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A MATHEMATICAL MODEL BASED ON MOLECUI.AR STRUCTUREOF VULCANIZED RUBBER UNDER TENSILE TESTS

CHAOWALUK THAOMO

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTSFOR THE DEGREE OF MASTER OF ENGINEERING

MA'OR IN MECHANICAL ENGINEERINGFACULTY OF ENGINEERING

UBON RATCHATHANI UNIVERSITYACADEMIC YEAR 2015

COPYRIGHT OF UBON MTCHATHANI UNIVERSITY

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TITLE

AUTHOR

DEGREE

MAJOR

ADVISOR

KE\lVORDS

A MATHEMATICAL MODEL BASED ON MOLECULAR STRUCTURE OFVULCANIZED RUBBER UNDER TENSILE TESTSCHAOWALUK THAOMOMASTER OF ENGINEERINGMECHANICAL ENGINEERING

MTCHADA SOPAKAYANG, Ph.D.MATHEMATICAL MODEL, NONLINEAR ELASICIry, HYPERELASICIry,VULCANIZED RUBBER

The aim of this research was to formutate a mathematical model based on themotecutar structure of vutcanized rubber under tensile tests. The assumption of themodel formutation was that the tinkages of polymer chains in rubber coutd beclassified as two different tinkages, physicat [inks and chemicaI tinks. ln the first regionof the tensile behavior, alt physica( links were assumed to be active before theygraduatly faited. ln the yield region, the physical tinks were stitl faiLing whil.e thechemical links were assumed to graduatty become active. ln the hardening region,onty chemical tinkages were assumed to play an impcrtant rote on the tensitebehavior, so the chemica[ links were progressively active in this region. The formutatemodet consisted of 5 parameters, Er, E., 0, a and B . E, and E. represented themodulus of etasticity of each physical link and chemical Link respectivety; /represented the faiting rate of physicat [ink; a was the shape parameter; / was thescale parameter in weibutl distribution function which expressed the distribution ofthe activation of chemical tink. The parameters in the model were determined by acurve fitting the numerical sotution with the experimentat data coltected fromvulcanized rubber in tensile tests. lt was shown that the model was abte tocharacterize the tensile behavior of vulcanized rubber very welt in every region. Thevariation of the parameters in the model was compared with the experimental resuttsof vulcanized rubbers with different amounts of chemical components during tensiletesting. lt was found that the variation of En related to the variation of the amountof carbon black (N330) white the variation of d related to the variation of theamount of tetra methyl thiuram disulphlde (TMTD) and sutphur (S) in vulcanizedrubber. lt is anticipated that the findings from this research couLd be developed toproduce an advanced mathematical model to predict the mechanical behavior ofvutcanDed rubber with various amounts of chemicaI components.

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rmfi 2.2 nrfldra Scanning Etectron Microscope to.lurlrfilnriuourir zo phr tql

5

Z.z aurihialaiardin (MscoeLastic properties) [3Jfr - J -riryiuiaofr Inrua!fA u!uia Indar aAn Li oi Bi{n: vrirri olnilrrrafl aronu 1n n1i

-^-.--.^--'-..-].r-.' o. ,t r' re Ja - - J ,no!4u0.: el0 u5.i vln: vvr'rn a tf, t! ra na0ura nufus Fil.rol nia nfrrnfuar1!-6truuaa1a6n t.lFi1n?'r!lniunnuu iaild'udrnrtrriulou, Lrlefifr'1urj:ranr?alrtrrrlrduido.t trrin:oiro{iao uuuialn6aradn kllraqaov6od'radrl{r 1 ou6.:anrrcikluraqavrnldno!auaroiou:ln:c.yir) "-adrralu:ruuavdloriroiou:.rn:vriroon ldllranaovrioul rio.ro"a{tio.:.jr! rtasn?lr.Jrniuony

,-'Js"ja na{danrrcrduriouflln:lairloviu:urn:vrir 6lnqfin::liaIn6arafin rijun:vlrunr:

r,-.Juouna!uto u,au!nl:aqlaufld,!.11r h.Junayrouno.riqoh:tolnr:r onr:uJ6uuu al; irl-^-& +e a,. I )quyrflulntuauust?dInaalannrulUnfland]ra1uyi.'lufr'Lrinrrlaulo rdu ulndrra

(Maxwett) luar{ulu (Bottzman) uasraaiu (Ketvin) nrnrtraui,olua'rutalnruallGnr:fi1d'r (Creep) uacnr:6un'r (Recovery) ,uo.:r-anyi,:LirirdrrYnnmuuavvrqufrrfir,rfir.,ouarrar.,rj6

