Composite Materials for Aircraft Structures:
A Brief Review of Practical Application
Jared W Nelson,
PhD Candidate
Department of Mechanical and Industrial Engineering
Montana State University
ME 480 Introduction to Aerospace,
FALL 2011
Introduction
• Composite materials are used more and more for
primary structures in commercial, industrial, aerospace,
marine, and recreational structures
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From Last Time
• Composite parts used for aircraft applications are defined by
– Material, process, and manufacturing specifications.
– Material allowable (engineering definition).
• All of these have a basis in regulatory requirements.
• Most efficient use of advanced composites in aircraft
structure is in applications with
– Highly loaded parts with thick gages.
– High fatigue loads (fuselage and wing structure, etc).
– Areas susceptible to corrosion (fuselage, etc).
– Critical weight reduction (empennage, wings, fuselage, etc).
• Use must be justified by weighing benefits against costs.
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Composition of Composites
Fiber/Filament
Reinforcement
Matrix
Composite
• High strength
• Good shear properties
• High strength
• High stiffness
• Low density
• High stiffness
• Low density
• Thermoset &
Thermoplastic
• Good shear properties
• Carbon, Glass,
Aramid, etc
• Epoxy, Polyester, PP,
Nylon, Ceramics, etc.
Design and Analysis of Aircraft Structures
• Low density
• Anisotropic!
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Overview
• Micromechanics
– Study of mechanical behavior of a composite material in terms of
its constituent materials
• Ply Mechanics
– Study of mechanical behavior of individual material plies based
on variations from global coordinate system
• Macromechanics
– Study of mechanical behavior utilizing ply mechanics of a
homogenized composite material
• Failure Theories
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CADEC: Introduction
Compliment to text: Barbero, EJ. Introduction to Composite
Materials Design; Taylor & Francis, 1999.
Software free online—search keywords CADEC & Barbero
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Micromechanics: Assumptions
• Lamina:
–
–
–
–
Macroscopically homogeneous
Linearly elastic
Macroscopically Orthotropic
Initially stress free
• Fibers:
–
–
–
–
–
Homogeneous
Linearly elastic
Isotropic/Orthotropic
Regularly spaced
Perfectly aligned
Carbon/epoxy (AS4/3501-6) composite (Vf=.70)
• Matrix:
–
–
–
–
Homogeneous
Linearly elastic
Isotropic
Assumptions in Micromechanics of Composites
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Micromechanics: Rule of Mixtures
Vf,max approximately 78%
Common range = 55-67%
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Micromechanics: Determining Properties
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Micromechanics: Rule of Mixtures (E1)
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Micromechanics: Determining Properties
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Micromechanics: Rule of Mixtures (E2)
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Micromechanics: Determining Properties
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Micromechanics: Rule of Mixtures (ν12)
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Micromechanics: Determining Properties
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Micromechanics: Rule of Mixtures (G12)
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Micromechanics: Other Methods & Strengths
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Micromechanics: Halpin-Tsai (E2)
Halpin-Tsai: “Semiempirical (1969) version to obtain better
prediction”—Barbero
ζ ≡ empirical curve fitting parameter, commonly 2a/b
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Micromechanics: Determining Properties
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Micromechanics: Longitudinal Tensile Strength
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Micromechanics: Determining Properties
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Micromechanics: Thermal & Electrical Cond
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Ply Mechanics
• So what happens if we vary the fiber direction angle
away from the 1-direction?
• CADEC uses Micromechanics results and fiber angle
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–
–
–
Plane Stress
Transform stress/strain
Off-Axis Compliance/Stiffness
3D Constitutive Equ’s
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Ply Mechanics: CADEC
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Ply Mechanics: Compliance Plane Stress
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Ply Mechanics: CADEC
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Ply Mechanics: Transformations
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Ply Mechanics: CADEC
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Ply Mechanics: Off-Axis Stiffness Matrices
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Ply Mechanics: CADEC
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Ply Mechanics: Stress-Strain Relationships
• Stress-Strain Relationship:
 ij  Cij ij
• With 3 planes  Cij has 81 terms, but since:
and:  ij   ji only 36 terms
 ij   ji
• Orthotropic material (2 planes of symmetry) reduces
to 9 terms:
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Ply Mechanics: Orthotropic Material
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Macromechanics
• What if there are multiple lamina at differing angles?
• CADEC uses Micromechanics and Ply mechanics to determine:
–
–
–
–
–
–
Stiffness and Compliance Equations
Laminate Moduli
Global and Material Stresses and Strains
Strains and Curvatures
Thermal and Hygroscopic loads
For both Intact and Degraded materials
• Assumes:
–
–
–
–
Plane sections remain plane
Symmetry about a neutral surface
No shear coupling
Perfect bonding
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Shorthand Laminate Orientation Code
Tapes or Undirectional Tapes
[45/0/-45/902 /-45/0/45
[45/0/-45/90] s
Tapes or undirectional tapes
• Each lamina is labeled by its ply orientation.
• Laminae are listed in sequence with the first number representing the
lamina to which the arrow is pointing.
• Individual adjacent laminae are separated by a slash if their angles
differ.
• Adjacent laminae of the same angle are depicted by a numerical
subscript indicating the total number of laminae which are laid up in
sequence at that angle.
• Each complete laminate is enclosed by brackets.
• When the laminate is symmetrical and has an even number on each
side of the plane of symmetry (known as the midplane) the code may
be shortened by listing only the angles from the arrow side to the
midplane. A subscript “S” is used to indicate that the code for only one
half of the laminate is shown.
