1 aerospace structures and materials: lamination theory and applications dr. tom dragone orbital...

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Aerospace Structures and Materials:

Lamination Theory and Applications

Dr. Tom Dragone

Orbital Sciences Corporation

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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?MS>0?

SHEAR-MOMENTDIAGRAM Section Loads

GLOBAL LOADS Aerodynamics Inertial Applied

GEOMETRY Planform Skin Construction Spar/Rib Layout

SIZING Thickness Ply Orientation

MATERIALS Metal Composite

StructureIdealization

Stiffness Lamination Theory

Done

FAILURE ANALYSIS

Yes No

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ABD Matrix Coupling: Uniaxial

ABD Matrix Types Showing Coupling

P Poissons Coupling StB Stretch-Bend CouplingBT Bend-Twist Coupling StT Stretch-Twist Coupling

StSh Stretch-Shear Coupling ShT Shear-Twist CouplingShB Shear-Bend Coupling

UniaxialStr1 Str2 Shr Bend1 Bend2 Twist

Str1 PStr2 PShrBend1 PBend2 PTwist

• 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

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Symmetric BalancedStr1 Str2 Shr Bend1 Bend2 Twist

Str1 PStr2 PShrBend1 P BTBend2 P BTTwist BT BT

ABD Matrix Coupling: Symmetric Balanced

ABD Matrix Types Showing Coupling

P Poissons Coupling StB Stretch-Bend CouplingBT Bend-Twist Coupling StT Stretch-Twist Coupling

StSh Stretch-Shear Coupling ShT Shear-Twist CouplingShB Shear-Bend Coupling

• 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)

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Symmetric UnbalancedStr1 Str2 Shr Bend1 Bend2 Twist

Str1 P StShStr2 P StShShr StSh StShBend1 P BTBend2 P BTTwist BT BT

ABD Matrix Coupling:Symmetric Unbalanced

ABD Matrix Types Showing Coupling

P Poissons Coupling StB Stretch-Bend CouplingBT Bend-Twist Coupling StT Stretch-Twist Coupling

StSh Stretch-Shear Coupling ShT Shear-Twist CouplingShB Shear-Bend Coupling

• Example: [0 45 90]S [303]S

• Unbalanced laminates have Stretch-Shear coupling

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0/90 Str1 Str2 Shr Bend1 Bend2 Twist

Str1 P StBStr2 P StBShrBend1 PBend2 PTwist

ABD Matrix Coupling:0/90 Coupling

ABD Matrix Types Showing Coupling

P Poissons Coupling StB Stretch-Bend CouplingBT Bend-Twist Coupling StT Stretch-Twist Coupling

StSh Stretch-Shear Coupling ShT Shear-Twist CouplingShB Shear-Bend Coupling

• Example: [0 90] [04 904]

• 0/90 laminates have Stretch-Bend coupling

0° (Stiff)90° (Weak) 0°

90°

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Unsymmetric BalancedStr1 Str2 Shr Bend1 Bend2 Twist

Str1 P StTStr2 P StTShr ShB ShBBend1 P BTBend2 P BTTwist BT BT

ABD Matrix CouplingUnsymmetric Balanced

ABD Matrix Types Showing Coupling

P Poissons Coupling StB Stretch-Bend CouplingBT Bend-Twist Coupling StT Stretch-Twist Coupling

StSh Stretch-Shear Coupling ShT Shear-Twist CouplingShB Shear-Bend Coupling

• Example: [02 ±45 90]3 [454 -454]

• Unsymmetric laminates have Stretch-Twist and Shear Bend coupling

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Unsymmetric UnbalancedStr1 Str2 Shr Bend1 Bend2 Twist

Str1 P StSh StB P StTStr2 P StSh P StB StTShr StSh StSh ShB ShB ShTBend1 P BTBend2 P BTTwist BT BT

ABD Matrix CouplingUnsymmetric Unbalanced

ABD Matrix Types Showing Coupling

P Poissons Coupling StB Stretch-Bend CouplingBT Bend-Twist Coupling StT Stretch-Twist Coupling

StSh Stretch-Shear Coupling ShT Shear-Twist CouplingShB Shear-Bend Coupling

• Example: [0 10 20 30 40 50]

• Unsymmetric Unbalanced laminates have all coupling including Shear-Twist coupling

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ABD Matrix CouplingABD Matrix Types Showing Coupling

P Poissons Coupling StB Stretch-Bend CouplingBT Bend-Twist Coupling StT Stretch-Twist Coupling

StSh Stretch-Shear Coupling ShT Shear-Twist CouplingShB Shear-Bend Coupling

Uniaxial 0/90 Str1 Str2 Shr Bend1 Bend2 Twist Str1 Str2 Shr Bend1 Bend2 Twist

Str1 P Str1 P StBStr2 P Str2 P StBShr ShrBend1 P Bend1 PBend2 P Bend2 PTwist Twist