- i i c. - !?a [n0araflnna1u[Uult?!ad1nrur.tnifllnt:1.lr]r:1yn1:rfrrLtu,uolnr:ld.l.tu1iao tcrn fi u,ayy 6!'vlonlnqoluaruallun[uniSoanuu! anrIrufl

a'ruiunqGn::r:r8rna,uornrualrifiiaIn6arafinta.:iaqloari'rhl arur:nuunloirflu- -iJ UUU On1/

2.2.1 n1:6u (Creep)vrqfi n::r nr:6urf,r nr:uaornlua'rn-udto.:rirnru rdr uavnru rni uo fiurrar

d d d . - --.J-- - ts

J e )a. r t- J on?''lrJ rnu loo.rn1 yt 2.4 ni:na1un']'urnufrrUuf,.lrit-ul,o,i r?a.tfrr?a.t1o "l ovfir.laf1lfin?1rlu )- ! I , - 4 , , q. J ,Lnuv]lnotu lut?.rtl5nto{n1:n{t1]unla.iaoLLau0vFiou 1ana.!gl,tu:yuut?a1 0.:t?a1u1nf,uFi.t-)?rann?1!tnunoJana.!n't!t?a1 no ut.:n1un1:dnaoanr:yucEnryi,tLri!

load) riaqrJ: v rnlr ut.!nsi n1i n:vn'] u1,o.:e .iy- dd -ina.:.r'ruyr''l [r[noHan:vylUfrriu n'ii darna5€a (Hysteresis) fianrlvn.rot"rovrioudi,: unnri.]n

i . o J- )- ,n1nAn1?vt:UnU [UUtny1rflrJA']:!l v nO!, L5 Un.j1 Stress-induced softening !1nn:-iOyd 4d Jna12o.!n21!rdu14'tun.!!a1r q!1o1nln:.:rirul,!ra nafr uu nr-too ano.tn,i'u u,avnlnn.t:udngT?

:s i1.!1r,raflaronu'tnflu61: tvnor firurii.',ur.rovin?tJu,{ {n 1u16'dn1?un1:yyiuiluou tu

6^zo(L

=E610I

.o.L

Eo

Time Time

nT lrd 2.4 n'l16a1un?1rtliudriufl .rrir'ut,oqrearujrrarln 1

2.2.3 n1:rfiaEidrnaioa (Hysteresis) [1J)an1Ulnnl:uytr uuuu'].rl OU (Cyctic

AiJ,fr ovoEurun: an1?vfru'r{ejoud'?al druan,rlunrnd 2.5 qfin::r,n.r5r,finatX16u6arnoi6a(Hysteresis toss) riunr:6luuuaaluurunuryirnjuro.lul.:ni:!tt6lfiuu d!u.].io::xt16rfilru{nriuousir 50 phr ua: nr:6.ru.1.:a',rrnlrv styrene butadiene rubber (SBR) rlnfilfiuuri'uSBR tfirnrnriuoueil 50 phr

NR'50ph rcarbon-

N3

123 4 5 6 7 tExtonsion ratio, i-o

12315678Extonsion ratio, L

SliR ' cQpr"ca,.bor>irack

n'lyrii 2.5 fiqAnir!nlrrfio6qrf,uEarnoE6a ttl

h Jlnalnyr-a'.:rJa.i1y:-un1:rnoEarnaS6ano.rul.r i 5 rJ:vnr:r.rdn 1 ryrfi2.2.3. I attutduoyrunr u1u (l nternat friction )

nrrurSoourudrfioiunr u1u rf,uruaaTndu: nta.r nr:o-o ri uror-rlyrito.rln:rairrllranaraa':ornkiiunr:vuacnr:6ulnaroiltiluraqa rJ:rnnnr:ni ualnlrrf,uoyru

- ..!nruluyioarrryIonruluiuoq'fi'lantvdorura4i4.r f,oi'ud:uvuaqjryrqruranidrororoov-J-!00u1utoilnLtu?non']:[,]4au!u un fr o nrltluioocaoa.:daoruran!a,:iu

2.2.3.2 SIrain-induced crytaLLizationnr:Uodurn (Large extension) uavnr:unndu (Retraction) yalu .l

.i.. -. - t 4-.-----,n:{toi'taq0a1a LnuJ0t0vr2ur !aq:.1n1:dost-[avo=n:rnr:aarutollanld':vr,l.jrldr.rnr:J- )vonau 0o:1n1:na1unt1l.lrnu!n.trnu0n:.tn.l:0oq.talltilurana rfr afr or:zurornnrufi 2.5

1t0v L14u?1u'r.rdiiut'tnuao.!y{qnn::l]aarnoiia!.tnn.jiy{oduoia-.:rn:rvr,i

2.2.3.3 nnootdlto.:Rrurdu (Stress softenin g)nr:rliu rrJd uuuav n r:fiu;rJluri t o.rla: rrjruln:,:airrto.: u rrrr n nr:

