كتاب Analysis and Performance of Fiber Composites
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 كتاب Analysis and Performance of Fiber Composites

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تاريخ التسجيل : 01/07/2009
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العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
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كتاب Analysis and Performance of Fiber Composites  Empty
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Analysis and Performance of Fiber Composites
Third Edition
Bhagwan D. Agarwal
Consultant
Lombard, Illinois, USA
Lawrence J. Broutman
Consultant
Chicago, Illinois, USA
K. Chandrashekhara
University of Missouri-Rolla
Rolla, Missouri, USA  

كتاب Analysis and Performance of Fiber Composites  A_a_p_11
و المحتوى كما يلي :


CONTENTS
Preface
1 Introduction
I.I Definition I
1.2 Characteristics I 2
1.3 Classification I 3
1.4 Particulate Composites I 5
1.5 Fiber-Reinforced Composites I 7
1.6 Applications of Fiber Composites I 10
Exercise Problems I 14
References I 15
2 Fibers, Matrices, and Fabrication of Composites
2.1 Advanced Fibers I l 6
2.1.1 Glass Fibers I l 6
2.1.1.1 Production of Glass Fibers I 17
2.1.1.2 Glass Composition and
Properties I 18
2.1.1.3 Su,face Treatment of Fibers: Sizes
and Coupling Agents I 18
2.1.1.4 Forms of Glass Fiber I 21
2.1.2 Carbon and Graphite Fibers I 23
2.1.3 Aramid Fibers I 26
2.1.4 Boron Fibers I 27
2.1.5 Other Fibers I 28
2.2 Matrix Materials I 30
2.2.1 Polymers I 30
xiii
1
16iv CONTENTS
2.2.1.1 Thermosetting and Thermoplastic
Polymers I 31
2.2.1.2 Polymer Properties of Importance to the
Composite I 31
2.2.1.3 Common Polymeric Matrix Materials I 34
2.2.1.4 Fillers I 39
2.2.2 Metals I 39
2.3 Fabrication of Composites 1 41
2.3.1 Fabrication of Thermosetting Resin Matrix
Composites I 42
2.3.1.1 Hand Lay-up Technique I 43
2.3.1.2 Bag Molding Processes I 46
2.3.1.3 Resin Transfer Molding I 49
2.3.1.4 Filament Winding I 49
2.3.1.5 Pultrusion I 51
2.3.1.6 Preformed Molding Compounds I 53
2.3.2 Fabrication of Thermoplastic-Resin Matrix
Composites (Short-Fiber Composites) I 55
27.3 Fabrication of Metal Matrix Composites I 58
2.3.4 Fabrication of Ceramic Matrix Composites I 59
Suggested Reading I 60
3 Behavior of Unidirectional Composites
3.1 Introduction I 62
3.1.1 Nomenchiture I 62
3.1.2 Volume and Weight Fractions I 64
3.2 Longitudjnal Behavior of Unidirectional C9mposites I 67
3.2.1 Initial Stiffness I 68
3.2.2 Load Sharing I 71
3.2.3 Behavior beyond Initial Deformation I 73
3.2.4 Failure Mechanism and Strength I 74
3.2.5 Factors Influencing Longitudinal Strei;igth and
Stiffness I 76 ·
3.3 Transverse Stiffness·and Strength I 80
3.3.1 Constant-Stress Model I 80
3.3.2 Elasticity Methods of Stiffness Prediction I 83
3.3.3 Halpin-Tsai' Equations for Transverse Modulus I 85
62CONTENTS V
3.3.4 Transvyrse Strength I 87
3.3.4.1 Micromechanics of Transverse Failure I 88
3.3.4.2 Prediction of Transverse Strength I 90
3.4 Prediction of Shear Modulus I 91
3.5 Prediction of Poisson's Ratio I 95
3.6 Failure Modes I 96
3.6.1 Failure under Longitudinal Tensile Loads I 100
3.6.2 Failure under Longitudinal Compressive Loads I 102
3.6.3 Failure under Transverse Tensile Loads I 106
3.6.4 Failure under Transverse Compressive Loads I 107
3.6.5 Failure under In-Plane Shear Loads I 107
3.7 Expansion Coefficients and Transport 'Properties I 108
3.7.l Thermal Expansion Coefficients I 108
3.7.2 Moisture Expansion Coefficients I 114
3.7.3 Transport Properties I 114
3.7.4 Mass Diffusion I 117
3.8 Typical Unidirectional Fiber Composite Properties I 123
Exercise Problems I 124
References I 129
4 Short-Fiber Composites
4.1 Introduction I 132
4.2 Theories of Stress Transfer I 133
4.2.1 Approximate Analysis of Stress Transfer I 133
4.2.2 Stress Distributions from FiniteJElement
Analysis I 137
4.2.3 Average Fiber Stress I 139
4.3 Modulus and Strength of Short-Fiber Composites I 140
4.3.1 Prediction of Modulus I 141
4.3.2 Prediction of Strength I 145
4.3.3 Effect of Matrix Ductility I 150
4.4 Ribbon-Reinforced Composites I 152
Exercise Problems I 155
References I l56
132vi CONTENTS
5 Analysis of an Orthotropic Lamina
5.1 Introduction I 158
5.1.1 Orthotropic Materials I 158
