was formed to ensure congruency between

the energy absorption abilities of the experimental curves and subsequent models.

Stress-strain curves were used to normalize the energy consumption quantities

by effectively computing the energy per unit volume. The stress-strain integral values

were computed by EasyPlot as 15 lbs-in/in and 29 lbs-in/in – shown in Figure 2.19 –

for the average Uniaxial Stress and Strain samples, respectively. The integral values

were incongruent due to the dissimilar plastic-semi-plateau and densification regions

as described in the preceding section. Through algebraic manipulation, this formula

was utilized to calculate the crushing stresses σcr for the EPPR replicas, forcing the

energy absorption capabilities of the experimental stress-strain curves and EPPR

models to be equal.

( ) (2.2)

The Equation 2.2 variables for the two foam tests are subsequently given. The

integral and crushing strain εcr were set to 15 psi-in/in and 0.05 in/in, respectively, for

the Uniaxial Stress formula, and for the Uniaxial Strain formula the integral and

crushing strain εcr were set to 29 psi-in/in and 0.06 in/in, respectively. The final

strains εmax for both specimen types was 0.97 in/in.

61

Figure 2.20 Uniaxial Stress – Stress vs. Axial Strain EPPR Model

Figure 2.21 Uniaxial Strain - Stress vs. Strain Foam EPPR Model

0

5

10

15

20

25

30

35

40

45

50

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

(0.97, 16)(0.05, 16)

Axial Strain, (in/in)

Str

ess, (

psi)

Uniaxial Stress Foam EPPR Model: Stress, (psi) vs. Axial Strain, (in/in)

0

5

10

15

20

25

30

35

40

45

50

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

(0.97, 31)(0.06, 31)

Axial Strain, (in/in)

Str

ess, (

psi)

Uniaxial Strain Foam EPPR Model: Stress, (psi) vs. Axial Strain, (in/in)

62

Through algebraic manipulation, the crushing stress σcr resulted in 16 psi and 31 psi

for the Uniaxial Stress and Strain formulae, respectively. Using these values, the

EPPR foam models for both specimen types were created.

The energy consumption capabilities of the polyisocyanurate foam will be

described. The subsequent equations – which will be used to determine the foam

energy absorption capabilities per unit volume – were created by utilizing Equations

1.6 and 1.7 and the force (F=σ*A) and displacement (δ=ε*L) formulae.

(2.3)

(2.4)

For both specimen types, the elastic energy stored was computed by Equation 2.3,

while the plastic energy absorbed was figured by Equation 2.4. The following Table

2.5 gives the linear-elastic region stored energy for both Uniaxial Stress and Strain

examinations. The energy dissipation plastic-plateau values determined for the

Uniaxial Stress and Strain foam EPPR Models were listed in the preceding table.

Conclusively, the total quantified energy consumption, which included both the

linear-elastic and plastic-plateau regions, was approximately 15 lb-in/in3 and 29 lb-

in/in3 for the Uniaxial Stress and Strain EPPR foam models, respectively. These

values were dissimilar because of the smaller Uniaxial Stress plastic-semi-plateau and

densification regions illustrated in Figures 2.18 and 2.19. This was described in the

previous section.

63

Table 2.5 Linear-Elastic Region Energy Absorption Values

Crushing Strain:

εcr (in/in)

Crushing Stress:

σcr (psi)

Energy: Ee (lb-

in/in3)

Uniaxial Stress 0.05 16 0.04

Uniaxial Strain 0.06 31 0.93

Table 2.6 Plastic-Plateau Region Energy Absorption Values

Crushing Strain:

εcr (in/in)

Final Strain:

εmax (in/in)

Crushing

Stress: σcr (psi)

Energy: Ea

(lb-in/in3)

Uniaxial Stress 0.05 0.97 16 15

Uniaxial Strain 0.06 0.97 31 28

2.5 Conclusion of Polyisocyanurate Foam

The polyisocyanurate foam is comprised of many closed-cells with cell walls,

which bend in the linear-elastic region and buckle and/or crush in the plastic region

during an applied compressive load. Consequently, the foam’s main energy

absorption mechanism was crushing. Quasi-static Uniaxial Stress and Strain

compression experiments were executed, and EPPR foam Uniaxial Stress and Strain

models were created. These models were employed to determine the foam’s energy

absorption abilities. The EPPR foam replicas will be further used in Chapter 5 Energy

Absorption Capabilities. The subsequent chapter comprehensively explains the E-

glass vinyl ester resin web of the web core.

64

Chapter 3

STATIC TESTING OF FIBERGLASS WEB

3.1 Introduction to Static Testing of E-Glass Web

In Chapter 2, the behavior of the foam was determined. In this chapter, the

web loaded in compression performance will be studied along with its energy storage

and absorption capabilities. Two failure modes and associated energy absorption

mechanisms were considered. The first was in-plane compression loading to failure.

The second considered non-linear buckling of the web with a combination of in-plane

compression and out-of-plane deformations. Quasi-static experiments, buckling

investigations, fiber volume fraction burn-off tests, and axial compression

examinations were conducted to gain knowledge about the E-glass webs.

3.2 Description of E-Glass Web

A G18TYCOR®web core preform was acquired from WebCore Technologies,

Inc. Two pictures are shown in Figure 3.1 which illustrate both a web sample before

and after the Fiber Volume Fraction Experiment discussed in Section 3.5.

65

Figure 3.1 Web Laminate (a) Before and (b) After Resin Removal

Figure 3.1 corresponded to the fibers illustrated in Figure 1.7. The vinyl ester resin

injected into this composite web was DERAKANE510A-40 detailed in Table 1.1.

This vinyl ester resin had “higher fracture strain” than most polyesters and produced

composites with relatively high “mechanical properties, impact resistance, and fatigue

life” [42].

Figure 3.2 Panel Infusion Illustration [17]

66

To prepare samples for testing, a panel was manufactured by a VARTM

process, depicted at the end of Section 1.3. The aforementioned vinyl ester resin was

infused mentioned in Section 1.3. Figure 3.2 illustrated the VARTM process that was

implemented, and Figure 3.3 shows the adopted coordinate system – on a web core

sample – for this research. The VARTM process was conducted by situating the web

core discussed in Chapter 1 between a top and bottom facesheet each comprised of ten

E-glass cross-weave layers.

Figure 3.3 Web Coordinate System

A peel ply fabric and breather cloth were placed above and below the facesheets to

easily separate the part after infusion and to reduce air bubbles from the part. For

VARTM one infusion line was situated adjacent to the part, and two suction lines

were positioned on top and next to the part to draw the resin through it as seen in

Figure 3.2. After the resin penetrated the entire E-glass material, the infusion line was

67

stopped and the resin was allowed to cure for twenty-four hours. The panel was post-

cured for approximately one hour at 200oF.

After processing, unit cell geometries – initially illustrated in Figure 1.13 –

were machined from the panels. The unit cells were first cut with a wet diamond-

tipped saw. The panels were measured numerous times prior to cutting to guarantee

the E-glass web was centered in the specimen. The unit cell samples with a web not

situated in the middle – with approximately 1/16” variability – were not used in this

research to minimize eccentric load paths. “Differences in the eccentricity [of the

applied load] have a marked effect on the load-carrying capacity of [webs]” [26].

Then, both fiberglass facesheets were sanded with a wet-sander to establish uniform

applied load over the specimen and through the web. To isolate the compression

behavior of the webs, the polyisocyanurate foam was completely removed from the

specimens by sandblasting.

Next, strain gages – one on each side – were systematically adhered to the

webs. The 350-ohm resistant Vishay Micro-Measurements ½-inch-long CEA-06-

250UW-350 gages with 0.2 ± 0.2% sensitivity were attached to the webs at mid-

height. The web surface was first rigorously abraded with 180-grit sandpaper and

then meticulously cleaned by following the Vishay Micro-Measurements Group M-

Bond 200 Adhesive Strain Gage Installation instructions. An E-glass web buckling

picture is shown in Figure 3.4. Strain gages were attached to both sides of the web in

this picture and a Linear Variable Differential Transducer (LVDT), which measured

the lateral deflection, was resting at mid-length of the web.

68

Figure 3.4 Fiberglass Web Deforming Out-Of-Plane with Axial Load

Subsequently, Figure 3.5 shows the load vs. axial displacement curve of an

ideal column undergoing buckling. An ideal column’s load-axial-displacement curve

would generally have a sharp linear-elastic region in which the column was

compressing under an axial load. If any additional load is applied to a column on the

verge of buckling, the column will bifurcate and deflect laterally [26]. The second

region would be a perfect plateau at the ideal column’s buckling load whereby the

load remained the same while the column continued to axially displace. The web

buckling specimen load-axial-displacement curves shown in Section 3.4 will be

compared to the subsequent figure.

Moreover, there were two failure modes of the composite web. Described in

the next several paragraphs, they were in-plane compression loading to failure and

buckling. The two modes will be linked to the laminate’s stacking sequence and

respective ply angles. The two ply angles 0o and 45o were compared to axial

compression failure and buckling.

69

Figure 3.5 Load vs. Axial Displacement of an Ideal Column

Greater in-plane stiffness is seen in a unidirectional 0o ply than a 45

o angle-ply

lamina [43, 44]. This greater stiffness corresponds to higher failure loads in axial

compression and buckling loads. Notably, buckling is heavily affected by ply angles

[45]. As a result, the 45o angle-ply lamina used in this research had lower buckling

and axial-compression failure loads. Notably, the TYCOR® preform described in

Section 1.3 had a decided stacking sequence of ±45o plies.

Additionally, the web laminate configuration geometry was intended to ensure

the sandwich panel had strong bending and shear stiffness. This sandwich panel was

also robust in blast protection. When the sandwich structure is loaded in through-the-

thickness compression by an impulse pressure loading, this laminate can exhibit

significant nonlinear stress-strain response and absorb a considerable amount of

energy. The load-displacement curve for the characteristic long-length web specimen

Axial Displacement,

Lo

ad

, P

Ideal Column Buckling: Load, P vs. Displacement,

70

IWB26JF shown in Figure 3.6 is an E-glass web laminate undergoing buckling. At

the end of this chapter it was decided that this specimen had buckled. The load-axial-

displacement curve in the following figure section A to B generally exhibited the ideal

response shown in Figure 3.5; a linear response was observed in the elastic region.

Notably, a load-unload experiment of axially-loaded E-glass composite web samples

described in the subsequent sections confirmed their linear-elastic nature.

After its linear-elastic region, Figure 3.6 did not match the ideal column

response. The following curve distorted and gradual softening occurred as it reached

its web buckling load at point B [46]. Due to “imperfections in initial column

straightness and load application,” the column in Figure 3.6 IWB26JF started to bend

prior to reaching its ideal buckling load [26]. The plastic-plateau region section B to

C was also not congruent with the preceding graph. In Figure 3.6 IWB26JF

specimen’s plastic-plateau region the load did not remain constant as the deformation

increased [26]. Using a screw-driven displacement-controlled Instron machine, the

gradual decline in load was most likely due to laminate damage. Rather than

remaining as a constant horizontal plateau as in Figure 3.5, the load in the following

graph steadily diminished from section B to C [26].

71

Figure 3.6 Load vs. Axial Displacement Graph of Long-Length

Specimen IWB26JF

Regarding this figure, the slender web plate buckled, significantly increasing

its energy absorption capabilities. Buckling occurs when an axial compressive load

imposes on a slender column causing lateral deflection [26]. Point B denotes the

load-axial-displacement curve’s gradual change from the linear-elastic-to-bifurcation

mechanism to the buckling mechanism. Point C (at approximately 0.06 inches) was

set at the average final displacement for a linear-elastic-to-failure specimen detailed in

Section 3.8 and shown in Figure 3.7. Prior to reaching point B, the web – due to its

linear-elastic nature – had not absorbed any energy from buckling. The web, in turn,

absorbed a significant amount of energy during buckling since, as stated in Chapter 1,

the web continued to axially displace as it remained at relatively the same load.

0

15

30

45

60

75

90

105

120

0 0.01 0.02 0.03 0.04 0.05 0.06

IWB26JF

C

B

A

In-Plane MembraneModulus = 1.0E6 psi

Experimental Maximum Load = 110 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

IWB26JF: Force, F (lb) vs. Axial Displacement, (in) from Instron

72

Based on Equation 1.6 the energy stored by this web in the linear-elastic region, from

points A to B, was ½ * 0.01 inches * 110 lbs, which equated to 1.1lbs-in. For

practical purposes the bifurcation load in the semi-plateau was assumed to be a

constant 100 lbs. As a result in the region between points B and C, the energy

absorbed by the web was approximated at 0.05 inches * (100 lbs), or 5.0lbs-in based

on Equation 1.7. Therefore, the total energy consumed was 6.1lbs-in.

The following computation was performed on a linear-elastic-to-failure, force-

axial-displacement curve of an E-glass web compression strength specimen. Figure

3.7 illustrates this curve. The following graph is for web compression strength

specimen WCS10, which had failed from an applied axial load. This sample was

continuously supported by an ASTM D695 support system further described and

illustrated in Section 3.8 Web Compression Strength Tests. The former curve

exhibited two loading mechanisms, while the proceeding Figure 3.7 illustrates a curve

undergoing only one loading mechanism, which is defined as linear elasticity to

failure.

To explain, this curve exhibited a linear-elastic region starting at point D and

then suddenly failed in compression at point E. Both of the curves in Figures 3.6 and

3.7 terminated at approximately 0.06 inches; this simplified absorbed energy

comparison. In the linear-elastic region the loaded specimen in Figure 3.7 stores

energy, and then at point E it fails, damage occurs, and in turn, it absorbs the resulting

energy.

73

Figure 3.7 Load vs. Axial Displacement of Compression Strength

Specimen WCS10 Using Side-Supported ASTM D 695

Fixture

Based on Equation 1.6, the amount of absorbed energy from the WCS10 curve is ½ *

180 lbs * 0.06 in, or 5.4lbs-in. The IWB26JF specimen had absorbed a greater

amount of energy (6.1 lbs-in) than the WCS10 sample. Since there was a significant

area under the IWB26JF curve, the linear-elastic-to-bifurcation and buckling

mechanisms consumed a considerable amount of energy.

The following discusses the shapes of the curves from Figures 2.18, 3.6, and

3.7. Notably, the shape of the foam crushing mechanism curve in the linear-elastic

and plastic regions was analogous, with different values, to the web buckling curve.

Both mechanisms remained at relatively the same load while they continued to

0

20

40

60

80

100

120

140

160

180

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

WCS10JF

E

D

Maximum Stress =180 lb/(0.4925"*0.0340")=10,700psi

Maximum Load = 180 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

WCS10JF: Force, F (lb) vs. Axial Displacement, (in) from Instron

74

deform axially. These shapes absorbed a substantial amount of energy. On the other

hand, the linear-elastic-to-failure mechanism exhibited a very different shape than the

buckling and crushing mechanisms. Since the linear-elastic-to-failure mechanism no

longer received any load or absorbed any energy once failure occurred, its shape was

limited to a single line.

After the web buckling experiments, web buckling loads were theoretically

figured. Using a theoretical solid mechanics analysis geared towards composites, the

simply-supported (SS) beam buckling load was determined, incorporating the effects

of transverse shear stiffness. These calculations approximated the buckling load of a

web with a given thickness, width, and length in the load direction. The following

equation is the “critical buckling load of a simply supported beam, including the

effects of transverse shear deformation” [47]

(3.1) [47]

In Equation 3.1 Pb is the conventional Euler buckling load formula absent of

transverse shear deformation effects of an SS beam, A is the web’s cross-sectional

area, and is the effective interlaminar shear modulus [47]. Pb is defined in the

next equation.

(3.2) [47]

Lw is the web length situated in the direction of the load labeled as the x

direction of Figure 3.3, and D11 is the bending stiffness in the x-direction for Equation

3.2 [47]. D11 was taken directly from CMAP – explained in Section 3.5 – for each

1 1.2

bcr

b

eff

xz

PP

P

AG

eff

xzG

2

11

2

( )wb

w

d DP

L

75

web specimen. Notably, the length influences the buckling load by a power of two.

The bending stiffness value is, however, impacted by thickness to a power of three.

Figure 3.8 is an elevation view of Figure 3.3. This image illustrates on a web

core specimen the dimension Lw along with the variables btf, bbf, and bw, being the

width of the top flange, the width of the bottom flange, and the thickness of the web,

respectively. All of the elements have the same dimension in the y direction, or into

the page of Figure 3.8. In this study, right foam and left foam were designated as RF

and LF. For simplicity, the vertical web was modeled as a beam; the underlying

reason for utilizing a beam buckling examination.

Figure 3.8 Web Core Variable Depiction, the Depth of the Web dw is

into the Page

76

3.3 Description of Web Buckling Tests

The following describes the web buckling experiments. Two different web

buckling tests were executed. Quasi-static load-unload tests – with a cross-head speed

of 0.025 in/min – were first performed to understand the linear-elastic region of the

web specimens. In addition, quasi-static web buckling tests in which the cross-head

speed was set at 0.05 in/min were executed in order to determine the web buckling

load values. The Instron 5567 screw-driven testing machine was employed with a

6000-pound load cell for both tests. The top and bottom flanges of the I-beam

specimen were precision-machined flat for accurate experiments. Before the tests

were performed, an aluminum Web Buckling Fixture was designed and fabricated to

securely position the I-beam foamless specimen. The three features that were

included in the Web Buckling Fixture were an attached LVDT, a fixed and movable

support used to prevent the bottom flange from moving during loading, and a

modified loading nose that would properly distribute the load directly to the vertical

web. The following Figures 3.9 and 3.10 are schematics of the Web Buckling Fixture

with final dimensions and a picture of the test setup including strain gages after the

web had buckled, respectively.

77

Figure 3.9 Web Buckling Fixture Schematics

The 5.25-in-long LVDT with an accuracy of ±0.02 inches precisely measured the

lateral web deflection of the web bowing out-of-plane. The Serial Number and Type

of the LVDT were 42129 and DCTH400AG, respectively. A block with a set screw

was placed on the Web Buckling Fixture to position the LVDT. This block is located

on the left sides of the Plan and Elevation Views, and it is situated at the center of the

Left Side View figure. The LVDT was positioned on the left side in Figure 3.10.

78

Figure 3.10 Complete View of Actual Web Buckling Test Setup

Figure 3.11 Loading Block Dimensions

There were also two previously-mentioned angle bracket supports in Figure 3.10; one

fixed and one sliding support that allowed for web buckling specimens with varying

sizes. In Figure 3.11 a rectangular prism loading block used to apply force to the

79

specimen can be viewed, which screws into a long cylindrical previously-constructed

loading nose.

Figure 3.12 shows specimen IWB44JF prior to and during loading. In this

figure and in all of the web buckling tests, only the specimen’s bottom flange was

constrained to prevent any movement during loading. The top flange was not

constrained in order to allow for free movement during the experiment.

Figure 3.12 (a) IWB44JF Specimen Prior to Loading (b) IWB44JF

Specimen during Loading

3.4 Web Buckling Results

This section completely explains the results for the composite fiberglass web

buckling tests. Two failure mechanisms were seen in the following experimental

graphs. From Section 3.2, the buckling mechanism absorbed more energy than the

linear-elastic-to-failure mechanism. Based on ease of design; however, the linear-

80

elastic-to-failure mechanism seems more desirable since it does not incorporate a

higher-order bifurcation.

To start with, the first experiment using the Web Buckling Fixture was the

load-unload test detailed in the previous section. Only four specimens were examined

in the load-unload test; the subsequent table lists their dimensions.

Table 3.1 Load-Unload Specimen Dimensions

Specimen

Number

Specimen

Name

Web Length:

Lw (in)

Total Web

Thickness: bw

(in)

Web Depth:

dw (in)

1 IWB31_LU 1.3525 0.0712 1.9719

2 IWB32_LU 1.3380 0.0577 1.9424

3 IWB33_LU 1.3825 0.0221 1.9428

4 IWB34_LU 1.3485 0.0794 1.9279

The web depths and lengths were kept relatively constant, while the total web

thicknesses were different for all four specimens. The following load-axial-

displacement graph illustrates the four load-unload specimens. The load values in

these curves were generally proportional to total web thickness bw. The thinnest web

specimen IWB33_LU (0.0221”) received the smallest loads, while the thicker webs

IWB31_LU (0.0712”) and IWB34_LU (0.0794”) experienced relatively higher loads.

A common region located at the left-side of the graph from approximately 0 to 75 lbs

was seen for all four load-unload curves.

81

Figure 3.13 Load vs. Axial Displacement of Load-Unload Specimens

This similar region verifies the linear-elastic nature prior to bifurcation of the

composite E-glass web. Once “the load is removed the specimen will still return back

to its original shape” since the load-unload cycles had remained in the E-glass web

linear-elastic region [26].

Even though the loading/unloading specimens were only tested to verify the E-

glass vinyl ester resin web’s linear-elasticity, there were other notable tendencies in

Figure 3.13. First, the curves began to plateau on the right-side of the graph as seen in

specimens IWB31_LU, IWB32_LU, and IWB33_LU. This plateau was most likely

their buckling load, which will be completely reviewed later in this chapter. Second,

the specimens’ in-plane membrane moduli appeared congruent. Due to research time

constraints the stiffnesses were never precisely computed from strain gage data.

0

50

100

150

200

250

300

350

400

450

0 0.005 0.010 0.015 0.020 0.025 0.030 0.035

IWB34_LUIWB33_LUIWB32_LUIWB31_LU

Axial Displacement, (in )

Lo

ad

, F

(lb

)

IWB31_LU: Force, F (lb) vs. Axial Displacement, (in) from Instron

82

However, based on their web lengths and depths being compatible and the total web

thicknesses being proportional to the forces in each specimen, their in-plane

membrane moduli were relatively similar. Their compatible web lengths and axial

displacements would result in similar axial strains, and their total web thicknesses

corresponding to their received loads would result in similar in-plane membrane

moduli. More computational research must be conducted to verify this. Third, there

were observed deviations from linearity in these curves of Figure 3.13. For an ideal

column with an applied axial load, the respective loading and unloading cycles would

be collinear in the linear-elastic region [26]. This, however, did not occur.

Deviations or offsets from linearity – most likely due to unavoidable imperfections

due to manufacturing discussed in previous sections – occurred in the

loading/unloading curves’ linear-elastic region [26]. This is illustrated in the left-side

of Figure 3.13 when each cycle parallels, yet is offset, from linearity. Theoretically,

the thinner specimens would tend to be more affected by imperfections than the

thicker ones [26]. More research must be performed including quantifying each

specimen’s imperfections in order to prove this. The subsequent paragraphs describe

the web buckling tests.

83

Table 3.2 Long-Length Web Buckling Specimen Dimensions

Specimen

Number

Specimen

Name

Web Length:

Lw (in)

Web Depth:

dw (in)

Total Web

Thickness: bw (in)

1 IWB26JF 1.3485 1.9804 0.0345

2 IWB27EP 1.3210 1.9706 0.0960

3 IWB28JF 1.3870 1.9435 0.0354

4 IWB29JF 1.3765 1.9403 0.0299

5 IWB36EP 1.3765 1.9272 0.0903

6 IWB37EP 1.3680 1.9253 0.0440

7 IWB38HEP 1.3615 1.9391 0.0469

8 IWB39EP 1.3785 1.9809 0.0924

9 IWB40EP 1.3930 2.0556 0.0812

10 IWB41HEP 1.3870 2.0376 0.0656

11 IWB42EP 1.3260 2.1068 0.0390

12 IWB43JF 1.3205 2.1113 0.0318

13 IWB44JF 1.3405 2.1214 0.0311

14 IWB45JF 1.3595 2.1093 0.0331

15 IWB46JF 1.3630 1.9716 0.0323

The web buckling tests involved a total of 26 specimens; 15 long-length and

14 small-length webs. These composite E-glass I-beam specimens without foam were

quasi-statically tested using the Web Buckling Fixture depicted in the preceding

section. Tables 3.2 and 3.3 supply the long-length and small-length specimen web

dimensions. These dimensions, especially the thicknesses, were measured several

times to ensure accuracy. The thicknesses were measured with digital calipers 10

times, the depths were measured 8 times, and the lengths were measured twice. The

procedure performed to machine the specimens is described in Section 3.2. The

successive paragraph explains the adopted naming convention used for the web

buckling samples.

84

Table 3.3 Small-Length Web Buckling Specimen Dimensions

Specimen

Number

Specimen

Name

Web Length:

Lw (in)

Web Depth:

dw (in)

Total Web

Thickness: bw

(in)

16 IWB47JF 0.9623 2.1114 0.0416

17 IWB48EP 0.9843 2.0364 0.0794

18 IWB49EP 0.9705 1.9080 0.0516

19 IWB50HEP 0.9785 2.1279 0.0689

20 IWB52JF 0.9683 2.1385 0.0434

21 IWB53HEP 0.9818 2.1207 0.0699

22 IWB54JF 0.9810 2.1226 0.0443

23 IWB55HEP 0.9675 2.1244 0.0662

24 IWB56EP 0.9638 2.1246 0.0655

25 IWB57HEP 0.9613 2.0798 0.0497

26 IWB58HEP 0.9625 2.0743 0.0478

27 IWB59HEP 0.9670 2.1854 0.0614

28 IWB60HEP 0.9685 2.1405 0.0630

29 IWB61JF 0.9773 2.1227 0.0435

The samples were fabricated by removing foam from previously cured web

core preforms. After the foam was discarded the webs were visually analyzed,

revealing three different material configurations of the webs. Three acronyms were

designated to characterize the various web compositions; Encrusted Polymer (EP),

Half-Encrusted Polymer (HEP), and Just Fiberglass (JF). A sectioned composite

fiberglass web with EP – encrusted polymer on both sides of the composite – is

illustrated in Figure 3.14. An HEP web was comprised of only one polymer section,

while a JF web had no polymer sections adhered to the composite fiberglass. The

preceding tables included the EP and HEP thicknesses in the areas listed.

To explain, the polymer adhered to the composite E-glass web during the

VARTM process when resin disseminated through the part. The surface of the foam

in contact with the web had open pores, which the resin had penetrated, at the foam-

85

web interface. Removing the foam from the web revealed a layer of encrusted

polymer, most likely composed of a foam-resin mixture.

Figure 3.14 Encrusted Polymer Representation of IWB42EP

The following paragraphs describe the long-length web buckling specimens

and their respective results. Figure 3.15 shows the load-axial-displacement graphs

from the Instron 5667 machine for the long-length specimens. The long-length web

buckling force-lateral-deflection and stress-strain graphs are illustrated in Figures 3.16

and 3.17, respectively.

