كتاب Elastomeric Polymers With High Rate Sensitivity - Applications in Blast, Shockwave, and Penetration Mechanics
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منتدى هندسة الإنتاج والتصميم الميكانيكى
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 كتاب Elastomeric Polymers With High Rate Sensitivity - Applications in Blast, Shockwave, and Penetration Mechanics

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كتاب Elastomeric Polymers With High Rate Sensitivity - Applications in Blast, Shockwave, and Penetration Mechanics  Empty
مُساهمةموضوع: كتاب Elastomeric Polymers With High Rate Sensitivity - Applications in Blast, Shockwave, and Penetration Mechanics    كتاب Elastomeric Polymers With High Rate Sensitivity - Applications in Blast, Shockwave, and Penetration Mechanics  Emptyالجمعة 03 نوفمبر 2023, 11:39 am

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Elastomeric Polymers With High Rate Sensitivity - Applications in Blast, Shockwave, and Penetration Mechanics
Edited by
Roshdy George Barsoum

كتاب Elastomeric Polymers With High Rate Sensitivity - Applications in Blast, Shockwave, and Penetration Mechanics  E_p_w_11
و المحتوى كما يلي :

Contents
List of Contributors xi
Preface . xv
Acknowledgments .xvii
1 History of High Strain Rate Elastomeric Polymers (HSREP) Application 1
Roshdy Barsoum
References 4
2 Phase Separated Microstructure and Structure–Property Relationships of High Strain Rate
Elastomeric Polyureas 5
James Runt, Autchara Pangon, Alicia Castagna, Yong He and Mica Grujicic
2.1 Introduction 5
2.2 Nanostructure and Dynamics of Bulk-Polymerized Polyureas 5
2.3 Influence of Thermal Treatments on Phase Separation and Dynamics 10
2.4 Influence of Mixed Soft Segments on Phase Separation and Dynamics 11
2.5 Role of Uniaxial Deformation on the Nanostructure and Dynamics of the P1000 Polyurea . 13
2.6 Role of Hard Segment Chemistry on Polyurea Nanostructure and Dynamics . 15
Acknowledgment . 16
References 16
3 Testing, Experiments and Properties of HSREP . 17
3.1 Pressure and Strain-Rate Sensitivity of an Elastomer: (1) Pressure-Shear
Plate Impact Experiments; (2) Constitutive Modeling . 17
Rodney J. Clifton and Tong Jiao
3.1.1 Introduction 17
3.1.2 Experiments 18
3.1.3 Experimental Results 31
3.1.4 Constitutive Model . 35
3.1.5 Numerical Simulations . 47
3.1.6 Discussion and Concluding Remarks . 52
Acknowledgments 55
Appendix A: Characterization of Pure Tungsten Carbide 55
Appendix B: Temperature Change During Pressure-shear Plate Impact Experiment . 61
References 63
3.2 Impact-Resistant Elastomeric Coatings . 65
C. Michael Roland and Carl B. Giller
3.2.1 Introduction 65
3.2.2 Experimental Methods . 65
3.2.3 Results 66
3.2.4 Summary 70
Acknowledgments 71
References 71vi Contents
3.3 Adhesive and Ultrahigh Strain Rate Properties of Polyurea Under Tension, Tension/Shear,
and Pressure/Shear Loadings with Applications to Multilayer Armors . 71
Vijay Gupta, Ryan Crum, Carlos Gámez, Brian Ramirez, Ninh Le,
George Youssef, Jason Citron, Andrew Kim, Amit Jain and Utkarsh Misra
3.3.1 Overall Structure and Executive Summary of the Chapter 71
3.3.2 Construction and Characterization of Polyurea Joints . 73
3.3.3 Behavior of Polyurea Under Ultrahigh Strain Rate Loading . 79
3.3.4 Application of Polyurea in Layered Armor Systems . 86
3.3.5 Conclusions 91
Acknowledgments 91
References 91
3.4 Time–Temperature Equivalence Under High and Ultrahigh Rates of Deformation . 92
Wolfgang G. Knauss and Guruswami Ravichandran
3.4.1 Introduction 92
3.4.2 Quasistatic Relaxation Behavior 93
3.4.3 Experimental Dynamic Arrangements . 94
3.4.4 Computed Simulation . 98
3.4.5 Comparison of Measured and Computed Dynamic Responses . 100
3.4.6 Summary 101
Acknowledgments 102
References 102
3.5 Optical Shock Hugoniot Measurements of Transparent and Translucent Polymers . 102
Gary S. Settles, Ryan M. Young, Forrest R. Svingala and Jeffrey F. Glusman
3.5.1 Introduction 102
3.5.2 Goals . 106
3.5.3 Experimental Methods . 106
3.5.4 Results and Discussion . 107
3.5.5 Conclusions 113
Acknowledgement 113
References 113
4 Constitutive Modeling of High Strain-Rate Elastomeric Polymers . 115
4.1 Mechanics of Large Deformation Behavior of Elastomeric Copolymers: Resilience,
Dissipation, and Constitutive Modeling . 115
Hansohl Cho and Mary C. Boyce
4.1.1 Introduction 115
4.1.2 Mechanical Behavior of Exemplar Elastomeric Segmented Copolymer Polyurea 116
4.1.3 Large Deformation Viscoelastic-Viscoplastic Constitutive Model 118
4.1.4 Stress–Strain Behavior of PU1000 at Low-to-High Strain Rate: Experiment versus Model . 121
4.1.5 Procedure for Determination of Material Parameters in PU1000 Model . 125
4.1.6 Stress–Strain Behavior of PU650 at Low-to-High Strain Rate: Experiment versus Model . 129
4.1.7 Conclusions 133
References 135
4.2 Environmental Test Methodology of Polymers 137
Daniel Hochstein, Lingqi Yang and Huiming Yin
4.2.1 Introduction 137
4.2.2 Accelerated Weathering Tests 139
4.2.3 A Multifunctional Weathering System . 140Contents vii
4.2.4 Acceleration Mechanisms of Long-term Performance of Polymers 142
4.2.5 Dimensional Analysis of Structural Model Testing . 146
4.2.6 Case Study of the Long-term Performance of Epoxy Adhesive Anchor Systems . 149
4.2.7 Conclusions 154
Acknowledgment . 156
References 156
4.3 An Investigation into the Nonlinearly Viscoelastic Behavior of Elastomeric Polymers
Under Dilatational and Shear Excitation . 159
Wolfgang G. Knauss and Guruswami Ravichandran
4.3.1 Introduction 159
4.3.2 Clock Models Versus Molecular Theories 160
4.3.3 Observation on the Importance of Dilatation in Nonlinear Viscoelasticity 161
4.3.4 An Application of the Dilatational Shift Phenomenon in Assessing the Yield-like
Behavior of PMMA 166
4.3.5 Nonlinear Behavior Induced by Shear . 174
Acknowledgments 183
References 183
5 Molecular Dynamics (MD) and Coarse Grain Simulation of High Strain-Rate
Elastomeric Polymers (HSREP) . 187
5.1 Molecular and Coarse-Grained (CG) Modeling of Shock Wave Mechanics in HSREP 187
Mica Grujicic, James Runt and James Tarter, Sr.
