Pierre Rahme, University of Notre Dame, Indiana, USA Considered to have contributed greatly to the pre-sizing of composite structures, Composite Materials: Design and Applications is a p
Trang 16000 Broken Sound Parkway, NW Suite 300, Boca Raton, FL 33487
711 Third Avenue New York, NY 10017
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COMPOSITE MATERIALS
T H I R D E D I T I O N
Design and Applications
Design and Applications
2 Park Square, Milton Park Abingdon, Oxon OX14 4RN, UK
an informa business
www.taylorandfrancisgroup.com
Composite materials
T h i r d E d i T i o n
design and Applications
design and Applications
daniel Gay
Gay
“This book covers the topics related to the mechanics of composite
ma-terials in a very simple way it is addressed to graduate and
under-graduate students as well as to practical engineers who want to
en-hance their knowledge and learn the guidelines of the use of composite
materials This book is a good classroom material [and] a good
reference.”
—Dr Pierre Rahme, University of Notre Dame, Indiana, USA
Considered to have contributed greatly to the pre-sizing of composite
structures, Composite Materials: Design and Applications is a popular
reference book for designers of heavily loaded composite parts Fully
updated to mirror the exponential growth and development of
compos-ites, this English-language Third Edition:
• Contains all-new coverage of nanocomposites and biocomposites
• reflects the latest manufacturing processes and applications in the
aerospace, automotive, naval, wind turbine, and sporting goods
industries
• Provides a design method to define composite multilayered plates
under loading, along with all numerical information needed for
implementation
• Proposes original study of composite beams of any section shapes
and thick-laminated composite plates, leading to technical
formula-tions that are not found in the literature
• Features numerous examples of the pre-sizing of composite parts,
processed from industrial cases and reworked to highlight key
in-formation
• includes test cases for the validation of computer software using
finite elements
Consisting of three main parts, plus a fourth on applications, Composite
Materials: Design and Applications, Third Edition features a technical
level that rises in difficulty as the text progresses, yet each part still can
be explored independently While the heart of the book, devoted to the
methodical pre-design of structural parts, retains its original character,
the contents have been significantly rewritten, restructured, and
expand-ed to better illustrate the types of challenges encounterexpand-ed in modern
engineering practice
Materials Science/Mechanical Engineering
“This book covers the topics related to the mechanics of composite
ma-terials in a very simple way It is addressed to graduate and
un-dergraduate students as well as to practical engineers who want to
enhance their knowledge and learn the guidelines of the use of
compos-ite materials This book is good classroom material [and] a good
reference.”
—Dr Pierre Rahme, University of Notre Dame, Indiana, USA
Considered to have contributed greatly to the pre-sizing of composite
structures, Composite Materials: Design and Applications is a popular
reference book for designers of heavily loaded composite parts Fully
updated to mirror the exponential growth and development of
compos-ites, this English-language Third Edition:
• Contains all-new coverage of nanocomposites and biocomposites
• Reflects the latest manufacturing processes and applications in the
aerospace, automotive, naval, wind turbine, and sporting goods
industries
• Provides a design method to define composite multilayered plates
under loading, along with all numerical information needed for
implementation
• Proposes original study of composite beams of any section shapes
and thick-laminated composite plates, leading to technical
formula-tions that are not found in the literature
• Features numerous examples of the pre-sizing of composite parts,
processed from industrial cases and reworked to highlight key
in-formation
• Includes test cases for the validation of computer software using
finite elements
Consisting of three main parts, plus a fourth on applications, Composite
Materials: Design and Applications, Third Edition features a technical
level that rises in difficulty as the text progresses, yet each part still can
be explored independently While the heart of the book, devoted to the
methodical pre-design of structural parts, retains its original character,
the contents have been significantly rewritten, restructured, and
expand-ed to better illustrate the types of challenges encounterexpand-ed in modern
Trang 2Composite materials
T h i r d E d i T i o n
design and Applications
Trang 3This page intentionally left blank
Trang 4Boca Raton London New York CRC Press is an imprint of the