86

Figure 3.15 Load vs. Axial Displacement Long-Length Web Buckling

Specimens

0

15

30

45

60

75

90

105

120

0 0.01 0.02 0.03 0.04 0.05

IWB26JF

Experimental Maximum Load = 110 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

IWB26JF: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

50

100

150

200

250

300

350

400

0 0.01 0.02 0.03 0.04 0.05

IWB27EP

Experimental Maximum Load = 380 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

IWB27EP: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

20

40

60

80

100

0 0.01 0.02 0.03 0.04 0.05

IWB28JF

ExperimentalMaximum Load = 92 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

IWB28JF: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

20

40

60

80

100

120

0 0.01 0.02 0.03 0.04 0.05

IWB29JF

ExperimentalMaximum Load = 100 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

IWB29JF: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

100

200

300

400

500

600

700

800

900

0 0.01 0.02 0.03 0.04 0.05

IWB36EP

ExperimentalMaximum Load = 880 lb

Axial Displacement, (in )

Fo

rce

, F

(lb

)

IWB36EP: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

50

100

150

200

250

300

0 0.01 0.02 0.03 0.04 0.05

IWB37EP

ExperimentalMaximum Load = 280 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

IWB37EP: Force, F (lb) vs. Axial Displacement, (in) from Instron

87

Figure 3.15 Continued

0

50

100

150

200

250

300

350

400

450

0 0.01 0.02 0.03 0.04 0.05

IWB38HEP

ExperimentalMaximum Load = 420 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

IWB38HEP: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

200

400

600

800

1000

1200

0 0.01 0.02 0.03 0.04 0.05

IWB39EP

ExperimentalMaximum Load = 1040 lb

Axial Displacement, (in )

Fo

rce

, F

(lb

)

IWB39EP: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

100

200

300

400

500

600

0 0.01 0.02 0.03 0.04 0.05

IWB40EP

ExperimentalMaximum Load = 550 lb

Axial Displacement, (in )

Fo

rce

, F

(lb

)

IWB40EP: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

100

200

300

400

500

0 0.01 0.02 0.03 0.04 0.05

IWB41HEP

ExperimentalMaximum Load = 400 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

IWB41HEP: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

20

40

60

80

100

120

140

0 0.01 0.02 0.03 0.04 0.05

IWB42EP

ExperimentalMaximum Load = 120 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

IWB42EP: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

20

40

60

80

100

120

0 0.01 0.02 0.03 0.04 0.05

IWB43JF

ExperimentalMaximum Load = 120 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

IWB43JF: Force, F (lb) vs. Axial Displacement, (in) from Instron

88

Figure 3.15 Continued

Figure 3.16 Force vs. Lateral Deflection from LVDT Long-Length

Buckling Specimens

0

10

20

30

40

50

60

70

80

90

0 0.01 0.02 0.03 0.04 0.05

IWB44JF

ExperimentalMaximum Load = 90 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

IWB44JF: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

20

40

60

80

100

120

140

160

0 0.01 0.02 0.03 0.04 0.05

IWB45JF

ExperimentalMaximum Load = 150 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

IWB45JF: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

20

40

60

80

100

120

140

160

0 0.01 0.02 0.03 0.04 0.05

IWB46JF

ExperimentalMaximum Load = 140 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

IWB46JF: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

15

30

45

60

75

90

105

120

-0.21 -0.18 -0.15 -0.12 -0.09 -0.06 -0.03 0 0.03

IWB26JF_LVDT

ExperimentalMaximum Load = 110 lb

Lateral Deflection, w (in)

Fo

rce

, F

(lb

)

IWB26JF: Force, F (lb) vs. Lateral Deflection, w (in) from LVDT

0

50

100

150

200

250

300

350

400

-0.21 -0.18 -0.15 -0.12 -0.09 -0.06 -0.03 0 0.03

IWB27EP_LVDT

ExperimentalMaximum Load = 380 lb

Lateral Deflection, w (in)

Fo

rce

, F

(lb

)

IWB27EP: Force, F (lb) vs. Lateral Deflection, w (in) from LVDT

89

Figure 3.16 Continued

0

15

30

45

60

75

90

105

-0.21 -0.18 -0.15 -0.12 -0.09 -0.06 -0.03 0 0.03

IWB28JF_LVDT

ExperimentalMaximum Load = 92 lb

Lateral Deflection, w (in)

Fo

rce

, F

(lb

)

IWB28JF: Force, F (lb) vs. Lateral Deflection, w (in) from LVDT

0

15

30

45

60

75

90

105

-0.03 0 0.03 0.06 0.09 0.12 0.15 0.18 0.21

IWB29JF_LVDT

ExperimentalMaximum Load = 100 lb

Lateral Deflection, w (in)

Fo

rce

, F

(lb

)

IWB29JF: Force, F (lb) vs. Lateral Deflection, w (in) from LVDT

0

100

200

300

400

500

600

700

800

900

-0.21 -0.18 -0.15 -0.12 -0.09 -0.06 -0.03 0

IWB36EP_LVDT

ExperimentalMaximum Load = 880 lb

Lateral Deflection, w (in )

Fo

rce

, F

(lb

)

IWB36EP: Force, F (lb) vs. Lateral Deflection, w (in) from LVDT

0

50

100

150

200

250

300

0 0.03 0.06 0.09 0.12 0.15 0.18 0.21

IWB37EP_LVDT

ExperimentalMaximum Load = 280 lb

Lateral Deflection, w (in)

Fo

rce

, F

(lb

)

IWB37EP: Force, F (lb) vs.Lateral Deflection, w (in) from LVDT

0

50

100

150

200

250

300

350

400

450

0 0.03 0.06 0.09 0.12 0.15 0.18 0.21

IWB38HEP_LVDT

ExperimentalMaximum Load = 420 lb

Lateral Deflection, w (in)

Fo

rce

, F

(lb

)

IWB38HEP: Force, F (lb) vs. Lateral Deflection, w (in) from LVDT

0

200

400

600

800

1000

1200

-0.21 -0.18 -0.15 -0.12 -0.09 -0.06 -0.03 0

IWB39EP_LVDT

ExperimentalMaximum Load = 1040 lb

Lateral Deflection, w in)

Fo

rce

, F

(lb

)

IWB39EP: Force, F (lb) vs. Lateral Deflection, w(in) from LVDT

90

Figure 3.16 Continued

0

100

200

300

400

500

600

-0.21 -0.18 -0.15 -0.12 -0.09 -0.06 -0.03 0 0.03

IWB40EP_LVDT

ExperimentalMaximum Load = 550 lb

Lateral Deflection, w in)

Fo

rce

, F

(lb

)

IWB40EP: Force, F (lb) vs. Lateral Deflection, w(in) from LVDT

0

100

200

300

400

500

600

-0.21 -0.18 -0.15 -0.12 -0.09 -0.06 -0.03 0 0.03

IWB40EP_LVDT

ExperimentalMaximum Load = 550 lb

Lateral Deflection, w in)

Fo

rce

, F

(lb

)

IWB40EP: Force, F (lb) vs. Lateral Deflection, w(in) from LVDT

0

20

40

60

80

100

120

-0.21 -0.18 -0.15 -0.12 -0.09 -0.06 -0.03 0 0.03

IWB42EP_LVDT

ExperimentalMaximum Load = 120 lb

Lateral Deflection, w (in)

Fo

rce

, F

(lb

)

IWB42EP: Force, F (lb) vs. Lateral Deflection, w (in) from LVDT

0

20

40

60

80

100

120

140

-0.03 0 0.03 0.06 0.09 0.12 0.15 0.18 0.21

IWB43JF_LVDT

ExperimentalMaximum Load = 120 lb

Lateral Deflection, w (in)

Fo

rce

, F

(lb

)

IWB43JF: Force, F (lb) vs.Lateral Deflection, w (in) from LVDT

0

15

30

45

60

75

90

105

-0.21 -0.18 -0.15 -0.12 -0.09 -0.06 -0.03 0 0.03

IWB44JF_LVDT

ExperimentalMaximum Load = 90 lb

Lateral Deflection, w (in)

Fo

rce

, F

(lb

)

IWB44JF: Force, F (lb) vs. Lateral Deflection, w (in) from LVDT

0

20

40

60

80

100

120

140

160

0 0.03 0.06 0.09 0.12 0.15 0.18 0.21

IWB45JF_LVDT

ExperimentalMaximum Load = 150 lb

Lateral Deflection, w (in)

Fo

rce

, F

(lb

)

IWB45JF: Force, F (lb) vs. Lateral Deflection, w (in) from LVDT

91

Figure 3.16 Continued

Figure 3.17 Stress vs. Strain from Strain Gages Long-Length Buckling

Specimens

0

20

40

60

80

100

120

140

160

-0.21 -0.18 -0.15 -0.12 -0.09 -0.06 -0.03 0

IWB46JF_LVDT

ExperimentalMaximum Load = 140 lb

Lateral Deflection, w (in)

Fo

rce

, F

(lb

)

IWB46JF: Force, F (lb) vs. Lateral Deflection, w (in) from LVDT

0

300

600

900

1200

1500

1800

-0.016 -0.012 -0.008 -0.004 0 0.004 0.008 0.012 0.016

Avg. SGSG2SG1

In-Plane Membrane Modulus = 1.0E6 psi

Strain, (in/in)

Str

ess, (

psi)

IWB26JF: Stress, (psi) vs. Strain, (in/in) from Strain Gages

0

300

600

900

1200

1500

1800

2100

-0.016 -0.012 -0.008 -0.004 0

Avg. SGSG 2SG 1

In-Plane MembraneModulus = 0.64E6 psi

Strain, (in/in)

Str

ess, (

psi)

IWB27EP: Stress, (psi) vs. Strain, (in/in) from Strain Gages

0

200

400

600

800

1000

1200

1400

-0.016 -0.012 -0.008 -0.004 0

Avg. SGSG 2SG 1

In-Plane MembraneModulus = 0.69E6 psi

Strain, (in/in)

Str

ess, (

psi)

IWB28JF: Stress, (psi) vs. Strain, (in/in) from Strain Gages

0

300

600

900

1200

1500

1800

2100

-0.016 -0.012 -0.008 -0.004 0 0.004 0.008

Avg. SGSG 2SG 1

In-Plane Membrane Modulus = 1.3E6 psi

Strain, (in/in)

Str

ess, (

psi)

IWB29JF: Stress, (psi) vs. Strain, (in/in) from Strain Gages

92

Figure 3.17 Continued

0

1000

2000

3000

4000

5000

6000

-0.016 -0.012 -0.008 -0.004 0

Avg. SGSG 2SG 1

In-Plane Membrane Modulus = 0.70E6 psi

Strain, (in/in)

Str

ess, (

psi)

IWB36EP: Stress, (psi) vs. Strain, (in/in) from Strain Gages

0

500

1000

1500

2000

2500

3000

3500

-0.016 -0.012 -0.008 -0.004 0 0.004 0.008

Avg. SGSG 2SG 1

In-Plane Membrane Modulus = 9.8E5 psi

Strain, (in/in)

Str

ess, (

psi)

IWB37EP: Stress, (psi) vs. Strain, (in/in) from Strain Gages

0

1000

2000

3000

4000

5000

-0.016 -0.012 -0.008 -0.004 0 0.004

Avg. SGSG2SG1

In-Plane Membrane Modulus = 0.92E6 psi

Strain, (in/in)

Str

ess, (

psi)

IWB38HEP: Stress, (psi) vs. Strain, (in/in) from Strain Gages

0

1000

2000

3000

4000

5000

6000

-0.016 -0.012 -0.008 -0.004 0

Avg. SGSG 2SG 1

In-Plane Membrane Modulus = 0.67E6 psi

Strain, (in/in)

Str

ess, (

psi)

IWB39EP: Stress, (psi) vs. Strain, (in/in) from Strain Gages

0

500

1000

1500

2000

2500

3000

3500

-0.016 -0.012 -0.008 -0.004 0

Avg. SGSG 2SG 1

In-Plane MembraneModulus = 0.81E6 psi

Strain, (in/in)

Str

ess, (

psi)

IWB40EP: Stress, (psi) vs. Strain, (in/in) from Strain Gages

0

500

1000

1500

2000

2500

3000

-0.012 -0.008 -0.004 0 0.004

Avg. SGSG2SG1

In-Plane Membrane Modulus = 0.71E6 psi

Strain, (in/in)

Str

ess, (

psi)

IWB41HEP: Stress, (psi) vs. Strain, (in/in) from Strain Gages

93

Figure 3.17 Continued

Notably, the force vs. lateral deflection graphs were created from the LVDT

experimental data, and the stress vs. strain curves were formed from compiling the

strain gage results. The strain gages utilized on these webs were depicted in Section

0

200

400

600

800

1000

1200

1400

1600

-0.016 -0.012 -0.008 -0.004 0 0.004 0.008 0.012 0.016

Avg. SGSG2SG1

In-Plane Membrane Modulus = 1.1E6 psi

Strain, (in/in)

Str

ess, (

psi)

IWB42EP: Stress, (psi) vs. Strain, (in/in) from Strain Gages

0

300

600

900

1200

1500

1800

2100

-0.016 -0.012 -0.008 -0.004 0 0.004 0.008 0.012

Avg. SGSG 2SG 1

In-Plane Membrane Modulus = 1.1E6 psi

Strain, (in/in)

Str

ess, (

psi)

IWB43JF: Stress, (psi) vs. Strain, (in/in) from Strain Gages

0

200

400

600

800

1000

1200

1400

1600

-0.016 -0.012 -0.008 -0.004 0 0.004 0.008 0.012 0.016

Avg. SGSG 2SG 1

In-Plane Membrane Modulus = 1.2E6 psi

Strain, (in/in)

Str

ess, (

psi)

IWB44JF: Stress, (psi) vs. Strain, (in/in) from Strain Gages

0

300

600

900

1200

1500

1800

2100

2400

-0.016 -0.012 -0.008 -0.004 0

Avg. SGSG2SG1

In-Plane MembraneModulus = 1.6E6 psi

Strain, (in/in)

Str

ess, (

psi)

IWB45JF: Stress, (psi) vs. Strain, (in/in) from Strain Gages

0

500

1000

1500

2000

2500

-0.016 -0.012 -0.008 -0.004 0 0.004 0.008 0.012

Avg. SGSG 2SG 1

In-Plane MembraneModulus = 9.6E5 psi

Strain, (in/in)

Str

ess, (

psi)

IWB46JF: Stress, (psi) vs. Strain, (in/in) from Strain Gages

94

3.2, while the LVDT specifications were given in Section 3.3. During the tests, the

Instron machine measured axial displacement, while the LVDT and strain gages

measured lateral deflection and strain, respectively. These graphs will be discussed in

the next paragraphs.

The previous experimental results were highly varied. This is most likely due

to the large difference in web laminate thickness. Since web bending stiffness is

proportional to thickness cubed, the bending stiffness of the web laminate denoted as

D11 in Equation 3.2 significantly affected the web buckling experimental results [44].

Each web laminate’s bending stiffness will be defined in Section 3.5 CMAP.

Furthermore, the force-lateral-deflection curves were utilized to determine the

lateral deflection at the instant each web began bifurcating. The lateral deflection data

will be used in the successive sections to categorize each specimen’s failure

mechanism, which will be further described at the end of this section. By dividing the

Instron machine applied force by the web area, the ordinate stresses in Figure 3.17

were computed. The blue solid line and red dotted line depicted the strain gage data,

and the black solid line is the calculated average of both strain gages in Figure 3.17.

95

Figure 3.18 Load vs. Axial Displacement Small-Length Web Buckling

Specimens

0

100

200

300

400

500

600

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

IWB47JF

Experimenta Maximum Load = 540 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

IWB47JF: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

200

400

600

800

1000

1200

0 0.01 0.02 0.03 0.04 0.05

IWB48EP

Experimental MaximumLoad = 1120 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

IWB48EP: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

100

200

300

400

500

600

700

800

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

IWB49EP

Experimental MaximumLoad = 780 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

IWB49EP: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

200

400

600

800

1000

1200

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

IWB50HEP

Experimental MaximumLoad = 1040 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

IWB50HEP: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

100

200

300

400

500

600

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

IWB52JF

Experimental MaximumLoad = 580 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

IWB52JF: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

200

400

600

800

1000

1200

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

IWB53HEP

Experimental MaximumLoad = 1110 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

IWB53HEP: Force, F (lb) vs. Axial Displacement, (in) from Instron

96

Figure 3.18 Continued

0

50

100

150

200

250

300

350

400

450

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

IWB54JF

Experimental Maximum Load = 440 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

IWB54JF: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

200

400

600

800

1000

1200

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

IWB55HEP

Experimental Maximum Load = 1130 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

IWB55HEP: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

200

400

600

800

1000

1200

1400

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

IWB56EP

Experimental Maximum Load = 1330 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

IWB56EP: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

100

200

300

400

500

600

700

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

IWB57HEP

Experimental Maximum Load = 650 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

IWB57HEP: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

100

200

300

400

500

600

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

IWB58HEP

Experimental Maximum Load = 520 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

IWB58HEP: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

200

400

600

800

1000

1200

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

IWB59HEP

Experimental Maximum Load = 1020 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

IWB59HEP: Force, F (lb) vs. Axial Displacement, (in) from Instron

97

Figure 3.18 Continued

Figure 3.19 Force vs. Lateral Deflection from LVDT Small-Length Web

Buckling Specimens

0

200

400

600

800

1000

1200

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

IWB60HEP

Experimental Maximum Load = 1130 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

IWB60HEP: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

100

200

300

400

500

600

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

IWB61JF

Experimental Maximum Load = 530 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

IWB61JF: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

200

400

600

800

1000

1200

1400

1600

-0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0

IWB47JF_LVDT

ExperimentalMaximum Load = 540 lb

Lateral Deflection, w (in )

Fo

rce

, F

(lb

)

IWB47JF: Force, F (lb) vs. Lateral Deflection, w (in) from LVDT

0

200

400

600

800

1000

1200

1400

1600

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

IWB48EP_LVDT

ExperimentalMaximum Load = 1120 lb

Lateral Deflection, w (in )

Fo

rce

, F

(lb

)

IWB48EP: Force, F (lb) vs. Lateral Deflection, w (in) from LVDT

0

200

400

600

800

1000

1200

1400

1600

-0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0 0.01

IWB49EP_LVDT

ExperimentalMaximum Load = 780 lb

Lateral Deflection, w (in )

Fo

rce

, F

(lb

)

IWB49EP: Force, F (lb) vs. Lateral Deflection, w (in) from LVDT

0

200

400

600

800

1000

1200

1400

1600

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

IWB50HEP_LVDT

ExperimentalMaximum Load = 1040 lb

Lateral Deflection, w (in )

Fo

rce

, F

(lb

)

IWB50HEP: Force, F (lb) vs. Lateral Deflection, w (in) from LVDT

98

Figure 3.19 Continued

0

200

400

600

800

1000

1200

1400

1600

-0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0

IWB52JF_LVDT

ExperimentalMaximum Load = 580 lb

Lateral Deflection, w (in )

Fo

rce

, F

(lb

)

IWB52JF: Force, F (lb) vs. Lateral Deflection, w (in) from LVDT

0

200

400

600

800

1000

1200

1400

1600

-0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0

IWB53HEP_LVDT

ExperimentalMaximum Load = 1110 lb

Lateral Deflection, w (in )

Fo

rce

, F

(lb

)

IWB53HEP: Force, F (lb) vs. Lateral Deflection, w (in) from LVDT

0

200

400

600

800

1000

1200

1400

1600

-0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0

IWB54JF_LVDT

ExperimentalMaximum Load = 440 lb

Lateral Deflection, w (in )

Fo

rce

, F

(lb

)

IWB54JF: Force, F (lb) vs. Lateral Deflection, w (in) from LVDT

0

200

400

600

800

1000

1200

1400

1600

-0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0

IWB55HEP_LVDT

ExperimentalMaximum Load = 1130 lb

Lateral Deflection, w (in )

Fo

rce

, F

(lb

)

IWB55HEP: Force, F (lb) vs. Lateral Deflection, w (in) from LVDT

0

200

400

600

800

1000

1200

1400

1600

-0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

IWB56EP_LVDT

ExperimentalMaximum Load = 1330 lb

Lateral Deflection, w (in )

Fo

rce

, F

(lb

)

IWB56EP: Force, F (lb) vs. Lateral Deflection, w (in) from LVDT

0

200

400

600

800

1000

1200

1400

1600

-0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0

IWB57HEP_LVDT

ExperimentalMaximum Load = 650 lb

Lateral Deflection, w (in )

Fo

rce

, F

(lb

)

IWB57HEP: Force, F (lb) vs. Lateral Deflection, w (in) from LVDT

99

Figure 3.19 Continued

Figure 3.20 Stress vs. Strain from Strain Gages Small-Length Web

Buckling Specimens

0

200

400

600

800

1000

1200

1400

1600

-0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0

IWB58HEP_LVDT

ExperimentalMaximum Load = 520 lb

Lateral Deflection, w (in )

Fo

rce

, F

(lb

)

IWB58HEP: Force, F (lb) vs. Lateral Deflection, w (in) from LVDT

0

200

400

600

800

1000

1200

1400

1600

-0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0

IWB59HEP_LVDT

ExperimentalMaximum Load = 1020 lb

Lateral Deflection, w (in )

Fo

rce

, F

(lb

)

IWB59HEP: Force, F (lb) vs. Lateral Deflection, w (in) from LVDT

0

200

400

600

800

1000

1200

1400

1600

-0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

IWB60HEP_LVDT

ExperimentalMaximum Load = 1130 lb

Lateral Deflection, w (in )

Fo

rce

, F

(lb

)

IWB60HEP: Force, F (lb) vs. Lateral Deflection, w (in) from LVDT

0

200

400

600

800

1000

1200

1400

1600

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

IWB61JF_LVDT

ExperimentalMaximum Load = 530 lb

Lateral Deflection, w (in )

Fo

rce

, F

(lb

)

IWB61JF: Force, F (lb) vs. Lateral Deflection, w (in) from LVDT

0

2000

4000

6000

8000

10000

-0.016 -0.012 -0.008 -0.004 0 0.004 0.008

Avg. SGSG 2SG 1

Membrane Modulus = 1.8E6 psi

Strain, (in/in)

Str

ess, (

psi)

IWB47JF: Stress, (psi) vs. Strain, (in/in) from Strain Gages

0

2000

4000

6000

8000

10000

-0.016 -0.012 -0.008 -0.004 0 0.004

Avg. SGSG 2SG 1

In-Plane MembraneModulus = 0.90E6 psi

Strain, (in/in)

Str

ess, (

psi)

IWB48EP: Stress, (psi) vs. Strain, (in/in) from Strain Gages

100

Figure 3.20 Continued

0

2000

4000

6000

8000

10000

-0.016 -0.012 -0.008 -0.004 0

Avg. SGSG 2SG 1

Membrane Modulus = 1.8E6 psi

Strain, (in/in)

Str

ess, (

psi)

IWB49EP: Stress, (psi) vs. Strain, (in/in) from Strain Gages

0

2000

4000

6000

8000

10000

-0.016 -0.012 -0.008 -0.004 0

Avg. SGSG 2SG 1

Membrane Modulus = 0.74E6 psi

Strain, (in/in)

Str

ess, (

psi)

IWB50HEP: Stress, (psi) vs. Strain, (in/in) from Strain Gages

0

2000

4000

6000

8000

10000

-0.016 -0.012 -0.008 -0.004 0 0.004 0.008

Avg. SGSG 2SG 1

Membrane Modulus = 1.4E6 psi

Strain, (in/in)

Str

ess, (

psi)

IWB52JF: Stress, (psi) vs. Strain, (in/in) from Strain Gages

0

2000

4000

6000

8000

10000

-0.016 -0.012 -0.008 -0.004 0

Avg. SGSG 2SG 1

Membrane Modulus = 0.84E6 psi

Strain, (in/in)

Str

ess, (

psi)

IWB53HEP: Stress, (psi) vs. Strain, (in/in) from Strain Gages

0

2000

4000

6000

8000

10000

-0.016 -0.012 -0.008 -0.004 0 0.004 0.008

Avg. SGSG 2SG 1

Membrane Modulus = 1.6E6 psi

Strain, (in/in)

Str

ess, (

psi)

IWB54JF: Stress, (psi) vs. Strain, (in/in) from Strain Gages

0

2000

4000

6000

8000

10000

-0.016 -0.012 -0.008 -0.004 0 0.004

Avg. SGSG 2SG 1

Membrane Modulus = 9.8E5 psi

Strain, (in/in)

Str

ess, (

psi)

IWB55HEP: Stress, (psi) vs. Strain, (in/in) from Strain Gages

101

Figure 3.20 Continued

0

2000

4000

6000

8000

10000

-0.016 -0.012 -0.008 -0.004 0

Avg. SGSG2SG1

Membrane Modulus = 1.0E6 psi

Strain, (in/in)

Str

ess, (

psi)

IWB56EP: Stress, (psi) vs. Strain, (in/in) from Strain Gages

0

2000

4000

6000

8000

10000

-0.016 -0.012 -0.008 -0.004 0 0.004 0.008 0.012 0.016

Avg. SGSG 2SG 1

Membrane Modulus = 1.6E6 psi

Strain, (in/in)

Str

ess, (

psi)

IWB57HEP: Stress, (psi) vs. Strain, (in/in) from Strain Gages

0

2000

4000

6000

8000

10000

-0.016 -0.012 -0.008 -0.004 0 0.004

Avg. SGSG 2SG 1

Membrane Modulus = 1.1E6 psi

Strain, (in/in)

Str

ess, (

psi)

IWB58HEP: Stress, (psi) vs. Strain, (in/in) from Strain Gages

0

2000

4000

6000

8000

10000

-0.016 -0.012 -0.008 -0.004 0 0.004 0.008 0.012

Avg. SGSG 2SG 1

Membrane Modulus = 1.2E6 psi

Strain, (in/in)

Str

ess, (

psi)

IWB59HEP: Stress, (psi) vs. Strain, (in/in) from Strain Gages

0

2000

4000

6000

8000

10000

-0.016 -0.012 -0.008 -0.004 0

Avg. SGSG 2SG 1

Membrane Modulus = 0.91E6 psi

Strain, (in/in)

Str

ess, (

psi)

IWB60HEP: Stress, (psi) vs. Strain, (in/in) from Strain Gages

0

2000

4000

6000

8000

10000

-0.016 -0.012 -0.008 -0.004 0 0.004 0.008

Avg. SGSG 2SG 1

Membrane Modulus = 1.1E6 psi

Strain, (in/in)

Str

ess, (

psi)

IWB61JF: Stress, (psi) vs. Strain, (in/in) from Strain Gages

102

Since a strain gage was adhered to each side of the web specimen, the strain gages

reported opposing values once the web buckled. One strain gage recorded

compression, while the other recorded tension. In addition, the in-plane membrane

modulus was calculated by using EasyPlot’s slope function prior to bifurcation in the

stress-strain curve’s linear-elastic region. For this computation, strain was defined as

the average of the two surface strains. Figure 3.15 was not utilized to compute in-

plane membrane modulus because of the inaccuracy of the cross-head displacement

and machine compliance. The long-length specimen strain ranges are detailed in

Table 3.4 along with the elastic moduli and compressive strengths at failure. The

lateral deflection and strain at bifurcation are listed in Table 3.5 for the long-length

webs. The bifurcation strain was taken at the point on the stress-strain graphs at

which the curve initiated bifurcation.

