Mechanics of Composite Materials, Second Edition

PREFACE TO THE SECOND EDITION xiii(2) PREFACE TO THE FIRST EDITION xv 1 INTRODUCTION TO COMPOSITE MATERIALS 1(54) 1.1 INTRODUCTION 1(1) 1.2 THE WHAT -- WHAT IS A COMPOSITE MATERIAL? 2(24) 1.2.1 Classification and Characteristics of Composite Materials 2(1) 1.2.1.1 Fibrous Composite Materials 3(3) 1.2.1.2 Laminated Composite Materials 6(2) 1.2.1.3 Particulate Composite Materials 8(2) 1.2.1.4 Combinations of Composite Materials 10(1) 1.2.2 Mechanical Behavior of Composite Materials 11(4) 1.2.3 Basic Terminology of Laminated Fiber-Reinforced Composite Materials 15(1) 1.2.3.1 Laminae 15(2) 1.2.3.2 Laminates 17(1) 1.2.4 Manufacture of Laminated Fiber-Reinforced Composite Materials 18(1) 1.2.4.1 Initial Form of Constituent Materials 18(1) 1.2.4.2 Layup 19(4) 1.2.4.3 Curing 23(3) 1.3 THE WHY -- CURRENT AND POTENTIAL ADVANTAGES OF FIBER-REINFORCED COMPOSITE MATERIALS 26(11) 1.3.1 Strength and Stiffness Advantages 27(4) 1.3.2 Cost Advantages 31(5) 1.3.3 Weight Advantages 36(1) 1.4 THE HOW -- APPLICATIONS OF COMPOSITE MATERIALS 37(15) 1.4.1 Introduction 37(1) 1.4.2 Military Aircraft 38(1) 1.4.2.1 General Dynamics F-111 Wing-Pivot Fitting 38(2) 1.4.2.2 Vought A-7 Speedbrake 40(2) 1.4.2.3 Vought S-3A Spoiler 42(1) 1.4.2.4 Boeing F-18 43(1) 1.4.2.5 Boeing AV-8B Harrier 44(1) 1.4.2.6 Grumman X-29A 45(1) 1.4.2.7 Northrop Grumman B-2 45(1) 1.4.2.8 Lockheed Martin F-22 46(1) 1.4.3 Civil Aircraft 47(1) 1.4.3.1 Lockheed L-1011 Vertical Fin 47(1) 1.4.3.2 Rutan Voyager 48(1) 1.4.3.3 Boeing 777 49(1) 1.4.3.4 High-Speed Civil Transport 49(1) 1.4.4 Space Applications 50(1) 1.4.5 Automotive Applications 50(2) 1.4.6 Commercial Applications 52(1) 1.5 SUMMARY 52(1) Problem Set 1 53(1) REFERENCES 53(2) 2 MACROMECHANICAL BEHAVIOR OF A LAMINA 55(66) 2.1 INTRODUCTION 55(1) 2.2 STRESS-STRAIN RELATIONS FOR ANISOTROPIC MATERIALS 56(7) 2.3 STIFFNESSES, COMPLIANCES, AND ENGINEERING CONSTANTS FOR ORTHOTROPIC MATERIALS 63(4) 2.4 RESTRICTIONS ON ENGINEERING CONSTANTS 67(3) 2.4.1 Isotropic Materials 67(1) 2.4.2 Orthotropic Materials 68(2) Problem Set 2.4 70(1) 2.5 STRESS-STRAIN RELATIONS FOR PLANE STRESS IN AN ORTHOTROPIC MATERIAL 70(4) 2.6 STRESS-STRAIN RELATIONS FOR A LAMINA OF ARBITRARY ORIENTATION 74(11) Problem Set 2.6 84(1) 2.7 INVARIANT PROPERTIES OF AN ORTHOTROPIC LAMINA 85(3) Problem Set 2.7 87(1) 2.8 STRENGTHS OF AN ORTHOTROPIC LAMINA 88(14) 2.8.1 Strength Concepts 88(3) 2.8.2 Experimental Determination of Strength and Stiffness 91(9) 2.8.3 Summary of Mechanical Properties 100(2) Problem Set 2.8 102(1) 2.9 BIAXIAL STRENGTH CRITERIA FOR AN ORTHOTROPIC LAMINA 102(16) 2.9.1 Maximum Stress Failure Criterion 106(1) 2.9.2 Maximum Strain Failure Criterion 107(2) 2.9.3 Tsai-Hill Failure Criterion 109(3) 2.9.4 Hoffman Failure Criterion 112(2) 2.9.5 Tsai-Wu Tensor Failure Criterion 114(4) 2.9.6 Summary of Failure Criteria 118(1) Problem Set 2.9 118(1) 2.10 SUMMARY 118(1) REFERENCES 119(2) 3 MICROMECHANICAL BEHAVIOR OF A LAMINA 121(66) 3.1 INTRODUCTION 