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Chapter 3 MECHANICAL PROPERTIES OF SHORT SISAL FIBRE-POLYSTYRENE COMPOSITES Abstract Short sisal fibre reinforced polystyrene composites were prepared by solution mixing technique. The influence of fibre length, fibre content and fibre orientation on the mechanical properties such as tensile strength, Young’s modulus, elongation at break, flexural properties and impact properties of the composites were evaluated. The tensile strength of the composites showed an initial reduction at 10% fibre loading followed by an increase at 20% fibre loading. However, at higher loading the properties levelled off. The tensile properties were found to be almost independent of the fibre length although the ultimate tensile strength shows marginal improvements at 10mm fibre length. The effect of fibre loading, fibre length and fibre orientation on the impact energy and flexural properties of the composites were also studied. Part of the results discussed in this chapter have been (a) published in Journal of Applied Polymer Science, 60, 1483, 1996 and (b) submitted for publication in Journal of Applied Polymer Science.

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Chapter

3

MECHANICAL PROPERTIES OF SHORT SISAL FIBRE-POLYSTYRENE

COMPOSITES

Abstract

Short sisal fibre reinforced polystyrene composites were prepared by

solution mixing technique. The influence of fibre length, fibre content

and fibre orientation on the mechanical properties such as tensile

strength, Young’s modulus, elongation at break, flexural properties and

impact properties of the composites were evaluated. The tensile strength

of the composites showed an initial reduction at 10% fibre loading

followed by an increase at 20% fibre loading. However, at higher

loading the properties levelled off. The tensile properties were found to

be almost independent of the fibre length although the ultimate tensile

strength shows marginal improvements at 10mm fibre length. The effect

of fibre loading, fibre length and fibre orientation on the impact energy

and flexural properties of the composites were also studied.

Part of the results discussed in this chapter have been (a) published in

Journal of Applied Polymer Science, 60, 1483, 1996 and (b) submitted for

publication in Journal of Applied Polymer Science.

3.1 Introduction

Several cellulosic products and wastes such as shell flour, wood flour and pulp

have been used as fillers in thermoplastics primarily to achieve cost savings1. The

use of cellulosic fillers of fibrous nature has been of greater interest, as they

would give composites with improved mechanical properties compared to those

containing non-fibrous fillers. The performance of short fibre reinforced

composites depends on factors like aspect ratio, orientation of fibres, and fibre

matrix adhesion2. In the case of fibre reinforced composites there exists a critical

aspect ratio at which the mechanical properties are maximised. Fibre orientation

has a significant influence on the mechanical properties of the composite in that

the stress value is maximum along the axis of orientation of the fibre. The

processing conditions also influence the properties of the composites due to the

chance for fibre breakage during the processing. The ultimate properties of the

composites depend on the extent of stress transfer from matrix to fibres. The

efficiency of this stress transfer depends on a number of factors such as fibre

concentration, fibre dispersion, orientation of fibre, geometry of the fibre and

fibre- matrix interfacial adhesion. Various researchers 3-6 have studied the tensile

properties of short natural fibre reinforced composites. Pavithran et al. have

reported the impact behaviour of unidirectionally oriented sisal fibre composites7.

Vipulanandan and Mebarkia8 reported on the flexural strength, toughness, and

fracture properties of particle filled, fibre reinforced polyester composites. Jancar

et al.9 studied the effects of deterioration of matrix and matrix fibre interface

caused by moisture, on the flexural properties of unidirectional E-glass fibre

Short Sisal Fibre Reinforced Polystyrene Composites 100

reinforced thermoplastics. Rozman et al.10 used hexamethylene diisocyanate

modified ALCELL lignin as a coupling agent in oil palm empty fruit bunch-

polypropylene composites and obtained a greater flexural strength. Gassan et al.11

studied the effects of interphase formed by a silicone interlayer on the mechanical

properties of natural fibre reinforced poly urethanes and an improvement of about

35% was found. The weak interlayer in this case led to a general improvement of

charpy impact energy depending on interphase thickness.

