Table of Contents

1. Cover
2. Title
3. Copyright
4. Foreword
5. Preface
6. Introduction
7. 1 Presentation of an Aeronautical Unidirectional Composite
   1. 1.1. Introduction
   2. 1.2. Carbon/epoxy composite T300/914
   3. 1.3. Polymers
8. 2 Characteristics of UD Ply
   1. 2.1. State of stress of UD ply
   2. 2.2. Tensile test in the l-direction
   3. 2.3. Tensile test along the t-direction
   4. 2.4. Shear test
   5. 2.5. General case
9. 3 Characteristics of a UD Ply in a Given Direction
   1. 3.1. Off-axis tensile test
10. 4 Fracture of a Laminated Composite
    1. 4.1. Fracture of a UD ply
    2. 4.2. Fracture of a laminate
11. 5 Fracture Criteria of a UD Ply
    1. 5.1. Maximum stress fracture criterion
    2. 5.2. Maximum strain fracture criterion
    3. 5.3. Hill’s criterion
    4. 5.4. Tsai–Wu criterion
    5. 5.5. Yamada–Sun criterion
    6. 5.6. Conclusion
12. 6 Membrane Behavior of a Laminated Composite Plate
    1. 6.1. Generalities and notations
    2. 6.2. Membrane behavior, bending behavior and mirror symmetry
    3. 6.3. Resultant forces
    4. 6.4. Displacement field, stress field and strain field
    5. 6.5. Tension / shear coupling
13. 7 Bending Behavior of a Laminated Composite Plate
    1. 7.1. Notations
    2. 7.2. Resultant moments
    3. 7.3. Displacement field, stress field and strain field
    4. 7.4. Bending/twisting coupling
14. 8 The Fracture Criterion of a Laminate
    1. 8.1. The sizing criterion
    2. 8.2. Test on a composite structure
    3. 8.3. Sizing principle
    4. 8.4. Sizing a given structure for a given loading
    5. 8.5. Optimal structure for a given load
15. 9 Damage Tolerance
    1. 9.1. The principle of damage tolerance
    2. 9.2. Damage during impact and compression after impact
    3. 9.3. Sizing for impact damage tolerance
16. 10 Interlaminar and Out-of-Plane Shear Stress
    1. 10.1. Tension of a cross-ply laminate [0,90]_S
    2. 10.2. Tension of a cross-ply laminate [45,–45]_S
    3. 10.3. Out-of-plane shear stress
17. 11 Holed and Bolted Plates
    1. 11.1. Calculating holed composite plates
    2. 11.2. Calculating the multi-bolt composite joints
18. 12 Buckling
    1. 12.1. Reminder surrounding beam buckling
    2. 12.2. Buckling of plates under compression
    3. 12.3. Plate buckling under shear loading
19. 13 Miscellaneous Rules for Stacking
20. 14 Exercises
    1. 14.1. Experimental determination of the characteristics of a UD material
    2. 14.2. Fracture of a laminate
    3. 14.3. Shear modulus
    4. 14.4. Optimization of stacking sequence
    5. 14.5. Composite tube
    6. 14.6. Laminate calculation without calculation.
    7. 14.7. Sandwich beam under bending
    8. 14.8. Laminate plate under compression
    9. 14.9. Tube under torsion/internal pressure
    10. 14.10. Optimization of a fabric with a strain fracture criterion
    11. 14.11. Open hole tensile test
    12. 14.12. Multi-bolt composite joint
21. 15 Solutions to the Exercises
    1. 15.1. Experimental determination of the characteristics of a UD material
    2. 15.2. Fracture of a laminate
    3. 15.3. Shear modulus
    4. 15.4. Optimization of stacking sequence
    5. 15.5. Composite tube
    6. 15.6. Laminate calculation without calculation
    7. 15.7. Sandwich beam under bending
    8. 15.8. Laminate plate under compression
    9. 15.9. Tube under torsion/internal pressure
    10. 15.10. Optimization of a fabric with a strain fracture criterion
    11. 15.11. Open hole tensile test
    12. 15.12. Multi-bolt composite joint
22. Bibliography
23. Index
24. End User License Agreement

List of Tables

1. 1 Presentation of an Aeronautical Unidirectional Composite
   1. Table 1.1. Comparison of the three primary resins used in aircraft structures
2. 14 Exercises
   1. Table 14.1. Stacking sequence for the four studied plates
   2. Table 14.2. Calculation of buckling resistance, bending stiffnesses and RF for eight stacking sequences (the two pure UD stacking sequences are entirely textbook cases only included for the purpose of the study, but are not real-world stacking sequences!)