Taylor & Francis Group, an informa business
Composite materials
T h i r d E d i T i o n
design and Applications
daniel Gay
Trang 5CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2015 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S Government works
Version Date: 20140611
International Standard Book Number-13: 978-1-4665-8488-4 (eBook - PDF)
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Trang 6Contents
Preface xix
Acknowledgments xxi
Author xxiii
SeCtion i PRinCiPLeS oF ConStRUCtion 1 Composite.Materials:.Interest.and.Physical.Properties 3
1.1 What Is a Composite Material? 3
1.1.1 Broad Definition 3
1.1.2 Main Features 4
1.2 Fibers and Matrices 4
1.2.1 Fibers 4
1.2.1.1 Definition 4
1.2.1.2 Principal Fiber Materials 5
1.2.1.3 Relative Importance of Different Fibers in Applications 6
1.2.2 Materials for Matrices 7
1.3 What Can Be Made Using Composite Materials? 7
1.4 A Typical Example of Interest 9
1.5 Some Examples of Classical Design Replaced by Composite Solutions 10
1.6 Main Physical Properties 10
2 Manufacturing.Processes 17
2.1 Molding Processes 17
2.1.1 Contact Molding 17
2.1.2 Compression Molding 18
2.1.3 Vacuum Molding 18
2.1.4 Resin Injection Molding 19
2.1.5 Injection Molding with Prepreg 20
2.1.6 Foam Injection Molding 20
2.1.7 Molding of Hollow Axisymmetric Components 20
2.2 Other Forming Processes 22
2.2.1 Sheet Forming 22
2.2.2 Profile Forming 23
2.2.3 Forming by Stamping 23
Trang 7vi ◾ Contents
2.2.4 Preforming by Three-Dimensional Assembly 24
2.2.4.1 Example: Carbon/Carbon 24
2.2.4.2 Example: Silicon/Silicon 24
2.2.5 Automated Tape Laying and Fiber Placement 24
2.2.5.1 Necessity of Automation 24
2.2.5.2 Example 24
2.2.5.3 Example 25
2.2.5.4 Example: Robots and Software for AFP—Automatic Fiber Placement Coriolis Composites (FRA) 25
2.3 Practical Considerations on Manufacturing Processes 26
2.3.1 Acronyms 26
2.3.2 Cost Comparison 27
3 Ply.Properties 29
3.1 Isotropy and Anisotropy 29
3.1.1 Isotropic Materials 31
3.1.2 Anisotropic Material 32
3.2 Characteristics of the Reinforcement–Matrix Mixture 33
3.2.1 Fiber Mass Fraction 34
3.2.2 Fiber Volume Fraction 34
3.2.3 Mass Density of a Ply 35
3.2.4 Ply Thickness 35
3.3 Unidirectional Ply 36
3.3.1 Elastic Modulus 36
3.3.2 Ultimate Strength of a Ply 38
3.3.3 Examples 39
3.3.4 Examples of High-Performance Unidirectional Plies 41
3.4 Woven Ply 41
3.4.1 Forms of Woven Fabrics 41
3.4.2 Elastic Modulus of Fabric Layer 42
3.4.3 Examples of Balanced Fabric/Epoxy 43
3.5 Mats and Reinforced Matrices 45
3.5.1 Mats 45
3.5.2 Example: A Summary of Glass/Epoxy Layers 45
3.5.3 Microspherical Fillers 45
3.5.4 Other Classical Reinforcements 48
3.6 Multidimensional Fabrics 49
3.6.1 Example: A Four-Dimensional Architecture of Carbon Reinforcement 49
3.6.2 Example: Three-Dimensional Carbon/Carbon Components 50
3.7 Metal Matrix Composites 50
3.7.1 Some Examples 50
3.7.2 Unidirectional Fibers/Aluminum Matrix 52
3.8 Biocomposite Materials 53
3.8.1 Natural Plant Fibers 53
3.8.1.1 Natural Fibers 53
3.8.1.2 Pros 53
Trang 8Contents ◾ vii
3.8.1.3 Cons 53
3.8.1.4 Examples 54
3.8.2 Natural Vegetable Fiber–Reinforced Composites 54
3.8.2.1 Mechanical Properties 54
3.8.2.2 Biodegradable Matrices 54
3.8.3 Manufacturing Processes 56
3.8.3.1 With Thermosetting Resins 56
3.8.3.2 With Thermoplastic Resins 57
3.9 Nanocomposite Materials 57
3.9.1 Nanoreinforcement 57
3.9.1.1 Nanoreinforcement Shapes 57
3.9.1.2 Properties of Nanoreinforcements 58
3.9.2 Nanocomposite Material 61
3.9.3 Mechanical Applications 62
3.9.3.1 Improvement in Mechanical Properties 62
3.9.3.2 Further Examples of Nonmechanical Applications 64
3.9.4 Manufacturing of Nanocomposite Materials 64
3.10 Tests 66
4 Sandwich.Structures 69
4.1 What Is a Sandwich Structure? 69
4.1.1 Their Properties Are Surprising 69
4.1.2 Constituent Materials 70
4.2 Simplified Flexure 71
4.2.1 Stress 71
4.2.2 Displacements 72
4.2.2.1 Contributions of Bending Moment M and of Shear Force T 72
4.2.2.2 Example: A Cantilever Sandwich Structure 73
4.3 Some Special Features of Sandwich Structures 74
4.3.1 Comparison of Mass for the Same Flexural Rigidity 〈EI〉 74
4.3.2 Deterioration by Buckling of Sandwich Structures 74
4.3.2.1 Global Buckling 75
4.3.2.2 Local Buckling of the Skins 75
4.3.3 Other Types of Damage 76
4.4 Manufacturing and Design Problems 76
4.4.1 Example of Core Material: Honeycomb 76
4.4.2 Shaping Processes 77
4.4.2.1 Machining 77
4.4.2.2 Deformation 77
4.4.2.3 Some Other Considerations 77
4.4.3 Inserts and Attachment Fittings 78
4.4.4 Repair of Laminated Facings 79
4.5 Nondestructive Inspection 80
4.5.1 Main Nondestructive Inspection Methods 80
4.5.2 Acoustic Emission Testing 81
Trang 9viii ◾ Contents
5 Conception:.Design.and.Drawing 85
5.1 Drawing a Composite Part 85
5.1.1 Specific Properties 85
5.1.2 Guide Values of Presizing 86
5.1.2.1 Material Characteristics 86
5.1.2.2 Design Factors 88
5.2 Laminate 88
5.2.1 Unidirectional Layers and Fabrics 88
