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 |  موضوع: كتاب Engineering Mechanics of Composite Materials الثلاثاء 01 ديسمبر 2020, 12:12 am | |
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أخوانى فى الله
أحضرت لكم كتاب
Engineering Mechanics of Composite Materials
Second Edition
Isaac M. Daniel
Department of Civil and Mechanical Engineering
Northwestern University, Evanston, IL
Ori lshai
F i i i d t y of Meclzariical Engineering
و المحتوى كما يلي :
Contents
Preface to the Second Edition
Preface to the First Edition
Introduction 1
1.1 Definition and Characteristics 1
1.2 Historical Development 2
1.3 Applications 3
1.4 Overview of Advantages and Limitations of Composite Materials 13
1.4.1 Micromechanics 14
1.4.2 Macromechanics 14
1.4.3 Mechanical Characterization 14
1.4.4 Structural Design, Analysis, and Optimization
1.4.5 ManufacturingTechnology 15
1.4.6 Maintainability, Serviceability,and Durability
1.4.7 Cost Effectiveness 15
1.5 Significanceand Objectives of Composite Materials Science and Technology
1.6 Current Status and Future Prospects
References 17
14
15
16
16
BASIC CONCEPTS, MATERIALS, PROCESSES, AND CHARACTERISTICS 18
2.1 Structural Performance of Conventional Materials 18
2.2 Geometric and Physical Definitions 18
2.2.1 Type of Material 18
2.2.2 Homogeneity 19
2.2.3 Heterogeneity or Inhomogeneity 19
2.2.4 Isotropy 19
2.2.5 Anisotropy/Orthotropy 20
2.3 Material Response Under Load
2.4 Types and Classification of Composite Materials
viii CONTENTS
2.5 Lamina and Laminate-Characteristics and Configurations 26
2.6 Scales of Analysis-Micromechanics and Macromechanics 27
2.7 Basic Lamina Properties 29
2.8 Degrees of Anisotropy 30
2.9 Constituent Materials 30
2.9.1 Reinforcement 30
2.9.2 Matrices 33
2.10 Material Forms-Prepregs 35
2.11 Manufacturing Methods for Composite Materials 36
2.11.1 Autoclave Molding 37
2.11.2 Filament Winding 37
2.11.3 Resin Transfer Molding 38
2.12 Properties of Typical Composite Materials
References 42
3. ELASTIC BEHAVIOR OF COMPOSITE LAMINA-MICROMECHANICS 43
Scope and Approaches 43
Micromechanics Methods 45
3.2.1 Mechanics of Materials Methods 46
3.2.2 Bounding Methods 46
3.2.3 Semiempirical Methods 48
Geometric Aspects and Elastic Symmetry
Longitudinal Elastic Properties-Continuous Fibers 49
Transverse Elastic Properties-Continuous Fibers 51
In-Plane Shear Modulus 56
Longitudinal Properties-Discontinuous (Short) Fibers 58
3.7.1 Elastic Stress Transfer Model-Shear Lag Analysis (Cox)
3.7.2 Semiempirical Relation (Halpin)
References 60
Problems 61
4. ELASTIC BEHAVIOR OF COMPOSITE LAMINA-MACROMECHANICS 63
4.1 Stress-Strain Relations 63
4.1.1 General Anisotropic Material 63
4.1.2 Specially Orthotropic Material 66
4.1.3 Transversely Isotropic Material 67
4.1.4 Orthotropic Material Under Plane Stress
4.1.5 Isotropic Material 71
4.2 Relations Between Mathematical and Engineering Constants
4.3 Stress-Strain Relations for a Thin Lamina (Two-Dimensional)
Transformation of Stress and Strain (Two-Dimensional)
Transformationof Elastic Parameters (Two-Dimensional)
Transformationof Stress-Strain Relations in Terms of Engineering Constants
(Two-Dimensional) 81
Transformation Relations for Engineering Constants (Two-Dimensional)
Transformationof Stress and Strain (Three-Dimensional)
4.8.1 General Transformation 88
4.8.2 Rotation About 3-Axis 89
Transformationof Elastic Parameters (Three-Dimensional)
References 92
Problems 92
5. STRENGTH OF UNIDIRECTIONAL LAMINA-MICROMECHANICS 98
5.1 Introduction 98
5.2 LongitudinalTension-Failure Mechanisms and Strength
5.3 LongitudinalTension-Ineffective Fiber Length
5.4 Longitudinal Compression 105
5.5 TransverseTension 110
5.6 Transverse Compression 113
5.7 In-Plane Shear 114
5.8 Out-of-Plane Loading 115
5.9 General Micromechanics Approach 116
References 116
Problems 117
6. STRENGTH OF COMPOSITE LAMINA-MACROMECHANICS 120
6.1 Introduction 120
