Vibration Damping Characteristics in Aerospace

Composite Materials

Dr Zaffar M. KhanInstitute of Space Technology, Islamabad

What are Composite Materials

Composite materials are macroscopic combination of two or more materials complimenting each other such that resulting product has superior properties:

1.Matrix (Black)2.Reinforcement Fibers (White)3.Inter-phase

STRONGER THAN STEEL YET LIGHTER THAN

ALUMINIUM

Boeing 7E7 Composite Structure.

• 1st Plastic Fuselage: composites 50% by weight.

• T800/ 924C carbon-toughened epoxy.

• Produced by carbon prepregtape onto rotating mendralmechanically.

The vibration damping characteristics of composites are far superior as compared to metals for following reasons;

1.Matrix visco-elastic effects andmicro-cracking

2.Blunting of crack by in fiberstransverse direction

3.Debonding and sliding of fibersin axial direction.

Influence of Vibrations on Composites

Fatigue Life of Composite Structures

CRACK PROPAGATION IN METALS AND COMPOSITES

TENSILE FAILURE

Energy Absorption Mechanism

Factor Affecting Energy Absorption

• Matrix: Toughened Epoxy, Thermplastics.• Fibers: Kevlar, Polyethylene fibers.• Interface treatment-Mechanical/ chemical

locking.• Fiber orientation wrt applied load.• Surface area of reinforcement: Nanofibers/

nanoparticles.

Superelastic behavior

T > Af

Hysteresis loop means energy dissipation, hence vibration damping

Stress

D

o

o

Hysteresis loop for a viscoelastic material

D = energy dissipation per cycle

Stress

Strain

Cyclic Bending Stiffness Test

• Bending stiffness tests consist of application of five (05) cyclic loads on the wings.

• Deflection (mm) is calculated using a linear regression method.

• The mean slope leads to determination of average bending stiffness.

• The values from bending stiffness and maximum deflection were used to calculate hysteresis percentage (H).

• The slopes of maximum bending stiffness, their differences, the projected zero load deflection and hysteresis value were found to be within limits as indicated in Fig

Cyclic Bending Stiffness Test

Cyclic Stiffness Test

-6

-4

-2

0

2

4

6

-80 -60 -40 -20 0 20 40 60 80

Di spl acement ( mm)

Structural Certification

• The wings must be able to sustain the aerodynamic loads and maintain its structural rigidity for stable flight configuration. The bending stiffness, the cyclic load, torsional stiffness and the difference between bending/ torsion stiffness in post/ SB wings were found to be well within the design limits 10 kN/m and 10 kNm/rad.

Test Parameters Units Allowable Limits Wing Port Wing Stbd

Hysteresis % 0~2 1.55 1.68

Bending Stiffness Upward unit kN/m 82~96 90.91 91.17

Bending Stiffness Downward unit kN/m 82~96 89.80 89.68

Mean Bending Stiffness unit kN/m 82~96 90.35 90.42

Torsional Stiffness unit kN-m/rad 50~63 61.91 59.21

Spring Mass Damper Systewm

• Let’s diagram our hardware. We have a “sprung mass” M and a spring with stiffness K.

• We also have a friction or damping element C. • C is not always visible, but is always present. No system exists without

some damping

Damping

Damping is the decrease in amplitude with time due to the resistance of the medium to the vibration.

Damping occurs progressively as energy is taken out of the system by another force such as friction. Damping is the conversion of mechanical energy of a structure into thermal energy. The amount of energy dissipated is a measure of the structure’s damping level.

If the damping is enough that the system just fails to oscillate, then it is said to be critically damped. The minimum damping that will prevent or stop oscillation in the shortest amount of time is critical damping.

Damping more than this is referred to as over damping and less is similarly underdamped.

Logarithmic Decrement

• Q = amplification factor (ratio of the response amplitude at resonance ω0 to the static response at ω = 0)

• Half-power bandwidth method (3 dB method)

• Loss factor,

Viscoelastic material

• A material in which the total strain developed has elastic and viscous components.

