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1 Aerospace Structures and Materials: Lamination Theory and Applications Dr. Tom Dragone Orbital Sciences Corporation

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2 Structure Design / Analysis Process BOX BEAM ANALYSIS Component Loads (Cap Forces, Shear Flow) BOX BEAM ANALYSIS Component Loads (Cap Forces, Shear Flow) JOINT LOADS Weld, Braze Bond, Bolt Metal Yield Rupture Composite FPF LPF Stability Buckling Crippling Fracture Toughness Crack Size Fatigue Crack Initiation Crack Growth MS>0? SHEAR-MOMENT DIAGRAM Section Loads GLOBAL LOADS Aerodynamics Inertial Applied GEOMETRY Planform Skin Construction Spar/Rib Layout SIZING Thickness Ply Orientation MATERIALS Metal Composite Structure Idealization Stiffness Lamination Theory Done FAILURE ANALYSIS YesNo

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3 ABD Matrix Coupling: Uniaxial Example: [0 6 ] In general, diagonal terms will be different –E 11 >>E 22 D 11 >>D 22 NOTE: Isotropic materials would have same terms populated, but –E 11 =E 22 D 11 =D 22

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4 ABD Matrix Coupling: Symmetric Balanced Example: [ ] S [ ] 2S [ ] S Balanced Symmetric laminates have Bend-Twist coupling In general, the diagonal terms will be different Quasi-Isotropic laminates have equal inplane moduli, but still have bend-twist coupling (hence, not truly isotropic)

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5 ABD Matrix Coupling: Symmetric Unbalanced Example: [ ] S [30 3 ] S Unbalanced laminates have Stretch-Shear coupling

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6 ABD Matrix Coupling: 0/90 Coupling Example: [0 90] [ ] 0/90 laminates have Stretch-Bend coupling 0° (Stiff) 90° (Weak) 0° 90°

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7 ABD Matrix Coupling Unsymmetric Balanced Example: [0 2 ±45 90] 3 [ ] Unsymmetric laminates have Stretch-Twist and Shear Bend coupling

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8 ABD Matrix Coupling Unsymmetric Unbalanced Example: [ ] Unsymmetric Unbalanced laminates have all coupling including Shear-Twist coupling

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9 ABD Matrix Coupling

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10 Introduction to COMPFAIL COMPFAIL (COMPosite FAILure analysis tool) is an Excel spreadsheet-based implementation of Composite Lamination Theory User enters –Lamina Information –Laminate Information –Loading Code calculates –ABD Matrix –Equivalent Moduli –Global Strains and Curvatures –Local Ply Stresses and Strains –Failure Indices

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11 COMPFAIL Process Choose Ply Material –Sets E, V f, X,Y,S,,t

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12 COMPFAIL Coordinate Systems Laminate Coordinate Systemx y z Material Coordinate System

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13 COMPFAIL Process Choose Ply Material –Sets E, V f, X,Y,S,,t Choose Layup –Ply by Ply definition of material and angle (relative to reference)

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14 COMPFAIL Process Choose Ply Material –Sets E, V f, X,Y,S,,t Choose Layup –Ply by Ply definition of material and angle (relative to reference) Intermediate Calculations –Define Q ij, A ij, B ij, D ij

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15 COMPFAIL Process Choose Ply Material –Sets E, V f, X,Y,S,,t Choose Layup –Ply by Ply definition of material and angle (relative to reference) Intermediate Calculations –Define Q ij, A ij, B ij, D ij Define ABD Matrix

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16 COMPFAIL Process Apply Loads –N 1, N 2, N 6, M 1, M 2, M 6

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17 COMPFAIL Process Apply Loads –N 1, N 2, N 6, M 1, M 2, M 6 Return Strains and Curvatures – 1, 2, 6, 1, 2, 6

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18 COMPFAIL Process Apply Loads –N 1, N 2, N 6, M 1, M 2, M 6 Return Strains and Curvatures – 1, 2, 6, 1, 2, 6 Return Equivalent Moduli (For Symmetric Laminates ONLY) –E InPlane, E Flexure

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19 COMPFAIL Process Apply Loads Return Strains and Curvatures Return Equivalent Moduli (For Symmetric Laminates ONLY) Return Ply Strains and Ply Stresses – 1, 2, 6, 1, 2, 6 for Global (Laminate) Coordinate System – x, y, s, x, y, s for Local (Material) Coordinate System Two Values: Top and Bottom of Ply

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20 COMPFAIL Process Apply Loads Return Strains and Curvatures Return Equivalent Moduli (For Symmetric Laminates ONLY) Return Ply Strains and Ply Stresses Ignore Failure Criteria for Now

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21 Satellite Solar Panel Example Spacecraft Bus Solar Array Panel Communications Antennae INDOSTAR SATELLITE

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22 Solar Panel Example LAMINATE REQUIREMENTS Stiff Substrate to Minimize Deflections => High Modulus Equal Stiffness in All Directions => Quasi-Isotropic Thermal Stability => High Conductivity Light Weight => Composite T Light & Heat Broken Connections Fragment Cracks Si or GaAs Solar Cells Connections Solar Panel

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23 Laminate Cure Effects Co-Cure (Both Skins at Same Time) Consider an 8-Ply Quasi-Isotropic Sandwich During Cure Process 80+psi Pressure Tool Core OML Skin Cure Pressure on Thin Sandwich Leads to Pillowing Poor Consolidation High Void Content Wavy Surface IML Skin

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24 Laminate Cure Effects Separate-Cure (Skins Cured Separately) Consider Same 8-Ply Quasi-Isotropic Sandwich During Cure Process OML Skin Skins Must be Cured Separately Uniform T During Cure is Like Uniform In-Plane Loads (N1, N2) Uniform Load on Non-Symmetric Laminate Results in Warping Individual Skins Must be Quasi-Isotropic IML Skin Adhesive Film Cold Bond (Room Temp)

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25 Flutter Effects Recall that Cp 1/4 MAC for Subsonic Flight –Results in Torsion that leads to Leading Edge Up CP Elastic Axis Torsion Axis Increases with Span LIFT

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26 Positive Feedback Flutter Effects Recall also that Lift Increases with Angle of Attack –Twist Increases the Local Angle of Attack on a Wing Segment System Becomes Unstable at Divergence Speed Subject to Pronounced Vibrations => Flutter TWIST HIGHER AOAHIGHER LIFT Lift Local AOA ( + ) Typical Operating Point

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27 X-29 Composite Wing Design Forward-Swept Wings Canards

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28 X-29 Composite Wing Design Forward-swept wings provide enhanced maneuverability –Would be an advantage to close-combat aircraft Forward-swept wings enhance flutter effects –Wing bending increases local AOA even without torsion Composites enable weight-efficient forward swept wings for the X- 29 aircraft by exploiting negative stretch-twist coupling

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29 Flutter Reduction Effect Wing bending causes tension (top) and compression (bottom) stretching in the skins Stretch-Twist coupling produces a twisting moment in the skins Since the wing is thin, this becomes a torque on the whole wing Upward Bending => LE Down Twist, reducing flutter effects

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