hybrid fibre reinforced polymer...

INTERNATIONAL PLASTICS ENGINEERING AND TECHNOLOGY VOL 1. 87-98 (1995)

HYBRID FIBRE REINFORCED POLYMER COMPOSITES

G Kalaprasao and Sabu Thornas Scnwl d Chem car Sctencer. Mahslme Gandh Unl8erstty

Pr~yadars n8 t + , s P 0 , Konayam-686 5W Herald, hO!a

ABSTRACT

Thfs paper pcovides an inslght into the mechanical propenies and failure behaviour of hybrid fibre reinforced polymer composnes. Thereare indlcationstnatthe reinforcement Mtwoiypes of fibres into a single matrix often leads to bener properties that would be expeaedfromtheconsideration of the rule of mixtures The recent developments in hybrid fibre reinforced polymer composites have been discussed These include the properties d synthnic fibre1 synthetic fibre, synthetic fibrelglassfibre, naurallibrelglassllbre. Morespecificallythe effectofincorporationotshongiass flble in sisal reinlorced low density polyethylene (LOPE) composles has been presented. It was found that addiiion of glass fibre considerably improves the tensile strength of sisal reinforced polyeihyiene. 1 he effect of orientatton of the fibres an tensile nrength was also studied. it was found thalthe composites containing longltudlnally orienledlibres exhibil bener tensilspropenies than those with randomly oriented znes

1. INTRODUCTION

The investigation of the novel propellies of hybrid composites has been of deep interest to the researchers for many years a$ evidenced by excellent reports [l-31. The incorporation of two or more fibres wittlin a single matrix, is known as hybridisation and the resulting material is referred to as 'hybrid' or 'hybrid composites'. Hybridisation offers a lucrative mode for fabricating producis with reduced cost, high specflic modulus, strength. corrosion resistance and in many cases excellent thermal stabiiity. Based on the-viay of fabrication, different types of hybrid composites can be prepared. Short and Summerscales (41 reviewed the literature related to different types of hybrid composites. The following are the different types of hybrid constructions (Figure 1).

(a) Mixed fibre tows

In this. two types of fibres are intimately mixed throughout the resin with no specific concentration of either types of fibres.

(b) Mixed fibre ply

This consists ol discrete layers of a rntxture of the individual fibres.

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2. EXPERIMENTAL

Luw tl?liSity pdyethylene (LDPE) granules obtnned from Mis Indian Petrochemical Corporat~r,r> Ltrl Barodti lltlilia wpre used The chopped glass libre (6 mm) was supplied by Ceat Ltd. Hydr?mlw,l hdia

sisal Itbrl1 *'as 01,tamed lrom local soi8ices The niain physical and mechanical propertas ot il;Pse rnnleria~ are llcted in Table t(a8b) All other ctiemicals used in the work were of rfagerit grade alld used v<itI,out funher purification

~ a b l a 1. ~ h y r , c a i and me~hancoal propenler 0 6 low density po,yetnyrens ( ~ ~ ~ ~ h i d o t h e n e ~ S M A 4001, glass l#bre and rlsal f i l e

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Clmpped sisal and glass fibres ot 6 mm length were used for making composites. Firstly. for the preparnl8otl 01 lhybra composite, the two fibres were intimately mixed with LDPE by a solullon mixing techoi<l\le developed by our re~earch group [12.13] The fibres were mixed with a slurry of LDPE in tduerli. Ilia1 has heen prewred by adding toluene to a melt of the polymer. The solvent lrorn thp mix was rrrlnoved lby evaporation The mix was lhen enruded through a ram type hand operated ir,jcction fnilulding machine at a temperature of 125 2 3°C. For the preparation of longitudinally oriented compozltes the extrudates having diameter 01 4 mm were cdlected and aligned In a leaky mould 1141. They were then Compression moulded at a pressure of about 8 MPa and a1 125 2 3'C The conlposites so 0btaiof4 were removed alter coding the mould below 50°C. Rectangular specimen having size l20 26 6 5 7 S mm were cut lrom abave composites for further testing Randomly oriented composite

slbeels (120 . 12 5 r 3mnr) were prepared by standard injection moulding of !he mix vsirly a rnrn type l la l l~ i l ~ l l ( i r t l ~ i l rilotcldfng machine

T l i i i1wrl1nnical lasting of the hybrid composites were carried out on a Zwick 1,165 Llo<veisal ir:sl,r!q t,laclllnn at a cross head speed of S mmimin and a gauge length of 50 mm 4 standard UThl IellcIr lnst t,rt,cl;lmmr *.'S used to evaluate tlie ililimate tensile strength.

3. RESULTS AND OfSCUSSlOM

(a) Synlhetic libre'synfhelic fibre hybrid composites

:~ rnr8 ' 8 ~ i c .>W d r ~ t c l *or* ?>as own r~pon6.,.1 rn tnc 18ed of s)r>ll8eloc ~,,f#to?!c ,ur , 1 , re r . ' i 1 t ..,?>rl r r o l ~ l ~ : o ~ . t ~ s Peq9 and Dc nuh1151 st.dato the enrcl 01 h,t,ra.rlt 71 1 11...11 , .~. . , fl.,r' t ..r'<>rlna!lr*, (X, yefhi snp n P PF a8)o coruon llnres 0 x 0 fne IOII!.~~ A ~ I l.11 .I ;. I . .U. ..r

of ei,oxy resin Tlrey oh~er.~rr i t,ig17er Ilylrrid enecl , W the case of iiltimatrly nltxcd hyllrld COIIII'(ISIIPT coiltaining H P ~ P E l i l~res and ca r l~a !~ fibres than sandwich tyDr (Figure 7) Potyutl~~lelle Ilhrr 15 . l lllgll eior><,atiocl c ~ o i ( > ~ ~ ~ c ! i ~ l t l ~ i ~ o C A ~ ~ O I I l8liic which \S a low elongatiotl co!~i(,onenl Tl~erefori.. 1111,y 1,4 griteif Illat 1hyhrid eRarl is oilsewed nofy 1 Ifhere 15 an enhancenlel~t in llle first failure ar:llll ill lrivi

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elangatior> fibre re in forc~f com~onent They could observe a first failure stralrl enhancemrl,l nl1iS : l

the case of intimately mixed hybrid, whereas for sandwich hybrids rlo strain enhancenlel~l detected Table 2 sllows rile terlsile test data 01 a series of composites lrom their experinlellt

~~- ~ ~ - . ~ ~~~~ ~ ~ ~~ -~

M O O U ~ ~ , ~ E i enr i~e Slrpngth F s u i e rtramn ~ ~ h ~ ~ r ! elcec! M~terlPl (GP-I IMPal 1'1) I I

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,nlermtngled (unlieateril AR ? 360 1 53 R 5

hlermingled Ifreildl 87 ,460 169 , U " ~~~. .~~

Marom et a l ( t 6 ~ repone* on the ffexural behaviour of aramfd!carbon hybrid fibre reicllorced eW*y resin compositns. They concluded that aramid l~t~relcarbon fibre sandwich hybrids (ACA) willi aramlil

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H$rid men of Shon SLrol/Glass Hybrid Composites 49

Hybrid Effect in the Mechanical Properties of Short SisalIGlass Hybrid

Fiber Reinforced Low Density Polyethylene Composites

G. KALAPRASAD AND SABU THOMAS* School of Chemical Sciences Mnhnha Gnndhi Universiry

Pn'yadnnini Hills EO. finayam-686 560

Kemln, India

C. PAWHRAN Regional Research Laboratory

' Ihim~~(lllthapumm-695 019 Kemln, India

N. R. N E E W A N AND S. BAUUWSHNAN Chemical Engineering Division Indim brrrifute of Technology

M&-WO 036 India

A B S T R A ~ ~ : Hybrid composites of low density plyethylene (LDPE) reinforced with intimately mixed short sisal and glass fiben were prepared by solution mixing technique. The mechanical properlies of these composites haw been investigated with reference 1" the dfm of orientation aod composition of fiben in them. It has been observed that Vle wmposites confaining longimdiily oriented fiben exhibit better mechanical pmpetiies than those with randomly oriented ones. Also it is seen that the mechanical pmpenies in- creare with increase in the wlume fraction of glass fiben in the hybrid wmposites. The e k t of chemical modification of sisal fiben on tie properties of 50:50 sisallglass fiber composites has also been studied. The hybrid effect was calculated by the additive rule of hybrid mixtures wing the mechanical properlies of individual composites. A positive hybnd e M wds exhibited by the composites for all the mechanical pmpefiies except b r elongation at brral.

~ u U w ~ , ~ h o m ~ ~ W d b c . d d r r r u d

48 Journal of REnu~o~cw PLASTICS A N 0 COM~SITES, %lbl- 15-JMWV 1996

m16844~)6/01 an8-26 SWlOOlo Q 1996 Techmmc Publtshng CO.. h.

INTRODUCXION

T HE INVESnCATlON OF the novel properties of hybrid composites has been of deep interest to researchers for many years as evidenced hy excellent rewrts

[l-61. The incorporation of two or more-fibers into a single matrix, leading b the development of hybrid composites, offers a lucrative mode for fabricating prod- ucts with reduced cost, high specific modulus, strength, corrosion resistance and in many cases emllent thermal stability It is generallv acceoted that the oroo enies of hybrid composites are contmlled by &tors suLh as nature of the &m;, nature, length and relative composition of the reinforcements, --fiber interface, hybrid design, etc. Miwa and Horiba [7] investigated the &t of fiber length on the tensile strength of epoxy resin reinforced with carbon and glass fibers. They observed an increase in tensile strength of these coinposites with increase in the fiber length of carbon and glass fib& up to a certain level. Beyond this level tensile strength remained unaltered. Peijs and De K& [S] studied the tensile and fatigue behavior of epoxy resin containing plyethylene and carbon fibers. They concluded that the intimately mixed hybrid composites containing chromic acid treated polyethylene fibers exhibit better tensile and fatigue properties than those containine untreated fibers. Mamm et al. 191 examined the hvbrid ~, ~ ~

effects in carbonlcarbon and glasslcarbon hybrid combsites based on epoxy resin matrix. They pointed out that cornposit& containing carbon and glass fiber exhibit maximum hybrid effect than those having carbodcarbon fibers. The reason has been attributed to the difference in fi;ber-matrix interface and the mechanical strewth of the fiben in the comwsite.

