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 composites, 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 formulations 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 information * 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 expanded to better illustrate the types of challenges encountered in modern engineering practice.
Preface xix
Acknowledgments xxi
Author xxiii
Section I Principles Of Construction
1 Composite Materials: Interest and Physical 3 (14)
Properties
1.1 What Is a Composite Material? 3 (1)
1.1.1 Broad Definition 3 (1)
1.1.2 Main Features 4 (1)
1.2 Fibers and Matrices 4 (3)
1.2.1 Fibers 4 (3)
1.2.1.1 Definition 4 (1)
1.2.1.2 Principal Fiber Materials 5 (1)
1.2.1.3 Relative Importance of 6 (1)
Different Fibers in Applications
1.2.2 Materials for Matrices 7 (1)
1.3 What Can Be Made Using Composite 7 (2)
Materials?
1.4 A Typical Example of Interest 9 (1)
1.5 Some Examples of Classical Design 10 (1)
Replaced by Composite Solutions
1.6 Main Physical Properties 10 (7)
2 Manufacturing Processes 17 (12)
2.1 Molding Processes 17 (5)
2.1.1 Contact Molding 17 (1)
2.1.2 Compression Molding 18 (1)
2.1.3 Vacuum Molding 18 (1)
2.1.4 Resin Injection Molding 19 (1)
2.1.5 Injection Molding with Prepreg 20 (1)
2.1.6 Foam Injection Molding 20 (1)
2.1.7 Molding of Hollow Axisymmetric 20 (2)
Components
2.2 Other Forming Processes 22 (4)
2.2.1 Sheet Forming 22 (1)
2.2.2 Profile Forming 23 (1)
2.2.3 Forming by Stamping 23 (1)
2.2.4 Preforming by Three-Dimensional 24 (1)
Assembly
2.2.4.1 Example: Carbon/Carbon 24 (1)
2.2.4.2 Example: Silicon/Silicon 24 (1)
2.2.5 Automated Tape Laying and Fiber 24 (2)
Placement
2.2.5.1 Necessity of Automation 24 (1)
2.2.5.2 Example 24 (1)
2.2.5.3 Example 25 (1)
2.2.5.4 Example: Robots and Software 25 (1)
for AFP-Automatic Fiber Placement
Coriolis Composites (FRA)
2.3 Practical Considerations on 26 (3)
Manufacturing Processes
2.3.1 Acronyms 26 (1)
2.3.2 Cost Comparison 27 (2)
3 Ply Properties 29 (40)
3.1 Isotropy and Anisotropy 29 (4)
3.1.1 Isotropic Materials 31 (1)
3.1.2 Anisotropic Material 32 (1)
3.2 Characteristics of the 33 (3)
Reinforcement-Matrix Mixture
3.2.1 Fiber Mass Fraction 34 (1)
3.2.2 Fiber Volume Fraction 34 (1)
3.2.3 Mass Density of a Ply 35 (1)
3.2.4 Ply Thickness 35 (1)
3.3 Unidirectional Ply 36 (5)
3.3.1 Elastic Modulus 36 (2)
3.3.2 Ultimate Strength of a Ply 38 (1)
3.3.3 Examples 39 (2)
3.3.4 Examples of High-Performance 41 (1)
Unidirectional Plies
3.4 Woven Ply 41 (4)
3.4.1 Forms of Woven Fabrics 41 (1)
3.4.2 Elastic Modulus of Fabric Layer 42 (1)
3.4.3 Examples of Balanced Fabric/Epoxy 43 (2)
3.5 Mats and Reinforced Matrices 45 (4)
3.5.1 Mats 45 (1)
3.5.2 Example: A Summary of Glass/Epoxy 45 (1)
Layers
3.5.3 Microspherical Fillers 45 (3)
3.5.4 Other Classical Reinforcements 48 (1)
3.6 Multidimensional Fabrics 49 (1)
3.6.1 Example: A Four-Dimensional 49 (1)
Architecture of Carbon Reinforcement
3.6.2 Example: Three-Dimensional 50 (1)