3. 15 Solutions to the Exercises
   1. Table 15.1. Stacking sequence for the four studied plates
   2. Table 15.2. Calculation of buckling resistance, bending stiffnesses and RF for eight stacking sequences (the two pure UD stacking sequences are entirely textbook cases only included for the purpose of the study, but are not real-world stacking sequences!)
   3. Table 15.3. Calculation of a stacking sequence for a tube under torsion/internal pressure

List of Illustrations

1. Introduction
   1. Figure I.1. Weight ratio of composite material in aircraft structures from the Airbus group and a few others (http://www.airbus.com/)
2. 1 Presentation of an Aeronautical Unidirectional Composite
   1. Figure 1.1. Material breakdown of the Boeing 787 (according to http://www.boeing.fr). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   2. Figure 1.2. Unidirectional carbon/epoxy laminate
   3. Figure 1.3. Unidirectional and quasi-isotropic laminate
   4. Figure 1.4. Tension along the longitudinal direction of a composite: behavior of fiber, resin and composite. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   5. Figure 1.5. Tension along the longitudinal direction: damaged area
   6. Figure 1.6. Young’s modulus according to density [ASH 00a] CFRP: carbon fiber reinforced plastic; GFRP: glass fiber reinforced plastic. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   7. Figure 1.7. Strength according to density [ASH 00a] CFRP: carbon fiber reinforced plastic; GFRP: glass fiber reinforced plastic. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   8. Figure 1.8. Structure of polyethylene
   9. Figure 1.9. Structure of polymer in monomer chains
   10. Figure 1.10. Rigidity of a polymer depending on temperature. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   11. Figure 1.11. Secondary links between monomer chains: cross-linking. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   12. Figure 1.12. Rigidity of a polymer depending on temperature and cross-linking. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   13. Figure 1.13. Autoclave for curing thermosetting compounds
   14. Figure 1.14. Photo of a roll of pre-preg (photo Hexcel^®)
   15. Figure 1.15. Thermoforming (SMC) for curing and shaping a thermoplastic
   16. Figure 1.16. Tensile test of a polymer
   17. Figure 1.17. Crystalline phases and amorphous areas of a thermoplastic polymer
   18. Figure 1.18. Rigidity of a thermoplastic polymer depending on temperature and degree of crystallinity. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
3. 2 Characteristics of UD Ply
   1. Figure 2.1. Defining the coordinate system of a UD ply. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   2. Figure 2.2. Tensile test of a UD ply along the longitudinal direction. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   3. Figure 2.3. Stress / strain curves of a tensile test of a UD ply in the longitudinal direction. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   4. Figure 2.4. Tensile test of a UD ply in the transverse direction. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   5. Figure 2.5. Stress / strain curves of a tensile test of a UD ply in the transverse direction. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   6. Figure 2.6. In-plane shear test. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   7. Figure 2.7. Stress / strain curve of an in-plane shear test of a UD ply. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   8. Figure 2.8. General case: tension along l-direction, along t-direction and in-plane shear. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   9. Figure 2.9. The six elementary stress states illustrated in the case of a UD ply. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
4. 3 Characteristics of a UD Ply in a Given Direction
   1. Figure 3.1. Off-axis tensile test of a UD ply. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   2. Figure 3.2. Principle for calculating the stiffness matrix in (x, y). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   3. Figure 3.3. Elasticity characteristics depending on the angle of tensile loading. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   4. Figure 3.4. The four typical directions of UD plies
   5. Figure 3.5. The three basic stress states applied to a UD ply at 45°. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   6. Figure 3.6. The three tensile tests used to characterize a UD ply. For
5. 4 Fracture of a Laminated Composite
   1. Figure 4.1. Longitudinal tension and schematic curves of stress/ strain in the fiber and resin of a composite. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   2. Figure 4.2. Fracture of a composite with a high a) and low b) interface resistance. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   3. Figure 4.3. Micrograph of a fracture facies after longitudinal tensile test [PET 05]
