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