5.2 Stress-Strain Relations and Engineering Constants I I 60
5.2.1 Stress-Strain Relations for Specially Orthotropic
Lamina I 161
5.2.2 Stress-Strain Relations for Generally Orthotropic
Lamina I 164
5.2.3 Transformation of Engineering Constants I I66
5.3 Hooke's Law and Stiffness and Compliance Matrices I 174
5.3.1 Geaeral Anisotropic Material I 174
5.3.2 Specially Orthotropic Material I 177
5.3.3 Transversely Isotropic Material I 180
5.3.4 Isotropic Material I 181
158
5.3.5 Specially Orthotropic Material under Plane Stress I 182
5.3.6 Compliance Tensor and Compliance Matrix I 184
5.3.7 Relations between Engineering Constants and Elements
of Stiffness and Compliance Matrices I 185
5.3.8 Restrictions on Elastic Constants I 187
5.3.9 Transformation of Stiffness and Compliance
Matrices I 189
5.3.10 Invariant Forms of Stiffness and Compliance
Matrices I 194
5.4 Strengths·of an Orthotropic Lamina I 196
5.4.1 Maximum-Stress Theory I 197
5.4.2 Maximum-Strain Theory I 200
5.4.3 Maximum-Work Theory I 203
5.4.4 Importance of Sign of Shear Stress on Strength of
Composites I 205
Exercise Problems I 209
References I 212
6 Analysis of Laminated Composites
6.1 Introduction I 213
6.2 Laminate Strains I 213
6.3 Variation of Stresses in a Laminate 21q
6.4 Resultant Forces and Moments: Synthesis of Stiffness
Matrix I 218
6.5 Laminate Description System I 225
6.6 Construction and Properties of Special Laminates I 226
6.6.1 Symmetric Laminates I 227
6.6.2 Unidirectional, Cross-Ply, and Angle-Ply
Laminates I 228
6.6.3 Quasi-isotropic Laminates I 229
6.7 Determination of Laminae Stresses and Strains I 238
6.8 Analysis of Laminates after Initial Failure I 247
6.9 Hygrothermal Stresses in Laminates I 263
6.9.1 Concepts of Thermal Stresses I 263
6.9.2 Hygrothermal Stress Calculations I 264
6.10 Laminate Analysis Through Computers I 272
Exercise Problems I 277
References I 281
Analysis of Laminated Plates and Beams
7.1 Introduction I 282
7.2 Governing Equations for Plates I 283
7.2.1 Equilibrium Equations I 283
7.2.2 Equilibrium Equations in Terms of
Displacements I 286
7.3 Application of Plate Theory I 288
7.3.1 Bending I 288
7.3.1.1 Bending of General Laminates I 294
7.3.2 Buckling I 295
7.3.3 Free Vibrations I 301
7.4 Deformations Due to Transverse Shear I 306
7.4.1 First-Order Shear Deformation Theory I 306
7.4.1.1 Transverse Shear Deformation Effects in
Bending of a Simply Supported Rectangular
Specially Orthotropic Plate I 309
7.4.2 Higher-Order Shear Deformation Theory I 311
7.5 Analysis of Laminated Beams I 314viii CONTENTS
7.5.1 Governing Equations for Laminated Beams--/ 314
7.5.2 Application of Beam Theory I 315
7.5.2.1 Bending I 315
7.5.2.2 Buckling I 318
7.5.2.3 Free Vibrations I 319
Exercise Problems I 320
References I 322
8 Advanced Topics in Fiber Composites
8.1 Interlaminar Stresses and Free-Edge Effects I 324
8.1.1 Concepts of lnterlaminar Stresses I 324
8.1.2 Determination of Interlaminar Stresses I 326
8.1.3 Effect of Stacking Sequence on Interlaminar
Stresses I 328
8.1.4 Approximate Solutions for Interlaminar
Stresses I 330
8.1.5 Summary I 334
8.2 Fracture Mechanics of Fiber Composites I 335
8.2.1 Introduction I 335
8.2.1.1 Microscopic Failure Initiation I 335
8.2.1.2 Fracture Process in Composites I 336
8.2.2 Fracture Mechanics Concepts and Measures of
Fracture Toughness I 338
8.2.2.1 Strain-Energy Release Rate (G) I 339
8.2.22 Stress-Intensity Factor (K) I 341
8.2.2.3 ]-Integral I 345
8.2.3 Fracture Toughness of Composite Laminates I 346
8.2.4 Whitney-Nuismer Failure Criteria for Notched
Composites I 349
8.3 Joints for Composite Structures I 355
8.3. l Adhesively Bonded Joints I 355
8.3.1.1 Bonding Mechanisms I 355
8.3.1.2 Joint Configurations I 356
8.3.1.3 Joint Failure Modes I 357
8.3.1.4 Stresses in Joints I 358
8.3.1.5 Advantages and Disadvantages of
Adhesively Bonded Joints I 359
324CONTENTS ix
8.3.2 Mechanically Fastened Joints I .360
8.3.2.1 Failure Modes of Mechanically Fastened
Joints I 360
8.3.2.2 Advantages and Disadvantages of
Mechanically Fastened Joints I 361
8.3.3 Bonded-Fastened Joints I 361
Exercise Problems I 362
References I 363
9 Performance of Fiber Composites: Fatigue, Impact, and
Environmental Effects 368
9.1 Fatigue I 368
