Vibrations and fatigue- vibration interactions of laminated composites

Study of Vibration Characteristics and Interaction of Cyclic Fatigue Loading on Vibration Responses of Thin Walled Woven Fabric Glass-

Carbon Epoxy Composites for Structural Applications

R. Murugan (Reg.No. 2714299703/PhD/AR7)

Research Scholar, Department of Mechanical Engineering, Sri Venkateswara College of Engineering, Sriperumbudur

SupervisorDr. K. PADMANABHANProfessor and Assistant Director

Centre for Excellence in Nano Composites

School of Mechanical & Building Sciences VIT University, Vellore

Joint SupervisorDr. R. RAMESHProfessorDepartment of Mechanical EngineeringSri Venkateswara College of Engineering Sriperumbudur – 602117

Introduction

Woven fabric reinforced polymer composites are the most widely used forms of textile composites

In woven fabric composite, fiber strands are interlaced in two mutually orthogonal directions to one another,

which promote Excellent integrity and

conformability More balanced properties within

the fabric plane 2

warp

weft

3

Woven fabric composites are more popular in structural applications such as

Automotive structuresAircraft structuresMarine structure etc.

Composite structures used in such applications experiencing vibration and considerable cyclic loading in operations, are inevitable in dynamic conditions

In all dynamic service conditions, to perform well, these composite structures should possess good vibration damping along with high stiffness

Introduction

Literature Review - Summary

Many researchers have contributed towards evaluation of Vibration performance of fiber reinforced polymer matrix composites but in the form of unidirectional and cross ply laminates

There are many investigations on damping performance/behaviour of various types of fundamental fibers as reinforcement under both analytical and experimental approach

The evaluation by controlling the geometric parameters like fibre orientation and laminate configuration was extensively studied with free end conditions and as well offering other boundary conditions

Limited experimental work/attention on vibration performance of woven fabric/hybrid fabric composite laminates

Increase in material damping along with stiffness of woven fabric polymeric composite by hybridization approach is much important for structural applications

There is little work on interaction of cyclic fatigue loading and Vibration characteristics of woven fabric hybrid composite beams

4

Detailed Literature survey reports that,

Objective of Research work

5

The main objective of the research work is

To understand and investigate the vibration characteristics, interaction of cyclic fatigue loading on vibration responses of thin walled woven fabric Glass-Carbon/Epoxy composites

To characterize the hybrid composites for automotive and aircraft structural applications

The objective includes : Understanding the Mechanical Properties of Dedicated Glass/Carbon

and its Hybrid composite laminates Evaluation of vibration characteristics of Hybrid composite plates

made of Glass/Carbon fabrics with different aerial density under free vibrating condition

Experimental investigation on modal analysis of thin walled composite beams for structural application

Study of Influence of the stacking sequence on vibration characteristics of beams of Glass/Carbon layered arrangement

Influence of size effect of hybrid composite beams on vibration characteristics using Finite Element Analysis for higher operating frequency range

Design and development of displacement controlled cyclic test rig to apply completely reversed cyclic bending stress on composite specimen

Influence of cyclic fatigue loading on vibration characteristics of composite beams

Modal response study of hybrid composite beams after cyclic loading.

6

7

Fabrication of Glass/Carbon Hybrid Composite Laminates with Different Fiber Aerial Densities using Epoxy as matrix

Fibers and Matrix material considered

Fiber: Plain woven fabric Type

E-GlassT300 Carbon

Aerial Density 200 gsm, 400 gsm , 600

gsmgsm – gram per square metre

Matrix: Epoxy - LY556Hardener - HY951

8

E-Glass Fabric

T300 Carbon fabric

Warp

Weft

Warp

Weft

Epoxy and Hardner

9

Specimen prepared by

Hand Layup technique

Cured for 24 hours with nominal pressure of 2.5 MPa in

Compression Moulding Machine

at room temperature

Volume fraction of laminate

Vf - 0.5

Processing by Hand Lay up technique

Curing by Compression Moulding Machine

Method of Fabrication

May 1, 2023 10

Symbol Aerial Density Specimen description Layer sequence

H1200200 gsm

4 layered Hybrid laminate Outer – Glass & Inner – Carbon GCCG

H22004 layered Hybrid laminate Outer – Carbon & Inner – Glass CGGC

H1400

400 gsm4 layered Hybrid laminate Outer – Glass & Inner – Carbon GCCG

H2400 4 layered Hybrid laminate Outer – Carbon & Inner – Glass CGGC

H1600

600 gsm

4 layered Hybrid laminate Outer – Glass & Inner – Carbon GCCG

H2600 4 layered Hybrid laminate Outer – Carbon & Inner – Glass CGGC

4G Dedicated 4 layered Glass laminate GGGG

4C Dedicated 4 layered Glass laminate CCCC

The layer arrangement of hybrid beam was selected in concerned towards

the balanced modulus property both in longitudinal and transverse direction w. r. t neutral axis of the beam

Types of Composite laminates fabricated

11

Fabricated Composite Plates

H1600 H1400 H1200

H2600 H2400 H2200

SymbolDimensions

(l*w*t)mm

H1200 250*250*1.0

H2200 250*250*1.0

H1400 250*250*1.8

H2400 250*250*1.8

H1600 250*250*2.4

H2600 250*250*2.4

Hybrid samples with different Aerial Density fabricated using Hand layup technique

Confirmation of Fiber Weight fraction through Burnout Test

ASTM STD: D3171-09 Sample Size: 25 x 25 mm The specimens were placed in an electric

furnace for 6 hrs at a temperature of 500oC Before and after the burn out test, the

specimens were weighed using a sensitive electronic balance

The fiber volume fractions of all the laminates were accurately estimated and the variation was found to be 2.5%

12Electronic

Balance

Electric Furnace

Mi = Initial mass of specimen (g) Mf = Final mass of specimen (g)

For 600 gsm

Specimen Mi(g)

Mf(g) Vol%

4G 2.454 1.501 48.28

4C 2.450 1.516 52.47

H1 2.347 1.447 47.41

H2 2.370 1.464 47.53

Understanding the Mechanical Properties of Dedicated Glass/Carbon and their Hybrid Composite Laminates