Carbon/Carbon Components
3.7 Metal Matrix Composites 50 (3)
3.7.1 Some Examples 50 (2)
3.7.2 Unidirectional Fibers/Aluminum 52 (1)
Matrix
3.8 Biocomposite Materials 53 (4)
3.8.1 Natural Plant Fibers 53 (1)
3.8.1.1 Natural Fibers 53 (1)
3.8.1.2 Pros 53 (1)
3.8.1.3 Cons 53 (1)
3.8.1.4 Examples 54 (1)
3.8.2 Natural Vegetable Fiber-Reinforced 54 (2)
Composites
3.8.2.1 Mechanical Properties 54 (1)
3.8.2.2 Biodegradable Matrices 54 (2)
3.8.3 Manufacturing Processes 56 (1)
3.8.3.1 With Thermosetting Resins 56 (1)
3.8.3.2 With Thermoplastic Resins 57 (1)
3.9 Nanocomposite Materials 57 (9)
3.9.1 Nanoreinforcement 57 (4)
3.9.1.1 Nanoreinforcement Shapes 57 (1)
3.9.1.2 Properties of Nanoreinforcements 58 (3)
3.9.2 Nanocomposite Material 61 (1)
3.9.3 Mechanical Applications 62 (2)
3.9.3.1 Improvement in Mechanical 62 (2)
Properties
3.9.3.2 Further Examples of 64 (1)
Nonmechanical Applications
3.9.4 Manufacturing of Nanocomposite 64 (2)
Materials
3.10 Tests 66 (3)
4 Sandwich Structures 69 (16)
4.1 What Is a Sandwich Structure? 69 (2)
4.1.1 Their Properties Are Surprising 69 (1)
4.1.2 Constituent Materials 70 (1)
4.2 Simplified Flexure 71 (3)
4.2.1 Stress 71 (1)
4.2.2 Displacements 72 (2)
4.2.2.1 Contributions of Bending Moment 72 (1)
M and of Shear Force T
4.2.2.2 Example: A Cantilever Sandwich 73 (1)
Structure
4.3 Some Special Features of Sandwich 74 (2)
Structures
4.3.1 Comparison of Mass for the Same 74 (1)
Flexural Rigidity <EI>
4.3.2 Deterioration by Buckling of 74 (2)
Sandwich Structures
4.3.2.1 Global Buckling 75 (1)
4.3.2.2 Local Buckling of the Skins 75 (1)
4.3.3 Other Types of Damage 76 (1)
4.4 Manufacturing and Design Problems 76 (4)
4.4.1 Example of Core Material: Honeycomb 76 (1)
4.4.2 Shaping Processes 77 (1)
4.4.2.1 Machining 77 (1)
4.4.2.2 Deformation 77 (1)
4.4.2.3 Some Other Considerations 77 (1)
4.4.3 Inserts and Attachment Fittings 78 (1)
4.4.4 Repair of Laminated Facings 79 (1)
4.5 Nondestructive Inspection 80 (5)
4.5.1 Main Nondestructive Inspection 80 (1)
Methods
4.5.2 Acoustic Emission Testing 81 (4)
5 Conception: Design and Drawing 85 (50)
5.1 Drawing a Composite Part 85 (3)
5.1.1 Specific Properties 85 (1)
5.1.2 Guide Values of Presizing 86 (2)
5.1.2.1 Material Characteristics 86 (2)
5.1.2.2 Design Factors 88 (1)
5.2 Laminate 88 (10)
5.2.1 Unidirectional Layers and Fabrics 88 (1)
5.2.1.1 Unidirectional Layer 88 (1)
5.2.1.2 Fabrics 89 (1)
5.2.2 Correct Ply Orientation 89 (1)
5.2.3 Laminate Drawing Code 90 (6)
5.2.3.1 Standard Orientations 90 (1)
5.2.3.2 Laminate Middle Plane 90 (3)
5.2.3.3 Description of the Stacking 93 (1)
Order
5.2.3.4 Midplane Symmetry 93 (1)
5.2.3.5 Specific Case of Balanced 94 (1)
Fabrics
5.2.3.6 Technical Minimum 95 (1)
5.2.4 Arrangement of Plies 96 (2)
5.2.4.1 Proportion and Number of Plies 96 (1)
5.2.4.2 Example of Pictorial 97 (1)
Representation
5.2.4.3 Case of Sandwich Structure 97 (1)
5.3 Failure of Laminates 98 (4)
5.3.1 Damages 98 (2)
5.3.1.1 Types of Failure 98 (1)