In this chapter a detailed investigation has been carried out on the effects of fibre

length, fibre loading and fibre orientation on tensile, impact and flexural

properties of short sisal fibre reinforced polystyrene composites. A comparison of

the experimental tensile strength and modulus of the composite with theoretical

models such as modified rule of mixtures, series, Halpin-Tsai and Bowyer-Bader

are also discussed in this chapter.

3.2 Results and discussion

3.2.1 Fibre length distribution

In the case of brittle fibres like glass there is chance for fibre breakage during

mixing and extrusion. However, in the case of sisal fibre, most of the fibres retain

their original length after mixing. This is clear from the number average ( nL )

and weight average ( wL ) fibre lengths of fibres before and after mixing given in

Table 3.1. This can be attributed to the flexible nature of cellulose fibre. This is in

agreement with the works reported by Czarnecki and White12. Table 3.1 also

summarises the poly dispersity index (PDI) values of fibres before mixing and

Mechanical Properties of Short Sisal Fibre - Polystyrene Composites 101

that of fibres extracted from the composites based on 100 fibres. The low values

of wL / nL indicate a narrow fibre length distribution before and after mixing.

Table 3.1 Fibre length distribution of chopped sisal fibre and

fibre in composite

Sample

nL (mm)

wL (mm)

wL / nL

Chopped sisal

fibre

6.02 6.12 1.02

Sisal fibre

extracted from

composite

5.69 5.75 1.01

3.2.2 Tensile properties of sisal fibre-PS composites

(a) Effect of fibre length In the case of fibre-reinforced composites, there exist a critical aspect ratio at

which the mechanical properties of the composites are maximized. The critical

aspect ratio depends on the volume fraction of the fibre and also on the ratio of

the modulus of fibre to the matrix modulus13. At low fibre volume fraction, the

fibres play no major role and the strength of the composite is matrix dominated.

The strength of the composite was found to increase above a critical volume

fraction of the fibre, which in fact depends on the aspect ratio. The critical

volume fraction was found to decrease with increase in aspect ratio. At relatively

low fibre volume fraction, the critical aspect ratio remains almost constant,

which, however shows a sharp decrease at higher fibre loading14. As the fibre

Short Sisal Fibre Reinforced Polystyrene Composites 102

length increases, there is a chance for better orientation, which may also lead to

an improvement in mechanical properties of the composite. In the case of low

density polyethylene/sisal fibre system a critical length of 6mm15 and for

NR/sisal fibre system16 and NR/coir system17 a critical fibre length of 10mm was

reported.

Table 3.2 Tensile properties of PS-Sisal fibre composites as a

function of fibre length (fibre loading 20 wt%)

Fibre length

(mm)

Ultimate

tensile

strength

(MPa)

Young’s

modulus

(MPa)

Elongation

at break

(%)

2 36.18 958 5.6

6 43.2 1000 7.8

10 46.87 1047 8.2

To study the effect of fibre length on the tensile properties of the present system

20% fibre loaded composites with average fibre length of 2,6,and 10mm were

prepared. The tensile properties of the composites (Table 3.2) show no

considerable variation with change in fibre length, although the ultimate tensile

strength showed marginal increase at 10mm fibre length.

(b) Effect of fibre loading and orientation

The tensile properties of highly viscous thermoplastics or rubber materials are

governed by several factors such as dispersion (agglomerate formation), increase

of stress concentration points at fibre ends and entrapped air during mixing

(wetting problem) 18. In the case of polystyrene specimens Murray and Hull19 and

Mechanical Properties of Short Sisal Fibre - Polystyrene Composites 103

Hull20 observed that micro voids and cavities occurred within the crazes at the

fibre ends and coalesced to generate planar cavities and or cracking within the

crazes. The chances for some amount of opened cleavage –type fracture during

the pullout process of fibres were also reported21. The broken ends of fibres

formed during the tensile deformation may induce crazes and cracks in the matrix

and may lead to a decrease in the tensile strength19-20. This phenomenon is more

pronounced in the case of samples where the probabilities of breaking of fibres

are higher. Fig.3.1 shows a typical stress-strain curve of sisal fibre-PS composite

at different fibre loadings.