-J:-rnt:yn:-.ru:n d uahinrruudtaoatuavnruaui6uoluouil.: (Damping) uJduuttfluiaqur.:rfi ru.:nriuouo"r nqfi n::la-nuzuvi'6an.jr ruan:yyutorlafiu (Muttin,s effect)

ntrd z.o nr:roaau6lrf,u?.lrou (Cyctic Load) til

ornnrnfi 2.6 uanrirlu nr:moa or o,: ruu ual: ou iaonnldnr:y1ua"nrsruvn'.:ornriloi'u oufilaarrvnrrtl rniufl " 1,, ufrun:rv{i.rhjsrrl rdunrl ,,a,, rfiorJriounr:voanrdun:t{ovilna'u n:rylnrrluriuniuaru rnSuoo:i.:lUnrr uduyx ,,u,, drkinr:vriohj6nouison "z" rfrun:ry,{oylriJouna'wrlrdu uas rfio!dounr:ynr:6u6'rocndurlrerruriumrl "c"

^aaindornn:rv'luanrl#rfiudrnrlrudlfiao a{urran finuruvto.rnqfi n::r:nr:ii oud'r rr or nr rr: udu uo n o r n nr : r!5 u u I ar ua c n r : rio :llv:"it o lIn :.r a irl t o.: u rl Jr firr a n: vyruto,:61:rJ:v n ouyr.: rnfi nr rr rf, oyraln:r airo":rnn oun rn n.:rrrfraurutorldl-.__- ! ,4'. . r , id! .r,- - !L Lana rldvn'rllju:uvrtlrd1L5a naLnr alt!a1U [vUdOnr:lUrud'rutnfrut o rounrntolut.r

2.2.3.4 atrutduuruto. n:.:airl (Structu ra t brea kdown)

boU'utcro

STMIN (cl

'tuur.ltfi lzurnriuouoir ounrnrornriuoun'roc rioFTr r{Juirrrruruu t!Lr,tftr,Jnfl t)uuun-l iruJt.tftljo.ln't:uou9l103n0n?LUu5,l{t!14 tlay-j-r--:-- 1 ,v - -ur,r20vrjn1:[ta!siadu Inr:riurndorto-lln:.:drutarlt"brrana:vyirlniuu?ulillfiu1ini:6ryr nlnr: rduu'ru ySouu nd1:uyir.:{ulura n a oyrirtrin"uo cLiu6! u: r Lflua1lilqlfirnonqfin::u6arnoi6aki

2.2.3.5 flaurterrolnr:rf,u:rJ (Domain deformation)n1lfi 01:ru1a11!rdu nruyio6oyuuutjloonrf,u z n:ni 1un:nidriu

, Jr , y a aJ :n?1 uo14uua!u: n1:rno 0etn::r0aLnol{a ov rn n Lutirlfr Lrinf rl usr-lun:dfrurliu:l, " --_-!- ,i 4_ - q , J v a g "au1.!01?:l'tay!urJn?luuol,tuu L0nlar qnn:5rluarno5{a oyrhnlutxfrnSrliurn{u

2.3 uuuiiraa.:ta.riaqiala5ara6n (Viscoetastic material modeLs) [5]o J . ly. u )qeu , Z -uuu0laanyllinayl0nul!.'lLrytlu.tu qnn: t}]?a Laiial a n nra.:iaofrltriutjo uni,rl

3 uuudra o.rd'ru ri'u 6o uuldraaluunrirra (Maxwett modet) uuuiiraoirnaiu (Ketvinmodet) uuuiiraonaunufllioe Liult6o (Standard Linear sotid modet) 6.i n1:i Ln:.tc#n?1rrtdu nrurniuno'rnuu!iirao.:flqfi n::r rfirnaro.:l-ao ur.: o vuaorviqF n::uyr'rnruu6.: u:.rttavalrur.rin uyunruudlu:.:drunluEnvtjuto,rarJi,: (Spring etement) n1!nflonDnuavttyuarruyioto.:rr,tarri:uet"ru ri (Dashpot etement) nrunntoli.lorll (NeMon,s taw) o-.1i"n1$yt 2.7 n1:n1a o.lnqnnl:r.l

Ltl0 Ery

n0 LUoaaflll!uolluu?ra !4115 i. '-,.Jn0 n1fl u:ya115n11r] !O10{Ft't14U2I

2.3.1 uuuiilaa.:rrundrra (MaxweLt modeL)