13

Evaluation of Tensile Strength

Make: SHIMAD2U Feed Rate: 5 mm/min Standard: ASTM 3039

14

190

250

End Tab length = 30

All Dimensions are in mm

25

Evaluation of Flexural Strength

Make: INSTRON 3382 Feed rate: 1.2 mm/min Standard: ASTM D790 Span : Thick = 16:1

15

W

48

63

12.5


16

Dynamic Mechanical Analysis Test

Standard : ASTM D4065Instrument : TA Q800 Frequency : 1 Hz Temperature Range : 30oC and

140oC Heating Rate : 5oC/min Amplitude : 15m Specimen Size : 63 13 t mm3

63

13


17

Mechanical Properties of Hybrid Composite Laminates of Three Different

Aerial Densities

* * Reported values are the average values obtained from four trials

Specimen

Tensile Strength(MPa)

Flexural Strength (MPa)

200 gsm

400 gsm

600 gsm

200 gsm

400 gsm

600 gsm

H1 286.41 342.57 413.62 314.38 392.97 491.21

H2 275.48 338.02 410.41 324.63 405.79 507.24

Irrespective of fibre aerial density, there is small variation in tensile and flexural strength among hybrid laminates

18

Static Mechanical Properties of Dedicated and Hybrid Composite Laminates

* * Reported values are the average values obtained from four trials

Specimen Tensile strength[MPa]

Flexural Strength[MPa]

4G 365.79 378.40

4C 462.08 573.27

H1 413.62 491.21

H2 403.41 507.24

Source: Murugan R, Padmanabhan K, Ramesh R, “Vibration Characteristics of Thin Walled Hybrid Carbon Composite Beams under Fixed Free Boundary Condition” in 3rd Asian Conference on Mechanics of Functional Materials and Structures (ACMFMS 2012) held on 5th -8th December 2012 at Indian Institute of Technology, New Delhi

Fibre Aerial Density 600 g/m2

19

Maximum stress is found for dedicated carbon laminate arrangement, 4C

Considerable tensile strength variation between dedicated 4G glass beam and dedicated 4C carbon laminate

This is due to high resistance offered by high modulus carbon fibre against tensile loading

0

100

200

300

400

500

600

4G 4C

Tensile Strain

Tens

ile S

tres

s (M

Pa)

Tensile behaviour of Composite Laminates

0 0.010.020.030.040.050.060.070.080.09 0.10

50100150200250300350400450500

H1 H2

Tensile Strain

Tens

ile S

tres

s (

MPa

)

Among hybrids, there is small variation in tensile strength irrespective of fiber aerial density

Tensile strength of H1 is greater than H2 Though the four layers of hybrid

laminate are equally loaded during tensile testing condition, the variation in axial strain between glass and carbon layers caused the marginal difference in tensile strength

Dedicated Glass, Carbon Laminates

Glass, Carbon Hybrid Laminates

20

Flexural strength of composite laminate is majorly controlled by the strength of outer layer which is in direct contact to bending load

There is a considerable flexural strength variation between dedicated 4G glass laminate and dedicated 4C carbon laminate

0 1 2 3 4 5 6 70

100

200

300

400

500

600

700

4G 4C

Deflection (mm)

Load

(N

)Flexural behaviour of Composite Laminates

0 1 2 3 4 5 60

50

100

150

200

250

300

350

400

450

H1 H2

Deflection (mm)

Load

(N

)

Among hybrid samples, H2 arrangement has higher flexural strength than H1 arrangement in all types of laminates

This is because the laminate in which high modulus carbon fibre is plied as outer layer offers more resistance to flexural loading than low modulus glass fibre plied as inner layer

Dedicated Glass, Carbon Laminates

Glass, Carbon Hybrid Laminates

21

Epoxy based woven fabric composites are viscoelastic in nature which exhibit a combination of both elastic and viscous behaviour

Complex modulus notation (E*) is used to define the viscoelastic material as shown in the following Equation

E* = E’ + E” = E’[1 + i (tan)]

where E’ = the elastic storage modulus, a measure of stored energy,

E” = the loss modulus, a measure of dissipation of energy as heat,

tan =the loss factor or damping factor

Characterization of composite material should include both the static mechanical properties like tensile, flexural

strength, etc. and the dynamic mechanical properties such as storage modulus, loss modulus and loss factor

Need for DMA study

22

Variation of Storage Modulus

Storage modulus E’ values increased with the increase of carbon fibre content

High modulus carbon fibre of dedicated carbon laminate caused the large storage modulus than dedicated glass laminate

Storage modulus of hybrid laminate H2 is higher than other laminates including dedicated carbon laminate due to Synergy and positive hybrid effect

There is significant fall in the storage modulus between the temperatures 80oC and 100oC

Increasing the temperature beyond the glass transition temperature Tg causes the change in state of composite laminates from solid to rubbery

Variation of Storage Modulus of

Dedicated Glass, Carbon and its Hybrid Laminates made of 600 gsm Fibre Aerial Density

Storage modulus (E’) is the measure of stores energy per cycle in a viscoelastic material under dynamic condition

20 30 40 50 60 70 80 90 100 110 120 130 140 1500

2000400060008000

1000012000140001600018000200002200024000

4GH1H2

Temperature (oC)

Stor

age

Mod

ulus

(G

Pa)

23

The glass transition temperature Tg of the resin is measured from the peak of the loss modulus curve as per ASTM D4065

The transition peak occurs at 85oC for the dedicated glass laminate and for the dedicated carbon laminate, it is 95oC

The increase in Tg, from 85oC to 90oC, with respect to 4G, is due to the

immobilization of the polymer molecules near the surface of the carbon fibre Loss modulus of hybrid laminate H2 is much higher than the other laminate H1

and raises to a larger extent than dedicated glass laminate, 4G Increased energy absorption due to the layering sequence, CGGC, caused the

large increase (89%) in loss modulus peak in hybrid H2

Variation of Loss Modulus

Variation of Loss Modulus of Dedicated Glass, Carbon and

its Hybrid Laminates made of 600 gsm Fiber Aerial Density

Loss modulus (E”) is the measure of dissipated heat energy per cycle in a viscoelastic material under dynamic condition

20 30 40 50 60 70 80 90 100 110 120 130 140 1500

500

1000

1500

2000

2500

3000

3500

4GH1

Temperature (oC)