6.2 Failure Theories 122
6.3 Maximum Stress Theory 123
6.4 Maximum Strain Theory 126
6.5 Energy-Based Interaction Theory (Tsai-Hill) 128
6.6 InteractiveTensor Polynomial Theory (Tsai-Wu) 130
6.7 Failure-Mode-Based Theories (Hashin-Rotem) 135
6.8 Failure Criteria for Textile Composites 137
6.9 Computational Procedure for Determinationof Lamina Strength-Tsai-Wu Criterion
(Plane Stress Conditions) 139
6.10 Evaluation and Applicability of Lamina Failure Theories
References 148
Problems 149
143x CONTENTS
7. ELASTIC BEHAVIOR OF MULTIDIRECTIONAL LAMINATES 158
7.1 Basic Assumptions 158
7.2 Strain-Displacement Relations 158
7.3 Stress-Strain Relations of a Layer Within a Laminate 160
7.4 Force and Moment Resultants 161
7.5 General Load-Deformation Relations: Laminate Stiffnesses 163
7.6 Inversion of Load-Deformation Relations: Laminate Compliances 165
7.7 Symmetric Laminates 167
7.7.1 Symmetric Laminates with Isotropic Layers
7.7.2 Symmetric Laminates with Specially Orthotropic Layers (SymmetricCrossply
7.7.3 SymmetricAngle-Ply Laminates 170
7.8.1 Antisymmetric Laminates 172
7.8.2 Antisymmetric Crossply Laminates 172
7.8.3 Antisymmetric Angle-Ply Laminates 174
168
Laminates) 169
7.8 Balanced Laminates 171
7.9 Orthotropic Laminates: Transformationof Laminate Stiffnessesand Compliances 175
7.10 Quasi-isotropic Laminates 177
7.11 Design Considerations 179
7.12 Laminate Engineering Properties 181
7.12.1 SymmetricBalanced Laminates 181
7.12.2 Symmetric Laminates 182
7.12.3 General Laminates 184
7.13 Computational Procedure for Determinationof Engineering Elastic Properties
7.14 Comparisonof Elastic Parameters of Unidirectional and Angle-Ply Laminates
7.15 Carpet Plots for Multidirectional Laminates
7.16 Textile Composite Laminates 192
7.17 Modified LaminationTheory-Effects of Transverse Shear
7.18 Sandwich Plates 196
References 200
Problems
8. HYGROTHERMAL EFFECTS 204
8.1 Introduction 204
8.1.1 Physical and Chemical Effects
8.1.2 Effects on Mechanical Properties
8.1.3 Hygrothermoelastic(HTE) Effects 205
8.2 Hygrothermal Effects on Mechanical Behavior
8.3 Coefficients of Thermal and Moisture Expansion of a Unidirectional Lamina
8.4 Hygrothermal Strains in a Unidirectional Lamina
212Contents xi
8.5 Hygrothermoelastic Load-Deformation Relations 213
8.6 HygrothermoelasticDeformation-Load Relations 215
8.7 Hygrothermal Load-Deformation Relations 216
8.8
8.9
8.10 Physical Significanceof Hygrothermal Forces and Moments
8.11 Hygrothermal Isotropy and Stability
8.12 Coefficients of Thermal Expansion of Unidirectional and Multidirectional
8.13 Hygrothermoelastic Stress Analysis of Multidirectional Laminates 225
8.14 Residual Stresses 227
8.15 Warpage 232
8.16 Computational Procedure for Hygrothermoelastic Analysis of Multidirectional
References 237
Problems 239
Coefficients of Thermal and Moisture Expansion of MultidirectionalLaminates
Coefficients of Thermal and Moisture Expansion of Balanced/Symmetric Laminates
Carbon/Epoxy Laminates 224
Laminates 235
9. STRESS AND FAILURE ANALYSIS OF MULTIDIRECTIONAL LAMINATES 243
Introduction 243
Types of Failure 244
Stress Analysis and Safety Factors for First Ply Failure of Symmetric Laminates (In-Plane
Loading) 244
Strength Components for First Ply Failure of Symmetric Laminates
Computational Procedure for Stress and Failure Analysis of General Multidirectional
Laminates (First Ply Failure) 252
Comparison of Strengths of Unidirectional and Angle-Ply Laminates
(First Ply Failure) 253
Carpet Plots for Strength of Multidirectional Laminates (First Ply Failure)
Effect of HygrothermalHistory on Strength of Multidirectional Laminates (First Ply
Failure; Tsai-Wu Criterion) 255
Computational Procedure for Stress and Failure Analysis of Multidirectional Laminates
Under Combined Mechanical and Hygrothermal Loading (First Ply Failure; Tsai-Wu
Criterion) 258
9.10 Micromechanicsof Progressive Failure