. riryunaufillilyi!:cnouriruarli,rnjud'tyrjr.: (Dashpot) 6lrio oun:lnlu n'lnrn--! ^^ o - i, " - i - o; i- -- "v z.u uu!n1a0.i u! nt t1a t! 0un1: Larl:u Ldl Ltl[ruJlirao:t o ovrdonr:rndouy-ytiufrvr"uloI A ,- --111- -- , ILournfl11nn11!U0vuL/1'0iaut{v5!n1:unounlniuovr o nr:6ulo u qruarLf6to.rsirlr rIluu;d-;[umr.: na'uri'u ri o:vu v 0nn.rfi nr:vfrtd rtrh]ov rir an a.:aoondor rylal nr: ra ndTnruu 16ua(ExponentiaI equation) uuurirao.: u! ncirraoyaur:n iiraolnqfin::rL nr:oar anru lduld

.+ ,+

I )-.! a.tnatnunn!?ao0:.Mnn21n1:n! n?1!rn5unyt.i14tloylrnntut u a:1!,iu:vy j,t.:Fi1d i, - in't1utn5uot0.!tua?uau:{uastud?un?141J1.:

=€E+€,1

o-_o, =o-t'n1flfi 2.8 uuudlao{utndna

.o..E

(,'4

ouuiu uuuiilaa.:ro.:ur.tnqirla Lfrnnin,Jai.:r:ro.la-n:rnrrurnicto i = i,. + Eiae

o 1 n a r n 1 I yr- ( 2. 1 ) tta y a ].r n 1 : fr ( 2. Z ) a u r : n rfi u uldo".r i

.o"o,,ooE=----t-+---_=-+-E n Eq

LUA 8 f]0 [l.Jf]aa n1]]J UOl4fiU?t0.: fl1 15.S

olnnl?o.:an o r = E . E r o"el5'tn1l1[niUolJalafil6nr.rt]lqounfiaur:nlfi uuld

dr=E'ir

olnnlroli?oir o 4 -- n i q o-n:rnruraEuoto.li'urirud'ryilr.: allr:0riuild

(2.1)

(2.2)

Q3)

10

,lo6-

o,o6E

d,€

iiE;

. '-,.Jn0 n1aulJIyd 5nl',r,lr41.Jo't 0,:9t114u?.rna n?1utnu5?lJ,u0{ulualao,t

6o nrtldutaraG.rno n21!tnulja.l9r?14u?n

,J,n0 09r:'tn1tr!auul'lua.:nl1!rnu:?lltatu!u0-1aaitio u?ut.]a.1.)

fr o d'n:rnr:uJduuu alnrurd'uto.:arjitqioilil'turlar.d..n0 00:1n1: tua uu Llua nn?1! Lnu,u 0.t 9l1t4u'] n 9t014u? u L?a,t

na n't']![n:ufi:?!ta{u!1J01a0.t6a nrurniuotalaGrna n21!tn:u010,lo?14u?n

,J,ao 0q:''1fl 11tuauuu,ua{n1'l!tn5un:'ul110n[!!uii1a0nr]a]1u?uL?a1',)6o d'n:rnr:uj6uuula.:arurniuoro{aGiqioy lur?a.l,J,no aol1n1: tuau! uua {n1'tr.l tn:uolJ0nfl?uu2.t0t 01.ru? u t? a1

2.3.2 uuudraalrnaiu (Ketvin model.)" - i-ttuuiirao.:rloi15undnotjr.:.jr uuuiirao.:raur{ (Voigt modet) r]:s nolriruarJ3l

n"u n"? 1.r ?,: ri o uu u r u l u nn o r n n l yr d 2. 9 ua o r ur u iir a a.: r o a i u ri o fi n r :1;i n r : c rdr'lilur!uo'raoru,iodovhifinr:rna'oudri'ufi ryr:ry6'rrar.irlocriluer'rruiurlil#riou1 rndouflttl---. -=-- i :, < .sn 1: Ina 0uyr?o.:9t?14u?n 0v!a nufuvtuua! n1t tont [ [!u[dua Lt!uii.]aon tna-uoviir a o.:vrqfrn::rnr:6ukilndr6u.:riuianoS,ur nnirnr:nar onrrrLrdu nrurduto.:uutdraolrnaiu

4 ,''- Ja1''l50tuuua!n1:Loo.:u

e=Er.=€q

O=Or+O

nrnfi 2.9 uuudraorrnaiu

n'rnnln0.:fln

11

n?rrtalrl{ud:u itnn?t!rdurrayn?rrtrn;unro{a i.i6ornduoolnfi

Q.4)

(2.5)