5.3.1.2 Note: Classical Maximum Stress 99 (1)
Criterion Shows Its Limits
5.3.2 Most Frequently Used Criterion: 100 (2)
Tsai-Hill Failure Criterion
5.3.2.1 Tsai-Hill Number 100 (1)
5.3.2.2 Notes 101 (1)
5.3.2.3 How to Determine the Stress 101 (1)
Components σl, σt, and
τlt in Each Ply
5.4 Presizing of the Laminate 102 (33)
5.4.1 Modulus of Elasticity-Deformation 102 (1)
of a Laminate
5.4.1.1 Varying Proportions of Plies 102 (1)
5.4.1.2 Example of Using Tables 103 (1)
5.4.2 Case of Simple Loading 103 (6)
5.4.3 Complex Loading Case: Approximative 109 (10)
Proportions According to Orientations
5.4.3.1 When the Normal and Tangential 109 (5)
(Shear) Loads Are Applied Simultaneously
5.4.3.2 Example 114 (3)
5.4.3.3 Note 117 (2)
5.4.4 Complex Loading Case: Optimum 119 (8)
Composition of a Laminate
5.4.4.1 Optimum Laminate 119 (3)
5.4.4.2 Example 122 (3)
5.4.4.3 Example 125 (1)
5.4.4.4 Notes 126 (1)
5.4.5 Notes for Practical Use Concerning 127 (8)
Laminates
5.4.5.1 Specific Aspects for the Design 127 (1)
of Laminates
5.4.5.2 Delaminations 128 (1)
5.4.5.3 Why Is Fatigue Resistance So 129 (4)
Good?
5.4.5.4 Laminated Tubes 133 (2)
6 Conception: Fastening and Joining 135 (20)
6.1 Riveting and Bolting 135 (8)
6.1.1 Local Loss of Strength 135 (3)
6.1.1.1 Knock-Down Factor 135 (1)
6.1.1.2 Causes of Hole Degradation 136 (2)
6.1.2 Main Failure Modes in Bolted Joints 138 (1)
of Composite Materials
6.1.3 Sizing of the Joint 138 (2)
6.1.3.1 Recommended Values 138 (2)
6.1.3.2 Evaluation of Magnified Stress 140 (1)
Values
6.1.4 Riveting 140 (1)
6.1.5 Bolting 141 (2)
6.1.5.1 Example of Bolted Joint 141 (2)
6.1.5.2 Tightening of the Bolt 143 (1)
6.2 Bonding 143 (9)
6.2.1 Adhesives Used 143 (2)
6.2.2 Geometry of the Bonded Joints 145 (1)
6.2.3 Sizing of the Bonding Surface Area 146 (4)
6.2.3.1 Strength of Adhesive 146 (1)
6.2.3.2 Design 147 (1)
6.2.3.3 Stress in Bonded Areas 148 (2)
6.2.3.4 Example of Single-Lap Adhesive 150 (1)
Joint
6.2.4 Case of Bonded Joint with 150 (1)
Cylindrical Geometry
6.2.4.1 Bonded Circular Flange 150 (1)
6.2.4.2 Tubes Fitted and Bonded into 150 (1)
One Another
6.2.5 Examples of Bonding 150 (2)
6.2.5.1 Laminates 150 (2)
6.3 Inserts 152 (3)
6.3.1 Case of Sandwich Parts 152 (2)
6.3.2 Case of Parts under Uniaxial Loads 154 (1)
7 Composite Materials and Aerospace 155 (48)
Construction
7.1 Aircraft 155 (24)
7.1.1 Composite Components in Aircraft 155 (1)
7.1.2 Allocation of Composites Depending 156 (2)
on Their Nature
7.1.2.1 Glass/Epoxy, Kevlar/Epoxy 156 (1)
7.1.2.2 Carbon/Epoxy 157 (1)
7.1.2.3 Boron/Epoxy 157 (1)
7.1.2.4 Honeycombs 157 (1)
7.1.3 Few Comments 158 (1)
7.1.4 Specific Aspects of Structural 158 (1)
Strength
7.1.5 Large Transport Aircraft 159 (6)
7.1.5.1 Example 159 (1)
7.1.5.2 How to Determine the Benefits 159 (2)
7.1.5.3 Example: Civil Transport 161 (1)
Aircraft A380-800, Airbus (EUR)
7.1.5.4 Example: Civil Transport 161 (2)
Aircraft B 787-800, Boeing (USA)
7.1.5.5 Example: Civil Transport 163 (2)