Research wurG on lignocellulosic fiber c o b s i t e s showed that their properties can effectivelv be utilized in hvbrid comwsim 110-121. Shah and Lakkad [U] followed the mechanical propekes of ep& and blyeskr resins reinforced by jute and glaqs fiber singly anJ in combinauon as a hybrid. They could observe a sig~ficanr unprovement in the strength and modulus of glass reinforced com- p s b s when j& fibers were addi t iody incorporated &to the matrix. They pointed out that the increase in the mechanical ~mperties mieht be due to the functioning of jute fibers as a filler. Clark and &sei [l01 repoU&d the improvement of various mechanical oro~enies of iutelelass hvbrid laminate wi!h different arrangement of plies in theala&ate. 6 e y sThowed.that the jute core laminates were the most cost effective from the tensile and flexural properties view point. According to than glass core laminates offer exceptionally low cost in terns of impact energy. b a et al. [l41 investigated the effect of three coupling agents, viz., silane, titanate, and toluene diisocymate on the mechanical ~ropenies of jutelglass hybrid fiber reinforced plye&r composites. They cohc6ded that composites containing titanate treated jute fabric exhibit better mechanical prop erties than those reinforced with silane or TDI modified jute fibers.

In the present paper, the enhancement in the mechanical properties of LDPE when reinforced with a synthetic fiber, i.e., glass as well as a lignocellulosic fiber. i.e.. sisal has been examined. Since the basic ~rooerties of the reinforcements, vu. , glass and sisal differ widely, the hybrid && caused.Ly these reinforcements in the same matrix is of considerable significance. Such an investiga-

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RESULIS AND DISCUSSION

Figure 1 shows the stress-strain behavior of pure LDPE, pure sisal, pure glass, and longitudinally oriented hybrid comwsites of sisal and glass reinforced in LDPE. It can be &n from the figure thai pure LDPE exhibitsquite a large necking behavior. Necking of LDPE cannot be xcn in the Firmre 1 due to the chance in-the strain percentage scale. In the case of pure sisal &d glass fiber, the stress increases proportional to shah and a sharp breaking is observed. No necking be- bavior is observed in the case of sisal and glass fibre. When sisal fibre is incorporated in the LDPE, the necking decreases to a large extent and as the volume fraction of glass fibre in the hybrid composites increases the necking again decreases for composite containing glass alone (GRP). This can be explained by the fact that the glass fiber shows more elasticity than sisal fiber which in turn

CP. T 1 . l s CP.

! 'I

l CP. ' ; l

0 2 4 6 8 10 12 63

STRAIN, %

Flgum 1. *ss-shin curves of LDPE, sisa! fiter, glass iiter, hgihldinally orienfed GRP. SRP end W i r hyMd mmposnes.

\

Hybrid Effen of Shon S i r o l / C b s Hybrid Composites 53

* * 90110 (SIG)

-70130 (SIG)

"3000 (SIG) 20 * GRP

0 2 1 6 8 10 12 1 4

STRAIN ( % )

Figure 2. Stress-swain curves olmdamly wientedGRP, SRPand W i r h ~ ~ d m m p o s i t e s .

shows more elasticity than LDPE. It can also be seen in the figure that the yield smss of the hybrid composite increases as the volume fractionif glass inc&ses. Also there is a reduction in the percenragc strain of the composites with i n c m u in the wlume fraction of glass. This is due to the fact that glass is highly brittle. As the volume fraction of glass increases the yield strcss of the mmwsite wstem increases but at the same L e the system b&mes more brittle. ~e increase in the value of yield stress with wlume fraction of glass fiber is attributed to the high modulus of glass fibem oriented perpendicular to the direction of crack propagation. Figure 1 clearly shows that as the wlume fraction of glass fiber increases, the area under the m e decreases. This indicates a reduction in the overall ductility of the samples.

The stress strain behavior of randomly oriented composites is depicted in Figure 2. It is o k e d that these composites exhibit lower tensile strength than

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the longitudinally oriented ones for all compositions. They also show necking behavior. Randomly oriented fiben act as barriers and prevent the distribution of stresses throughout the matrix and this in turn causes higher concentration of localised stresses. This explains the reduction in tensile pmperties of randomly oriented comwsites. But the wrcentaee strain is hieher for randomlv oriented ones com& to their ~ o n ~ i ~ d i n a l &nterpam (Figure 1) for all compositions. The enhancement in the Dercentaee strain of randomlv oriented comwsites is attributed to the d e c k . effecI2 randomly o r i e n d fibers on ma& shain. It may be noted that the fibers have considerably l m percentage strain compared to the matrix and their alignment in the direction of the applied sh'ess effectively reduces the percentage strain of the matrix. Hence composites containing longitudinally oriented fibers exhibit lower percentage strain than the randomly oriented ones.

Firmre 3 show the s t r e s s - s h behavior of 5050 sisallelass hvbrid comwsites containing alkali mated and untreated sisal fibers (both?ongi&dinal and &random). The firmre clearlv indicates that the tensile svenmh of comwsites wntain- ing heated :sal fiber is higher than those with un&ted fiberf. The effect is pronounced only in the case of samples containing longitudinally oriented fiber composites. AlkaIi mahllent improves the m u d ~ e s s of the sisal fiber surface as can be seen hum Figure 4. ThiIhib enhances the-mechanical interlocking between fiber and mauix (LDPE). The enhancement in tensile strenmh of veared sisal hybrid composites may be ateibuted to the efficient stress &sfer between the fiber and the matrix due IO impmved adhesion between mated fibers and matrix. Figure 3 also shavs a decrease in percentage strain of alkali eeated sisal fiber hybrid composites compared to untreated ones for longitudinal orientation. The decrease in strain clearly indicates the enhanced compatibility between treated sisal fiber and polyethylene matrix.

Figures 5.6.7.8 and 9 show the miation in tensile strenmh. Youne's modulus. elon&tion at break, tear strength and hardness respectivel~ofhybridcomposit& as a function of wlume fraction of elass fibers. The firmres reveal that all onoer- - . . ties except elongation at break inc& with increase in volume fraction of glass fibers. Addition of glass in the sisal-LDPE system helps to attain a uniform dispersion of the sisal fiber and prevent fiber to fiber contact in the matrix. This can be understood hum the opti& photographs shown in Figure 10. Figure IC(a) and IO(b) mresent GRP and SRP rcs~ecovelv. Flrmre 10(c) indicates the decreased fibe; to fiber contact on addition of glass he;. As ie'volume fraction of glass increases, agglomeration of glass fiber takes place [(Figure 10(d)]. This in fact accounts for the decrease in positive hybrid &ed at high glass fibre loading which is discussed in me coming section. The increase in tensile strength of hybrid composites (Figure 5) is due to the higher tensile strenmh of glass fiber than sisal fiber and a& the digh degree of dispersion of the si& by h e additional incor- oration of alass fibers. Fieure 5 also shows that in the case of tensile streneth of bdomly Griented composite addition of glass fiber results then L no remarkable impmvernent in tensile strength. 6 i s clearly highlights the fact that if glass fibers an not oriented. Irybridsation makes no improvement in the tensile

Hybrid men ofShon Sisal/Clars Hybrid C o m p o s i I C S

LONGITUDINAL: -- RANDOM 25v,

STRAIN ( % )

Fbun 3. Swss~rmin curves of50:50 sidglass hybrid corn- Cmfalning L I ~ ~ ~ and elkall beefed W fibem (k+X~iiUdininlll and mm).

sWngth of the composites. ~cadning electron micmgrapl;s of the tensile fracture

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&1 G. KALAPRA~AO ET AL.

surfaces shown in Figure 11 reveal that tensile failure of untreated fiber wmposites is mainly due to fiber pull out. Variation in Young's modulus values of longmtudinal and randomly oiiented composivs ulth volime frdctlon of glass IS

\een in the Fmeurc 6 It IS ohxrved lhat increase in Youne's modulus of both the directions (loigitudinal and random) is due to higher young's modulus of glass fiber wmpared m sisal fiber. Figure 7 reveals the reduction in elongation at break values of hybrid composites by the addition of glass fibers. It is interesting to see that in both cases (lonaitudinal and random). eloneation at break values were decreased by the addition of glass fibers. ~ i & r e 7 Zso shows that elongation at bnxk values of loneitudinallv oriented comwsite arc lower than that of randomlv oriented composites.

Figure 8 shows the tear strength of longitudinally aligned hybrid composites. The property increases with increase in volume fraction of glass fibers. The tear strength of LDPE is very low compared to h) brld wmposmlei At the llme of tear- mng fiben in the composite prevent the gmwth of crack front because the fikn ari aligned to-the direction of crack growth. This in fact increases the tear strength of the composite. Tear strength of glass fiber composites is higher than that of sisal filled composites. Load-displacement curves (tear curves) of the sample arc given in Figure 12. Polyethylene tears at the minimum force with maximum displacement. GRP tears at the highest force and at the smallest displacement. This indicates that glass reinforced composites have high resistance to tearing. It is seen that the tearing force decreases and displacement increases with the decrease in the amount of glass fiben.