• Part of the total strain recovers similar to elastic strain.

• Some part of the total strain recovers over a period of time.

• Examples: polymer melts.

The combined viscous and elastic behavior (viscoelasticity) can be examined by determining the effect that an oscillating force has on the movement of the material.

All the energy stored during loading is returned when the load is removed.

Stress is proportional to strain.

φ = 0°

The material does not return any of the energy stored during loading. All the energy is lost once the load is removed.

Stress is proportional to the strain rate.

φ = 90°

Some of the energy stored is recovered upon removal of the load; the remainder is dissipated in the form of heat.

The angel φ (0 < φ < 90°) is a measure of the damping level.

G* = G' + iG'‘where G* is the complex shear modulus, G' is the in-phase storage modulus and G'' is the out-of-phase loss modulus; G* = √(G'2 + G''2). The frequency where these parameters cross over corresponds to a relaxation time () specific for the material.

tan δ = G''/G’where tan δ (also called loss tangent) quantifies the balance between energy loss and storage.

As tan 45° =1, a value for tan greater than unity indicates more "liquid" properties, whereas one lower than unity means more "solid" properties, regardless of the viscosity.

Constrained layer damping

• Embedding a viscoelastic layer in a structural material

• Shear deformation of viscoelastic layer provides energy dissipation.

• Slight slippage at interface during vibration providing a mechanism for damping.

• Defects such as dislocations contribute to damping.

Use of interfaces for damping

Discontinuous nanofiber between continuous conventional fiber layers for damping enhancement

Tough competition with composites with viscoelastic interlayer for damping

Hybrid composite composition

Nanofiber: 0.6 vol.%Continuous carbon fiber: 56.5

vol.%

Carbon nanofiber

Fishbone morphology 0.16 micron diameterDiscontinuous IntertwinedHollow channel along axis of

nanofiberGrown catalytically from methane

Nanofiber as interlaminar filler

Nanofiber enhances both transverse and longitudinal vibration damping ability (due to large area of the interface between nanofiber and matrix)

Nanofiber increases the transverse storage modulus (due to presence of nanofibers that are oriented near the direction perpendicular to the fiber layers)

Nanofiber decreases the longitudinal storage modulus slightly.

Table 1 Dynamic flexural behavior of materials at 0.2 Hz.

Material tan Storage modulus (GPa) Loss modulus (GPa)

Cement paste (plain) 0.016 13.7 0.22

Mortar (plain) < 10-4 9.43 < 0.001

Mortar with silica fume (treated) (15% by wt. of cement)

0.021 13.11 0.28

Aluminum, pure 0.019 51 1.0

Al/AlNp (58 vol.%) 0.025 120 3.0

Zn-Al 0.021 74 1.5

Zn-Al/SiCw (27 vol.%) 0.032 99 3.0

Carbon-fiber epoxy-matrix composite (without interlayer)

0.008 101 0.8

Carbon fiber epoxy-matrix composite (with vibration damping interlayer)

0.017 92 1.6

Neoprene rubber 0.67 0.0075 0.0067

PTFE 0.189 1.2 0.23

PMMA 0.09 3.6 0.34

PA-66 0.04 4.4 0.19

Acetal 0.03 3.7 0.13

Epoxy 0.03 3.2 0.11

Matrix Polystyrene High Density

(BDH with molecular weight

100,000)

Filler Particles Carbon Black

(Printex ® L6, Degussa,

Germany)

Substrate E-Glass fibre woven

reinforcement

Solvent Benzene

Medium for electrical

connections

Conductive silver paint

(RS 186-3600)

Materials Specifications

The Equations governing to calculate the Resistivity , stress, strain

0outV

Under balanced configuration the Vout is zero, i.e. the sum of the two voltages of the voltage dividers is equal (considering the branches of Wheatstone bridge),

)()(

)()(

43

4

21

1

RRR

VRR

RV inin

3

4

2

1

RR

RR

From this it is evident that if anychange occurs in R4 (gaugeresistance), R3 has to be changed inorder to balance the bridge i.e. tomaintain Vout at zero

4

44tanReR

RRRRcesisNormalised

Instrumentation amplifier INA 101 is used for signal amplification purpose.

