Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Introduction
Composites have found their place in aerospace and in the sporting
goods industry, where they have displaced many metal applications.
The replacement of metal by composite directly has major pitfalls.
When an isotropic metal is replaced by an orthotropic system, care
must be taken to include biased material to overcome the weakness
(resin matrix) in the transverse direction thus adding more weight.
This Achilles Heel (resin) is aggravated by the operating
environment of moisture and temperature causing a major
degradation in strength.
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Differences Between Metals and Composites
CONDITION
COMPOSITE BEHAVIOR RELATIVE TO METALS
Load –Strain Relationship
More Linear Strain to Failure
Notch Sensitivity: Static
Greater Sensitivity
Fatigue Less Sensitivity
Transverse Properties
Variability in Mechanical
Properties
Sensitivity to
Hygrothermal Environment
Damage Growth
Mechanism
Weaker
Higher
Greater
In-Plane Delamination Instead of ThroughThickness Cracks
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Elevated temperature and moisture reduce the material
operational limits.
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Degradation of S-Glass/Epoxy Tape
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
= 50oF
Ref. MIL. HNDBK. 17
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
In a multidirectional laminate, the stiff fibers in adjacent plies
will not let much contraction or swelling take place. Therefore...
due to matrix contraction.
due to matrix expansion.
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Any moisture absorbed into the resin causes each ply to try to
swell in the 2-direction.
Fiber Direction
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
At any temperature below the cure temperature, each ply in a
laminate wants to contract in the 2-direction.
Built-in thermal stresses resulting from post cure cool-down
to room temperature must be considered in the structural
analysis.
Fiber Direction
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Damage Tolerance Overview - Life Criteria
Non-Detectable Damage
Detectable Damage
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Application of Advanced Composites
to Helicopter Structures
Kt
Strengths and Weaknesses
Under static loading, composites have a higher
notch sensitivity than metals.
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Under fatigue loading, composites have a lower
notch sensitivity than metals.
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Composites must be protected against service environment.
Exposure to Fluids
Effect is accommodated by reduced
design allowables.
Apply conventional (polyurethane)
finishes.
Abrasion and Rain Erosion
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Composites must be protected against service environment.
Heat Absorption
Lightning Strike and P-Static
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Composites must be protected against galvanic corrosion.
BMS 5095 is Boeing
Material Specification
for sealant. Ref. Only.
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Structural Composites Property Definition
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Mathematicians have “saved the day.”
MATERIAL PROPERTIES AND LAMINATE ANALYSIS THEORY
There is an infinite number of combinations of material form
(tape and fabric), lamina ply orientation to the reference axis
(X) of the part, reinforcing fiber, ply stacking sequence, etc.,
from which the designer can select to best fit his need for
strength, stiffness, weight, damage tolerance, and/or
endurance of the resulting laminate. Having determined the
physical properties of the lamina by test, the calculation of the
properties and performance of the final laminate is very
complex and cannot be achieved without a computer. The
alternative was to build and test the actual laminate and still is
the best way, but $$$…$.
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Materials Properties and Laminate Analysis Theory
Physical Properties include ply (laminae) modulus, thickness, matrix/fiber fraction, and
weight. These properties are used with laminated plate theory to derive laminate
moduli, Poisson’s ratios, and thermal expansion coefficients. Laminated plate theory is
presented. Carpet plots providing laminate moduli have been verified by tests of
selected multi-directional layups.
Material Properties constitute the second category of structural composite properties.
Included are strain and stress statistical average B-basis values. Both unnotched and
notched material values are provided.
Structural Design Allowables are the third category of structural composite properties.
This information is to be used for the design and analysis of all structures. Structural
design allowables are not the same as material strengths, and the two categories should
not be used interchangeably. The structural design allowables are discussed in detail in
Section 4 of this presentation. Design allowables include all knock-down factors
required to accommodate statistical variations and losses due to manufacturing defects
and the environment.
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
The analysis for continuous fiber-reinforced, laminated
composites differs from that of metals because:-
a. The directionality of composite materials results in different
material properties with orientation.
b. Ply stacking sequence (position) and ply orientation can also affect
material properties, such as flexural stiffness and thermal stresses.
c. A major shift in emphasis from stress to strain is required for
composite analysis; strain is assumed constant and/or linear through
the thickness while stress varies from ply orientation.
d. Need to analyze each ply, each fiber direction in each ply, and
examine principle shear strain in each ply.
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Analyses of laminated composites utilize two types of
mathematical models to define material behavior:

Micromechanics models the interaction of constituent materials
within a composite, i.e., the fiber and matrix, to define composite
expected performance.