5.1.1 Introduction 187
5.1.2 All-atom Computational Shock-wave Physics . 190
5.1.3 Coarse-grained Computational Analysis 202
5.1.4 Concluding Remarks 212
References 214
5.2 Molecular and Coarse-Grained Methods for Microstructure-Property
Relations in HSREP . 216
Jay Oswald, Gaurav Arya, Zhiwei Cui and L. Catherine Brinson
5.2.1 Introduction 216
5.2.2 Qualitative Insights from Simple Coarse-grained Models . 216
5.2.3 Systematically Coarse-grained Model of Polyurea 225
5.2.4 Outstanding Challenges for CG Models 229
References 231
6 Computational Simulation, Multi Scale Computations, and Issues Related
to Behavioral Aspects of HSREP 233
6.1 Singlescale and Multiscale Models of Polyurea and High-Density Polyethylene (HDPE)
Subjected to High Strain Rates . 233
Vasilina Filonova, Yang Liu and Jacob Fish
6.1.1 Introduction 233
6.1.2 Viscoplasticity Model Based on Overstress and Generalization 234
6.1.3 Validation of the GVBO Model . 236
6.1.4 Multiscale Modeling of Polymers 244
6.1.5 Conclusion 252
Acknowledgment . 254
References 254viii Contents
6.2 Computational Simulation, Multiscale Computations, and Issues Related
to Behavioral Aspects of High Strain-Rate Elastomeric Polymers 256
S. Heyden and M. Ortiz
6.2.1 Introduction 256
6.2.2 Optimal Scaling and Specific Fracture Energy 257
6.2.3 Numerical Implementation . 258
6.2.4 Results 259
Acknowledgments 262
References 262
7 Properties of Hard and Soft Viscoelastic Polymers Under Blast Wave Loading 264
Susan Bartyczak and Willis Mock, Jr.
7.1 Introduction 264
7.2 Muzzle Adapter and Target Assembly 265
7.3 Experimental Details 267
7.4 Results and Discussion . 269
Acknowledgments 278
References 278
8 Modeling and Simulations, Applications in Ballistic and Blast . 280
8.1 Investigation of Phase Transformations in Impacted Polyurea Coatings Using
Small Angle X-Ray Scattering (SAXS) . 280
Edward Balizer, Susan Bartyczak and Willis Mock
8.1.1 Introduction 280
8.1.2 Experimental Procedures 281
8.1.3 Experimental Results 283
8.1.4 Conclusions 288
Acknowledgments 288
References 289
8.2 Mechanics of the Taylor Impact Behavior of Elastomeric Copolymers 290
Hansohl Cho, Susan Bartyczak, Willis Mock and Mary C. Boyce
8.2.1 Introduction 290
8.2.2 Constitutive Behavior of Glassy and Rubbery Polymers . 291
8.2.3 Taylor Impact Behavior of “Model” Glassy and Rubbery Polymers . 292
8.2.4 Taylor Impact Behavior of Elastomeric Copolymer Polyurea 1000 293
8.2.5 Conclusions 297
Appendix A: Experimental and Computational Setup of Taylor Impact Test 298
Appendix B: Effect of Adiabatic Heating and Temperature Rise
Due to Inelastic Deformation .299
Appendix C: Energy Storage Mechanism in Hyperelastic Rods Under High Speed Impact 300
Appendix D: Taylor Impact Behavior of PU650: Simulation Result . 301
References 303
8.3 A Modified Rate-Dependent Ballistic Impact Model for Polyurea 304
Christopher T. Key and Joshua E. Gorfain
8.3.1 Introduction 304
8.3.2 Constitutive Model . 305Contents ix
8.3.3 Model Demonstration . 308
8.3.4 Conclusions 317
Acknowledgments 317
References 317
9 Modification and Engineering of HSREP to Achieve Unique Properties . 319
9.1 Block Copolymer-based Multiscale Composites for Shock Mitigation . 319
Sia Nemat-Nasser, Alireza Amirkhizi, Kristin Holzworth, Zhanzhan Jia,
Wiroj Nantasetphong and Yesuk Song
9.1.1 Introduction 319
9.1.2 Polyurea-based Composites . 323
9.1.3 Characterization . 327
Acknowledgments 333
References 333
9.2 Effect of Polymer Coating on Helmet on Brain Injury-Associated Parameters 335
Philip Dudt, William Lewis, Kent Rye and Jonathan Kruft
9.2.1 Introduction 335
9.2.2 Instrumentation and Set-up 337
9.2.3 Results 339
9.2.4 Summary 345
References 345
10 The Interaction of High Strain-Rate Elastomeric Polymer Coating with the Substrate
Material and the Mechanisms of Failure . 346
10.1 Mechanisms Associated with High Strain Rate Elastomeric Polymers (HSREP)
and Interactions with Other Materials 346
Roshdy Barsoum
10.1.1 Mechanisms and Interaction with Substrate Material . 346
10.1.2 Effectiveness of HSREP in Suppressing Localization . 348
10.1.3 Mechanism in Steel Plates Subject to Blast, Underwater Explosion Testing and
Implications in Penetration Mechanics .349
10.1.4 Shock Wave Interaction/Attenuation at Interfaces and Dissipation . 353
10.1.5 Shock Wave Mitigation and Applications Related to the Protection Against
Traumatic Brain Injury 354
10.1.6 Conclusions 358
References 358
10.2 Characterization of the Mechanical Behavior of Polyurea and Polyurea-Coated
Metallic Components . 359
Kenneth M. Liechti and Krishnaswamy Ravi–Chandar
10.2.1 Introduction 359
10.2.2 Quasistatic Nonlinear Viscoelastic Behavior of Polyurea . 360
10.2.3 Dynamic Nonlinear Behavior of Polyurea . 367
10.2.4 Dynamic Experiments to Examine Response of Polyurea-coated Metal Specimens 371
Acknowledgments 398
References 399
Subject Index . 403
Subject Index
A
Abaqus
commercial FEM code, 83
simulation of, 33
Accelerated tests, 138
weathering tests, 139–140
Acrylic plate, 41
incident stress wave profile, 51
transmitted stress wave profile, 51
Adiabatic heating, 299
Adiabatic process, 138
Advanced combat helmet (ACH), 339
intracranial gage, 340
impulse comparison, 344
locations for, 344
intracranial gages, impulse
comparison, 344
Kevlar-based helmets, 339
polyurea coating, 339, 341
acceleration, 344
pressure–time plots, 341, 343
pressure wave, 343
Advanced Concept Technology
Demonstration-ACTD, 3
Aging effects, 138
Air Force material and the Navy’s
formulations, 3
Air Products Versalink P-1000
diamine, 17
All-atom computational shock-wave
physics, 190
all-atom computational model, 190
computational methods, 192
computational modeling and analysis,
190
force-fields, 190
generation of shock waves within
framework, 192–193
problem formulation, 193
AL-6XN stainless steel, 40
Amino alkoxysilanes, 325
Amirkhizi’s constitutive model, 304, 305
Annealing, 11
Arcan test, 365
calibration of distortional parameters,
365
comparison of best fits
from nonlinear analysis for cast
polyurea, 365
Armor-Piercing (AP) defeat, 46
Arruda–Boyce eight-chain elasticity
model, 120
Atmospheric test fixtures, 330
Atomic force microscopy (AFM) phase
image
baseline P1000 polyurea, 6
tapping mode phase images, 12
Axisymmetric finite element simulation,
298
B
Ballistic mitigation, mechanism of, 38
ballistic performance of steel substrates
with coatings of butyl/nitrile rubber, 30
improvement in ballistic performance,
28
material adjacent to impacted region, 66
maximum out-of-plane displacement, 29
Ballistic protective composites, 115
Bar (Hopkinson) alignment, specimen
preparation, 78–79
Bergstrom and Boyce constitutive model,