Circuit Diagram of INA 101

Fatigue testing of specimens with Data Acquisition Setup

Universal Testing Machine

Mounted Specimen

Electrical wires connecting specimen to module

Keithley KUSB 310

Personal Computer

(a) (b)

(c)

(a) Full experimental setup(Data Acquisition setup with specimen

mounted in UTM) (b) Mounted specimen (c) Electrical connection using

Conductive Silver Paint

1. Dynamic response of PS/CB coating sensor isinvestigated.

2. Multicyclic Fatigue tests were performed to check therepeatability of the sensor.

3. The dimensions of these specimens are reported in table.4. A smart PS/CB sensing layer described earlier was

deposited on 8 layered cross ply GFRP specimens in thecenter using doctor blade and a slot die.

5. The lengths of these smart layers on the specimensurfaces and the testing parameters have also beenmentioned in table

Dynamic response of Smart PS/CB Coated Composite structures

SpecimenNo

File name

Widthmm

Specimen length

Thickness

(mm)

Piezo Gauge Length (mm)

Initial resistance(Kohms)

Gain Resistance

Rg (Kohms)

Input voltage

V

Initial force(ma

chine)KN

Amplitude(mm)

1 Spec-1 25.3 24.9 cm 1.05 10 3.9 50+15 to -15

V3.1 0.55

2 Spec-2 25.3 24.9 cm 1.14 12.3 8.6 50+15 to -15

V0.63 0.25

3 Spec-3 25.8 24.9 cm 1.10 11.54 7.0 50+15 to -15

V0.63 0.25

4 Spec-4 25.7 24.95 cm 1.07 12.32 10.8 50+15 to -15

V0.63 0.25

5 Spec-5 25.5 24.95 cm 1.10 12.81 11.8 50+15 to -15

V0.63 0.25

6 Spec-6 25.1 24.95 cm 1.11 12.91 10.4 50+15 to -15

V0.63 0.25

Geometry & Testing Parameters

Specimens with smart coating and conductive silver paint connections

• Gain for amplification of resistance data was set at 1.8.

• These specimens were mounted on MTS 810 for tensile

loading.

• A maximum load of 5% of the breaking load was applied

in multicyclic configuration.

• The strain rate kept constant 1mm/sec for all specimens.

• Total numbers of cycles were kept 20 for all the tests.

• The frequency of cyclic loading was 0.5 Hz.

•Specimen 1 broke out immediately from grips after only 3

cycles because of high Initial force (Machine 3.1 KN) applied.

• Then it has been reduced for next specimens as per 5%

breaking load (0.63 KN= 25 % of 475 MPa).

•The results are presented in Fig. 5.13, Fig 5.14, Fig 5.15, and

Fig 5.16.

Multicyclic Fatigue (Time-Strain) diagram compared with dR/R-Strain for the specimen 3

Multicyclic Fatigue (Time-Strain) diagram compared with dR/R-Strain for the specimen 4

Multicyclic Fatigue (Time-Strain) diagram compared with dR/R-Strain for the specimen 5

Multicyclic Fatigue (Time-Strain) diagram compared with dR/R-Strain for the specimen 6

•These plots demonstrate that the sensors are capable of followingloading and unloading cycles of the specimens without any offset ordelay.

•This particular characteristic of smart layers can be effectively used forlong term life cycle monitoring of composite parts in civil andaeronautical structures.

Conclusions

•The PS/CB coating sensor showed repeatability when multicyclicloadings were applied. The intelligent coating effectively respondedto the applied strain under dynamic conditions.

•The cyclic response of the smart coating shows that the sensors arecapable of following loading and unloading cycles of thespecimens without any delay.