Figure 9 shows the hardness values of hybrid composites with increase in

Fbum 11. SuvrnlfIg elecmm micwraph of hactum surface of hybrid composite containing unmated m.

Hybrid Effen of Son Sisol/Glm Hybrid Composires

DISPLACEMENT, mm

Flgura 12. Load-displacement curves of LDPE, SRP, GRP, and their hybrid C o r n M s .

Table 3. Varlatlon 01 tensNe strength wlth volume fractlon o f GRP In slsal/glass hvbrld comwslles.

Tmslle Stmngth of Tensile Stmngth of Volume Fractlon Longltudlnslly Oriented Randomly Oriented

of F l k m Composltss (MPa) Hybrld Composites (MPa) Dealgnation Slsal Glass VS.. v,. Experimantal Theomtlcal Expcrlmantal Theomtlcal

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7 - l:?,, 0.2 - 0.8 %ix%i 21 .X7 9 8.87 GRP - 1 22.94 9.28

SRP-SIMI relnlorced pla~tlc; GRP-G18a reinforced plastic. P

r:

r 0

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Young's ~odulus of Young's ~oduius of S. Volume Fnctlon Longltudlnally Oriented Randomly Orlenled 6

of Flbsn Composltra (MPa) Composites (MPa) Hybrld

8 Dealgnstlon Sisal Glass V, Vmr Experimental Theoretical Experimental Theomtlcal g

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13' 151 ! 158

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7 0.06 0.16 0.2 0.8 210 202.66 194.6 186

GRP - 0.2 1 220 - - 200

SRP-Sisal nlnforcsd plastic: GRP-4 laa reinforced plastlc.

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Influence of Short Glass Fiber Addition on the Mechanical Properties of Sisal

Reinforced Low Density Polyethylene Composites

G. KALAPRASAD, KURUYILLA JOSEPH AND SABU THOMAS* School of Clrcnrical Sciencrr Mahnofta Gandhi Universiv

Pri?adarshri Hills PO. Korrrrynm-686560

Kerala, India

ABSTRAm: Thls paper presents the evaluation of enhancement in the mechanical pmpenies of sholr sisal fiber reinforced polyethylene composites by the incorporation of shon glass fib r as an intimate mix with sisal, Intimately mixed shon glass-sisal hybrid fiber reinforce3 polyethylene composites (GSRP) were prepared by solulion mixing tech- ntque. The effects of fiber orientation and alkali treatment on sisal fiber in GSRP were studied. Addition of relatively small volume fraction of glass (0.03) to the sisal reinforced polyethylcne matrix (SRP) enhances the tensile strength of longirudinally oriented composites by about 80%. Addition of the same volume fraction of glass to the alkali treated !,(sal incorporated SRP enhances the tensile strength by more than 90%. The flexural strength of lhc longitudinally oriented composites was also studied. The incorporation of $lass fiber (V, = 0.03) to SRP enhances the flexural strength by more than 60%. The effect of hvbridimlion on water absomtion tendencv ofthe sisal fiber was studied bv im-

KEY WORDS: hybrid. siral reinforced composites. glass reinforced composites. tmcchanical prupenies.

INTRODUCTION

T HE REINFORCEMENT OF two o r more fibers into a single matrix leads to the development o f hybrid composites with a great diversity of material prop-

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sJaqg paleaJtun 8u!u!auo~ asoql ueqi 'sa!l~ado~d anS!tej pue a[!susl Janaq l!q!qxa sJaqy auaLlqlaLlod paleaJ1 p!se s~ruo~qs 8u!u!e1uos sa!sodiuos p!lq.iq pax!m L[a~e~u!lu! leql punoj ,Laq~ -1aqy uoq~es pue aualLqlaLlod asue~ulo~~ad q81q Bu!u!muos u!sa~ Lxoda Jo Jo!neq -aq an2!1ej pue al!sual aql pa!pnls [6] qoyaa pup s!l!ad 'ql8uaJls IrJnxay ~!aq1 U! uaya p!~qLq ~n!l!sod e si!q!qra paa~oju!~~ Jaqy uoq~e~ pup u!ys pa3loJ -u!aJ Jaqy p!UIeJe ql!m pllqkq q3!npUeS ad,<] (VJ~) p!Ull?Je/Uoqle~ip!lU"rp 1Pql papnlsuos iaq~ -cal!sodtuos p!~qiq ulsal ixoda p~sloju!a~ laqy uoqJe3/p!tusJe JO Jo!neqaq [CJnxaU aql uo pallodal [g] 'll! I3 UJoJe~ Is\al [Ps!Ul?q3aluOl3!lll e uo SJolsalle y~e12 ay![ saAeqaq lsqy uolle8uola q2!q anuaq pue sa~~sodmos aql q3noJql SyJRJ3 ale8edold 01 paJ!llbaJ [JnsI U!PJls aql SJXIFqUs ~~!SO~LLIO> aql u! snqy uo!ie2uola qX!q 'sa~!sodmos p!lqLq aql jo aJnl!eJ uo 1~111 papnlsuos aH -s~aqy uo!leZuola q8!q pue MO[ ;?U!U!PIUOS sa~!sodu!os p!~qLq JO ~I~U~JIS al!s -U21 3ql "0 p3llod3l [L] uaqamz Jla .u$l<ap p!lq,<q '32l?JJallI! X!llI?lll-Jaq!J 'SlUslll -a3Joju!a aqr jo uo!~!soduo~ aA!lrlaJ pue qlSua1 'alnleu .Y!JIPUI JO 3JnlPU se qJns S1OIJPj .iq Pl'[llllIu03 318 sal!sodu~os p!rqiiq Jo sa!l~ado~d 541 leql palda~se (I~B

~aus3 S! 11 le!raleu al!sodtuos Luv ui IuaJaqu! ca;imuc,ipos!p pue sa2muehpe aql uaamlaq axelcq alqnJo.\ej alou e S! alaql q2!q~ U! sruauodmos jelip!n!pu! aql jo tuns pnqZ!aw e ii[dn~!s aq ol s~eadde sal!sodulos p!~qLq j0 ~oi?l?qaq Jl~l leql pai~udal ~usq~ jo ISON -[g-l] sJaqsloa\a iuem <q paq!jssap uaaq aneq xlllern aldu!s r u! s~aq!( jo spu!y OM] i;u!u!qluos sade~ue~pr le!lualod aql sa!lJa

512 G. KALAPRASAO. KUKL'VILLA J ~ S E P H AND SABII THOMAS

testins machine with a cross head speed of 50 n~rnlmin and a gauge length of 50 mm. The lcnsiie n~odulus and elongation at break ialues of the composites were calculated tnlm the stress-strain curve. Stress-strain data was obtained from load vs. extensii~n curves obtained during the tensile testing.

The flexural testing of rectangular specimens of the size (120 x 20.5 X 2.5 mm) uah carried out, by three point bending mode. using an lnstron testing machinc at a cross head speed of 2.8 n~rnlmin and a span length of 100 mm.

RESClLTS AND DISCUSSION

Stress-strain curves of hybrid composites under tension are shown in Figures 1-3. Figure I shows the stress-strain behavior of longitudinally oriented fiber composite>. I t can be seen from the figure that the sisal reinforced low density polyethylene exhibits yielding behavior but the yielding tendency decreases to a large extent as the volume fraction of glass fibcr in the hybrid composites increases. This is due to the more elastic nature of glass fiber than sisal fiber. The yielding behavior also decreases as the volume fraction of glass fiber increases. This may be attributed to the brittle nature of glass fiber compared to sisal fiber. But as the \.olume fraction of glass increases the yield stress of the composite in-

. .

LONGITUDINAL TYPE O S R P ( S I S A L 0 I*) *GSRP G l a n 0 015 X G S R P GI.3. 0 031

*GSRP Glass 0 0 5 "GAP I G U S S O I 0

-- 0 l 2 3 4 5

STRAW, %

Figure l . Slress-strain curves of SRP. GRP and GSRP with Iongitudmal fiber 0r;entalron.

Mcchmiical Properties of Six01 Retnfurcrd Low Detirn A,h.rrhylme Cunrpo~irr.r 513

RANDOM TYPE

OSRP [SISALO 141 *GSRP ( G I ~ T S o o l i i

* G S R P [Glass 0 0 3 0 *GSRP iGil.3 0 05)

0 GRP (GLI\SS 0 14,

STRAIN. %

Figure 2. Stress-strain CUNes of SRP, GRP and GSRP with randam fiber oiientatron

creases. The increases in the value of yield stress with volume fraction of glass fiber is due to the high strength of the glass fibers which are oriented pcrpendicu- lar to the direction of crack propagation. The shapes of the stres-strain curves in Figure I also indicates that. as the volume fraction of glass fiber incrcases, the hybrid coniposites (GSRP) become stronger and hardcr compared to SRP.