9.11 Progressive and Ultimate Laminate Failure-Laminate Efficiency
9.12 Analysis of Progressive and Ultimate Laminate Failure
9.12.1 Determinationof First Ply Failure (FPF) 267
9.12.2 Discounting of Damaged Plies
9.12.3 Stress Analysis of the Damaged Laminate
9.12.4 Second Ply Failure 268
268xii CONTENTS
9.12.5 Ultimate Laminate Failure 268
9.12.6 Computational Procedure 269
9.13 Laminate Failure Theories-Overview, Evaluation, and Applicability
9.14 Design Considerations 276
9.15 Interlaminar Stresses and Strength of MultidirectionalLaminates: Edge Effects
9.15.1 Introduction 277
9.15.2 Angle-Ply Laminates 277
9.15.3 Crossply Laminates 278
9.15.4 Effects of Stacking Sequence
9.15.5 Interlaminar Strength 282
279
9.16 Interlaminar Fracture Toughness 284
9.17 Design Methodology for Structural Composite Materials
9.18 Illustration of Design Process: Design of a Pressure Vessel
286
289
9.18.1 Aluminum Reference Vessel 290
9.18.2 Crossply [0,/90,], Laminates 290
9.18.3 Angle-Ply [+O],, Laminates 291
9.18.4 [9O/+e],, Laminates 292
9.18.5 [O/+e],, Laminates 293
9.18.6 Quasi-isotropic [0/+45/90],,,Laminates 293
9.18.7 Summary and Comparisonof Results 294
9.19 Ranking of Composite Laminates
References 295
Problems 298
294
10. EXPERIMENTALMETHODS FOR CHARACTERIZATION AND TESTING OF COMPOSITE MATERIALS 303
10.1 Introduction 303
10.2 Characterizationof Constituent Materials 304
10.2.1 Mechanical Fiber Characterization 304
10.2.2 Thermal Fiber Characterization 307
10.2.3 Matrix Characterization 308
10.2.4 Interface/Interphase Characterization 308
10.3.1 Density 310
10.3.2 Fiber Volume Ratio 310
10.3.3 Void Volume Ratio (Porosity) 311
10.3.4 Coefficients of Thermal Expansion 313
10.3.5 Coefficients of Hygric (Moisture)Expansion 314
10.3 Physical Characterization of Composite Materials 310
10.4 Determinationof Tensile Properties of Unidirectional Laminae 316
10.5 Determinationof Compressive Properties of Unidirectional Laminae 318
10.6 Determinationof Shear Properties of Unidirectional Laminae 322Contents xiii
10.7 Determination of Through-Thickness Properties 329
10.7.1 Through-Thickness Tensile Properties 329
10.7.2 Through-Thickness Compressive Properties 331
10.7.3 Interlaminar Shear Strength 331
10.8.1 Mode I Testing 335
10.8.2 Mode 11 Testing 337
10.8.3 Mixed-Mode Testing 339
10.8.4 Mode I11Testing 341
10.9.1 Introduction 342
10.9.2 Off-Axis Uniaxial Test 343
10.9.3 Flat Plate Specimen 345
10.9.4 Thin-Wall Tubular Specimen 346
10.10.1 Introduction 348
10.10.2 Laminates with Holes 348
10.10.3 Laminates with Cracks 352
10.11 Test Methods for Textile Composites
10.8 Determination of Interlaminar Fracture Toughness 335
10.9 Biaxial Testing 342
10.10 Characterization of Composites with Stress Concentrations 348
355
10.1 1.1 In-Plane Tensile Testing
10.11.2 In-Plane Compressive Testing 356
10.11.3 In-Plane Shear Testing 357
10.11.4 Through-Thickness Testing 357
10.11.5 Interlaminar Fracture Toughness 359
355
10.12 StructuralTesting 359
10.13 Summary and Discussion 360
References 364
APPENDIX A: MATERIAL PROPERTIES 373
APPENDIX B: THREE-DIMENSIONAL TRANSFORMATIONS OF ELASTICPROPERTIES OF
APPENDIX C: ANSWERS TO SELECTED PROBLEMS
AUTHOR Index 397
SUBJECT Index 40
SUBJECT Index
Index Terms Links
A
Acid digestion method 311
Aeolotropic material. See General anisotropic material
Allowable laminate thickness 256–57
Alumina fibers 32 374
Angle-ply laminates
coefficients of thermal expansion 224–25
interlaminar stresses 277–79
properties of 190–92
strengths of 253–55
stress concentration 349–51
Anisotropy
definition of 20
degrees of 30
Antisymmetric laminates 172–75
angle-ply 174–75
crossply 172–73
Applications of composites
Aberfeldy footbridge 13
Airbus A380 3 5
B-2 stealth bomber 6
bicycle frame 12
Boeing 777 3 4
Boeing 787 3 4
Cirrus aircraft 5 Index Terms Links
Applications of composites (Cont.)