Figures 3.18, 3.19, and 3.20 illustrated the small-length web buckling

specimens’ load-axial-deflection, force-lateral-deflection, and stress-strain curves. By

following the same procedure as the long-length web buckling specimen curves, the

data in these graphs were compiled. The long-length and small-length mechanical

results are depicted in Tables 3.4 to 3.7. The results of both the long-length and

small-length web specimens are discussed in the subsequent paragraphs.

103

Table 3.4 Experimental Long-Length Applied Load, Stress, and

Modulus Mechanical Results

Specimen

Name

Experimental

Maximum

Load (lb)

Experimental

Maximum

Stress (psi)

In-Plane Membrane

Modulus from Strain

Gage Graphs (psi)

Elastic Modulus

Strain Range

(x10-6

in/in)

IWB26JF 110 1600 1.0E6 (-1280,-156)

IWB27EP 380 2000 6.4E5 (-1700,-4.4)

IWB28JF 92 1300 6.9E5 (-1000,-5.4)

IWB29JF 100 1700 1.3E6 (-243,0.0)

IWB36EP 880 5100 7.0E5 (-6900,-53.4)

IWB37EP 280 3300 9.8E5 (-2440,-164)

IWB38HEP 420 4600 9.2E5 (-2080,0.0)

IWB39EP 1040 5700 6.7E5 (-3410,0.0)

IWB40EP 550 3300 8.1E5 (-2770,0.0)

IWB41HEP 400 3000 7.1E5 (-2800,0.0)

IWB42EP 120 1500 1.1E6 (-910,0.0)

IWB43JF 120 1800 1.1E6 (-980,0.0)

IWB44JF 90 1400 1.2E6 (-500,0.0)

IWB45JF 150 2100 1.6E6 (-340,0.0)

IWB46JF 140 2200 9.6E5 (-500,0.0)

Averages 320 2700 9.6E5

Standard

Deviation 300 1400 2.7E5

Coefficient

of

Variation

0.94 0.48 0.28

To start with, the long-length experimental maximum loads, lateral deflections

at bifurcation, and bifurcation strains differed significantly with coefficients of

variation of 0.94, 0.69, and -0.61, respectively. In turn, the long-length web

coefficients of variation were not as considerable for the experimental maximum

stresses (0.48) and in-plane membrane moduli (0.28). With respect to each data

category’s coefficient of variation, the small-length web values were consistently less

than the long-length web values.

104

Table 3.5 Experimental Long-Length Displacement, Deflection, and

Strain Mechanical Results

Specimen Name

Absolute Value of

Lateral Deflection

at Bifurcation from

LVDT (in)

Bifurcation Axial

Displacement from

Instron (in)

Bifurcation Strain

(in/in)

IWB26JF 0.066 0.01 -0.0013

IWB27EP 0.040 0.01 -0.0033

IWB28JF 0.015 0.02 -0.0048

IWB29JF 0.009 0.02 -0.0021

IWB36EP 0.011 0.02 -0.0079

IWB37EP 0.026 0.01 -0.0041

IWB38HEP 0.022 0.01 -0.0040

IWB39EP 0.009 0.02 -0.0090

IWB40EP 0.003 0.01 -0.0044

IWB41HEP 0.011 0.01 -0.0040

IWB42EP 0.030 0.01 -0.0015

IWB43JF 0.037 0.01 -0.0023

IWB44JF 0.039 0.01 -0.0012

IWB45JF 0.025 0.02 -0.0026

IWB46JF 0.018 0.01 -0.0030

Averages 0.024 0.01 -0.0037

Standard

Deviation 0.017 0.005 0.0023

Coefficient of

Variation 0.69 0.4 -0.61

The small-length webs’ lateral deflections at bifurcation (0.53), bifurcation strains (-

0.42), and experimental maximum loads (0.35) exhibited the largest variability, while

the experimental maximum stresses (0.19) and in-plane membrane moduli (0.30) had

not differed as much. The high variability in several of the categories may be due to

the variation in the web thicknesses. The long-length and small-length web thickness

ranges were 0.0311”-0.0960” and 0.0416”-0.0794”, and the coefficients of variations

listed in Tables 3.15 and 3.16 were 0.4852 and 0.2156, respectively.

105

Table 3.6 Experimental Small-Length Applied Load, Stress, and

Modulus Mechanical Results

Specimen

Name

Experimental

Maximum

Load (lb)

Experimenta

l Maximum

Stress (psi)

In-Plane Membrane

Modulus from Strain

Gage Graphs (psi)

Elastic Modulus

Strain Range

(x10-6

in/in)

IWB47JF 540 6100 1.8E6 (-1570,0.0)

IWB48EP 1120 6900 9.0E5 (-3180,0.0)

IWB49HEP 780 7900 1.8E6 (-560,0.0)

IWB50HEP 1040 7100 7.4E5 (-1640,0.0)

IWB52JF 580 6200 1.4E6 (-3000,0.0)

IWB53HEP 1110 7500 8.4E5 (-4420,0.0)

IWB54JF 440 4700 1.6E6 (-1090,0.0)

IWB55HEP 1130 8000 9.8E5 (-2970,-181)

IWB56EP 1330 9600 1.0E6 (-2120,0.0)

IWB57HEP 650 6300 1.6E6 (-2170,-67.8)

IWB58HEP 520 5200 1.1E6 (-2900,0.0)

IWB59HEP 1020 7600 1.2E6 (-3130,0.0)

IWB60HEP 1130 8400 9.1E5 (-1530,0.0)

IWB61JF 530 5700 1.1E6 (-770,0.0)

Averages 850 6900 1.2E6

Standard

Deviation 300 1300 3.6E5

Coefficient

of

Variation

0.35 0.19 0.30

These values – greater for the long-length webs – justified the higher variability for

these samples. In addition, length may also be the reason for the long-length being

approximately twice the small-length coefficient of variation. Web length affects the

maximum load by a power of two, so small deviations in length from the mean for the

long-length samples equates to a greater variation in experimental maximum loads.

This was depicted at the end of Section 3.2.

106

Table 3.7 Experimental Small-Length Displacement, Deflection, and

Strain Mechanical Results

Specimen Name

Absolute Value of

Lateral Deflection

at Bifurcation from

LVDT (in)

Bifurcation Axial

Displacement from

Instron (in)

Bifurcation Strain

(in/in)

IWB47JF 0.024 0.009 -0.0038

IWB48EP 0.021 0.02 -0.0040

IWB49HEP 0.003 0.01 -0.0061

IWB50HEP 0.018 0.01 -0.0092

IWB52JF 0.013 0.009 -0.0053

IWB53HEP 0.045 0.01 -0.0080

IWB54JF 0.023 0.007 -0.0044

IWB55HEP 0.025 0.01 -0.0088

IWB56EP 0.011 0.01 -0.0100

IWB57HEP 0.029 0.007 -0.0024

IWB58HEP 0.011 0.006 -0.0063

IWB59HEP 0.009 0.01 -0.0047

IWB60HEP 0.025 0.01 -0.0092

IWB61JF 0.021 0.008 -0.0030

Averages 0.020 0.01 -0.0061

Standard

Deviation 0.010 0.003 -0.0025

Coefficient of

Variation 0.53 0.3 -0.42

To be specific, the experimental maximum loads for the long-length

specimens ranged from 90 lbs to 1040 lbs. The small-length experimental maximum

loads ranged from 440 lbs to 1330 lbs. Since the small-length webs had a smaller

value for Lw in Equation 3.2, the buckling loads were larger. The maximum and

minimum lateral deflection at bifurcation values for long-length webs were 0.003 and

0.066 inches, respectively. The small-length lateral deflections at bifurcation ranged

from 0.003 to 0.045 inches. The lateral deflections at bifurcation were larger for the

long-length web buckling specimens than for the small-length samples. The

experimental maximum stresses, prior to categorizing the failure mode for each

107

specimen, were not congruent between the long-length and small-length web

specimens. The 2700 psi ± 1400 psi and 6900 psi ± 1300 psi were the average long-

length and small-length experimental maximum stresses, respectively. Although the

long-length and small-length maximum stresses were inconsistent, the experimental

in-plane membrane moduli from the strain gage graphs were comparable. The

average in-plane membrane modulus for the long-length webs (9.6E5 psi ± 2.7E5 psi)

was approximately ¾ the small-length web average modulus amount (1.2E6 psi ±

3.6E5). As a result, the long-length and small-length web material compositions were

similar. In Section 3.6 Critical Beam Buckling Analysis, the buckling loads will be

compared to theoretical simply-supported and clamped-clamped buckling loads.

Additionally, the theoretical and experimental maximum compression strengths for an

E-glass laminate are described in Section 3.8.

To explain the following tables, Tables 3.8 and 3.9 list the ε values from

ASTM D 3410 and the computed percent bending of each web buckling specimen.

Strain values ε1, ε2, and εavg, taken at the midpoint of the stress-strain curve linear-

elastic region based on ASTM specifications, were from strain gage 1, strain gage 2,

and the average of the strain gages, respectively. Equation 3.3 from ASTM D 3410

shows the percent bending formula.

Percent Bending = (ε_1-ε_2)/ε_avg *100 (3.3)

108

Table 3.8 Long-Length Percent Bending Calculations

Specimen Epsilon_1

(x106 in/in)

Epsilon_2

(x106 in/in)

Epsilon_Avg

(x106 in/in)

Percent

Bending

IWB26JF -1300 210 -560 270%

IWB27EP -1110 -560 -850 65%

IWB28JF -710 -270 -500 88%

IWB29JF -180 -60 -120 100%

IWB36EP -3190 -3690 -3490 14%

IWB37EP -1820 -470 -1140 118%

IWB38HEP -1050 -1030 -1040 2%

IWB39EP -1760 -1670 -1710 5%

IWB40EP -1680 -1090 -1390 42%

IWB41HEP -1140 -1680 -1400 39%

IWB42EP -560 -360 -460 43%

IWB43JF -230 -750 -490 106%

IWB44JF -90 -820 -450 162%

IWB45JF -240 -110 -170 76%

IWB46JF -280 -220 -250 24%

Averages -1020 -840 -930 77%

Standard

Deviation 850 960 860 70%

Coefficient of

Variation -0.83 -1.14 -0.92 0.91

This value denotes the degree of bending seen by the fiberglass composite web. As

seen in Tables 3.8 and 3.9, the strain values exhibited significant variation for both

long-length and small-length webs. The percent bending results were especially

scattered with standard deviations close to their averages. Specimens IWB26JF

(270%), IWB44JF (162%), and IWB54JF (133%) had the greater percent bending due

to the observable difference between their ε1 and ε2 values, which were 1090

microstrain, 730 microstrain, and 730 microstrain, respectively.

109

Table 3.9 Small-Length Percent Bending Calculations

Specimen Epsilon_1

(x106 in/in)

Epsilon_2

(x106 in/in)

Epsilon_Avg

(x106 in/in)

Percent

Bending

IWB47JF -500 -1080 -790 73%

IWB48EP -1780 -1420 -1590 23%

IWB49EP -290 -270 -280 7%

IWB50HEP -920 -710 -820 26%

IWB52JF -1220 -1770 -1500 37%

IWB53HEP -1710 -2730 -2210 46%

IWB54JF -190 -920 -550 133%

IWB55HEP -1350 -1430 -1390 6%

IWB56EP -1180 -940 -1060 23%

IWB57HEP -770 -1340 -1050 54%

IWB58HEP -1160 -1730 -1450 39%

IWB59HEP -1230 -1940 -1570 45%

IWB60HEP -710 -850 -770 18%

IWB61JF -570 -220 -390 90%

Averages -970 -1240 -1100 44%

Standard

Deviation 490 680 540 35%

Coeffici

ent of

Variati

on

-0.51 -0.55 -0.49 0.79

These three specimens’ graphs initially exhibited divergent strain gages 1 and

2 curves. The large percent bending was most likely due to the web bifurcation

mechanism. If these three percent bending values were removed from the standard

deviation computations, the coefficients of variation would be greatly reduced. In

addition, the average percent bending for the small-length webs was approximately

9/16 of the long-length webs’ average value. With all things being equal, this was

qualitatively due to the longer webs lateral deflecting more than the shorter webs.

Accordingly, a theoretical quantitative analysis was performed to categorize

the web buckling specimens’ failure mechanisms using the percent bending data. The

two mechanisms – mentioned in Section 3.1 – for the web were in-plane compression

110

loading to failure and non-linear buckling. This was executed prior to the theoretical

critical buckling analyses in Section 3.6, Southwell Plots in Section 3.7, and E-glass

composite web compression strength investigations in Section 3.8. From Tables 3.8

and 3.9, specimens IWB38HEP, IWB39EP, IWB49EP, and IWB55HEP demonstrated

percent bending values below 10%. Additionally, IWB36EP and IWB60HEP

exhibited percent bending results of 14% and 18%, respectively. Based on ASTM D

3410 specifications, a tested sample which had a computed percent bending less than

10% was deemed to have failed in axial compression. This theory may be applied to

specimens that exhibited percent bending values close to 10%. As a result, specimens

IWB36EP, IWB38HEP, IWB39EP, IWB49EP, IWB55HEP, and IWB60HEP may

have not buckled with respect to their percent bending values. These specimens’

strain gages 1 and 2 curves in the linear-elastic region were relatively collinear. The

bifurcation/failure modes will be refined in the subsequent buckling analysis sections.

The following gives the maximum compression stress ranges. For the long-

length webs, the experimental stress range was between 1300 psi and 5700 psi.

Appropriately, specimens IWB28JF (0.0354”) and IWB44JF (0.0311”), the lower

stress range bounds, had relatively thinner webs compared to the other specimens.

Stress is inversely proportional to thickness. The small-length webs’ experimental

stress range was between 4700 psi and 9600 psi. The web thicknesses for the small-

length webs’ lower bounds IWB54JF and IWB61JF were relatively thin at 0.0443”

and 0.0435”, respectively. For the upper bounds, the long-length webs were more

consistent than the small-length specimens. The thicker long-length webs IWB36EP

(0.0903”) and IWB39EP (0.0924”) had experimental maximum stresses of 5100 psi

and 5700 psi, respectively. Unfortunately, specimen IWB27EP, which had the

111

thickest long-length web of 0.0960 inches, had an experimental stress of only 2000

psi. This opposed the long-length trend. The small-length specimens, however, did

not exhibit a similar thickness-experimental-maximum-stress trend. The small-length

upper bound web thicknesses were 0.0794” for IWB48EP and 0.0699” for

IWB53HEP. These webs only had stresses of 6900 psi for the thickest specimen and

7500 psi for the second thickest web. The subsequent section calculates the bending

stiffnesses of the web buckling specimens, and the failure mode of each web buckling

specimen will be completely investigated in the Sections 3.6 to 3.8.

3.5 CMAP

The Composite Materials Analysis of Plates (CMAP) Graphical User Interface

(GUI) software package created by Dr. John W. Gillespie, Jr. and Dr. John Tierney

was used to determine each web buckling specimen’s effective properties. The

material properties of the E-glass fiber and vinyl ester resin matrix were inputted into

the CMAP Microply form. The vinyl ester resin matrix properties shown in Table 1.1

were taken from the manufacturer. The E-glass fiber properties used in the CMAP

Microply form – obtained from the CES Selector 4.5 software created by Granta

Design Limited – are in the following table. Table 3.11 shows the E-glass composite

lamina input mechanical values after micromechanics was performed, and Table 3.12

gives the assumed EP lamina properties used for the EP and HEP web samples.

112

Table 3.10 E-Glass Fiber Properties [4]

Elastic Modulus (psi) Shear Modulus (psi) Poisson’s Ratio

1.044E7 4.351E6 0.21

Table 3.11 E-Glass – Vinyl Ester Resin Composite Lamina Properties

E1 (psi) E2 (psi) G12 (psi) G23 (psi) ν12 Vf

3.398E6 1.045E6 3.259E5 3.058E5 0.3307 29%

Table 3.12 Encrusted Polymer (EP) Isotropic Lamina Properties [1]

E1 (psi) E2 (psi) G12 (psi) G23 (psi) ν12

5.22E5 5.22E5 1.890E5 1.890E5 0.38

Since the Encrusted Polymer lamina was decidedly composed of the vinyl ester resin

matrix, the EP was assumed to be isotropic [44]. Fiber Volume Fraction Vf – an

examination was executed for the web and reviewed in the successive paragraphs –

was obtained from Table 3.14.

The fiber volume fraction value, necessary to completely define the composite

E-glass webs, was determined by experimentally executing a resin burn-off test.

Figure 3.1(a) shows a fiber volume fraction coupon.

113

Table 3.13 Dimensions of Fiber Volume Fraction Coupons

Coupon

Number

Coupon

Name

Thickness

(in)

Thickness

Standard

Deviation

(in)

Length

(in)

Width

(in)

Density

(pci)

1 FVFW29 0.0263 8.56E-4 0.7810 1.0440 0.0688

2 FVFW30 0.0262 8.51E-4 0.8565 1.0350 0.0706

3 FVFW31 0.0270 9.26E-4 1.0175 0.8115 0.0710

4 FVFW32 0.0257 1.51E-3 0.8435 1.0545 0.0680

5 FVFW33 0.0253 8.90E-4 0.8120 1.0140 0.0685

6 FVFW34 0.0190 8.50E-4 0.8565 1.0240 0.0683

7 FVFW38 0.0180 1.14E-3 0.8555 1.0400 0.0711

Average 0.0695

Standard Deviation 1.374E-3

Coefficient of Variation 0.0198

Table 3.14 Summary of Fiber Volume Fraction Experiment

Number of

Coupon

Coupon

Name

Mass of

Coupon (g)

Mass of

Fiber (g)

Mass of

Matrix (g)

Fiber Volume

Fraction Vf (%)

1 FVFW29 0.669 0.309 0.360 29.3

2 FVFW30 0.742 0.344 0.398 29.4

3 FVFW31 0.717 0.344 0.373 30.8

4 FVFW32 0.705 0.330 0.375 29.8

5 FVFW33 0.646 0.302 0.344 29.7

6 FVFW34 0.516 0.232 0.284 28.3

7 FVFW38 0.515 0.234 0.281 28.7

29.4

0.823

0.028

Average Fiber Volume Fraction Vf (%)

Standard Deviation Fiber Volume Fraction Vf (%)

Coefficient of Variation of Fiber Volume Fraction Vf

Following ASTM D 2584 Ignition Loss of Cured Reinforced Resins, seven different

web sections were weighed and then heated in a crucible to 1000oF in order to burn

off the resin-infused web laminate. Table 3.13 details the fiber volume fraction

114

coupon dimensions and densities. The density column will be used in Chapter 5. The

seven coupons were compliant with ASTM standards measuring approximately 1 inch

by 13/16 inches by 1/64 inches. Notably, the thicknesses were measured 10 times per

coupon with digital calipers prior to resin burn-off. The measured masses and

computed fiber volume fraction for the seven web coupons are displayed in Table

3.14. After burn-off, each coupon was weighed to determine the percentage of fiber

in the composite. Figure 3.1(b) illustrates a coupon after resin burn-off, and Figure

3.21 exemplifies the web core preform – with the unsymmetric ±45o laminate between

the foam core sections – prior to resin infusion. The coupons after burn-off and E-

glass webs prior to resin infusion were visually similar. The average fiber volume

fraction was 29.4%. As seen in the preceding table, the fiber volume fraction standard

deviation and coefficient of variation were relatively small compared to the average.

This ensured that the fiber volume fraction results were accurate.

Figure 3.21 Web Core Preform Prior to VARTM

115

Back to the CMAP program after the Micromechanics section, each composite

web laminate, in the web buckling examinations, was broken down into specific

laminae. As previously stated, each web was comprised of 4 E-glass layers with

infused vinyl ester resin.

Table 3.15 Long-Length Web Laminates’ Input in CMAP

Web Buckling

Specimens

Single EP Thickness

per Side (in)

Thickness of Single

E-Glass Lamina (in)

Total Thickness of

Web Laminate: bw (in)

IWB26JF 0 0.0086 0.0345

IWB27EP 0.032 0.008 0.0960

IWB28JF 0 0.0089 0.0354

IWB29JF 0 0.0075 0.0299

IWB36EP 0.0305 0.008 0.0903

IWB37EP 0.006 0.008 0.0440

IWB38HEP 0.0149 0.008 0.0469

IWB39EP 0.0302 0.008 0.0924

IWB40EP 0.0246 0.008 0.0812

IWB41HEP 0.0336 0.008 0.0656

IWB42EP 0.0035 0.008 0.0390

IWB43JF 0 0.008 0.0318

IWB44JF 0 0.0078 0.0311

IWB45JF 0 0.0083 0.0331

IWB46JF 0 0.008 0.0323

Average - 0.008 0.0522

Standard

Deviation - 0.0003 0.0253

Coefficient of

Variation 0.04 0.4852

In addition, the EP and HEP samples consisted of encrusted polymer layers adhered to

the composite web. The laminae thicknesses – including the encrusted polymer layers

– were listed in Tables 3.15 and 3.16 for the long-length and small-length webs.

116

Table 3.16 Small-Length Web Laminates’ Input in CMAP

Web Buckling

Specimens

Single EP Thickness

per Side (in)

Thickness of Single

E-Glass Lamina (in)

Total Thickness of

Web Laminate: bw (in)

IWB47JF 0 0.0104 0.0416

IWB48EP 0.0237 0.008 0.0794

IWB49EP 0.0098 0.008 0.0516

IWB50HEP 0.0369 0.008 0.0689

IWB52JF 0 0.0109 0.0434

IWB53HEP 0.0379 0.008 0.0699

IWB54JF 0 0.0111 0.0443

IWB55HEP 0.0342 0.008 0.0662

IWB56EP 0.0168 0.008 0.0655

IWB57HEP 0.0177 0.008 0.0497

IWB58HEP 0.0158 0.008 0.0478

IWB59HEP 0.0294 0.008 0.0614

IWB60HEP 0.0310 0.008 0.0630

IWB61JF 0 0.0109 0.0435

Average - 0.009 0.0569

Standard

Deviation - 0.001 0.0123

Coefficient of

Variation 0.15 0.2156

The EP, HEP, and JF samples had two layers of adhered encrusted polymer, one layer

of adhered encrusted polymer, and no layers of adhered encrusted polymer,

respectively.

Next, the theoretical mechanical properties for each web were recorded from

CMAP. Tables 3.17 and 3.18 list the long-length and small-length laminate

mechanical properties. E_x, G_xy, G_xz, and v_xy were the In-Plane Elastic

Modulus, Shear Modulus in the XY-plane, Interlaminar Shear Modulus, and Poisson’s

Ratio in the XY-plane. The measured thicknesses and previous material properties

were inputted into CMAP to determine the mechanical properties.

117

Table 3.17 Effective Long-Length Web Laminate Mechanical Properties

E_x (psi) G_xy (psi) G_xz (psi) v_xy

IWB26JF 1.035E6 9.183E5 3.159E5 0.588

IWB27EP 7.079E5 4.476E5 2.182E5 0.508

IWB28JF 1.035E6 9.183E5 3.159E5 0.588

IWB29JF 1.035E6 9.183E5 3.159E5 0.588

IWB36EP 7.186E5 4.633E5 2.203E5 0.513

IWB37EP 9.038E5 7.322E5 2.670E5 0.566

IWB38HEP 8.342E5 5.676E5 2.603E5 0.532

IWB39EP 7.147E5 5.462E5 2.195E5 0.511

IWB40EP 7.392E5 4.935E5 2.246E5 0.521

IWB41HEP 7.154E5 3.711E5 2.350E5 0.477

IWB42EP 9.489E5 7.962E5 2.819E5 0.574

IWB43JF 1.035E6 9.183E5 3.159E5 0.588

IWB44JF 1.035E6 9.183E5 3.159E5 0.588

IWB45JF 1.035E6 9.183E5 3.159E5 0.588

IWB46JF 1.035E6 9.183E5 3.159E5 0.588

Table 3.18 Effective Small-Length Web Laminate Mechanical Properties

E_x (psi) G_xy (psi) G_xz (psi) v_xy

IWB47JF 1.035E6 9.183E5 3.159E5 0.588

IWB48EP 7.438E5 5.002E5 2.255E5 0.523

IWB49EP 8.518E5 6.576E5 2.517E5 0.555

IWB50HEP 7.035E5 3.549E5 2.323E5 0.471

IWB52JF 1.035E6 9.183E5 3.159E5 0.588

IWB53HEP 7.003E5 3.506E5 2.316E5 0.469

IWB54JF 1.035E6 9.183E5 3.159E5 0.588

IWB55HEP 7.131E5 3.679E5 2.345E5 0.476

IWB56EP 7.865E5 5.628E5 2.350E5 0.537

IWB57HEP 8.084E5 5.208E5 2.549E5 0.521

IWB58HEP 8.255E5 5.516E5 2.585E5 0.528

IWB59HEP 7.334E5 3.970E5 2.390E5 0.486

IWB60HEP 7.261E5 3.863E5 2.374E5 0.482

IWB61JF 1.035E6 9.183E5 3.159E5 0.588

The effective shear modulus in the XZ-plane was figured using the appendix

of the “Evaluation of the IITRI Compression Test Method for Stiffness and Strength

118

Determination” article. Notably, the JF samples had congruent elastic moduli, shear

moduli, and Poisson’s Ratio since they all had the same E-glass cross-section. The

web thicknesses did not influence these mechanical values. In addition, the elastic

moduli for the JF webs were different than the EP and HEP elastic moduli. Since the

EP and HEP webs exhibited smaller elastic moduli than the JF webs, the encrusted

polymer layers significantly affected the elastic modulus of the web laminate.