The stress-strain bchavior of randomly oriented complsites is dcpicted in Figure 2 . All the hamplo show necking beha\ior. I t i \ observed that these composites exhibit lower value of yield stress than longitudinally oriented ones for all compositions. The randomly oriented fibers act as harriers and prevent the stress transfer between fiber and matrix. and thus contribute to higher concentration of localized stresses. This explains the reduction in yield stress value and necking behavior of random type hybrid composites. Randomly oriented con~pcrsites exhibit high value of percentage strain compared to longitudinal and transverse type compoiites (Figures 1-3). This can be due to the decreased elkct of rdndomly oriented fibers on matrix strain than trans\.ersely o r longitudinall! orientcd fibers. It may be noted that thc libers have considerably lou'cr percentage strain compared to the matrix. and their alignment in the direction of the applied stress eRectively reduces thc perccnwge strain of the matrix

Figure 3 shows the \tress-strain behavior of transverse type hybrid composites.

q13ua~ls apsual aql ins .auo JSIIPI aq~ 01 paleduos SP JSMOI ~JE L;an[e,\ aq1 SJUO

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SVNOHL nev~ UNV H~~SO[ vi rl.\iln~~y 'o~~vnd~ivy 9 PIS

G. KALAPRASAD, KURUVILLA JOSEPH AND SABU THOMAS

O G S R P LONGITUDINAL ~ G S R P R A N D O M

* G S R P T R I N S V E R S E GSRP TREhTED LONG,

*GRP LONGITUDINAL * GRP RANDOM

40 l

* GRPIRANSVERSE

"5

0 0 02 0.04 0.06 0.08 01

VOLUME FRACTION OF GLASS

F~gure 5 . a , a ' - - 0 1 teils e srrengrh n m .c .me lractcri cl y ass l ~ r GPPana GSRP *.m 0 ' C Id .C .-C 1ra:l.- olglass ,n GRPano 0 l4 ,n ra ' ,O!*me lracron of $,Sal ~n GSRP a1 ln'ee o,t - i !a ' . o' roe ' ce rs

Mechanic01 Proprnies of Sisol Reinforced Lon. Denriq Polyethylene C ~ n , ~ o s i r e r 517

values of transversely oriented GSRP and GRP are nearly the same at all volume fractions of glass. Figurp 5 also shows that at 0.03 volume fraction of glasb (V, = 0.03) the alkali treated sisal incorporated GSRP has higher values than GRP. Howevcr. furthcr increase in \,olume fraction of glass fiher beyond 0.03 decreases the tensile strength of GSRP This reduction in tcnsile strength is due to the a ~ l o m e r a t i o n of fibers at hieh volume fraction of elass fibers. At IOU - volume fraction of glass fiber the increasing trend in tensile strength is attributed to the inloroved disocnion of sisal fibers bv the addition of elass fibers. In a re- , ~~~

-~~ - cent study 1191 we have already reported that the improvement in mechanical

~~ ~ . . properties of sisal-glass hybrid composites is mainly due to impro\,ed dispersion of sisal fibers bv the additional incorporation of elass fibers.

Figures 8(a),.8(b) and 8(c) represent the photomicrographs of tensile fracture surfaces of the SRP. GRP and GSRP resoectivelv. From these ~hotoeraphs it is - . seen that as a resul; of poor interfacial bonding between fiber and matrix shcar failure occurred in SRP, GRP and GSRP composites. Scanning electron micrographs of the same composites are shown in Figures 9(a), 9(b) and 9 ( c ) High degree of fiber pull out as seen in these photographs gives a cicar evidence for

" 0 0.02 0.04 0.06 0.08 01


Figure 6. Variation of tensile modulr?s with volume fraction of glass for GRP and GSRP with 0.14 initial volume fraction of glass in GRP and 0.14 initial volume fracfion of srsal in GSRP at three orientatron of the fibers.

Mcrhanicul Propvrficr < fS i .~n l Reinforced Low Detirit? P<,lr.efhylene Comporifer 519

0' l 0 0.02 0.04 0.06 0.08 0.1

\L\ VOLUME FRACTION OF GLASS

Figure 7. Vanafion of elongation ar break wifh volume fracfion of glass for GRP and GSRP with 0 14 rnifial volume fraction 01 glass ,n GRP and 0.14 ml!,al volume fraction of sisal in GSRP at fhree orientalion of the libers.

the shear failure in all these composite\. The micrograph given in Figure 8(c) shows failure surface of GSRP containing 0.05V, of glass lihers. i t i s seen that

. , - to SRP and GRP I n GSRP interface hctween glass-polyethylene is u,e;ll, compared to sisal-pjlyeth! lcne due to the smooth surface of the glass tiher compared to the surfidce ofthe sisal fiher. Therefore. failure initiates and randomly propagates through the weal. glass-po1)cth)lcne intcrfiace.

Figure 6 shows the variation oitenkile moduli as a function of volume fraction of glass tibers. Tensile moduli of all composites increase with increase i n volume fraction o f g las tibcr. Generally as the volunle fraction of non-bonded fihers increase. the tensile modulidecrease because non-honded tibers act as failure ini- tiators. I n the prexent cabc there is no chemical interactton hetuecn the fiher and the nmtrin. However, thereehisr only physical bendins duc to the mechanical in- terlockin: of fiher and matrix. Addition of glass fiber increases the efiecti\,e mechanical interlock in^ betwcen sisal and plyethylene u,hich increases the fric- tional force hetween the fiher and matrix. Therefore. one o f the reason for en-

Figure 8. Photomicrographs of fensile fadure suflaces of (a] SRP (V, sisal = 0.14). (b) GRP (V, of glass = 0.14) and (c) GSRP (V, sisa1:V of glass = 0.14:0.05)

- -. 520 G. KALAPRASAD, KURUVILLA JOSEPH AND SABU THOMAS

(Cl

Figure 9. Scanning electron micrographs af tensile lailure surfaces of (a1 SRP ( V , sisal = 0 741. lb) GRP ( V 01 glass = D. 74) and (c) GSRP /V. s,sal.V. of glass = 0.14 0.05).

Mechanical Properties of Sisal Reinforced Law Uenxiw Polyethylene Composites 521

hancement in tensile moduli is attributed to the fractional force existing between fiber and matrix. Tensile modulus of glass fiber is higher than that of sisal fiber. Thi* also may be another reason for the enhancement in modulus upon glass fiber addition. Figurc 7 sh(ws the elongation at break values of composite at different volume Sraction of glasr fiher. In all cases addition of glass fiber reduces the elon- gallon at break value becauhe of the lower clongation at break value of glass fiber compared to thore of siral fiber and polycthylene.

Figures 10 and I I depict the Rexural properties of GSRP and GRP (longitudinal oriented) as a function of volume fraction of glass fibers. Figure 10 shows that the flexural strength of GRP is almost unaffected by the incorporation of glass fibers. However. in the case of GSRP i t goes on increasing with addition of glass fibers. l'hc incorporation of glass liber by about 0.03 volume fraction in SRP containing about 0.14 volume fraction of sisal increascs the flexural strength by 65% (14.12 to 23.23 MPa). Howe\,er. beyond 0.04 volume fraction the value increases and levels of. This levelling off tendency indicates that the optimum volurnc fraction of glass fiber for maximuni flexural strength is 00.1. It is interesting to note that when the volume fraction of glass reacheh 0.09 the flexural strength of GSRP is

O G S R P OGRP

0 ' _____I

0 0.02 0.04 0.06 0.08 0.1


Figure 10. Variation of flexural strengrh with volume fractron of glass for GRP and GSRP wirh 0. 74 initial volume fracr~on of glass ;n GRP and 0.14 initial volume fraction of sisal in GSRP at longitudinal orientation.

522 G. KALAPRAS~D, KURWILLA J ~ S E P H AND SABU THOMAS Mrchonical Properties ofSi.ia1 Reinforced Lo*, Densily Poiyethylene Compurirc~ 523

LONGITUDINAL I *GSRP " G R P

l 0 1 0 0.02 0.04 006 0 08 0 1


Figure 11 . Variation of flexural modulus with volume fraction of glass for GRP and GSRP with 0.14 inrtial volume fraction of glass m GRP and 0.14 initial volume haclion of sisal m GSRP a: langiludioal or!knta:ioion.

i" very much closer to that of CRP. Figure 10 indicates that in the case of GRP. the flexural modulus does not chanee considerably up to 0.04 volume fraction of glass. Beyond 0.01 volume fraction of glass the value incrcases and finally levels off. For hybrid composites (GSRPI the Rexural modulus regularly incrcases with increase in volume fraction of glass and then levels off. This regular increase i h

due to the hybrid effect caused by the incorporation of glass fibers into SRP. Photographs of the flexural tested samples of SRP, GSRP and GRP are shown

in Figure 12. Figure 12(a) indicates the conipressive side o f a flexural tested SRP. A small whitening region of the surfacc of the sample denotes the formation of a craze at the failure of the sample. Figure !?(h) indicates the compressive side of GSRP. In this case. crazing increases a little more which can be observed from a clear white marking o n the surface of the sample. Figure 12(c) indicates the failure surface of the compressive side of GRP. A sharp white marking on the material indicates that the crazing is brill higher in G R P That is, as g l a s content increases, crazing of the conlpo\ite al\o increases. This may be due to the more brittle nature of glass iiber than s i ~ l fiber.

From the analyiis of mechanical propertie5 ofthe coniposites i t can be said that

(Cl

Figure 72. Pho(om,crographs of the fa,lure surfaces 01 flexural tested (a) SRP (V,sisal = 0.14). (bj GSRP ( V . s,sal:V, a1 glass = 0.14:0.05) and (c) GRP (V, af glass = 0 14).

G. KALAPRASAD, KURWIL.LA JOSEPH A N D SABU THOMAS

Table 2. Weights of sample before a n d after immersion in boiled water.

Weight of Weight the Sample aner 3 h % of Water

Sample (9) (4) Uptake

SRP 0.571 1 0.6372 11.57 GSRP 0.734 0.7566 3.07

sisal behaves not as defects in GSRP but function as a good reinforcing agent in GSRP The results show that from the economic point of view, the maximum benefit out of hybridizatoin is obtained at the volume fraction of glass around 0.03 or at the volume fraction of glass to sisal ratio of 0.03:0.14 in the present case.