Cobra tram 8
Corvette leaf spring 7
foot and leg prostheses 11
hip prosthesis 11
offshore oil drilling riser 10
Royal Danish Navy corvette 8
Royal Swedish Navy Visby 9
solar-powered Helios 7
unmanned aircraft 7
water pipeline 12
wind turbine blade 9
Aramid/epoxy composites. See Kevlar/epoxy composites
Aramid fibers (or Kevlar fibers) 31 32 374–75
Arcan test. See Shear testing
Area method (for strain energy release rate) 286
Autoclave molding 37
Average stress criterion 350–54
B
Balanced laminates 171–75
Balanced symmetric laminates. See Orthotropic laminates
Bending coupling stiffnesses. See Laminate properties
and characteristics; Stiffnesses
Bending laminate stiffnesses. See Laminate properties
and characteristics; Stiffnesses
Betti’s reciprocal law 74
Biaxial testing 342–48 355–53
flat plate test 345–46
off-axis test 343–45
thin-wall tube test 346–48 Index Terms Links
Bismaleimide 34
Boron/aluminum composites 381
Boron/epoxy composites
coefficients of thermal expansion 210
properties of 41 378
Boron fibers 31 32 374–75
Boron/polyimide composites
Coefficients of thermal expansion 210
Bounding method 44–48
Buckling of fibers. See Microbuckling of fibers
Burnout method. See Ignition method
C
Calcium aluminosilicate 35
Carbon/carbon composites 25 381
Carbon/epoxy composites
coefficients of thermal expansion 210–11 224–25
critical strain energy release rates 338
engineering constants 84–86 377–80
hygric strains 315
hygrothermal effects on 205–8
properties of 377–80
strength reduction of plates with cracks 353–54
strength reduction of plates with holes 350–52
thermal strains 210
Carbon fibers 31 32 374–75
Carbon matrix 35
Carbon/PEEK composites 378
Carbon/polyimide composites
coefficients of thermal expansion 210
properties of 378–81 Index Terms Links
Carpet plots
for coefficient of thermal expansion 225
for laminate engineering properties 191–92
for strength of laminates 254–55
Ceramic fibers 32 374–75
Ceramic matrices 35
Ceramic matrix composites 25 381
Characteristic damage state (CDS) 261
Characterization of composite materials. See Testing of
composite materials
Characterization of constituent materials 304–9
Classical lamination theory (CLT) 158–67
Coefficients of hygric expansion. See Coefficients of
moisture expansion
Coefficients of moisture expansion
of balanced/symmetric laminates 217–19
measurement of 314–16
of multidirectional laminates 216–17
prediction of 211
of unidirectional lamina 208–11
Coefficients of thermal expansion
of balanced/symmetric laminates 217–19
of carbon/epoxy lamina and laminates 224–25
of fibers 307–8
measurement of 307 313–14
of multidirectional laminates 226–17
prediction of 208–11
of unidirectional lamina 208–11
Comparison of unidirectional and angle-ply laminates
elastic parameters 190–91
strength 253–54 Index Terms Links
Compliance method (for strain energy release rate) 285–86
Compliances
of general anisotropic material 63–65
of lamina 70 76
of specially orthotropic material 66
transformation of 80–81 92 175–76 386–87
of transversely isotropic material 67–69
Composite materials
advantages and limitations of 13–15
applications of 3–13
classification of 24–25
current status 16–17
definition of 1
future prospects 16–17
history of 2
interphase of 1
matrix of 1
performance map 41
properties of 40–42 377–81
reinforcement 1
significance and objectives of technology 16
types of 24–25
typical stress-strain curves 41 42
Compressive testing 318–22
IITRI test 318–19
measurement of properties 338–22
NU test 319–21
sandwich test 320–22
through-thickness testing 331 Index Terms Links
Computational procedures
for calculation of residual stresses 235–37
for calculation of warpage 235–37
for determination of laminate strengths 252–53
for hygrothermoelastic analysis 235–37
for lamina elastic constants 84
for lamina safety factor 139–40
for lamina strength 139–41
for laminate engineering properties 189–90
for laminate safety factors 252–53
for multiple ply failure analysis 269–71
for progressive and ultimate failure of laminates 269–71
for stress and failure analysis of laminates 252–53
Concepts and characteristics 18–30
Constitutive relations. See Load-deformation relations
Stress-strain relations
Continuous-fiber composites 24–25
in-plane shear modulus 56–58
longitudinal elastic properties 49–51
transverse elastic properties 51–56
Conventional materials
advantages and limitations of 13–15
performance ranking 19
structural performance 18
Coupling stiffnesses. See Laminate properties and
characteristics; Stiffnesses
Cracked-lap shear specimen 339–40
Critical strain energy release rates 335–42
Critical stress intensity factor 354–55 Index Terms Links
Crossply laminates
interlaminar stresses 278–79
progressive failure 260–65
stress concentration 349–51
D
Degrees of anisotropy 30
Delamination 277 331 335–42
Delamination fracture toughness. See Interlaminar
fracture toughness
Delamination modes 284–85
Density, measurement of 310
Design
for damage tolerance 286 288
for dynamic stability 286–89
for environmental stability 286 288–89
methodology 286–89
objectives 286–89
optimization 256 290–94
process (example) 289–94
for stiffness 286–88
for strength 286–88
Design considerations 179–81 276
Discontinuous-fiber composites 24 58–60
elastic properties 58–60
semiempirical relation for 60
shear lag analysis 58–59
Double cantilever beam (DCB) specimen
analysis of 284–86
Interlaminar fracture toughness
Doubly-split DCB specimen 341–42 Index Terms Links
E