. ,. - talUltotl'UU Ln 9l.tu

ot: = E'e

olnnlrani?eriu o'n:rnrurniunto.:durirupTrrarjrrarur:nriuuld o-rd

or=4'i,

01nn?1uarltu6 0 = oE + 04 9i.!uuuLluii1aa.:[naaui{ tnno.]n at?ul,o{n?11ltdutorarnr:fi Q.4) uat aln1inr (2.5) arur:oriauki o-.ti

o=E.e+q.in

2.3.4 uuudraoslrn:muirfiufic6a (Standard tinear sotid modeL). - iduu!d'raonriofrrSu ndn o tir.:yfi.r.ir ull iiraol6ruoi (Zener modet) rilu

u!ua1aa{yr:?llta'tuuun laa{ Lr!nt[?an!tua?uarJ5.t[t-]olunu tnodra a:nqd n::utollyr6ruLoi rilnrufi 2. 1o uaoruuuil'rao.:rrsr:oru6riuflof, o

(2 6)

ntrfi 2. lo uuu;irao.:urn:oruirfi aflr6o

aur:oi rn:rvdnrrrr6'uuaynlrurniuoli nid

o=Et.q=fE e.+ry irl (2 7)

lO

*€. Q8)

)

72

nlnaunl:fi (2.7) rar (2.8) ovld'

Q.e)

z.+ alrihlauJoi6ara6n!ruciuu:l6l (Hyperetastic properties)lrqin::uto.:urrnr:rltruviuu:lo,rriu nlu r6'uuayn?urniuodrinfiurdold'iunr:yoyi

n?1rauliu6 [ua=nuruv hjr urt,rrdl (Nontinearity retation) tluonoirtornian :ymylar,rv.i,r, er ).yr? LU n::!?5n1:,.1anu1,:n{!U1ln15 telr.tdlu :v noua1:rnut.firlUrfr o1fi nruarlJ6in21!

i - '- ,, J-vruvr1u!rniu uqfi n:ix?0.:u'l.ti.rr!duuhlnlr]a1:rJ:cnoufi rFlriirlil^- &e- J,.r1uii"uillri'Anulurlfrairun:curu rhiur.:n.:1J (Vutcanization) t'.:ovfirarirtfiqzualtG

rir.:1 to.rurlu.JduuLJ rirluqa'anrr!6oudu?,o.: uliurac nr:6on-rovLir,iJua-odrulsruqr:rnTrJr ,-n'r:srlriiu rSunar r qdn:i!uurlhiriluri.: rdu (Non[inear behavior) firr:raur:nu .t

a"flufuvn1:uaonllqfin::!rtlnato.:tLr.l,Uzuviu u:.16 r'[6riu a drl 6o,tjrlGloiu (First region)tirrn:rn (Yietd region) uavtjr.rarSoroufi{ (Hardenins region) oYluaollunl d 2.1 1 uaolvrq6 n::uuuuhJ riu ril rd'u,uol url

t1.l 15lJOLJ t?.1fl:1n(YieLd region)

j{?no1:oLnuun

(First region (Hardening region)

Strain

n1l^rii 2.1 1 uqfi n::uuuubirflur0lrduuo.rurl

. E. le. *r.l ae + ___!_. E = | ___r_________L l. O + _n Ln'E, ) E,

73

z.s .rrui{adrntar{olornnrlfr nuruaym!yr?L/?i5tun::rarrn:oa:rllonrudr6'rpli' d'.:iTomita, y and et al. (2006) t6l ld'oSurul{ir ur.:il:vnor:trjsir alr'll rana (chain)

)tertorLriarTuvaru lrduourflula:.:dru (Network) 6.:l,rlrTrrana usiavrdri6r.J:vnouhJdrurJdo.:

,y ) q(5e9ment) a1U 1!a0.:ti tuu,flayrja0{ frocrijudru Iu [urloi (Monomer) ra{a1i!lrna!rorur.: ri'utri 2. 1 2 In:.:rirukllrana

/= 1.51,{

Chrin Nt't'.rork

ntud z.n la:.rriruIiilu rana [o]

rIofr or:rurln:.:airlnrulutruyiu u:lnuirarlr:n utir nr: rtarL rio: vnirlltilu uanaoonrf,u 2 dnuruv 6o nr:riorrionnuuuur.:r[uocrniuavttuull1.!n']ufl1vl 6.:o3uronintrfi2.13 nr:ujSururjailn:rairrairlnruh or.: ornln:.:air.:nru1un"r 2 a'nururd 6.rr:rovtduur6ndhnr:oon*uulr:roa,uo.rur,:n.:: rruciuu:.lo.rlu.:rui,i'ufi oioltl

i"'"1 chemicat tinkage C) physicat. tinkage

(a) Gududouo'.: (b) r,td-.:orndlntrfi z.t3 nr:uJiuuurja{n:lair.rair.rnruluurr [6]

a s4{ment

t4

Goktepe, S uav Miehe C. (2005) tql 1d'06lruirur.:rJ:ynouhJoiru nr:rdoudori'u rfluIn:.:rjru:cu'jr{rhraqa6.:ItLraqa (crosstink-to-crosstink (CC) network) uacinr:rda!eiannor nounrnfiraunrn (particte-to-particle (PP) network) r,riolrYlldtirnr:roao.l rdoirn:rvriaraornaran:vyruto{!aeu 6.r rfinor n nr: rf, u:rJr o.:Ia:rair.rnroluurrd.: u