5.2.1.1 Unidirectional Layer 88
5.2.1.2 Fabrics 89
5.2.2 Correct Ply Orientation 89
5.2.3 Laminate Drawing Code 90
5.2.3.1 Standard Orientations 90
5.2.3.2 Laminate Middle Plane 90
5.2.3.3 Description of the Stacking Order 93
5.2.3.4 Midplane Symmetry 93
5.2.3.5 Specific Case of Balanced Fabrics 94
5.2.3.6 Technical Minimum 95
5.2.4 Arrangement of Plies 96
5.2.4.1 Proportion and Number of Plies 96
5.2.4.2 Example of Pictorial Representation 97
5.2.4.3 Case of Sandwich Structure 97
5.3 Failure of Laminates 98
5.3.1 Damages 98
5.3.1.1 Types of Failure 98
5.3.1.2 Note: Classical Maximum Stress Criterion Shows Its Limits 99
5.3.2 Most Frequently Used Criterion: Tsai–Hill Failure Criterion 100
5.3.2.1 Tsai–Hill Number 100
5.3.2.2 Notes 101
5.3.2.3 How to Determine the Stress Components σℓ, σt, and τℓt in Each Ply 101
5.4 Presizing of the Laminate 102
5.4.1 Modulus of Elasticity—Deformation of a Laminate 102
5.4.1.1 Varying Proportions of Plies 102
5.4.1.2 Example of Using Tables 103
5.4.2 Case of Simple Loading 103
5.4.3 Complex Loading Case: Approximative Proportions According to Orientations 109
5.4.3.1 When the Normal and Tangential (Shear) Loads Are Applied Simultaneously 109
5.4.3.2 Example 114
5.4.3.3 Note 117
5.4.4 Complex Loading Case: Optimum Composition of a Laminate 119
5.4.4.1 Optimum Laminate 119
5.4.4.2 Example 122
Trang 10Contents ◾ ix
5.4.4.3 Example 125
5.4.4.4 Notes 126
5.4.5 Notes for Practical Use Concerning Laminates 127
5.4.5.1 Specific Aspects for the Design of Laminates 127
5.4.5.2 Delaminations 128
5.4.5.3 Why Is Fatigue Resistance So Good? 129
5.4.5.4 Laminated Tubes 133
6 Conception:.Fastening and.Joining 135
6.1 Riveting and Bolting 135
6.1.1 Local Loss of Strength 135
6.1.1.1 Knock-Down Factor 135
6.1.1.2 Causes of Hole Degradation 136
6.1.2 Main Failure Modes in Bolted Joints of Composite Materials 138
6.1.3 Sizing of the Joint 138
6.1.3.1 Recommended Values 138
6.1.3.2 Evaluation of Magnified Stress Values 140
6.1.4 Riveting 140
6.1.5 Bolting 141
6.1.5.1 Example of Bolted Joint 141
6.1.5.2 Tightening of the Bolt 143
6.2 Bonding 143
6.2.1 Adhesives Used 143
6.2.2 Geometry of the Bonded Joints 145
6.2.3 Sizing of the Bonding Surface Area 146
6.2.3.1 Strength of Adhesive 146
6.2.3.2 Design 147
6.2.3.3 Stress in Bonded Areas 148
6.2.3.4 Example of Single-Lap Adhesive Joint 150
6.2.4 Case of Bonded Joint with Cylindrical Geometry 150
6.2.4.1 Bonded Circular Flange 150
6.2.4.2 Tubes Fitted and Bonded into One Another 150
6.2.5 Examples of Bonding 150
6.2.5.1 Laminates 150
6.3 Inserts 152
6.3.1 Case of Sandwich Parts 152
6.3.2 Case of Parts under Uniaxial Loads 154
7 Composite.Materials.and.Aerospace.Construction 155
7.1 Aircraft 155
7.1.1 Composite Components in Aircraft 155
7.1.2 Allocation of Composites Depending on Their Nature 156
7.1.2.1 Glass/Epoxy, Kevlar/Epoxy 156
7.1.2.2 Carbon/Epoxy 157
7.1.2.3 Boron/Epoxy 157
7.1.2.4 Honeycombs 157
7.1.3 Few Comments 158
Trang 11x ◾ Contents
7.1.4 Specific Aspects of Structural Strength 158
7.1.5 Large Transport Aircraft 159
7.1.5.1 Example 159
7.1.5.2 How to Determine the Benefits 159
7.1.5.3 Example: Civil Transport Aircraft A380-800, Airbus (EUR) 161
7.1.5.4 Example: Civil Transport Aircraft B 787-800, Boeing (USA) 161
7.1.5.5 Example: Civil Transport Aircraft A350-900, Airbus (EUR) 163
7.1.6 Regional Aircraft and Business Jets 165
7.1.6.1 Example: Regional Aircraft ATR 72-600, EADS (EUR), Alenia (ITA) .165
7.1.6.2 Example: Business Aircraft Falcon, Dassault Aviation (FRA) 165
7.1.6.3 Example: Cargo Aircraft WK2 and Suborbital Space Plane SST2, Scaled Composites (USA)–Virgin Group (UK) 166
7.1.7 Light Aircraft 168
7.1.7.1 Trends 168
7.1.7.2 Aircraft with Tractor Propeller 168
7.1.7.3 Aircraft with Pusher Propeller 169
7.1.7.4 Modern Glider Planes 170
7.1.8 Fighter Aircraft 170
7.1.9 Architecture and Manufacture of Composite Aircraft Parts 171
7.1.9.1 Sandwich Design 171
7.1.9.2 Rib-Stiffened Panels 173
7.1.10 Braking Systems 178
7.2 Helicopters 179
7.2.1 Situation 179
7.2.2 Composite Areas 180
7.2.2.1 Example: Helicopter EC 145 T2, Airbus-Helicopter (EUR) 180
7.2.2.2 Example: Helicopter X4, Thales–Safran (FRA), Airbus- Helicopter (EUR) 180
7.2.3 Blades 181
7.2.3.1 Design of a Main Rotor Blade 181
7.2.3.2 Advantages 181
7.2.3.3 Consequences 181
7.2.4 Rotor Hub 183
7.2.4.1 Example: Rotor Hub Starflex, Eurocopter (FRA–GER) 183
7.2.4.2 Example: Rotor Hub Spheriflex, Eurocopter (FRA–GER) 184
7.2.5 Other Working Composite Parts 184
7.3 Airplane Propellers 186
7.3.1 Propellers for Conventional Aerodynamics 186
7.3.1.1 Example: Propeller Blade, Hamilton Sundstrand (USA)– Ratier Figeac (FRA) 186
7.3.1.2 Example: Airplane with Tilt Rotors, V-22 Osprey Bell Boeing (USA) and Dowty Propellers (UK) 187
7.3.2 High-Speed Propellers 188
Trang 12Contents ◾ xi
7.4 Aircraft Reaction Engine 190
7.4.1 Employed Materials 190
7.4.2 Refractory Composites 191