Fig.3.1 Atypical stress-strain curve of sisal fibre-PS composite

Table 3.3 and Figs. 3.2 to 3.6 show the effect of fibre loading and orientation on

the tensile properties of sisal fibre–polystyrene composites. In the case of

longitudinally oriented composite, a reduction in ultimate tensile strength was

observed at lower fibre loading (Table-3.3 and Fig. 3.2). However, increase in

Short Sisal Fibre Reinforced Polystyrene Composites 104

fibre loading above 20% improves the tensile strength considerably and produces

no appreciable change with further increase in fibre loading. At 10% fibre

loading, the fibre may act as a flaw in the matrix, reducing the tensile strength of

the composite. At low fibre loadings, the matrix is not restrained by enough fibres

and highly localized strain occurs in the matrix at low stresses, causing the bond

between the fibre and matrix to break, leaving the matrix diluted by non-

reinforcing debonded fibres.

Table 3.3 Tensile properties of PS-Sisal fibre composites as a

function of fibre loading and orientation (fibre length-6mm)

Tensile Strength

(MPa)

Young’s

Modulus (MPa)

Elongation at

Break (%)

L T R L T R L T R

PS 34.9 34.9 34.9 390 390 390 8.7 8.7 8.7

U106 21.3 14.8 18.2 629 597 517 8.6 4.7 6.9

U206 43.2 12.4 26.0 1000 488 554 7.8 2.8 5.7

U306 45.1 11.0 20.4 1033 578 624 6.7 1.9 3.6

L – longitudinally oriented, T- transversely oriented, R- randomly oriented

As the fibre loading increases, the stress is more evenly distributed and the

strength of the composite increases. The modulus of the longitudinally oriented

fibre composites (Table 3.3, Fig.3. 3) increases with fibre content up to 20% fibre

loading and level off with further loading. In this case, as the fibres are oriented

perpendicularly to the direction of the crack propagation, the crack will be

hindered and accounts for the increase in tensile strength and modulus.

Mechanical Properties of Short Sisal Fibre - Polystyrene Composites 105

0 5 10 15 20 25 30

10

15

20

25

30

35

40

45

50

55

U(R)U(T)

U(L) B C D

Tens

ile s

treng

th (M

Pa)

Fibre content (wt%)

Fig. 3.2 - Variation of tensile strength of PS-sisal fibre composite as a function of fibre loading.

0 5 10 15 20 25 30

400

500

600

700

800

900

1000

U(R)

U(T)U(L) B

C D

Youn

g's

Mod

ulus

(MPa

)

Fibre content (wt %)

Fig. 3.3- Variation of Young’s modulus of PS-sisal fibre composite as a function of fibre loading.

Short Sisal Fibre Reinforced Polystyrene Composites 106

In the case of transversely oriented fibre composites, Fig.-3.2 shows a

considerable deterioration in strength with increase in fibre loading. In this case

the crack propagates in the direction of fibre alignment. The transversely oriented

fibres acts as a barrier and prevents the distribution of stresses throughout the

matrix, and this in turn causes higher concentration of localized stresses. This

explains the reduction in the tensile properties of transversely oriented composite.

In this case, the modulus shows a value higher than that of neat PS and lower

than those of longitudinally oriented composites (Table3.3, Fig.3.3).

0 5 10 15 20 25 30

2

3

4

5

6

7

8

9

U(R)

U(T)

U(L) B C D

Elon

gatio

n at

bre

ak (%

)

Fibre content (wt%)

Fig. 3.4- Variation of elongation at break (%) of PS-sisal fibre composite as a function of fibre loading.