17
Blast protection, 256, 264, 355, 359
Blending, 12, 281
Bone simulant materials
polystyrene foam manikin head, 336
titanium powder metallurgy
components, 336
Brain
Gauge EGA3-5000D, location, 337, 339
Gauge EGA3-M-50D, location, 337,
339
fabrication steps, 336
skull simulation, fabrication steps for,
336
traumatic injury, 41, 50, 138, 210, 264,
335, 347
Brain injury-associated parameters
ACH helmet with polymer
pressure wave, 343
helmet variations, 341
impulse, 344
instrumentation and set-up, 337
intracranial gage, 340, 342
polymer coating effect on helmet, 335
power intensity, 344
pressure, 339
behind ear, 343
gages/accelerometers, 335
reflected, 341
test setup, 340
Bright-field Schlieren arrangement, 25
optics for gas–gun polyurea testing, 23
Brillouin-scattering test technique, 331
Bulk-polymerized polyurea, 17
C
Carbodiimide modified MDI triisocyanate,
281
Carleton Laboratory of Columbia
University, 139
Case studies
creep behavior of epoxy adhesive anchor
systems, 139
of long-term performance of epoxy
adhesive anchor systems,
149–154
Cauchy Green deformation tensors, 38
Cauchy stress, 120
tensor, 37
Ceramic, 39, 40, 140, 290, 397
Chemical degradation, 139
Chemical variations, 5
Clausius–Duhem inequality, 138
Clock models vs. molecular theories,
160–161
Coarse-grained computational analysis,
202
blast-induced shock wave mitigation,
211–212
demonstration of shock wave capture
and neutralize effect, 213
computational modeling, and analysis,
202, 205
coarse-graining, 202
force-fields, 202–205
fully supported shock wave mitigation,
206
hard-domain densification induced by
shock wave loading, 210
longitudinal shock wave generation
and propagation, 206
shock wave front profile, and width,
207
shock wave Lagrangian speed, 210
generation of shock waves within
framework, 205
linear-response mechanical properties,
206
microstructure characterization, 205
problem formulation, 205
Coarse-grained (CG)
molecular model, 7
of polyurea demixing, 7
simulation, 216, 226, 227
Coating
material, 42
polymer-coated ACH helmet, 341
of polyurea, 339404 Subject Index
Compression behavior, 116, 123, 170
Computed dynamic responses
comparison of measured and, 82–84
Computed simulation, 82
Constitutive behavior, 161, 290
of glassy and rubbery polymers, 291
Constitutive model, 35, 118, 119
ballistic limit of polyurea coated Armor,
310–313
effect of coating placement, 313–316
effect of coating thickness, 316–317
confined compression at various
temperatures, 308
elastomers, instantaneous finite elastic
deformation of, 40
elastic wave and Poisson’s ratio,
relation between, 41
transverse velocity–time profiles,
40, 41
elastomers, quasi-linear viscoelasticity,
43
finite deformations, work conjugates
for, 36
instantaneous elastic response under
pressure-shear loading, 38
material parameters, determination of,
42
elastic response, 43
partial differential equations, 42
model demonstration, 308
model modifications, 306–307
original viscoelastic model, 305
temperature shift relationship, 305
time–temperature superposition, 305
total deviatoric and creep strains, 306
using Prony series, 305, 306
measured relaxation data master
curve, 306
pressure, relaxation of, 47
pressure–shear plate impact, 309–310
CTH model of polyurea test (CTH
Shock wave Physics Code,
Developed by Sandia National
Lab), 310
material constants used for flyer/
sandwich plates, 310
measured and predicted, normal
velocity profiles/shear stress–
strain responses, 311
measured and predicted pressure
dependent shearing resistance,
312
test conditions examined, 258
representation of, 118
shear stress, relaxation of, 46
schematic interpretation of, 47
thermodynamics of elasticity, 38
first law of thermodynamics, 38
Rivlin model, 39
of VBO and GVBO, 234
Copolymer polyurea, mechanical behavior
of, 116
Corrosion resistance, 5, 138
Covalent cross-linking, effect of, 201
Crack propagation theory, 160
Crazing process, in steel/polyurea/steel
sandwich specimen, 256
Cryogenic temperature, 40
CTH model
of polyurea pressure–shear plate impact
test, 310
shock physics hydrocode, 304
Cyclic compression testing, 124
D
Deformation
ballistic, 37
behind-helmet, 335
creep, 143
elastic, 119, 280
high strain rate, 47
homogeneous, 58
inelastic, 201, 234, 294, 299
effect of adiabatic heating and
temperature rise, 299
inhomogeneous, 296
localized, 295
mechanical, 138
nonlinear, 115
plastic, 44, 119, 280, 389
profiles of glassy and rubbery polymeric
rods
during a Taylor impact test with, 292,
293
rates, 59, 76
residual, 117
shear, 396
ultrafast, 290
uniaxial, 13
uniform, 375, 377
viscoelastic–viscoplastic constitutive
model, large, 118–121
Degradation
and aging of, 146
chemical, 139
due to presence of moisture, 145
due to weathering, 139
of green technologies, 92
HSREP by distributed damage or failure
by fracture, 256
photodegradation of polymers, 145
of polymeric materials, 138
Dielectric relaxation spectroscopy
(DRS), 6
polymers characterization, 6
Differential scanning calorimetry (DSC),
10, 13, 15
Diisocyanate, 116
Dilute-randomly distributed inclusions
model, 326
Discovery and Invention (D&I), 3
DMA. See Dynamic mechanical analysis
(DMA)
Dog bone-shaped polyurea tensile test,
325
Doppler interferometer, 47
Double cantilever beam (DCB)
experiment, 32, 40
experimentally recorded load vs. load
point displacement curves, 33
Dow Corning Sylgard 527 silicon-based
gel, 335
Dow Isonate 143L, 17
Dragonshield, 37, 359
DRS. See Dielectric relaxation
spectroscopy (DRS)
DSC. See Differential scanning calorimetry
(DSC)
Dynamic experiments
dynamic response of Al 6061-O without
and with polymer coating,
374–375
nucleation of cracks and fragment
generation, 383
onset of strain localization, 375–381
statistics of strain localization,
381–383
uniform deformation, 375
dynamic response of polyurea, coated
metal rings and tubes, 389
dynamic tensile response of ductile
metals
stages, 389
experimental, 389
specimen preparation, 389–390
test method, 390–391
test procedures, 391
rate-dependent adhesion of polyurea
to steel, 389
traction-separation relations, 398
results/discussions, 391–395
comparison of softening stress with
maximum traction levels, 397
entire sequence of crack initiation
under shear loading, 396
intrinsic toughness in mode 1 and
mode 2 as a function of, 398
mode 1 fracture, 393–395
mode 2 fracture, 395
response of uncracked sandwich
specimens compared with, 397
tension and shear behavior of
sandwich specimens, 392
traction–separation relation for
shear for fracture at different
loading rates, 395
traction–separation relation in
opening mode fracture at
different loading rates, 394
