Analysis and Performance of Fiber Composites

576 Pages·2006·12.759 MB·English

by  Bhagwan D. Agarwal, Lawrence J. Broutman, K. Chandrashekhara

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
WILEY
Analysis and Performance of Fiber Composites
Third Edition
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CONTENTS
Preface xiii
1 Introduction 1
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 16
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
iv 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 62
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
CONTENTS 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 132
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 l 56
vi CONTENTS
5 Analysis of an Orthotropic Lamina 158
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 I 66
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
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 21~
6.1 Introduction I 213
6.2 Laminate Strains I 213
6.3 Variation of Stresses in a Laminate 21 q
CONTENTS vii
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
7 Analysis of Laminated Plates and Beams 282
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 314
viii 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 324
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 32 6
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
CONTENTS 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 401
X 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
Temperatures I 429
Exercise Problems I 431
References I 431
10 Experimental Characterization of Composites 439
10.1 Introduction I 439
l 0.2 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
I 0.2.6 Moisture Expansion Coefficients I 444
I 0.3 Measurement of Mechanical Properties I 445
10.3.1 Properties in Tension I 445
I 0.3.2 Properties in Compression I 449
I 0.3.3 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