Randomly oriented fibre composite shows tensile strength that lies between those

of longitudinally and transversely oriented fibre composites as expected

(Table3.3, Fig.3.2). At 20 and 30% fibre loading the modulus values also show a

Mechanical Properties of Short Sisal Fibre - Polystyrene Composites 107

similar trend. However, at 10% fibre loading the modulus shows a value less than

that of transversely and longitudinally oriented fibre composite. The reason for

this reduction is not clear.

The data given in Table3.3 and Fig.3.4 also show that in almost all experiments

the ultimate elongation of composites is less than that of unfilled polymer and

decreases with increasing fibre concentration.

3.2.2 Impact properties

The fracture toughness of the composite materials is one of the important

engineering properties. Generally, the impact strength may increase by the

presence of fibres. The presence of filler can impede crack growth due to the

possibility of imposing a greater tendency for plastic deformation in the matrix.

The increase in impact strength is associated with an ability to produce an

increase in the cohesive strength of the matrix or to the change in the distribution

stresses over a larger area. The actual mechanisms for the increase in the impact

strength are numerous and vary depending on the nature of the composites,

temperature and test conditions. During impact testing, the craze formed at a

point of maximum strain grows until it meets another particle or till the stress

concentration at the craze tip falls to zero. Thus, instead of producing large crazes

leading to cracks, when filler is present a large number of micro cracks are

formed. Another possibility that leads to enhance impact resistance is that of

shear yielding in toughened plastics or a combination of crazing and yielding.

In the case of fibre reinforced resins the improvement in impact strength may

also be attributed to the extra energy needed for fibre pullout, debonding or

Short Sisal Fibre Reinforced Polystyrene Composites 108

redistribution of stress, involving creation of new surfaces. Factors affecting the

mode of fracture in fibre reinforced composites are (a) Fibre and matrix strength

(b) Load transfer efficiency (c) Resistance to crack propagation (d) Bond strength

between fibre and matrix and (e) Volume concentration of the fibre and its

geometrical organization22. In the case of short fibre reinforced thermoplastic

composites, the fracture is controlled by fibre pullout. Cracks are found to form at

the fibre ends and misaligned fibres are pulled through the matrix along with

some fibre fracture. In the case of short fibre reinforced composites, fibre length

is also found to be an important parameter in controlling the impact strength, and

the best results are obtained with fibres having critical fibre length. Inter laminar

shear strength also affects the impact strength and increases with increasing shear

strength. Impact strength can be improved by a number of ways23 (a) by using

intrinsically tough matrices, (b) by the application of a soft coating to the fibres

that will act as an interlayer after the composite is fabricated, (c) Utilization of

the energy required to debond the fibres from the matrix and then to pull the

fibres completely out of the matrix and (d) by using a weak interface between

fibre and the matrix.

(a) Effect of fibre loading

Fig 3.5 shows the effect of fibre loading on the impact strength of longitudinally

oriented sisal fibre reinforced PS composites. From this figure, it is clear that at

10% fibre loading the impact strength shows a sharp decrease followed by an

increase at 20 and 30% fibre loading. The maximum impact strength is observed

with 30% fibre loading. At low loading levels, fibres introduce a

Mechanical Properties of Short Sisal Fibre - Polystyrene Composites 109

disproportionately high degree of critical defects to the composite structure,

perhaps in the form of voids or poorly bonded interface regions and reduce the

impact strength. As the fibre loading is increased, reinforcing nature of the

cellulose counterbalances the inclusion of defects and imparts improved

toughness24. The extra energy needed to fibre pullout, debonding and

redistribution of stresses are also responsible for the improvement in impact

strength.

0

5

10

15

20

25

30U306 L

U206 L

U106 L

PS

Impa

ct E

nreg

y (K

J/M

2 )

Fig.3.5- Variation of impact energy of sisal fibre-PS composites as a function of fibre loading

(b) Effect of fibre length and orientation

In the case of short fibre reinforced composites, there exist a critical fibre length

at which the mechanical properties are maximized. In the case of banana fibre

Short Sisal Fibre Reinforced Polystyrene Composites 110

epoxy composites Tobias23 reported that smaller fibre length leads to higher

impact strength at constant fibre loading.