Loss

Mod

ulus

(G

Pa)

24

00.050.1

0.150.2

0.250.3

0.350.4

0.450.5

95

10095

90

4GH1

Temperature (oC)

Tan

Variation of Loss Factor

Variation of Loss Factor of Dedicated Laminates made of 600 gsm Fiber Aerial Density

Loss factor (Tan), the ratio of the loss modulus to the storage modulus (E”/E’), gives balance between the elastic and viscous phase in a polymeric material

Below Tg, the chain segments present in the resin are in frozen state causes low Tan values in all laminates

In the transition region resin molecules attain high mobility which causes high Tan values

The Tan value is high for hybrid laminate, H2, than dedicated carbon and dedicated glass laminate

Among hybrids, transition peak values, Tg are same as 95oC however the Tan value at the Tg is 17% higher for H2 arrangement than H1 arrangement

25

3 3.2 3.4 3.6 3.8 4 4.2 4.4 4.61

1.5

2

2.5

3

3.5

4

4GH1H24C

Log E'

Log

E"

Imperfect semi-circular curve of dedicated and hybrid composite laminates indicates the heterogeneity of the laminates with a good matrix and fibre bonding

Cole-Cole Plot

Measure viscoelastic properties of FRP materials

Perfect semi-circle for pure polymeric material

26

SpecimenStorage Modulus

(E’max) [GPa]

Loss Modulus (E”max) [GPa]

Tg from E”max

[oC]

4G 12.684 1.665 85

4C 18.849 1.250 95

H1 13.033 1.771 90

H2 21.601 3.150 90

Dynamic Mechanical Properties of Dedicated and Hybrid Composite Laminates - Summary

27

SummaryStatic Mechanical Properties Investigations on variation of mechanical properties of woven fabric composite

laminates for varying stacking sequence with different fiber aerial density were carried out

Dedicated carbon laminate has higher mechanical strengths than dedicated glass laminate

Laminate with glass as envelope layer, H1 (GCCG), has marginally higher tensile strength than the other arrangement H2 (CGGC)

Carbon enveloped hybrid laminate, H2 (CGGC), has higher flexural strength

Dynamic Mechanical Properties Storage modulus, loss modulus and loss factor of hybrid laminate H2 is greater than

H1 hybrid laminate and dedicated carbon laminate

The glass transition temperature, Tg of H2 laminate was shifted through 5o C from dedicated glass laminate which facilitates the higher operating temperature

Hybrid laminate with carbon fibre as enveloping layer, H2, performs better than other hybrid arrangement, H1

28

Evaluation of vibration characteristics of Hybrid composite plates made of Glass/Carbon fabrics with different aerial density under free vibrating condition

Quasi Static Table with Impulse Excitation Testing facility

29

Impulse excitation technique Free-free boundary condition Impulse hammer (DYTRAN®)

is used to induce the excitation

Flexural vibrations of the hybrid composite plates were tapped by a dynamic analyser (LDS DACTRON Photon+®) supported with RT Pro® software

Frequency response functions (FRF) of all specimens were recorded

(1) Quasi-static Table(2) Composite Specimen (3) Impact Hammer (B&K Type 5800B4) (4) Uniaxial Accelerometer (B&K Type 3055B2) (5) Data Acquisition Card (B&K Type Photon+) (6) PC with RT Pro Software showing FRF

6

5

123

4

30

FRF response of Plates - 400 gsm FAD

Screen shot of RT Pro® showing FRF of 400 gsm AD Plates

H1400 Plate

H2400 Plate

31

Comparison of FRF plots among Hybrid Plates

Free vibration response of hybrid Plate H1 shows modified amplitude over the other hybrid arrangement, H2

The difference in natural frequency of carbon and glass fabric layers interplied in hybrid beams together promotes the increased amplitude under free vibration

0 200 400 600 800 10000

10

20

30

40

50

60

70H1H2

Frequency (Hz)

Am

plit

ude

(gn/

N)

0 200 400 600 800 10000

10

20

30

40

50

H1H2

Frequency (Hz)

Am

plit

ude

(gn/

N)

0 200 400 600 800 10000

10

20

30

40

50

60

H1H2

Frequency (Hz)

Am

plit

ude

(gn/

N)

32

Mode200 gsm 400 gsm 600 gsm

H1 H2 H1 H2 H1 H2

1 64 72 124 162 162 202

2 284 338 334 454 440 576

3 538 696 582 776 784 960

Comparison of Modal frequency of Plates with different Fiber Aerial Densities

Increase in Aerial Densities of fiber in epoxy matrix increases the modal frequency values indicating an increase in the dynamic stability for a thickness range of 1-2.5 mm for the four layered beams

33

Comparison of Loss Factor of Plates with different Fiber Aerial Densities

Mode200 gsm 400 gsm 600 gsm

H1 H2 H1 H2 H1 H2

1 0.089 0.087 0.047 0.033 0.031 0.030

2 0.028 0.027 0.025 0.019 0.017 0.010

3 0.014 0.018 0.012 0.012 0.012 0.013

There is consistency in material damping under the control of stacking sequence over each plate made of different aerial density of fiber in epoxy matrix

34

Variation in resonant frequency level in successive transverse modes of hybrid composite plates made

of three different fibre aerial densities

1 2 30

100200300400500600700800

H1H2

Mode No.

Freq

uenc

y in

Hz

1 2 30

100200300400500600700800900

H1H2

Mode No.

Freq

uenc

y in

Hz

1 2 30

200

400

600

800

1000

1200

H1H2

Mode No.