   4. Figure 4.4. Tensile test specimen, with tabs and strain gauges, of a quasi-UD composite [ABI 08]. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   5. Figure 4.5. Tensile test at 0° and 90° of a quasi-UD composite [ABI 08]. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   6. Figure 4.6. Longitudinal compression fracture: diagram a) and micrographic cut b) [PIN 06] of a kink band. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   7. Figure 4.7. Longitudinal compression a) and geometry of the specimen b) [ABI 08]. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   8. Figure 4.8. Longitudinal compression test of a UD composite [ABI 08]. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   9. Figure 4.9. Transverse tension a) and associated damage scenario b). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   10. Figure 4.10. Transverse compression a) and associated damage scenario b). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   11. Figure 4.11. Shear fracture without a) and with b) compression. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   12. Figure 4.12. In-plane shear loading a) and appearance of shear cracks along 45°-direction b). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   13. Figure 4.13. In-plane fracture: creation of cusps. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   14. Figure 4.14. Shear fracture: creation of cusps in a carbon/epoxy UD [ROG 08]. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   15. Figure 4.15. Different fracture modes of composites [EVE 99]
   16. Figure 4.16. Matrix cracking in transverse tension a) and shearing b). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   17. Figure 4.17. Characterization test of composite under out-of-plane shearing. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   18. Figure 4.18. Damage scenario of a quasi-isotropic laminate
   19. Figure 4.19. Damage scenario of a laminate [45,–45]_S
6. 5 Fracture Criteria of a UD Ply
   1. Figure 5.1. The five elementary stress states of a UD ply. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   2. Figure 5.2. Maximum stress criterion. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   3. Figure 5.3. Off-axis tensile test of a UD ply. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   4. Figure 5.4. Tensile stress limit of an off-axis UD ply. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   5. Figure 5.5. Shear test of an off-axis UD ply. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   6. Figure 5.6. Shear limit stress of an off-axis UD ply. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   7. Figure 5.7. Effect of the shear sign on the fracture of a UD ply at 45°. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   8. Figure 5.8. Maximum stress and strain fracture criteria. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   9. Figure 5.9. Tensile limit stress of an off-axis UD ply. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   10. Figure 5.10. Fracture criteria for a UD ply. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   11. Figure 5.11. Tension of an off-axis UD ply. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   12. Figure 5.12. Tensile limit stress of an off-axis UD ply. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   13. Figure 5.13. Comparison of the four terms of the Hill’s criterion. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   14. Figure 5.14. Study of a tube under torsion. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   15. Figure 5.15. Fracture of a UD tube under torsion: shear stress limit a) and influence of the different terms of the Hill’s criterion b). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   16. Figure 5.16. Shear fracture of a ply at 45°. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   17. Figure 5.17. Shear fracture of a ply at −45°. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   18. Figure 5.18. Limit stress of a UD ply. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   19. Figure 5.19. Tensile limit stress of an off-axis UD ply. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   20. Figure 5.20. Comparison of different fracture criteria during the “World Wide Failure Exercise” in the plane (σl, σt) [SOD 04] a) and comparison with the criteria presented here b). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   21. Figure 5.21. Comparison of different fracture criteria during the “World Wide Failure Exercise” in the plane (σt, τlt) [SOD 04] (a) and comparison with the criteria presented here (b). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
7. 6 Membrane Behavior of a Laminated Composite Plate
   1. Figure 6.1. Notation of the plies within a laminate. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   2. Figure 6.2. Diagram of membrane and bending behavior. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   3. Figure 6.3. Effect of mirror symmetry during cooldown after manufacturing of the laminate
   4. Figure 6.4. Diagram and draping sequence of a rear helicopter rotor blade [BIZ 09]. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   5. Figure 6.5. Displacements during membrane and bending loadings. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   6. Figure 6.6. Stresses on a face of normal vector y. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   7. Figure 6.7. Resultant forces for membrane behavior. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   8. Figure 6.8. Forces on a square with sides dx and dy under membrane loading. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   9. Figure 6.9. Displacement of a plate under membrane loading. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   10. Figure 6.10. Strains and stresses in a laminate subject to membrane loading. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   11. Figure 6.11. Laminate [0,90]_S. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   12. Figure 6.12. Tension of a laminate [0,90]_S. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   13. Figure 6.13. Strains and stresses in the plies of a laminate [0,90]_S under tensile loading. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   14. Figure 6.14. Off-axis tension of a laminate [0,90]_S. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   15. Figure 6.15. E_lasticity characteristics of an off-axis laminate [0,90]_S. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   16. Figure 6.16. Laminate [45,–45]_S