0

5

10

15

20

25

30

35

U2010(T)

U202(T)

U206(L)

U206(T)

PS

Impa

ct E

nerg

y (K

J/m

2 )

Fig.3.6- Variation of impact energy of sisal fibre-PS composites as a function of fibre orientation and length

In the case of oriented system fracture energy is maximum in the direction of

fibre. As mentioned earlier, one of the mechanisms utilized to improve the impact

strength is to utilize the energy to debond the fibres from the matrix and then to

pull the fibres completely out of the matrix. Fibres shorter than Lc will be pulled

out from the matrix, rather than broken, when a crack passes through the

composite sample. This means that for maximum toughness it is desirable to have

a weak interface or use fibres having length L< Lc. Fig.3.6 shows the effect of

fibre length and orientation on the impact strength of PS- sisal composites. It is

observed that the impact energy increases with fibre length up to 6mm followed

Mechanical Properties of Short Sisal Fibre - Polystyrene Composites 111

by a decrease at 10mm fibre length at 20% fibre loading. This is in agreement

with the Cottrell model 25 for unidirectional reinforcement, which includes all the

energy dissipation mechanism like matrix fracture, fibre fracture, debonding and

pullout. As per the model predictions, the impact energy is expected to increase

with increasing fibre length up to fibre lengths equal to the critical fibre length.

At fibre lengths above the critical fibre lengths the impact energy is expected to

decrease again25. This occurrence of a maximum in impact strength can be

attributed to the predicted change in failure mode from fibre pullout at short fibre

lengths (sub critical) to fibre breakage at high fibre length (supercritical) fibre

lengths. This theory is applicable for systems where pullout is the major fracture

mechanism. In thermoplastic composites, no maximum in toughness is observed

but plateau is reached with increasing fibre length26-29. In the present study we

observe a maximum in impact energy at 6mm fibre length followed by a decrease

at 10mm fibre length.

In the case of oriented systems fracture energy is higher for composites with

fibres oriented in the direction of applied force and the highest impact strength is

observed with critical fibre length and poor fibre- matrix bonding. However, for

transverse loading a good bonding is preferred for better impact strength. From

Fig.3.6, it is clear that for sisal fibre- PS composites, the impact energy follows

the order U206 (L)> U206 (T) as expected. It may be noted that in impact testing

U206 (L) corresponds to U206 (T) in tensile testing and vice versa as the force is

applied in different directions in these testing.

Short Sisal Fibre Reinforced Polystyrene Composites 112

3.2.4 Flexural properties

(a) Effect of fibre loading

The loading in flexure in an ideal case causes normal stresses in the direction of

fibres and shear stresses in the plane perpendicular to the loading nose. The

mode of failure of unidirectional composites in flexure is very complex.

Unidirectional composites, when loaded in flexure can fail in tension either

longitudinally or transversely, or in shear in the matrix, interface or fibre30 The

most common modes of failure are transverse splitting, brittle tensile failure, with

fibre pullout, interfacial shear failure, compressive failure due to micro buckling

or localized kinking of fibres and intra-laminar shear failure. When the span /

thickness L/d ratio is less than 25, the failure occurred by fibre buckling localized

in very narrow bands (kink bands). This was reported to be the mechanism of

failure mode in carbon fibre reinforced epoxy. When loaded, either in flexure or

in compression30-32, some relief of local stresses accompanies the micro processes

as the crack propagates from compressive side to the neutral plane. Further

deflection of the beam causes a tensile failure of fibres on the tensile side of the

beam, which leads to catastrophic failure of the specimen. In some cases, some

amounts of inter laminar shear failure, initiated from the kink bands, was

observed on the compressive side8. Constraints imposed on the beam by contact

with the load pin may also inhibit the initiation of bukling in flexural testing.

Fig. 3.7, 3.8 and 3.9 show the effect of fibre loading, fibre length and fibre

orientation on the flexural strength, flexural modulus and flexural strain of sisal

fibre-PS composites.