Table 3.19 Long-Length Elastic Moduli Comparison

Specimens

Elastic Modulus Values (psi)

Percent Difference Experimental from

Strain Gages Theoretical

IWB26JF 1.0E6 1.035E6 -4%

IWB27EP 6.4E5 7.079E5 -11%

IWB28JF 6.9E5 1.035E6 -50%

IWB29JF 1.3E6 1.035E6 20%

IWB36EP 7.0E5 7.186E5 -3%

IWB37EP 9.8E5 9.038E5 8%

IWB38HEP 9.2E5 8.342E5 9%

IWB39EP 6.7E5 7.147E5 -7%

IWB40EP 8.1E5 7.392E5 9%

IWB41HEP 7.1E5 7.154E5 -1%

IWB42EP 1.1E6 9.489E5 14%

IWB43JF 1.1E6 1.035E6 6%

IWB44JF 1.2E6 1.035E6 14%

IWB45JF 1.6E6 1.035E6 35%

IWB46JF 9.6E5 1.035E6 8%

Absolute Value Average 13%

Absolute Value Standard Deviation 13%

119

Table 3.20 Small-Length Elastic Moduli Comparison

Specimen

Elastic Modulus Values (psi) Percent

Difference Experimental from

Strain Gages Theoretical

IWB47JF 1.8E6 1.035E6 43%

IWB48EP 9.0E5 7.438E5 17%

IWB49EP 1.8E6 8.518E5 52%

IWB50HEP 7.4E5 7.035E5 5%

IWB52JF 1.4E6 1.035E6 26%

IWB53HEP 8.4E5 7.003E5 17%

IWB54JF 1.6E6 1.035E6 35%

IWB55HEP 9.8E5 7.131E5 27%

IWB56EP 1.0E6 7.865E5 21%

IWB57HEP 1.6E6 8.084E5 49%

IWB58HEP 1.1E6 8.255E5 25%

IWB59HEP 1.2E6 7.334E5 39%

IWB60HEP 9.1E5 7.261E5 20%

IWB61JF 1.1E6 1.035E6 6%

Absolute Value Average 27%

Absolute Value Standard Deviation 15%

The preceding tables compared the experimental and CMAP theoretical elastic

modulus values for the long-length and small-length webs. The averages and standard

deviations were computed with respect to the absolute values of the percent

differences. The experimental values were figured by using the EasyPlot software

program slope function, which were originally listed in Tables 3.4 and 3.6. The

theoretical CMAP elastic modulus values E_x were given in Tables 3.17 and 3.18. As

seen from the previous tables, the experimental and theoretical values were relatively

similar with the averages being 13% and 27% for the long-length and small-length

web buckling specimens, respectively. Since the web thicknesses varied

considerably, detailed in Section 3.4, the percent difference standard deviations for

the long-length and small-length webs were relatively high.

120

To be specific, several webs had percent differences close to 0%; there was

negligible difference between the theoretical and experimental values. This data

verified the accuracy of the in-plane elastic moduli models. Consequently, specimens

IWB26JF, IWB36EP, and IWB41HEP exhibited percent differences of -4%, -3%, and

-1% in Tables 3.19 and 3.20.

Table 3.21 Stiffness Matrix Values

On the other hand, the following samples had absolute values of their percent

differences greater than 40%: IWB28JF, IWB47JF, IWB49EP, and IWB57HEP. For

reasons not understood in this research due to time constraints, the elastic moduli for

these webs were not modeled accurately.

Long-Length Specimens Small-Length Specimens

Specimen A_xx (x10

4

lb/in)

D_xx (lb-

in) Specimen

A_xx (x104

lb/in)

D_xx (lb-

in)

IWB26JF 5.690 5.611 IWB47JF 6.881 9.923

IWB27EP 9.198 47.83 IWB48EP 8.185 28.30

IWB28JF 5.889 6.219 IWB49EP 6.489 9.836

IWB29JF 4.962 3.722 IWB50HEP 7.544 30.85

IWB36EP 8.856 40.41 IWB52JF 7.212 11.42

IWB37EP 6.025 7.182 IWB53HEP 7.605 32.21

IWB38HEP 6.202 9.950 IWB54JF 7.344 12.07

IWB39EP 8.978 42.96 IWB55HEP 7.380 27.37

IWB40EP 8.295 30.07 IWB56EP 7.343 17.20

IWB41HEP 7.343 26.63 IWB57HEP 6.373 11.71

IWB42EP 5.720 5.867 IWB58HEP 6.257 10.49

IWB43JF 5.293 4.517 IWB59HEP 7.087 21.84

IWB44JF 5.161 4.186 IWB60HEP 7.184 23.59

IWB45JF 5.492 5.044 IWB61JF 7.212 11.42

IWB46JF 5.293 4.517

121

Conclusively, the stiffness values from CMAP are shown in Table 3.21.

These tables include the in-plane stiffness A_xx, and bending stiffness D_xx from

CMAP. The numbers from the bending-stretching coupling matrix were not listed.

Since the E-glass composite web was an unsymmetric laminate, a significant amount

of out-of-plane macroscopic deformation may have occurred from the applied axial

load. Due to research time constraints, the bending-stretching coupling matrix values

were not incorporated into this investigation. To briefly review the previous table, the

thicker webs exhibited higher bending stiffness numbers since the bending stiffness is

proportional to the thickness cubed [44]. The JF web bending stiffnesses were on

average approximately 7 lb-in, while the EP and HEP web bending stiffnesses were

an average of 24 lb-in. Calculation of the web buckling loads in Section 3.6 will

utilize the preceding tabulated values.

3.6 Critical Beam Buckling Analysis

The Critical Beam Buckling Analysis was the central issue of the web

buckling analyses. The theoretical simply-supported (SS) load for each web was

calculated using Equations 3.1 and 3.2, while the clamped-clamped (CC) value was

figured by multiplying the calculated load by 4 [26]. Due to the complex nature of the

web-flange interface of the specimens, an exact calculated web buckling load was not

determined in this investigation.

122

Table 3.22 Long-Length Web Buckling Loads

Specimen

Name

Calculated SS

Buckling Load (lb)

Experimental

Maximum Load (lb)

Calculated CC

Buckling Load (lb)

IWB26JF 60.11 110 240.4

IWB27EP 524.9 380 2100

IWB28JF 61.80 92 247.2

IWB29JF 38.03 100 152.1

IWB36EP 400.6 880 1602

IWB37EP 72.64 280 290.6

IWB38HEP 102.2 420 408.8

IWB39EP 436.2 1040 1745

IWB40EP 311.3 550 1245

IWB41HEP 275.4 400 1102

IWB42EP 69.13 120 276.5

IWB43JF 53.81 120 215.3

IWB44JF 48.64 90 194.5

IWB45JF 56.64 150 226.6

IWB46JF 47.18 140 188.7

Table 3.23 Small-Length Web Buckling Loads

Specimen

Name

Calculated SS

Buckling Load (lb)

Experimental

Maximum Load (lb)

Calculated CC

Buckling Load (lb)

IWB47JF 221.2 540 884.7

IWB48EP 575.9 1120 2304

IWB49EP 194.8 780 779.2

IWB50HEP 660.9 1040 2644

IWB52JF 254.4 580 1018

IWB53HEP 682.7 1110 2731

IWB54JF 260.0 440 1040

IWB55HEP 599.7 1130 2399

IWB56EP 382.8 1330 1531

IWB57HEP 257.1 650 1028

IWB58HEP 229.3 520 917.3

IWB59HEP 494.4 1020 1978

IWB60HEP 520.9 1130 2084

IWB61JF 247.9 530 991.8

123

The SS and CC were the minimum and maximum buckling values, respectively, for

each web specimen. The measured dimensions from Tables 3.2 and 3.3, the bending

stiffnesses from Table 3.21, and the interlaminar shear moduli from Tables 3.17 and

3.18 were utilized for the calculations. Tables 3.22 and 3.23 show the calculated

theoretical and experimental loads of the long-length and small-length webs. The

experimental maximum loads from Tables 3.4 and 3.6 are included in the previous

tables.

Generally, the webs were encompassed by their theoretical SS and CC

buckling bounds; 13 out of 15 for the long-length samples and 13 out of 14 for the

small-length samples. Web specimens IWB27EP, IWB38HEP, and IWB49EP were

the only web specimens that had experimental maximum load values not

encompassed by the simply-supported clamped-clamped web buckling range. The

experimental maximum load of IWB27EP (380 lbs) was less than its calculated

buckling range, the IWB38HEP experimental maximum load (420 lbs) was greater

than its calculated buckling limits, and the experimental maximum load of IW49EP

(780 lbs) was also higher than its calculated buckling range. The webs IWB38HEP

and IWB49EP surpassed their buckling limits, which meant that they may have failed

in axial compression. The subsequent sections will verify this.

In addition, the experimental maximum loads were relatively close to the

median of their SS and CC theoretical buckling loads for most of the long-length and

small-length webs. Table 3.24 lists the median between the theoretical SS and CC

buckling loads, or twice the SS buckling loads.

124

Table 3.24 Long-Length and Small-Length Differences between

Experimental and Calculated Loads

Long-Length Webs Small-Length Webs

Specimen

Name

Median

Between SS

and CC (lb)

Over /

Under

Specimen

Name

Median

Between SS

and CC (lb)

Over /

Under

IWB26JF 150 0.73 IWB47JF 550 0.98

IWB27EP 1300 0.29 IWB48EP 1400 0.80

IWB28JF 160 0.58 IWB49EP 490 1.59

IWB29JF 95 1.05 IWB50HEP 1700 0.61

IWB36EP 1000 0.88 IWB52JF 640 0.91

IWB37EP 180 1.56 IWB53HEP 1700 0.65

IWB38HEP 260 1.62 IWB54JF 650 0.68

IWB39EP 1100 0.95 IWB55HEP 1500 0.75

IWB40EP 780 0.71 IWB56EP 960 1.39

IWB41HEP 690 0.58 IWB57HEP 640 1.02

IWB42EP 170 0.71 IWB58HEP 570 0.91

IWB43JF 135 0.92 IWB59HEP 1200 0.85

IWB44JF 120 0.75 IWB60HEP 1300 0.87

IWB45JF 142 1.07 IWB61JF 620 0.85

IWB46JF 120 1.17

Average - 0.90 Average - 0.92

Standard

Deviation

- 0.36

Standard

Deviation

- 0.27

Also, the over/under values are given, which were the division of the experimental

maximum and the median loads. If the experimental load is greater than the median

load, the over/under is greater than unity, while the over/under is less than one when

the experimental load is less than the median load. The long-length (36%) and small-

length (27%) standard deviations were compatible. In general, the long-length and

small-length webs had similar web-flange interfaces, denoted as the web supports in

this chapter. On average for the long-length and small-length webs, the quotients of

experimental maximum loads vs. calculated SS buckling loads were nearly congruent.

Therefore, the long-length and small-length web-facesheet supports were

125

quantitatively similar. Notably, the 4 greatest over/under values were observed in

specimens IWB56EP (1.39), IWB37EP (1.56), IWB49EP (1.59), and IWB38HEP

(1.62). The last 2 webs had surpassed their SS and CC buckling ranges.

To conclude, from these calculations only 3 webs did not exhibit buckling.

These were IWB27EP, IWB38HEP, and IWB49EP. Also, the web supports for the

long and small length samples were congruent. A more accurate buckling analysis

was performed on the webs in the next section.

3.7 Southwell Plots

Another method was utilized to determine the critical buckling load of

columns. This graphical analysis was applied to imperfect columns [46]. “Due to

imperfections in manufacturing or application of the load, a column will never

suddenly buckle, instead it begins to bend” [26]. This bending is evident in the force-

lateral-deflection curves in Figures 3.16 and 3.19 [26]. As soon as the force was

applied, most of these webs had begun to bend [26]. This method was designed by R.

V. Southwell used for columns with “unavoidable imperfections of workmanship,”

which as a result yielded a non-linear curve in the load-axial-displacement graph [46].

This graphical method was compared to the preceding Critical Buckling Analysis

performed in the previous section. The computations included in Figures 3.23 and

3.24 were employed to determine the Critical Buckling Load of the specimen

described in the referenced Southwell and Leal papers.

The theoretical method utilized to form the Southwell Plots will be explained.

The load-displacement curve must be transformed by changing the ordinate axis to the

126

formula axial displacement Δ divided by applied load P [18]. The abscissa axis

remained as the axial displacement Δ creating a graph similar to the example shown in

Figure 3.22 [18].

Figure 3.22 Southwell Plot [18]

Figures 3.23 and 3.24 are the Southwell Plots of the long-length and small-length web

buckling specimens from the Instron load-axial-displacement curves. The axial-

displacement curves taken from Figures 3.15 and 3.18 were modified to create the

Southwell Plots. This method, considering the column did not contain any

“nonlinearities at low loads” or “errors in the deflection-scale zero”, formed a

Southwell Plot curve [46]. By changing coordinates, a load-axial-displacement curve,

with manufacturing or loading inaccuracies, may be transformed into a straight line;

the slope being a measure of the column’s critical buckling load [46]. Utilizing the

EasyPlot slope function, the slope of the line was figured and then compared to the

experimental maximum load by the simple formula shown in Figure 3.22. The

approximate location at which the load-axial-displacement curve reached its

127

maximum point and the experimental maximum loads from Tables 3.4 and 3.6 were

both included.

Moreover, several of the curves did not exhibit a definitive linear section, so

an accurate slope was not figured for these Southwell Plots. In addition, the curves

that exhibited a non-linear irregularity in which the curve skipped to another point

were not viable specimens for the Southwell Plot investigation. The following were

the non-viable long-length and small-length webs: IWB29JF, IWB36EP, IWB37EP,

IWB38HEP, IWB39EP, IWB40EP, IWB41HEP, IWB48EP, IWB50HEP, IWB52JF,

IWB53HEP, IWB55HEP, IWB56EP, IWB57HEP, IWB59HEP, and IWB60HEP.

From the long-length and small-length specimens there were 7 out of 15 and 9 out of

14, respectively, that exhibited a non-viable Southwell Plot response. As a result,

these curves were not used to compute a Southwell Plot buckling load.

Corresponding to their load-axial-displacement curves, these 16 webs did not exhibit

a linear horizontal or semi-horizontal region after reaching their maximum load. For

example, the load vs. axial displacement curve for IWB40EP shown in Figure 3.15

had a sharp decline immediately after reaching its maximum load, which correlated to

a sharp Southwell Plot curve that had no distinct linear region.

128

Figure 3.23 Long-Length Southwell Plots

0

1x10-4

2x10-4

3x10-4

4x10-4

5x10-4

0 0.01 0.02 0.03 0.04 0.05

y = +0.0106244x1 -1.54993E-5

IWB26JF_South

MAXIMUMPOINT

Southwell Plots Theoretical Buckling Load = 1/0.011 = 91 lbs

Experimental MaximumLoad = 110 lb

Displacement, (in)

Dis

pla

cem

ent/Load, /P

(in

/lb)

IWB26JF: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

0

1x10-5

2x10-5

3x10-5

4x10-5

5x10-5

0 0.002 0.004 0.006 0.008 0.010 0.012 0.014

y = +0.00273740x1 -1.45993E-6

IWB27EP_South

MAXIMUMPOINT

Southwell Plots Theoretical Buckling Load = 1/0.0027 = 370 lbs

Experimental MaximumLoad = 380 lb

Displacement, (in)

Dis

pla

cem

ent/Load, /P

(in

/lb)

IWB27EP: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

0

0.2x10-4

0.4x10-4

0.6x10-4

0.8x10-4

1.0x10-4

0 0.002 0.004 0.006 0.008 0.010

y = +0.0104188x1 +3.07039E-6

IWB28JF_South

MAXIMUMPOINT

Southwell Plots Theoretical Buckling Load = 1/0.010 = 100 lbs

Experimental MaximumLoad = 92 lb

Displacement, (in)

Dis

pla

cem

ent/Load, /P

(in

/lb)

IWB28JF: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

0

0.5x10-4

1.0x10-4

1.5x10-4

2.0x10-4

2.5x10-4

3.0x10-4

0 0.004 0.008 0.012 0.016 0.020

IWB29JF

MAXIMUMPOINT

Experimental Maximum Load = 100 lb

Displacement, (in)

Dis

pla

cem

en

t/L

oa

d, /P

(in

/lb

)

IWB29JF: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

0

0.5x10-5

1.0x10-5

1.5x10-5

2.0x10-5

2.5x10-5

3.0x10-5

0 0.003 0.006 0.009 0.012 0.015

IWB36EP_South

Experimental MaximumLoad = 880 lb

MAXIMUMPOINT

Displacement, (in)

Dis

pla

cem

ent/Load, /P

(in

/lb)

IWB36EP: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

0

1x10-5

2x10-5

3x10-5

4x10-5

5x10-5

0 0.002 0.004 0.006 0.008 0.010 0.012 0.014

IWB37EP_South

MAXIMUMPOINT

Experimental Maximum Load = 280 lb

Displacement, (in)

Dis

pla

cem

ent/Load, /P

(in

/lb)

IWB37EP: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

129

Figure 3.23 Continued

0

1x10-5

2x10-5

3x10-5

4x10-5

5x10-5

6x10-5

7x10-5

8x10-5

0 0.003 0.006 0.009 0.012 0.015 0.018 0.021

IWB38HEP_South

MAXIMUMPOINT

Experimental Maximum Load = 420 lb

Displacement, (in)

Dis

pla

cem

ent/Load, /P

(in

/lb)

IWB38HEP: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

0

0.5x10-4

1.0x10-4

1.5x10-4

2.0x10-4

2.5x10-4

3.0x10-4

0 0.005 0.010 0.015 0.020 0.025 0.030

IWB39EP_South

MAXIMUMPOINT

Experimental Maximum Load = 1040 lb

Displacement, (in)

Dis

pla

cem

ent/Load, /P

(in

/lb)

IWB39EP: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

0

0.3x10-4

0.6x10-4

0.9x10-4

1.2x10-4

1.5x10-4

1.8x10-4

2.1x10-4

2.4x10-4

2.7x10-4

0 0.003 0.006 0.009 0.012 0.015 0.018 0.021

IWB40EP_South

MAXIMUMPOINT

Experimental Maximum Load = 550 lb

Displacement, (in)

Dis

pla

cem

ent/Load, /P

(in

/lb)

IWB40EP: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

0

1x10-5

2x10-5

3x10-5

4x10-5

5x10-5

0 0.002 0.004 0.006 0.008 0.010 0.012 0.014

IWB41HEP_South

MAXIMUMPOINT

Experimental Maximum Load = 400 lb

Displacement, (in)

Dis

pla

ce

men

t/L

oa

d,

/P (

in/lb

)

IWB41HEP: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

0

0.5x10-4

1.0x10-4

1.5x10-4

2.0x10-4

2.5x10-4

0 0.005 0.010 0.015 0.020 0.025

y = +0.00889612x1 -7.86056E-6

IWB42EP_South

MAXIMUMPOINT

Southwell Plots Theoretical Buckling Load = 1/0.0089 = 110 lbs

Experimental Maximum Load = 120 lb

Displacement, (in)

Dis

pla

cem

ent/Load, /P

(in

/lb)

IWB42EP: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

0

0.5x10-4

1.0x10-4

1.5x10-4

2.0x10-4

2.5x10-4

3.0x10-4

3.5x10-4

4.0x10-4

0 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040

y = +0.00886084x1 -4.64992E-6

IWB43JF_South

MAXIMUMPOINT

Southwell Plots Theoretical Buckling Load = 1/0.0089 = 110 lbs

Experimental Maximum Load = 120 lb

Displacement, (in)

Dis

pla

cem

ent/Load, /P

(in

/lb)

IWB43JF: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

130

Figure 3.23 Continued

Likewise, these webs shared another similarity. Generally, the specimens with

a definitive Southwell Plot linear region had thinner cross-sections. On the other

hand, the webs with thicker cross-sections comprised of a greater amount of encrusted

polymer tended to not have distinctive linear regions in their Southwell Plots. This

was evident when the web thicknesses listed in Tables 3.2 and 3.3 were compared

with the Southwell Plots in this section. Length was a factor in this pattern; the long-

length and small-length webs had different bounds. This was reasonable based on the

exponential length factor in the beam buckling Equation 3.2. If a long-length web’s

thickness was greater than 0.039” resulting in 0.007” of EP (approximately 1/6 the

total web thickness), a definitive Southwell Plot linear region was not produced.

0

1x10-4

2x10-4

3x10-4

4x10-4

5x10-4

6x10-4

0 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040

y = +0.0123988x1 -1.15499E-5

IWB44JF_South

MAXIMUMPOINT

Southwell Plots Theoretical Buckling Load = 1/0.012 = 83 lbs

Experimental Maximum Load = 90 lb

Displacement, (in)

Dis

pla

cem

ent/Load, /P

(in

/lb)

IWB44JF: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

0

0.2x10-4

0.4x10-4

0.6x10-4

0.8x10-4

1.0x10-4

1.2x10-4

1.4x10-4

0 0.003 0.006 0.009 0.012 0.015 0.018 0.021 0.024

y = +0.00597005x1 -4.65643E-6

IWB45JF_South

MAXIMUMPOINT

Southwell Plots Theoretical Buckling Load = 1/0.0060 = 170 lbs

Experimental Maximum Load = 150 lb

Displacement, (in)

Dis

pla

ce

men

t/L

oa

d,

/P (

in/lb

)

IWB45JF: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

0

0.5x10-4

1.0x10-4

1.5x10-4

2.0x10-4

2.5x10-4

3.0x10-4

0 0.005 0.010 0.015 0.020 0.025 0.030

y = +0.00855805x1 -1.03834E-5

IWB46JF_South

MAXIMUMPOINT

Southwell Plots Theoretical Buckling Load = 1/0.0086 = 120 lbs

Experimental Maximum Load = 140 lb

Displacement, (in)

Dis

pla

cem

ent/Load, /P

(in

/lb)

IWB46JF: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

131

Consequently, the small-length web’s upper bound thickness – ensuring a definitive

linear region in its Southwell Plot – was 0.0478”. For any thickness greater than this,

the Southwell Plot analysis was inconclusive. The 0.0478” small-length upper bound

thickness equated to 0.0158” of EP (approximately 1/3 the total thickness). The next

paragraph discloses the four exceptions to this pattern.

With respect to the long-length specimens IWB27EP (0.0960” thick) exhibited

a distinct Southwell Plot linear region, while the graph of IWB29JF (0.0299” thick)

did not contain a distinct Southwell Plot linear region. The former and latter were

greater and less than the long-length’s upper bound, respectively. As a result, these

two samples opposed the defined pattern. There were also two small-length webs that

opposed the previously-defined Southwell Plot pattern. With respect to the thickness

upper bound of 0.0478”, IWB49EP (0.0516” thick) exhibited a definitive linear

region, while IWB52JF (0.0434” thick) did not have a definitive linear region. The

former and latter samples were greater than and less than the small-length upper

bound, opposing the web thickness pattern. To summarize, the web thickness

appeared to have an effect on its Southwell Plot shape for 14 out of 16 total webs.

To continue with this discussion, there are two possibilities for the Southwell

Plot analysis not being effective. First, a web’s composition may affect whether or

not the Southwell Plot analysis may be utilized. The encrusted polymer, being more

brittle than the E-glass vinyl ester resin composite, may have limited this graphical

analysis’ ability to figure a web’s critical buckling load.

132

Figure 3.24 Small-Length Southwell Plots

0

1x10-4

2x10-4

3x10-4

4x10-4

5x10-4

6x10-4

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

y = +0.00250492x1 -7.50945E-6

IWB47JF_South

MAXIMUMPOINT

Southwell Plots Theoretical Buckling Load = 1/0.0025 = 400 lbs

Experimental Maximum Load = 540 lb

Displacement, (in)

Dis

pla

cem

en

t/L

oa

d, /P

(in

/lb

)

IWB47JF: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

0

0.3x10-3

0.6x10-3

0.9x10-3

1.2x10-3

1.5x10-3

1.8x10-3

2.1x10-3

0 0.01 0.02 0.03 0.04 0.05 0.06

IWB48EP_South

MAXIMUMPOINT

Experimental Maximum Load = 1120 lb

Displacement, (in)

Dis

pla

cem

en

t/L

oa

d, /P

(in

/lb

)

IWB48EP: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

0

0.3x10-4

0.6x10-4

0.9x10-4

1.2x10-4

1.5x10-4

0 0.01 0.02 0.03 0.04 0.05

y = +0.00131453x1 -5.72365E-7

IWB49EP_South

MAXIMUMPOINT

Southwell Plots Theoretical Buckling Load = 1/0.0013 = 770 lbs

Experimental Maximum Load = 780 lb

Displacement, (in)

Dis

pla

cem

en

t/L

oa

d, /P

(in

/lb

)

IWB49EP: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

0

0.3x10-4

0.6x10-4

0.9x10-4

1.2x10-4

1.5x10-4

1.8x10-4

2.1x10-4

0 0.01 0.02 0.03 0.04

IWB50HEP_South

MAXIMUMPOINT

Experimental Maximum Load = 1040 lb

Displacement, (in)

Dis

pla

cem

ent/Load, /P

(in

/lb)

IWB50HEP: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

0

0.2x10-3

0.4x10-3

0.6x10-3

0.8x10-3

1.0x10-3

1.2x10-3

0 0.01 0.02 0.03 0.04 0.05

IWB52JF_South

MAXIMUMPOINT

Experimental Maximum Load = 580 lb

Displacement, (in)

Dis

pla

cem

ent/Load, /P

(in

/lb)

IWB52JF: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

0

1x10-5

2x10-5

3x10-5

4x10-5

5x10-5

6x10-5

0 0.005 0.010 0.015 0.020 0.025 0.030

IWB53HEP_South

MAXIMUMPOINT

Experimental Maximum Load = 1110 lb

Displacement, (in)

Dis

pla

cem

en

t/L

oa

d, /P

(in

/lb

)

IWB53HEP: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

133

Figure 3.24 Continued

0

0.5x10-5

1.0x10-5

1.5x10-5

2.0x10-5

2.5x10-5

3.0x10-5

0 0.002 0.004 0.006 0.008 0.010 0.012

y = +0.00273805x1 -3.42690E-6

IWB54JF_South

MAXIMUMPOINT

Southwell Plots Theoretical Buckling Load = 1/0.0027 = 370 lbs

Experimental Maximum Load = 440 lb

Displacement, (in)

Dis

pla

cem

ent/Load, /P

(in

/lb)

IWB54JF: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

0

1x10-5

2x10-5

3x10-5

4x10-5

5x10-5

0 0.005 0.010 0.015 0.020 0.025

IWB55HEP_South

MAXIMUMPOINT

Experimental Maximum Load = 1130 lb

Displacement, (in)

Dis

pla

cem

en

t/L

oa

d, /P

(in

/lb

)

IWB55HEP: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

0

0.5x10-5

1.0x10-5

1.5x10-5

2.0x10-5

2.5x10-5

3.0x10-5

0 0.003 0.006 0.009 0.012 0.015 0.018

IWB56EP_South

MAXIMUMPOINT

Experimental Maximum Load = 1330 lb

Displacement, (in)

Dis

pla

cem

en

t/L

oa

d, /P

(in

/lb

)

IWB56EP: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

0

0.2x10-4

0.4x10-4

0.6x10-4

0.8x10-4

1.0x10-4

1.2x10-4

0 0.005 0.010 0.015 0.020 0.025 0.030

IWB57HEP_South

MAXIMUMPOINT

Experimental Maximum Load = 650 lb

Displacement, (in)

Dis

pla

cem

ent/Load, /P

(in

/lb)

IWB57HEP: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

0

1x10-5

2x10-5

3x10-5

4x10-5

5x10-5

6x10-5

7x10-5

8x10-5

0 0.003 0.006 0.009 0.012 0.015 0.018 0.021

y = +0.00298349x1 -6.49838E-6

IWB58HEP_South

MAXIMUMPOINT

Southwell Plots Theoretical Buckling Load = 1/0.0030 = 330 lbs

Experimental Maximum Load = 520 lb

Displacement, (in)

Dis

pla

cem

ent/Load, /P

(in

/lb)

IWB58HEP: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

0.5x10-5

1.0x10-5

1.5x10-5

2.0x10-5

2.5x10-5

3.0x10-5

3.5x10-5

0 0.003 0.006 0.009 0.012 0.015 0.018 0.021

IWB59HEP_South

MAXIMUMPOINT

Experimental Maximum Load = 1020 lb

Displacement, (in)

Dis

pla

cem

ent/Load, /P

(in

/lb)

IWB59HEP: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

134

Figure 3.24 Continued

Southwell’s graphical method was based on Euler’s elastic column buckling analysis

[26, 46]. Consequently, the thickness of EP attached to the specific web cross-section

may affect the ductile nature of the composite web, which results in the inability to

utilize Southwell’s graphical analysis. Second, the Southwell Plots investigation does

not account for damage occurring during testing. This graphical analysis may not be

employed if the material’s elasticity is impaired [46]. Failure of the encrusted

polymer or nonlinear behavior of the E-glass composite may have affected the

specimen’s elasticity during testing causing the Southwell Plots analysis unusable

[26]. More research is required to verify this theory.