Macromechanics ignores the fiber-matrix behavior and models the
individual lamina (plies) as thin homogeneous orthotropic media in a
state of plane stress or strain.
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Classical Laminated Plate Theory
The basis for the majority of analysis methods for laminated composite materials is
classical laminate theory for thin plates (Kirchhoff’s thin plate hypothesis applies). The
basic building block in lamination theory is the individual lamina in a state of plane
stress. The following basic steps are used to establish laminate properties from lamina
(ply) properties.
1.
Establish the lamina (ply) properties on the ply axis directions (1, 2, and 3) for
each lamina. The constituent properties required are E 11, E22, G12,  12, 1,
and 2.
2.
Determine the lamina (ply) elastic stiffness and compliance (relationship)
matrices of stiffness [C] or [Q] and compliance [S] in the ply axes (1, 2 and 3)
based on the properties in Step 1.
3.
Determine the lamina (ply) properties transformed to the laminate axes (x, y,
and z) using the transformation matrix [T]. The transformed lamina properties
are the matrix functions [C] and [S].
4.
Stack the lamina properties (summed over the laminate thickness) and
determine the laminate extensional stiffness [A], coupling [B], and flexural
stiffness [D] matrices, and on the laminate axes (x, y, and z).
5.
Determine the laminate compliance relationships by inverting the stiffness
matrix for extension [A’], coupling [B’], and flexural stiffness [D’] on the
laminate axes (x, y and z).
6.
Determine the derived laminate properties E x, Ey, Gxy,  xy, x, and y on the
laminate axes (x, y and z).
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Establishing Lamina (Ply) Properties
Composite materials are treated in the analysis of
mechanical stress and strain states in a parallel
manner to metals. There are, however, four basic
material constitutive constants (E1, E2, G12, )
required rather than two (E, ) for isotropic
metals. The added properties reflect the large
differences in elastic properties parallel and
perpendicular to the fiber.
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Work in strain instead of stress.
Strain
Stress
P
P/S(E*A)
e*Elamina
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Work in strain instead of stress.
Ei=
Strain
Stress
ei*Elamina
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Lamina Ply 1, 2, 3 Coordinate System
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Laminate Ply X, Y, Z Coordinate System
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Laminate Theory for An Orthotropic (Different)
Properties in Material Lamina All Directions - 2-D
transpose
transpose
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
3-D Lamina Analysis
0
0
0
0
0
0
21
21
21
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Compliance
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
For An Isotropic Material (Homogeneous Metal)
NOTE THAT FOR AN ISOTROPIC MATERIAL
(SAME PROPERTIES IN ALL DIRECTIONS)
i.e. E1  E 2  E3  E ,
 1

 E
 1  
   E
 2  
3   E
   
 23   0
 31  
  
 12   0

 0

G13  G31  G12  G ,

E
1
E

E

E

E
1
E
0
0
0
0
0
0
0
0
0
1
G
0
0
0
1
G
0
0
0
0
 21   31   32  

0

0   1 
  
 2 
0   
3
 
0  1 
  2 
 
0   3 
1

G
G
E
2(1   )
OR
 1     
1
 2        2 S11  S1 
G
 E   E  
EXAMPLE: FOR A LOAD(σ 1 )
IN T HE(1) DIRECT IONONLY
I.E.  2   3   23   31   12  0
1 