The water absorption tendency of SRP (V, of sisal = 0.14) and GSRP (V , of sisal:glass = 0.14:0.03) were determined by immersing these compositcs in boil- ing water for three hours. Circularly shaped samples having diameter 1.96 cm and thickness 2.5 mm were used for water absorption studies. The water absorption of GSRP was found to be 2 to 4 times less than that of SRP (Table 2). The fibers are arranged in randomly close packed manner in which water im- permeable glass fibers act as barriers and prevent the contact between water and hydrophilic sisal fibers and hence prevent the water absorption of sisal fibers.

Comparison with Theoretical Predictions

Tensile modulus of the same hybrid composite was calculated using the modified Halpin-Tsai equation. According to the Halpin-Tsai equation

C, I +A?!', - - - c, l - ? $ v ,

(1)

where C,, and C, are the modulus of the hybrid composite and matrix. V, is the volume fraction of the fibers. In this case V, is the tow1 volume fraction of the two fibers. A is a constant cdlled Einstein's coefficient for composites which is governed by the geometry of the reinforcement. In this equation thc ~ a l u e oCA is found to he 2.5. I t was reported that the A value for aggregates of \pheres can have the sarne value as that of short fibers'or rods [ 2 4 ] The values of 7 and i: are given by the equations.

C, and C, are the modulus values of the fiber and matrix respectivel!.

where m, is the packing fraction of fibers

Mechmical Propenies rfSixa1 Reinforced Low Densif? Polyerhylene Cornpositer 525 ....... SOWRE PACKING ....... p m = o 7 @ 5 ....... ! ....... HEULGOlUL PACKING I ........ 1 h=..907 ....... i Figure 13. Different packing arrangements of libers in the composite.

340 v- GSRP (Long~tua~nall

0 EXPERIMENTAL CTHEORETICAL

l 2 2 0 '

A

0 002 0.04 0.06 0.08 0.1


Figure 14. Variafion of experimental and theoretical tensile modulus with volume fracrion of glass lor GSRP containing an initial volume fraction 01 0.14 sisial m longrtudrnal orientafloo.

It has already been reported on the value of packing fraction for different tiber arrangements in the matrix [ ? 5 ) The different arrangements of fiber5 in the niatrlx are shown in Flgure I 3 These include square packing. hexagonal packing and random packing. In the present caie it is assunled that the fihers arc randomly close ~ a c k e d in the matrix. Therefore. the value of @.. = 0.82 is substi- tuted in thc Equation ( 3 ) . Figure I4 shows the rhcoretical and experimental \aria- r i m o l tensile modulus \r ith volume fraction of glass fibcrs. The figure shows that the experimental \.alues o f tensile modulus is higher than the theoretical predictions. The reasons ma! he attributed to the diflerent diameters of the sisal and glass fiber which afcct the packing fraction. The mixtures of fibers with difierent diameter can pack more densely than one type of fihers having larger diameter. Diameter of the sisal fiber is \,cry much larger rhan that of glass fiber and hence glass fiber can fill the interstitial space between thc closely packed sisal fibers to h r m an aeglomeratc. These agglomerate fibers may be able to carry a larger pro- portion of the load there by increasing the moduluh of the system.

CONCLUSIOS

The enhancement in the mechanical properties of sisal fiher reinforced polyethylene composites by the incorporation of short glass fibers has been described in this pdper. For longitudinally oriented composites the tensile strength has been found to increase by about 80% by the addition of quite a small volume fraction, around 0.03, of glass. The tensile strength of alkali treated sisal fiber containing composite shows an improvement of more than 90% by the addition of the same \,olurne fraction of glass. The flexural strength is found to increase by about 60% for the same composition. It is also observed that water absorption tendenq of the composite decreases by the process of hybridization. The theoretical values of the tensile modulus calculated by Halpin-Tsai equation have been found to he 1ou.er rhan that of experimental values which has been attributed to the increased fiber dispersion with the incorporation of glass fibers into the composites.

REFERENCES

1 Sulllalcr~i.rler. J and D. S h ~ ~ r c 198. G,iriporirc~,~. YI3l 157

2. Loucll. I 1 R IVfi R<.ircl Plc i$ i . ??i71.216

3. Bunrcll. 4 R and B H.<rr#\ 1TI-I. (b,,~p,lrii<%, LlJ1l57. 4 l~i\chri . S ;and G \lrronl 1487 Cirlziiioi. Sr i . Z,,b,iiil.. Z X 2'1.

5 h p h . G. l t i t C H l , 5 I . H;incr,\. cd . I.,,nd,>n: Allied Sciuncc Puhli,hcr\

6. Arrincr>n. h1 and H H r r m 1Y7n C,,niparia~$. 9131:I-IY 7 Zurhen. C. 1W: l .lf,,rc'r Li . lZ:l3?5 X M a n ~ n l . G.. H . l i ~ i ~ l . S. \ i .nn~nn. K . Frlcdrrch. h Schulicand H D \\j:ncr. I Y X Y Crl,ni,i,nr~

du.5. Z(lt6l

Mechonicul Propenies of Sisol Reinforced Low Dmsir? Polycrhylene Comporirrs 527

I ? . A\'cslon. l. and I. hl S ~ l l u r ~ , ~ d . 1W6 .I Moi,r 4 ; . 11.1877

I ? . Ritthcr. H. l477 K~ i rn i r i r~ I~~ , 671121739. I 4 Clarl. R A . a d h4 P Ansell I986 J Marer Sr i . 21.269,

l5 Shah. A . h' am1 S C Lai lad . 19RI f i h i ~ r S c ~ . Z~cl~, i i~ / . . l541

Ih hl<~h:tn. R . Kl,hore. 51 K . Shrldhaiand K. hl V. G K . b o . IUB.2 .l. .Ifiii<'r: 4'4. k v . 2'49 l 7 Pavlllirrn. C . P S \lulher)ee. h 1 Br~hinAurnnr and A . D D a m ~ ~ i l v r i n . 1941 J. .hl,rrcr Sci.

26 455. l 8 Paulthr;m. C . P. S M u l h e r ~ s r and M. Brahrnakurnar 1491. l ReiraJ Pluii. Cot,ii,o,.. 11191 14 ICllaprarad. G.. S. Thunm?. C. Pavnhran. N. R. Neelakanlan and S Riilalr~rhnan 199.1. 1

R<,(,$ Plasr C ~ o ~ n ~ ~ ~ . ~ ZO. kneph. K . . S. Tltoma\. C. Pavichran and h4 Brahlnakurnar. 1993. J. API,~. h,lroi. S<'<.. 4717.

21 Joreph. K.. S. Thornas and C. Pavilhran. I n Prcss. Cr,,npo~. Scr. Z'chrioi

22 1,ad'i~esky. M. H . and l M . Ward 1986. Cutr~por. Sri. T~rJztzol.. 26:129 23 P;nlthiiln. C.. P. S hlukhcrlsr., hl. Brahinskumsr and A D. Darnadaian. 1988. l. Mriii.!: Sci.

L.o. 7:825. 24. N~eibun. L. E l W 4 Rkrrd Acizi. 1386. 25 chawta. K . K . 1987. C,,rrrpuria. ~f~,rcr in l .~ SCIE,~CP and t i i g i n ~ m n f i . Nuu Yorl. NY Sprlngcr

9. PCIII,. A A . I > I .,",I I \I \I r )~L , i 1992 c , , , , ~ ~ ~ ~ , ~ ~ ~ ~ ~ , l J i l l l Y

10. Mnmn,. G . S. Fr.hi.i. F K Tulcr and H D U j g n c ~ Iwn 1 hfoir.r S,# . . 13 1119-1126. 1 1 . Amnhime. J.. H Hxrcl. A Fllhcn and G. Marurn. 149Z Or,,no. .Pi i~clirinl . 43105-116.

J O l I K h A I 0 1 M A T L K I A L S S C I L k C b 32 lI'lY71 4261 4 2 6 7 -

Theoretical modelling of tensile properties of short sisal fibre-reinforced low-density polyethylene composites

G . K A L A P R A S A D , K. J O S E P H , S. T H O M A S * School of Chemical Sciences, Mahatma Gandhi University, Priyadarshini Hills P.O., Kottayam, 686560, Kerala, lndia

C. P A V I T H R A N Regional Research Laboratory, Thiruvananthapuram, 695079, Kerala, lndia

T h e e x p e r i m e n t a l l y o b s e r v e d t e n s i l e p r o p e r t i e s ( t ens i l e s t r e n g t h a n d m o d u l u s ) of s h o r t sisal f ibre-re inforced LDPE w i t h d i f ferent f i b r e l o a d i n g h a v e b e e n c o m p a r e d w i t h t h e ex i s t ing t h e o r i e s of re in fo rcement . T h e macroscopic b e h a v i o u r o f fibre-filled composites is affected b y f ib re load ing , o r i e n t a t i o n a n d l e n g t h o f t h e fibres in t h e c o n t i n u o u s m e d i u m . T h e interfacial a d h e s i o n b e t w e e n f ib re a n d m a t r i x also plays a m a j o r ro le in con t ro l l ing t h e m e c h a n i c a l p r o p e r t i e s of t h e fibre-filled composites. In t h i s study, a c o m p a r i s o n is made between e x p e r i m e n t a l data a n d di f ferent theore t i ca l m o d e l s . C o m p o s i t e models, s u c h as parallel a n d s e r i e s , Hirsch, Cox , Halpin-Tsai, m o d i f i e d H a l p i n - T s a i a n d m o d i f i e d B o w y e r a n d Bader , h a v e b e e n t r i ed to fit t h e e x p e r i m e n t a l data.