Furthermore, the experimental maximum loads and theoretical buckling loads

from the Southwell Plots are listed in Tables 3.25 and 3.26. The percent differences

between the experimental and theoretical Southwell Plot loads are also given. As

previously-mentioned, the Southwell Plot curves without a linear region were not

analyzed. The small-length webs (19% ± 13% average) had greater percent

differences than the long-length webs (10% ± 5% average). Notably, depicted in

0

1x10-5

2x10-5

3x10-5

4x10-5

5x10-5

6x10-5

7x10-5

0 0.005 0.010 0.015 0.020 0.025

IWB60HEP_South

MAXIMUMPOINT

Experimental Maximum Load = 1130 lb

Displacement, (in)

Dis

pla

cem

ent/Load, /P

(in

/lb)

IWB60HEP: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

0

0.3x10-4

0.6x10-4

0.9x10-4

1.2x10-4

1.5x10-4

1.8x10-4

0 0.01 0.02 0.03 0.04

y = +0.00217641x1 -2.61315E-6

IWB61JF_South

MAXIMUMPOINT

Southwell Plots Theoretical Buckling Load = 1/0.0022 = 450 lbs

Experimental Maximum Load = 530 lb

Displacement, (in)

Dis

pla

cem

ent/Load, /P

(in

/lb)

IWB61JF: Displacement/Load, /P (in/lb) vs. Displacement, (in) from Instron

135

Tables 3.15 and 3.16 there were 8 and 10 EP or HEP designations for the long-length

and small-length webs, respectively. As previously discussed the increase of

encrusted polymer may have affected the Southwell Plot graphical analysis. Although

it must be verified, this may be a reason for this graphical approximation only

working for 5 out of 14 small-length webs.

Table 3.25 Long-Length Southwell Plots Comparison

Specimen Experimental

Maximum Load (lb)

Theoretical Southwell

Plots Buckling Load (lb)

%

Difference

IWB26JF 110 91 17%

IWB27EP 380 370 3%

IWB28JF 92 100 -9%

IWB29JF 100 - -

IWB36EP 880 - -

IWB37EP 280 - -

IWB38HEP 420 - -

IWB39EP 1040 - -

IWB40EP 550 - -

IWB41HEP 400 - -

IWB42EP 120 110 8%

IWB43JF 120 110 8%

IWB44JF 90 83 8%

IWB45JF 150 170 -13%

IWB46JF 140 120 14%

Average 10%

Standard Deviation 5%

Additionally, the results of the two buckling analyses will be compared. The

critical beam buckling load calculation and Southwell Plot investigation were

inconclusive for some web specimens. The beam buckling computations determined

that the experimental maximum loads for specimens IWB27EP, IWB38HEP, and

IWB49EP were not encompassed by the theoretical buckling range. The former web

was less than its calculated buckling range, while the last two were higher than their

136

calculated range. Southwell Plot approximated loads along with the percent

differences when compared with the experimental maximum load will be supplied.

Table 3.26 Small-Length Southwell Plots Comparison

Specimen Experimental

Maximum Load (lb)

Theoretical Southwell

Plots Buckling Load (lb)

%

Difference

IWB47JF 540 400 26%

IWB48EP 1120 - -

IWB49EP 780 770 1%

IWB50HEP 1040 - -

IWB52JF 580 - -

IWB53HEP 1110 - -

IWB54JF 440 370 16%

IWB55HEP 1130 - -

IWB56EP 1330 - -

IWB57HEP 650 - -

IWB58HEP 520 330 37%

IWB59HEP 1020 - -

IWB60HEP 1130 - -

IWB61JF 530 450 15%

Average 19%

Standard Deviation 13%

Two out of the three specimens IWB27EP and IWB49EP had theoretical Southwell

Plot loads of 370 and 770 lbs with percent differences from their experimental loads

of 3% and 1%, respectively. Web specimen IWB38HEP, on the other hand, was not

figured in this graphic analysis since its graph was inconclusive. Specifically, the

critical beam buckling calculations qualitatively determined whether or not the web

buckling, while the Southwell Plots figured their expected buckling load.

The tables and figures in this section illustrated Southwell Plots’ ability – from

the experimental test results of an imperfect column – to estimate the buckling load of

137

a corresponding perfect column [18]. The combination of the web buckling analyses

helped to determine the bifurcation load more effectively. The Critical Beam

Buckling results determined whether or not the specimen buckled, while the

Southwell Plots discovered their approximate buckling load with relative accuracy.

3.8 Web Compression Strength Tests

Compression strength experiments were completed to ascertain the average

compressive strength and compression failure strain of the E-glass composite webs

from the aforementioned Tycor® G18 Web Core. The displacement data from these

tests were not utilized to figure modulus due to the inaccuracy of the cross-head

displacement and machine compliance. Web compression strength (WCS) specimens

were comparable to the web buckling specimens. This is due to the fact that WCS

specimens were taken from the same composite VARTM-infused web core panel

from which the web buckling specimens were originally cut. WCS investigations

were executed by following ASTM D 695. Using a milling machine, WCS specimens

were precision-machined to approximately ½-inch-wide by 3-1/8-inch-long coupons.

These coupons were positioned inside the ASTM support fixture illustrated in Figure

3.25. In addition, per ASTM D 695 standards, coupons were milled so their shorter

edges were made parallel to within 0.001 inches; ensuring that the Instron force was

applied axially.

138

Figure 3.25 ASTM D 695 Fixture

Figure 3.26 Example of Web Compression Strength Coupon

The coupons were machined by first cutting them to an approximate length

and then sanding the faces to allow for a smooth minimal-friction coupon surface that

would slide in the fixture during loading. To guarantee a smooth test and ensure the

force was applied uniformly to the coupon, the fixture was sprayed with WD-40

139

lubricant prior to loading. The Instron 5567 machine was used, the cross-head speed

was set at 0.05 in/min, and a 6000-pound load cell was utilized.

Figure 3.26 illustrates a WCS coupon through-the-thickness, and Table 3.27

gives the dimensions of the thirteen WCS coupons. To obtain accurate dimensions

throughout the specimen, each coupon’s depth and thickness were measured a

multiple of ten times, while the lengths were measured five times. The depth and

thickness of the coupon were deemed crucial. The averages and standard deviations

in Table 3.27 correlated with measuring each WCS coupon’s dimensions multiple

times. The maximum standard deviations for the coupons’ thicknesses and depths

were 0.0133” and 0.0239”, respectively. The lengths, which were paralleled utilizing

a milling machine, exhibited much smaller standard deviations (a maximum of

0.0022”). As a result, the standard deviation values were small enough to ensure a

viable examination.

To discuss Table 3.28, the web coupons were supported during testing, which

eliminated any buckling or bending that would inaccurately influence the web

compressive strength. The samples, however, tended to fail at an unacceptable

location per ASTM standards at their ends. Table 3.28 lists the location of failure for

each coupon and the calculated cross-sectional area from Table 3.27.

140

Table 3.27 Web Compression Strength Coupon Dimensions

Name Value Length (in) Depth (in) Total Thickness (in)

WCS1JF Average 3.1566 0.5313 0.0316

Standard Deviation 0.0031 0.0068 0.0027

WCS2EP Average 3.1694 0.5237 0.0411

Standard Deviation 0.0013 0.0216 0.0133

WCS3HEP Average 3.1277 0.5156 0.0441

Standard Deviation 0.0019 0.0080 0.0130

WCS4HEP Average 3.1278 0.5986 0.0596

Standard Deviation 0.0033 0.0100 0.0040

WCS5EP Average 3.1349 0.5170 0.0979

Standard Deviation 0.0021 0.0080 0.0089

WCS6HEP Average 3.1315 0.5181 0.0588

Standard Deviation 0.0050 0.0157 0.0031

WCS7EP Average 3.1381 0.5178 0.0743

Standard Deviation 0.0005 0.0149 0.0030

WCS8JF Average 3.1279 0.5215 0.0353

Standard Deviation 0.0022 0.0239 0.0037

WCS9EP Average 3.1388 0.4987 0.1157

Standard Deviation 0.0009 0.0089 0.0034

WCS10JF Average 3.1252 0.4925 0.0340

Standard Deviation 0.0010 0.0053 0.0035

WCS11EP Average 3.1388 0.4859 0.1013

Standard Deviation 0.0008 0.0111 0.0033

WCS12HEP Average 3.1338 0.4570 0.0740

Standard Deviation 0.0014 0.0105 0.0060

WCS13EP Average 3.1345 0.4986 0.0617

Standard Deviation 0.0009 0.0053 0.0024

141

Table 3.28 Web Compression Strength Failure and Area

Coupon Failure Location Cross-Sectional Area (in2)

WCS1JF End 0.0168

WCS2EP End 0.0214

WCS3HEP End 0.0227

WCS4HEP End 0.0356

WCS5EP Middle 0.0506

WCS6HEP End 0.0304

WCS7EP End 0.0385

WCS8JF End 0.0184

WCS9EP Middle 0.0577

WCS10JF Middle 0.0167

WCS11EP End 0.0492

WCS12HEP Middle 0.0338

WCS13EP End 0.0308

Table 3.29 WCS Acceptable Coupon Thicknesses (in)

Coupon Total E-glass Vinyl

Ester Resin Encrusted Polymer

WCS5EP 0.0979 0.0320 0.0660

WCS9EP 0.1157 0.0320 0.0840

WCS10JF 0.0340 0.0340 0

WCS12HEP 0.0740 0.0320 0.0420

Average 0.0804 - -

Standard Deviation 0.0353 - -

The web coupons, which failed at their ends, were deemed unsuitable since the

“external loads…cause[d] localized distortions” [26]. Specimens WCS1JF, WCS2EP,

WCS3HEP, WCS4HEP, WCS6HEP, WCS7EP, WCS8JF, WCS11EP, and WCS13EP

were decided to be unsuitable. Table 3.29 gives the thicknesses of the acceptable

coupons WCS5EP, WCS9EP, WCS10JF, and WCS12HEP including the encrusted

polymer. Notably, the average thickness of the web coupons was larger than the

average web buckling specimen thickness from Tables 3.15 and 3.16. The average

142

web buckling thicknesses were 0.0522 inches and 0.0568 inches for the long-length

and small-length specimens, respectively, while the acceptable WCS coupon average

thickness was 0.0804”.

Figures 3.27 to 3.30 are pictures of satisfactory specimens WCS5EP,

WCS9EP, WCS10JF, and WCS12HEP after the tests. Even though an HEP coupon

was used, the half-encrusted unsymmetrical twisting-stretching coupling and bending-

shearing coupling properties would not be a factor in the WCS tests with the ASTM D

695 fixture [44]. Each figure shows a top and side view of the web coupon.

(a)

(b)

Figure 3.27 WCS5EP Shear Failure (a) Top View and (b) Side View

143

(a)

(b)

Figure 3.28 WCS9EP Shear Failure (a) Top View and (b) Side View

(a)

(b)

Figure 3.29 WCS10JF Shear Failure (a) Top View and (b) Side View

144

(a)

(b)

Figure 3.30 WCS12HEP Shear Failure (a) Top View and (b) Side View

Fiberglass composites with an applied axial-compression quasi-static-in-plane-

loading may undergo a variety of failure modes [48]. The two main failure modes are

longitudinal fiber matrix splitting and laminate shearing; the maximum strengths of

both modes are congruent [48]. All the pictures show the laminate shearing failure

mode; this results in a 45o crack across the specimen thickness [48]. Moreover,

“existing models for compressive strength of ± θ [fiberglass] layers indicate that

shear, rather than compression, dominates the failure of ± θ layers when the angle is

larger than 30o” [49]. This explained the reason for all the specimens failing in shear,

shown in the previous figures.

To clarify the mechanical experimental data, Figure 3.31 illustrates the force

vs. axial displacement curves – for the acceptable coupons – from the Instron

machine. The total thicknesses were included for reference. Figure 3.32 gives the

stress-axial-strain curve of the specimens from the Instron machine. The stress was

145

calculated by dividing the load from Figure 3.31 by the measured cross-sectional area

from Table 3.28, while the axial strain was determined by dividing the original

measured length by its axial displacement. The coupons failed at axial displacements

proportional to their thicknesses.

Figure 3.31 WCS Force vs. Axial Displacement from Instron

The thinner specimens WCS10JF and WCS12HEP failed at lower maximum

compression loads than the thicker coupons WCS5EP and WCS9EP. As seen from

the previous graph, the thicker coupons WCS5EP (0.0979”) and WCS9EP (0.1157”)

had larger maximum strengths than the thinner WCS specimens. This occurred even

0

100

200

300

400

500

600

0 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18

WCS12HEP - t = 0.0740 inWCS10JF - t = 0.0340 inWCS9EP - t = 0.1157 inWCS5EP - t = 0.0979 in

Axial Displacement, (in)

Fo

rce

, F

(lb

)

WCS: Force, F (lb) vs. Axial Displacement, (in) from Instron

146

though the increased thickness was due to the weaker encrusted polymer adhered to

the composite web coupon. The data in Tables 3.11, 3.12, and 3.29 was used to

determine this inconsistency. The encrusted polymer modulus (5.22 x 105 psi) was

approximately an eighth of the E-glass vinyl ester modulus (3.398 x 106 psi).

Figure 3.32 WCS Stress vs. Axial Strain from Instron

However, the encrusted polymer thickness was approximately double the E-glass

composite thickness for samples WCS5EP and WCS9EP. Specifically, WCS5EP and

WCS9EP had 2.1 and 2.6 times the amount of encrusted polymer as the E-glass vinyl

ester resin composite, respectively. Even though the encrusted polymer layer was

0

2000

4000

6000

8000

10000

12000

0 0.02 0.04 0.06 0.08 0.10

WCS12HEPWFC10JFWFC9EPWCS5EP

= /L

T = P/bd

Axial Strain, (in/in)

Str

ess, (

psi)

Stress, (psi) vs. Axial Strain, (in/in) from Instron

147

weak compared to the E-glass composite, its large thickness considerably augmented

the coupon’s maximum compression strength. “Compression strength of composites

is mainly controlled by matrix strength, matrix stiffness and accompanying fiber

support, and matrix-fiber interface strength” [50].

Notably, the right-most sides of the web buckling and WCS force

displacement curves in Figures 3.18 and 3.31 exhibited opposing shapes. Most of the

small-length webs had progressively reached zero load after bifurcation, while the

WCS force displacement curves had received no load once they failed [51].

Explained in the Description of E-Glass Web Section a web received no load after it

had failed.

Table 3.30 summarized the WCS experimental results. The experimental

results from the following table were comparable to the experimental results found in

other compressive testing research. The “Experimental Determination of the

Compressive Strength of Pultruded Structural Shapes” article by E.J. Barbero, S.

Makkapati, and J.S. Tomblin had given similar results with respect to the materials

and thicknesses [49]. Vinyl ester D1419 resin with E-glass stitched mats at ± 45o

layers were employed in the Barbero compressive strength research [49].

148

Table 3.30 WCS Experimental Results

Specimens

Failure

Displacement

(in)

Failure Strain

(in/in)

Maximum

Compression

Load (lb)

Maximum

Compression

Stress (psi)

WCS5EP 0.079 0.025 550 10,900

WCS9EP 0.080 0.026 530 9,210

WCS10JF 0.060 0.019 180 10,700

WCS12HEP 0.067 0.021 350 10,300

Average 0.072 0.023 400 10,300

Standard

Deviation 0.010 0.0033 170 750

Coefficient of

Variation 0.14 0.15 0.43 0.073

The standard deviations and coefficients of variation for Table 3.30 were

relatively insignificant except for the maximum compression load. The standard

deviation and coefficient of variation were 170 lbs and 0.43, respectively, for the

maximum compression load data. This was due to the varied thicknesses in the

acceptable coupons; the thickness range was from 0.0340 inches to 0.1157 inches for

only four coupons. Comparatively, the maximum compression stress coefficient of

variation (0.073) was reasonable. By dividing the maximum compression loads by

their respective depths and thicknesses, and in turn normalizing the data, the load

variation was reduced. The other WCS mechanical results had coefficients of

variation of 0.14 and 0.15 for the failure displacements and failure strains,

respectively.

As previously-stated coupon thickness significantly affected maximum

compression load. WCS10JF, which had the smallest measured thickness of 0.0340”,

exhibited a relatively small maximum compression load (180 lbs) compared to the

other coupons. Both WCS10JF’s thickness and maximum compression load were

approximately three-eighths of the other WCS coupons’ thicknesses and maximum

149

compression loads. This corresponded with the linear nature of the WCS curves. On

the other hand, the thicker coupons exhibited higher maximum compression loads.

WCS5EP and WCS9EP had thicknesses of 0.0979 inches and 0.1157 inches and

maximum compression loads of 550 lbs and 530 lbs, respectively.

Table 3.31 Compression Load of Long-Length Webs

Web Buckling

Specimen

Area: Depth x

Thickness (in2)

Experimental

Maximum Load (lb)

Back Calculated

Maximum Compression

Load (lb)

IWB26JF 0.0683 110 700

IWB27EP 0.1892 380 1900

IWB28JF 0.0688 92 700

IWB29JF 0.0580 100 600

IWB36EP 0.1740 880 1800

IWB37EP 0.0847 280 900

IWB38HEP 0.0909 420 900

IWB39EP 0.1830 1040 1900

IWB40EP 0.1669 550 1700

IWB41HEP 0.1337 400 1400

IWB42EP 0.0822 120 800

IWB43JF 0.0671 120 700

IWB44JF 0.0660 90 700

IWB45JF 0.0698 150 700

IWB46JF 0.0637 140 700

Average 1100

Standard Deviation 500

Moreover, Table 3.31 was formed to compare the experimental findings

between the WCS examinations and the long-length web buckling tests. By including

the web lengths and depths from Table 3.2 and back calculating the maximum

compression loads, the previous table was formed. The back calculated maximum

compression load was computed by multiplying the average maximum compression

stress (10,300 psi) from Table 3.30 by each web’s cross-sectional area. These

150

findings correlated with the previous critical beam buckling and Southwell Plot

analyses; nearly all of the samples buckled prior to reaching their compression load.

Table 3.32 Compression Load of Small-Length Webs

Web Buckling

Specimen

Area: Depth x

Thickness (in2)

Experimental

Maximum Load (lb)

Back Calculated

Maximum Compression

Load (lb)

IWB47JF 0.0878 540 900

IWB48EP 0.1617 1120 1700

IWB49EP 0.0985 780 1000

IWB50HEP 0.1466 1040 1500

IWB52JF 0.0928 580 1000

IWB53HEP 0.1482 1110 1500

IWB54JF 0.0940 440 1000

IWB55HEP 0.1406 1130 1400

IWB56EP 0.1392 1330 1400

IWB57HEP 0.1034 650 1100

IWB58HEP 0.0992 520 1000

IWB59HEP 0.1342 1020 1400

IWB60HEP 0.1349 1130 1400

IWB61JF 0.0923 530 1000

Average 1200

Standard Deviation 300

“Depending upon the slenderness or frailty of the structure, the buckling (internal)

stresses associated with the buckling load can be a fraction of the strength of the

material” [44]. As stated in the Critical Beam Buckling Section, there were only 2

long-length specimens IWB27EP and IWB38HEP specimens that were not

encompassed by the SS and CC theoretical buckling bounds. The webs that were

outside the SS and CC theoretical buckling range were compared to their percent

bending values from Table 3.8. Since specimen IWB27EP exhibited a percent

bending value of 65% and its experimental maximum load was below its SS and CC

151

theoretical buckling range, the web may have had imperfections that significantly

affected its buckling ability [46]. On the other hand, IWB38HEP exhibited a

relatively small percent bending (2%), and its experimental maximum load was

greater than its SS and CC theoretical buckling range. As a result, specimen

IWB38HEP failed in axial compression. Conclusively, all of the long-length samples

had decidedly buckled except IWB27EP and IWB38HEP.

Table 3.32 lists the areas, experimental maximum loads, and back calculated

maximum compression loads for the small-length webs. The preceding table was

compiled by the same methods as Table 3.31. To begin with, this data was

compatible with the previous beam buckling results, in which almost all of the small-

length webs had buckled. Web buckling specimen IWB49EP, however, did not

conform. Sample IWB49EP was the only small-length web that was greater than its

SS and CC theoretical buckling range, and it exhibited a rather small percent bending

of 7% from Table 3.9. These two statistics categorized IWB49EP as a web that had

failed in axial compression. In conclusion, all of the small-length webs had buckled

except IWB49EP.

The following table lists the buckled small-length webs. Table 3.33 lists the

mechanical values from the small-length webs that were deemed to have definitively

buckled summarized from the tables in Section 3.4. These values will be utilized in

the Energy Absorption Capabilities Chapter.

152

Table 3.33 Small-Length Buckled Energy Absorption Values

Small-Length

Web

Experimental

Buckling Load

(lb)

Experimental

Buckling Stress

(psi)

Critical Buckling

Strain from Strain

Gages (in/in)

IWB47JF 540 6100 0.0038

IWB48EP 1120 6900 0.0040

IWB50HEP 1040 7100 0.0092

IWB52JF 580 6200 0.0053

IWB53HEP 1110 7500 0.0080

IWB54JF 440 4700 0.0044

IWB55HEP 1130 8000 0.0088

IWB56EP 1330 9600 0.0100

IWB57HEP 650 6300 0.0024

IWB58HEP 520 5200 0.0063

IWB59HEP 1020 7600 0.0047

IWB60HEP 1130 8400 0.0092

IWB61JF 530 5700 0.0030

Average 860 6900 0.0061

Standard

Deviation 310 1400 0.0026

Coefficient of

Variation 0.36 0.20 0.43

Consequently, the small-length webs exhibited greater calculated theoretical

buckling loads than the long-length webs. This is due to the small-length webs being

approximately two-thirds the length of the long-length webs, and as stated in Section

3.2, the length is very significant in the Beam Buckling Equation 3.2. In addition, the

average small-length web thickness (0.0568”) was approximately 9% more than the

average long-length web thickness (0.0522”). As previously stated, the web thickness

influences the bending stiffness and theoretical calculated buckling load by a power of

three. The final section will summarize the findings of the entire chapter.

153

3.9 Conclusion of Fiberglass Web

This chapter reviewed the experiments and results of the E-glass vinyl ester

resin composite webs. Web buckling tests, fiber volume fraction experiments, and

compression strength tests were conducted to understand their mechanical and

physical properties. The web buckling results, percent bending data, Critical Beam

Buckling calculations, Southwell Plots, and axial compression data were generally in

agreement. The following summarizes the findings of this chapter.

Most of the long-length web specimens had buckled. Specimens IWB26JF,

IWB28JF, IWB29JF, IWB36EP, IWB37EP, IWB39EP, IWB40EP, IWB41HEP,

IWB42EP, IWB43JF, IWB44JF, IWB45JF, and IWB46JF had bifurcated and the

Southwell Plots had approximated their buckling loads. The two long-length samples

that did not buckle were IWB27EP and IWB38HEP. Using the percent bending

values and Critical Beam Buckling formulae these specimens had not buckled.

Specimen IWB38HEP had failed in axial compression.

For the small-length webs, one specimen had not buckled. Specimens

IWB47JF, IWB48EP, IWB50HEP, IWB52JF, IWB53HEP, IWB54JF, IWB55HEP,

IWB56EP, IWB57HEP, IWB58HEP, IWB59HEP, IWB60HEP, and IWB61JF had

bifurcated based on the percent bending and Critical Beam Buckling values.

Specimen IWB49EP, however, failed in axial compression.

To reference the main reason for this research, the bifurcation mechanism was

more beneficial with respect to energy absorption. From Section 3.2 the buckling

specimens, which exhibited linear-elastic-to-bifurcation and buckling mechanisms,

absorbed more energy than the webs that had linear-elastic-to-failure load-axial-

displacement curves. In this chapter, web buckling experiments determined the

154

bifurcation load and axial strain, fiber volume fraction was used for the theoretical

calculations, and the compressive strengths determined the maximum compressive

stresses. The following chapter describes the web core, the web-foam compression

tests, and the analysis performed on the experimental results.