Marckmanna G and et at. (2002) IZI ldoiuru6.:yqufrrir.:1 lt'rir1#rfio,ran:vyruro.lrraau uav Lou'rt u0'tinrt lnl 't:1ltn o: uaJa! n.ny r.ln runnraotirirtl t ol uuuiira ollr,:

' jvnrinoraoririrll fil{o6urunr:rfi orJan:uyt!ro,:!aAuld'Tezopoutos D and et at. (1988) t8l 16'uao,:hiuiuir nr:srouauolrio u:{uas:vuc6o -

vo taltorianlyi6uLoiaur:oumukidrunr:rJ:cnouri'uta,rrarjruqruarrJ6o'.:d

Elastk un

r^ ,r,---,F"-.{Vis.ous ur

f-r-=-*,F"-.1

Plastk unit

f.+'-,F" --l

nt'rfi 2.t4 n'rinouaua{isr,r.ir.ru:rriu:vucEa [8]

r.rrjrunruaurj6uti.:rf,u 3 tin 6o yrjru6ara6n (Elastic unit) yr.iruian'a (Viscous unit)ruasu ru arafin (Ptastic unit) 6:nq6n::r:nr:r!f,uu[rJa.r:;us ionouauolsiou:.:fiidrrjrh, c ^ - i- .- Jroi14!'tuvrn 3 ruflu no lnirudara6n o6l rulddruarJS16.:nr:uJSuuutjal:vus60ovur.J:rTun:rn-r u: rfildrirhi lutrurfiuriruian-aovoilr ulddruor-rv r: fi r osr:rnr:uJduuurlal:vuv6oovutJ:fiun:tnluu:.:fl,tirdrhJ a'ruu runarafinovfinqfrn::trfrlna 6o rflokiu:.:rdrhjritu

i - : .! c-i -'uinn.r,1 iJUuuoivrnltuLor:ou.,l oiuaq.:Lun.tflyt 2. I4Sopakayang R and et a[. (2011) tz] kirjrrauoullqiraolmr rnfinaraoiuullr,tri 6lutlu, ;--n'r:yr1u1Jllita0trt.:n flfl 1an: [d uu rL!!1.l 1n t n a nuruu [n: lair rnru Luta liaol:vrnrnfri riu

'ludunoaarror (A type rcottagen fiber) 6:rrnzuanr:riru rrut o:rruuriraolurj:'uuufiur rirr an1:yroao.!rannluiiudr{6rfl!.irfinrrrLaoqndo.irYu 6'rriuur udra o.:iir a rrr:noBur a

- &.e.n aMnll rtluoalaFr nIav.]d [n0arasrnto.riaou Loruu oti r r6

75

Yang L and et al.. (2000) [9] ldrirnr:yoaoiuav L!;uurfiuu anl:roao{riui.tanr:a ir -J .Jn 1u2 ru n't n ttuu 01a oryrlnnflo fl1a n5 Luyl'Nflqu, r110flayanu.tu1{qn n:.5! n1:n oua1.la{9ia

i*n?1![nuttaJfi?1rJn?1!tn:u9lt0.lu1.: t!nu uannnuax!fln?1!r,uuaa9]l'l'uula [nda1a0lnl.tauruu ula ril a i6 a r a 6 nr o.r u1.: 6'1 u

dorynrflo.rfiu ,,if lcblL

khanitha

uvrtl 3fl 1:A:1{UUU0',lao{ytlrtR0inf, ,ldniua Jn1:ilnaa.l

11-v !q --&v J -uuunlaa!yl1tn n61an:ral1.:1u [u{1u2iuu [oo.]n n.t:n.ra:J!d51UO1nn1li rn51ul,iIn:rair'lnruluta.!u1{ Iouriafrldolnnl:fi.ru?rura.:uu!d1ao{nc0nriuruJiuurfiur ri'uara___.-_-_. J , - .r . .i,rn1:yloa0{t or41n1Ir'D1tltna: Luuuuola0{ {.! [ouaolnl:ai1.: uuuii.] aa{y't{n ofl1afliuau