Mechanical Properties of Short Sisal Fibre - Polystyrene Composites 113

0

20

40

60

80

100

120

U20

6 T

U20

10 L

U20

2 L

U30

6 L

U20

6L

U10

6 L

PS

Flex

ural

stre

ngth

(Mpa

)

Fig. 3.7 – Variation of flexural strength of sisal fibre –PS composite as a function of fibre loading, orientation and length

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

U20

6 T

U20

10 L

U20

2 L

U30

6 L

U20

6 L

U10

6 L

PS

Flex

ural

mod

ulus

(MPa

)

Fig. 3.8– Variation of flexural modulus of sisal fibre –PS composite as a function of fibre loading, orientation and length

Short Sisal Fibre Reinforced Polystyrene Composites 114

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

U20

6 T

U20

10 L

U20

2 L

U30

6 L

U20

6 L

U10

6 L

ps

Flex

ural

stra

in

Fig. 3.9 – Variation of flexural strain of sisal fibre –PS composite as a function of fibre loading, orientation and length

From the figures it is clear that the flexural strength and modulus increases with

fibre loading. It is also interesting to note that the addition of 10% fibre reduces

the flexural strain of PS followed by improvement at higher fibre loadings. The

maximum flexural strain was observed at 30% fibre loading (Fig.3.9).

(b) Effect of fibre length and orientation

The effect of fibre length on the flexural strength, modulus and strain is given in

Figs.3.7, 3.8 and 3.9 respectively and shows that all the flexural properties

increases with increase in fibre length and follows the order U210 >U206 >

U202. Ultimate failure is controlled by the strain magnification caused by the

presence of fibres. It is also interesting to note that the flexural strain of 2mm

composites is less than that of neat PS. The effect of fibre orientation on the

Mechanical Properties of Short Sisal Fibre - Polystyrene Composites 115

flexural properties of composites given in Fig.3.7, 3.8 and 3.9 show that the,

when the fibres are oriented perpendicular to the applied force, flexural properties

are maximum.

3.3 Theoretical modelling of tensile properties

The modulus of a material depends primarily on geometry, particle size

distribution and concentration of the filler. In addition to the above factors,

tensile strength depends strongly on the geometry of filler particle and

polymer/filler interaction. In literature a number of models have been developed

to predict the tensile properties of the composites. The suitability of some

important models for predicting the tensile strength and modulus of sisal fibre –

PS composites is examined in below.

(a) Modified rule of mixtures (MROM)

The modified rule of mixtures (MROM) 33 to predict the tensile properties of the

composites can be written as

( ) )1.3........(..........1 ffufmcu VV σσσ +−=

Where,

cuσ is the ultimate strength of the composite, mσ is the matrix strength at the

failure strain of the fibre, fuσ is the ultimate strength of the fibre, is the volume

fraction of fibre and is the effective volume fraction of the fibre. The

effective fibre volume fraction is given in terms of the fibre volume fraction and

the ratio of real contribution as follows

fV

feV

( ) )2.3.......(..........1 PVV ffe −=

Short Sisal Fibre Reinforced Polystyrene Composites 116

Where,

P is the degradation parameter for the effective fibre volume fraction and 0<P<1.

P can be calculated from the micro geometry of the composite component and

depends only on the fibre volume fraction because the micro geometry depends

mainly on fibre volume fraction under identical manufacturing conditions.

P can be calculated from the equation

)3.3......(..........ffu

cu

VP

σσΔ

=

Where,

cuσΔ is the difference between the experimentally measured strength and the

strength predicted from the rule of mixtures.

(b) Parallel and series model

According to these models, Young’s modulus and tensile strength and modulus

of the composite is given by,

Series model

)4.3......(..........mfufm

fmcu VV σσ

σσσ

+=

)5.3......(..........mffm

fmc VEVE

EEE

+=

Where, Ec, Em, and Ef are the Young’s moduli of the composite, matrix and fibre

respectively. cuσ , mσ and fuσ are the ultimate strength of the composite, matrix,

Mechanical Properties of Short Sisal Fibre - Polystyrene Composites 117

and the fibre respectively. In this model the stress was assumed to be uniform in

both matrix and fibre34.