155

Chapter 4

STATIC TESTING OF WEB CORE

4.1 Introduction to Static Testing of Web Core

Chapter 4 will explain the web core’s characteristics, its involvement with the

explosion protection research, and the compression quasi-static tests executed on the

web core. The web core compression tests had the load applied axial to the webs

similar to the web buckling tests from Chapter 3. Web failure modes will also be

conveyed in the Discussion of Web Core Test Results section.

4.2 Description of Web Core Experiments

As mentioned in Chapter 1 Section 1.3, the TYCOR® web core preform was

manufactured by Webcore Technologies, Inc. The web core specimens used for these

experiments were cut from the VARTM, vinyl-ester-resin-infused panel described in

Section 1.3. A section of the blast research panel was shown in Figure 1.1, and the

VARTM process is illustrated in Figure 1.12 and 3.2.

Although long-length and small-length specimens were manufactured for the

web buckling tests, only the 1-inch-long small-length webs were fabricated for the

web plus foam compression (WFC) tests. The small-length webs were utilized for

156

WFC experiments due to their higher buckling loads and smaller sandwich panel areal

densities. These are based on the web length affecting the web buckling load by a

power of 2 – mentioned in Section 3.2 – and the areal density formula from The

Behavior of Sandwich Structures of Isotropic and Composite Materials book.

The following explains the fabrication process. The blast protection panel

WFC unit cell, which was chosen to represent the panel structure, is shown in Figure

4.1. The unit cell contained a single 1-inch-long small-length web, which is

illustrated in Figure 1.13. Figure 4.2 also exemplifies the average web core specimen

dimensions. Similar to the fabrication web buckling processes in Section 3.2, the

WFC samples were cut, measured to guarantee a centered web, and sanded ensuring

uniform load applied to the specimen. The foam, contrary to the web buckling

specimens, was not removed from the WFC samples. Strain gages were not used for

this investigation because foam was incorporated into the WFC samples. There was

no suitable method to adequately attach strain gages to the webs.

Figure 4.1 WFC Unit Cell

157

Figure 4.2 View of Web Core Dimensions

Figure 4.3 represents a web core specimen situated in the web buckling

fixture. The web core specimen’s bottom facesheet was supported in the fixture

similar to the web buckling specimens to prevent any movement during loading. In

addition, the steel loading block – which rested on the specimen – was centered

directly over the specimen’s web ensuring insignificant eccentricity in the web.

Figure 4.3 Web Core in Buckling Fixture

158

Figure 4.4 Web Core Specimen WFC1 Prior to Loading

The subsequent elevation views illustrate four of the twelve WFC specimens,

which were loaded at a speed of 0.05 in/min by an Instron 5567 machine using the

6000-pound load cell. Figure 4.4 shows specimen WFC1 prior to loading. Figures

4.5(a), (b), (c), and (d) all show the web laterally deflecting and, in turn, separating

from the foam after bifurcation. The webs in these pictures appeared to have

bifurcated similarly to the webs in Figures 3.4 and 3.12(b). The buckling and in-plane

compression failure modes will be explained in the next section.

159

(a) (b)

(c) (d)

Figure 4.5 Web Core Specimens after Bifurcation (a) WFC1, (b)

WFC2, (c) WFC3, and (d) WFC4

160

Table 4.1 WFC Dimensions

Specimen

Width of Foam Width of

Sample:

b (in)

Depth:

d_w (in)

Planform:

A (in2)

Web

Length:

L_w (in) Left:

b_LF (in)

Right:

b_RF (in)

WFC1 0.5821 0.5737 1.2753 2.0353 2.5956 0.9590

WFC2 0.6038 0.6407 1.3617 2.0694 2.8179 0.9648

WFC3 0.7266 0.7146 1.5425 2.0410 3.1482 0.9153

WFC4 0.6634 0.5530 1.3145 2.0885 2.7453 0.9208

WFC5 0.8100 0.7006 1.5610 2.0819 3.2498 0.9053

WFC6 0.7784 0.7521 1.6100 2.0433 3.2897 0.9033

WFC7 0.7698 0.6933 1.5393 2.0939 3.2231 0.9125

WFC8 0.6634 0.6300 1.3640 2.0421 2.7854 0.9143

WFC9 0.6074 0.6254 1.2975 2.0391 2.6457 0.9273

WFC10 0.6983 0.7015 1.4933 2.0657 3.0847 0.9253

WFC11 0.7418 0.8121 1.6342 2.1193 3.4634 0.9138

WFC12 0.6977 0.6964 1.5070 2.0356 3.0676 0.9098

Average 0.6952 0.6744 1.4584 2.0629 3.0097 0.9226

Standard

Deviation 0.0737 0.0734 0.1279 0.0279 0.2823 0.0197

Table 4.1 lists the dimensions of the WFC specimens with their foam widths,

sample widths, depths, cross-sectional areas, and web lengths. Due to the minimal

differences between the left and right foam widths, it was assumed that the load had

been applied in-line with the web. The foam widths were used to create the foam

model in the next chapter, while the sample widths and depths were utilized to

compute the planform areas. The planform areas and web lengths assisted in

computing the sample applied stress and theoretical buckling load, respectively.

Table 4.2 catalogues the thicknesses of each web and encrusted polymer per side.

The WFC web thickness was measured with electronic calipers ten times due to its

importance with the subsequent calculations. The average and standard deviation

values correlate with the number of measurements taken for each web.

161

Table 4.2 WFC Web and Encrusted Polymer Thicknesses

Specimen

Web Thickness (in) Single EP

Thickness per

Side (in) Average Standard Deviation

WFC1 0.1373 0.0169 0.0527

WFC2 0.1324 0.0155 0.0502

WFC3 0.1174 0.0084 0.0427

WFC4 0.1210 0.0101 0.0445

WFC5 0.0759 0.0137 0.0220

WFC6 0.0938 0.0073 0.0309

WFC7 0.0848 0.0090 0.0264

WFC8 0.0818 0.0112 0.0249

WFC9 0.0649 0.0077 0.0165

WFC10 0.1120 0.0145 0.0400

WFC11 0.1114 0.0116 0.0397

WFC12 0.1303 0.0242 0.0492

Average 0.1052 - 0.0366

Standard

Deviation 0.0242 - 0.0121

The standard deviations, which were approximately 10% of their averages, signified

that the thickness of each web was not uniform. They varied considerably in their 1”±

length. This was most likely due to the vinyl ester resin, which combined with the

non-uniform Polyiso Foam microscopic structure forming the heterogeneous

encrusted polymer.

The WFC dimensions will be compared to the web buckling and WCS

measurements. The average WFC web thickness (0.1052 in ± 0.0242 in) was

dissimilar to the average long-length (0.0522 in ± 0.0253 in) and small-length (0.0568

in ± 0.0123 in) web thicknesses from Tables 3.15 and 3.16. The average WFC web

thickness was approximately twice the long-length and small-length average web

thicknesses. Comparatively, the average WCS coupon thickness (0.0804 in ± 0.0353

in) from Table 3.29 was less than the average WFC web thickness by approximately

162

25%. Notably, all the WFC specimens had encrusted polymer adhered to the webs

due to the resin mixing with the foam during the VARTM process.

Since the WFC web thickness was relatively large, the WFC samples will have

a greater experimental maximum load than the web buckling and WCS samples.

With respect to the web buckling comparisons, “the load-carrying capacity of a

column will increase as the moment of inertia of the cross-section increases” [26].

The following discusses the flexural responses of plates subjected to impact tests.

These articles are related to the web buckling investigation in this research since

flexural response is related to buckling [44]. Quasi-static and impact loadings on a

blast protection panel are greatly affected by laminate thickness, and in turn, related to

flexural stiffness [52]. In N. K. Naik’s 2000 article titled “Polymer matrix woven

fabric composites subjected to low velocity impact. II. Effect of plate thickness” the

effect of plate thickness on low-velocity impact behavior was tested [52]. The plates

– 0.18” to 0.31” thick – were comprised of E-glass epoxy with transversely imparted

dynamic loads from an object of 2 mph to 7 mph velocities [52]. “In general, a linear

relation between the peak contact force and the composite plate thickness can be

assumed” [52].

163

Figure 4.6 WFC Force in Sample vs. Axial Displacement

0

300

600

900

1200

1500

1800

2100

2400

0 0.05 0.10 0.15 0.20 0.25

WFC1_Cin

Experimental Maximum Load = 2100 lb

Axial Displacement, (in )

Fo

rce

, F

(lb

)

WFC1_Cin: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

300

600

900

1200

1500

1800

2100

2400

0 0.05 0.10 0.15 0.20 0.25

WFC2_Cin

Experimental Maximum Load = 2200 lb

Axial Displacement, (in )

Fo

rce

, F

(lb

)

WFC2_Cin: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

300

600

900

1200

1500

1800

2100

2400

0 0.05 0.10 0.15 0.20 0.25

WFC3_Cin

Experimental Maximum Load = 1700 lb

Axial Displacement, (in )

Fo

rce

, F

(lb

)

WFC3_Cin: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

300

600

900

1200

1500

1800

2100

2400

0 0.05 0.10 0.15 0.20 0.25

WFC4_Cin

Experimental Maximum Load = 2300 lb

Axial Displacement, (in )

Fo

rce

, F

(lb

)

WFC4_Cin: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

300

600

900

1200

1500

1800

2100

2400

0 0.05 0.10 0.15 0.20 0.25

WFC5_Cin

Experimental Maximum Load = 810 lb

Axial Displacement, (in )

Fo

rce

, F

(lb

)

WFC5_Cin: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

300

600

900

1200

1500

1800

2100

2400

0 0.05 0.10 0.15 0.20 0.25

WFC6_Cin

Experimental Maximum Load = 1700 lb

Axial Displacement, (in )

Fo

rce

, F

(lb

)

WFC6_Cin: Force, F (lb) vs. Axial Displacement, (in) from Instron

164

Figure 4.6 Continued

0

300

600

900

1200

1500

1800

2100

2400

0 0.05 0.10 0.15 0.20 0.25

WFC7_Cin

Experimental Maximum Load = 1500 lb

Axial Displacement, (in )

Fo

rce

, F

(lb

)

WFC7_Cin: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

300

600

900

1200

1500

1800

2100

2400

0 0.05 0.10 0.15 0.20 0.25

WFC8_Cin

Experimental Maximum Load = 1400 lb

Axial Displacement, (in )

Fo

rce

, F

(lb

)

WFC8_Cin: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

300

600

900

1200

1500

1800

2100

2400

0 0.05 0.10 0.15 0.20 0.25

WFC9_Cin

Experimental Maximum Load = 1200 lb

Axial Displacement, (in )

Fo

rce

, F

(lb

)

WFC9_Cin: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

300

600

900

1200

1500

1800

2100

2400

0 0.05 0.10 0.15 0.20 0.25

WFC10_Cin

Experimental Maximum Load = 1500 lb

Axial Displacement, (in)

Fo

rce

, F

(lb

)

WFC10_Cin: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

300

600

900

1200

1500

1800

2100

2400

0 0.05 0.10 0.15 0.20 0.25

WFC11_Cin

Experimental Maximum Load = 2200 lb

Axial Displacement, (in )

Fo

rce

, F

(lb

)

WFC11_Cin: Force, F (lb) vs. Axial Displacement, (in) from Instron

0

300

600

900

1200

1500

1800

2100

2400

0 0.05 0.10 0.15 0.20 0.25

WFC12_Cin

Experimental Maximum Load = 1600 lb

Axial Displacement, (in )

Fo

rce

, F

(lb

)

WFC12_Cin: Force, F (lb) vs. Axial Displacement, (in) from Instron

165

Figure 4.7 WFC Stress in Sample vs. Axial Strain

0

100

200

300

400

500

600

700

800

900

0 0.05 0.10 0.15 0.20 0.25

WFC1

Experimental Failure Strain = 0.029 in/in

Experimental Maximum Stress of Sample = 820 psi

Axial Strain, (in/in )

Str

ess in

Sa

mp

le, (

psi)

WFC1: Stress in Sample, (psi) vs. Axial Strain, (in/in) from Instron

0

100

200

300

400

500

600

700

800

900

0 0.05 0.10 0.15 0.20 0.25

WFC2

Experimental FailureStrain = 0.027 in/in

Experimental Maximum Stress of Sample = 780 psi

Axial Strain, (in/in )

Str

ess in

Sa

mp

le, (

psi)

WFC2: Stress in Sample, (psi) vs. Axial Strain, (in/in) from Instron

0

100

200

300

400

500

600

700

800

900

0 0.05 0.10 0.15 0.20 0.25

WFC3

Experimental FailureStrain = 0.022 in/in

Experimental MaximumStress of Sample = 550 psi

Axial Strain, (in/in )

Str

ess in

Sa

mp

e, (

psi)

WFC3: Stress in Sample, (psi) vs. Axial Strain, (in/in) from Instron

0

100

200

300

400

500

600

700

800

900

0 0.05 0.10 0.15 0.20 0.25

WFC4

Experimental MaximumStress of Sample = 820 psi

Experimental FailureStrain = 0.027 in/in

Axial Strain, (in/in )

Str

ess in

Sa

mp

le, (

psi)

WFC4: Stress in Sample, (psi) vs. Axial Strain, (in/in) from Instron

0

100

200

300

400

500

600

700

800

900

0 0.05 0.10 0.15 0.20 0.25

WFC5

Experimental FailureStrain = 0.012 in/in

Experimental Maximum Stress of Sample = 250 psi

Axial Strain, (in/in )

Str

ess in

Sa

mp

le, (

psi)

WFC5: Stress in Sample, (psi) vs. Axial Strain, (in/in) from Instron

0

100

200

300

400

500

600

700

800

900

0 0.05 0.10 0.15 0.20 0.25

WFC6

Experimental FailureStrain = 0.022 in/in

Experimental Maximum Stress of Sample = 510 psi

Axial Strain, (in/in )

Str

ess in

Sa

mp

le, (

psi)

WFC6: Stress in Sample, (psi) vs. Axial Strain, (in/in) from Instron

166

Figure 4.7 Continued

Therefore, even though the thicknesses of the web buckling and WCS samples were

approximately ½ and ¾ of the WFC web thicknesses, respectively, there was a linear

0

100

200

300

400

500

600

700

800

900

0 0.05 0.10 0.15 0.20 0.25

WFC7

Experimental FailureStrain = 0.018 in/in

Experimental Maximum Stress of Sample = 470 psi

Axial Strain, (in/in )

Str

ess in

Sa

mp

le, (

psi)

WFC7: Stress in Sample, (psi) vs. Axial Strain, (in/in) from Instron

0

100

200

300

400

500

600

700

800

900

0 0.05 0.10 0.15 0.20 0.25

WFC8

Experimental FailureStrain = 0.017 in/in

Experimental Maximum Stress of Sample = 490 psi

Axial Strain, (in/in )

Str

ess in

Sa

mp

le, (

psi)

WFC8: Stress in Sample, (psi) vs. Axial Strain, (in/in) from Instron

0

100

200

300

400

500

600

700

800

900

0 0.05 0.10 0.15 0.20 0.25

WFC9

Experimental FailureStrain = 0.019 in/in

Experimental Maximum Stress of Sample = 460 psi

Axial Strain, (in/in )

Str

ess in

Sa

mp

le, (

psi)

WFC9: Stress in Sample, (psi) vs. Axial Strain, (in/in) from Instron

0

100

200

300

400

500

600

700

800

900

0 0.05 0.10 0.15 0.20 0.25

WFC10

Experimental FailureStrain = 0.018 in/in

Experimental Maximum Stress of Sample = 470 psi

Axial Strain, (in/in)

Str

ess in

Sa

mp

le, (

psi)

WFC10: Stress in Sample, (psi) vs. Axial Strain, (in/in) from Instron

0

100

200

300

400

500

600

700

800

900

0 0.05 0.10 0.15 0.20 0.25

WFC11

Experimental FailureStrain = 0.026 in/in

Experimental Maximum Stress of Sample = 630 psi

Axial Strain, (in/in )

Str

ess in

Sa

mp

le, (

psi)

WFC11: Stress in Sample, (psi) vs. Axial Strain, (in/in) from Instron

0

100

200

300

400

500

600

700

800

900

0 0.05 0.10 0.15 0.20 0.25

WFC12

Experimental FailureStrain = 0.019 in/in

Experimental Maximum Stress of Sample = 520 psi

Axial Strain, (in/in )

Str

ess in

Sa

mp

le, (

psi)

WFC12: Stress in Sample, (psi) vs. Axial Strain, (in/in) from Instron

167

relationship between their thicknesses and results. Consequently, the web buckling

calculations were applicable to the WFC investigation; once the increased thicknesses

were inputted into CMAP. The encrusted polymer was included in the input.

The preceding load vs. axial displacement and stress vs. axial strain graphs in

Figures 4.6 and 4.7 illustrate the results of the WFC experiments. The stress-axial-

strain curves illustrate the stress observed in the sample. Figure 4.7 was formed by

dividing the load and axial displacement obtained from the Instron machine by the

planform area of the sample and original web length, respectively. The maximum

load was referenced in each load-axial-displacement graph, and the maximum stress

and compression strain were incorporated into the stress-axial-strain figures.

Figure 4.8 supplied the force-in-web vs. axial displacement curves for the

WFC samples. These curves utilized Equation 4.1 – a Hooke’s Law, force

equilibrium formula – to obtain the force observed in the composite web.

( ) (4.1)

168

Figure 4.8 WFC Force in Web vs. Axial Displacement

0

300

600

900

1200

1500

1800

2100

2400

0 0.05 0.10 0.15 0.20 0.25

WFC1

Experimental Maximum Load = 2100 lb

Axial Displacement, (in )

Fo

rce

in

We

b,

F (

lb)

WFC1: Force in Web, F (lb) vs. Axial Displacement, (in) from Instron

0

300

600

900

1200

1500

1800

2100

2400

0 0.05 0.10 0.15 0.20 0.25

WFC2

Experimental Maximum Load = 2200 lb

Axial Displacement, (in )

Fo

rce

in

We

b,

F (

lb)

WFC2: Force in Web, F (lb) vs. Axial Displacement, (in) from Instron

0

300

600

900

1200

1500

1800

2100

2400

0 0.05 0.10 0.15 0.20 0.25

WFC3

Experimental Maximum Load = 1700 lb

Axial Displacement, (in )

Fo

rce

in

We

b,

F (

lb)

WFC3: Force in Web, F (lb) vs. Axial Displacement, (in) from Instron

0

300

600

900

1200

1500

1800

2100

2400

0 0.05 0.10 0.15 0.20 0.25

WFC4

Experimental Maximum Load = 2200 lb

Axial Displacement, (in )

Fo

rce

in

We

b,

F (

lb)

WFC4: Force in Web, F (lb) vs. Axial Displacement, (in) from Instron

0

300

600

900

1200

1500

1800

2100

2400

0 0.05 0.10 0.15 0.20 0.25

WFC5

Experimental Maximum Load = 800 lb

Axial Displacement, (in )

Fo

rce

in

We

b,

F (

lb)

WFC5: Force in Web, F (lb) vs. Axial Displacement, (in) from Instron

0

300

600

900

1200

1500

1800

2100

2400

0 0.05 0.10 0.15 0.20 0.25

WFC6

Experimental Maximum Load = 1600 lb

Axial Displacement, (in )

Fo

rce

in

We

b,

F (

lb)

WFC6: Force in Web, F (lb) vs. Axial Displacement, (in) from Instron

169

Figure 4.8 Continued

0

300

600

900

1200

1500

1800

2100

2400

0 0.05 0.10 0.15 0.20 0.25

WFC7

Experimental Maximum Load = 1500 lb

Axial Displacement, (in )

Fo

rce

in

We

b,

F (

lb)

WFC7: Force in Web, F (lb) vs. Axial Displacement, (in) from Instron

0

300

600

900

1200

1500

1800

2100

2400

0 0.05 0.10 0.15 0.20 0.25

WFC8

Experimental Maximum Load = 1300 lb

Axial Displacement, (in )

Fo

rce

in

We

b,

F (

lb)

WFC8: Force in Web, F (lb) vs. Axial Displacement, (in) from Instron

0

300

600

900

1200

1500

1800

2100

2400

0 0.05 0.10 0.15 0.20 0.25

WFC9

Experimental Maximum Load = 1200 lb

Axial Displacement, (in )

Fo

rce

in

We

b,

F (

lb)

WFC9: Force in Web, F (lb) vs. Axial Displacement, (in) from Instron

0

300

600

900

1200

1500

1800

2100

2400

0 0.05 0.10 0.15 0.20 0.25

WFC10

Experimental Maximum Load = 1400 lb

Axial Displacement, (in)

Fo

rce

in

We

b,

F (

lb)

WFC10: Force in Web, F (lb) vs. Axial Displacement, (in) from Instron

0

300

600

900

1200

1500

1800

2100

2400

0 0.05 0.10 0.15 0.20 0.25

WFC11

Experimental Maximum Load = 2200 lb

Axial Displacement, (in )

Fo

rce

in

We

b,

F (

lb)

WFC11: Force in Web, F (lb) vs. Axial Displacement, (in) from Instron

0

300

600

900

1200

1500

1800

2100

2400

0 0.05 0.10 0.15 0.20 0.25

WFC12

Experimental Maximum Load = 1600 lb

Axial Displacement, (in )

Fo

rce

in

We

b,

F (

lb)

WFC12: Force in Web, F (lb) vs. Axial Displacement, (in) from Instron

170

Figure 4.9 WFC Stress in Web vs. Axial Strain

0

2000

4000

6000

8000

10000

0 0.05 0.10 0.15 0.20 0.25

WFC1

Experimental Failure Strain = 0.029 in/in

Experimental Maximum Stress of Web = 7500 psi

Axial Strain, (in/in )

Str

ess in

We

b, (

psi)

WFC1: Stress in Web, (psi) vs. Axial Strain, (in/in) from Instron

0

2000

4000

6000

8000

10000

0 0.05 0.10 0.15 0.20 0.25

WFC2

Experimental FailureStrain = 0.027 in/in

Experimental MaximumStress of Web = 7900 psi

Axial Strain, (in/in )

Str

ess in

We

b, (

psi)

WFC2: Stress in Web, (psi) vs. Axial Strain, (in/in) from Instron

0

2000

4000

6000

8000

10000

0 0.05 0.10 0.15 0.20 0.25

WFC3

Experimental FailureStrain = 0.022 in/in

Experimental MaximumStress of Web = 7100 psi

Axial Strain, (in/in )

Str

ess in

We

b, (

psi)

WFC3: Stress in Web, (psi) vs. Axial Strain, (in/in) from Instron

0

2000

4000

6000

8000

10000

0 0.05 0.10 0.15 0.20 0.25

WFC4

Experimental MaximumStress of Web = 8800 psi

Experimental FailureStrain = 0.027 in/in

Axial Strain, (in/in )

Str

ess in

We

b, (

psi)

WFC4: Stress in Web, (psi) vs. Axial Strain, (in/in) from Instron

0

2000

4000

6000

8000

10000

0 0.05 0.10 0.15 0.20 0.25

WFC5

Experimental FailureStrain = 0.012 in/in

Experimental Maximum Stress of Web = 5000 psi

Axial Strain, (in/in )

Str

ess in

We

b, (

psi)

WFC5: Stress in Web, (psi) vs. Axial Strain, (in/in) from Instron

0

2000

4000

6000

8000

10000

0 0.05 0.10 0.15 0.20 0.25

WFC6

Experimental FailureStrain = 0.022 in/in

Experimental Maximum Stress of Web = 8600 psi

Axial Strain, (in/in )

Str

ess in

We

b, (

psi)

WFC6: Stress in Web, (psi) vs. Axial Strain, (in/in) from Instron

171

Figure 4.9 Continued

In this equation, Fw was the force in the web, FT was the force in the sample depicted

in Figure 4.6, and ε is the strain in the sample computed as the axial displacement

divided by its original length. The constant EF was the average foam compressive

0

2000

4000

6000

8000

10000

0 0.05 0.10 0.15 0.20 0.25

WFC7

Experimental FailureStrain = 0.018 in/in

Experimental Maximum Stress of Web = 8400 psi

Axial Strain, (in/in )

Str

ess in

We

b, (

psi)

WFC7: Stress in Web, (psi) vs. Axial Strain, (in/in) from Instron

0

2000

4000

6000

8000

10000

0 0.05 0.10 0.15 0.20 0.25

WFC8

Experimental FailureStrain = 0.017 in/in

Experimental Maximum Stress of Web = 8000 psi

Axial Strain, (in/in )

Str

ess in

We

b, (

psi)

WFC8: Stress in Web, (psi) vs. Axial Strain, (in/in) from Instron

0

2000

4000

6000

8000

10000

0 0.05 0.10 0.15 0.20 0.25

WFC9

Experimental FailureStrain = 0.019 in/in

Experimental Maximum Stress of Web = 9000 psi

Axial Strain, (in/in )

Str

ess in

We

b, (

psi)

WFC9: Stress in Web, (psi) vs. Axial Strain, (in/in) from Instron

0

2000

4000

6000

8000

10000

0 0.05 0.10 0.15 0.20 0.25

WFC10

Experimental FailureStrain = 0.018 in/in

Experimental Maximum Stress of Sample = 6200 psi

Axial Strain, (in/in)

Str

ess in

Sa

mp

le, (

psi)

WFC10: Stress in Web, (psi) vs. Axial Strain, (in/in) from Instron

0

2000

4000

6000

8000

10000

0 0.05 0.10 0.15 0.20 0.25

WFC11

Experimental FailureStrain = 0.026 in/in

Experimental Maximum Stress of Sample = 9100 psi

Axial Strain, (in/in )

Str

ess in

Sa

mp

le, (

psi)

WFC11: Stress in Web, (psi) vs. Axial Strain, (in/in) from Instron

0

2000

4000

6000

8000

10000

0 0.05 0.10 0.15 0.20 0.25

WFC12

Experimental FailureStrain = 0.019 in/in

Experimental Maximum Stress of Sample = 6000 psi

Axial Strain, (in/in )

Str

ess in

Sa

mp

le, (

psi)

WFC12: Stress in Web, (psi) vs. Axial Strain, (in/in) from Instron

172

modulus (440 psi) of the previously-tested Uniaxial Strain foam core from Table 2.4.

The planform areas ALF and ARF are listed in Table 4.1 for each WFC sample.

The shapes of all the sole web WFC experimental graphs were all compatible.

They all rapidly increased in the linear-elastic region and then suddenly declined.

They behaved in an inelastic nature on the right-side of the graphs [26]. There was a

sudden decline once the curve reached its maximum point [26].