9.1.1 Introduction I 368
9.1.2 Fatigue Damage I 370
9.1.2.1 Damage/Crack Initiation I 370
9.1.2.2 Crack Arrest and Crack Branching I 370
9.1.2.3 Final Fracture I 373
9.1.2.4 Schematic Representation I 373
9.1.2.5 Damage Characterization I 374
9.1.2.6 Influence of Damage on Properties I 375
9.1.3 Factors Influencing Fatigue Behavior of
Composites I 378
9.1.4 Empirical Relations for Fatigue Damage and Fatigue
Life I 385 --
9.1.5 Fatigue of High-Modulus Fiber-Reinforced
Composites I 386
9.1.6 Fatigue of Short-Fiber Composites I 390
9.2 Impact I 395
9.2.1 Introduction and Fracture Process I 395
9.2.2 Energy-Absorbing Mechanisms and Failure
Models I 396
9.2.2.1 Fiber Breakage I 396
9.2.2.2 Matrix Deformation and Cracking I 398
9.2.2.3 Fiber Debonding I 399
9.2.2.4 Fiber Pullout I 399
9.2.2.5 Delamination Cracks I 401
9.2.3 Effect of Mater;als and Testing Variables on Impact
Properties I 401X CONTENTS
9.2.4 Hybrid Composites and Their Impact Strength /. 407
9.2.5 Damage Due to Low-Velocity Impact I 411
9.3 Environmental-Interaction Effects I 416
9.3.1 Fiber Strength I 416
9.3.1.l Features ofStress Corrosion I 416
9.3.1.2 Static Fatigue and Stress-Rupture of
Fibers I 417
9.3.1.3 Stress Corrosion of Glass Fibers and
GRP I 419
9.3.2 Matrix Effects I 422
9.3.2.l Effect of Temperature and Moisture I 422
9.3.2.2 Degradation at Elevated Temperatures I 426
9.3.2.3 Stress-Rupture Characteristics at Modest
Exercise Problems I 431
References I 431
Temperatures I 429
10 Experimental Characterization of Composites
10.1 Introduction I 439
l0.2 Measurement of Physical Properties I 440
10.2.l Density I 440
10.2.2 Constituent Weight and Volume Fractions I 441
10.2.3 Void Volume Fraction I 442
10.2.4 Thermal Expansion Coefficients I 442
10.2.5 Moisture Absorption and Diffusivity I 443
I0.2.6 Moisture Expansion Coefficients I 444
I0.3 Measurement of Mechanical Properties I 445
10.3.1 Properties in Tension I 445
I0.3.2 Properties in Compression I 449
I0.3.3 In-Place Shear Properties I 452
10.3.3.1 Torsion Tube Test I 452
10.3.3.2 Iosipescu Shear Test I 453
10.3.3.3 [±45Js Coupon Test I 455
10.3.3.4 Off-Axis Coupon Test I 456
10.3.3.5 Other Tests I 458
10.3.4 Flexural Properties I 459
439CONTENTS xi
10.3.5 Measures of In-Plane Fracture Toughness I 463
10.3.5.J Critical Strain-Energy Release
Rate,(GJ I 463
10.3.5.2 Critical Stress-Intensity Factor or Crack
Growth Resistance (K_R) I 464
10.3.5.3 Critical J-Intergral (J) I 470
10.3.6 Interlaminar Shear Strength and Fracture
Toughness I 471
10.3.7 Impact Properties I 475
10.4 Damage Identification Using Nondestructive Evaluation
Techniques I 481
10.4.1 Ultrasonics I 481
10.4.2 Acoustic Emission I 483
10.4.3 x-Radiography I 485
10.4.4 Thermography I 486
10.4.5 Laser Shearography I 488
10.5 General Remarks on Characterization I 488
Exercise Problems I 490
References I 491
11 Emerging Composite Materials
11.1 Nanocomposites I 496
11.2 Carbon-Carbon Composites I 498
11.3 Biocomposites I 498
11.3.1 Biofibers I 498
11.3.2 Wood-Plastic Composites (WPCs) I 501
11.3.3 Biopolymers I 502
11.4 Composites in "Smart" Structures I 503
Suggested Reading I 504
Appendix 1 Matrices and Tensors
Appendix 2 Equations of Theory of Elasticity
Appendix 3 Laminate Orientation Code
Appendix 4 Properties of Fiber Composites
Appendix 5 Computer Programs for Laminate Analysis 55;
Index
an, 482
1stic emission, 483
tropic material, 175
otropic material, 175
otropy, 3
ntrolled, 10, 11
thermal expansion, 111
nid fibers, see Kevlar
iclave, 46, 47, 48
age fiber stress, 139-140
age stress criterion, 349
; of symmetry, 63, 160
an, 482
molding, 46-48
essure, 46, 47
ocesses, 46-48
lCUUm, 46, 47
ging, 46
,need orthotropic lamina,
172
ding
'beams, 315
' general laminates, 294
' plates, 288
:omposites, 499-503
fibers, 499-501
product, 499
ding mechanisms, 355-
356
on fibers, 27-28
y CVD, 27
roperties of, 28
indary-layer phenomenon,
328
kling, 296
iad, 296
critical, 298
1ode, 296
f plates, 295
f square plate, 300
n off method, 441
can, 483
bon black, 6
bon-carbon composites,
498-499
Carbon fibers, 23-26 also see
graphite fibers
carbon yield, 24
form of, 26
PAN, 24
precursor, 24
process of nfuk.ing, 24, 35
properties of, 25, 26
roving of, 26
yarn of, 26
Cermets, 6
oxide-based, 6
carbide-based, 6