   17. Figure 6.17. Shear stress of a 45° ply. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   18. Figure 6.18. Quasi-isotropic laminate [0,45,90,–45]_S. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   19. Figure 6.19. Quasi-isotropic laminate [0,45,90,–45]_S under tension. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   20. Figure 6.20. Quasi-isotropic laminate [0,45,90,–45]_S under off-axis tensile loading. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   21. Figure 6.21. E_lasticity characteristics of a quasi-isotropic laminate [0,45,90,–45]_S under off-axis traction. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
8. 7 Bending Behavior of a Laminated Composite Plate
   1. Figure 7.1. Notation of the plies within a laminate. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   2. Figure 7.2. Laminate under membrane/bending loading (3D diagram). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   3. Figure 7.3. Laminate under membrane and bending loading (in-plane diagram). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   4. Figure 7.4. The three bending/twisting resultant moments. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   5. Figure 7.5. Displacement field of a plate under bending loading. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   6. Figure 7.6. Displacement field of a plate under bending loading. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   7. Figure 7.7. Membrane and bending strains within a plate. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   8. Figure 7.8. Bending strain and stress within a laminate. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   9. Figure 7.9. Illustration of membrane/bending coupling within a plate. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   10. Figure 7.10. Laminate [0,90]_S. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   11. Figure 7.11. Stress field within the plies of a laminate [0,90]_S under bending moment Mx. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   12. Figure 7.12. Stress field within the plies of a laminate [0,90]_S under bending moment My. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   13. Figure 7.13. Stress field within the plies of a laminate [0,90]_S under twisting moment Mxy. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   14. Figure 7.14. Laminate [0,90]_S. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   15. Figure 7.15. Strain field within the plies of a laminate [0,90]_S under bending moment Mx. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   16. Figure 7.16. Laminate [45,-45]_S. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   17. Figure 7.17. Quasi-isotropic laminate [0,45,90,-45]_S. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   18. Figure 7.18. Quasi-isotropic laminate [0,45,90,-45]_S under off-axis loading. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   19. Figure 7.19. E_lastic bending characteristic D11 of a quasi-isotropic laminate [0,45,90,-45]_S under off-axis loading
9. 8 The Fracture Criterion of a Laminate
   1. Figure 8.1. Diagram curve of a fracture test on a composite structure. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   2. Figure 8.2. Sizing a composite laminate under membrane loading. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   3. Figure 8.3. Sizing of a composite laminate under bending loading. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   4. Figure 8.4. Tension of a laminate [0,90]_S. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   5. Figure 8.5. Quasi-isotropic laminate [0,45,90,–45]_S under tensile loading. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   6. Figure 8.6. Quasi-isotropic laminate [0,45,90,-45]_S under off-axis tension. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   7. Figure 8.7. RF under off-axis tension and compression of a quasi-isotropic laminate [0,45,90,–45]_S. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   8. Figure 8.8. Laminate [0,90]_S. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   9. Figure 8.9. Strains within the plies of a laminate [0,90]_S under bending resultant moment Mx. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   10. Figure 8.10. Optimization of a laminate for a given load under membrane loading. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   11. Figure 8.11. Equivalence between shearing and tension / compression at 45°. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
   12. Figure 8.12. Optimization of a laminate for a given bending loading. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
10. 9 Damage Tolerance
    1. Figure 9.1. General principle of damage detection and repair in metallic a) and composite materials b). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    2. Figure 9.2. Diagram of fatigue curves in a UD laminate composite composed of carbon and glass fibers