Freq

uenc

y in

Hz

200 g/m2 400 g/m2

600 g/m2

Hybrid plate with H2 layer arrangement

exhibited higher resonant frequencies

than the other layer arrangement, H1 in all modes of vibration

35

0

50

100

150

200

250

H1 H2

Fiber Areial Density (g/m2)

Mod

al F

requ

ency

(H

z)

00.010.020.030.040.050.060.070.080.090.1

H1 H2

Fiber Aerial Density (g/m2)

Loss

FAc

tor

Variation of Modal frequency for first mode due to different Fiber Aerial Density

Effect of Fiber Aerial Densities on Modal frequency and Loss factors

Variation of Loss factor for first mode due to different Fiber Aerial Density

200 gsm

400 gsm

600 gsm

600 gsm

400 gsm

200 gsm

First Mode values alone considered

First Mode values alone considered

36

Summary

The aerial density of woven fabric affects the vibration characteristics significantly

Increased Resonant frequency was attained with increase in fibre aerial densities

Magnitude of material damping value is more or less consistent in terms of all fibre aerial densities

Loss factor is lesser in higher aerial densities

37

Experimental Investigation on Modal analysis of Thin walled Glass/Carbon Composite beams for Structural applications

Beam Specimen

4G

H2

H1

4C

600 g/m2 Aerial Density - Dedicated and Hybrid samples fabricated using Hand layup Technique

38

Dimensions and Mass properties of Composite Beams

39

** l – length of the beam; w – width of the beam; t – thickness of the beam

Laminates Dimension (l*w*t) mm

Density() Kg/m3

4G 250*250*2.1 1881

H1 250*250*2.4 1640

H2 250*250*2.4 1627

4C 250*250*2.5 1446

Experimental Test Conditions

Impulse excitation technique

Fixed-free boundary condition

Impulse hammer (DYTRAN®) is used to induce the excitation

Flexural vibrations of the beam were tapped by a dynamic analyser (LDS DACTRON Photon+®) supported with RT Pro® software

Frequency response functions (FRF) of all specimens were recorded

40

Experimental Setup

(1) Composite Specimen (2) Impact Hammer (B&K Type 5800B4) (3) Uniaxial Accelerometer (B&K Type 3055B2) (4) Data Acquisition Card (B&K Type Photon+) (5) PC with RT Pro Software showing FRF

FRF of Dedicated Beam – 4G Arrangement (GGGG)

Screen shot of RT Pro® showing FRF of 4G600 BeamMay 1, 2023 41

FRF of Hybrid Beam – H2 Arrangement (CGGC)

Screen shot of RT Pro® showing FRF of H2600 BeamMay 1, 2023 42

43

0 15 30 45 600

0.2

0.4

0.6

0.8

14GH1

Frequency (Hz)

Am

plitu

de (g

n/N

)

(a)

60 80 100 120 140 160 180 200 220 240 260 280 3000

5

10

15

20

254GH1H2

Frequency (Hz)

Am

plitu

de (g

n/N

)

(b)

Comparison of FRF of Dedicated and Hybrid Beams Tested

FRF curves of various specimen obtained from RT Pro® software

Mode I

Mode II

44

Among all samples tested, the spectrum of glass fabric beams, 4G, showing relatively less amplitude at all successive resonance levels

This attribute indicates increased damping performance of glass fabric beam

Vibration response of hybrid beam H1 shows modified amplitude over the other hybrid beam arrangement H2

The difference in natural frequency of carbon and glass layers interplied in hybrid beams together promotes the increased amplitude under free vibration

Carbon beam which keeps relatively high strength and stiffness as compared to other test specimens showed higher amplitude frequency spectrum

The uniform rate of deformation and retrieval with higher modulus attribute caused less damping performance

Comparison of FRF of Dedicated and Hybrid Beams Tested – Contd…

Modal Analysis Roving Hammer method FRF results were given as input to ME SCOPE VES®

software for evaluating mode shape and modal frequency

All Dedicated and Hybrid beams were tested

45

Schematic diagram showing the various points of measurement

All Dimensions in mm

46

Collective FRF Signals as Input for attaining Mode shapes of Beams

Collective FRF curves obtained by exerting disturbing force at various target region of H2 specimen

Transverse Mode Shapes of 4G Beam (GGGG) represented by three axial components

47

First Mode at 13 Hz Second Mode at 108 Hz

Third Mode at 301 Hz

Transverse Mode Shapes of H1 Beam (GCCG) represented by three axial components

48

Second Mode at 145 HzFirst Mode at 18 Hz


Transverse Mode Shapes of H2 Beam (CGGC) represented by three axial components

49



Transverse Mode Shapes of 4C Beam (CCCC) represented by three axial components

50



Influence of Stacking sequence on Modal frequencies of Dedicated and Hybrid Beams

SampleMode I

Hz

Mode II

Hz

Mode III

Hz

4G 13 108 301

H1 18 145 401

H2 21 201 540

4C 29 280 766

Modal frequencies of high modulus carbon beam are higher than that of dedicated glass fabric beam

Modal frequencies of hybrid beams are lying in between the dedicated glass and carbon beams

Among the two hybrid beams H2(CGGC) has higher frequency values than GCCG 51

Sample

Mode I

Mode

IIMode

III

4G 0.468 0.065 0.035

H1 0.241 0.024 0.019

H2 0.248 0.031 0.020

4C 0.125 0.050 0.033

Hybrid beams indicate improved damping and dynamic stability against the dedicative glass beam

Among the hybrid beams, the carbon layers preferred as envelope in the fabric sequence, H2 (CGGC), resulted in minimal variation in damping and increased frequency resonance set

Improved flexural strength of this stacking sequence promotes this modified performance

52

Influence of Stacking sequence on Loss Factor of Dedicated and Hybrid Beams

53

1 2 30

50100150200250300350400450500

H1 H2 4C

Mode No.

Freq

uenc

y Va

riat

ion

(Hz)

Variation in successive resonance frequency sets of hybrid and carbon beams

compared with dedicated glass beamCarbon fabric beam showed relatively very high resonance frequency level and H2 stacking sequence exhibited nearly 50% performance of dedicated carbon fabric beam

Nearly 50% of performance exhibited for hybrid beam, H2, as compared to carbon fabric beam indicates its effective hybridization achieved by interplying arrangement of carbon/glass layers

Evaluation of Effective Modulus Effective modulus values for all samples were

calculated by using the frequency equation based on Euler-Bernoulli’s beam theory

54

Euler-Bernoulli’s Frequency equation

Source: ASTM Standard E756-05, Standard Test Method for Measuring Vibration Damping Properties of Materials, ASTM International, West Conshohocken, PA, 2003

Eeff

where = Density of the beam in kg/m3

n = Mode numberCn = Coefficient for nth mode,

(for first transverse mode, C1 = 0.55959)

l = length in mH = thickness of beamfn = the resonance frequency of nth mode in Hz

and Eeff = the effective modulus in Pa

Combined Stiffness and Damping Performance of Dedicated and Hybrid Beams

Eeff - a figure of merit for combined stiffness damping performance of viscoelastic polymeric composite materials