Ceramic fibers, 28-29
Alumina, 28, 29
Fibers FP, 28, 29
properties of, 29
silicon carbide, 28, 29
Charpy tests, 475
Classical lamination theory,
214
CLT, see classical lamination
theory
COD, see crack-opening
displacement
Code, laminate orientation,
544-548
Coefficient of thermal
expansion, 111
Cold solders, 6
Combustion method, 441
Compliance curve, 467
Compliance matching
procedure, 467
Compliance matrix, 184
invariant form of, 194
transformation of, 189
Compliance tensor, 184
Composite materials:
applications of, 10-14
bridge, 12-14
characteristics of, 2-3
classification of, 3-5
consumption of, 12
continuous fiber, 9
cross-ply, 3
definition of, 1-2
degradation of, 426-429
INDEX
density of, 65-66, 440
discontinuous fiber, 7, 9
fabrication of, 41-60
fiber-reinforced, 5, 7-10
fibrous composite, 7-11
growth of, 11
hybrid, 9, 407-411
multilayered, 7, 8
particulate, 1, 5-7
particle-reinforced, 5
properties of, 2, 123-124,
550-554
quasi-isotropic, 147
ribbon reinforced, 152-155
short-fiber, 132-155
single layer, 7, 8, 9
tape reinforced, see ribbon
reinforced
unidirectional, 3, 9, 62-131
use in U.S. industries, 12
Compounding, 57
Compression molding, 56
Computer:
laminate analysis through,
272
programs, 550
software, commercial, 556
Concentration, 2
Constant-stress model, 80
Constitutive equations, 192
for laminates, 221. 224-225
Contact Jay-up, 43
Continuous fiber reinforced
composite, 9
Coupling agents, 16, 19
Coupling coefficients, see
Cross-coefficients
Crack-driving force, 466
Crack extension, 342
Crack-extension force, 466
Crack-extension force curve,
466
Crack-growth resistance, 466
Crack-growth resistance curve,
466,467
Crack-length-estimation curve,
467,469556 INDEX
Crack-opening displacement,
467
Crack opening mode, 342
Creel, 49
Critical buckling load, 298
Critical fiber length, 136
Critical volume fraction, 75,
76, 146
Cross-coefficients, 168-170
Cross-linking, 42
Cumulative weakening, 78
Curing agent, 35
Curing stresses, 268
Damage:
due to low velocity impact,
411-416
fatigue, 368
identification, 481-488
initiation, 96
DCB see double-cantileverbeam
Debonding, 96, 370
of fibers, 399
Degradation of composites,
at elevated temperatures,
426-429
Delamination, 96
Delamination crack, 370, 373,
396,401
DEN, see double edge notched
Density, 57-58, 440
Diffusion, mass, 106
Diffusivity, 120
longitudinal, 120, 121
measurement of, 443
transverse, 120, 121
Discontinuous fiber reinforced
composites,
see Short-fiber composites
Double-cantilever-beam, 472,
473
Double edge notched
specimen, 465
Drop-weight impact test, 476
Ductility index, 409
Edge delamination
suppression, 335
Edge effects, 324-335
Effect of temperature and
moisture on composite
properties, 422-426
Effective modulus, 252
Elastic constants, 175, see also
Engineering constants
number of, 182
relations with compliance
matrix, 185
relations with stiffness
matrix, 185-187
restrictions on, 187-189
symmetry of, 175
variation of, 170-172
Elasticity methods, 83
Electrical conductivity, 115,
I 16, 118
End effects, 78
End tabs, 445, 446
Energy absorbing mechanisms,
396
fiber breakage, 397
fiber debonding, 399
matrix cracking, 398
matrix deformation, 398
Energy curves, 471
Engineering constants, 160
determination of, see
Testing of composites
extremum value of, 170
for orthotropic lamina, 160,
161
restrictions on, 187-189
relations with compliance
matrix, 185
relations with stiffness
matrix, 185-187
transformation of, 166-172
variation of, 170-172
variations with fiber
orientation, 169-172
Environmental interaction
effects, 416-431
Epoxy, 36-38
properties of, 37
Epoxy resin, 36
Equations of motion, 302
Experimental characterization,
431-495
See also Testing of
composites
Fabrication of composites, 41-
60
by bag molding, 46-48
by contact lay-up, 43
by hand lay-up, 43--45
by resin transfer molding,
49
by stamping, 57
by thermoforming, 57, 58
ceramic matrix, 59-60
filament winding, 49-51
metal matrix, 58-59
molding compounds, 53
prepregs, 55
pultrusion, 51-53
thermoplastic resin
55-58
thermosetting resin
42-55
Failure:
envelop, 204-205, 2
initiation, 88, 96
microscopic, 335
internal, 96
load, 97
models, 78-79
modes of, 96-108
shear, 107, 109
Failure criteria, see als
Failure theories
for biaxial stress fie!