Edge-cracked torsion (ECT) specimen 342
Edge effects 277–79
angle-ply laminates 277–78
crossply laminates 278–79
effects of stacking sequence 279–81
See also Interlaminar stresses
E-glass/epoxy composites
failure envelopes 135
off-axis strength 125 134
properties of 377 379–80
E-glass fibers 30–32 374–75
Elastic constants
comparison between unidirectional and angle-ply
laminates 190–91
micromechanical predictions of 49–60
number of 71
relations between engineering and mathematical
constants 71–76
transformation of 78–81 90–92 175–76
See also Compliances; Continuous-fiber composites;
Stiffnesses
End constraints on off-axis specimen, effects of 343–45
End-loaded split (ELS) laminate test 339
End-notched flexure (ENF) test 337–39
Energy-based interaction theory. See Tsai-Hill theory
Engineering constants, relations for 71–76
Engineering properties of laminates. See Laminate
properties and characteristics
Environmental effects. See Hygrothermal effects Index Terms Links
Epoxy 33 34 376
Experimental methods. See Testing of composite
materials
Extensional stiffness. See Laminate properties and
characteristics; Stiffnesses
F
Fabrication methods. See Manufacturing methods
Fabric weave styles 33–34
Failure analysis of laminates 243–98
Failure mechanisms/modes 98–115
in-plane shear 114–15
longitudinal compressive 105–9
longitudinal tensile 98–105
out-of-plane loading 115 358
transverse compressive 113–14
transverse tensile 110–13
Failure of laminates, types of 244
Failure patterns
in-plane shear 115
in laminates with holes 352
longitudinal compressive 106–7
longitudinal tensile 102–3
through-thickness loading 358
transverse tensile 112–14
Failure theories. See Lamina strength—Macromechanics;
Laminate failure theories
Fiber breaks 99–101
Fiber characterization 304–8
Fiber/matrix debonding 100–101
Fiber/matrix interphase. See Interphase Index Terms Links
Fiber pullout test 308–9
Fibers
advantages and disadvantages 31
performance map 32
properties of 374–75
specific modulus 32
specific strength 32
stress-strain curves 32
testing of 304–8
types of 30–32
Fiber strength utilization 266 287 292
Fiber volume ratio
definition of 29
measurement of 310–11
Fiber weight ratio 29
Filament winding 37–38
First ply failure (FPF)
definition of 244
safety factors for 244–46
strength components for 246–47
stress analysis for 244–46
Tsai-Wu criterion 245–46
Flat plate specimen (for biaxial testing) 345–46
Flexural laminate stiffnesses. See Laminate properties
and characteristics; Stiffnesses
Force resultants. See Multidirectional laminates
Fracture mechanics
in analysis of interlaminar fracture 284–86
in analysis of laminates with cracks 354–55
Fracture toughness. See Interlaminar fracture toughness;
Laminates with cracks Index Terms Links
G
General anisotropic material
definition of 20
stress-strain relations 63–66
Generalized Hooke’s law 63–66
Glass-ceramic matrices 35
Glass fibers 30–32 374–75
Graphite/epoxy composites 378
Graphite fibers 31–32 374–75
H
Halpin-Tsai relations 48–49 53 57 60
Heterogeneity, definition of 19
Holes, laminates with. See Laminates with holes
Homogeneity, definition of 19
Hooke’s law. See Generalized Hooke’s law
Hybrid composites 26 27
Hybrid failure envelope 146
Hygric strains, measurement of 334–16
Hygroelastic isotropy. See Hygrothermoelastic isotropy
Hygroelastic stability. See Hygrothermoelastic stability
Hygrothermal effects 204–39 255–60
on laminate safety factor 255–60
on laminate strength 255–60
on mechanical behavior 205–8
physical and chemical 205
Hygrothermal force resultants 214
Hygrothermal forces, physical significance of 219–20
Hygrothermal load-deformation relations 216
Hygrothermal moment resultants 214 Index Terms Links
Hygrothermal strains in a lamina 212
Hygrothermoelastic effects 204–8
Hygrothermoelastic isotropy 220–22
Hygrothermoelastic load-deformation relations 213–15
Hygrothermoelastic stability 220–22
Hygrothermoelastic stress analysis 225–27
computational procedure for 235–37
Hygrothermoelastic stress and failure analysis 255–60
I
Ignition method 311
IITRI test method. See Compressive testing
Image analysis method 331–12
Ineffective fiber length 102–5
Inhomogeneity, definition of 19
Initial laminate failure. See First ply failure
In-plane shear modulus
measurement of 322–29
prediction of 56–58
In-plane shear strength
measurement of 322–29
prediction of 114–15
Interactive tensor polynomial theory. See Tsai-Wu theory
Interface/Interphase characterization 308–9
Interfiber failure 27
Interlaminar failure 244
Interlaminar fracture toughness 284–86 335–42
fracture mechanics 284–86
measurement of 335–42 359
See also Mixed mode testing; Mode I testing; Mode II
testing; Mode III testing Index Terms Links
Interlaminar shear strength, measurement of 331–34
Interlaminar strength 120 282
Interlaminar stresses 277–79
effects of stacking sequence 279–81
See also Edge effects
Interlaminar tensile strength, measurement of 329–33
Interphase
characterization of 308–9
definition of 1
role of 2
Intralaminar shear strength. See In-plane shear strength
Iosipescu shear test. See Shear testing
Isotropy, definition of 19–20
K
Kevlar/epoxy composites
coefficients of thermal expansion 210
properties of 377 379–80
thermal strains 210
Kevlar fibers. See Aramid fibers
Kink band. See Kink zone
Kink zone 105–6
L
Lamina
definition of 26
properties of 29
See also Unidirectional lamina
Lamina elastic behavior
macromechanics 63–92 Index Terms Links
Lamina elastic behavior (Cont.)