121(5) 3.2 MECHANICS OF MATERIALS APPROACH TO STIFFNESS 126(11) 3.2.1 Determination of E(1) 127(2) 3.2.2 Determination of E(2) 129(3) 3.2.3 Determination of v(12) 132(1) 3.2.4 Determination of G(12) 133(2) 3.2.5 Summary Remarks 135(1) Problem Set 3.2 135(2) 3.3 ELASTICITY APPROACH TO STIFFNESS 137(21) 3.3.1 Introduction 137(1) 3.3.2 Bounding Techniques of Elasticity 137(8) 3.3.3 Exact Solutions 145(2) 3.3.4 Elasticity Solutions with Contiguity 147(4) 3.3.5 The Halpin-Tsai Equations 151(6) 3.3.6 Summary Remarks 157(1) Problem Set 3.3 158(1) 3.4 COMPARISON OF APPROACHES TO STIFFNESS 158(5) 3.4.1 Particulate Composite Materials 158(2) 3.4.2 Fiber-Reinforced Composite Materials 160(3) 3.4.3 Summary Remarks 163(1) 3.5 MECHANICS OF MATERIALS APPROACH TO STRENGTH 163(21) 3.5.1 Introduction 163(1) 3.5.2 Tensile Strength in the Fiber Direction 164(7) 3.5.3 Compressive Strength in the Fiber Direction 171(13) Problem Set 3.5 184(1) 3.6 SUMMARY REMARKS ON MICROMECHANICS 184(1) REFERENCES 185(2) 4 MACROMECHANICAL BEHAVIOR OF A LAMINATE 187(90) 4.1 INTRODUCTION 187(3) Problem Set 4.1 190(1) 4.2 CLASSICAL LAMINATION THEORY 190(13) 4.2.1 Lamina Stress-Strain Behavior 191(1) 4.2.2 Stress and Strain Variation in a Laminate 191(4) 4.2.3 Resultant Laminate Forces and Moments 195(4) 4.2.4 Summary 199(3) Problem Set 4.2 202(1) 4.3 SPECIAL CASES OF LAMINATE STIFFNESSES 203(19) 4.3.1 Single-Layered Configurations 203(3) 4.3.2 Symmetric Laminates 206(8) 4.3.3 Antisymmetric Laminates 214(4) 4.3.4 Unsymmetric Laminates 218(1) 4.3.5 Common Laminate Definitions 219(2) 4.3.6 Summary Remarks 221(1) Problem Set 4.3 222(1) 4.4 THEORETICAL VERSUS MEASURED LAMINATE STIFFNESSES 222(15) 4.4.1 Inversion of Stiffness Equations 222(2) 4.4.2 Special Cross-Ply Laminate Stiffnesses 224(5) 4.4.3 Theoretical and Measured Cross-Ply Laminate Stiffnesses 229(3) 4.4.4 Special Angle-Ply Laminate Stiffnesses 232(3) 4.4.5 Theoretical and Measured Angle-Ply Laminate Stiffnesses 235(2) 4.4.6 Summary Remarks 237(1) Problem Set 4.4 237(1) 4.5 STRENGTH OF LAMINATES 237(23) 4.5.1 Introduction 237(3) 4.5.2 Laminate Strength-Analysis Procedure 240(2) 4.5.3 Thermal and Mechanical Stress Analysis 242(3) 4.5.4 Hygroscopic Stress Analysis 245(1) 4.5.5 Strength of Cross-Ply Laminates 246(9) 4.5.6 Strength of Angle-Ply Laminates 255(3) 4.5.7 Summary Remarks 258(2) Problem Set 4.5 260(1) 4.6 INTERLAMINAR STRESSES 260(15) 4.6.1 Classical Lamination Theory 262(2) 4.6.2 Elasticity Formulation 264(3) 4.6.3 Elasticity Solution Results 267(2) 4.6.4 Experimental Confirmation of Interlaminar Stresses 269(2) 4.6.5 Interlaminar Stresses in Cross-Ply Laminates 271(1) 4.6.6 Implications of Interlaminar Stresses 272(2) 4.6.7 Free-Edge Delamination-Suppression Concepts 274(1) Problem Set 4.6 275(1) REFERENCES 275(2) 5 BENDING, BUCKLING, AND VIBRATION OF LAMINATED PLATES 277(54) 5.1 INTRODUCTION 277(2) 5.2 GOVERNING EQUATIONS FOR BENDING, BUCKLING, AND VIBRATION OF LAMINATED PLATES 279(10) 5.2.1 Basic Restrictions, Assumptions, and