Symmetric Balanced Unsymmetric BalancedStr1 Str2 Shr Bend1 Bend2 Twist Str1 Str2 Shr Bend1 Bend2 Twist

Str1 P Str1 P StTStr2 P Str2 P StTShr Shr ShB ShBBend1 P BT Bend1 P BTBend2 P BT Bend2 P BTTwist BT BT Twist BT BT

Symmetric Unbalanced Unsymmetric UnbalancedStr1 Str2 Shr Bend1 Bend2 Twist Str1 Str2 Shr Bend1 Bend2 Twist

Str1 P StSh Str1 P StSh StB P StTStr2 P StSh Str2 P StSh P StB StTShr StSh StSh Shr StSh StSh ShB ShB ShTBend1 P BT Bend1 P BTBend2 P BT Bend2 P BTTwist BT BT Twist BT BT

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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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COMPFAIL Process

• Choose Ply Material– Sets E, Vf, X,Y,S,,t

Number 1Fiber AS4

Matrix 3501-6Form (T/C) Tape

X (ksi) 209.8X' (ksi) 209.8Y (ksi) 7.54Y' (ksi) 29.87S (ksi) 13.49

thickness (in) 0.005density (pci) 0.054

Vf (%) 62%Vm (%) 38%

Ex (Msi) 18.50Ey (Msi) 1.30

Gxy (Msi) 1.030Nuxy 0.3alphx (1e-6F-1) -0.22alphy (1e-6F-1) 12

Minv= 0.99368

Qxx (Msi) 18.61767Qyy (Msi) 1.307464Qxy (Msi) 0.392239Qss (Msi) 1.030

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COMPFAIL Coordinate Systems

2

1

3

Laminate Coordinate System

x

y

z

Material Coordinate System

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COMPFAIL Process

• Choose Ply Material– Sets E, Vf, X,Y,S,,t

• Choose Layup– Ply by Ply definition of material and angle (relative to reference)

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COMPFAIL Process

• Choose Ply Material– Sets E, Vf, X,Y,S,,t

• Choose Layup– Ply by Ply definition of material and angle (relative to reference)

• Intermediate Calculations– Define Qij, Aij, Bij, Dij

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COMPFAIL Process

• Choose Ply Material– Sets E, Vf, X,Y,S,,t

• Choose Layup– Ply by Ply definition of material and angle (relative to reference)

• Intermediate Calculations– Define Qij, Aij, Bij, Dij

• Define ABD Matrix

6

2

1

6

2

1

662616662616

262212262212

161211161211

662616662616

262212262212

161211161211

6

2

1

6

2

1

DDDBBB

DDDBBB

DDDBBB

BBBAAA

BBBAAA

BBBAAA

M

M

M

N

N

N

DB

BA

M

N

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COMPFAIL Process

• Apply Loads

–N1, N2, N6, M1, M2, M6

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COMPFAIL Process

• Apply Loads

–N1, N2, N6, M1, M2, M6

• Return Strains and Curvatures

– 1, 2, 6, 1, 2, 6

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COMPFAIL Process

• Apply Loads

–N1, N2, N6, M1, M2, M6

• Return Strains and Curvatures

– 1, 2, 6, 1, 2, 6

• Return Equivalent Moduli (For Symmetric Laminates ONLY)

– EInPlane, EFlexure

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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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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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Satellite Solar Panel Example

Spacecraft Bus

Solar Array Panel

CommunicationsAntennae

INDOSTAR SATELLITE

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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

FragmentCracksSi or GaAs

Solar Cells

Connections

Solar Panel

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Laminate Cure Effects

Co-Cure(Both Skins at Same Time)

Consider an 8-Ply Quasi-Isotropic Sandwich During Cure Process

80+psi Pressure

ToolCore

OML Skin

• Cure Pressure on Thin Sandwich Leads to Pillowing

• Poor Consolidation• High Void Content• Wavy SurfaceIML Skin

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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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Flutter Effects

• Recall that Cp is @ 1/4 MAC for Subsonic Flight– Results in Torsion that leads to Leading Edge Up

CPElastic AxisTorsion Axis

Increases with Span

LIFT

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Positive FeedbackPositive 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 AOA HIGHER LIFT

Lift

Local AOA ( + )

Typical Operating Point

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X-29 Composite Wing Design

Forward-SweptWings

Canards

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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

6

2

1

6

2

1

662616662616

262212262212

161211161211

662616662616

262212262212

161211161211

6

2

1

6

2

1

DDDBBB

DDDBBB

DDDBBB

BBBAAA

BBBAAA

BBBAAA

M

M

M

N

N

N

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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

6

2

1

6

2

1

662616662616

262212262212

161211161211

662616662616

262212262212

161211161211

6

2

1

6

2

1

DDDBBB

DDDBBB

DDDBBB

BBBAAA

BBBAAA

BBBAAA

M

M

M

N

N

N