7.4.2.1 Specific Features 191
7.4.2.2 Fibers 191
7.4.2.3 Matrices 192
7.4.2.4 Applications 192
7.4.2.5 Example: Jet Engine Leap®, CFM International, General Electric (USA)–SNECMA (FRA) .193
7.5 Space Applications 194
7.5.1 Satellites 194
7.5.2 Propellant Tanks and Pressure Vessels 195
7.5.3 Nozzles 196
7.5.4 Other Composite Components for Space Application 198
7.5.4.1 For Engines 198
7.5.4.2 For Thermal Protection 198
7.5.4.3 For Energy Storage 200
8 Composite.Materials.for Various.Applications 203
8.1 Comparative Importance of Composites in Applications 203
8.1.1 Relative Importance in terms of Mass and Market Value 204
8.1.2 Mass of Composites Implemented According to the Geographical Area 205
8.1.3 Average Prices 205
8.2 Composite Materials and Automotive Industry 206
8.2.1 Introduction 206
8.2.1.1 Example: Golf Model, Volkswagen (GER) 206
8.2.1.2 Relative Weight Importance of Materials 207
8.2.2 Composite Parts 208
8.2.2.1 Brief Reminder 208
8.2.2.2 Current Functional Design 208
8.2.2.3 Notable Composite Components 210
8.2.2.4 Notes 212
8.2.2.5 Use of Natural Fibers 213
8.2.3 Research and Development 214
8.2.3.1 Structure 215
8.2.3.2 Mechanical Parts 215
8.2.4 Motor Racing 216
8.3 Wind Turbines 217
8.3.1 Components 217
8.3.2 Manufacturing Processes 218
8.4 Composites and Shipbuilding 219
8.4.1 Competition 219
8.4.1.1 Example: Ocean-Going Maxi-Trimaran 220
8.4.1.2 Example: Single Scull 222
8.4.1.3 Example: Surfboard 223
8.4.2 Vessels 223
Trang 13xii ◾ Contents
8.5 Sports and Leisure 223
8.5.1 Skis 223
8.5.1.1 Equipment of a Skier 223
8.5.1.2 Main Components of a Ski 224
8.5.2 Bicycles 225
8.5.2.1 Machine 226
8.5.2.2 Other Specific Equipments 226
8.5.3 Tennis Rackets 226
8.6 Diverse Applications 226
8.6.1 Pressure Gas Bottle 226
8.6.2 Bogie Frame 227
8.6.3 Tubes for Offshore Installations 227
8.6.4 Biomechanical Applications 228
8.6.5 Cable Car 229
SeCtion ii MeChaniCaL BehavioR oF LaMinated MateRiaLS 9 Anisotropic.Elastic.Medium 233
9.1 Some Reminders 233
9.1.1 Continuum Mechanics 233
9.1.2 Number of Distinct φijkℓ Terms 234
9.2 Orthotropic Material 236
9.3 Transversely Isotropic Material 236
10 Elastic.Constants.of Unidirectional.Composites 239
10.1 Longitudinal Modulus E ℓ 239
10.2 Poisson Coefficient 241
10.3 Transverse Modulus E t 242
10.4 Shear Modulus G ℓt 244
10.5 Thermoelastic Properties 245
10.5.1 Isotropic Material: Recall 245
10.5.2 Case of Unidirectional Composite 246
10.5.2.1 Coefficient of Thermal Expansion along the Direction ℓ 246
10.5.2.2 Coefficient of Thermal Expansion along the Transverse Direction t 247
10.5.3 Thermomechanical Behavior of a Unidirectional Layer 248
11 Elastic.Constants.of.a Ply in.Any.Direction 249
11.1 Flexibility Coefficients 249
11.2 Stiffness Coefficients 255
11.3 Case of Thermomechanical Loading 257
11.3.1 Flexibility Coefficients 257
11.3.2 Stiffness Coefficients 259
12 Mechanical.Behavior.of Thin.Laminated.Plates 263
12.1 Laminate with Midplane Symmetry 263
12.1.1 Membrane Behavior 263
12.1.1.1 Loadings 263
12.1.1.2 Displacement Field 264
Trang 14Contents ◾ xiii
12.1.2 Apparent Elastic Moduli of the Laminate 267
12.1.3 Consequence: Practical Determination of a Laminate Subject to Membrane Loading 267
12.1.3.1 Givens of the Problem 267
12.1.3.2 Principle of Calculation 268
12.1.3.3 Calculation Procedure 269
12.1.4 Flexure Behavior 272
12.1.4.1 Displacement Field 272
12.1.4.2 Loadings 273
12.1.4.3 Notes 275
12.1.5 Consequence: Practical Determination of a Laminate Subject to Flexure 278
12.1.6 Simplified Calculation for Bending 278
12.1.6.1 Apparent Failure Strength in Bending 278
12.1.6.2 Apparent Flexure Modulus 279
12.1.7 Thermomechanical Loading Case 280
12.1.7.1 Membrane Behavior 280
12.1.7.2 Behavior under Bending 283
12.2 Laminate without Midplane Symmetry 283
12.2.1 Coupled Membrane–Flexure Behavior 283
12.2.2 Case of Thermomechanical Loading 285
SeCtion iii JUStiFiCationS, CoMPoSite BeaMS, and thiCk LaMinated PLateS 13 Elastic.Coefficients 289
13.1 Elastic Coefficients for an Orthotropic Material 289
13.1.1 Reminders 289
13.1.2 Elastic Behavior Equation in Orthotropic Axes 290
13.2 Elastic Coefficients for a Transverse Isotropic Material 292
13.2.1 Elastic Behavior Equation 292
13.2.2 Rotation about an Orthotropic Transverse Axis 295
13.2.2.1 Problem 295
13.2.2.2 Technical Form 300
13.3 Case of a Ply 302
14 Damage.in.Composite Parts:.Failure.Criteria 303
14.1 Damage in Composite Parts 303
14.1.1 Industrial Emphasis of the Problem 303
14.1.1.1 Causes of Damage 303
14.1.1.2 Diversity of Composite Parts 304
14.1.2 Influence of Manufacturing Process 304
14.1.2.1 Example: Injected Part with Short Fibers 305
14.1.2.2 Example: Parts with Pronounced Curvatures 305
14.1.3 Typical Area and Singularities in a Same Part 305
14.1.4 Degradation Process within the Typical Area 306
14.1.4.1 Example: Composite Short Fiber Plate 306
14.1.4.2 Example: Laminate Consisting of Unidirectional Plies 307