uniaxial tension and shear behavior
of polyurea, 391–392
electromagnetic loading method
for dynamic tensile deformation of
metallic specimens, 372–374
to examine response of polyurea-coated
metal specimens, 371
modeling and numerical simulation,
384–389
Dynamic fracture strength, 40, 45Subject Index 405
Dynamic mechanical analysis (DMA), 6,
11, 17, 116, 131, 142, 229, 327,
329, 332
polymers characterization, 6
TTS of, 332
Dynamic nonlinear behavior, of polyurea,
367
experimental technique, 368
nonlinear waves, 367
results on one-dimensional nonlinear
waves, 369–371
E
E-glass composite, 40, 45
Elastic shear modulus, 296
Elastic wave theory, 26
Elastomeric coatings, impact-resistant
Armor-piercing (AP) defeat, 46
ballistic mitigation, 38
coating material, 42
effect of substrate, 40–42
multiple bilayers and laminates, 43
Elastomeric copolymers, 290
glassy/rubbery polymers, constitutive
behavior, 291
mechanical behavior, schematics of, 291
polyurea 1000, 293
polyurea 650, 293
stress–strain behavior, 292
Elastomeric polymers, 18
under dilatational and shear excitation
nonlinearly viscoelastic behavior, 110
Elastomeric polyurea, 37
processing advantages, 37
replacing continuous PU coatings with
cylinders, 19
STANAG 4241 and 4496 specifications,
39
“toughness,” 37
Elastomeric segmented copolymers, 115
Elastomers, 17
acoustic impedances, 17
wave speeds, 17
Elastomer sandwich, schematic, 268
Electric conductivity, 138
Electromagnetism, 44
Energy absorbing (EA) material, 359
Entropy, 6, 138, 161, 187, 192, 193, 222,
259
Environmental test methodology, for
polymers, 88
accelerated weathering tests, 139–140
acceleration mechanisms, long-term
performance of, 142
accelerated aging due to temperature,
144–145
accelerated fatigue, 143–144
aging due to moisture, 145
aging due to UV, 145–146
Boltzmann superposition principle,
143
dynamic mechanical thermal analysis,
142
time–temperature superposition
principle, 143
case studies, 149–154
dimensional analysis of structural model
testing, 146
Buckingham’s theorem, 146–147
similarity and model testing, 147–148
stress analysis of a flexible pavement,
example for, 148–149
multifunctional weathering system,
140–142
EPDM rubber, 17
tensile behaviour study, 17
Epoxy, 41, 55, 138, 149, 174, 268, 298
ERC. See Explosion resistant coating
Eshelby tensor, 326
Euler’s constant, 45
Experimental dynamic arrangements, 78
Experimental precision, 79
Explosion resistant coating (ERC), 1
Explosions, 1. See also Underwater
explosion (UNDEX) test
Explosive blast, 335
Extended finite element method (XFEM),
349, 355
F
Fabrication
brain, 336
manikin, 338
of mold, 337
skull simulation, steps, 336
techniques, 275
Fatigue, 138, 139, 143
tests, 144
First law of thermodynamics, 38
Flory-Huggins parameter, 218
Flory’s theory, 5
Force–displacement–temperature
controller, 330
setup, 329
Fourier series, 326
Fourier transform infrared (FTIR)
spectroscopy, 6, 142
Fragmentation, 37
Free energy, 119, 120, 192, 225, 229, 230,
257, 302
G
Gas-driven shock tube, pressure
measurements, 320
Gas-gun test, 26
Generalized viscoplasticity model, based
on overstress (GVBO), 233
high-density polyethylene, 236
experimental validation, 237–240
identification of VBO model
parameter, 236
polyurea, 240
model parameter identification,
240–241
validation for polyurea/steel bilayer,
241–244
validation of model, 236
Glass fibers
micron-scale, milled glass, 323
scanning electron microscope, 324
single fiber fragmentation test, 325
Glass microballoons, 325
Glass transition temperature (T
g
), 5, 14,
328
Glassy and rubbery polymers
constitutive behavior, 291
Taylor impact behavior, 292
selected geometric dimensions
and kinetic energy, evolution of,
293
Glassy polymers, 38, 48, 118, 160, 230,
291, 292, 297
constitutive behavior of, 291
deformation profiles of, 292
stress–strain behavior of, 292
Taylor impact behavior of, 292
H
HDPE. See High-density polyethylene
(HDPE)
Herman’s orientation factor, 14
High-density polyethylene (HDPE), 233,
236
High strain rate elastomeric polymers
(HSREP), 187, 256
computational models, 256
experiments and simulations test case
velocities, comparison, 261
OTM simulations for moderate and
high impact velocities, 260
postmortem damage, and fracture
patterns, 261
Taylor anvil test cases, 260
effectiveness in suppressing localization,
348
interactions with other materials,
mechanisms, 346
for coated high strength/high
toughness steel plates, 346–347
optimum thickness, coating for, 349
molecular and coarse-grained methods
microstructure-property relations in,
216–230
molecular and coarse-grained modeling
of shock wave mechanics, 187
numerical implementation, 258–259
crack-tracking scheme, for material
point discretization, 259
spatial discretization, used in optimal
transportation, 259
optimal scaling, and specific fracture
energy, 257–258
Hole size, in steel substrate, 30
Hopkinson bar
equipment, 61
technique, 17
HSREP. See High strain rate elastomeric
polymers (HSREP)
Hugoniot curve, 30406 Subject Index
Hugoniot data, 17, 18, 22
for PMMA, 55
Hugoniot elastic limit, 32
Humidity, 19, 139, 143, 145
Huntsman Rubinate 1680, 17
HybridSil™, NanoSonic Inc., polysiloxanebased coating, 3
Hydrogen bonding, 39
Hyperelastic rods
amplitude of kinetic energy oscillation,
300
evolution of normalized kinetic energy,
294
under high speed impact, energy
storage, 300
Hyperelastic polymer, 292, 300
Hysol 9394 epoxy, 40
Hysteresis, 116
loop and hysteresis stretch cycles
for PU250/1000, PU650, and
PU1000, 281
I
IED (Improvised Explosive Devices)
protection, 3
In situ X-ray scattering data, 115
Instron, 58
Instrumentation/gage diagrams, 337, 338
Intermolecular stress, 120
Internal energy, 138
change of, 138
density, 187, 193, 199
Isentrope (quasi-isentrope), 29, 31–33, 307
Isonate 143L isocyanate, 5
Isotropic linear elastic material, 40
J
J-integral curve, 44
J-integral time history, 44, 47
J-integral value, 43
Joint Enhanced Explosion Resistant
Coating Exploration–
JEERCEACTD, 3
K
Kapton electrical insulation film, 268
Kelvin model of linear viscoelasticity, 44
Kevlar KM2
helmet material, 277
polyurea 1000, 269, 277
Kremer–Grest model, 217
Kroner decomposition, 118
L
Laminates, 43
Laplace transform, 46
Large deformation viscoelastic–
viscoplastic constitutive model,
118–121
Large-scale atomic/molecular massively
parallel simulator (LAMMPS),
218
Layered armor systems
application of polyurea in, 86
high strain rate behavior
interferometrically reduced stress
wave profiles, 59
of polyurea-based multilayer
sections, 71–72
resonance frequencies for an
acrylic/polyurea/acrylic sample,
59
orientation-dependent impact
behavior of polymer/EVA bilayer
