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Transcript of 1 Aerospace Structures and Materials: Lamination Theory and Applications Dr. Tom Dragone Orbital...
1
Aerospace Structures and Materials:
Lamination Theory and Applications
Dr. Tom Dragone
Orbital Sciences Corporation
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?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
3
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
4
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)
5
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
6
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°
7
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
8
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
9
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
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
11
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
12
COMPFAIL Coordinate Systems
2
1
3
Laminate Coordinate System
x
y
z
Material Coordinate System
13
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)
14
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
15
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
16
COMPFAIL Process
• Apply Loads
–N1, N2, N6, M1, M2, M6
17
COMPFAIL Process
• Apply Loads
–N1, N2, N6, M1, M2, M6
• Return Strains and Curvatures
– 1, 2, 6, 1, 2, 6
18
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
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
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
21
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)
25
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
26
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
27
X-29 Composite Wing Design
Forward-SweptWings
Canards
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
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
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
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