Trang 15xiv ◾ Contents
14.2 Form of a Failure Criterion 310
14.2.1 Features of a Failure Criterion 310
14.2.1.1 Failure Criterion Is a Design Tool 310
14.2.1.2 Many Criteria 310
14.2.2 General Form of a Failure Criterion 310
14.2.2.1 Development of a Criterion 310
14.2.2.2 Case of an Orthotropic Material 311
14.2.3 Linear Failure Criterion 312
14.2.3.1 Example: Plane State of Stress in an Orthotropic Material 312
14.2.3.2 Example: Maximum Stress Failure Criterion 313
14.2.3.3 Note: Maximum Eligible Strain Criterion 313
14.2.4 Quadratic Failure Criterion 314
14.2.4.1 General Form 314
14.2.4.2 Specific Case of Plane Stress 314
14.2.4.3 Note: Simplified Form for the Quadratic Criterion 315
14.3 Tsai–Hill Failure Criterion 316
14.3.1 Isotropic Material: The von Mises Criterion 316
14.3.1.1 Material Is Elastic and Isotropic 316
14.3.1.2 Notes 318
14.3.2 Orthotropic Material: Tsai–Hill Criterion 320
14.3.2.1 Notes 320
14.3.2.2 Case of a Transversely Isotropic Material 321
14.3.2.3 Case of Unidirectional Ply under In-Plane Loading 323
14.3.3 Evolution of Strength Properties of a Unidirectional Ply Depending on the Direction of Solicitation 324
14.3.3.1 Tensile and Compressive Strength 324
14.3.3.2 Shear Strength 325
15 Bending.of.Composite.Beams.of.Any.Section.Shape 327
15.1 Bending of Beams with Isotropic Phases and Plane of Symmetry 328
15.1.1 Degrees of Freedom 329
15.1.1.1 Equivalent Stiffnesses 329
15.1.1.2 Longitudinal Displacement 329
15.1.1.3 Rotation of the Section 329
15.1.1.4 Elastic Center 330
15.1.1.5 Transverse Displacement along y Direction 330
15.1.1.6 Transverse Displacement along z Direction 331
15.1.2 Perfect Bonding between the Phases 332
15.1.2.1 Displacements 332
15.1.2.2 Strains 332
15.1.2.3 Stress 333
15.1.3 Equilibrium Relationships 333
15.1.3.1 Longitudinal Equilibrium 333
15.1.3.2 Transverse Equilibrium 334
15.1.3.3 Moment Equilibrium 335
Trang 16Contents ◾ xv
15.1.4 Constitutive Equations 336
15.1.5 Technical Formulation 337
15.1.5.1 Assumptions 337
15.1.5.2 Expression of Normal Stress 337
15.1.5.3 Expression of Shear Stress 338
15.1.5.4 Shear Coefficient for the Section 340
15.1.6 Energy Interpretation 342
15.1.6.1 Energy Due to Normal Stress σxx 342
15.1.6.2 Energy Due to Shear Stress τ 343
15.1.7 Extension to the Dynamic Case 344
15.2 Case of Beams of Any Cross Section (Asymmetric) 346
15.2.1 Technical Formulation 347
15.2.2 Notes 351
16 Torsion.of.Composite.Beams.of.Any.Section.Shape 353
16.1 Uniform Torsion 353
16.1.1 Torsional Degree of Freedom 354
16.1.2 Constitutive Equation 354
16.1.3 Determination of Φ(y, z) 355
16.1.3.1 Local Equilibrium 355
16.1.3.2 External Boundary Condition 356
16.1.3.3 Internal Boundary Conditions 356
16.1.3.4 Uniqueness of Function Φ 356
16.1.4 Energy Interpretation 357
16.2 Location of the Torsion Center 358
16.2.1 Coordinates in Principal Axes 358
16.2.2 Summary of Results 359
16.2.3 Flexion–Torsion Coupling 361
17 Bending.of.Thick.Composite.Plates 363
17.1 Preliminary Remarks 363
17.1.1 Transverse Normal Stress σz 363
17.1.2 Transverse Shear Stress τxz and τyz 364
17.1.3 Assumptions 365
17.2 Displacement Field 367
17.3 Strains 369
17.4 Constitutive Equations 369
17.4.1 Membrane Behavior 369
17.4.2 Bending Behavior 370
17.4.3 Transverse Shear Behavior 372
17.4.3.1 Transverse Shear Resultant Q x 372
17.4.3.2 Transverse Shear Resultant Q y 373
17.5 Equilibrium Relationships 373
17.5.1 Transverse Equilibrium 373
17.5.2 Equilibrium in Bending 374
Trang 17xvi ◾ Contents
17.6 Technical Formulation for Bending 374
17.6.1 Stress Due to Bending 375
17.6.1.1 Plane Stress Values 375
17.6.1.2 Transverse Shear Stress Values 376
17.6.2 Characterization of Warping Increments in Bending ηx and ηy 376
17.6.3 Particular Cases 377
17.6.3.1 Orthotropic Homogeneous Plate 377
17.6.3.2 Cylindrical Bending about x- or y-Axis 378
17.6.3.3 Multilayered Plate 379
17.6.3.4 Consequences 380
17.6.4 Warping Functions 380
17.6.4.1 Boundary Conditions 380
17.6.4.2 Interfacial Continuity 381
17.6.4.3 Formulation of Warping Functions 381
17.6.5 Consequences 382
17.6.5.1 Expression of Transverse Shear Stress 382
17.6.5.2 Transverse Shear Coefficients 382
17.6.6 Energy Interpretation 384
17.7 Examples 385
17.7.1 Orthotropic Homogeneous Plate 385
17.7.2 Sandwich Plate 387
17.7.2.1 Case of Two Orthotropic Materials 387
17.7.2.2 Warping Functions 388
17.7.2.3 Transverse Shear Stress 389
17.7.2.4 Transverse Shear Coefficients 389
17.7.3 Conclusion 390
SeCtion iv aPPLiCationS 18 Applications.Level.1 393
18.1 Simply Supported Sandwich Beam 393
18.2 Poisson Coefficient of a Unidirectional Layer 396
18.3 Helicopter Blade 397
18.4 Drive Shaft for Trucks 402
18.5 Flywheel in Carbon/Epoxy 408
18.6 Wing Tip Made of Carbon/Epoxy 410
18.7 Carbon Fiber Coated with Nickel 423
18.8 Tube Made of Glass/Epoxy under Pressure 425
18.9 Filament-Wound Pressure Vessel: Winding Angle 428