Aircraft A350-900, Airbus (EUR)
7.1.6 Regional Airciaft and Business Jets 165 (3)
7.1.6.1 Example: Regional Aircraft ATR 165 (1)
72-600, FADS (EUR), Alenia (ITA)
7.1.6.2 Example: Business Aircraft 165 (1)
Falcon, Dassault Aviation (FRA)
7.1.6.3 Example: Cargo Aircraft WK2 and 166 (2)
Suborbital Space Plane SST2, Scaled
Composites (USA)-Virgin Group (UK)
7.1.7 Light Aircraft 168 (2)
7.1.7.1 Trends 168 (1)
7.1.7.2 Aircraft with Tractor Propeller 168 (1)
7.1.7.3 Aircraft with Pusher Propeller 169 (1)
7.1.7.4 Modern Glider Planes 170 (1)
7.1.8 Fighter Aircraft 170 (1)
7.1.9 Architecture and Manufacture of 171 (7)
Composite Aircraft Parts
7.1.9.1 Sandwich Design 171 (2)
7.1.9.2 Rib-Stiffened Panels 173 (5)
7.1.10 Braking Systems 178 (1)
7.2 Helicopters 179 (7)
7.2.1 Situation 179 (1)
7.2.2 Composite Areas 180 (1)
7.2.2.1 Example: Helicopter EC 145 T2, 180 (1)
Airbus-Helicopter (EUR)
7.2.2.2 Example: Helicopter X4, 180 (1)
Thales-Safran (FRA), Airbus-Helicopter
(EUR)
7.2.3Blades 181 (2)
7.2.3.1 Design of a Main Rotor Blade 181 (1)
7.2.3.2 Advantages 181 (1)
7.2.3.3 Consequences 181 (2)
7.2.4 Rotor Hub 183 (1)
7.2.4.1 Example: Rotor Hub Starflex, 183 (1)
Eurocopter (FRA-GER)
7.2.4.2 Example: Rotor Hub Spheriflex, 184 (1)
Eurocopter (FRA-GER)
7.2.5 Other Working Composite Parts 184 (2)
7.3 Airplane Propellers 186 (4)
7.3.1 Propellers for Conventional 186 (2)
Aerodynamics
7.3.1.1 Example: Propeller Blade, 186 (1)
Hamilton Sundstrand (USA)-Ratier Figeac
(FRA)
7.3.1.2 Example: Airplane with Tilt 187 (1)
Rotors, V-22 Osprey Bell Boeing (USA)
and Dowty Propellers (UK)
7.3.2 High-Speed Propellers 188 (2)
7.4 Aircraft Reaction Engine 190 (4)
7.4.1 Employed Materials 190 (1)
7.4.2 Refractory Composites 191 (3)
7.4.2.1 Specific Features 191 (1)
7.4.2.2 Fibers 191 (1)
7.4.2.3 Matrices 192 (1)
7.4.2.4 Applications 192 (1)
7.4.2.5 Example: Jet Engine Leapｮ, CFM 193 (1)
International, General Electric
(USA)-SNECMA (FRA)
7.5 Space Applications 194 (9)
7.5.1 Satellites 194 (1)
7.5.2 Propellant Tanks and Pressure 195 (1)
Vessels
7.5.3 Nozzles 196 (2)
7.5.4 Other Composite Components for 198 (5)
Space Application
7.5.4.1 For Engines 198 (1)
7.5.4.2 For Thermal Protection 198 (2)
7.5.4.3 For Energy Storage 200 (3)
8 Composite Materials for Various Applications 203 (30)
8.1 Comparative Importance of Composites in 203 (3)
Applications
8.1.1 Relative Importance in terms of 204 (1)
Mass and Market Value
8.1.2 Mass of Composites Implemented 205 (1)
According to the Geographical Area
8.1.3 Average Prices 205 (1)
8.2 Composite Materials and Automotive 206 (11)
Industry
8.2.1 Introduction 206 (2)
8.2.1.1 Example: Golf Model, Volkswagen 206 (1)
(GER)
8.2.1.2 Relative Weight Importance of 207 (1)
Materials
8.2.2 Composite Parts 208 (6)
8.2.2.1 Brief Reminder 208 (1)
8.2.2.2 Current Functional Design 208 (2)
8.2.2.3 Notable Composite Components 210 (2)
8.2.2.4 Notes 212 (1)
8.2.2.5 Use of Natural Fibers 213 (1)
8.2.3 Research and Development 214 (2)