The preceding graphs illustrate the stress-strain curves for the web. These

were simply figured by dividing the web load by its area – depth multiplied by web

thickness – given in Tables 4.1 and 4.2. The axial strain was taken from Figure 4.7;

both the axial strains in the sample and web were assumed congruent. Due to the load

applied normal to the flanges and their large stiffness in this direction, they were

considered to add an insignificant affect to the sample’s strength.

Noticeably, a minimal amount of force was received by the foam in each WFC

sample. This can be first observed by comparing the load-axial-displacement graphs

in Figures 4.6 and 4.8. There are minor differences between the two types labeled as

the force in sample and force in web graphs. Quantitatively, in the linear region the

foam accepted approximately 1% of the total force; figured by dividing the rightmost

term by the average total force in the sample. The rightmost term (12.7 lbs) was

approximated as the constant EF (440 psi) multiplied by the sum of the average foam

areas (0.6952” and 0.6744”) and the average failure strain (0.021 in/in). The numbers

for EF, ALF, and ARF were obtained from the aforementioned Tables 2.4 and 4.1, while

the average failure strain was taken from Table 4.4 in the next section. Since the

average foam compressive modulus was approximately 0.04% of the web

compressive moduli (9.6E5 psi and 1.2E6 psi), the foam received minimal amount of

173

force imparted to each sample [26]. Tables 3.4 and 3.6 listed the average web

compressive moduli.

Likewise, the foam had elicited a plastic response in half of the stress-strain

curves in Figure 4.7. This was based on the Uniaxial Strain foam crushing strain from

Table 2.4. The next section continues with this discussion and tabulates this data.

The WFC experimental results will be completely analyzed in the following section.

Worthwhile, whether or not the polyisocyanurate foam increased the web buckling

loads of the WFC samples will be discussed towards the end of the next section.

4.3 Discussion of Web Core Test Results

In this section, the WFC results will be summarized. First, the foam

mechanical results will be compared to the WFC data. Next, the theoretical buckling

and maximum compression failure loads will be figured for the WFC samples. Then,

the bifurcation mechanism for the WFC webs will be determined.

To start with, the foam and WFC experimental results were compared. In

order to determine if the foam in each WFC sample had begun to crush, the average

crushing strain from Table 2.4 was matched against each WFC stress-strain graph in

Figure 4.7. These graphs depicted the stress in the sample, which included the foam

contribution. Consequently, the Uniaxial Strain value – utilized because a blast panel

comprised of repeating unit cells would encompass each section of foam similar to the

Uniaxial Strain experiment – was 0.06 in/in ± 0.02 in/in.

174

Table 4.3 Foam Crushing in WFC Samples

In Table 4.3 the foam-WFC comparison was summarized, which lists whether or not

the foam in the WFC samples had crushed or not. As stated at the end of the previous

section, the foam had reached its plastic nature for half of the WFC samples. These

samples were WFC4, WFC7, WFC8, WFC10, WFC11, and WFC12. In addition, the

foam had begun to crush after the curves had reached their maxima and had begun to

decline. Through extrapolation the graphs of specimens WFC1, WFC2, WFC3,

WFC5, WFC6, and WFC9 would most likely result in crushing of the foam. More

research must be conducted to confirm this.

To continue with the WFC research, Table 4.4 summarized the WFC web

mechanical results, excluding the foam contribution, taken directly from Figures 4.8

and 4.9. After reviewing this data, it was observed that the web thicknesses recorded

in Table 4.2 had greatly influenced the webs’ experimental maximum loads. The

thinner webs WFC5 and WFC9 with thicknesses of 0.0759” and 0.0649” had

Specimen

WFC Experimental

Failure Strain at

Maximum Stress

(in/in)

WFC Experimental

Final Strain Seen in

Curves (in/in)

Yes Foam Crushed or

No Foam Did Not

Crush in Graph

WFC1 0.029 0.039 No

WFC2 0.027 0.035 No

WFC3 0.022 0.027 No

WFC4 0.027 0.041 Yes

WFC5 0.012 0.018 No

WFC6 0.022 0.027 No

WFC7 0.018 0.050 Yes

WFC8 0.017 0.076 Yes

WFC9 0.019 0.24 No

WFC10 0.018 0.058 Yes

WFC11 0.026 0.069 Yes

WFC12 0.019 0.052 Yes

175

relatively small maximum loads of 800 lbs and 1200 lbs, respectively. In addition, the

thicker webs generally exhibited larger maximum loads. Samples WFC1, WFC2,

WFC4, and WFC11, which had thicknesses of 0.1373”, 0.1324”, 0.1210”, and

0.1114” had experimental maximum loads of 2100 lbs, 2200 lbs, 2200 lbs, and 2200

lbs, respectively. The failure strain was also proportional to the web thickness since

the thicker web specimens WFC1 (0.029 in/in), WFC2 (0.027 in/in), and WFC4

(0.027 in/in) had the greatest failure strains. Notably, the average foam crushing

stress of 27 psi ± 3 psi from Chapter 2 was undeniably smaller than the WFC web

maximum compression stresses. The average web maximum compression stress of

the WFC samples was 7600 psi ± 670 psi.

The following explanation examined the small-length experimental web

buckling stresses from Table 3.33 and the web only WFC experimental maximum

stresses. The small-length web data from Table 3.33 was utilized since it had been

verified to only correspond with buckled webs. To compare the data, the average

small-length web buckling stress (6900 psi ± 1400 psi) was approximately 90% of the

average web only WFC maximum stress.

176

Table 4.4 WFC Experimental Results in Web Only

Even though these webs were comprised of the same E-glass vinyl ester resin

composite material, there was a noticeable difference in the maximum stresses. The

difference between these two values may be due to the thickness variation; the small-

length webs were approximately half the thickness of the WFC webs. Since the

critical buckling load of a column depicted in Equation 3.2 is based on thickness

cubed, web buckling stress (load divided by thickness and depth) did not normalize

the webs [26, 44]. As a result, this mechanical property was not based on

Web

Specimen

Experimental

Bifurcation

Axial

Displacement

(in)

Experimental

Bifurcation

Strain (in/in)

Experimental

Maximum

Load (lb)

Experimental

Maximum

Stress (psi)

WFC1 0.027 0.029 2100 7500

WFC2 0.026 0.027 2200 7900

WFC3 0.020 0.022 1700 7100

WFC4 0.025 0.027 2200 8800

WFC5 0.011 0.012 800 5000

WFC6 0.020 0.022 1600 8600

WFC7 0.017 0.018 1500 8400

WFC8 0.016 0.017 1300 8000

WFC9 0.018 0.019 1200 9000

WFC10 0.017 0.018 1400 6200

WFC11 0.024 0.026 2200 9100

WFC12 0.018 0.019 1600 6000

Average 0.020 0.021 1700 7600

Standard

Deviation 0.0048 0.0051 450 1300

Coefficient

of

Variation

0.24 0.24 0.27 0.17

177

composition alone. Therefore, the small-length and WFC web buckling stresses were

not congruent.

Table 4.5 WFC CMAP Laminate Values for Web

E_x (psi) G_xy (psi) G_xz (psi) v_xy

WFC1 6.547E5 3.706E5 2.085E5 0.481

WFC2 6.595E5 3.774E5 2.093E5 0.484

WFC3 6.760E5 4.012E5 2.123E5 0.493

WFC4 6.717E5 3.949E5 2.115E5 0.491

WFC5 7.529E5 5.136E5 2.284E5 0.526

WFC6 7.120E5 4.536E5 2.190E5 0.510

WFC7 7.307E5 4.809E5 2.227E5 0.518

WFC8 7.378E5 4.913E5 2.243E5 0.520

WFC9 7.887E5 5.661E5 2.358E5 0.538

WFC10 6.829E5 4.113E5 2.135E5 0.496

WFC11 6.838E5 4.124E5 2.136E5 0.497

WFC12 6.615E5 3.802E5 2.097E5 0.485

Average 7.010E5 4.378E5 2.174E5 0.503

Standard

Deviation 4.293E4 6.266E4 8.699E3 0.019

Coefficient

of Variation 0.0612 0.143 0.0400 0.037

To compare the web buckling and WFC strains, Table 3.33 was juxtaposed to

Table 4.4. The WFC failure strains were dissimilar to the web buckling bifurcation

strains recorded by their strain gages. The average small-length bifurcation strain was

-0.0058 in/in, respectively, while the average experimental WFC failure strain was

0.021 in/in. This was most likely due to the inaccurate displacements measured for

the WFC samples. More research must be executed to further compare the web

buckling and WFC experimental properties.

The web buckling and WCS analyses were applied to the WFC samples. Each

WFC web thickness was inputted into CMAP and the web buckling equations to

178

calculate the theoretical SS and CC buckling loads. In addition, the maximum

compression failure load for each WFC sample was determined by utilizing the

average WCS maximum compression failure stress. Even though the average WFC

web thickness was approximately 31% greater than the WCS coupons, it was assumed

that the WCS compression failure stress and WFC maximum experimental stresses

were comparable. Compression failure stress is linear based on thickness [26]. The

failure mechanism of each WFC sample is quantitatively figured in the following

paragraphs.

To determine the WFC specimen’s web buckling loads, the web measurements

were inputted into the previously-mentioned computer software program CMAP. The

same method used in Section 3.5 was utilized. Tables 3.11 and 3.12 were used in the

CMAP materials section, while the thicknesses including the encrusted polymer were

supplied by Table 4.2. The CMAP web laminate results – including the mechanical

properties and stiffnesses – are listed in Tables 4.5 and 4.6. The theoretical buckling

loads will be discussed in the next paragraph.

Table 4.7 gives the calculated SS buckling loads, experimental maximum

loads from Table 4.4, calculated CC buckling loads, and back calculated maximum

compression failure loads for the WFC samples. The same beam buckling process

was performed as described in Section 3.6; WFC web dimensions and determined

stiffnesses were inputted into Equations 3.1 and 3.2.

179

Table 4.6 WFC CMAP Matrix Stiffness Values for Web

Specimen A_xx (x10^4 lb/in) D_xx (lb-in)

WFC1 1.172E5 134.7

WFC2 1.142E5 120.9

WFC3 1.050E5 85.12

WFC4 1.072E5 92.92

WFC5 7.978E4 25.17

WFC6 9.064E4 44.81

WFC7 8.514E4 33.85

WFC8 8.331E4 30.68

WFC9 7.306E4 16.81

WFC10 1.017E5 74.28

WFC11 1.014E5 73.14

WFC12 1.130E5 115.6

Average 9.764E4 70.67

Standard Deviation 1.478E4 40.41

Coefficient of Variation 0.1514 0.5718

The theoretical beam buckling formulae including transverse shear deformation was

utilized by inserting the web cross-sectional area A, effective shear stiffness G_xz,

bending stiffness D_xx, length Lw, and width dw parameters into the aforementioned

equations. The cross-sectional area A was defined by the total web thickness

multiplied by the web depth from Tables 4.1 and 4.2. The other parameters were

taken from Tables 4.1, 4.4, and 4.5.

A Southwell Plot graphical analysis was never employed for these samples.

As discussed in Section 3.7, this was due to their load-axial-displacement curves not

exhibiting a linear horizontal or semi-horizontal region after reaching their maximum

load. As a result their Southwell Plots were inconclusive.

180

Table 4.7 WFC Theoretical Buckling and Maximum Compression

Loads for Web Only

Specimen

Calculated SS

Buckling

Load (lb)

Experimental

Maximum

Load (lb)

Calculated

CC Buckling

Load (lb)

Back Calculated

Maximum

Compression Failure

(lb)

WFC1 2774 2100 11100 2900

WFC2 2514 2200 10050 2800

WFC3 1953 1700 7810 2500

WFC4 2150 2200 8600 2600

WFC5 618.1 800 2472 1600

WFC6 1074 1600 4294 2000

WFC7 819.2 1500 3277 1800

WFC8 722.6 1300 2891 1700

WFC9 387.6 1200 1550 1400

WFC10 1696 1400 6784 2400

WFC11 1756 2200 7023 2400

WFC12 2646 1600 10583 2700

Average 1592 1700 6370 2200

Standard

Deviation 845.2 450 3380 510

Coefficient

of

Variation

0.5307 0.27 0.5308 0.23

Likewise, the back calculated compression failure value was computed similar

to the web buckling specimens in Tables 3.31 and 3.32 by multiplying the web area

by the average experimental maximum compression stress of 10,300 psi from Table

3.30. The average stress was figured from the WCS experiments in Section 3.8. As

previously-mentioned a Hooke’s Law relationship was not employed due to the

WFC’s inaccurate measured axial strain and displacement.

Since the WFC web thicknesses – which impacted the calculated buckling

load by a power of 3 – were relatively large, the calculated buckling loads were

substantially greater than the web buckling specimens in Chapter 3. To start with, all

of the experimental maximum loads were less than the back calculated maximum

181

compression failure loads by approximately 81%. In turn, there were seven WFC

webs WFC4, WFC5, WFC6, WFC7, WFC8, WFC9, and WFC 11 that were

encompassed by their calculated SS and CC buckling loads. There were, however,

five samples WFC1, WFC2, WFC3, WFC10, and WFC12 that were smaller than their

calculated SS buckling loads. This may be due to imperfections in the sample during

manufacturing, or the applied load was not perfectly in-line with the centroid of the

web [26]. Imperfections in the web appeared to have contributed to a nonlinear nature

in which the ideal buckling load was never reached [53]. “The nonlinearity associated

even with small imperfections can substantially change…the associated prebuckling

stiffness” [53]. In turn, this affected the experimental maximum load. Listed in Table

4.2 the standard deviations of each web were relatively large due to the non-uniform

EP at an aforementioned ±10%. Even though average web thicknesses were

computed from 10 different measurements, their non-uniformity may have added

another variable in this investigation. The WFC web’s experimental buckling load

may be based on the web’s thinnest measurement, rather than its average.

Furthermore, “if a short or intermediate-length stocky column is considered, then the

applied load, as it is increased, may eventually cause the material to yield, and the

column will begin to behave in an inelastic manner” [26]. As a result, these webs

never achieved their critical buckling loads [26]. For simplification these samples

were not included in the subsequent research.

The pertinent data for the seven acceptable samples was listed in Tables 4.8

and 4.9. Included in these tables were their depths, foam widths, web thicknesses, and

web lengths along with their theoretical compressive moduli, maximum loads, and

maximum stresses. The theoretical, instead of experimental, compressive moduli

182

were tabulated since the strains were not accurately computed in the WFC

experiments. Strain gages were not included in these experiments, and as previously-

stated the Instron machine inaccurately measured displacements.

Whether or not the Polyiso Foam augmented the WFC web buckling loads

will be decided. The WFC buckled samples – tabulated in the last two tables of this

section – will be compared with the small-length web buckling specimens. Since the

average buckling stresses of these two samples were originally incompatible (due to

their difference in average thickness), a simple computation was executed for

comparison. Their buckling stresses were normalized by the constant maximum

compression stress (10,300 psi). The small-length normalized value, from the 6900

psi buckling stress listed in Table 3.33, equaled 0.67. The normalized WFC value

was computed as 0.79 from the 8100 psi WFC average buckling stress disclosed in

Table 4.9. The WFC normalized value was greater than the small-length number.

This demonstrates on average that the Polyiso Foam strengthened the WFC web’s

experimental buckling strength.

To conclude seven WFC webs had buckled. The accepted WFC buckled webs

were WFC4, WFC5, WFC6, WFC7, WFC8, WFC9, and WFC11. The other five

WFC specimens (WFC1, WFC2, WFC3, WFC10, and WFC12), however, were

deemed inconclusive since their experimental maximum loads were smaller than their

SS theoretical buckling loads.

183

Table 4.8 WFC Dimensions for Acceptable Samples

Sample Total Foam

Width (in)

Depth: d_w

(in)

Web Length:

L_w (in)

Web Thickness:

b_w (in)

WFC4 1.2164 2.0885 0.9208 0.1210

WFC5 1.5106 2.0819 0.9053 0.0759

WFC6 1.5305 2.0433 0.9033 0.0938

WFC7 1.4631 2.0939 0.9125 0.0848

WFC8 1.2934 2.0421 0.9143 0.0818

WFC9 1.2328 2.0391 0.9273 0.0649

WFC11 1.5539 2.1193 0.9138 0.1114

Average 1.4001 2.0726 0.9139 0.0905

Standard

Deviation 0.1472 0.0313 0.0083 0.0198

Coefficient of

Variation 0.1051 0.0151 0.0091 0.2189

Table 4.9 WFC Experimental Mechanical Properties Web Only for

Acceptable Samples

Sample

Theoretical

Compressive

Modulus (psi)

Critical Buckling

Load (lb)

Critical Buckling

Stress (psi)

WFC4 6.717E5 2200 8800

WFC5 7.529E5 800 5000

WFC6 7.120E5 1600 8600

WFC7 7.307E5 1500 8400

WFC8 7.378E5 1300 8000

WFC9 7.887E5 1200 9000

WFC11 6.838E5 2200 9100

Average 7.254E5 1500 8100

Standard

Deviation 4.029E4 520 1400

Coefficient of

Variation 0.06 0.33 0.18

In addition, the theoretical compressive moduli for the long-length and small-length

webs were computed in Section 3.5 at averages of 13% and 27%, respectively. These

values show that CMAP had figured the compressive moduli with relative accuracy.

184

Utilizing the average theoretical compressive modulus (7.253E5 psi) for the WFC

samples, an average theoretical bifurcation strain was figured (0.011 in/in ± 0.0026

in/in), which will be used in Chapter 5. Notably, the standard deviation of this value

was computed by comparing the standard deviations of the theoretical modulus and

experimental stress values. The next section summarizes the WFC chapter.

4.4 Conclusion of Web Core

Web core compression tests were performed in this chapter. The experiments

consisted of applying a quasi-static force in-line with the web. After compiling the

data, graphs were created of the samples’ responses with and without the foam

contribution. The WFC web results without foam contribution were quantitatively

compared to theoretical calculations. The figured theoretical buckling loads and

computed maximum compression loads were set against the experimental findings.

As a result, the WFC webs had buckled instead of failed in axial compression as seen

in Table 4.7. This correlated with the WFC web buckled photographs shown in

Figure 4.5. Consequently, the WFC webs had absorbed a significant amount of

energy since they had buckled instead of failed. Notably, the foam had decidedly

augmented the WFC web’s experimental buckling strength. These findings will be

incorporated into the next chapter. A complete description of the web core energy

absorption strength will be explained in Chapter 5.

185

Chapter 5

ENERGY ABSORPTION CAPABILITIES

5.1 Introduction to Energy Absorption Capabilities

This chapter combines the information from the preceding three chapters and

the extensive energy absorption analyses completed on the polyisocyanurate foam, E-

glass web, and web core. At first, a conceptual representation of mine blast theory

will be disclosed followed by an examination of the materials’ energy consumption

behavior. Maximization studies of the web core specimen will be discussed in the

Optimization and Design Improvement section of this chapter.

5.2 Mine Blast Theory

The theory behind the blast protection using advanced composites research

will be explained. To start with, one of the most effective ways to eliminate damage

to infrastructure from a blast is to utilize composites [54]. Figure 5.1 illustrates a blast

panel after fabrication, and Figure 5.2 represents a cross-section of the panel after it

was cut by a wet-diamond saw and the facesheets were grinded with a wet-sander to

ensure they were parallel. The composite blast panel shown in Figures 5.1 and 5.2

will be analyzed and designed to absorb a blast impulse.

186

Figure 5.1 Web Core Blast Panel Representation [17]

Figure 5.2 Web Core Blast Protection Panel Cross-Section [17]

To explain, a blast impulse, or dynamic loading, is the “time integral of force”

shown in Equation 1.4 and defined as the change in momentum with an applied force

[55]. A plan and section view of a panel impacted by a blast loading was illustrated in

Figures 5.3 and 5.4. A blast loading from an incendiary device is composed of a

spherical pressure moving at extremely rapid velocity, which as a result applies a

radial pressure [56]. Figure 1.14 depicted a spherical blast pressure representation.

The following paragraphs further discuss blast panels. Figures 5.3 and 5.4

were taken from a report by Hee-June Kim titled “Processing and Performance

Evaluation of Thick-Section Sandwich Composite Structures”; the foundation for this

187

research. This report along with other interim reports written by Kim had explored

the processing and ballistic testing of web core panels [9]. Westine’s model was also

explored to understand applied blast loading. As visualized in Figure 1.17, the blast

loading applied to a plate, or blast panel, is related to a mine’s stand-off distance,

dimensions, density, and embedment distance in a specific medium along with the

panel’s thickness and density [35]. Equation 1.3, which defines Figure 1.17, models

an impulse from a spherical blast applied over a plate [57]. In the aforementioned

equation, the variable for stand-off distance s is found numerous times. This is a

significant factor – second only to charge mass – in blast wave propagation since it

governs “the magnitude and duration of the blast loads” [56, 58]. Therefore, this was

included in the proceeding discussions.

Accordingly, the idealized overpressure versus time curve shown in Figure

1.15 is a representation of blast applied to an object. As explained in Chapter

1, the blast pressure applied to a panel rapidly increases and then decreases

exponentially with respect to time [58]. Jun Wei in 2006 formed an empirical

formula established to define the overpressure versus time curve is

( ) (

) (5.1) [59].

This was supplied in Wei’s article titled “Response of laminated architectural

glazing subjected to blast loading.” In this equation p(t) is overpressure as a function

of time, p0 is “peak overpressure observed when t is 0”, α is the “decay factor”, and td

is the duration of time overpressure remains in the positive phase [59].

188

Figure 5.3 Web Core Plan View of Blast Protection Panel after

Pressure Experiment [9]

Figure 5.4 Web Core Section View of Blast Protection Panel after

Pressure Experiment [9]

The variables p0, td, and α are “functions of the stand-off distance (radial distance) of

the target” [56]. This is complementary to the stand-off distance discussion from the

previous paragraph, which had also stated that stand-off distance is an important

element of dynamic loading. In Jun’s 2006 article, he had discussed an applied blast

loading. “The explosive blast wave has an instantaneous rise [having to do with p0 at

189

the instant the pressure acts on the blast panel], rapid decay, and relatively short

positive phase duration” illustrated in Figure 1.15 [59]. The blast impulse discussion

is continued in the next paragraph, which discusses what occurs when the blast

impulse reaches a protection panel.

To start with, a blast protection panel is designed to absorb more energy

through core crushing. The crush zone forms when the core plastically deforms

through squashing due to an applied compression normal to its facesheet.

Specifically, when a blast pressure p exceeds a panel’s constitutive crush pressure

pcrush, a panel’s crush zone develops. The larger the crush zone, the more energy is

absorbed by a blast protection panel. If the blast pressure p is less than pcrush the

panel’s core remains in the linear-elastic region of its stress-axial-strain curve. To

obtain pcrush for a blast panel, the WFC experimental maximum compression load was

used from Chapter 4. The experimental maximum load including the foam

contribution for exemplary specimen WFC8 was 1400 lbs over the unit cell planform

area. This value was given in Figure 4.6. As a sample computation, the WFC8

experimental maximum load was divided by the unit cell planform area (2” x 1.5”)

given in Figure 1.13. This equates to a pcrush of 470 psi for a blast protection panel

composed of WFC8 unit cells.

Furthermore, extensive research is required to optimize a panel’s energy

absorption capabilities. This research explains two methods to potentially increase

blast panel energy consumption. They are increasing the time the pressure wave

impacts the blast panel and modifying the blast panel components to optimize energy

absorption. The former method is discussed in the following paragraphs, while the

latter is examined in the next section.

190

The amount of time that a blast pressure wave collides with a panel may be

increased. Figures 5.5 to 5.9 illustrated this. An impulse curve first conceptualized in

Figure 1.16 was further elaborated in the preceding figures, which related blast

pressure to the crush zone of a protection panel.

Figure 5.5 Blast Representation 1

191

Figure 5.6 Blast Representation 2

Figure 5.7 Blast Representation 3

192

Figure 5.8 Blast Representation 4

Figure 5.9 Blast Representation 5

193

In these blast representations the middle vertical line was time, and point B denoted

the time at which the blast wave impacted the panel. Point B correlated with the

variable tB in Figure 1.16. The curve – exemplifying the pressure applied to the blast

panel – spread out from B in the subsequent blast representations. The blast panel

was depicted as the green-orange rectangle with its crush and no crush zones, and the

charge from which the blast pressure initiates was situated at the center of the panel at

some undefined stand-off distance. In addition, the horizontal line denoted the

constant crushing stress quantity pcrush based on the composition of the core. Each

blast representation figure showed different periods of time that a blast pressure wave

was applied to an energy absorption blast panel. In Figure 5.5 blast representation 1,

the pressure wave impacted for a small amount of time. The successive blast

representations continually increased the amount of time the blast wave was applied

to the panel. The longest amount of time that a pressure wave impacted a panel was

shown in blast representation 5.

As the wave pressure’s applied time was increased the blast panel crush zone

was expanded. This increased the panel’s energy consumption. Blast representation

1 only crushed a minimal amount of the panel, while blast representation 5 crushed a

large amount. Consequently, as time increased and the blast wave spread away from

panel point B the wave’s strength decreased. This was illustrated by the blast wave

approaching the pcrush threshold. In fact, the wave’s extremes in blast representation 5

were below the pcrush threshold. At some period of time, the blast wave no longer

crushed the panel core; i.e., had not caused any damage. To conclude, the crush zone

was maximized by increasing the period of time that the wave was applied to the

panel.

194

Furthermore, the resulting load from the applied blast pressure will be

imparted to the panel supports. An entire blast pressure p applied over a specific

panel area will react as loads through its supports [60]. As a result crushing will occur

at the panel’s supports (see for example Figure 4.5). This is due to large forces being

applied to the supports which have relatively small areas. Consequently, the stress of

the blast panel supports will exceed the pcrush threshold shown in the previous figures,

and the supports will exhibit damage. The supports need to be analyzed in further

blast protection panel research. The following section discusses crush zone

optimization techniques.

5.3 Modeling Foam, Web, and Web Core Failure Modes

This section involves arranging the experimental data into more simplistic

theoretical piece-wise linear curves. Load versus strain curves were first modeled for

the Polyiso Foam and E-glass web failure modes. Load-strain curves were employed

simplifying the foam, E-glass web, and web core comparisons.

To start with, a Polyiso Foam model was formed. An EPPR model was

created for simplicity since only three parameters were needed to compose this model

[23]. The foam Uniaxial Strain curve in Figure 2.21 was modified to construct a load-

axial-strain foam EPPR web core unit cell model in Figure 5.10. The foam Uniaxial

Strain curve in Figure 2.21 was modified to construct a web core unit cell model.