Consequences 279(3) 5.2.2 Equilibrium Equations for Laminated Plates 282(3) 5.2.3 Buckling Equations for Laminated Plates 285(3) 5.2.4 Vibration Equations for Laminated Plates 288(1) 5.2.5 Solution Techniques 288(1) 5.3 DEFLECTION OF SIMPLY SUPPORTED LAMINATED PLATES UNDER DISTRIBUTED TRANSVERSE LOAD 289(12) 5.3.1 Specially Orthotropic Laminated Plates 290(1) 5.3.2 Symmetric Angle-Ply Laminated Plates 291(4) 5.3.3 Antisymmetric Cross-Ply Laminated Plates 295(3) 5.3.4 Antisymmetric Angle-Ply Laminated Plates 298(3) Problem Set 5.3 301(1) 5.4 BUCKLING OF SIMPLY SUPPORTED LAMINATED PLATES UNDER IN-PLANE LOAD 301(14) 5.4.1 Specially Orthotropic Laminated Plates 303(3) 5.4.2 Symmetric Angle-Ply Laminated Plates 306(1) 5.4.3 Antisymmetric Cross-Ply Laminated Plates 307(5) 5.4.4 Antisymmetric Angle-Ply Laminated Plates 312(3) Problem Set 5.4 315(1) 5.5 VIBRATION OF SIMPLY SUPPORTED LAMINATED PLATES 315(8) 5.5.1 Specially Orthotropic Laminated Plates 315(2) 5.5.2 Symmetric Angle-Ply Laminated Plates 317(1) 5.5.3 Antisymmetric Cross-Ply Laminated Plates 318(2) 5.5.4 Antisymmetric Angle-Ply Laminated Plates 320(2) Problem Set 5.5 322(1) 5.6 SUMMARY REMARKS ON EFFECTS OF STIFFNESSES 323(6) REFERENCES 329(2) 6 OTHER ANALYSIS AND BEHAVIOR TOPICS 331(36) 6.1 INTRODUCTION 331(1) 6.2 REVIEW OF CHAPTERS 1 THROUGH 5 332(1) 6.3 FATIGUE 333(3) 6.4 HOLES IN LAMINATES 336(3) 6.5 FRACTURE MECHANICS 339(6) 6.5.1 Basic Principles of Fracture Mechanics 340(3) 6.5.2 Application of Fracture Mechanics to Composite Materials 343(2) 6.6 TRANSVERSE SHEAR EFFECTS 345(11) 6.6.1 Exact Solutions for Cylindrical Bending 346(4) 6.6.2 Approximate Treatment of Transverse Shear Effects 350(6) 6.7 POSTCURING SHAPES OF UNSYMMETRIC LAMINATES 356(3) 6.8 ENVIRONMENTAL EFFECTS 359(2) 6.9 SHELLS 361(1) 6.10 MISCELLANEOUS TOPICS 362(1) REFERENCES 362(5) 7 INTRODUCTION TO DESIGN OF COMPOSITE STRUCTURES 367(100) 7.1 INTRODUCTION 368(4) 7.1.1 Objectives 368(1) 7.1.2 Introduction to Structural Design 368(1) 7.1.3 New Uses of Composite Materials 368(1) 7.1.4 Manufacturing Processes 368(1) 7.1.5 Material Selection 369(1) 7.1.6 Configuration Selection 369(1) 7.1.7 Joints 369(1) 7.1.8 Design Requirements 370(1) 7.1.9 Optimization 370(1) 7.1.10 Design Philosophy 371(1) 7.1.11 Summary 372(1) 7.2 INTRODUCTION TO STRUCTURAL DESIGN 372(17) 7.2.1 Introduction 372(1) 7.2.2 What Is Design? 372(4) 7.2.3 Elements of Design 376(4) 7.2.4 Steps in the Structural Design Process 380(1) 7.2.4.1 Structural Analysis 381(1) 7.2.4.2 Elements of Analysis in Design 381(1) 7.2.4.3 Failure Analysis 382(1) 7.2.4.4 Structural Reconfiguration 383(1) 7.2.4.5 Iterative Nature of Structural Design 384(1) 7.2.5 Design Objectives and Design Drivers 385(1) 7.2.6 Design-Analysis Stages 386(1) 7.2.6.1 Preliminary Design-Analysis 387(1) 7.2.6.2 Intermediate Design-Analysis 388(1) 7.2.6.3 Final Design-Analysis 388(1) 7.2.7 Summary 389(1) 7.3 MATERIALS SELECTION 389(11) 7.3.1 Introduction 389(1) 7.3.2 Materials Selection Factors 390(1) 7.3.3 Fiber