205
for notched composi
maximum distortion
91
Whitney-Nuismer, 3,
Failure theories:
maximum strain, 20(
maximum stress, l 9i
maximum work, 203
Tsai-Hill, 203
Fatigue, 368-395
characterization of, 3
crack arrest in, 370
crack branching in, 3
cross-ply cracks in, 3
372
damage, 370
damage initiation, 37
delamination crack, 3
empirical relations fo
386
factors influencing be
378
Goodman-Boller
relationship, 384
influence of mean str1
383
influence on propertie
375-377
of high modulus fiber
composites, 386-
of short fiber composi
390-395
schematic representati
373-374
shear, 382-383
S-N curve, 375
Fibers:
advanced, 16-30
aramid, 7, 26
average stress on, 139
boron, 27-28eaking of, 96, 100-101,
397
1ckling of, 102, 103
:rbon, 23-26
:ramie, 28
1opped, 10
itical length of, 136
ushing of, 107
:bonding of, 399
1d effects, 133
iber FP, 28
lass, 7, 16-23
cake, 17
composition, 18
end, see strand
production of, 17, 18
properties, 18, 19
roving, 21
sizes, 17
staple, 17, 18
strand, 17
surface treatment of, 18-
20
yield, 21
:raphite, 7, 33-26
see also Carbon-fibers
neffective length of, 136
(evlar, 26-27
oad transfer length of, 136
nan-made, 7
nicrobuckling of, 102
Jolyethylene, 28-30
Jroperties of, 7, 8
,ullout, 100-101
;ilicon carbide, 28
Spectra, 29
,er aspect ratio, 140
ier composites,
applications of, 10-14
properties of, 10
oer packing, 124
oer pullout, 396, 399-401
oer splitting, 106, 107
ber volume fraction
minimum, 75, 146
critical, 75, 146
berglass, see glass fibers
ber-reinforced composites,
7-10
fament winding, 49-51
patterns, 50, 51
Hers, 39
inorganic, 6
.nite element analysis codes,
555,556
inish, 18
iakes, 6
mica, 6
racture mechanics, 335-355
Fracture mechanics concepts,
338-346
Fracture process in
composites, 336-338
Fracture process in impact,
395-396
Fracture process zone, 397
Fracture surface work, 341
Fracture toughness
measures of, 338
of composite 1;:lminates,
346-349
Fundamental frequency, 303
Gel coat, 43
Generalized Hooke's law, 175
Generally orthotropic lamina,
164
Glass fibers, 7, 16-23
cake, 17
composition, 18
chopped-strand mat, 22
continuous-strand mat, 22
coupling agent, 18
E-, 19
end, 17
fabric, 23
finish, 18
forms of, 21-23
mat, 22
milled, 23
production of, 17-18
properties of, 8, 18, 19
roving, 21
S-, 19
sizes, 17
compatible, 18, 19
temporary, 18
staple, 17-18
strand, 17
surface treatment of, 15
surfacing mat, 22
veil, 22
woven roving, 22
yarn, 23
Goodman-Boller relationship,
383,384
Graphite fibers, 23
from PAN, 24
precursor, 24
tows, 26
Gel coating, 43
Haplin-Tsai equations
for ribbon reinforced
composites, 154
for shear modulus, 93
INDEX 557
for short-fiber composites,
141-144
for transverse modulus, 85
for transverse transport
properties, 115
Hand lay-up technique, 43
Hole size effect, 349
Homogeneity, 3
Hooke's law, 174
for generally isotropic
material, 174-177
for generally orthotropic
material, 174-177
for isotropic material, 181-
182
for specially orthotropic
material, 177-180
for transversely isotropic
material, 180-181
generalized, 175
in contracted notation, 179-
180
Hybrid, see hybrid composites
Hybrid composites, 9, 397,
407-411
Hybrid laminates, 3, 5
Hybridization, 407
Hygrothermal forces, 268
Hygrothermal moments, 268
Hygrothermal stresses, 263-
273
Calculations, 264-273
IITRI test fixture, 450
Impact:
energy absorbed, 396
energy absorbing
mechanisms, 396-401
failure modes, 396-401
initiation energy, 408
low velocity, damage due
to, 411-416
propagation energy, 408
hybrid composites, 407-411
strength of short-fiber
composites, 152
Charpy, 475
drop weight, 476
instrumented Charpy, 477
lzod, 475-476
Impact energy values for
materials, 408
Impact properties,
effect of materials variables
on, 401-407
effect of testing variables
on, 401-407558 INDEX
Impact properties (Continued)
of unidirectional fiber-epoxy
composites, 410
Ineffective length, 136
Interfacial bond, 79
Interfacial area, 1
Interfacial conditions, 79
Initiation energy, 405, 408
Intelligent structures, 503
Interlaminar fracture
toughness,
determination of, 471-
475
Interlaminar shear strength,
determination of, 324-
335, 471
Interlaminar stresses, 471, 472
approximate solutions for,
330--334
concepts of, 324-326
determination of, 326-328
effect of stacking sequence
on, 328-330
Invariant forms of
compliance matrix, 194-196
stiffness matrix, 194-195
Isotropic composite, 132
Isotropy, 3, 159
Izod tests, 475
J-curve, 471
J-integral, 345-346
critical, 470
determination of, 470-471
energy interpretation, 470
Joints
adhesively bonded, 355-360
advantages of, 359
configuration, 356-357
design of, 355
failure modes, 357
stresses in, 358
bonded-mechanically
fastened, 361-362
for composite structures.