    3. Figure 9.3. Residual strength after impact and detectability of impact. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    4. Figure 9.4. Size of detectable damage depending on the type of inspection. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    5. Figure 9.5. The two types of matrix cracks: transverse cracks due to transverse tension σt a) and at 45° due to out-of-plane shear stress τtz b). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    6. Figure 9.6. Damage scenario during impact of a UD laminate [0,90]_S [CHA 87]
    7. Figure 9.7. Damages in a carbon / epoxy UD laminate [02,452,902,–452]_S after a 25 J impact. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    8. Figure 9.8. Typical scenario of damage and fracture during CAI. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
11. 10 Interlaminar and Out-of-Plane Shear Stress
    1. Figure 10.1. Diagram of interlaminar stresses during the tensile test of a laminate [0,90]_S. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    2. Figure 10.2. Diagram curve of the interlaminar stress during the tensile test of a laminate [0,90]_S
    3. Figure 10.3. Diagram of interlaminar stresses during the tensile test of a laminate [45,–45]_S. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    4. Figure 10.4. Diagram curves of interlaminar stresses during the tensile test of a laminate [45,–45]_S. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    5. Figure 10.5. Diagram curve of out-of-plane shear stresses of a laminate. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    6. Figure 10.6. Diagram a) [CHO92] and micrograph b) [PET05] of the interaction of matrix cracks (due to out-of-plane shear stress) with delamination
12. 11 Holed and Bolted Plates
    1. Figure 11.1. Holed plate under tension. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    2. Figure 11.2. Stress concentration at hole edge for an isotropic material
    3. Figure 11.3. Stress concentration ratio at the hole edge depending on the stacking sequence
    4. Figure 11.4. Splitting at the hole edge
    5. Figure 11.5. Holed specimen after fracture [XU 14]
    6. Figure 11.6. Principle of net stress in a holed plate under tension
    7. Figure 11.7. Comparison between net stress and shape factor coefficient. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    8. Figure 11.8. Principle of the “point stress” theory. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    9. Figure 11.9. Geometry of a holed plate under tension
    10. Figure 11.10. Illustration of the hole size effect
    11. Figure 11.11. Hole size effect under tensile loading
    12. Figure 11.12. Influence of d0 in calculating the hole size effect under tensile loading. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    13. Figure 11.13. Point stress method for different orientations of the plies. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    14. Figure 11.14. Blind fastener Fybrflush^® (www.ahg.fr). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    15. Figure 11.15. Application of a Fybrflush^® blind fastener (www.ahg.fr). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    16. Figure 11.16. Principle of equivalent stress for the calculation of a bolt composite joint
    17. Figure 11.17. The four primary fracture modes in a bolt composite joint. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    18. Figure 11.18. Filled hole tension with non-loaded bolt a) and loaded bolt b). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    19. Figure 11.19. Open hole tension a), filled hole with non-loaded bolt b) and loaded bolt c). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    20. Figure 11.20. Stress at the hole edge of an open-holed plate, filled hole with non-loaded bolt, and with loaded bolt. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    21. Figure 11.21. Principle of equivalent stress for calculating a bolt composite joint. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    22. Figure 11.22. Bearing stress. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    23. Figure 11.23. Sizing of a multi-bolt composite joint depending on the number of bolts. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    24. Figure 11.24. Diagram of a multi-bolt composite joint with the bypass loads. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
13. 12 Buckling
    1. Figure 12.1. Beam buckling. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    2. Figure 12.2. Plate under compression simply supported at two ends. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    3. Figure 12.3. Calculation of a plate under compression [ESD 95]. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    4. Figure 12.4. Laminate [0n,90 n]_S. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    5. Figure 12.5. Laminate plate [0n,90n]_S under compression. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    6. Figure 12.6. Buckling of a simply supported plate under shear loading. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    7. Figure 12.7. Calculation of a plate under shear loading [ESD 95]. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
14. 14 Exercises
    1. Figure 14.1. Tensile tests for the characterization of a UD ply. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    2. Figure 14.2. Geometry of the tensile specimen