Stacking sequence is influencing the combined stiffness-damping values

Among hybrid form, H2 (CGGC) has higher value of Eeff

H2 arrangement is most preferable to use where strength and damping are important parameters

Specimen

Eeff(GPa) Eeff

(GPa)4G 7.02 0.468 3.29

H1 8.35 0.241 2.01

H2 11.37 0.248 2.82

4C 12.8 0.125 1.60

55

Eeff – Effective Modulus - Loss Factor

56

Summary Vibration characteristics of thin walled woven fabric

composite beams were experimentally investigated

There is appreciable raise in damping performance and structural stability by modifying the glass laminates with carbon plies by interply method

Modal analysis of hybrid structure exhibits increased frequency range for resonance set

The hybrid samples fabricated under varying stacking sequence showed very minimal variation in damping performance, but influencing greatly on combined stiffness-damping values

57

Influence of Size effect of hybrid composite beams on vibration characteristics using Finite Element Analysis for higher operating frequency range

Theoretical Evaluation of Elastic Constants

Elastic constants of woven fabric glass and carbon composite laminate were evaluated from the constituent material properties using the standard rule-of-mixture equations

58

Physical properties Carbon fiber Glass fiber Epoxy

Elastic modulus (GPa) 230 74 4.3

Shear modulus (GPa) 96 30 1.5

Poisson’s ratio 0.20 0.25 0.35

Mechanical properties of constituent materials

Source: Mallick. P. K. (2008). Fibre reinforced composites, materials and manufacturing and Design. CRC Press, Taylor & Francis Group

Evaluation of Elastic Constants for Unidirectional Lamina

59

Properties Carbon Glass

Elastic modulus E1

(GPa)94.58 32.18

Elastic modulus E2

(GPa)9.691 9.055

Shear modulus G12

(GPa)2.474 2.419

Shear modulus G23

(GPa)3.47 3.211

Poisson ratio 12 0.29 0.31

Poisson ratio 23 0.396 0.41

Source: Mallick. P. K. (2008). Fibre reinforced composites, materials and manufacturing and Design

Properties Carbon Glass

Elastic modulus E1=E2(GPa)

52.665 21.387

Elastic modulus E3(GPa) 11.285 10.427

Shear modulus G12 (GPa) 2.474 2.419

Shear modulus G13(GPa) 2.889 2.76

Shear modulus G23 (GPa) 2.889 2.76

Poisson ratio u12 0.054 0.136



60

Evaluation of Elastic Constants for Woven Fabric Lamina

Source: Mohammed F. Aly., Goda. I.G.M., Galal A. Hassan. (2010). Experimental investigation of the dynamic characteristics of laminated composite beam. International Journal of Mechanical & Mechatronics IJMME-IJENS 10(03): 59-58

Selection of Finite Element for Woven fabric Composite Beam

61

ANSYS v12.0 SHELL 99 - layered

element 8 node element 6 DOF at each node

Beam Dimension 220 mm length and 25 mm width

Four layer arrangement was selected in defining the thickness of beam

Actual specimen thickness was equally divided for four layers

SHELL 99

FE model of composite beam

Finite Element Modeling of Dedicated and Hybrid Composite Beam

62

Material Properties

The elastic constants of glass and carbon fabric lamina evaluated using rule of mixture were assigned as input according to required stacking sequence Actual density evaluated

from fabricated samples was given for the model for imposing mass properties of beam

Each woven fabric lamina was modeled as a layer of 0o fiber orientation

Lay plot with 0o orientation of CGGC woven fabric beam

[02/01/01/02]

Linear Regression analysis for evaluating Effective Elastic Constants

63

First 10 transverse mode frequency values are considered which is much higher than the number of elastic constants to be evaluated

Error function * = [(fi – fi

*)/ fi*]2 i =

1 to 10where fi

* is the experimental resonant frequency and fi is

numerical modal frequency Error function is minimized by

simple regression analysis The degree of deviation obtained

from regression analysis is used for finding the effective elastic constants of hybrid composite beams

Yes NoEffective Elastic constants

Error Function Computation (*)

If *is min

Elastic constants derived through Rule of Mixture

Equations

Finite Element Modelling and Analysis of unit plied

composite beam

Regression Analysis

Experimental modal frequency

values (fi*)

Theoretical modal frequency values (fi)

Flow chart for identification of effective elastic constants

May 1, 2023

Effective elastic constants of woven fabric lamina evaluated using Regression

analysis

May 1, 2023 64

Material

Effective elastic constants of glass/carbon woven fabric lamina

E11=E22 [GPa]

E33 [GPa]

G12 (GPa)

G13= G23 (GPa) 12 13=23

Glass 14.8 7.21 1.66 1.94 0.094 0.277

Carbon 29.4 6.3 1.39 1.62 0.030 0.216

Experimental frequency obtained from unit plied dedicated composite beams were helpful in establishing effective elastic constants of fibre reinforced polymer composite material with specified volume fraction

Influence of size on hybrid beam under higher operating frequency

65

Size of the unit plied composite beam was amplified by repeating three times (3T)

Modal analysis was carried out for all the four types of composite beams with fixed-free boundary condition using FE method

The frequency range set for the analysis was 1-10000 Hz The basic mode shapes such as

• Transverse mode,• Twisting mode and • Shear mode were tapped and

corresponding resonant frequency values were recorded May 1, 2023

Modal frequencies of various modes of composite specimen with unit plied and

increased thickness beams

66

ModeNo.