specimens at long wavelengths,
73
experimental procedure, 73
peak transmitted force recorded
in, 17
sample preparation, 73
LCA. See Life cycle assessment (LCA)
LCC. See Life cycle cost (LCC) analysis
Lennard–Jones model, 32
Lennard–Jones potential, 218
Life cycle assessment (LCA), 139
Life cycle cost (LCC) analysis, 139
Life cycle mechanical performance, 138
Life cycle performance, 138
of sustainable materials, 138
Long-term performance, of polymers
acceleration mechanisms of, 142
accelerated aging due to temperature,
143–145
accelerated creep strength, 143
accelerated fatigue, 143
aging due to moisture, 145
aging due to UV, 145–146
Boltzmann superposition principle,
143
dynamic mechanical thermal analysis,
142
time–temperature superposition
principle, 143
M
Manikin fabrication, 338
Marine Corps.(USMC), 3
Materials, dynamic response of, 17
Maxwell–Wagner–Sillars interfacial
polarization, 7
Mechanical behavior
under combined pressure–shear loading,
70
sample preparation, 70–71
under combined tension–shear loading,
71–85
constitutive models, features of PU1000
and PU650, 117
of elastomeric copolymers, 291
of exemplar elastomeric segmented
copolymer polyurea, 116–117
of PU650, 116
under tension, 70
Mechanical performance, of segmented
copolymer, 115
Methylene diphenyl diisocyanate (MDI)
polymers, 15
polyureas, 6
Microballoons, 324
Microstructure characterization, 205
hard-domain bridging by soft segments,
206
hard-domain formation, 205
nano-phase segregation, 205
Mie–Gruneisen equation, 304
Mie–Gruneisen parameters, for polyurea,
307
mild Traumatic Brain Injury (mTBI), 3
criteria, 3
MIL-Standards, 3
Moduli
quasi-linear viscoelasticity model, 52
rubbery values, 52
storage and loss, 54
vs. density, contour plot of fast wave
speed, 53
Moisture, 41, 44, 45, 138, 145, 156
Mold, fabrication, 337
Molecular dynamics (MD), 5, 14, 189,
192, 225. See also Coarsegrained (CG), simulation
Molecular segregation, 5
MTS equipment, 58
Multifunctional weathering system,
140–142
Multiple bilayers, 43
Multiscale modeling, of polymers, 233,
244
dispersion contribution, 247
reduced order homogenization, 244–247
validation of model, 247
HDPE, 247–248
polyurea, 249–252
N
Nanoparticles, 42
Nanosilicates, 42
Nanostructure and dynamics, of P1000
polyurea
role of uniaxial deformation on, 13
National Aeronautics and Space
Administration (NASA), 160
National Traffic Safety Board, 137
Navy-associated polyurea polymer, 1
NDI. See Normal displacement
interferometers (NDI)
Nd:YAG laser, 46
Neo-Hookean model, 32
Nonlinear behavior
induced by shear, 174–178
application of model, to multiple
element/spectral representations,
180–182
“ball-model” for segmental motion,
175
comparison of numerical data, 178
force-displacement relation of
equation for initial positions, 176Subject Index 407
molecular mechanics model, 175
normalization of data in by respective
maximal coordinate values, 177
relation between maximum force F
required for immediate slipping
as, 178
role of molecular interference on, 175
simple example for exploring model
characteristics, 178–180
of polymers/elastomers, 160
Nonlinearly viscoelastic behavior, of
elastomeric polymers, 159
Clock models vs. molecular theories,
160–161
under dilatational and shear excitation,
159
dilatational shift phenomenon, in
assessing yield-like behavior of
PMMA, 166
evaluation/observation, 169–174
initial analysis, 166–169
nonlinear behavior induced by shear,
174–178
application of model to, 180–182
exploring model characteristics,
178–180
summary/observation, 182
observation on importance of dilatation,
161–164
elastomer behavior, 162
note on apparent role of
entanglements, 162
volume-affiliated time-scaling in
polymers, 162–164
Nonlinear viscoelastic properties, of
polyurea
characterization, 359–360
parameters for model for polyurea, 367
Nonsulfur plastine modeling clay, 336
Normal displacement interferometers
(NDI), 19, 20, 26, 31, 56
NRL Naval research Lab, 1, 65
NSWC-CD’s (Naval Surface Warfare
Center, Carderock Div.)
recommendations, 3
Numerical simulations, 47
instantaneous elastic response, 47, 48
quasi-linear viscoelasticity model,
relaxation parameters, 48
velocity–time profile
comparison of, 48, 49
simulated and experimental, 50, 51
O
One-dimensional elastic wave theory, 19
Optical interferometer, 46
Optical setup for weak-shock Hugoniot
measurement
of polymer samples, 25
P
Parker 2-134 O-ring, 265
PCB 132A31 gauge, 265
Penn State Gas Dynamics Lab’s singlestage light-gas gun facility, 18
Phase separation and dynamics
influence of mixed soft segments on, 11
Influence of thermal treatments on, 10
Phase transformations, 281
experimental procedures
polymer/metal bilayer plate, crosssection of, 282
small angle X-ray scattering (SAXS),
280, 282
experimental results
metal/polymer layers, out-of-plane
deformation, 288
polymer orientation/plate geometry,
287
polyurea 250/1000 blend meridional
intensities, 287
polyurea 250/1000 blend SAXS
intensity patterns, 286
polyurea 650 meridional intensities,
285
polyurea 1000 meridional intensities,
284
polyurea 650 SAXS intensity
patterns, 284, 285
polyurea 1000 SAXS intensity
patterns, 283
high strain rate impact, 282
hysteresis loop and hysteresis stretch
cycles, 281
materials, 281
polyurea coatings using small angle
X-ray scattering (SAXS), 280
strain hardening, 280
Phenolic microballoons (PMB), 325
coefficients of thermal expansion (CTE),
325
microstructure of, 324
Photron Model SA-5, 19
Photron SA-5 camera, 31
50 phr N234 carbon black, 42
Piezoelectric pressure transducer
stagnation overpressure measurement, 322
Piola–Kirchoff stress tensor, 37
Piston impact, 35
PMB. See Phenolic microballoons (PMB)
Poisson’s ratio, 54, 120
Polarity, 39, 42
Polycarbonate plate, 41
Polyester, 138
Polyhedral oligomeric silsesquioxane
(POSS), 42
Polymer behavior, 17
Bergstrom and Boyce constitutive
model, 17
Polymer-coated ACH helmet, 341
Polymerization, 5
isonate 143L isocyanate, 5
temperature behavior, 34
temperature shift, 29
Polymer materials, 138
stress–strain relations, 271
Polymer protective coating, 138
Polymers explosion resistant coating
(ERC), 1, 2
applications, 3
Polytetramethylene oxide (PTMO), 5, 116
Poly(tetramethylene oxide di-paminobenzoate)s, 5
Polytetramethyleneoxideglycol, 281
Polyurea (PU). See also PU250; PU650;
PU1000; Versalink
ballistic limit of polyurea coated Armor,
310
behavior, under ultrahigh strain rate
loading, 69
block copolymer, 319
failure mitigation, effects, 319
microphase separation, 319
Schlieren/shadowgraph setup, 320
characterization
dynamic mechanical analysis (DMA),
327
ultrasonic wave measurements, 329
equipment/procedure, 329