1. I n t r o d u c t i o n The mechanical propcrtics of fibre-filled composites arc alrectcd by a number of parameters such as libre length, tibre orientation, fibre dispersion, fibre geo- mctry and tlic degree of interfacial adhesion between fibre and matrix [l-51. In the literature, a number of equations and theories have been developed to de- scribe the relation bctwccn these paralneters and properties of constituent components of composites. Tlie ellicicncy or load transfcr li-om matrix to librc in a composite is strongly related to the optimun~ mechanical properties of the composite.

One of the earliest theories of reinforcement developed by Cox [6] is based on shear-lag mechanism obscrvcd ill librous composites. According to Cox, il l hear-lag analysis, the main aspects of controlling the propcrtics of a co~iiposite are critical length oftlie fibre and intcrFacia1 shear strcngth between librc and matrix. The critical length of tlie fibre, l,, in composites is ;I parameter which dctcrmincs the atnoullt of \tress transferred to tlic libre. Thilt is, if tlic length-to- di;~metcr ratio is higher than the critical aspect ratio, cu~iiposites show superior propcrtics, while for a libre wliosc aspecl ratio is smaller than tlie critical aspect ratio, colnposites show weaker properties. In Cox's treatment, interfacial shear strength is produccd on the su r f~~cc or the libre due to the "shear lag" bctwccn libre and matrix during the failure of the composite. I~lowever. Cox's shear-lag analysis has two rnajor dis- advantageb. The lirst one is tliat stress amplification

elfscts at the fibre cnds are not taken into ilccount, :~nd the second is tliat the matrix tensilc stress possesses no radial dependence.

Piggot modilied Cox's tlicory by introducing a new theory which combines plastic deformation at the libre ends with elastic deformation towards the centre of the libre during tensile loiiding [7].

It was also reported tliat tlic strength of short fibrc- rcinforced thermoplastics and tliermosets are highly dependent on two Factors, such its "fibre orientation factor" and "fibre length factor" which contribute to the strength of the composite 181. In another study, Piggot developed an equation for calculating the minimum volulne fraction of libres for a good reinforcement [9].

Ter~nonia [l01 presented a computer model to study the elfect of libre characteristics on the mecha~l- ical properties or short libre-reinforced composites. Their studies rcvcaled t l ~ i i t t l ~ e cllect of librc orientation on lnodulus atid tcnsile strc~~gtl i or the composite is very weak ilnd it11 . x ~ ~ ) t i ~ i i ~ ~ l i l librc a s p ~ c t ratio is essetitial for clkctive rrinforccmcnt. Tllcy modelled the whole collipositc rnatcrii~l as ;I thrce-dimensional lattice of bonds having dilrcrcnt elastic constants for the fibre and for (lie matrix. They also found that in composites, a micro-Qilure nlechanisrn origin:iles at tlie libre cnds and propagates along the libre inatrix interface with no libre breaking. Tcrmonia [l01 ciil- culated a value for tlie rci~~forceliient elliciency filctor based on their observations i n that study.

' A t ~ i l ~ u r tu whotn all currcbponderice h b o ~ l l d bc addrcned

(X122 2461 i 1997 Ciiu/,nzutt & l lull

Mo~ieuc ri t r i . [I l] suggested a computer ~i iodcl l ing for the thcorctical undcrst;lnding of tile concept o f critical length in composites. The clkcts of intcrhcc ;lnd 11l;ltrix propertics on critical aspect ratio was also s t ~ ~ d i c d by them. They found that critrcal aspect ratio i s rel i~tcd to interracial shear strength and fibre strength on11 and not ICI matrix properties. They fur- lher ihowcd that under certain circumstances. matrix visco\ity il l id s t r , ~ i i i r i ~ t c c i ~ n itifl i~cncc the c r i t i ~ l l ahpect ratio. Karain 1121 studied the efect of fibre volumc fraction on lllc strength properties of sh0l.t i r - i ~ r c c ~ i c I Ic prnposcil ;I niodi l icat io~~ to tlic cx~sti l i f inlodel ill order to calculate the strength of ilic c ~ ~ t i i ~ ~ ~ ~ s i t c s . Tlic m(xiilici1tio11 is bilscd on the reduction of'intcrli~ci;il surf;~ccs due to libre fibrc and lihrc bold inter;~ctions.

2. Theory Scvcral thcorics h;~vc been prop~lsed to model the ~cnsilc properties of co~~lposi tc ~i i ;~tcrial i n terms or d i l k r c ~ ~ t p;~ran~cters [ l 3 161. These thcorics can be

.: ,1\>111cd into two groups. b;iscd on the nature or the ~nittr ix and tlic rcink,rccments. Thesc are the theories

where V, is the matrix \~olume fraction, v,,, is the Poisson's ratio of the tn;ltrix.

Nielscn ~nodi l icd Kerncr's equation hy i~ i t roducing

a function called the particle packing lac~or. BF [ ? I ]

A accounts for tlie hclors such as gcolllctry of thc filler and Poisson's ratio of the m;~trix. U accounts for tlie rzliitive moduli of lillcr and m;~trix

wlicrc !Cl,, ;~nd XI,,, are tlic Yoling's moduli of pilrtic- ulate filler and ni;ttrix, rcspccti\.ely.

Eqo;lfions l 7 ;ire rnz~itily ;~pplicablc only in the field of parliculatc-rcit~fc~rccd polymers, especially i n non-rigid polytner tn;~triccs.

c11 rc~nf<~l-cc~nents in ;I non-rigiil matrix 2nd those in ;I ~ r i y c l ~ i i ;~tr ix. 2.2. The theories of rigid reinforcement

articulate and f ibrous) in a rigid matrix

2.1. Theories of rigid particulate These thcorics can he successfully applied in the sys-

reinforcement in non-rigid polymer tcms of both p;~rticul;~tc ;~nd lihrous rcinforccmcnl. matrices

2.7.7. Einstein and Guth equations I'hcse equations arc mainly used for tlie theoretical c:~lclll;,tii,n of the properties of particulatc (spherical)-

2.2.1. Parallel and series model c c o n l i n g to tliese modcls. You~lp's modulus and

reiliklrccd ~pi>lyincr c0111positc\ 117. I X ] . te~~s i lc stre~igtli arc c i ~ l c ~ ~ l i ~ t c d ~is ing tlic IOIIOUIII~

According to tlie Einstein ecluation equ;~tio~~s.

\i,liere \ I , and ;\I,,, are the Young's modulus of con - .\I, = !\I, L , + .\I,,,L',,, 1x1

positc and matrix. rcspectivcly. V,, 1s the particle vol- 7', = T,V, t T,,,L'6,, time fr;~ction. Guth derived an equation [ l81

i'll

(21 Scrtcs l l lo~ lc l \I, = ,,,,(I t 25V, ,+ 14.lV,'l

.\l,>, .\l, \ . l 101 Tlris c q ~ ~ ; ~ t i o n i s furtllcr rc1;ltcd to the tensile slrcngth, 1',. IIIC composite .,\l,,LL; ,!I, l',,,

2.7.2. Modified Guth equation ('oh;in 1191 in t r~duccd a particle shape filctor. S, for non-spherical particles. whcrc S is defined as the ratio , ) l ' the l c i i g t l i - t ~ ~ - ~ ~ ~ ~ I t l ~ pilrticlch.

The rnodilicd C;uth relation is given by

AI, - .%1,,,(1 + 0675SV, + 1.62~ '~ ; ) (4)

where AI,. hl,,, and !\l, arc the Young's nloduli of composite, m:l[rtx ;~nd lihrc. rcspcc~ivcly. T,. T,,, itnd T , are the tensile strength of the co~iipositc. ~ i ia t r ix arid librc, respectively.

I n tlic case of :l l~;~l-;~llcl rncrdel. il i s assutncd that isostr;~i~i conditiolls cxirl f i ~ r b i ~ t l i t r :111d libre, whcrc;~s in the c;~sc of :I rcrics modcl. slrcss was nssumcd to be u n l h r ~ n in hcllli matrix :llld librc [E].

2.7.3. Modified Kerner equation 2.2.2. Hirsch's model Young's ~nodulus of spherically shaped particulatc- Hirsch's illodel is a cornhination or parallel ~ l n d series

lilled polylncl- composites is given by Kcrner's models 1231. This model cat1 be rcprescntcd h) Fig. I.

4262

1 Matrix

-Fibre

/ Parallel Series

Stress Hirsch direction

According 10 [his model, Young's tnodulus and tensile strength ;ire c;~lculatzd using the fullowing equations

7, = v ( , ' + I l ' ) + ( T'Tc" ( 13) L, VC + T f VC,>

1- l i e p:irarncler. v. is cxpl;iincd in Section 4.

2.2.3. The Halpin-Tsai model This niodcl lins been used by several researchers i n tlie systctn of polymeric blc~ids which consist of continu- <)us slid discontinuous phases [24,25]. However, i t

was rcporteil ili;lt this modcl was ;~lso i ~ s c f i ~ l in detcr- mining the properties of composites that contain dis- contini~uus lihrcs oriented in tlie loading direction [?(l 2x1.

Aceill-di~ig to H;ilpili Tsai. Young's modulus. 1\,1,. of tllc cr)~iiposilc i s g i \ 'c~i h)

\i.hcrc <I IS tile iiic;lsure of libre geometry. lihre distri- h~ i t~ , )n and lihrc loading conditions.