8.2.3.1 Structure 215 (1)
8.2.3.2 Mechanical Parts 215 (1)
8.2.4 Motor Racing 216 (1)
8.3 Wind Turbines 217 (2)
8.3.1 Components 217 (1)
8.3.2 Manufacturing Processes 218 (1)
8.4 Composites and Shipbuilding 219 (4)
8.4.1 Competition 219 (4)
8.4.1.1 Example: Ocean-Going 220 (2)
Maxi-Trimaran
8.4.1.2 Example: Single Scull 222 (1)
8.4.1.3 Example: Surfboard 223 (1)
8.4.2 Vessels 223 (1)
8.5 Sports and Leisure 223 (3)
8.5.1 Skis 223 (2)
8.5.1.1 Equipment of a Skier 223 (1)
8.5.1.2 Main Components of a Ski 224 (1)
8.5.2 Bicycles 225 (1)
8.5.2.1 Machine 226 (1)
8.5.2.2 Other Specific Equipments 226 (1)
8.5.3 Tennis Rackets 226 (1)
8.6 Diverse Applications 226 (7)
8.6.1 Pressure Gas-Bottle 226 (1)
8.6.2 Bogie Frame 227 (1)
8.6.3 Tubes for Offshore Installations 227 (1)
8.6.4 Biomechanical Applications 228 (1)
8.6.5 Cable Car 229 (4)
Section II Mechanical Behavior Of Laminated
Materials
9 Anisotropic Elastic Medium 233 (6)
9.1 Some Reminders 233 (3)
9.1.1 Continuum Mechanics 233 (1)
9.1.2 Number of Distinct φijkl Terms 234 (2)
9.2 Orthotropic Material 236 (1)
9.3 Transversely Isotropic Material 236 (3)
10 Elastic Constants of Unidirectional 239 (10)
Composites
10.1 Longitudinal Modulus El 239 (2)
10.2 Poisson Coefficient 241 (1)
10.3 Transverse Modulus Et 242 (2)
10.4 Shear Modulus Glt 244 (1)
10.5 Thermoelastic Properties 245 (4)
10.5.1 Isotropic Material: Recall 245 (1)
10.5.2 Case of Unidirectional Composite 246 (2)
10.5.2.1 Coefficient of Thermal 246 (1)
Expansion along the Direction l
10.5.2.2 Coefficient of Thermal 247 (1)
Expansion along the Transverse
Direction t
10.5.3 Thermomechanical Behavior of a 248 (1)
Unidirectional Layer
11 Elastic Constants of a Ply in Any Direction 249 (14)
11.1 Flexibility Coefficients 249 (6)
11.2 Stiffness Coefficients 255 (2)
11.3 Case of Thermomechanical Loading 257 (6)
11.3.1 Flexibility Coefficients 257 (2)
11.3.2 Stiffness Coefficients 259 (4)
12 Mechanical Behavior of Thin Laminated 263 (26)
Plates
12.1 Laminate with Midplane Symmetry 263 (20)
12.1.1 Membrane Behavior 263 (4)
12.1.1.1 Loadings 263 (1)
12.1.1.2 Displacement Field 264 (3)
12.1.2 Apparent Elastic Moduli of the 267 (1)
Laminate
12.1.3 Consequence: Practical 267 (5)
Determination of a Laminate Subject to
Membrane Loading
12.1.3.1 Givens of the Problem 267 (1)
12.1.3.2 Principle, of Calculation 268 (1)
12.1.3.3 Calculation Procedure 269 (3)
12.1.4 Flexure Behavior 272 (6)
12.1.4.1 Displacement Field 272 (1)
12.1.4.2 Loadings 273 (2)
12.1.4.3 Notes 275 (3)
12.1.5 Consequence: Practical 278 (1)
Determination of a Laminate Subject to
Flexure
12.1.6 Simplified Calculation for Bending 278 (2)
12.1.6.1 Apparent Failure Strength in 278 (1)
Bending
12.1.6.2 Apparent Flexure Modulus 279 (1)
12.1.7 Thermomechanical Loading Case 280 (3)
12.1.7.1 Membrane Behavior 280 (3)
12.1.7.2 Behavior under Bending 283 (1)
12.2 Laminate without Midplane Symmetry 283 (6)
12.2.1 Coupled Membrane-Flexure Behavior 283 (2)