pressure/rate/temperature, effects
of, 331
Prony series, 332
chemical structure of, 217
coarse-grained molecular level
analysis, 7
coated metal specimens
dynamic experiments to examine
response of, 371
coating, 321
construction and characterization of
joints. See Polyurea joints
DH-36 steel plate, coating, 320
dilute-randomly distributed inclusions
model, 326
dynamic nonlinear behavior, 367
effect of aging shock Hugoniot, 25
elastomeric coatings, 138
applications on metallic and
nonmetallic structures, 138
force modulation microscopy, 320
formulation effect
upon shock Hugoniot behavior, 24
function of temperature, 328
intrinsic tensile strengths of interfaces,
66
isocyanate and amine component, 319
longitudinal storage/loss moduli, 327,
331
mechanical and physical attributes of,
323
milled glass reinforced
storage modulus/loss modulus, 324
nanostructure, and dynamics
of bulk-polymerized polyureas, 5
role of hard segment chemistry on, 15
nonlinear viscoelastic behavior, 365
periodically distributed inclusions
model, 327
phenolic microballoon, 324408 Subject Index
longitudinal storage modulus of, 328
storage and loss moduli, 325
with phenolic microballoons, 326
polymerization temperature effect on
shock Hugoniot, 22
polyurea-based composites
micromechanical modeling, 326
microscale inclusions, effect of, 323
surface treatment, 325
quasi-isentrope of, 31
equation integration of, 32
group interaction modeling, 32
Lagrangian wave speeds, 31, 32
Lennard-Jones model, 32
Neo-Hookean model, 32
ring-up process analysis, 32
thick sample profiles, 31
thin sample profiles, 31
velocity–time profile, comparison
of, 33
quasistatic nonlinear viscoelastic
behavior, 360
role of hard segment chemistry, 15
role of uniaxial deformation, 13
SAXS intensity patterns, 283, 286
shearing resistance of, 34
pressure dependence of, 35
shear strain rate, 34
shear-stress vs. shear-strain curve,
34, 35
transverse velocities of, 34
shock mitigation, 320
shock wave mechanics, 187
steel, bonding strength, 319
systematically coarsegrained model, 225
Taylor impact behavior, 293
uniaxial tension and shear behavior, 391
Polyurea 250. See PU250
Polyurea 650. See PU650
Polyurea 1000. See Polyurea P-1000
Polyurea deformation. See Deformation
Polyurea elastomers. See various
elastomers and coating
Polyurea joints, 55
construction and characterization, 55
E-glass/polyurea/stainless steel joints,
construction of, 55
experimental procedures, 57–59
double cantilever beam experiment,
33
for dynamic fracture energy, 42
G
o
and G
c
values, 42
inelastic deformations, 42
intrinsic fracture energy of the joint,
33
laser spallation setup, 34
transient J-integral value, 43
experimental results for E-glass/
polyurea/steel joints, 61
dynamic fracture energy, 65
effect of hygrothermal loading on the
fracture energy, 66
intrinsic fracture energy, 65
intrinsic tensile strengths of
interfaces, 66
total fracture energy, 76
Polyurea polymers, 5
aging of, 34
derived stress–strain response, 53
wide- and small-angle X-ray scattering
profiles, 14
dynamic tensile strength and fracture
energy, 41
H–H bonding, 8
methylene diphenyl diisocyanate
(MDI)-based, 6
P1000 and P650, 6, 116
prototypical coarse-grained
microstructures, 9
schematic x – t diagram, 26
2, 6- toluene diisocyanate (TDI), 15
435 Polyurethane, 19
Polyurethanes, 6, 20, 22, 50
Polyvinyl chloride plastic, 336
Polyvinylidene difluoride (PVDF)
stress measurements, 268
p, p’-Diphenylmethane diisocyanate
(MDI), 281
Pressure-change, stress- and strain-rate
histories for, 53
Pressure-shear plate impact (PSPI)
simulations of, 54
temperature change, 61
Principal of virtual power, 36
Prony series
frequency-domain master curves, 332
relaxation modulus, 332
Pseudo-streak imaging, 21
ballistic-piston impact upon a clear
polyurethane test sample, 21
PU250, 281, 286, 287
PU650
Cauchy stress, 131
2D SAXS patterns for, 285
dynamic mechanical analysis (DMA)
data, 130
“effective” scaling factors, 131
hysteresis loop and hysteresis stretch
cycles for, 281
low to high strain rate behavior of, 132
mechanical behavior, 116
meridional intensities, 285
multiple cyclic tensile behavior, 133
parameters in the hard/soft network
mechanism, 122
phases, 131
resilient yet dissipative mechanical
behavior, 133
SAXS intensity patterns, 284–285
stress–strain behavior, at low to high
strain rate, 129
stress–strain data, 117
Taylor impact behavior of, 301
weight fraction of hard and soft
contents, 116
PU1000, 17, 19, 20
constitutive components, 131
dynamic mechanical analysis (DMA)
data, 130
elastic resilience, 133
flow stress in experiment and model
as a function of strain rate at,
132
hysteresis loop and hysteresis stretch
cycles for 250/1000 blends,
281
material parameters in, 125
mechanical behavior, 116
meridional intensities, 284
polymerization temperature effect on
Shock Hugoniot, 22–29
polyurea shock Hugoniot, 28
effect of aging on, 25–34
effect of repeated impacts on, 28
pressure and temperature dependence,
61, 62
procedure for determination of material
parameters in, 125
hard component, 126–128
soft component, 128–129
resilient yet dissipative mechanical
behavior, 133
SAXS intensity patterns, 283–284
shock Hugoniot effect of aging on, 25
shock wave energy dissipation, 24
stress–strain behavior, at low to high
strain rate, 121–123, 125
two-phase microstructures, 117
uniaxial compression of, 117
weight fraction of hard and soft
contents, 116
Pulse shaping, 79
Q
Qualitative insights, from simple
coarse-grained models,
216, 219
dynamical viscoelastic properties,
calculation of, 222–224
stress-relaxation spectrum/Fourier
transform, 223, 224
outstanding challenges for CG models,
229–230
polyurea modeling, 217–218
quasistatic thermomechanical properties,
calculation of, 218–221
computed bulk modulus and elastic
modulus, 221
H–H vs. S–S interactions, 218
structural differences between hard
and soft domains, 219
temperature-dependent specific
volume, 220
simple models, summary, 224
systematically coarsegrained model of
polyurea, 225
calibration of coarsegrained
potentials, 226
Polyurea (PU) (cont.)Subject Index 409
five bead coarse-grained model,
226
fully atomistic simulations, 225
stress relaxation function and
dynamic moduli, 227–229
comparison of frequencydependent, 229
dynamic scaling factor, 228
relaxation functions computed for,
228
Quartz gages
comparison between measurements and
simulation results at 20˚C, 69
extended time history of, 66
oscillation in, 67
for a pulse shaper of polyurea
room temperature record of forces
at, 63
split Hopkinson bar, 63, 71
“transmission strain,” 67
Quasi-isentrope. See Isentrope
(quasi-isentrope)