2.2.4. Modified Halpin-Tsai equation NI~I\OII ~ i i od~ l i cd tlic l la lp in Tsa~ cqu;~lion hy includ- ing IIIC ~I:,,,I~I~~II I~;,~!.III~ l'r;tct~,u~. +,.,,,>z. ,>l' t11c rcitl- io lccn l~ :~ ,~ L291 A ~ c ( > r d ~ ~ l 10 th i i

11 is givcn by Equations 16 i ~ n d 17. i l l id ;ICC~IIII~\ fur the relative moduli of libre and ~ ~ i : ~ l r i s . rcspccti\ciy. J, depends ilpoli the p:~rticlc packing fri~clion. Tlic v;~luc of A is deter~nincd from the Einslcin cocllicicnl. K, rcporlcd in a p rc \ . i o~~ \ \ t~ ldy [30], d),,,,,, is t l ~ e maximum packing rri~ction. ;~ i id Ii;is a vi~luc 0.785 for square arrangement o f librcs. 0.')07 fur I ~ e x i ~ g ~ n i ~ l i ~ r - ray of libres and 0.82 for r:tlldolll p i l ~ k i l l g l i b rc~ .

2.2.5. Cox model According l o Cox':. theory. long~tudin;~l Youny's niodulus, M,, is gi\,en by the equ;~tion [6]

+ l,,,',,, (221

where )M,,, i ~ n d A l , arc ihc Young'\ ~ l m d u l i of ~ i i ;~ l r i x and lihrc

wlicrc !.is the radius o f i l i c l i b~c . (;,,, the s l i ~ . ; ~ r modillus of matrix. K the ccntrc-to-ccntrc dislancc of the lihrcs. and A , tlie i t rw of the libre.

For licxagon;~lly packed lihrcs

For squ;~rc pi~ckcd libre5

According to Cox's mcidcl. lc~isilc s i rc~~gl l i . 7,. is pivcn by [6]

p is givcn by the E q ~ i i l t i o ~ l 24.

2.2.6. Modified Bowyer and Bader's model According to Uowycr i ~ n d Ui~dcr'h 1110dcl. the t cns i l~ strength of short fibrc-rcinf~irccd lliermopli~stic composites i s the sum of contributions frotn subcritic.~l ;IIICI s~~pcrcrit ic;~l fibres ;111cl !II;II l'ro111 tllc 111;1trih r j l ] . Tcrisilc s t r c ~ ~ g t l ~ is given h)

wlicrc K , i s the libre oriclit;~tion f:~ctur. I lcpcndi~lg librc orientarions. K, also cli;~ngcs [X]. K 2 13 IIIC lihrc l c n ~ t l i factor.

For lihrcs with l > l , . X

Fol- lihrcs with 1 < I , . TA & L E I I I'l>y\icel a c ~ d ntccli;tct~c;tl p~opcrlici o l \~r;tl lihre

(g an ') ,Ir~.ngll~ nlodulus at hrcak t l lo11 wlicre I is the length of the libre and i, is thc critical IC;I'~) ~c;t':t~ I'%I length cif the lihre. You~ig's modulus ;llso can bc cal- cui:~ted uhing tlic sanlc cqu;~tion 1.41 (1.3 0.7 'I zo 5 14 11x1 WO

if, = M r K L K 2 V l + M,,I'., (31)

The main purpose of this study was to correlate the cxpcriiiicnt;~I tensile propertics or shorc slsal fibre- rcinlorccd low-dcnsily polycthylenc with theoretical \;~liics. c:~lcui;~lcd h) v;~rious rhcort.ric;~l niodc!~. I t L\;Is rllllld II~~II sUIlle 01 II~C IIIU~CIS SI~OW a ~ L I O ~

;~gree~i icn~ with cxpcrimental villucs. The models clc;~rly i~idicalc that the parilmelcrs such as libre ori- c~ l tn t io~ l . tibre length, fibre lo;rding, librc dispersion and interf:tcial shcar strength hctwecn libre and iii;~irix 11l:i) ;I nl;?jr>r role in conlributing to the lcnsilc pr<,pcrl~ci of i l ior t librc-rcinli~rccd polymer com- posilc\. The 11mit;~tion of lhcsc ~iiodcls was also con- \idcrcil in this sludv.

3. Experimental procedure Sls;il lihrc was obtained from local sources. I.I)I'E. fl.il(ied ;IS i~idotl icnc l h MA 400, was supplied by Indian Petrochcniic;~l Corporation Ltd. ha rod;^. In- di;l The properlies or sisal and L D P E are listcd in Tahlcs I and II.

Sisal. ILDPE compositcs \vcrc prepared by the solu- 11,111 ~ l i i x i i lg ICC~III~~IC. 1:ihrc was ildded to s viscous \litrr) of p~ilyctliqlcnc in lo l i~cnc wliich was prcp;~rcd l h j ;~cI<li~ig IIIILICII~ 10 ;I ~ i i c l l o l 1!1e polyl i~cr. T11e ~n ix i i ig war c;irricd out man~~;!lly in a st;linlcss stecl lha~kcr ~ls ing ;I s!;~lnicss slccl slirrcr. The icmpcr:lturc was m:~itit;~incd at 110 C' during lnixing for ;tbout 10 tiiin. The niix u;ls then tr;insfcrrcd into ;I llat tray ;IS

lumps and kept ill ;I vacuuni oven at 70 C for 2 h 10

rcliiove the s o l e ~ i l . Composites containing l0'%. ?O"~U. ;ind 30"/,, h> weight oi l ihrc were prepared using lihres oflctiglli in the range 2 10 mni. The niix is then cx~ruilcd t l i r o ~ ~ g h ;I ram-type li;~nd-opcr;~ted injec- tioii-moulding m;icliinc at a tcmpcraturc of 125 r 3 C. For the prepar;~lian or longitudin;~lly and l~-:~ns\crs;~l ly oricntcd compositcs. the extrudiitcs linv- Ins ;I J~at~rclcr 0l.l mm well: crillcctcd ~ I I I~ irl ig~icd ill ;I leaky mould [ 3 2 ] They were then comprcssion r~ l i~ l l ldcd ;l1 prcsstirc o f i ~ h o l ~ t K MP:I and ill ;I lcmpcr- ;~tusc 111' 125 i7 C ' . .lhc co~nposi!cs s o obl;~incd were rcriiovcd :~flcr coolitig tlic 111o~1ld below 50 C 1 I<ecti~li- g~i lar hpccimcns or s i ~ c l 2 0 mlii X 20.5 rnln X 2.5 m m ucrc cut iroi i i aho\.c co~iipositus for further tcstinp. Ilandonily oricntcd composite sheets (120 mm X

12.5 111111 X 3 111111) wcrc prepared by standard injection mot~l i l ing of tlic niix using n ram-lypc hand-i~ijeclion ~ i h o i ~ l d ~ n g tii;~cIiinc. Fig. 2. shows the optic;~l photo-

4264

g ~ l p l i s of d11I2rcl11 or~c~i l ; i i io~ is ill tlic lilhrc in ~ l i c ~ii;\trix. Tcns~le tcslillg 111' ( l i e c ( > ~ i i l x ~ s i t c ~ \\;IS ci~rried 0111 using ;III inr l ron i i ics t ing M;~cliine rnoilcl I I ' J O ;l1 ;I cro\\lic;id \pccd of 200 i l l111 111il1

' and gauge l c ~ i g t l ~ o i i(l lnlii. At lc;~st l i \ c cpecilncns were leslcd h r ~:ICIT SCI c ~ i s:~~iil?lcs i t ~ i c l 111c 11ic;~ti vitlucs arc rcpi,ricd.

4. Results and discussion ('~~1ii1h0siles COLII:IIIIIII~ 2 10 111111 1 ~ 1 1 ~ 1 1 1 libre, \ \ ~ I c an;~lyscd in l l i i s s111dy. l l ~ ~ ~ v c ~ ~ c r , i t \v;is ~ O L I I I ~ t l i ; ~ t

composites sri~li incorpor;llcd h n l m librc lengllis showed ~ i ~ ; ~ x i ~ i i ~ ~ r n tclisilc s~ rc t~g t l i [33]. ~l ' l icrc~orc, h mli i librc Ic11f11i \vi~s used ill ill is s t ~ ~ d y . Fig. 3 shows ;l compariso~r of the v;lri;~lion in tlicorclic;~l ;III~ ex- p c r i ~ i i c ~ ~ t a l tensile strength vi~lucs of l o n g i r ~ ~ d i ~ ~ ; ~ l l y oric~itcd composilcs wiih \olunic l ract io~i <,I lihrcs.

alq!, $0 uo!13eq aunloA CZ'O OZ'O LL'O PI0 LL'O 80'0 90'0

," "l[llpD"l s.;?""",~ !!sla.loal P"'! ~1?l11"11!1"d~a U! IIIA a111 JO ~~x!~t!dtuon I: smoqs p 21~