(c) Hirsch model

Hirsch model is a combination of both parallel and series models35. According to

this model the tensile strength and Young’s modulus are calculated using

equations

( ) ( ) )6.3......(..........1mfufm

fumffummcu VV

xVVxσσσσ

σσσ+

−++=

( ) ( ) )7.3......(..........1mffm

fmffmmc VEVE

EExVEVExE

+−++=

Where,

‘x’ is a parameter, which determines the stress transfer between fibre and matrix

and the value of ‘x’ mainly depends on fibre orientation, fibre length and stress

amplification effect at the fibre ends.

(d) Halpin –Tsai model

This model can predict the modulus of the blends and oriented composites and

can be represented by the equation

)8.3......(....................1

1⎟⎟⎠

⎞⎜⎜⎝

+=

f

fmc V

VAEE

η

Where,

)9.3........(..................../

1/AEE

EE

mf

mf

+

−=η and

‘A’ is measure fibre geometry, fibre distribution and fibre loading conditions.

Short Sisal Fibre Reinforced Polystyrene Composites 118

0 5 10 15 20 25 300

20

40

60

80

100

120

140

Series modelMROM model

Bowyer model

Hirsh model

Experimental B C D E G

Tens

ile s

treng

th (M

Pa)

Fibre content (wt %)

Fig.3.10 - Comparison of experimental and theoretical tensile strength values of PS-sisal fibre composites.

0 5 10 15 20 25 300

300

600

900

1200

1500

1800

2100

Series modelBowyer modelHalpin- Tsai modelHirsh modelExperimental B

C D E G

Youn

g's

mod

ulus

(MP

a)

Fibre content (wt%)

Fig.3.11 - Comparison of experimental and theoretical modulus values of PS-sisal fibre composites.

Mechanical Properties of Short Sisal Fibre - Polystyrene Composites 119

(e) Bowyer and Bader model

As discussed in chapter 1, according to this model, the tensile strength of short

fibre reinforced composite is the sum of contributions from sub critical and

supercritical fibres and that from the matrix36. According to this model, the

tensile strength is given by

)10.3........(..........21 fufmmcu VKKV σσσ +=

Where, K1 and K2 are the fibre orientation and fibre length factor respectively.

Depending on the fibre orientations the value of K1 changes. K2, the fibre length

factor is given by, K2 = L- Lc /2L ( for fibres with L>Lc) and, K2 =Lc /2l (for

fibres with L< Lc) . In these equations L is the length of the fibre and Lc is the

critical fibre length.

Theoretical tensile strength values of PS-sisal composites calculated using

different models given in Fig 3.10 shows that the models give tensile strength

values comparable to experimental values except at 10% fibre loading.

Theoretical modulus values calculated using different models given in Fig 3.11

shows that Halpin-Tsai model gives good agreement with experimental values up

to 20% fibre loading. All other models give modulus values much lower than the

experimental values. The deviation from the models could be due to various

factors. The chance for the formation of micro voids between the fibre and matrix

during the preparation of composites greatly influence the tensile properties of

the composites. This factor is not accounted for in any of the models used.

Moreover, in all models used it is assumed that the fibres are cylindrically

Short Sisal Fibre Reinforced Polystyrene Composites 120

shaped. However, the actual shape of the sisal fibre is not perfectly cylindrical

due to surface irregularities.

3.4 References

1. G.R.Lightsey, in Polymer Application of Renewable Resource Materials,

C.E.Carraher, Jr. and L.H.Sperling, Eds., Pleanum Press, New

York,1983,p.193.

2. W.D.Callister.Jr., Materials Science and Engineering, John Wiley and

Sons, Inc., New York, 1985.

3. B.Sing, M.Gupta and A.Verma, Polymer Composites, 17,910,1996.

4. J.K.Kim, S.Lu and Y.W.Mai, J.Mater. Sci., 29,554,1994.

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