355
mechanically fastened, 360--
361
advantages of, 361
disadvantages of, 361
failure modes of, 36
K-calibration factor, 465
K,-curve, see crack extension
force curve
Kevlar fibers, 26-27
chemistry of, 26
properties of, 27
Knee of stress-strain curve,
250
Lamina, 63, 158, see also
Orthotropic lamina
Laminate:
analysis after initial failure,
247-262
analysis of, 213-281
analysis through computers,
272-277
angle-ply, 228-229
constitutive equations for,
221, 224-225
cross-ply, 228-229
curing stresses, 268
definition of, 158
description system, 225-
226, see also laminate
orientation code
effective modulus, 251
fracture mechanics of, 335-
355
hygrothermal forces in, 268
hygrothermal moments in,
268
hygrothermal stresses in,
263-272
interlaminar stresses in,
324-335, 471
load carrying capacity of,
255
mechanical strains in, 266
netting analysis, 280
orientation code, 544-549
primary modulus, 250
quasi-isotropic, 229-230
residual stresses, 268
resultant force, 218
resultant moment, 218
secondary modulus, 250
specially orthotropic, 228
stacking sequence, 219,
328, 544-549
stiffness matrices, 221
strains in, 238
strength analysis, 274-276
stress analysis, 273-274
stresses and strains in,
determination of, 238-
247
stresses in, 238
symmetric, 227-228
thermal strain, 263
thermal stresses, see
Laminate,
hygrothermal stresses
unidirectional, 228-2
Laminated beams
bending of, 315-318
buckling of, 318-319
free vibrations of, 31·
governing equations J
314
Laminated plates
bending of, 288
buckling of. 295
equilibrium equations
283-286
free vibrations of, 30
governing equations f
283
in terms of
displacements, 2:
288
Laminates, 8, 158
bidirectional, 10
Laser shearography, 488
Law of mixtures, see Rt
mixtures
Load coefficients, 290
Load sharing, 71-73
Load transfer length, 131
Longitudinal direction, t
Longitudinal stiffness:
factors influencing, 76
prediction of, 68-69
Longitudinal strength:
factors influencing, 76
prediction of, 75-76
Low velocity impact, 41
damage due to, 411-4
Mass diffusion, 117-123
Major Poisson's ratio, 95
Mandrel, 50
MAPLE, 555, 556
Mat, 10, 22
chopped-strand, 22-23
continuous-strand, 22-
surfacing, 22-23
Material axes, 63
Mathcad, 520, 555, 556
MATLAB,520, 555,556
Matrix material, 2, 7, 30-
Bismaleimides, 38
effect of temperature a1
moisture on, 422-
elevated temperature,
degradation at, 421
429
epoxy,36-38
metals, 39,41
microcracking, 96
phenolics, 381stics, 30-40
lyester, 34-35
,Iyimides, 38
,Iymers, 30-40
~yl esters, 38
ix (mathematical):
dition, 514
lumn, 510
finitions, 509
terminant, 513
agonal, 511
ements of, 509
entity, 511
verse, 517
ultiplication, 516
1erations, 514-520
thogonal, 519
incipal diagonal of. 511
w, 510
.ew symmetric, 511
uare, 510
.btraction, 514
mmetric, 511
msformation of, 519
mspose of, 5 I 0
tit, 511
:ix digestion method, 441
:ix dissolution method,
441
rix ductility, 150
.imum strain. theory, 200-
203
.imum stress theory, 197-
200
.imum work theory, 203-
205
.sure of fiber orientation,
148
.surement of
jtical crack growth
resistance, 464
·itical I-integral, 470
·itical strain-energy release
rate, 463
·itical stress-intensity
factor, 464
ensity, 440
iffusivity, 444-445
exure properties, 459
npact properties, 475
1-plane shear properties,
452
1terlaminar fracture
toughness, 471
1terlaminar shear strength,
471
1easures of fracture
toughness, 463
1echanical properties, 445-
481
moisture absorption, 444-
445
moisture expansion
coefficients, 444-445
physical properties, 440-
445
properties in compression,
449
properties in tension, 445
stiffness and strength, see
testing of composites
thermal expansion
·
0coefficients, 442
void volume fraction, 442
volume
0
frnction, 441
weight fractions, 441
Microbuckling of fibers, 102,
. 103
in extension niode, I02
in shear mode, 102, 103
Micromechanics of transverse
failure, 88
Microscopic failure initiation,
3,35
Milled fibers, 23
Minimum volume fraction:
of short fiber composite,
146
of unidirectional composite,
76
Minor Poisson's ratio, 95
Modulus:
effective, 252
longitudinal, 68, 160
primary, 250, 375
residual, 375
secondary, 250, 375
shear, 91-95, 160
of short-fiber composites,
141-145
transverse, 80-91, 141, 160
Moisture absorption, I I 4
Moisture expansion
coefficients, 114
longitudinal, 114
transverse, 114
Mold release, 43
Molding compounds, 10, 53-
55
BMC, 42, 53
bulk, 42, 53
DMC, 53
dough, 53
prepregs, 42, 55
sheet, 42, 53, 54
SMC, 42, 53, 54
Nanocomposites, 7, 496-498
Clay-reinforced, 7
INDEX 559
Nanotube-reinforced, 7
Nanotubes, 7, 496
Single walled, 497
Multi-walled, 497
Natural fibers, 499
properties of, 500
Navier's approach
NDE, see nondestructive
evaluation
Neutral axis, 460
Nodal lines, 304
Nondestructive evaluation,
481-488
Nondestructive evaluation
techniques:
acoustic emission, 483
laser shearography, 488.
