application of advanced composites to helicopter structures strengths and weaknesses introduction...
TRANSCRIPT
Application of Advanced Composites
to Helicopter Structures
Strengths and Weaknesses
IntroductionComposites 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
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Strengths and Weaknesses
CONDITION COMPOSITE BEHAVIOR RELATIVE TO METALSLoad –Strain Relationship More Linear Strain to FailureNotch Sensitivity: Static Greater Sensitivity Fatigue Less Sensitivity
Transverse Properties WeakerVariability in MechanicalProperties
Higher
Sensitivity toHygrothermal Environment
Greater
Damage GrowthMechanism
In-Plane Delamination Instead of Through-Thickness Cracks
Differences Between Metals and Composites
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Application of Advanced Composites
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Strengths and Weaknesses
Elevated temperature and moisture reduce the material operational limits.
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Application of Advanced Composites
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Degradation of S-Glass/Epoxy Tape
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Application of Advanced Composites
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Strengths and Weaknesses
= 50oFRef. MIL. HNDBK. 17
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Application of Advanced Composites
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Strengths and Weaknesses
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Application of Advanced Composites
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Application of Advanced Composites
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Application of Advanced Composites
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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
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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
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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
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Damage Tolerance Overview - Life Criteria
Non-Detectable Damage Detectable Damage12
Application of Advanced Composites
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Under static loading, composites have a higher notch sensitivity than metals.
Kt
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Application of Advanced Composites
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axim
um
Co
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n F
atig
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Str
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Under fatigue loading, composites have a lower notch sensitivity than metals.
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Application of Advanced Composites
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Strengths and Weaknesses
Composites must be protected against service environment.
Exposure to Fluids
Abrasion and Rain Erosion
Effect is accommodated by reduced design allowables.
Apply conventional (polyurethane) finishes.
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Application of Advanced Composites
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Composites must be protected against service environment.
Heat Absorption
Lightning Strike and P-Static
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Application of Advanced Composites
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Composites must be protected against galvanic corrosion.
BMS 5095 is Boeing Material Specification for sealant. Ref. Only.
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Structural Composites Property Definition
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Application of Advanced Composites
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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 forstrength, stiffness, weight, damage tolerance, and/orendurance of the resulting laminate. Having determined thephysical properties of the lamina by test, the calculation of theproperties and performance of the final laminate is verycomplex and cannot be achieved without a computer. Thealternative was to build and test the actual laminate and still isthe best way, but $$$…$.
Mathematicians have “saved the day.”
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Application of Advanced Composites
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Physical Properties include ply (laminae) modulus, thickness, matrix/fiber fraction, andweight. These properties are used with laminated plate theory to derive laminatemoduli, Poisson’s ratios, and thermal expansion coefficients. Laminated plate theory ispresented. Carpet plots providing laminate moduli have been verified by tests ofselected 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 andnotched 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. Structuraldesign allowables are not the same as material strengths, and the two categories shouldnot be used interchangeably. The structural design allowables are discussed in detail inSection 4 of this presentation. Design allowables include all knock-down factorsrequired to accommodate statistical variations and losses due to manufacturing defectsand the environment.
Materials Properties and Laminate Analysis Theory
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Application of Advanced Composites
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a. The directionality of composite materials results in differentmaterial properties with orientation.
b. Ply stacking sequence (position) and ply orientation can also affectmaterial properties, such as flexural stiffness and thermal stresses.
c. A major shift in emphasis from stress to strain is required forcomposite analysis; strain is assumed constant and/or linear throughthe thickness while stress varies from ply orientation.
d. Need to analyze each ply, each fiber direction in each ply, andexamine principle shear strain in each ply.
The analysis for continuous fiber-reinforced, laminated composites differs from that of metals because:-
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Application of Advanced Composites
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Micromechanics models the interaction of constituent materialswithin a composite, i.e., the fiber and matrix, to define compositeexpected performance.
Macromechanics ignores the fiber-matrix behavior and models theindividual lamina (plies) as thin homogeneous orthotropic media in astate of plane stress or strain.
Analyses of laminated composites utilize two types of mathematical models to define material behavior:
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Application of Advanced Composites
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The basis for the majority of analysis methods for laminated composite materials isclassical laminate theory for thin plates (Kirchhoff’s thin plate hypothesis applies). Thebasic building block in lamination theory is the individual lamina in a state of planestress. 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) foreach lamina. The constituent properties required are E11, 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 propertiesare the matrix functions [C] and [S].
4. Stack the lamina properties (summed over the laminate thickness) anddetermine the laminate extensional stiffness [A], coupling [B], and flexuralstiffness [D] matrices, and on the laminate axes (x, y, and z).
5. Determine the laminate compliance relationships by inverting the stiffnessmatrix for extension [A’], coupling [B’], and flexural stiffness [D’] on thelaminate axes (x, y and z).