Foam in the web core sandwich panel was encompassed by the vertical webs; the

reason for utilizing the Uniaxial Strain model. This was comparable to the Uniaxial

Strain setup shown in Figure 2.5 in which the foam sample was prevented from

195

laterally expanding. As mentioned in Sections 1.3 and 2.3, the E-glass composite web

– similar to the steel collar – was orders of magnitude stiffer than the foam. By

multiplying the stress values in Figure 2.21 by the unit cell foam width and depth, the

subsequent EPPR model was formed. The unit cell depth was 2 inches. The

approximated 1.4-inch foam width was computed by subtracting the unit cell width

(1.5”) shown in Figure 1.13 from the WFC web thickness (0.0905”) from Table 4.8.

Figure 5.10 Load vs. Axial Strain Foam EPPR Model with Web Core

Dimensions

Next, the E-glass web buckling and axial compression failure models were

created given in Figures 5.11 and 5.12, respectively. Since the axial compression

failure model was simpler, it was created first. The model was taken directly from the

Web Compression Strength Tests Section. Even though the average WCS coupon and

0

20

40

60

80

100

120

140

160

180

200

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

(0.97, 87)(0.06, 87)

Axial Strain, (in/in)

Lo

ad

, P

(lb

)

Foam EPPR Model for WFC: Load, P (lb) vs. Axial Strain, (in/in)

196

WFC web thicknesses were not equal, their failure compressive stresses were

congruent. This was due to the WCS and WFC stresses being normalized by their

respective cross-sectional areas. The web compression failure model – illustrated in

Figure 5.11 – was a linear-elastic-to-failure curve. The linear-elastic-to-failure shape

is similar to the load-axial-displacement curves given in Figure 3.31. The WCS

specimens’ failure stress-strain data from Table 3.30 was used; the most important

values being the maximum compression stress (10, 300 psi ± 750 psi) and failure

strain (0.023 in/in ± 0.0033 in/in). To determine the model failure load for Figure

5.11, the simple stress formula was utilized. Hooke’s Law and the material’s elastic

moduli were not utilized, mentioned in the preceding chapters, due to the inaccuracy

of the axial strain measurements in the WCS experiments. The model maximum

compression load, using the aforementioned unit cell depth and average WFC web

thickness, equated to 1900 lbs ± 140 lbs. The model Figure 5.11 failure strain was

equal to the aforementioned WCS average experimental value.

The web buckling model was more complex. As previously-mentioned in

Section 4.3, the critical buckling load of a column is based on thickness cubed and

dividing load by area does not normalize stress results. Critical buckling stress is still

a function of thickness. Consequently, the thicknesses of the web buckling and WFC

webs were not similar.

197

Figure 5.11 Load vs. Strain Web Compression Failure Model using Unit

Cell Dimensions

The average small-length buckling web thickness (0.0569”) was approximately 60%

of the acceptable average WFC web thickness (0.0905”). Since critical buckling

stress is proportional to thickness squared, a web buckling model was not formed

from the small-length web buckling data. Even though their lengths were congruent,

their thicknesses were not similar. As a result, the average mechanical properties of

the WFC webs, which had decisively buckled, were utilized to develop the buckling

model given in Figure 5.12. These results were tabulated in Tables 4.8 and 4.9. The

buckling model’s bifurcation strain and critical buckling load were set at 0.011 in/in

and 1500 lbs, respectively.

0

300

600

900

1200

1500

1800

2100

0 0.005 0.010 0.015 0.020 0.025

Standard Deviation forLoad = 140 lbs

Standard Deviation forStrain = 0.0033 in/in

(0.023,1900)

Axial Strain, (in/in)

Lo

ad

, P

(lb

)

Web Compression Failure Model: Load, P (lb) vs. Axial Strain, (in/in)

198

Figure 5.12 Load vs. Strain Web Buckling Model using Unit Cell

Dimensions

An ideal column representation was formed for simplicity with the final strain equal

to 0.025 in/in. From Table 4.4, the final strain (0.014 in/in) was chosen as the

bifurcation strain (0.011 in/in) plus the standard deviation (0.0025 in/in), but limiting

the final strain’s value to only two significant figures.

Furthermore, non-linear failure and/or bifurcation regimes were conceived to

model a unit cell load-axial-strain curve. Figure 1.31 gives an example of a WFC

model, which is similar to the regimes described in this paragraph. The colors in the

subsequent graphs were congruent to Figure 1.31 with the red foam, blue web, and

black WFC unit cell. These regimes were reviewed to understand the unit cell’s

energy absorption profile. The (1) web buckled then the foam crushed, the (2) foam

crushed then the web buckled, the (3) web failed then the foam crushed, and the (4)

0

200

400

600

800

1000

1200

1400

1600

0 0.003 0.006 0.009 0.012 0.015

(0.014,1500)

Standard Deviation forLoad = 520 lbs

Standard Deviation for Strain = 0.0025 in/in

(0.011,1500)

Strain, (in/in)

Lo

ad

, P

(lb

)

Web Buckling Model: Load, P (lb) vs. Strain, (in/in)

199

foam crushed then the web failed were the four different unit cell model regimes.

Regimes 2 and 4 were decidedly impossible to achieve with the materials in this

research. The strain of the composite web, which buckled at 0.011 in/in and failed in

maximum compression at 0.023 in/in, would never be greater than the foam crushing

strain of 0.06 in/in. Regime Graphs 1 and 3 are illustrated in Figures 5.13 and 5.14.

They were setup as separate piecewise functions formed by combining the models

from Figures 5.10, 5.11, and 5.12. Notably, the foam in these curves had absorbed

more energy than the web since it had continued to crush and consume energy until its

final strain of 0.97 in/in. These figures were similar to the Chapters 2, 3, and 4

experimental results.

Figure 5.13 1) Web Buckles then Foam Crushes Regime

0

300

600

900

1200

1500

1800

2100

2400

0 0.02 0.04 0.06 0.08 0.10

UNIT CELLWEBFOAM

Unit CellIntegral = 95 lb-in/in

(0.011,1516)

(0.014,20) (0.06,87)

(0.011,1500)

(0.014,1500)

(0.014,1520)

Axial Strain, (in/in)

Lo

ad

, P

(lb

)

1) Web Buckles then Foam Crushes Model: Load, P (lb) vs. Axial Strain, (in/in)

200

Figure 5.14 3) Web Fails then Foam Crushes Regime

This paragraph compares the Regime Graphs to the WFC curves. At the end

of Chapter 4, seven of the twelve WFC webs were deemed acceptable samples. They

had decidedly buckled. With this experimental data the web bucking model of Figure

5.12 was formed. Consequently, Regime Graph 1 was naturally similar to the WFC

curves, and Regime Graph 3 was not. The values in Regime Graph 3 were

consistently greater than the WFC experimental numbers. To conclude, Regime

Graph 1 – the web buckled and then the foam crushed – was the most compatible to

the WFC experimental curves.

Moreover, the WFC experimental curves in Figure 4.6 exhibited a non-linear

section after bifurcation. Since the web no longer received any force, the

experimental curve appeared to have asymptoted towards the foam crushing load.

The foam crushing load was 87 lbs in Figure 5.10, and WFC7, WFC8, WFC9,

0

300

600

900

1200

1500

1800

2100

2400

0 0.02 0.04 0.06 0.08 0.10

UNIT CELLWEBFOAM

(0.06,87)(0.023,33)

(0.023,1900)(0.023,1933)

Axial Strain, (in/in)

Lo

ad

, P

(lb

)

3) Web Fails then Foam Crushes Model: Load, P (lb) vs. Axial Strain, (in/in)

201

WFC10, WFC11, and WFC12 appeared through graphic analysis to converge on this

value. More research needs to be conducted to verify this by extending the duration

of the experiment. By applying the load to the WFC samples for a longer period of

time, the WFC curves may resemble the foam experimental curves from Chapter 2.

This would verify my hypothesis.

In addition, the WFC graphs – after the web had buckled – contained a section

in which the curve gradually declined. This section was denoted as a progressive

collapse behavior. In order to more accurately model the WFC graphs, this behavior

must be understood. Modeling the web’s progressive collapse would allow one to

understand how the web and foam complement each other. The progressive collapse

behavior of the WFC specimens was not reviewed and incorporated into these models

since strain gages were not employed with the web plus foam compression tests. As

previously-mentioned in Section 3.8, cross-head displacement was utilized in the

WCS experiments which had inaccurately recorded displacement. Due to research

time constraints, more accurate methods of obtaining displacement data were not

used. More accurate strain gages, rather than a screw-driven Instron testing machine,

are required to quantitatively understand the progressive collapse nature of the WFC

samples.

Conclusively, Regime Graph 1 the web buckled prior to foam crushing was

compatible with the WFC quasi-static experimental results. More comprehensive

tests need to be executed to understand the WFC mechanical behavior after web

bifurcation and to incorporate this evidence in Regime Graph 1. The following

section optimizes and designs an improved web core unit cell.

202

5.4 Optimization and Design Improvement

Once the existing web core unit cell model was linearly defined, the quasi-

static model was perfected. The Polyiso Foam was optimized instead of the E-glass

vinyl ester resin web, since various types of foam with different mechanical properties

were more accessible. The Uniaxial Strain dimensions and mechanical properties

from Tables 2.2 and 2.4 were used for optimization. The foam’s compression

modulus, crushing stress, and density parameters of 440 psi, 27 psi, and 1.3E-3 pci

(2.24 pcf), respectively, were enhanced. Two methods were used to perfect the

polyisocyanurate foam in the web core unit cell.

Table 5.1 Mechanical Properties of DIAB Divinycell H-Grade Foam [5]

Property Unit Divinycell H Grade

H45 H60 H80 H100 H130 H200 H250

Nominal

Density: ρ0 pcf 3.0 3.8 5.0 6.3 8.1 12.5 15.6

Compressive

Stress psi 87 130 203 290 435 696 899

Compressive

Modulus psi 7250 10,150 13,050 19,575 24,650 34,800 43,500

First, the foam was optimized by replacing it with DIAB Divinycell H-Grade

Polymeric Foam. Second, the Polyiso foam was enhanced by defining a foam with

specific mechanical properties in order to perfect the web-foam relationship. This

method is explained at the end of this section. For comparison, an EPPR curve was

formed for each foam in this section.

DIAB Divinycell H-Grade Polymeric Foams were proposed due to their

availability. The H-Grade Foam density, compression strength, and compression

203

modulus – located on the DIAB website and listed in Table 5.1 – were utilized to

create a foam EPPR model as a load-strain curve for each grade. Equation 1.1 final

strain εmax was used for these analyses to compute the final strain εmax for each foam

representation. The preceding table data values along with the 81.16 pcf original

polymer density ρc acquired from DIAB Technical Services Manager Mr. James Jones

on 11/07/2007 were inputted into each foam EPPR curve. With this data, the final

strains listed in Table 5.2 were calculated for each Divinycell H-Grade Foam model.

The nominal foam density ρ0 and original polymer density ρc were entered as the

numerator and denominator, respectively, to figure the final strain εmax. In addition

explained in the subsequent verbiage, Table 5.2 lists each foams’ maximum

compression load and crushing strain.

Table 5.2 Divinycell H-Grade Foam Model Values

Divinycell H-

Grade

Final Strain εmax

(in/in)

Crushing Load

(lb)

Crushing Strain

(in/in)

H45 0.96 250 0.012

H60 0.95 369 0.013

H80 0.94 576 0.016

H100 0.92 822 0.015

H130 0.90 1230 0.018

H200 0.85 1970 0.020

H250 0.81 2550 0.021

Using the stress-load formula, each DIAB Divinycell Foam maximum

compression load was figured by multiplying each foam compression strength by the

subsequent unit cell dimensions. The unit cell depth shown in Figure 1.13 was 2” and

the total foam width was 1.4”.

204

Figure 5.15 H-Grade Foams in Unit Cell

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 0.01 0.02 0.03 0.04 0.05 0.06

UNIT CELLWEBH45 DIAB FOAM

(0.011,1500)

(0.012,1750)

Unit Cell Integral = 251 lb-in/in

(0.014,1750)

(0.014,250)

(0.012,250)

(0.014,1500)

(0.011,1729)

Axial Strain, (in/in)

Lo

ad

, P

(lb

)

Divinycell H45 Foam Regime Graph 1: Load, P (lb) vs. Axial Strain, (in/in)

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 0.01 0.02 0.03 0.04 0.05 0.06

UNIT CELLWEBH60 DIABFOAM

(0.014,1500)

(0.014,369)

(0.013,1869)

(0.011,1812)

Unit Cell Integral = 361 lb-in/in

(0.014,1869)

(0.011,1500)

(0.013,369)

Axial Strain, (in/in)

Lo

ad

, P

(lb

)

Divinycell H60 Foam Regime Graph 1: Load, P (lb) vs. Axial Strain, (in/in)

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 0.01 0.02 0.03 0.04 0.05 0.06

UNIT CELLWEBH80 DIABFOAM

(0.014,1500)

(0.011,1500)

(0.011,1896)

(0.020,2004)

(0.014,504)

Unit Cell Intregal = 550 lb-in/in

(0.016,576)

Axial Strain, (in/in)

Lo

ad

, P

(lb

)

Divinycell H80 Foam Regime Graph 1: Load, P (lb) vs. Axial Strain, (in/in)

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 0.01 0.02 0.03 0.04 0.05 0.06

UNIT CELLWEBH100 DIABFOAM

(0.014,1500)(0.011,1500)

(0.014,2267)

(0.011,2103)

Unit CellIntegral = 763 lb-in/in

(0.015,822)

(0.014,767)

Axial Strain, (in/in)

Lo

ad

, P

(lb

)

Divinycell H100 Foam Regime Graph 1: Load, P (lb) vs. Axial Strain, (in/in)

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 0.01 0.02 0.03 0.04 0.05 0.06

UNIT CELLWEBH130 DIABFOAM

(0.014,957)

(0.011,2251)

(0.014,2457)

(0.014,1500)

(0.011,1500)

Unit CellIntegral = 1109 lb-in/in

(0.018,1230)

Axial Strain, (in/in)

Lo

ad

, P

(lb

)

Divinycell H130 Foam Regime Graph 1: Load, P (lb) vs. Axial Strain, (in/in)

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 0.01 0.02 0.03 0.04 0.05 0.06

UNIT CELLWEBH200 DIABFOAM

(0.014,1500)

(0.014,2879)

(0.014,1379)

(0.011,2583)

(0.011,1500)

Unit CellIntegral = 1668 lb-in/in

(0.020,1970)

Axial Strain, (in/in)

Lo

ad

, P

(lb

)

Divinycell H200 Foam Regime Graph 1: Load, P (lb) vs. Axial Strain, (in/in)

205

Figure 5.15 Continued

The foam width value was computed by subtracting the 1.5-inch unit cell foam width

by the average WFC web thickness of 0.0905”. To determine the crushing strain for

each DIAB Foam, each compressive stress was divided by each compression modulus

from Table 5.1.

Appropriately, a theoretical graphic analysis was completed for the various

foam grades. Figure 5.16 detailed the Regime Graph 1 model with the various DIAB

H-Grade Foam mechanical properties replacing the Polyiso Foam for the red foam

and black unit cell lines. These curves were only theoretical models of the web core

unit cell; experiments need to be conducted to verify these curves are valid.

Normalized Energy Absorption = a_loadstrain/(A_F ρ_F+A_w ρ_w ) (5.2)

In order to compare the various foam grades and their energy absorption

capabilities a quantitative study was performed. Energy consumptions for each

Divinycell H-Grade Foam were computed by utilizing the EasyPlot integral function

and Equation 5.2. Equation 5.2 computes a normalized energy absorption value for

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 0.01 0.02 0.03 0.04 0.05 0.06

UNIT CELLWEBH250 DIABFOAM

(0.021,2550)

(0.011,1500)

(0.014,1500)

Unit CellIntegral = 2051 lb-in/in

(0.014,3200)

(0.014,1700)

(0.011,2835)

Axial Strain, (in/in)

Lo

ad

, P

(lb

)

Divinycell H250 Foam Regime Graph 1: Load, P (lb) vs. Axial Strain, (in/in)

206

each DIAB Foam unit cell in Figure 5.16. By normalizing the energy consumption of

each unit cell curve, each model was standardized.

Table 5.3 Constant Values for Equation 5.2

Area of Foam AF 2.8 in2

Density of Web ρw 0.0695 pci

Area of Web Aw 0.18 in2

The following explains the normalization of each unit cell’s energy absorption

capabilities. In addition to the piece-wise linear curves, Figure 5.16 depicted the unit

cell integral. Explained in Section 1.5 Maximizing Energy Absorption, an integral of

a linear load-axial-strain curve – or area under its curve – equates to energy absorbed.

This value was defined as aloadstrain. The normalized energy absorption numbers were

calculated by dividing the area under each unit cell curve by the density and area of

both web and core materials defined in Equation 5.2. The different foam mechanical

properties supplied in Table 5.1 and reproduced in Table 5.4 were taken into account.

In addition to the aloadstrain character, the variables AF, ρF, Aw, and ρw were

established as the unit cell foam area, foam density, unit cell web area, and web

density, respectively. The preceding tables depicted these variables. Table 5.3

provided the constant values used in Equation 5.2, and Table 5.4 detailed the density,

area under the unit cell curve, and the normalized energy absorption value for each

foam grade. The average density of the E-glass composite web was obtained from

Table 3.13. As seen in the following table and Figure 5.16, foam density and crushing

strength were directly related to energy absorption capacity.

207

Table 5.4 Normalized Energy Absorption Value from Equation 5.2

Foam

Grade

Foam Density:

ρF (pci)

Area under Unit Cell Curve:

aloadstrain (lb-in/in)

Normalized Energy

Absorption Value (in)

H45 1.7E-3 251 15,000

H60 2.2E-3 361 19,000

H80 2.9E-3 550 27,000

H100 3.6E-3 763 34,000

H130 4.7E-3 1109 43,000

H200 7.2E-3 1668 51,000

H250 9.0E-3 2051 54,000

The relationship between density and energy consumption is illustrated in Figure 5.17.

Each point represented the density-normalized-energy-absorption coordinate for the

corresponding DIAB Foam. The curve appeared to plateau as density increased; the

normalized energy absorption value seemed to asymptote approximately at 6E4

inches. As a result, the curve began to asymptote for foam density – and crushing

stress since it is proportional – at the DIAB Foam H250 coordinate [23]. Therefore,

any foam density or crushing stress greater than 9E-3 pci or 899 psi, respectively,

would not significantly increase the foam’s normalized energy absorption.

The following paragraphs detail the most optimal DIAB Divinycell H-Grade

Foam. The H200 and H250 Foams performed the best, viewed in Figure 5.16 and

Table 5.4. These foams had larger areas under their black unit cell curves than the

other samples. As the foam density increased, the crushing load increased; and

thereby, the unit cell absorbed more energy in the plastic-plateau region. The foam

crushing load was the defining factor in web core unit cell energy consumption.

208

Figure 5.16 Divinycell H-Grade Foams Normalized Energy Absorption

vs. Foam Density

Even though the H200 and H250 Foams had crushing loads greater than the H130

Foam, these two DIAB Foams were dismissed. The WFC experiments did not

examine a foam with a greater crushing strength than the web buckling load. In fact,

the Polyiso Foam crushing load was approximately 5% of the web buckling load in

the WFC experiments. A unit cell model in which the foam crushing strength was

greater than the web buckling load was not examined. In fact, this may have

introduced another variable into the experiment since a foam with a large crushing

strength – acting as supports detailed in Section 3.8 – may force axial compression

failure of the web. A unit cell of this nature was not examined due to research time

constraints. Consequently, a unit cell model with the foam crushing strength greater

0

2

4

6

8

10

1 2 3 4 5 6 7 8 9

Foam H250

Foam H200

Foam H130

Foam H100

Foam H80

Foam H60

Foam H45

Foam Density, (pci *10E-3)

No

rma

lize

d E

ne

rgy A

bso

rptio

n (

in *

10

E4

)

Divinycell H-Grade Foams: Normalized Energy Absorption (in) vs. Foam Density, (pci)

209

than the web buckling load was decidedly rejected. More research must be executed

to comprehend foams with relatively high crushing strengths. The next paragraph

designs the most optimal foam.

The second method of foam optimization was employed. By selecting specific

mechanical foam properties, the web core unit cell was perfected. A foam was

designed by picking specific mechanical properties to enhance the web core unit cell.

The most advantageous foam would have mechanical properties equal to the

composite web buckling model. This foam will have a crushing load and strain taken

from Figure 5.12 of 1500 lbs and 0.011 in/in, respectively. Based on the unit cell

dimensions and Hooke’s Law, the crushing stress equaled 540 psi, while the

compressive modulus computed as 4.9E5 psi utilizing the aforementioned crushing

strain. Since the crushing stress was between the H130 (435 psi) and H200 (696 psi)

compressive stresses listed in Table 5.1, the optimal foam density (10 pcf or 5.8E-3

pci) was chosen approximately halfway between the two. The final strain of 0.87

in/in between H130 and H200 from Table 5.2 was decided as the optimal foam’s final

strain.

Next, after the mechanical properties were chosen, models were formed. A

foam EPPR model was created, and then, a unit cell Regime Graph 1 model was

formed shown in Figure 5.17. Accordingly, a normalized energy absorption value

was figured for the optimal foam. The aloadstrain (1310 lb-in) and foam density ρF

(5.8E-3) values were inputted into Equation 5.2 along with the constants from Table

5.3. This resulted in the optimal foam’s normalized energy absorption value of

46,000 in. Since the H200 and H250 DIAB Divinycell Foams were dismissed, the

optimal, or perfected, foam exhibited the greatest energy consumption.

210

Figure 5.17 Optimal Foam in Unit Cell Based on Regime Graph 1

Notably, the original polyisocyanurate foam situated in the unit cell would

only have a normalized energy absorption value of approximately 5900 lb-in/in. With

the variables aloadstrain and foam density equal to 95 lb-in/in from Figure 5.13 and 1.3E-

3 pci from Table 2.2, respectively, the Polyiso Foam’s energy absorption value was

computed. This verified that the perfected foam was superior to the Polyiso Foam.

The optimal foam was approximately 4.5 times the density of the original unit cell

foam and nearly 7.8 times the energy absorption capacity. Consequently, weight was

increased by only 4.5 times the original unit cell foam weight, while energy

consumption was increased by a factor of 7.8. Matching the foam mechanical

properties with the web buckling values formed an optimized web core unit cell. To

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 0.01 0.02 0.03 0.04 0.05 0.06

UNIT CELLOPTIMAL FOAMWEB

(0.011,3000)

(0.014,3000)

(0.014,1500)

(0.011,1500)

Unit CellIntegral = 1310 lb-in/in

Axial Strain, (in/in)

Lo

ad

, P

(lb

)

Optimal Foam Regime Graph 1: Load, P (lb) vs. Axial Strain, (in/in)

211

verify the preceding theoretical graphic analyses, further research is required. Quasi-

static and dynamic experiments are necessary.

5.5 Conclusion of Energy Absorption Capabilities

In this chapter, the mine blast theory of an advanced composite web core blast

panel with an applied impulse was first reviewed. A unit cell was understood and

devised. Then, the E-glass vinyl ester resin web and Polyiso Foam materials

comprising the unit cell were modeled from the quasi-static mechanical tests executed

in Chapters 2, 3, and 4. Next, unit cell failure mode representations were formed.

Through quantitative and graphic analyses Regime Graph 1was deemed an accurate

representation of the web core failure mechanisms. In this graph the E-glass

composite web had buckled prior to the foam crushing. Finally, the web core unit cell

through foam design was optimized for quasi-static energy absorption. The designed

optimal foam offered superior energy absorption over the baseline polyisocyanurate

foam situated in the web core unit cell.

212

Chapter 6

CONCLUSIONS AND FUTURE WORK

6.1 Summary of Results for Each Chapter

Chapter 1 introduced the reasons for this research. First, the polyisocyanurate

foam and E-glass vinyl ester resin web mechanical properties were revealed. Then,

the unit cell dimensions were determined. Afterwards, the 2005 journal article by

Patrick M. Schubel and 1983 article by Wolf Elber exposed the similarities between

the quasi-static and low velocity impact behaviors of a composite sandwich panel.

Chapter 2 discovered the mechanical properties of the Uniaxial Stress and

Strain tests. By simple computation foam EPPR models were formed, which were

used in the Energy Absorption Capabilities Chapter. These models revealed that the

foam’s main energy consumption mechanism was by crushing.

Chapter 3 completely detailed the E-glass composite web. Along with the

extensive experimental results from the long-length and small-length web buckling

tests, several web analyses were executed. The composite web’s 29% fiber volume

fraction was disclosed. Additionally, the web buckling percent bending results,

theoretical web buckling loads, Southwell Plots, and web maximum compression

strengths were revealed. At the end of this chapter, it was discovered that all of the

specimens except four had buckled in the web buckling experiments.

213

Chapter 4 determined the web + foam compression test results. It was

discovered that the foam had crushed after the web had bifurcated, and after

compiling the data the WFC mechanical properties were tabulated. By calculating the

theoretical web buckling and maximum compression failure loads, seven of the

twelve WFC webs had decidedly buckled. The foam had decidedly augmented the

web’s experimental buckling strength.

Chapter 5 developed the materials’ energy consumption abilities. First, foam

in a web core unit cell, web buckling, and web failure models were formed. Then,

Regime Graph 1, in which web buckles then foam crushes replica, was discovered to

best represent the WFC curves. Next, the web core unit cell energy absorption was

maximized by replacing the Polyiso Foam with a more superior foam. The optimal

foam, which was designed by matching the web buckling model values, was the most

advantageous foam replacement in the TYCOR® web core unit cell. Based on

normalized energy absorption values, it consumed the most energy.

6.2 Future Work

The quasi-static impact defense research spawned two potential investigations

to increase the effectiveness of the blast protection panel. First, quasi-static optimal

foam web core studies shall be completed to verify the consumption optimization

study. Second, dynamic tests, employing a compressed air gun encased in an impact

chamber, shall be executed on the web core to verify the accuracy of both the Patrick

Schubel study from 2005 and the Wolf Elber examination in 1983. These were

explained in Section 1.4. These studies discovered that a web core’s mechanical

214

properties at a distance from the applied load did not differ significantly depending on

the applied load rate. Third, the WFC experimental curves must be comprehensively

understood to produce a more complete unit cell model. This would include modeling

the web’s progressive collapse behavior and revealing the symbiotic nature of the

combined foam and web unit cell. The energy absorption blast protection panel will

be undoubtedly augmented by these future research investigations. A better, more

robust, and more efficient blast panel to safeguard against potential attacks on crucial

infrastructure will be procured.

215

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Appendix

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