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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
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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.
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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.
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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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.
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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.
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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.
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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
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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
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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.
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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].
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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].
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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
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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.
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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.
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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
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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.
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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].
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Figure 1.10 G18 TYCOR® Plan View prior to Resin Infusion
Figure 1.11 G18 TYCOR® Side View Prior to Resin Infusion
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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]
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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
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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
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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].
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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
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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
Page 38
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.
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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)
Page 40
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 *
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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
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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
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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]
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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.
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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
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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.
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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
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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.
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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
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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,
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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,
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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.
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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,
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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.
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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.
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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.
Page 57
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.
Page 58
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)
Page 59
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
Page 60
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.
Page 61
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
Page 62
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
Page 63
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.
Page 64
48
Figure 2.6 All Uniaxial Strain Specimens
Figure 2.7 All Uniaxial Stress Specimens
Page 65
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
Page 66
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
Page 67
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)
Page 68
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)
Page 69
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.
Page 70
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)
Page 71
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)
Page 72
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
Page 73
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].
Page 74
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)
Page 75
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
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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.
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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)
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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.
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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.
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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.
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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]
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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
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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.
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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.
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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,
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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].
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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
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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.
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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
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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
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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
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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.
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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.
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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
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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-
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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.
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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
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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.
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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.
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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-
Page 101
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.
Page 102
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
Page 103
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
Page 104
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
Page 105
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
Page 106
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
Page 107
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
Page 108
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
Page 109
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
Page 110
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.
Page 111
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
Page 112
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
Page 113
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
Page 114
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
Page 115
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
Page 116
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
Page 117
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
Page 118
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.
Page 119
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.
Page 120
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.
Page 121
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.
Page 122
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
Page 123
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)
Page 124
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.
Page 125
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
Page 126
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
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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.
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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.
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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
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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
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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.
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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.
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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
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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%
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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.
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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
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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.
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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
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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.
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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
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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
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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
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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.
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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
Page 145
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
Page 146
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
Page 147
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.
Page 148
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
Page 149
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
Page 150
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
Page 151
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
Page 152
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
Page 153
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.
Page 154
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
Page 155
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.
Page 156
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
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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
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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
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(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
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(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
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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
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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
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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].
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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
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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
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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
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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.
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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.
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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
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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.
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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
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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
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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
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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.
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(a) (b)
(c) (d)
Figure 4.5 Web Core Specimens after Bifurcation (a) WFC1, (b)
WFC2, (c) WFC3, and (d) WFC4
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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.
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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
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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].
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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
Page 180
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
Page 181
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
Page 182
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
Page 183
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)
Page 184
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
Page 185
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
Page 186
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
Page 187
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
Page 188
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
Page 189
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.
Page 190
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
Page 191
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.
Page 192
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
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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
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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.
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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.
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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
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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
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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.
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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.
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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.
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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.
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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
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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].
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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
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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.
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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
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Figure 5.6 Blast Representation 2
Figure 5.7 Blast Representation 3
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Figure 5.8 Blast Representation 4
Figure 5.9 Blast Representation 5
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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.
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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
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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)
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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.
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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)
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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)
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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)
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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)
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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.
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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
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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”.
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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)
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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)
Page 222
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.
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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.
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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)
Page 225
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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.
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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)
Page 227
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.
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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.
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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
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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.
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Appendix
REPRINT PERMISSION LETTERS
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