18.10 Filament-Wound Pressure Vessel: Consideration of Openings in the Bottom Heads 431
18.11 Determination of Fiber Volume Fraction by Pyrolysis 435
18.12 Reversing Lever Made of Carbon/PEEK (Unidirectional and Short Fibers) 436
18.13 Glass/Resin Telegraph Pole 439
18.14 Unidirectional Layer of HR Carbon 443
18.15 Manipulator Arm for a Space Shuttle 444
Trang 18Contents ◾ xvii
19 Applications.Level.2 449
19.1 Sandwich Beam: Simplified Calculation of the Shear Coefficient 449
19.2 Procedure for a Laminate Calculation Program 451
19.3 Kevlar/Epoxy Laminates: Stiffness in Terms of the Direction of Load 455
19.4 Residual Thermal Stress Due to the Laminate Curing Process 459
19.5 Thermoelastic Behavior of a Glass/Polyester Tube 462
19.6 Creep of a Polymeric Tube Reinforced by Filament Wound under Thermal Stress 465
19.7 First-Ply Failure of a Laminate: Ultimate Strength 471
19.8 Optimum Laminate for Isotropic Plane Stress 475
19.9 Laminate Made of Identical Layers of Balanced Fabric 481
19.10 Carbon/Epoxy Wing Spar 484
19.11 Elastic Constants of a Carbon/Epoxy Unidirectional Layer, Based on Tensile Test 491
19.12 Sailboat Hull in Glass/Polyester 492
19.13 Balanced Fabric Ply: Determination of the In-Plane Shear Modulus 498
19.14 Quasi-Isotropic Laminate 499
19.15 Pure Torsion of Orthotropic Plate 502
19.16 Plate Made by Resin Transfer Molding 506
19.17 Thermoelastic Behavior of a Balanced Fabric Ply 512
20 Applications.Level.3 523
20.1 Cylindrical Bonding 523
20.2 Double-Lap Bonded Joint 528
20.3 Composite Beam with Two Layers 533
20.4 Buckling of a Sandwich Beam 537
20.5 Shear Due to Bending in a Sandwich Beam 540
20.6 Shear Due to Bending in a Composite Box Beam 544
20.7 Torsion Center of a Composite U-Beam 547
20.8 Shear Due to Bending in a Composite I-Beam 549
20.9 Polymeric Column Reinforced by Filament-Wound Fiberglass 553
20.10 Cylindrical Bending of a Thick Orthotropic Plate under Uniform Loading 563
20.11 Bending of a Sandwich Plate 564
20.12 Bending Vibration of a Sandwich Beam 567
Appendix.A:.Stresses.in.the.Plies.of.a.Carbon/Epoxy.Laminate.Loaded.in.Its.Plane 571
Appendix.B:.Buckling.of.Orthotropic.Structures 585
Bibliography 595
Index 599
Trang 19This page intentionally left blank
Trang 20Preface
The developments in the field of composite materials since the last quarter of a century have made this area popular due to the breadth and universality of applications
The annual global growth rate of composites is 5%–6%, and tonnage, which was 8 million tonnes in 2010, could rise to 10 million tonnes by 2015—a growth driven by advances in the transportation and wind industries The sector of composites is an area of business that is always evolving
The cost of composites is becoming increasingly competitive For a quarter of a century, the price of high-performance composites used in aerospace declined by more than half to compete with sophisticated metal alloys At the same time, the quality of semifinished products reached remarkable levels For example, the unidirectional prepreg tapes carbon/epoxy have their widths defined within 0.2 mm, and their fiber volume content controlled within only a few fractions of a percent, with obvious consequences for the evolution of the quality of parts
nificant increases in research and development on topics concerning natural fibers and biodegrad-able polymers
The legislation on recyclability obligation also affects the composite activities It leads to sig-The growth in the use of composites has been aided by the development of modern design and manufacturing methods for industrial components, which allow functional optimization based on multiple technical and economic criteria A good knowledge of what already exists helps develop and use reliable numerical simulations for in-service behavior as well as for implementation during the manufacturing
The development of simulation tools is an important component of industrial development,
in general, and in composite domains, in particular Without trying to replace testing, these tools allow full exploitation of the experimental results in a much more complete manner, creating a powerful synergy that saves time and cost
This third edition has been updated to take into account this rapidly changing field as well as the emergence and development of additional areas, such as those of bio- and nanocomposites The core of the book devoted to the methodical predesign of structural parts has been preserved As in previous editions, we have considered only a limited number of significant reinforcements and have highlighted the specific features needed for predimensioning This is, in fact, to limit the number
of performance tables accompanying the text Other reinforcements not detailed in this book can