489
thermography, 486
ultrasonics, 481
X-radiography, 485
Notch sensitivity, 346
Notched-bend tests, 464-465
Notched plate, 465
Notched-plate test, 472, 473
Orthotropic lamina, 161
analysis of, 158
balanced, 172
engineering constants of,
160. 166
generally, 161
shear strength, importance
of sign, 205-209
specially, 161
strength of, 196-209
strength under biaxial
stresses, 196-209
stress-strain relations in
arbitrary direction,
164-166
transformation of
engineering constants,
166-174
variation of elastic
constants, 170-172
Orthotropic materials, 158-
160, see also
Orthotropic lamina
definition of, 158-160
deformation behavior of,
159
Hooke's law for, 160-174
PAN, 24
Particulate composites, I, 5-7
Plasma spraying, 59560 INDEX
Plastics, see polymers
Platelets, 2, 496
Ply, 63
Point of instability, 466
Point-stress criterion, 349
Poisson's ratio:
major, 95, 161
minor, 95, 161
orediction of, 95
restriction on, 188, 189
Polyester, 34-36
properties of, 35, 36
Polyethylene fibers, 28-30
Dyneema, 29
properties of, 29
Spectra, 29
Polymerization, 42
Polymers, 30-40
crystalline melt
temperatures of, 32
epoxy, 36-38
properties of, 37
glass transition temperatures
of, 32, 33
melting point of, 32
network, 31
polyester, 34-35
properties of, 35, 36
properties of, 31-34
epoxy resin, 37
phenolics. 38
polyester resin, 34
polyimide, 38
thermoplastic resins, 40
thermoplastic, 31, 38-39
high temperature, 39
properties of, 39, 40
thermosets, 31
temperature for
processing of, 32
thermosetting, 31
Preform, 10
Preimpregnated fibers, see
prepregs
Premixes, 42
Prepregs, 9, 42, 55
Primary modulus, 375
Propagation energy, 405, 408
Properties of fiber composites,
550-554
Properties of unidirectional
composites, 123-124
Pultruded shapes, 51, 52
Quasi-isotropic laminate, 229-
230
R-curve, see crack-growth
resistance curve
Rail shear test, 458
Reinforcements, 2
geometry of, 3
orientation of, 3
Reinforcing material, 2
Residual strength, 376 .
Residual stresses, 79-80, 268
Resin transfer molding (RTM),
49
vacuum assisted (VARTM),
49
Resultant forces, 218
Resultant moments, 218
Ri~bon-reinforced composites,
152-155
Halpin-Tsai equations for,
154
in-plane transverse modulus
of, 154
Rule of mixtures, 69
for density, 65
for longitudinal diffusivity,
120
for longitudinal modulus,
69
for Poisson's ratio, 96
for stress, 68
for transport properties, 114
Sandwich cross-beam, 459
Secondary cracks, 398
Secondary modulus, 250, 375
Self-consistent models, 84, 85
Self-similar crack growth, 337
SEN, see single edge notched
Series solution, 290
Shear coupling, 164
Shear deformation theory
first-order, 306-311
higher-order, 311-314
Shear failure, 107, 109
Shear-lag analysis, 134
Shear modulus, 91-95, 160
Shear strain:
engineering, 180, 534-535
tensorial, 180, 535
Shear strength, 197
Shearography, laser, 488
Short beam shear test, 472
Short-fiber composites, 132-
157
critical fiber length, 136
critical fiber volume fraction
of, 146, 147
effect of matrix ductility on
properties of, 150-152
examples of, 133
failure initiation of, J
fatigue of, 390-395
impact strength of, 1.