mathematical and engineering constants 71–76
micromechanics 43–60
Lamina strength—Macromechanics
computational procedure 139–41
evaluation of failure theories 143–48
failure theories 122–48
Hashin-Rotem theory 135–37
maximum strain theory 126–27
maximum stress theory 123–25
Tsai-Hill theory 128–30
Tsai-Wu theory 130–35
Lamina strength—Micromechanics
ineffective fiber length 102–5
in-plane shear 114–15
longitudinal compression 105–9
longitudinal tension 98–105
micromechanical failure analysis 116
out-of-plane behavior 115
transverse compression 113–14
transverse tension 110–13
Laminate failure theories 271–76
Laminate properties and characteristics
compliances 165–67
computational procedures for engineering properties 189–90
definition of 26
efficiency ratio of 265–67 287
engineering properties of 181–89
stiffnesses of 163–65
stiffness-strength ratio of 287
See also Multidirectional laminates Index Terms Links
Laminates
antisymmetric 172
antisymmetric angle-ply 174–75
antisymmetric crossply 172–74
balanced 171–75
orthotropic 175–76
orthotropic with tetragonal symmetry 176–77
quasi-isotropic 177–79
symmetric 167–70
symmetric angle-ply 170
symmetric with isotropic layers 168–69
symmetric with specially orthotropic layers 169–70
textile 192–93
Laminates with cracks 352–55
strength reduction of 353–54
Laminates with holes 280-81 348–54
biaxial testing of 352–53
failure pattern of 352
strength reduction of 350–54
Lamination residual stresses 227–29
Layup, laminate 26
Lithium aluminosilicate (LAS) 35
Load-deformation relations 163–65
Longitudinal compressive failure. See Longitudinal
compressive strength
Longitudinal compressive strength
measurement of 318–22
prediction of 105–9
Longitudinal modulus
of fiber 304–6
measurement of 316–18
prediction of 49–51 Index Terms Links
Longitudinal tensile failure. See Longitudinal tensile
strength
Longitudinal tensile strength
of fiber 304–6
measurement of 316–18
prediction of 99–100
M
Macromechanics, definition of 28
Manufacturing methods 36–40
autoclave molding 37
filament winding 37–38
resin transfer molding (RTM) 38–40
vacuum assisted RTM 39–40
Material response 20–23
Material symmetry
plane of 20
principal axes of 20
Material types 18
Matrix characterization 308
Matrix cracking 102 260–65
Matrix material
definition of 1
properties of 376
role of 2
stress-strain curves of 34–35
types of 33–35
Matrix volume ratio
definition of 29
measurement of 312
Matrix weight ratio 29 Index Terms Links
Maximum strain theory 126–27
failure envelope 127
Maximum stress theory 123–25
failure envelope 124–25
off-axis strength 124–25
Mechanics of materials approach 46
Metal matrices 35
Metal matrix composites 25
properties of 381
Metals, properties of 382
Microbuckling of fibers 105–6
Micromechanics
definition of 27
of discontinuous-fiber composites 58–60 104
of lamina elastic constants 43–60
of lamina failure 98–116
of lamina hygrothermal properties 208–11
of progressive failure 260–65
Micromechanics methods 43–49
bounding 46–48
mechanics of materials 44 46
self-consistent field 44–45
semiempirical (Halpin-Tsai) 48–49
Mixed mode testing 339–41
Cracked-lap shear (CLS) test 339–40
edge delamination tension (EDT) test 339–40
mixed mode bending (MMB) test 340
Mode I testing 335–37
double cantilever beam (DCB) specimen 335–36 359
height-tapered DCB (HTDCB) specimen 337
width-tapered DCB (WTDCB) specimen 336–37 Index Terms Links
Mode II testing 337–39
Arcan fixture 339
cantilever beam with enclosed notch (CBEN) 339
end-loaded split laminate (ELS) 339
end-notched cantilever beam (ENCB) test 339
end-notched flexure (ENF) test 339
Mode III testing 341–42
doubly split DCB specimen 341–42
edge-cracked torsion (ECT) test 342
Modulus reduction ratio 263–65
Moiré technique 235
Moisture concentration
effect on mechanical behavior 205–7
measurement of 314–16
Moisture effects. See Hygrothermal effects
Moment deformation relations 163–65
Multidirectional laminates
carpet plots for engineering properties 191–92
carpet plots for strength 254–55
classical lamination theory 158
coefficients of thermal and moisture expansion 216–19
compliances 165–67
computational procedure for hygrothermoelastic
analysis 235–37 258–59
computational procedure for stress and failure analysis 252–53
design considerations 179–81
elastic behavior 158–98
engineering properties 181–84
force and moment resultants 161–63
load-deformation relations 163–65
modified lamination theory 193–96 Index Terms Links
Multidirectional laminates (Cont.)