.Lla~!lnadsa~ 'ZZ

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areanu! ql!m LllelnSa~ sasl?ar3o! q18uarls al~sua 'sasea [l'! I,! 11~~[1 uaas aq 111:~ 11 .a.1114!1 3111 LI! 11,n(lqs SI! s[apoul sno!li!n ay1 4u!sn pa1~lnsl1:s slan snnll?.t [l!o(laJoaql

aq!) )a uo!iDe,) alunloA CZ'O OZ'O LL'O PLO LL'O 800 S00

longitudinally oricntcd co~nposites with [he volume fraction of fibres. I t was observed t1i;it a very re;lson. able corrcl;~tion exist between theoretical 2nd experi. ment;ll v:tIucs in most of tlic modcls except series a ~ ~ d p;lrallcl nlodcls. A good ;~grccmcn[ is sec11 i l l [he cast

of Hzilpin Ts;~i, and modified Bowyer and Bader models. 111 the c;ise of the Hil lpi l l Tsai and modilicd H T mndcls, ;I pood ilgrccment hctwecn cxperimcntal ;ind t l l e ~ r c l i c i ~ ~ Y~ul lg 's ~i iodulus vi~lttcs was observed as co~?iparcd to the f i t of the experimental and theorcl- ical tensile strc~i f t l i values. Fig. 5 shows ;I comparison of the v ;~r i ; i~ io~ i 111 ihcorctical as well as cxpcrimc~ital Yoilng's r n ~ ~ d u l ~ i s \,:ilues of ral ido~nly oriented composites \villi v(i1~1nc fr:~ci i i)~i ~ f l i b r c s . The tlirsch and lnodilicd Bo\bycr and l3;ldcr nlodcls are used fkr the c;llcill;~lioll of thcurclical values. Roll1 rnodcls par- tially ;[pi-cc with the cxpcrimcnlal v;llues. Al l other rnodcls L I S O ~ ill tlie study are not applicable in the systc~ii ill' ~ l n d o n l l y orienteci cnmposiles. I n the case o l llirscli's iniodcl. lcl~silc strength ill id Yoi~ng's modulus v;~lucs were ~ l l cu ln tcd using Equations 12 and 13. 111 lhis c;~sc. agreement between expcrimcntal and tlieorc1ic;tl valucs has hecn found only when the v;~luc o l \ in Lqilations I ? and 13 is 0.1 For ralidomly oric~ilct l co~nposilcs. Tllc v;ilue of Y li;~s same meillling ;IS in 11ic C:IX ~ ) f l o ~ ~ g i l ~ ~ d i ~ i i ~ l l y oriented cotnpositcs. 111

the cusc of the ~ilodil icd llowycr ;lnd 13;1dcr niodcl. tcti\ilc slrcngtli and Young's modulos villucs were c;ilc~il;itcd ~ls i i ig Equiili(>lis 28 i l l id 31. The V R ~ L I C o f K 2 in lllc equ;~tioti is ! l ie s;inlc for both longitudinally and sandornly oric~lted coliiposites, but libre orientation fi~ctor, K,. is dillcrent for randomly oriented corn- posites. I n this c;~sc, tlic value of K,, For good agreement hetwcc~i theoretical and experimental valucs, u,;I!, found to be 0.2. bcc;iusc i t has already bccn reported 11i;it tllc v;iluc of K , for fibres ;irr;~ngcd i n the random f:isllion i s 0.2 [X].

I i s ? 5, i t is clci~rly observed that, in gcn- cr;11. tc i i~ i lc lpropcrtics of l>otli l ~ ~ ~ i g i t ~ ~ ~ l i ~ i ~ ~ l l y ;III~ ~ 1 1 1 -

cloilil) or~cii tcd composi~cs show a re;ison;ible iigree- mcnt u i th ill1 tlic i i i ~dc l s ill IOW volume lr;~ction o f lihrcs. This may he due to proper orientation of fibres and uniforln distribution olapplied load as a rcsult o f well-di\pcrscd lihrcs in the m;ltrix at low volunic fr;lc- tion o f the librcs.

t'ip. (1 s l i ~ w s ;I c01iipiiris011 of the v a r i i ~ t i ( ~ ~ i 111 tlicor- ctical and cxpcrimcntal icnsile properties of randomly oricmcd cr~mposites 3 s ;I f ~ ~ ~ l c t i o ~ i of librc length. The inodilicd Bou'ycr and Badcr no del is used for the calculatio~i of tensile properties. The critical length OF the fihrc u'as found to be 6 lrnn from the carlier study [M]. tlcncc the otlicr lengths o f 2 atid 10 m m arc taken :IS suhcritic;~l ;ind supercritical lengths, rcspectivcly. l 'hc 2. h ;~nd 10 mm libru composites were ~prclx~rcti ;II 10. 211 a ~ ~ d 10 vtll'X, librcs, 'rc~lsilc 1)ropcr- tic5 were c;ilculatcd 11si11g Eq~l ;~ t io l~s 28 and 31. I ' l lc value of K 2 it1 Equiitio~is 28 i111d 31 is dilfcrent for dilfercnt lihre lcnpths. For 2 ;~nd 10 m m tibres, the v;tlucs of K , wcrc c;~lculated using Equations 30 tlnd 29, rcspcctively. L i l l t any oft l ie ;~bovc cqu;~lions c.111 he used for c;~lcul:lting K, in thc c;tsc of 6 lnrli lihrcs. hccause i!Iic~i 1 = l L both cquat~ons g~vc the s;~mc \ i l l ~cs .

4266

Volume fraction of fibre

10 3 6 9 12

Fibre length Imml

I t can be seen froni Fig, h that ;I( h mlii lihrc Icnglll. thcrc i s a good agi-ecmcnl ~ ~ I \ \ C C I I I I ~co re t i c~~ I il i ld cxperimcntal values in the c;~sc u l tcnsilc slrc~igl l l ;IIIJ Young'xmod~llus v;~l~ics. ' l ' l~ i r rlc;~rly t~idic;~tc> U1:il i t 1

cril ic;~l lihrc Ic~lgtl i . c~>nipori lc\ \ l t~,n i n i : ~ ~ i r i i ~ ~ ~ i l pro^-

crtics. The limitation o f the ~nodcls i~ \c r I ill t l l is stody

mainly depends on dilTerc~il i;~ctors, The ch;~ncc of thc form;ition of microvoids bct\vccn libre ; ~ n d in:llrix during the prcparatioli <,l cc,ntp<,~ilc.; grc;~lly i ~ i l l u c t ~ - ccs 1I1c rcnhtlc properllcs. 'l'llis l';tctc~r I\ 1101 ~ ~ c c ~ ~ i t l l l ~ ' ~ l for in ;111y o l ihe iliodcls u.;cd in 1111s study. 111 ,111 ~i iodcls used hcrc. 11 IS ;is.;i~~~icd tI i ;~t 11ic lihrc. :ire

strength. I'aramctcrs concern ing the surfi lcc i r rcgu lar -

it ies o f s i sa l l i b r c and microvo ids formed he lwccn l i b r c

a n d ~ n a t r i x are no1 accounlcd (or in (hi\ study.

cyl indr ical l ! shapcd. However, the actual shape o f t h e

zis;~l lihrc 1s 1101 pcrfcctly cy l indr ic i l l due lo surf;~cc

irregul;tritics. Fig. 7 is cle;tr cvidence for th is k t c t T h e

non -un i fo rm shape o f the sisal also accounts for the

dev ia t ion o f t h c t cns~ lc properl ies from the t l i co rc~ i c ;~ l

predict ions.

5. Conclusion A cotnparlson bctwccn experimental r c s u l ~ s illid the

p r e d ~ c t i o n f rom theory o f t h e tensile propert ies (tensile

strength and Young's modulus) of shor t sisal fibre-

reinforced low-densi ty polycthylene co~npos i t cs has

been presented. The models selected wcrc scrics a n d

par;lllcl. t l i rsch. H a l p i n Ts :~ i . mod i l i cd H a l p i n Ts;ti.

Cox, and mod i l i cd Bowyer a n d Badcr models. Tensi le

propcr t ics of I o n g i t u d i ~ i i l l i l l id i . i l nd~mly or ien(cd

c o ~ i i ~ ~ o s i t c s i vc~ i . ~ p r c \ c ~ i t c d ;I\ :I 1111icli01i 01 v o l i ~ ~ i i c

fr. ‘ ~ c t l o n . ' of l l i c librcs. A l l models were app l ied in the

system 01 I o n g ~ t i ~ i l i n a l l y or iented compositcs, bill the

Hi rhch a n d i i iodi ! icd 13o\vyur and Bader equat ions

\\,ere app l ied in thc c;tsc of r i l ndomly or iented c o m -

pos i~cs , A l l n iodcls c x c c p ~ the scrics :~nd pnral le l

mode l show rc :~s~n ; l h l c agrccmcl i t w i t h experi tncntal

tcnsilc propcrt ics o f long i tud ina l ly or iented com-

posites, especially at l o w vo lun ie fract ion o f the l ibre.

Amolig the v;rrious modcls, the H i r s c h a n d mod i f i ed

Uuwycr a n d l%adcr equat ions show \'cry good corrcl ;~-

lion w i t h c x p c r i ~ i i c n t ; ~ l results. I l i r sc l i and l3owyer

+ and Badcr models also s l iow good corrcl;tt ion w i t h

exi1et-inlcnt;il results u f r ; t ~ i ~ l ~ i m l y or icn led composites.

'The cli'cct o f l i b r c length on t c l~s i l c propert ies was also

an i~ l yscd i n this s t ~ ~ d y . T'hc l l owyer and Uadcr m o d e l

rcvc:ilcd 111;11 the cr i t i ca l I c i ~ ~ t h pl;iys :I rnitior ro lc in c o n t r i h u l ~ ~ r g t o the ~ c n s i l e propcrt ics o f short l ib rc-

reinforced po l ymer compusiles. Al l theoret ical models

used i n [hi, .;111dy c1c;irly indic;tte t I i ; ~ l tcnsilc proper-

tics c i f \ I ro r l l ihrc-rcinfc)rccd ccr~r~pohi lcs s t rong ly dc-

pc i id on l ihrc lcngtl i . l i h r c lo;tding l i h r c dispersion. fibre o r i c n t ; ~ l ~ o ~ ~ i ~ l ~ d I ibrc i i i i ~ t ~ i i l i terf itci;~l bond

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Sclcncc. Loodcln. 1982) p. 58. 3. h K F l I.\ ixcltl N 11 L IA( 'MI I .L .A~, "Slr,>#~g St~ l~~ ls ' '

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hybrid fibre reinforced polymer...

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