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Shorthand Laminate Orientation Code
Fabrics and Tapes and Fabrics
[(45)/(0)/(45)]
Midplane
Fabrics
[(45)/0(-45)/90]
Midplane
Tapes & Fabrics
• When plies of fabric are used in a laminate. The
angle of the fabric warp is used as the ply direction
angle. The fabric angle is enclosed in parentheses
to identify the ply as a fabric ply.
• When the laminate is composed of both fabric and
tape plies (a hybrid laminate). The parentheses
around the fabric plies will distinguish the fabric
plies from the tape plies.
• When the laminate is symmetrical and has an odd
number of plies, the center ply is overlined to
indicate that it is the midplane.
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Macromechanics: CADEC
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Macromechanics: CADEC
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Macromechanics: Defining Laminate
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Macromechanics: Defining Laminate
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Macromechanics: Material Properties
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Macromechanics: CADEC Quirkiness
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Macromechanics: Review Outputs
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Macromechanics: Global Stresses
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Macromechanics: ABD Matrices
• Stiffness of composite
where:
– [A] = in-plane stiffness.
– [D] = bending stiffness.
– [B] relates in-plane strains to
bending moments and
curvatures to in-plane
forces—bending-extension
coupling.
– [H] relates transverse shear
strains to transverse forces.
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Macromechanics: ABD Matrices
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Macromechanics: ABD Matrices
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Macromechanics: Stiffness Equations
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Macromechanics: Stiffness Equations
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Macromechanics: Laminate Moduli
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Macromechanics: Laminate Moduli
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Macromechanics: Degraded Material
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Macromechanics: Degraded Material
• What is a degraded material?
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Macromechanics: ABD Comparison
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Macromechanics: CADEC Alt Methods
• Data can be entered into
.DAT and .DEF files
– Easily reloaded into CADEC
– More user friendly
•
•
•
•
•
•
Enter laminate
Save
Open CADEC
Load Laminate
Run Laminate Analysis
Analyze
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Failure Theories
• Many failure criteria, most popular:
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–
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Maximum stress criterion
Maximum strain criterion
Tsai-Hill failure criterion
Tsai-Wu failure criterion
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Not Just An Academic Exercise
Consequence of Misalignment in Large, Composite Structure
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Failure Theories: CADEC
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Failure Theories: CADEC
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Failure Theories: Max Stress Criterion
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Failure Theories: Tsai-Wu Criterion
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CADEC Demo
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Compression Fixture for Thick Laminates
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•
•
•
Analysis as performed by Julie Workman, Research Assistant
Design Impetus
Design challenges – Brute force solution
CADEC solution for loading based on 2% strain
Design and Analysis of Aircraft Structures
Shear Loading
• Clamping fixtures apply a shear load to the specimen in order to
introduce an axial load
• Tabbing required, very precise tolerances required for coupons,
IITRI structure is very massive
• Can result in end crushing (Adams; 2005)
Design and Analysis of Aircraft Structures
End Loading/ Combined Loading
• End Loading Fixtures apply load axially to fibers
• Low transverse shear strength can result in end-brooming in a
tabbed or un-tabbed specimen
• Some question in the D 695 Fixture as to whether the fixture
carries some of the load (Wegner, Adams; 2000)
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Proposed Components
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• Challenges
Geometric Challenges:
•
Gage section which will accommodate flaws – coupon geometry
•
Utilize existing back component with bolt threads and coupon keyway
• Match materials, dimensions and bolt axes on existing fixture components
• Axis of symmetry of alignment rods and coupon in plane with each other
• Massive structure
Design Challenges
•
Coupon must carry all of the load, no fixture interference
•
zero binding
• Zero misalignment
Design and Analysis of Aircraft Structures
Laminated Plate Theory
• Strains refer to middle surface strains, k-terms are curvature terms
• Q is the stiffness matrix in terms of layer engineering constants
in the coordinates of the material
Nx is the resultant force in the x-direction of the laminate
obtained by integrating the stress in that direction through
the thickness.
Design and Analysis of Aircraft Structures
• Laminated Plate Theory
• [Q] is actually [Q-bar] – the transformed stiffness matrix. [Q-bar]
multiplied by the strain of each layer integrated over the thickness of
the laminate is equal to strain multiplied by thickness.
• Where [A] is [Q-bar]*t ---Assumed all layers with misalignment have
same properties
• Enter strain, εx = .02
• CADEC calculates [N]
• Stress and subsequent force is backed out from there
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• CADEC Analysis
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• CADEC Analysis
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• CADEC Analysis
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• Results
Figure 1: 20-ply Variable Angle
Angle
σy
Ny
Force in y
0
4.29
5.72
6.435
5
205.24
273.65333
307.86
10
672.6
896.8
1008.9
15
1388.6
1851.4667
2082.9
20
2266.94
3022.5867
3400.41
25
3201.62
4268.8267
4802.43
30
4079.96
5439.9467
6119.94
35
4795.96
6394.6133
7193.94
40
5263.32
7017.76
7894.98
45
5425.62
7234.16
8138.43
Design and Analysis of Aircraft Structures
Concluding Remarks
• Composite design fairly simple
– Assumptions lead to simplified analysis
– Idealized
– Real-world?
• CADEC
–
–
–
–
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Begin with component properties
Micromechanic, Ply and Macromechanic analysis
Apply loads and match against failure criteria
Simple structures (Not covered)
Software options: COMPRO, MSExcel, Matlab, MathCAD, etc.
• Composites still require significant analysis and physical testing
• Parts/Structures are only as good as the manufacturing
– “You can never make good parts with bad materials, but you can easily make bad
parts with good materials!”
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