safety factors 244–46
stiffnesses 163–65
strain-displacement relations 158–60
strength components 246–47
stress and failure analysis 243–95
types of failure 244
N
Notched laminates. See Laminates with cracks;
Laminates with holes
O
Off-axis uniaxial test 343–45
Orthotropic laminates 175–77
Orthotropy, definition of 20
Out-of-plane loading
failure modes 115
shear moduli 327–28 358
P
Particulate composites 24
Phenolic resin 34
Photoelastic methods 28 281 350 354
Physical characterization 330–16
Plane stress 69–70
Ply. See Lamina
Ply discount method 268–70 Index Terms Links
Poisson’s ratio
of lamina 29 71–76 81–85
of laminates 181–84 186–92
measurement of 316–17
prediction of 50
reciprocity relations 74 82
of various types of materials 20–23
See also Engineering constants, relations for
Polyester 33 376
Poly-ether-ether-ketone (PEEK) 35 376
Polyimide 33 376
Polymeric matrices 33–35 376
Polymer matrix composites 25 377–81
Polyphenylene sulfide 35
Polypropylene 35
Polysulfone 35
Porosity. See Void volume ratio
Prepregs 35–36
Principal coordinate axes for lamina 26
Principal modulus ratio 287
Principal strength ratio 287
Progressive degradation model 348 352–53 355
Progressive laminate failure 260–71
Properties of composite materials 40–42 377–88
Q
Quasi-isotropic laminates 177–78 Index Terms Links
R
Rail shear test 325–26
Ranking of laminates 294–95
Reinforcement
definition of 1
role of 2
Residual stresses 111 127–229
Resin transfer molding (RTM) 38–40
Rule of mixtures 46 49 98–100
S
Safety factors
for lamina 139–41
for laminates 244–46 255–59
Sandwich core materials, properties of 383
Sandwich plates 196–98
Sandwich test specimens 320–22 333 359–60
Self-consistent field method 44–45
Semiempirical methods 48–49 60
S-glass/epoxy composites
coefficients of thermal expansion 210
properties of 377
thermal strains 210
S-glass fibers 30–32 374–75
Shear coupling coefficients
definition of 23 82
of lamina 182–85
of laminates 183–84 189–91
Shear coupling effect 23 Index Terms Links
Shear coupling stiffnesses. See Laminate properties and
characteristics; Stiffnesses
Shear lag analysis 58–59 104–5 262–65
Shear modulus
of fiber 306
of laminates 182–83 186 189–92
measurement of 322–29
See also In-plane shear modulus
Shear strength. See In-plane shear strength; Interlaminar
shear strength, measurement of
Shear testing 322–29
[±45]s angle-ply specimen 322–23
10° off-axis test 323–25
Arcan test 328–29
double-notch shear test 333–34
Iosipescu test 328–29 334
measurement of in-plane shear properties 322–29
rail shear tests 325–26
short-beam shear test 331–33
textile composites of 357–58
torsion tests 326–28
Short-fiber composites. See Discontinuous-fiber
composites
Short sandwich beam (SSB) test 333
Silicon carbide/aluminum composites
properties of 381
temperature effects 206
Silicon carbide/ceramic composites 41
properties of 381
Silicon carbide fibers 30–32 374–75
Specially orthotropic material 66–67 Index Terms Links
Specific modulus. See Specific stiffness
Specific stiffness 13 32 41 288–89
Specific strength 13 32 41
Stacking sequence
definition of 26
effects of 277 279–81 350–51
Stiffness degradation. See Stiffness reduction factors;
Stiffness reduction of laminates
Stiffnesses
bending 164–65
coupling 164–65
extensional 164–65
of general anisotropic material 63–66
inversion of 165–67
of isotropic material 71
of lamina 70
of laminates 164–65
of specially orthotropic material 66–67
transformation of 79 81 175–76
of transversely isotropic material 67–69
Stiffness reduction factors 263 270
Stiffness reduction of laminates 260–65
Stiffness to strength ratio 287
Strain concentration factor 110–11
Strain-displacement relations 158–60
Strain energy release rate
fracture mechanics 284–86
measurement of 335–42
See also Interlaminar fracture toughness
Strain gage method 313–14 323–27 Index Terms Links
Strains
hygric 315
hygrothermal 212
in laminates 160
tensor 63–64
thermal 210 308 313
transformation of 77–78
ultimate 126–27 305 316
Strain-stress relations. See Stress-strain relations
Strain transformation 77–78
Strength
basic parameters of lamina 120–21
biaxial 142–43 342–48
comparison between unidirectional and angle-ply
laminates 253–54
of composite lamina 120–48
of fibers 304–5 374–75
in-plane shear 114–15 322–24
interlaminar 120 282
of laminates 243–71
longitudinal 98–109 316–22
notched 350–55
transverse 110–14 316–19
of typical composites 377–81