be readily adapted; the reader will find everything needed to use a spreadsheet in order to get the desired results He or she may also download a dedicated free utility as indicated in the book The chapters on composite beams of any cross-sectional shape and the chapter on laminated thick plates still retain their original character, both with regard to the proposed method and to the results
Trang 21xx ◾ Preface
The book is structured into three levels of difficulty (even with regard to the applications) The technical level becomes increasingly complicated from one section to the next The first sec-tion corresponds to the undergraduate level, while the second and third sections correspond to the graduate level One can, however, work on each part independently
be defined It is addressed to teachers who want to structure a course on the subject, or simply talk about composites It is also addressed to students pursuing undergraduate and postgraduate degrees and can help PhD students do an apprenticeship before moving on to specialized research.This book does not focus on very detailed theoretical developments, which would not meet the requirements of the targeted audience In industry, there is little time for the consultation of books, and the academic nature of initial training is often far from the daily concerns of the design office I have therefore adapted this presentation by taking into account readers who are always
in a hurry and who use the tools available to them or ones that they remember The content of this book is nevertheless anchored on solid scientific basis and will allow potential users to derive maximum benefit from it
Trang 22acknowledgments
I express my sincere thanks and gratitude to.Dr Stephane Gay,.who wrote parts of the text and
reviewed and verified the appropriate use of technical terminology contained in this third edition, especially in the field of aeronautics I am also grateful to Pr Suong Van Hoa, who kindly took
on the important task of translating the first edition of this book that I had originally written
in French
Trang 23This page intentionally left blank
Trang 24author
Daniel Gay.is a former student of the Ecole Normale Superieure de Cachan and served as a professor at the University Paul Sabatier Toulouse III He led the Laboratory of Mechanical Engineering of Toulouse, now the Clément Ader Institute, from its inception for over 15 years
Dr Gay has taught composite materials and structures at the undergraduate, graduate, and postgraduate levels in many French schools and institutions (University of Toulouse III, IUT, INSA, ENSICA, Supaero (ISAE), ENSTA, etc.) He is the author of numerous articles, scientific publications, and industrial reports on the subject
Trang 25This page intentionally left blank
Trang 26PRinCiPLeS
oF ConStRUCtion
ent the following points, while remaining as clear as possible:
Second, this part of the book extends to the problems and solutions brought on when designing
a composite part, and particularly the concerns related to the resistance and deformation under loading, as well as the connections with the surrounding
Trang 27This page intentionally left blank
Trang 28of some conventional weapons For example,
◾ In the Mongolian bows, the compressed parts are made of horn, and the stretched parts are made of wood and cow tendons glued together
◾ Damask sword or Japanese sabers have their blades made of steel and soft iron: the steel part
tion* (see Figure 1.1), and then formed into a U shape into which the soft iron is placed The sword then has good resistance for flexure and impact
is stratified like a flaky pastry, with orientation of defects and impurities in the long direc-* In folding a sheet of steel over itself 15 times, the final sheet is made of 2 15 = , 32 768 layers.
Trang 294 ◾ Composite Materials: Design and Applications
This period marks the beginning of the distinction between the common composites used universally and the high-performance composites
1.2 Fibers and Matrices
The bonding between fibers and matrices is created during the manufacturing phase of the composite material This has fundamental influence on the mechanical properties of the com-posite material
1.2.1 Fibers
1.2.1.1 Definition
Fibers consist of several hundreds or thousands of filaments, each of them having a diameter of between 5 and 15 μm, allowing them to be processable on textile machines*; for example, in the
Stress concentration
Random defects Poor tensile resistance Good tensile resistanceOriented defects
Figure 1.1 effect of orientation of impurities.
Trang 30Composite Materials: Interest and Physical Properties ◾ 5
1.2.1.2 Principal Fiber Materials
◾ Improving the fiber–matrix adhesion
Other types of reinforcements are also used as fillers: full or empty microspheres, powders,* and nanoreinforcements.†
* See Section 3.5.3.
† See Section 3.9.
Continuous fiber
Textile filament
Roving
or strand
Glass staple fiber
Fibers for weaving
Filaments
Discontinuous fiber
Figure 1.2 different fiber forms.