 1  e 
 1  S11 *  1 





2  * 1  or 2 1 S12 * 1 
E


   S * 
 3 13 3 
3   *  
  E    0, since   0
1
2
3
WHICH AGREES WITH SIMPLE TENSION THEORY
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Stiffness Matrix (Inverted Compliance Matrix )
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Stiffness Matrix Applied to Isotropic Metals
and 
)(1-2)] then the terms in the stiffness (C)
If V =1/[(1+
matrix are:
Normal Stiffnesses:alone)
Couplings:-
C11=C22=C33=(1- )*V*E (not E
C12=C13=C23=( )*V*E
Shear Stiffnesses:-
C44=C55=C66=G=E/2(1- )
FOR ALUMINUM
=1/3 V=1/(4/3*1/3)=9/4
C11=C22=C33=(1-)*V*E =2/3*9/4*E =3/2*E = C11
C12=C13=C23=()*V*E
=1/3*9/4*E =3/4*E = C12
C44=C55=C66=G=E/2(1-** C44
NOTE: C11=C22=C33=3/2*10.5E06 =15.75E06lb/in^2
NOT=E
C12=C13=C23= 1/2* C11
= 7.87E06 lb/in^2
C 44=C55=C66= 1/4* C11
=G
= 3.94E06 lb/in^2
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Laminate Analysis
LAMINATE ANALYSIS
We have represented the material by an [S] matrix of compliance coefficients for each of the
three mutually orthogonal directions [1, 2, and 3]. A laminate is made up of layers (lamina),
each oriented in different directions relative to the common reference axes [x, y and z] of the
laminate.
The next step is to transform the lamina matrices so that their coefficients apply in the
laminate axes system.
q = 45o
q = 0o
q = -45o
A simplification can be applied by assuming that the out-of-plane stresses are neglible, i.e.,
3 = 0, 23 = 0 and 31 = 0.
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Laminate Analysis
LAMINATE ANALYSIS (continued)
This reduces each of the [6 x 6] compliance and stiffness matrices to [3 x 3]’s.
For each lamina in the laminate:
THSARTHBASICBUILDINGBLOCKSFORTH
CLASSICALLAMINATANALYSIS.
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Transformation Matrix
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Stress Strain Relationship
STRESS-STRAIN RELATIONSHIP
FOR EACH LAMINA
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Laminate Properties from Lamina Properties
We have transformed the ply lamina characteristics in the [1,2] system into the laminate
axes [x, y] system. So now we can build up the laminate by stacking one upon the other,
and assuming that the laminate is loaded, the resultant forces acting on the laminate can be
obtained by integrating the lamina stresses through the laminate thickness.
The resulting form is:
[A]= Extensional Stiffness Matrix
[B]= Bending Coupling Matrix
[D]= Bending Stiffness Matrix
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Composite Analysis Flow Diagram
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Comparison Between Engineering Constants of Angle-Ply
and Unidirectional Composite Lamina
Lamina
Laminate
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Inplane Stiffness and Strength
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Laminate Bending Behavior
STIFFER
STIFF
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
So far, we have considered one class of laminates.
Symmetric Balanced Laminate
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Unbalanced Laminates
Unbalanced and Nonsymmetric Laminates Result In Warping
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Unbalanced laminates shear when you pull on them.
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Unsymmetric laminates bend when you pull on them.
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Bending
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Curvature
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Coupling
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Laminate Average Tensile Modulus (Ex)
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Laminate Average Shear Modulus (Gxy)
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Thermal Expansion Coefficient
TYPICAL RANGE USED
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
GENLAM
“Composites Design”, by Stephen W. Tsai,
published by Think Composites, P.O. Box 581,
Dayton, Ohio 45419,
Telephone: (513) 429-4594
Explains the complicated processes in laminate analysis in great detail. With the book,
comes the “GENLAM” software. GENLAM is a through-the-thickness point stress analysis
that computes the strength and thickness of unsymmetric hybrid laminates subject to
complex in-plane mechanical and hygrothermal loads.
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
The absorption of moisture by the matrix is the major
environmental hazard to composite strength.
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Absorption of Moisture With Time
Saturation
Saturation
(Epoxy Matrix)
F/G 3% by Wt.
Gr
2% by Wt.
K49 4% by Wt.
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Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
Equilibrium Moisture Content as a Function of
Relative Humidity for AS/3501-6
57