Modal frequency of various modes (Hz)Transverse Mode Twisting Mode Shear Mode

H1 H2 H1 H2 H1 H2

1T 3T 1T 3T 1T 3T 1T 3T 1T 3T 1T 3T

1 25 75 32 97 220 611 211 587 291 291 291 2912 157 465 202 593 675 1864 658 1816 1494 1494 1494 14943 439 1275 564 1605 1173 3205 1177 3188 3434 3434 3434 34344 857 2427 109

8 3005 1739 4672 1801 4751 5551 5551 5551 5551

5 1411 3872 180

2 4711 2390 6283 2552 6508 7743 7743 7743 7743

6 2096 5556 266

7 6639 3137 8036 3441 8435 9936 9936 9936 9936

May 1, 2023

The layer arrangement of H2 exhibited higher transverse and twisting resonant frequencies than H1 arrangement both in unit plied beam and enlarged size beam

There is no frequency variation in shear mode for both hybrid samples tested. The identical inter laminar shear strength of hybrid beams facilitates negligible effect in shear mode

Various mode shapes of enlarged size H2 beam under free vibration

67

5th Transverse mode at 4711 Hz

5th Twisting mode at 6508 Hz

5th Shear mode at 7743 Hz

6th Transverse mode at 6639

6th Shear mode at 9936 Hz

6th Twisting mode at 8435 Hz

May 1, 2023

It is evident from the mode shape plots that in higher operating frequency level both the hybrid beams are subjected to transverse mode, twisting mode and shear mode with more number of node points

Size effect on Modal frequency of Hybrid Beams in transverse mode

68

Stacking sequence of hybrid beam influences the vibration characteristics even at higher vibrating frequency level

Frequency values of hybrid beam manifolds as the number of unit plied arrangement used for fabricating composite laminate

1 2 3 4 5 60

1000

2000

3000

4000

5000

6000

7000

H1 (1T) H1 (3T)

H2 (1T) H2 (3T)

Successive Transverse Mode in Number

Nat

ural

Fre

quen

cy in

kH

z

May 1, 2023

Mean shift in frequency at various modes among unit plied and enlarged size beams

69

In all successive transverse and twisting modes, carbon plies maintained as envelope and glass plies as core stock, H2, showed relatively increased resonant frequency and confirms its improved dynamic performance

May 1, 2023

Transverse mode Twisting Mode0

500

1000

1500

2000

2500

3000

H1 H2

Mea

n sh

ift in

Fre

quen

cy

(Hz)

70

SummaryFinite element modal analysis was carried out for

finding out the vibration characteristics of hybrid carbon composite beam with fixed-free boundary condition under higher operating frequency range

The stacking sequence maintained for increased size of beam affects the modal response even at higher vibrating frequency level

Finite element results obtained using effective elastic constants shows that carbon fabric plied as envelope offered enhanced vibration stability than the envelope replaced by low modulus glass fabric

71

Influence of Cyclic Fatigue loading on Vibration Characteristics of thin walled Glass-Carbon Epoxy Hybrid Composite Beams

Fully Reversed Bending Stress

Beam element subjected to a repeated and alternating tensile and compressive stresses

72

Applying alternating fluctuating load on the composite specimen to subject reversed bending stress Total deflection D = 2 times of dFixing the specimen

dd

Functional Requirements

Driving mode is the DC electric motorRotary motion reciprocating motionEccentric crank mechanism is used to bring in this conversionTotal Displacement (D) = twice of eccentricity (e)

ee

D

Selection of Mechanism

Stress Ratio R = -1 R = σmin / σmax

Completely Reversed cycle

Eccentric crank

Dis

plac

emen

t

Angle of Rotation

D/4 D/4 D/4 D/4

D/2 D/2D

0 180

360

Reciprocating MechanismSPECIMEN HOLDER

lINEAR MOTIONBEARING

ROD END BEARING

YOKE AND DOWELPIN ASSEMBLY

HEIGHT ADJUSTER ROD

ECCENTRIC DISC

NEEDLE BEARINGBLOCK

ECCENTRICITYADJUSTING PLATE

A

SPECIMEN HOLDERON TABLE

A

VIEW AA

75

Parts of Test Rig

1) DC Motor of the calculated power rating and corresponding DC drive.

2) Gear Box Assembly3) Eccentric disc assembly4) Rotating Rod Eye and Dowel pin setup5) Exciter rod 6) Linear movement bearing to arrest the

sway and guide the vertical to-and-fro motion of the exciter rod

7) Clamp designed to hold the test specimen8) Table enclosing the whole setup9) R.P.M Counter and Revolution Counter

76

Machine Layout

10

50100

=125

=40

14020 20

A

VIEW - AA

145

280

1

2

12

13

14

15

16

1718

1920

21

50D

D

C

C

330

B

B

VIEW - BB

= 44 == 28 =

1010

1

SECTION - CC SECTION - DD

M6 HSHC BOLTS4 NOS M6 HSHC BOLTS

4 NOS

180

60

90

A

9

10

11

BILL OF MATERIAL

PART NO

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

1 MOTOR - 1

2 LOVE JAW COUPLING - 1

SL.NO DESCRIPTION MATL QTY

3 GEAR BOX - 1

4 FLYWHEEL EN24 1

5 VIBRATION PAD - 2

LEVELING PAD - 4

DRIVING SHAFT EN24 1

DRIVEN SHAFT 1

ECCENTRIC DISC 1

ADJUSTER PLATE

NEEDLE BEARING BLOCK 1

ADJUSTING ROD-1 1

ROD END BEARING - 1

DOWEL PIN - 1

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

YOKE MS 1

LINEAR BEARING - 1

EXCITER ROD MS 1

SPECIMEN HOLDER-1 MS 1

SPECIMEN HOLDER-2 MS 1

FRAME MS 1

16

17

18

19

20

21

EN24

EN24

1EN24

EN24

MS

1MSADJUSTING ROD-2

ALL DIMENSIONS ARE IN mm

FATIGUE TEST RIG: ASSEMBLY DRAWING

ASSY 01

DRAWING NAME

DRN BY

CHK BY

DATE

DRAWING NO.

ORGANISATION SRI VENKATESWARA COLLEGE OF ENGG.