Trang 316 ◾ Composite Materials: Design and Applications
1.2.1.3 Relative Importance of Different Fibers in Applications
◾ leum products) are oxidized at high temperatures (300°C) and then heated further to 1500°C
Carbon fiber: Filaments of polyacrylonitrile or pitch (obtained from residues of the petro-in a nitrogen atmosphere Only the black and bright filaments of hexagonal carbon chains remain, as shown in Figure 1.4 The high modulus of elasticity is obtained by stretching at high temperature
◾ Boron fiber: Tungsten filament (diameter 12 μm) is used to catalyze the reaction between boron chloride and hydrogen at 1200°C The boron fibers obtained have a diameter of about
100 μm (the growth speed is about 1 μm/s)
◾ Silicon carbide: The principle of fabrication is analogous to that of boron fiber—chemical vapor deposition (1200°C) of methyl trichlorosilane mixed with hydrogen
Trang 32Composite Materials: Interest and Physical Properties ◾ 7
1.2.2 Materials for Matrices
Trang 338 ◾ Composite Materials: Design and Applications
Trang 34Composite Materials: Interest and Physical Properties ◾ 9
◾ The subsequent weight reduction leads to fuel saving, increase in payload, or increase in range that improves performances
◾ The good fatigue resistance leads to enhanced life, which involves saving in the long-term cost of the product
◾ The good corrosion resistance means fewer requirements for inspection, which results in saving on maintenance cost
ventional solution, one can state that composites fit the demand of aircraft manufacturers
Trang 35Moreover, taking into account the cost of the composite solution as compared with the con-10 ◾ Composite Materials: Design and Applications
1.5 Some examples of Classical design
Replaced by Composite Solutions
Table 1.1 shows a few significant cases illustrating the improvement on price and performance that can be obtained after the replacement of a conventional solution with a composite solution
1.6 Main Physical Properties
ments, or matrices
Tables 1.2 through 1.5 take into account the properties of only individual components, reinforce-The characteristics of composite materials resulting from the combination of reinforcement and matrix depend on
table 1.1 Some Significant Cases
Support for helicopter
hoist
Welded steel: Mass = 16 kg;
Price = 1
Carbon/epoxy: Mass = 11 kg; Price = 1.2
Helicopter motor hub Mass = 1; Price = 1 Carbon/Kevlar/epoxy:
Mass = 0.8; Price = 0.4 X–Y table for fabrication
of integrated circuits
Cast aluminum: Rate of fabrication = 30 plates/h
Carbon/epoxy honeycomb sandwich: Rate of
fabrication = 55 plates/h Drum for drawing plotter Drawing speed = 15–30 cm/s Kevlar/epoxy, 40–80 cm/s Head of welding robot Aluminum: Mass = 6 kg Carbon/epoxy: Mass = 3 kg Projectile for loom Aluminum: Rate = 250 shots/min Carbon/epoxy: Rate =
350 shots/min Aircraft floor Mass = 1; Price = 1 Carbon/Kevlar/epoxy:
Mass = 0.8; Price = 1.7
Trang 36table 1.2 Properties of Commonly Used Metals and alloys and Silicon
Metals and Alloys ρ (kg/m Density, 3 )
Elastic Modulus,
E (MPa)
Shear Modulus,
G (MPa) Poisson Ratio, ν
Tensile Strength,
σrupture
(MPa) Elongation, A (%)
Coefficient
of Thermal Expansion
at 20°C,
Coefficient
of Thermal Conductivity
at 20°C,
λ (W/m °C)
Heat Capacity,
c (J/kg °C)
Temperature Limit for Use,
Trang 37d (μm) ρ (kg/m Density, 3 )
Modulus
of Elasticity,
E (MPa)
Shear Modulus,
G (MPa)
Poisson Ratio, ν
Tensile Strength
α (°C −1 )
Coefficient
of Thermal Conductivity,
λ (W/m °C)
Heat Capacity,
c (J/kg °C)
Temperature Limit for Use,
T max (°C)
Price ($/kg)
Trang 38E (MPa)
Shear Modulus,
G (MPa)
Poisson Ratio, ν
Tensile Strength,
α (°C −1 )
Coefficient
of Thermal Conductivity,
λ (W/m °C)
Heat Capacity,
c (J/kg
°C)
Temperature Limit for Use,
T max (°C)
Price ($/kg) Thermosets
Trang 39E (MPa)
Shear Modulus,
G (MPa) Poisson Ratio, ν
Compressive Strength,
α (°C −1 )
Coefficient
of Thermal Conductivity,
λ (W/m °C)
Heat Capacity,
c (J/kg
°C)
Temperature Limit for Use,
T max (°C)
Price ($/kg)
Trang 40Composite Materials: Interest and Physical Properties ◾ 15
ferent fiber fractions and different forms of reinforcement for the case of glass/resin composite,
These characteristics may be observed in Figure 1.5, which shows the tensile strength for dif-and Figure 1.6, which gives an interesting view on the specific.resistance of the major types of
structural composites as a function of temperature Here, the specific strength is defined as the tensile strength divided by the density: σrupture/σ
◾ Composite materials are not sensitive to the common chemicals used in engines: grease, oils, hydraulic liquids, paints and solvents, petroleum However, cleaners for paint attack the epoxy resins
* The cured epoxy resin can absorb water by diffusion up to 6% of its mass; the fiber-reinforced epoxy composite can absorb up to 2%.
Glass percentage in volume
Auto body
Panels
Diverse applications
Mechanical components
Mats/cut fibers Bidirectional fabric Unidirectional fabric
Figure 1.5 tensile strength of glass/resin composites.