    3. Figure 14.3. UD ply at 45°. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    4. Figure 14.4. Composite tube under tension/compression/torsion/bending. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    5. Figure 14.5. Studied laminates. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    6. Figure 14.6. Sandwich beam under bending. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    7. Figure 14.7. Nomex^® honeycomb
    8. Figure 14.8. Simply supported panel under compression. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    9. Figure 14.9. Stiffened panel under buckling. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    10. Figure 14.10. Stiffened panel using T-shaped stiffeners. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    11. Figure 14.11. Composite tube under torsion/internal pressure. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    12. Figure 14.12. Ply of 8 harness satin fabric. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    13. Figure 14.13. Holed plate under tension
    14. Figure 14.14. Stress concentration ratio at the hole edge
    15. Figure 14.15. Principle of the point stress method
    16. Figure 14.16. Multi-bolt composite joint. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
15. 15 Solutions to the Exercises
    1. Figure 15.1. Tensile tests for the characterization of a UD ply. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    2. Figure 15.2. Position of the principal strain frame. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    3. Figure 15.3. Compression test [ABI 08]. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    4. Figure 15.4. Example of a fabric ply (satin 8HS). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    5. Figure 15.5. Composite tube under tension/compression/torsion/bending. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    6. Figure 15.6. Composite tube under tension. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    7. Figure 15.7. Composite tube under torsion. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    8. Figure 15.8. Shear induced by shear force: if rigidity xy were the same everywhere a), and in reality b). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    9. Figure 15.9. Composite tube under bending: stress resultant due to the bending moment a) and shear force b). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    10. Figure 15.10. Sandwich beam under bending. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    11. Figure 15.11. Nomex^® honeycomb
    12. Figure 15.12. Sandwich beam under bending. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    13. Figure 15.13. Internal forces in a clamped beam under bending. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    14. Figure 15.14. Stresses in a clamped solid cross-section beam under bending. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    15. Figure 15.15. Stresses in a clamped sandwich cross-section beam under bending. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    16. Figure 15.16. Plate hypothesis or beam hypothesis
    17. Figure 15.17. Simply supported panel under compression. For
    18. Figure 15.18. Stiffened panel under buckling. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    19. Figure 15.19. T-shaped stiffener and omega-shaped stiffener
    20. Figure 15.20. Fuselage with omega-shaped stiffeners (San Diego Composites^®) and a low-cost composite fuselage with T-shaped stiffeners (Muratec^®)
    21. Figure 15.21. Stiffened panel with T-shaped stiffeners
    22. Figure 15.22. First buckling modes of a flat panel [45, −45]_8S and a panel with T-shaped stiffeners [(45, −45)₅, 45]_S (the perspective of the stiffened panel can be deceiving; the panel is seen from below and the blister is facing away from the stiffeners). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    23. Figure 15.23. Buckling of a stiffened panel with longitudinal and transverse stiffeners. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    24. Figure 15.24. Composite tube under torsion/internal pressure. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    25. Figure 15.25. Resultant force under torsion a) and internal pressure b). For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    26. Figure 15.26. Ply of 8 harness satin fabric. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    27. Figure 15.27. Strains of the laminate under bending Mx. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    28. Figure 15.28. Holed plate under tension
    29. Figure 15.29. Principle of the “point stress” theory. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    30. Figure 15.30. Hole size effect of holed plate under tension and accounting for this using the “point stress” theory. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    31. Figure 15.31. Multi-bolt composite joint
    32. Figure 15.32. Diagram of the multi-bolt composite joint with varying thickness. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    33. Figure 15.33. Ply drop-offs at the edge of the multi-bolt joint. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    34. Figure 15.34. Real and theoretical ply drop-offs [ABD 15]. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    35. Figure 15.35. Multi-bolt joint with alignment of the midplanes. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip
    36. Figure 15.36. Multi-bolt joint with stiffener. For a color version of this figure, see www.iste.co.uk/bouvet/aeronautical2.zip

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