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

Structure Design / Analysis Process GLOBAL LOADS Aerodynamics Inertial Applied GEOMETRY Planform Skin Construction Spar/Rib Layout MATERIALS Metal Composite SIZING Thickness Ply Orientation SHEAR-MOMENT DIAGRAM Section Loads Structure Idealization Stiffness Lamination Theory BOX BEAM ANALYSIS Component Loads (Cap Forces, Shear Flow) FAILURE ANALYSIS 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? Done Yes No

ABD Matrix Coupling: Uniaxial Example: [06] In general, diagonal terms will be different E11>>E22 D11>>D22 NOTE: Isotropic materials would have same terms populated, but E11=E22 D11=D22

ABD Matrix Coupling: Symmetric Balanced Example: [0 45 -45 90]S [+30 -30]2S [0 +253 -45 -253 45 90]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)

ABD Matrix Coupling: Symmetric Unbalanced Example: [0 45 90]S [303]S Unbalanced laminates have Stretch-Shear coupling

ABD Matrix Coupling: 0/90 Coupling Example: [0 90] [04 904] 0/90 laminates have Stretch-Bend coupling 0° 90° 0° (Stiff) 90° (Weak)

ABD Matrix Coupling Unsymmetric Balanced Example: [02 ±45 90]3 [454 -454] Unsymmetric laminates have Stretch-Twist and Shear Bend coupling

ABD Matrix Coupling Unsymmetric Unbalanced Example: [0 10 20 30 40 50] Unsymmetric Unbalanced laminates have all coupling including Shear-Twist coupling

ABD Matrix Coupling

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

COMPFAIL Process Choose Ply Material Sets E, Vf, X,Y,S,a,t

COMPFAIL Coordinate Systems x y z Material Coordinate System 2 1 3 Laminate Coordinate System q

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

COMPFAIL Process Choose Ply Material Choose Layup Sets E, Vf, X,Y,S,a,t Choose Layup Ply by Ply definition of material and angle (relative to reference) Intermediate Calculations Define Qij, Aij, Bij, Dij

COMPFAIL Process Choose Ply Material Choose Layup Sets E, Vf, X,Y,S,a,t Choose Layup Ply by Ply definition of material and angle (relative to reference) Intermediate Calculations Define Qij, Aij, Bij, Dij Define ABD Matrix

COMPFAIL Process Apply Loads N1, N2, N6, M1, M2, M6

COMPFAIL Process Apply Loads N1, N2, N6, M1, M2, M6 Return Strains and Curvatures e1, e2, e6, k1, k2, k6

COMPFAIL Process Apply Loads N1, N2, N6, M1, M2, M6 Return Strains and Curvatures e1, e2, e6, k1, k2, k6 Return Equivalent Moduli (For Symmetric Laminates ONLY) EInPlane, EFlexure

COMPFAIL Process Apply Loads Return Strains and Curvatures Return Equivalent Moduli (For Symmetric Laminates ONLY) Return Ply Strains and Ply Stresses e1, e2, e6, s1, s2, s6 for Global (Laminate) Coordinate System ex, ey, es, sx, sy, ss for Local (Material) Coordinate System Two Values: Top and Bottom of Ply

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

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

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

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

Consider Same 8-Ply Quasi-Isotropic Sandwich During Cure Process Laminate Cure Effects Consider Same 8-Ply Quasi-Isotropic Sandwich During Cure Process Separate-Cure (Skins Cured Separately) Cold Bond (Room Temp) IML Skin OML Skin Adhesive Film Skins Must be Cured Separately Uniform DT 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

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

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

X-29 Composite Wing Design Canards Forward-Swept Wings

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

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