Application of Advanced Composites to Helicopter Structures Strengths and Weaknesses Introduction...

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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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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Elevated temperature and moisture reduce the material operational limits.

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Degradation of S-Glass/Epoxy Tape

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= 50oFRef. MIL. HNDBK. 17

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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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Any moisture absorbed into the resin causes each ply to try to swell in the 2-direction.

Fiber Direction

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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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Damage Tolerance Overview - Life Criteria

Non-Detectable Damage Detectable Damage12




Under static loading, composites have a higher notch sensitivity than metals.

Kt

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Strengths and WeaknessesM

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Under fatigue loading, composites have a lower notch sensitivity than metals.

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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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Composites must be protected against service environment.

Heat Absorption

Lightning Strike and P-Static

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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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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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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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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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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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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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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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Work in strain instead of stress.

Strain Stress

e*ElaminaP/S(E*A)

P

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Work in strain instead of stress.

Strain Stressei*Elamina

Ei=

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Lamina Ply 1, 2, 3 Coordinate System

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Laminate Ply X, Y, Z Coordinate System

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transpose

transpose

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Laminate Theory for An Orthotropic (Different) Properties in Material Lamina All Directions - 2-D




0 0

00

0 0

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21 21

3-D Lamina Analysis

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Compliance

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(SAME PROPERTIES IN ALL DIRECTIONS)

i.e. 323121123113321 , , GGGGEEEE

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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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Stiffness Matrix (Inverted Compliance Matrix )

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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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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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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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Transformation Matrix

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STRESS-STRAIN RELATIONSHIPStress Strain Relationship

FOR EACH LAMINA

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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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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




Inplane Stiffness and Strength

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Laminate Bending Behavior

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STIFFER STIFF




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Symmetric Balanced Laminate

So far, we have considered one class of laminates.




Unbalanced Laminates

Unbalanced and Nonsymmetric Laminates Result In Warping

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Unbalanced laminates shear when you pull on them.

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Unsymmetric laminates bend when you pull on them.

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Bending

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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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The absorption of moisture by the matrix is the major environmental hazard to composite strength.

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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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Equilibrium Moisture Content as a Function of Relative Humidity for AS/3501-6

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Application of Advanced Composites to Helicopter Structures Strengths and Weaknesses Introduction...

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