12.2.2 Case of Thermomechanical Loading 285 (4)
Section III Justifications, Composite Beams,
And Thick Laminated Plates
13 Elastic Coefficients 289 (14)
13.1 Elastic Coefficients for an 289 (3)
Orthotropic Material
13.1.1 Reminders 289 (1)
13.1.2 Elastic Behavior Equation in 290 (2)
Orthotropic Axes
13.2 Elastic Coefficients for a Transverse 292 (10)
Isotropic Material
13.2.1 Elastic Behavior Equation 292 (3)
13.2.2 Rotation about an Orthotropic 295 (8)
Transverse Axis
13.2.2.1 Problem 295 (5)
13.2.2.2 Technical Form 300 (2)
13.3 Case of a Ply 302 (1)
14 Damage in Composite Parts: Failure Criteria 303 (24)
14.1 Damage in Composite Parts 303 (7)
14.1.1 Industrial Emphasis of the Problem 303 (1)
14.1.1.1 Causes of Damage 303 (1)
14.1.1.2 Diversity of Composite Parts 304 (1)
14.1.2 Influence of Manufacturing Process 304 (1)
14.1.2.1 Example: Injected Part with 305 (1)
Short Fibers
14.1.2.2 Example: Parts with Pronounced 305 (1)
Curvatures
14.1.3 Typical Area and Singularities in 305 (1)
a Same Part
14.1.4 Degradation Process within the 306 (4)
Typical Area
14.1.4.1 Example: Composite Short Fiber 306 (1)
Plate
14.1.4.2 Example: Laminate Consisting 307 (3)
of Unidirectional Plies
14.2 Form of a Failure Criterion 310 (6)
14.2.1 Features of a Failure Criterion 310 (1)
14.2.1.1 Failure Criterion Is a Design 310 (1)
Tool
14.2.1.2 Many Criteria 310 (1)
14.2.2 General Form of a Failure Criterion 310 (2)
14.2.2.1 Development of a Criterion 310 (1)
14.2.2.2 Case of an Orthotropic Material 311 (1)
14.2.3 Linear Failure Criterion 312 (2)
14.2.3.1 Example: Plane State of Stress 312 (1)
in an Orthotropic Material
14.2.3.2 Example: Maximum Stress 313 (1)
Failure Criterion
14.2.3.3 Note: Maximum Eligible Strain 313 (1)
Criterion
14.2.4 Quadratic Failure Criterion 314 (2)
14.2.4.1 General Form 314 (1)
14.2.4.2 Specific Case of Plane Stress 314 (1)
14.2.4.3 Note: Simplified Form for the 315 (1)
Quadratic Criterion
14.3 Tsai-Hill Failure Criterion 316 (11)
14.3.1 Isotropic Material: The von Mises 316 (4)
Criterion
14.3.1.1 Material Is Elastic and 316 (2)
Isotropic
14.3.1.2 Notes 318 (2)
14.3.2 Orthotropic Material: Tsai-Hill 320 (4)
Criterion
14.3.2.1 Notes 320 (1)
14.3.2.2 Case of a Transversely 321 (2)
Isotropic Material
14.3.2.3 Case of Unidirectional Ply 323 (1)
under In-Plane Loading
14.3.3 Evolution of Strength Properties 324 (4)
of a Unidirectional Ply Depending on the
Direction of Solicitation
14.3.3.1 Tensile and Compressive 324 (1)
Strength
14.3.3.2 Shear Strength 325 (2)
15 Bending of Composite Beams of Any Section 327 (26)
Shape
15.1 Bending of Beams with Isotropic Phases 328 (18)
and Plane of Symmetry
15.1.1 Degrees of Freedom 329 (3)
15.1.1.1 Equivalent Stiffnesses 329 (1)
15.1.1.2 Longitudinal Displacement 329 (1)
15.1.1.3 Rotation of the Section 329 (1)
15.1.1.4 Elastic Center 330 (1)
15.1.1.5 Transverse Displacement along 330 (1)
y Direction
15.1.1.6 Transverse Displacement along 331 (1)
z Direction