Mr. R. MURUGAN

Dr.RAMESH

10/11/2011

6

3

4

5

TEST SPECIMEN

5

8

7

160 70

77

78

(1) DC Motor (2) Eccentric Crank (3) Linkage (4) DC Control unit (5) Speed Indicator (6) Total number of cycles counter

Experimental Set-up for completely reversed bending test

(1) Fixed end (2) Composite Specimen (3) Free End

Work holding devices for fixed and free end

of the specimen

Evaluation of Optimum span length for two different Hybrid specimens

-0.5

0

0.5

1

1.5

2

2.5

3

0 50 100 150 200 250

Beam length

Def

lect

ion CGGC

GCCGLinear (CGGC)Linear (GCCG)

79

136

25


80

Evaluation of Equivalent beam deflection for two different hybrid beams• Stress controlled fatigue test

• 20% of flexural strength of hybrid beams, i.e. 100 MPa, as limiting stress

• Equivalent load for the limiting bending stress for the hybrid beams H1 and H2 are arrived by using the bending equation, b = M/Z

• Based on the dimensions of the hybrid beams the equivalent load P was evaluated and it was found as 19.15 N

F=19.15 N

136mm

Equivalent deflection of the beam is calculated by using standard beam deflection equation, max = Pl3/3EI

The equivalent deflection of the hybrid beams with different flexural modulus of 10.55 MPa and 17.41 MPa respectively are evaluated as 17 mm and 12 mm respectively

81

Test specimen type : H1 & H2 Free length, L : 136 mmTest frequency, f :10HzInduced deflection, d :

±17 mm - H1 & ±12 mm - H2

Equivalent load, F : 19.15 NInduced stress, σb : ± 100

MPaStress Ratio, R = σmax/σmin : -1

Experiment test conditions

(1) DC Motor (2) Eccentric Crank (3) Linkage (4) DC Control unit (5) Speed Indicator (6) Total number of cycles counter (7) Composite Specimen (8) Impact Hammer (B&K Type 5800B4) (9) Accelerometer (B&K Type 3055B2) (10) Data Acquisition Card (B&K Type Photon+) (11) PC with RT Pro Software showing FRF

Experimental Setup for measuring vibration characteristics of hybrid composite beam after completely reversed bending cyclic loading

82

0 100 200 300 400 500 600 700 800 900 100002468

101214161820

0 cycle1 Lakh cycles2 Lakh cycles

Frequency (Hz)

Am

plitu

de (

gn/N

)Comparison of FRF plots of Hybrid beams

after cyclic loading

0 100 200 300 400 500 600 700 8000

5

10

15

20

25

0 cy-cle

Frequency (Hz)

Am

plitu

de (g

n/N

)There is reduction in modal frequency values at successive modes of hybrid beams, H1 and H2 due to cyclic loading, accordingly peaks in FRF plot were shifted in opposite direction

83

No. of Cycles(x 105)

Mode 1 Mode 2 Mode 3

Frequency

(Hz)

% of Dampin

g

Frequency

(Hz)

% of Damping

Frequency

(Hz)

% ofDampin

g

0.0 33.75 6.52 302.50 2.62 757.50 1.34

0.5 23.75 15.60 265.00 3.78 632.50 3.05

1.0 22.50 17.69 266.25 3.48 647.50 2.74

1.5 22.50 18.89 255.00 6.71 620.00 2.89

2.0 20.00 23.20 247.50 6.71 697.50 2.48

Variation of Modal frequency and Damping values at successive Resonance set of H1 hybrid beam

subjected to cyclic loading

Resonance frequency set values at successive modes decreasing trend Vibration damping shows increasing trend with respect to number of cycles

84

No. of Cycles(x 105)


Frequency (Hz)

% of Dampin

g

Frequency (Hz)

% of Dampin

g

Frequency (Hz)

% of Dampin

g

0.0 46.88 6.06 386.72 1.14 962.40 1.79

0.5 45.41 6.18 373.54 2.23 887.70 2.31

1.0 43.12 8.76 366.21 2.94 823.24 2.24

1.5 38.09 12.04 342.77 4.39 805.66 2.55

2.0 36.62 12.14 339.84 5.72 783.84 3.46

Variation of Modal frequency and Damping values at successive Resonance set of H2 hybrid beam

Due to cyclic loading

Resonance frequency set values at successive modes decreasing trend Vibration damping shows increasing trend with respect to number of cycles

85

No. of Cycles( 105)

Modal Stiffness (kN/m)


H1 H2 H1 H2 H1 H2

0.0 0.59 1.14 47.64 77.85 298.72 482.18

0.5 0.29 1.07 36.56 72.64 208.26 410.22

1.0 0.26 0.97 36.90 69.82 218.26 352.82

1.5 0.26 0.76 31.89 61.17 200.11 337.91

2.0 0.24 0.70 31.89 60.12 200.11 319.85

Variation in Modal Stiffness of Hybrid beams due to cyclic loading

Modal Stiffness values are evaluated based on experimental modal frequency values of H1 and H2 hybrid beams

86

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.0

0.2

0.4

0.6

0.8

1.0

1.2 Mode 1

No. of Cycles (x105)

Nor

mal

ised

Mod

al S

tiffn

ess

H2

Influence of cyclic loading on Modal stiffness

H1

Rate of loss of stiffness in H1 beam is larger than the other arrangement H2 due to cyclic loading at all successive modes

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.0

0.2

0.4

0.6

0.8

1.0

1.2 Mode 2


Nor

mal

ised

Mod

al S

tiffn

ess

H1

H2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00.0

0.2

0.4

0.6

0.8

1.0

1.2 Mode 3


Nor

mal

ised

Mod

al S

tiffn

ess

H1

H2

87

Mode shapes of hybrid beam H1 before and after Cyclic loading

Mode I

303 Hz

758 Hz

20 Hz

248 Hz

698 Hz

34 Hz

Mode II

Mode III

Before After

88

Mode shapes of Hybrid beam H2 before and after Cyclic loading

46 Hz

386 Hz

963 Hz

Mode I

Mode II

Mode III

36 Hz

339 Hz

783 Hz

Before After

89

Severe breakages of fibre roving in H1 (GCCG) as fundamental arrangement

Morphology of H1 BeamH1 Beam after 2x105 cycles of Reversed

bending load

90

Severe delamination of the epoxy resin reveals longitudinal and lateral fibres. Longitudinal fibre breakage near the fixed end appears to be predominant

In addition to the delamination of the surface resin revealing the longitudinal glass fibres below, transverse matrix fatigue striations are also found. Fibre breakage is also seen.

Figure reveals transverse matrix cracking in agreement with the fatigue cycling. Notice the total debonding and peel off of the longitudinal fibres in vibration

Scanning Electron Microscopy

91

Morphology of H2 Beam

Limited breakages of fibre roving in H2 (CGGC) as fundamental arrangementand crack propagation predominantly through Epoxy matrix

H2 Beam after 2x105 cycles of Reversed

bending load

92

Longitudinal carbon fibres exhibiting breakage. However, the fibre damage in H2 is lesser than what is exhibited by H1.