ineffective fiber leng1
load transfer length,
matrix ductility, effec
150-152
minimum fiber volun
fraction of, 146,
modulus of, 140
prediction of, 141
randomly oriented,
randomly oriented, l·
ribbon reinforced, 15
strength of, 140, 145
prediction of, 145
strength of random fl
composite, 147,
stress distribution in,
139
theories of stress trar
for, 133-140
Single edge notched sp,
465
Sizes, 17, 18-20
compatible, 18, 19
temporary, 18
Smart structl!res, 503
S-N curve, 378
Software packages,
commercially a,
556
Sound deadener, 6
Specially ortbotropic .la
161
stress-strain relations
161-164
under plane stress, 1:
constitutive equati1
192
stiffness coefficien
183
Specially orthotropic m
177
Specific stiffness, 7-8,
Specific strength, 7-8,
Speckle effect, 488
Spray-up, 44, 45
Stamping, 57
Staple fibers, 18
Static fatigue, 417
Static fatigue of fibers,
Static-rupture of fibers,
Stiffness:
factors influencing, 7
methods of predictin
longitudinal, 68
residual, 376
transverse, 84-87ess matrix, 183
1ding, 221
1pling, 221
:ineering constants,
relations with, 185-187
ensional, 221
orthotropic materials,
183
ariant form of, 194
ersion of, 238
:ractured plies, 248
thesis of, 218-221
1sformation of, 189
lysis of, 532-535
1patibility conditions,
535
:rmination of, 238
ineering, 180, 535
;hanical, 26t;
;orial. 180, 535
1sformation equation,
534
-displacement relations,
533
-energy release rate,
339-341
ical, 341
magnification factor, 90
-stress relations, see
Stress-strain relations
🇹🇭
ors influencing, 76-80
situdinal compressive,
103-106, 197
situdinal tensile, 75-76,
197
:hed, 351-355
,rthotropic lamina, 196
1uasi-isotropic laminate,
257
dual, 376
hort-fiber composite,
145-149
sverse, 87-91, 197
>ries of, 197-205
th reduction factor, 90
thening mechanisms, 3,
5
ysis of, 536-540
ndary conditions, 537,
539
ng, 268
rmination of, 238-247
ilibrium equations, 539
rothermal, 263-272
rlaminar, 324-335
lual, 79-80, 268
sign convention for, 205,
537
symmetry of, 538
thermal, see, hygrothermal
transformation, 539-540
Stress concentration factor, 88,
90
Stress corrosion, 419
features of, 416
of glass fibers, 419-422
of GRP, 419-422
Stress-intensity factor, 339,
341-344
critical, 464
determination of, 464-470
relation with strain energy
release rate, 342
Stress-rupture characteristics,
429-431
Stress-rupture of fibers, 418
Stress-strain relations, 160
for anisotropic materials,
175-176
for generally orthotropic
lamina, 164-166
for isotropic materials, 540
for specially orthotropic
lamina, 161-164
generalized, 175
in terms of engineering
constants, 163
Surface energy, 341
Surfacing mat, 44
Symmetric laminates, 227
Tensors:
definition of, 527
laws of transformation, 527
Tests,
bend, four point, 459, 460
bend, three point, 459, 460
compression, 449
coupon, [±45],, 455
coupon, off-axis, 456
double cantilever beam, 472
flexural, 459
fracture toughness, 463
impact, 475
drop weight, 476
Charpy, 476
Izod, 476
in-plane shear, 452
Iosipescu shear, 453
notched plate, 472
picture frame, 458
rail shear, 458
sandwich cross beam, 459
sandwich beam, 448
INDEX 561
short beam shear, 472
tension, 445
torsion tube, 452
Testing of composites:
bending, 459
Charpy, 475-481
compression, 449
drop weight, 476
flexural, 459
four-point bending, 459
fracture toughness, 463-475
in-plane shear, 452-459
Iosipescu, 453
[ ± 45], coupon, 455
off-axis coupon, 456
torsion tube, 452
instrumented Charpy, 475-
481
Izod, 475-481
notched bend, 465
notched plate, 463
off-axis shear, 457
off-axis tension, 447
picture frame, 458
rail shear, 458
sandwich crossbeam, 459
short beam shear. 472
tension, 445-449
three point bending, 459
Thermal stresses
concepts of, 263-264
Thermography, 486-488
pulse-echo, 487
through transmission. 487
Thickness shear, 472
Transverse shear
deformations due to, 306-
311
effects of, 306
Transverse splitting, 102
Transversely isotropic, 63, 160
Theories of failure, see failure
theories
Theories of stress transfer,
133-140
Thermal conductivity, 115-
117
Thermal expansion
coefficients, 108-114
longitudinal, 111
transverse, 111
Thermal strains, 264
Thermal stress, see
Hygrothermal stress
Thermoforming, 57
Them10plastic polymers, 31
properties of, 40
Total impact energy, 405
Transformation:
matrix, 190562 INDEX
Transformation (Continued)
of strain, 534
of stress, 539
relations. 190
Transport properties, 114
Transverse:
isotropy, 63
splitting, 102-106
stiffness, 80-87
srrength, 87-91
Transverse direction, 63
Tsai-Hill theory, 203
Ultrasonics, 481-483
pitch-catch method of, 481,
482
pulse-echo method of, 481,
482
through transmission
method of, 482, 483
Unidirectional composites:
anisotropy of thermal
expansion, 112
coefficient of thermal
expansion, 108-114
critical volume fraction, 75-
76
expansion coefficients, 108-
114
failure initiation, 74
failure mechanism of, 74
failure modes, 96-108
longitudinal behavior of, 67
longitudinal stiffness, 68-71
longitudinal strength, 75-76
factors influencing, 76
statistical models for, 77
mass diffusion in, 117-123
model for, 68
moisture in, 114
minimum volume fraction,
75
Poisson's ratio, 95
major, 95
minor, 95
prediction of, 95-96
properties of, typical, 113,
123, 124
shear modulus of, 91-95
prediction of, 91
Haplin-Tsai equations for,
93
thermal conductivities, 115-
117
thermal expansion, 108-114
transport properties, 114
transverse stiffness, 80-87
transverse strength, 87-91
prediction of, 90
empirical approa
91
transversely isotror
Unstable crack growtl
Variation of stresses i
laminate. 216-
Veil, 23, 44
Voids. 67
volume fraction, 6~
Void content, 67
Volume fraction, 64, ,
critical, 76, 146.
definition of, 65:_6(
minimum, 75, 146
Weight fractions, 2, 6
Whitney-Nuismer fail
criteria, 349-'.1
for notched compo
349-355
Winding angle, optim
Wood-plastic compos
502
X-radiography, 485~
penetrant-enhanced


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