Quasi-linear viscoelastic model, 17
Quasistatic nonlinear viscoelastic behavior,
58, 360
experimental procedures, 361
Arcan specimens and grips, 362
uniaxial/confined compression, 362
nonlinear viscoelastic models, 360–361
parameters for nonlinear viscoelastic
model for polyurea, 367
shear and bulk relaxation master curves,
362–365
Quasistatic relaxation behavior, 77
Questar DR1 “telemicroscope,” 31
R
Rate-dependent ballistic impact model, for
polyurea
constitutive model, 305
model modifications, 306
original viscoelastic model, 305
model demonstration
coating placement, effect, 313
coating thickness, effect, 316
confined compression, at various
temperatures, 308
polyurea coated armor, limit of, 310
pressure–shear plate impact testing,
309
overview of, 304
Ree–Eyring viscoplastic flow model, 118,
302
Release wave experiments, 28
Abaqus simulation of, 33
impact configuration for, 28
reflection phenomena, 28
t–X diagram for, 29
velocity–time profile, 29, 30
Resilience behavior, 116
Rivlin model, 39
Rubbery polymer
constitutive behavior of, 291
deformation profiles of, 292
taylor impact behavior of, 292
S
Sandwiched pressure-shear plate impact
experiment, 18
compressive stress–strain curves,
26–28
configuration for, 25, 26
constant-pressure, 20
quasi-isentrope, study of, 20
shearing resistance, 20
elastic wave theory, 19
free surface velocity, 19
shearing resistance, 21
velocity–time profiles, 21
low-pressure, 24
normal velocities, 24, 25
shear stress, history of, 25
transverse velocities, 24, 25
t–X diagram for, 24
polyurea P-1000, experimental results
of, 19, 20
pressure-change, 22
normal stress for, 23
shear stress for, 23
projectile velocity, 19
symmetric, 25
t–X diagram, 18
Schlieren effect, 24
Schlieren imaging
average effective plastic strain, history
of, 321
dual lens arrangement, schematic
diagram, 321
shock interaction with obstacles, 320
Schlieren optics, 23
Schlieren photographs, 322
Schlieren setup, elastic response, 321
Segmental dispersion, 66
Segmental dynamics, 66, 69, 346, 353
Shadowgraph optical system
for shock Hugoniot testing of
transparent polymers, 20
Shear viscosity, 128
Shear wave measurements, 329
Shear yield stress, 128
Shift factor, 60
for compression at lower temperatures,
174
Shock Hugoniot measurements, in
polymers, 23
data for polyurethane and P-1000
polyurea, 22
results in (Us, Up) space for polyurea
formulation, 25
Shock-Hugoniot relations, determination
of, 196
analysis of, 197–198
fully mixed polyurea, 196–197
nanosegregated polyurea, 197
Shock-induced changes, in material-level
microstructure, 198–201
Shock-loading tests, 321–323
high-speed camera, 323
Shock transmission, 35
Shock wave, 17, 22, 24, 26, 32, 37
energy dissipation, 24
front structure, and motion dynamics,
193
fully mixed polyurea, 193–195
nanosegregated polyurea, 195
mechanics, in polyurea, 187
all-atom and coarsegrained
computational study, 188
ballistic protection, 189
shock-wave mitigation, 189
generation of a pair of shocks in a
molecular-level system, 188
mitigation, and applications
dynamic effects for, 320
location and propagation, 321
polyurea, 320
related to protection against traumatic
brain injury, 354–358
tests on animals, computations,
354–355
speed, 22
Shock wave interaction/attenuation, at
interfaces and dissipation,
353–354
effect of HSREP
on failure of thick composite plate
with HSREP (polyurea) due to
blast, 357
on vehicle dynamics, 358
experimental results of sabot impact and
confirmation of FE simulation
for, 354
HSREP coating applied to undercarriage
of vehicle, 357
Sabot impacting steel plated backed
with HSREP, 353
simulation using
multiscale FE with “solitons” for
shockwave interaction, 356
XFEM of continuous coating
(top) and diced coating with,
355
thick composite plate (without and
with HSREP) subject to blast,
356
Shore-40A hardness, 336
Shore 00 scale, 265
Shots 1303, 1202, 404
estimated temperature history, 63
SHPB. See Split-Hopkinson pressure bar
(SHPB) experiments
Silicon photodiode, 24
Simulation, 123, 125, 126, 142
deformation profiles of, 301
multiscale FE with “solitons” for
shockwave interaction, 356
results for test, 154, 155
XFEM of continuous coating and diced
coating with, 355410 Subject Index
Skull
accelerometer locations, 339
pressure gage locations, 337, 338
simulation, 336
fabrication steps, 336
Small-angle X-ray scattering (SAXS), 6,
12, 29, 116, 280, 282
absolute scattered intensity versus
scattering vector, 7
intensities, 6
investigation of phase transformations
in impacted polyurea coatings
using, 280–288
experimental procedures, 281–282
impacted plate geometry and
correlation to polymer
orientation, 287
polyurea 250/1000 blend meridional
intensities, 287
polyurea 250/1000 blend SAXS
intensity patterns, 286–299
polyurea 650 meridional intensities,
285
polyurea 1000 meridional intensities,
284
polyurea 650 SAXS intensity
patterns, 284–285
polyurea 1000 SAXS intensity
patterns, 283–284
x-ray scattering measurements, 282
synchrotron profile, 11
temperature dependent, 11
Smooth-On Dragon Skin®, 336
Soft-segment molecular weight, effect of,
201
Sorbothane, soft viscoelastic polyurethane
foam, 264
Sorbothane 30/Zorbium 83i bilayer
attenuation, 277
Spall plane, 29, 30
Split-Hopkinson bar apparatus, 46
Split-Hopkinson pressure bar (SHPB)
experiments, 34
SPSPI. See Symmetric pressure-shear plate
impact (SPSPI) experiment
Stagnation overpressure measurement
using piezoelectric pressure transducer,
322
Strain hardening, 280
Strain rate, 116, 128
Streak camera, 21
Stress–strain behavior, 116, 123
glassy polymer at a strain rate of, 292
hyperelastic polymer, 292
of PU1000 at low to high strain rate,
121–125
of PU650 at low to high strain rate
experiment vs model, 129
Stress-strain curve, 127
Stress waves, 18, 35
Structural damping, 44
Structural model testing
dimensional analysis of, 146
Buckingham’s theorem, 146–147
similarity and model testing, 147–148
stress analysis of a flexible pavement,
example for, 148–149
Structure failure, factors, 138
Substrate, effect of, 40
ballistic performance of polyurea
coatings
of varying thickness on HHS of
different Brinell hardnesses, 31
effect of rust on bilayer performance, 20
isolated contribution of coating to V-50
calculated assuming additivity of
coating and substrate, 31
penetration velocity of bilayers of butyl
rubber over HHS and polyurea
over HHS or UHHS, 32
Surface soiling, 138
Surface velocity, 46
Surrogate brain, 336
Sylgard brain simulant, 335
Sylgard gel, 335
Symmetric pressure-shear plate impact
(SPSPI) experiment, 25, 26
impact conditions for, 26
normal stress vs. free surface velocity,
60