15.1.2 Perfect Bonding between the Phases 332 (1)
15.1.2.1 Displacements 332 (1)
15.1.2.2 Strains 332 (1)
15.1.2.3 Stress 333 (1)
15.1.3 Equilibrium Relationships 333 (3)
15.1.3.1 Longitudinal Equilibrium 333 (1)
15.1.3.2 Transverse Equilibrium 334 (1)
15.1.3.3 Moment Equilibrium 335 (1)
15.1.4 Constitutive Equations 336 (1)
15.1.5 Technical Formulation 337 (5)
15.1.5.1 Assumptions 337 (1)
15.1.5.2 Expression of Normal Stress 337 (1)
15.1.5.3 Expression of Shear Stress 338 (2)
15.1.5.4 Shear Coefficient for the 340 (2)
Section
15.1.6 Energy Interpretation 342 (2)
15.1.6.1 Energy Due to Normal Stress 342 (1)
σxx
15.1.6.2 Energy Due to Shear Stress 343 (1)
->τ
15.1.7 Extension to the Dynamic Case 344 (2)
15.2 Case of Beams of Any Cross Section 346 (7)
(Asymmetric)
15.2.1 Technical Formulation 347 (4)
15.2.2 Notes 351 (2)
16 Torsion of Composite Beams of Any Section 353 (10)
Shape
16.1 Uniform Torsion 353 (5)
16.1.1 Torsional Degree of Freedom 354 (1)
16.1.2 Constitutive Equation 354 (1)
16.1.3 Determination of Φ(y, z) 355 (2)
16.1.3.1 Local Equilibrium 355 (1)
16.1.3.2 External Boundary Condition 356 (1)
16.1.3.3 Internal Boundary Conditions 356 (1)
16.1.3.4 Uniqueness of Function Φ 356 (1)
16.1.4 Energy Interpretation 357 (1)
16.2 Location of the Torsion Center 358 (5)
16.2.1 Coordinates in Principal Axes 358 (1)
16.2.2 Summary of Results 359 (2)
16.2.3 Flexion-Torsion Coupling 361 (2)
17 Bending of Thick Composite Plates 363 (30)
17.1 Preliminary Remarks 363 (4)
17.1.1 Transverse Normal Stress σz 363 (1)
17.1.2 Transverse Shear Stress τxz 364 (1)
and τyz
17.1.3 Assumptions 365 (2)
17.2 Displacement Field 367 (2)
17.3 Strains 369 (1)
17.4 Constitutive Equations 369 (4)
17.4.1 Membrane Behavior 369 (1)
17.4.2 Bending Behavior 370 (2)
17.4.3 Transverse Shear Behavior 372 (1)
17.4.3.1 Transverse Shear Resultant Qx 372 (1)
17.4.3.2 Transverse Shear Resultant Qy 373 (1)
17.5 Equilibrium Relationships 373 (1)
17.5.1 Transverse Equilibrium 373 (1)
17.5.2 Equilibrium in Bending 374 (1)
17.6 Technical Formulation for Bending 374 (11)
17.6.1 Stress Due to Bending 375 (1)
17.6.1.1 Plane Stress Values 375 (1)
17.6.1.2 Transverse Shear Stress Values 376 (1)
17.6.2 Characterization of Warping 376 (1)
Increments in Bending ηx and ηy
17.6.3 Particular Cases 377 (3)
17.6.3.1 Orthotropic Homogeneous Plate 377 (1)
17.6.3.2 Cylindrical Bending about x- 378 (1)
or y-Axis
17.6.3.3 Multilayered Plate 379 (1)
17.6.3.4 Consequences 380 (1)
17.6.4 Warping Functions 380 (2)
17.6.4.1 Boundary Conditions 380 (1)
17.6.4.2 Interfacial Continuity 381 (1)
17.6.4.3 Formulation of Warping 381 (1)
Functions
17.6.5 Consequences 382 (2)
17.6.5.1 Expression of Transverse Shear 382 (1)
Stress
17.6.5.2 Transverse Shear Coefficients 382 (2)
17.6.6 Energy Interpretation 384 (1)
17.7 Examples 385 (8)
17.7.1 Orthotropic Homogeneous Plate 385 (2)
17.7.2 Sandwich Plate 387 (3)
17.7.2.1 Case of Two Orthotropic 387 (1)
Materials
17.7.2.2 Warping Functions 388 (1)