- ', .!nl: naa{ nnnatuu

3. 1 fl llail.ruuudraolnrtanf naranio1nn1:finu1ii?u!:cno!.i1ii'rgra.:1n:nai1!n1uluro,1u1.in{: fi0 kluuana,tro{ur.i6{fi) ,-unr:rt-o!siarTudruyr"uoyrnilrf,uln:l jrlnrrjru (Cross unk) Iounr:rdourionlutollr1rlranad)..,arlr:nu roonld'rilu nr:riolriorYu lnnrunl (physicat. Linkage) uavfi'uovrni (Chemicat

linkage) [6J o".:urulruii'udi.:airruuudraolyrr.:nrisraraninruld'auqfigruiir lurjxGroiu- ! S , s,s Ji10.! qnn::!nltiuu:tdlriu n'silr ll,riLlra nafr rfrauriariuvrr.: nrunrnn-lr,tlnuasr(uayrnfi

ur':drufiuyruryrrir6'rulunr:iuu:,: uiartr{drrn:rnvir.fltfuranadrdorrio ryuyrrnranruovtr - d , .ty,s I v,, r .t , -,L:U aoaann'lnnu 0{ai a [ua1[! ndato.:u 1:un1an a{ uac r! at{rdti,: lariotoufr lyirlld

I J{ , u e q ! J-!,- I -LUranarLta!nonum'tn?ru53rn tu6?r.i vtu{ Lr]Suut{ny15r5utr:.1i.:d{r.]allirirluoalalolur lfrrirdgl lJ?u-- :- c e':ruio'ufri.:kiairluuuo"raolrrlndnnrani lnu16uuuuu qfin::!n.r:r 6uuuUalnr:

i , J- o -rdaldorouii 2 uuu truviuu:.:61 d'luao{unrnfr 3.1 nr:oonuuuuuuiirao{lnura'uuttuu,i-sjnr:riouriodunruluu'1.:nt:U Iounr:riouriorluyrtnrunrrumudluilil?uaU3l (Spring unit)

i, -firia nr"uuuuturur,raru 1rd'urr.,fiallr'luranaluln:iai1.rntuluu1in,::rJ 6rnq6n::unr:iunr:vu:':toraGouuunrun.,nd oriru:r#.:urn,zurG!6{uacdou 1 r,,,aooonornri'ulotrtduqufrnruriuvrr uvrlaifi uavflrritlunruvuru utolnrrurirovrilu (probabitity densityfunction) tarnr:yaoriunr: uonuolnruduulronrilnrlurfiua (Exponentiat distribution)-l4a'run1:rfror.reioriuuulnr.:n'uor rnfr uuupiruaJiruaru 1d'ruaioultlr:rar-raluln:tair.rir . , u - -Znru tuul.lnn:utt!nr L[na!:{tluu uoutnr.tUuoyr qqn::unr:iunr:su:lttnnsitlornulu

53-

i"' j ct,".ni."t

t7

[inkage

----r,z\Az1z1^-niyrd 3.r n1:oonuuuuuuiirao{aurf, uuuuunr:rdoun'oriunru'lutnlnr;rJ I61

o'rnn'r:'ldal!Airurr".:ndi? a1 'ri0a51{ur.lun1}luulJiiiaanyi,:ndnflra0floura'uuu!!nq6n::rnr:ilar:vu:.:,uora-nuruvnr:rdouriorYu#raoruwtorurlnl:tJ,trilci!rL:.!6{6'n'r

q i-- .ttao.i1un1 fr 3.2 tt!!iirao.il11.:nfinnramira{ur.in,::!truviuu:r6l

€_-J.ntnfi 3.2 uuuiilao{x'1.!6rin616n{ro{u1{n{t:rhruciuu:ln'.t

"iotn uaunrnuwiirao{froc rliuira iltolvi.: Z n(rLtYuo:rio rYu uurlruru rirlririrn't't! tn I uo lvl'r fl uo.lu

tlr 0 6a nrurniuorirr.r!oro.:u1.:a.r:U

(31)

18

i,a_ a0 R?1rJta5utll0nn1:ttounauuuytl{n,lun1P

Ec fio nrrrLrnieroto{nr:riarsiouuufliuovrnfie?trrduyr"rulroo"rvirfiunruriu:al#.:ulnto.raG.:vi,: z ndrri'uov:rlri'u rYrd

O = O_+O-

Ja.Xu0 0 aa n21!LRu:?Ltyt,:14l]o Luu'tifi{:u! A. J -o - ao n?1![nu:?l]y1{14!]oatnnllnn1:[t0!nu[u1Jyl.].:n1un1z a_ J -o. noa?1![nu:?Iylnu!o tnoo1nnl:tto!nutlu!fluocLn!