Selection Factors 391(1) 7.3.4 Matrix Selection Factors 392(1) 7.3.5 Importance of Constituents 393(1) 7.3.6 Space Truss Material Selection Example 394(6) 7.3.7 Summary 400(1) 7.4 CONFIGURATION SELECTION 400(17) 7.4.1 Introduction 400(1) 7.4.2 Stiffened Structures 400(1) 7.4.2.1 Advantages of Composite Materials in Stiffened Structures 401(2) 7.4.2.2 Types of Stiffeners 403(2) 7.4.2.3 Open- versus Closed-Section Stiffeners 405(2) 7.4.2.4 Stiffener Design 407(3) 7.4.2.5 Orthogrid 410(1) 7.4.3 Configuration in Design Cost 411(2) 7.4.4 Configuration versus Structure Size 413(1) 7.4.5 Reconfiguration of Composite Structures 414(3) 7.4.6 Summary 417(1) 7.5 LAMINATE JOINTS 417(5) 7.5.1 Introduction 417(2) 7.5.2 Bonded Joints 419(1) 7.5.3 Bolted Joints 420(1) 7.5.4 Bonded-Bolted Joints 421(1) 7.5.5 Summary 422(1) 7.6 DESIGN REQUIREMENTS AND DESIGN FAILURE CRITERIA 422(3) 7.6.1 Introduction 422(1) 7.6.2 Design Requirements 422(2) 7.6.3 Design Load Definitions 424(1) 7.6.4 Summary 425(1) 7.7 OPTIMIZATION CONCEPTS 425(28) 7.7.1 Introduction 425(1) 7.7.2 Fundamentals of Optimization 426(1) 7.7.2.1 Structural Optimization 426(3) 7.7.2.2 Mathematics of Optimization 429(2) 7.7.2.3 Optimization of a Composite Laminate 431(4) 7.7.2.4 Strength Optimization Programs 435(5) 7.7.3 Invariant Laminate Stiffness Concepts 440(1) 7.7.3.1 Invariant Laminate Stiffnesses 440(3) 7.7.3.2 Special Results for Invariant Laminate Stiffnesses 443(3) 7.7.3.3 Use of Invariant Laminate Stiffnesses in Design 446(1) Problem Set 7.7.3 447(1) 7.7.4 Design of Laminates 447(6) 7.7.5 Summary 453(1) 7.8 DESIGN ANALYSIS PHILOSOPHY FOR COMPOSITE STRUCTURES 453(10) 7.8.1 Introduction 453(1) 7.8.2 Problem Areas 454(1) 7.8.3 Design Philosophy 455(1) 7.8.4 `Anisotropic' Analysis 455(1) 7.8.5 Bending-Extension Coupling 456(1) 7.8.6 Micromechanics 457(1) 7.8.7 Nonlinear Behavior 458(1) 7.8.8 Interlaminar Stresses 459(1) 7.8.9 Transverse Shearing Effects 460(1) 7.8.10 Laminate Optimization 461(1) 7.8.11 Summary 462(1) 7.9 SUMMARY 463(2) REFERENCES 465(2) APPENDIX A: MATRICES AND TENSORS 467(12) A.1 MATRIX ALGEBRA 467(5) A.1.1 Matrix Definitions 467(3) A.1.2 Matrix Operations 470(2) A.2 TENSORS 472(5) A.2.1 Transformation of Coordinates 473(1) A.2.2 Definition of Various Tensor Orders 474(1) A.2.3 Contracted Notation 475(1) A.2.4 Matrix Form of Tensor Transformations 476(1) REFERENCE 477(2) APPENDIX B: MAXIMA AND MINIMA OF FUNCTIONS OF A SINGLE VARIABLE 479(6) REFERENCE 483(2) APPENDIX C: TYPICAL STRESS-STRAIN CURVES 485(10) C.1 FIBERGLASS-EPOXY STRESS-STRAIN CURVES 485(1) C.2 BORON-EPOXY STRESS-STRAIN CURVES 485(1) C.3 GRAPHITE-EPOXY STRESS-STRAIN CURVES 485(9) REFERENCES 494(1) APPENDIX D: GOVERNING EQUATIONS FOR BEAM EQUILIBRIUM AND PLATE EQUILIBRIUM, BUCKLING, AND VIBRATION 495(12) D.1 INTRODUCTION 495(1) D.2 DERIVATION OF BEAM EQUILIBRIUM EQUATIONS 495(3) D.3 DERIVATION OF PLATE EQUILIBRIUM EQUATIONS 498(7) D.4 PLATE BUCKLING EQUATIONS 505(1) D.5 PLATE VIBRATION EQUATIONS 506(1) REFERENCES 506(1) INDEX 507