17.7.2.3 Transverse Shear Stress 389 (1)
17.7.2.4 Transverse Shear Coefficients 389 (1)
17.7.3 Conclusion 390
Section IV Applications
18 Applications Level 1 393 (56)
18.1 Simply Supported Sandwich Beam 393 (3)
18.2 Poisson Coefficient of a 396 (1)
Unidirectional Layer
18.3 Helicopter Blade 397 (5)
18.4 Drive Shaft for Trucks 402 (6)
18.5 Flywheel in Carbon/Epoxy 408 (2)
18.6 Wing Tip Made of Carbon/Epoxy 410 (13)
18.7 Carbon Fiber Coated with Nickel 423 (2)
18.8 Tube Made of Glass/Epoxy under Pressure 425 (3)
18.9 Filament-Wound Pressure Vessel: 428 (3)
Winding Angle
18.10 Filament-Wound Pressure Vessel: 431 (4)
Consideration of Openings in the Bottom
Heads
18.11 Determination of Fiber Volume 435 (1)
Fraction by Pyrolysis
18.12 Reversing Lever Made of Carbon/PEEK 436 (3)
(Unidirectional and Short Fibers)
18.13 Glass/Resin Telegraph Pole 439 (4)
18.14 Unidirectional Layer of HR Carbon 443 (1)
18.15 Manipulator Arm for a Space Shuttle 444 (5)
19 Applications Level 2 449 (74)
19.1 Sandwich Beam: Simplified Calculation 449 (2)
of the Shear Coefficient
19.2 Procedure for a Laminate Calculation 451 (4)
Program
19.3 Kevlar/Epoxy Laminates: Stiffness in 455 (4)
Terms of the Direction of Load
19.4 Residual Thermal Stress Due to the 459 (3)
Laminate Curing Process
19.5 Thermoelastic Behavior of a 462 (3)
Glass/Polyester Tube
19.6 Creep of a Polymeric Tube Reinforced 465 (6)
by Filament Wound under Thermal Stress
19.7 First-Ply Failure of a Laminate: 471 (4)
Ultimate Strength
19.8 Optimum Laminate for Isotropic Plane 475 (6)
Stress
19.9 Laminate Made of Identical Layers of 481 (3)
Balanced Fabric
19.10 Carbon/Epoxy Wing Spar 484 (7)
19.11 Elastic Constants of a Carbon/Epoxy 491 (1)
Unidirectional Layer, Based on Tensile Test
19.12 Sailboat Hull in Glass/Polyester 492 (6)
19.13 Balanced Fabric Ply: Determination of 498 (1)
the In-Plane Shear Modulus
19.14 Quasi-Isotropic Laminate 499 (3)
19.15 Pure Torsion of Orthotropic Plate 502 (4)
19.16 Plate Made by Resin Transfer Molding 506 (6)
19.17 Thermoelastic Behavior of a Balanced 512 (11)
Fabric Ply
20 Applications Level 3 523 (48)
20.1 Cylindrical Bonding 523 (5)
20.2 Double-Lap Bonded Joint 528 (5)
20.3 Composite Beam with Two Layers 533 (4)
20.4 Buckling of a Sandwich Beam 537 (3)
20.5 Shear Due to Bending in a Sandwich Beam 540 (4)
20.6 Shear Due to Bending in a Composite 544 (3)
Box Beam
20.7 Torsion Center of a Composite U-Beam 547 (2)
20.8 Shear Due to Bending in a Composite 549 (4)
I-Beam
20.9 Polymeric Column Reinforced by 553 (10)
Filament-Wound Fiberglass
20.10 Cylindrical Bending of a Thick 563 (1)
Orthotropic Plate under Uniform Loading
20.11 Bending of a Sandwich Plate 564 (3)
20.12 Bending Vibration of a Sandwich Beam 567 (4)
Appendix A: Stresses in the Plies of a 571 (14)
Carbon/Epoxy-Laminate Loaded in Its Plane
Appendix B: Buckling of Orthotropic Structures 585 (10)
Bibliography 595 (4)
Index 599
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