6. Determine the derived laminate properties Ex, Ey, Gxy, xy, x, and y on thelaminate axes (x, y and z).
Classical Laminated Plate Theory
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Application of Advanced Composites
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Composite materials are treated in the analysis ofmechanical stress and strain states in a parallelmanner to metals. There are, however, four basicmaterial constitutive constants (E1, E2, G12, )required rather than two (E, ) for isotropicmetals. The added properties reflect the largedifferences in elastic properties parallel andperpendicular to the fiber.
Establishing Lamina (Ply) Properties
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Application of Advanced Composites
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Work in strain instead of stress.
Strain Stress
e*ElaminaP/S(E*A)
P
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Application of Advanced Composites
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Work in strain instead of stress.
Strain Stressei*Elamina
Ei=
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Application of Advanced Composites
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Lamina Ply 1, 2, 3 Coordinate System
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Application of Advanced Composites
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Laminate Ply X, Y, Z Coordinate System
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Application of Advanced Composites
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transpose
transpose
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Laminate Theory for An Orthotropic (Different) Properties in Material Lamina All Directions - 2-D
Application of Advanced Composites
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Strengths and Weaknesses
0 0
00
0 0
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21 21
3-D Lamina Analysis
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Application of Advanced Composites
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Compliance
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(SAME PROPERTIES IN ALL DIRECTIONS)
i.e. 323121123113321 , , GGGGEEEE
3
2
1
3
2
1
12
31
23
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1
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N O T E T H A T F O R A N I S O T R O P I C M A T E R I A L
111 2 1
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LOADA FOR :
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0 since ,0321
W H I C H A G R E E S W I T H S I M P L E T E N S I O N T H E O R Y
For An Isotropic Material (Homogeneous Metal)
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Application of Advanced Composites
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Stiffness Matrix (Inverted Compliance Matrix )
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Application of Advanced Composites
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Stiffness Matrix Applied to Isotropic Metals
and
If V =1/[(1+)(1-2)] then the terms in the stiffness (C)matrix are:
Normal Stiffnesses:- C11=C22=C33=(1-)*V*E (not Ealone)
Couplings:- C12=C13=C23=()*V*E
Shear Stiffnesses:- C44=C55=C66=G=E/2(1-)
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 = 3.94E06 lb/in^2 =G
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
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Application of Advanced Composites
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LAMINATE ANALYSIS
We have represented the material by an [S] matrix of compliance coefficients for each of thethree 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 thelaminate.
The next step is to transform the lamina matrices so that their coefficients apply in thelaminate axes system.
A simplification can be applied by assuming that the out-of-plane stresses are neglible, i.e.,
3 = 0, 23 = 0 and 31 = 0.
Laminate Analysis
q = 45o
q = 0o
q = -45o
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Application of Advanced Composites
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LAMINATE ANALYSIS (continued)
This reduces each of the [6 x 6] compliance and stiffness matrices to [3 x 3]’s.
Laminate Analysis
For each lamina in the laminate:
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Application of Advanced Composites
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Transformation Matrix
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Application of Advanced Composites
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STRESS-STRAIN RELATIONSHIPStress Strain Relationship
FOR EACH LAMINA
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Application of Advanced Composites
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We have transformed the ply lamina characteristics in the [1,2] system into the laminateaxes [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 beobtained 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
Laminate Properties from Lamina Properties
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Application of Advanced Composites
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Composite Analysis Flow Diagram
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Lamina
Laminate
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Comparison Between Engineering Constants of Angle-Ply and Unidirectional Composite Lamina
Application of Advanced Composites
to Helicopter Structures
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Inplane Stiffness and Strength
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Laminate Bending Behavior
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STIFFER STIFF
Application of Advanced Composites
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Symmetric Balanced Laminate
So far, we have considered one class of laminates.
Application of Advanced Composites
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Unbalanced Laminates
Unbalanced and Nonsymmetric Laminates Result In Warping
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Application of Advanced Composites
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Unbalanced laminates shear when you pull on them.
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Application of Advanced Composites
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Unsymmetric laminates bend when you pull on them.
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Application of Advanced Composites
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Bending
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Application of Advanced Composites
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Curvature
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Coupling
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Laminate Average Tensile Modulus (Ex)
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Laminate Average Shear Modulus (Gxy)
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Thermal Expansion Coefficient
TYPICAL RANGE USED
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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 analysisthat computes the strength and thickness of unsymmetric hybrid laminates subject tocomplex in-plane mechanical and hygrothermal loads.
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Application of Advanced Composites
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The absorption of moisture by the matrix is the major environmental hazard to composite strength.
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Application of Advanced Composites
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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
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Equilibrium Moisture Content as a Function of Relative Humidity for AS/3501-6
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