shear stress vs. free surface velocity, 60
"Simple Wave” approach, 57
transverse velocity, 60
tungsten carbide (WC)
inferred relation, 58
simulation of, 57
Voce-Palm model, 59
T
Taylor impact behavior
axial-stress/inelastic strain rate, contours
of, 295
axisymmetric finite element simulations,
schematic for, 298
contours, 295
deformation profiles, 292, 293, 295
elastic shear modulus, 296
elastomeric copolymer polyurea,
293–296
energy storage, in hyperelastic rods,
300
evolution of
normalized kinetic energy, 297
selected geometric dimensions and
kinetic energy, 294
experimental/computational setup, 298
for testing, 298
geometric dimensions and kinetic
energy, 293, 294, 296
glassy and rubbery polymers, 292
inelastic deformation
adiabatic heating and temperature,
299
kinetic energy and deformation profile,
300
model glassy/rubbery polymers, 292
normalized kinetic energy, 297
polyurea 650, behavior of, 303
Taylor impact test, 290, 292, 293, 300
contours of axial-stress, and inelastic
strain rate, 295
contours of temperature evolution, 300
deformation profiles, 292, 295
experimental and computational setup
of, 298
geometric dimensions and kinetic
energy, evolution, 293–295, 297,
300
TDI. See Transverse displacement
interferometers (TDI)
2, 6-TDI polymer, 15
2, 4-TDI polymers, 15
Tearing resistance, 259
Temperature control
chamber, 62
and effect on transducers, 79
Tensile strength, 41
Thermodynamic incompatibility, 115
Thermoplastic elastomers, 5
Time–temperature equivalence. See also
WLF (Wiliam-Landel-Ferry)
equation
under high rates of deformation, 71
comparison of measured and computed
dynamic responses, 82–84
computed simulation, 82
experimental dynamic arrangements,
78
experimental precision, method and
pulse shaping, 79–80
quasistatic relaxation behavior, 77
specimen preparation and bar
alignment, 78–79
temperature control and effect on
transducers, 79
Time–temperature superposition (TTS),
305, 329. See also WLF
(Wiliam-Landel-Ferry) equation
principle, 70
at higher strain rates, 51
Time–temperature trade-off, 59
Toepler-type focusing shadowgraph
system, 19, 26
Total deformation gradient, 118
Transducers, 79
Transilluminated polymer samples for gasgun testing, 21
Transverse displacement interferometers
(TDI), 19
Traumatic brain injury (TBI), 335
blast-induced, 264
human threshold, 264
mild, 347
TTS. See Time-temperature superposition
(TTS)
Tungsten carbide (WC)
mechanical properties of flyers and
bounding plates used in PSPI
experiments, 19Subject Index 411
VISAR signals, 56
“Tuning” of polyurea shock-response
properties, 36
U
Ultraclear 435 Polyurethane, 22
Ultra high hard steel, 37
Ultrasonic wave measurement setup, 329,
330
Ultrasonic wave test fixture
high pressure, 330
low pressure, 330
Underwater Explosion (UNDEX) test, 1,
349
ballistic performance of HSRP–polyurea
and increase in ballistic
performance, 352
comparison studies
between computations using ductile
necking criterion and, 350
of failure of 2 in. thin steel plate
laboratory test vs. full-scale test
failure, 351
failure of small thin steel plate with and
without HSRP coating, 352
measuring HSREP effectiveness, 349
suppression of ductile necking by HSRP
for circular steel plate, 350
UNDEX. See Underwater Explosion
(UNDEX) test
Uniaxial compression test, 365–366
of responses and predictions from, 366
and tension data, of polyurea 1000 and
650, 117
Uniaxial tension behavior, 116
United States Army Long-Term Armor
Strategy (LTAS) specification, 39
USAF Tyndall AFB, 1
US Air Force, 1
USMC Iraqi Freedom Operations, 3
USMC. See Marine Corps
USS Cole disaster, 1
UV radiation, 138
V
van der Waals bonding, 138
VBO model parameter, identification of,
236
Velocity interferometer system for any
reflector (VISAR), 28
Velocity per fringe (VPF) value, 56
Versalinks, 5–7, 359
Very-weak-shock Hugoniot testing, 34
VISAR. See Velocity interferometer
system for any reflector (VISAR)
Viscoelastic deformation, 46
Viscoelasticity, 115
linearized theory, 159
Viscoelastic moduli, 329
Viscoelastic polymers, hard/soft
blast attenuation
bilayer targets, 276
for monolayer targets, 276
blast wave amplitude vs. polymer
thickness, 277
density/hardness measurements, 265
elastomer sandwich, schematic of, 268
energy absorption, 275
experimental work, 267
gas gun muzzle region, schematic of,
268
helmet–skull–brain system, 264
Kevlar KM2 fiber, 264
micrographs of, 266
monomer blast experiments, percent
energy absorbtion, 274
monomer targets, attenuation
coefficients, 277
muzzle adapter, 265
schematic of, 267
6061-T6 Al tube, 265
NSWCDD research gas gun, 264
overview of, 264
particle velocity, measurement, 270
polymer materials
longitudinal wave velocity vs. particle
velocity, 272
uniaxial stress vs. uniaxial strain, 273
results/discussion, 269
Sorbothane 50 equation, 275
Sorbothane 50 stress, stress-particle
velocity plot, 275
stress attenuation calculations, 275
6061-T6 Al, 270
target assembly, 265
pressure–time profiles, for PG1, 267,
269
schematic of, 267
Young’s Modulus, 270
Zorbium 83i, 274, 278
load and unload curves, 274
Viscoelastic properties, 57
of material, 58
Viscoelastic relaxation behavior, 331
Viscoelastic–viscoplastic constitutive
model, 115, 118, 121
athermal shear strength, 120
“average” chain stretch, 120
Cauchy stress, 120
chain limiting extensibility, 121
effective shear stress, 119
effective tensile stress, 121
initial bulk modulus of the material, 120
intermolecular elastic shear modulus,
120
intermolecular stress, 120
inverse Langevin function, 120
Kroner decomposition, 118
magnitude of inelastic flow, 119
normalized deviatoric stress tensor, 119
orientation parameter, 121
rate of plastic stretching, 119
total deformation gradient, 118
velocity gradient, decomposed into, 119
Viscoplasticity model based, 115
on overstress and generalization, 234
deformation-dependent elastic
constitutive tensor, 235
deformation-dependent viscosity
function, 235–236
VBO model for large rotation
problems, 234–235
Voce-Palm model, 59
W
WC. See Tungsten carbide (WC)
Weathering, 139
Weeks–Chandler–Anderson (WCA)
potential, 217
Wide-angle X-ray diffraction (WAXD)
profiles, 14
Wide angle X-ray scattering (WAXS)
measurements, 116, 280
WLF (Wiliam-Landel-Ferry) equation,
94, 161, 331. See also Timetemperature superposition (TTS)
200W Xenon, 19
X
XFEM. See Extended finite element
method
Y
Yield-like behavior, of PMMA, 166
dilatational shift phenomenon in
assessing, 166
evaluation, 169–173
initial analysis, 166–169
Young’s modulus, 46
Z
Zhou–Cilfton viscoplastic material model,
371
Zorbium
83i soft foam, 269
viscoelastic polyurethane hard foam


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