Mechanics of Aeronautical Composite Materials

Christophe Bouvet, ISAE-SUPAÉRO, France.

Foreword ix

Preface xi

Introduction xiii

Chapter 1 Presentation of an Aeronautical Unidirectional Composite 1

1.1 Introduction 1

1.2 Carbon/epoxy composite T300/914 2

1.3 Polymers 5

Chapter 2 Characteristics of UD Ply 15

2.1 State of stress of UD ply 15

2.2 Tensile test in the l-direction 16

2.3 Tensile test along the t-direction 17

2.4 Shear test 19

2.5 General case 20

Chapter 3 Characteristics of a UD Ply in a Given Direction 27

3.1 Off-axis tensile test 27

Chapter 4 Fracture of a Laminated Composite 37

4.1 Fracture of a UD ply 37

4.1.1 Longitudinal tension 37

4.1.2 Longitudinal compression 40

4.1.3 Transverse tension 42

4.1.4 Transverse compression 43

4.1.5 In-plane shear 44

4.2 Fracture of a laminate 46

Chapter 5 Fracture Criteria of a UD Ply 49

5.1 Maximum stress fracture criterion 50

5.2 Maximum strain fracture criterion 54

5.3 Hill’s criterion 58

5.4 Tsai–Wu criterion 65

5.5 Yamada–Sun criterion 70

5.6 Conclusion 71

Chapter 6 Membrane Behavior of a Laminated Composite Plate 73

6.1 Generalities and notations 73

6.2 Membrane behavior, bending behavior and mirror symmetry 75

6.3 Resultant forces 78

6.4 Displacement field, stress field and strain field 80

6.5 Tension / shear coupling 83

Chapter 7 Bending Behavior of a Laminated Composite Plate 97

7.1 Notations 97

7.2 Resultant moments 97

7.3 Displacement field, stress field and strain field 99

7.4 Bending/twisting coupling 105

Chapter 8 The Fracture Criterion of a Laminate 115

8.1 The sizing criterion 115

8.2 Test on a composite structure 117

8.3 Sizing principle 119

8.4 Sizing a given structure for a given loading 119

8.5 Optimal structure for a given load 131

Chapter 9 Damage Tolerance 139

9.1 The principle of damage tolerance 139

9.2 Damage during impact and compression after impact 144

9.3 Sizing for impact damage tolerance 148

Chapter 10 Interlaminar and Out-of-Plane Shear Stress 151

10.1 Tension of a cross-ply laminate [0,90]s 151

10.2 Tension of a cross-ply laminate [45,–45]s 153

10.3 Out-of-plane shear stress 154

Chapter 11 Holed and Bolted Plates 157

11.1 Calculating holed composite plates 157

11.2 Calculating the multi-bolt composite joints 167

Chapter 12 Buckling 179

12.1 Reminder surrounding beam buckling 179

12.2 Buckling of plates under compression 180

12.3 Plate buckling under shear loading 186

Chapter 13 Miscellaneous Rules for Stacking 189

Chapter 14 Exercises 191

14.1 Experimental determination of the characteristics of a UD material 191

14.2 Fracture of a laminate 193

14.3 Shear modulus 194

14.4 Optimization of stacking sequence 195

14.5 Composite tube 195

14.6 Laminate calculation without calculation 196

14.7 Sandwich beam under bending 197

14.8 Laminate plate under compression 200

14.9 Tube under torsion/internal pressure 203

14.10 Optimization of a fabric with a strain fracture criterion 204

14.10.1 Part 1: preamble 204

14.10.2 Part 2: quasi-isotropic stacking sequence 205

14.10.3 Part 3: stacking sequence optimization 206

14.10.4 Part 4: stacking sequence optimization under bending 206

14.11 Open hole tensile test 206

14.12 Multi-bolt composite joint 209

Chapter 15 Solutions to the Exercises 211

15.1 Experimental determination of the characteristics of a UD material 211

15.2 Fracture of a laminate 219

15.3 Shear modulus 225

15.4 Optimization of stacking sequence 229

15.5 Composite tube 233

15.6 Laminate calculation without calculation 240

15.7 Sandwich beam under bending 242

15.8 Laminate plate under compression 253

15.9 Tube under torsion/internal pressure 263

15.10 Optimization of a fabric with a strain fracture criterion 266

15.11 Open hole tensile test 276

15.12 Multi-bolt composite joint 280

Bibliography 289

Index 293