Strength reduction ratio of notched laminates 316–22
Stress analysis of laminates 243–98
Stress concentration factor
macromechanical (laminate) 349–51
micromechanical 110 115
Stress concentrations, composites with 348–55 Index Terms Links
Stresses
hygrothermal 225–27
interlaminar 277–81
residual 227–31
tensor 63–64
Stress-strain relations
of general anisotropic material 63–66
hygrothermal 216
hygrothermoelastic 213–15
of isotropic material 71
of orthotropic material under plane stress 69–71
of specially orthotropic material 66–67
of thin lamina 76–77
of transversely isotropic material 67–69
Stress transformation 77–78
Structural testing 359–60
Symmetric balanced laminates. See Orthotropic laminates
Symmetric laminates 167–70
angle-ply 170
isotropic layers and 168–69
specially orthotropic layers (crossply) and 169–70
stress and failure analysis of 244–51
T
Temperature, effect of 205–8
Tensile testing
of fibers 304–6
measurement of lamina properties 316–18
ring specimen 317–18
specimen geometry 317
through-thickness testing 329–31 Index Terms Links
Testing. See Biaxial testing; Compressive testing;
Interlaminar fracture toughness; Interlaminar tensile
strength, measurement of; Shear testing; Tensile
testing; Testing of composite materials
Testing of composite materials 303–64
Test methods for unidirectional lamina 362
Tetragonal symmetry 176–77
Textile composites
failure criteria 137–38
in-plane compressive testing 356–57
in-pIane shear testing 357
in-plane tensile testing 355–56
interlaminar fracture toughness 359
laminates 192–93
test methods 355–59
through-thickness testing 357–59
Thermal forces 214 218–20
Thermal moments 214 219–20
Thermal strains 210 307–8 313–14
Thermal stresses. See Residual stresses
Thermoelastic isotropy. See Hygrothermoelastic isotropy
Thermoelastic stability. See Hygrothermoelastic stability
Thermoplastics 35
Thermoset polymers 33–35
Thin-wall tubular specimen 346–48
Through-thickness testing 329–34
compressive testing 331
interlaminar shear testing 331–33
tensile testing 329–31
Torsion coupling stiffnesses. See Laminate properties and
characteristics; Stiffnesses Index Terms Links
Torsion tube test 226–27
Transformation
Computational procedure for 84
of elastic parameters (three-dimensional) 90–92 386–87
of elastic parameters (two-dimensional) 78–81
of engineering constants 83–87
of lamina stiffnesses and compliances 79–81
of laminate stiffnesses and compliances 175–77
of stress and strain (three-dimensional) 88–90
of stress and strain (two-dimensional) 77–78
of stress-strain relations 81
Transverse compressive strength
measurement of 318–22
prediction of 113
Transversely isotropic material 67–69
Transverse modulus
measurement of 316–17
prediction of 51–56
Transverse shear
effect of 193–96
Transverse tensile strength
measurement of 316–17
prediction of 110–13
Tsai-Hill criterion. See Tsai-Hill theory
Tsai-Hill theory 128–30
off-axis strength 129 134
Tsai-Wu criterion
for first ply failure 244–46
with hygrothermal stresses 255–56 Index Terms Links
Tsai-Wu theory 130–35
biaxial strength 142–43
failure envelope 135
lamina strength components 139–41
off-axis strength 134
safety factor 139
U
Ultimate laminate failure 244 265–71
Ultimate strains, measurement of 305 316–17
Unidirectional composites, properties of 40–42 377–81
Unidirectional lamina
characterization of 316–29
coefficients of thermal and moisture expansion 208–11
determination of strength components 140–41
failure mechanisms 98–116
hygrothermal strains 212
macromechanical failure theories 122–48
macromechanical strength parameters 120–21
measurement of compressive properties 318–22
measurement of shear properties 322–29
measurement of tensile properties 316–18
micromechanics of failure and strength 98–116
off-axis strength 124–25 129
See also Lamina elastic behavior; Lamina
strength—Macromechanics; Lamina
strength—Micromechanics Index Terms Links
V
Vacuum-assisted resin transfer molding (VARTM) 39–40
Vinylester 33 34 376
Void volume ratio
definition of 29
measurement of 311–12
W
Warpage of laminates 232–33
Woven carbon/epoxy 85–86 379–80
Woven fabrics 33–34
Woven glass/epoxy 379–80
Woven Kevlar/epoxy 379–80
X
X-radiography 261
Y
Young's modulus
of fiber 304–6
of lamina 81–85
of laminates 181–92
measurement of 316–17
of off-axis lamina 343–45
prediction of 49–53
See also Engineering constants, relations fix
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