Longitudinal carbon fibre damage associated with matrix striations in fatigue transverse to the interface.

Scanning Electron Microscopy

Conclusion

A displacement controlled fully reversed bending cyclic test rig for testing the cantilever type hybrid composite laminates was designed and developed

Experiments were conducted to determine the effects of cyclic loading on vibration characteristics like natural frequency, percentage of damping and the modal stiffness of the glass/carbon hybrid composite laminate specimen under fully reversed bending cyclic loading

Resonance frequency set at successive modes show decreasing trend and the vibration damping shows increasing trend with respect to number of cycles

Rate of loss of stiffness in H1 beam is larger than the other arrangement H2 during cyclic loading at all successive modes

Macrographs and SEM fractography of damaged hybrid sample H1 (GCCG) showed severe breakages in fibre roving whereas in H2 (CGGC) sample there are only limited breakages of fibre roving and crack propagation is predominantly through Epoxy matrix

Paper Publications

94

International Journal

95

1. R. Murugan, R. Ramesh, K. Padmanabhan, “Investigation on Vibration Behaviour of Cantilever Type Glass/Carbon Hybrid Composite Beams at Higher Frequency Range using Finite Element Method” in Advanced Materials Research, Vols. 984-985 (2014) pp 257-265, Trans Tech Publications, Switzerland DOI:10.4028/www.scientific.net/AMR.984-985.257

2. R. Murugan, R. Ramesh, K. Padmanabhan, “Experimental Investigation on the Different Aerial Density of Woven Fabric Glass, Carbon and its Hybrid Composite Beam Subjected to Free Vibrating Condition” International Journal of Earth Sciences and Engineering (Accepted for publication)

3. R. Murugan, R. Ramesh, K. Padmanabhan, “Investigation on Static and Dynamic Mechanical Properties of Epoxy Based Woven Fabric Glass/Carbon Hybrid Composite Laminates” Procedia Engineering, Elsevier Publications (Accepted for publication)

4. R. Murugan, R. Ramesh, K. Padmanabhan, “Vibration Characteristics of Thin Walled Glass/Carbon Hybrid Composite Beams subjected to Fixed Free Boundary Condition” International Journal of Mechanics of Advanced Materials and Structures, Taylor & Francis Publications. (Communicated)

5. R. Murugan, R. Ramesh, K. Padmanabhan, “Investigation of Fibre Aerial Density effects on Mechanical Properties and Vibration Characteristics of Epoxy based Glass/Carbon Hybrid composite Plates made of Two fundamental Stacking Sequences” Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, SAGE Publications (Communicated)

International Conference

96

1. Murugan R, Padmanabhan K, Ramesh R, Rajesh M, “Hybrid effect on damping behavior of epoxy based woven fabric composite beams” in the International conference on Advancements in Polymeric materials during March 25-27, 2011 at CIPET, Chennai

2. Murugan R, Padmanabhan K, Ramesh R, “Vibration Characteristics of Thin Walled Hybrid Carbon Composite Beams under Fixed Free Boundary Condition” in 3rd Asian Conference on Mechanics of Functional Materials and Structures (ACMFMS 2012) held on December 5-8, 2012 at Indian Institute of Technology, New Delhi

3. R. Murugan, K. Padmanabhan, R. Ramesh, M. Arulkumar, “An Investigation on Static Mechanical Properties of Epoxy based Glass/Carbon Woven Fabric Hybrid Composites” on 2013 International Conference on Energy Efficient Technologies for Sustainability at St. Xaviers College of Engineering, Kanyakumari

4. R. Murugan, R. Ramesh, K. Padmanabhan, “Investigation on Vibration Behaviour of Cantilever Type Glass/Carbon Hybrid Composite Beams at Higher Frequency Range using Finite Element Method” in International Conference on Recent Advances in Mechanical Engineering and Interdisciplinary Developments - ICRAMID 2014 held on 7-8 March 2014 at Ponjesly College of Engineering, Nagercoil

5. R. Murugan, R. Ramesh, K. Padmanabhan, “Experimental Investigation on the Different Aerial Density of Woven Fabric Glass, Carbon and its Hybrid Composite Beam Subjected to Free Vibrating Condition” in International Conference on Modelling Optimization and Computing (ICMOC 2012), held at Noorul Islam University, Kumaracoil, during 10-11 April 2014.

6. R. Murugan, R. Ramesh, K. Padmanabhan, “Investigation on Static and Dynamic Mechanical Properties of Epoxy Based Woven Fabric Glass/Carbon Hybrid Composite Laminates” in 12th Global Congress on Manufacturing and Management, GCMM 2014, held at VIT University, Vellore, during 8-10 December 2014

National Conference

97

1. Murugan R, Padmanabhan K, Ramesh R, Anandakannan P, “Design and Development of Fatigue Testing Facility” in the National conference on Recent Trends in Mechanical Engineering (NCRTIME’12) held on 22nd March 2012 at Saveetha School of Engineering, Saveetha University, Chennai-602105.

(Received First Prize)

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materials, Annual book of ASTM standards, Philadelphia, 20054)ASTM D3039, Standard test method for tensile properties of polymer matrix composite

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electrical Insulating Materials, Annual book of ASTM standards, Philadelphia, 20056)ASTM D256-05, Standard test method for Determining the Izod Pendulum Impact

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2) Gibson. R. F. (2000). Modal vibration response measurements for characterization of composite materials and structures. Composites Science and Technology (60): 2769-2780.

3) Hajime Kishi, Manabu Kuwata, Satoshi Matsuda, Toshihiko Asami, Atsushi Murakami. (2004). Damping properties of thermoplastic-elastomer interleaved carbon fiber-reinforced epoxy composites. Composite and Technology (64): 2517-2523.

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5) Botelhoa. E.C., Campos. A.N., E. de Barros., Pardini. L.C., Rezende. M.C. (2006). Damping behavior of continuous fiber/metal composite materials by the free vibration method. Composites: Part B (37): 255–263.

6) Sanchez-Saez. S, Barbero. E, Navarro. C (2007). Analysis of the dynamic flexural behaviour of composite beams at low temperature. Composite and Technology (67): 2616-2632

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Thank You !

101