; , J, v - - inlrrtnuulu!un1:tt0llnau!uy1nn1un1nylu:cnouo?utdlxtanayaturduyrJunr-uq-luyru-Jd'ruarJiuaarul d'r16olrio6'uuur:tururiuGl:-uu:,r (qctive) nfouriuyY.rr.trnri'ufidurrririu

ru:.:6ludr6lriou 1 r,taotro oanorn riu ouf,.:dtlun:rur,tururjutarnrrtLriroyrf,u uurronrib,rrur16ua (ExponentiaI distribution) Inualrll:0!fiuuatnllo6uranlrlfrutr'ud:vra.jrlnlu

9 . ,--!tnuuaunll!ratun Loo.:u

o, = E,e ol[ pGyle - t p{e nldeo) O.3)00

o,, = rnefi p@'sde -i n@)de ol O.4)00

rdo Ep 6o rirllqa'anrrlOor.4tjurooiuscnrunrfieh no n?l![n:uo nl:rtornonu linlun1 uanoonn1nf]-u

.1nr:lrnnrlonn2r!d,uonn1:,u'rooonro.:It'llranauuuurrniunrnriurruuronfiuruurtua(ExponentiaI distribution) aur:nufi uukio'lalnr:fi (f .S) rilfi

p(e)= @-F' (3 s)

si,^iLOtOvt Q> 0 u]o / na n1t[anin?1!.]r-1lunl:uaoto !14',uf,yn1un.]11ornarnr:fi (3.4) uav (3.5) a,l1lr:nrarruaraautolalnr:fi (3.4) Inunr:5ufirn:n ki6'.ri

o, = E ofl! p@)de - [ p@)deo)00

o.2)

19

o, = e ,c1f p+ at -ifu-*^ar,l00

or=Eo4(1)-(l-e-F)l (3.6)

drufiuocrnfioydau l iuu:.1 (Aaive) nruflrritnnrruraururjurjrov rflu (probabititydensity function) uudrqa (WeibuL[ Distribution) aur:o riouaunr:oBurun'lrua'lriuii:vy'irrnrurd'uuac nl!r raiuoldd'rd

rlJo E"€

6" = [e.6-e,)p(e,)de"0

n0 a1 uJoaan?'[JUnuu1.l10.:1ru6s[n!4A6a nrrura5aofr nr:rialrioriuuuufiuocrniriil:"uu:.i (Active)

(3.7)

rirrauolri p(e ) 6o fl.:ri.ilunllr.ruruilurjroyrf,u (probabitity density function) ro.td - - dJnr: t5liuu:.1 raln'uoc rnifi e > q Io u1,dnr:uo nuolarrl6 ulutrqa (weibutt

distribution) oclti

ot ,t=1(L)"' ,l;l (3 8)idtIo a do rirrr:rfrrnai:rjd1.: (Shape parameter)loud a > 0

p 6o rirn, :rirsroituro (Scale parameter) Ioufi / > 0

ornalnr:fi (3.7) uac (3.8) al llol4llaroautoralnr:fi (3.7) ld'o"larnr:d ta.sl tslonu

,. = r,(,-*,

20

L!0 60 lncomptete gamma function

uiokiaunr:a,rLrdu:rornr:rdorrioniui'.: z uurudliu Srir6unr:yrrruuodtrihjuvru'tu.l . c ,ea!n1:vl (3.2) o = oe+oc ioc [na!ni:n2i'la-'l,riuii:su'irlnrrrJr6unr"unrrurn5unlu

uuuiirao.lrrr.rnfi naranito.lorrnrgrJdrrui6'udoonuuuuavairriuld o-rd

(3.1 1)

3.2 nlrfloaa{ [10]--i.:ruioiufiovrirnr:roaornualrjfinr:6lurl (Tensite properties) lua'nurusnr:l{t[:ltu

ls ov Iuurdrloulfrn5olroaauu:lal Inuoc oaold'r.t6lnrurn:_qru tSo 37 Type 1 Rubber intensite mode rdorirrirdkilrrGourfi uuriuuuliiraaofi air.:?u

-Jur.:nl:locfrahuzuv ra rvor"lfr uqnrirlorniaotin6u 6o ar lr: n6o oonldraaruryir d'r- | I Aedr - 1 eLtayuouaou LrL uaa:y noya'tr]1:o nafun-uanrn rdlld lunr:yroaouaut6rr.:nrunuto I

) t - )'"urrov rfiurio,:riuu:,rfiai.rhjn:nir rioiuur{ uacio rualuJrJrolnr: rUduuurjal:rjjrl ra6o.Luurrnafuriurirlo'lounr:rirlriiuar.rinr:uJduuurJargrJir.:trJudrina aluiura.rrilu:{d[d1u

. "z.r 6 - d,! J .--! -

nllntuyt.luu t1.tfl 't:yloaouaxunnl:nnU'tunlytuilurnl:5ond.iiririlqd'a (Modutus) rf,unr:ion'ru:lr6'u (Force stress) tolurlfinndoaanl nrunlrr

i"urrfrriruun rdu 100% Modutus 14!1u6i nl:iodlu:nrduronurn ur'our.londooon 100%- i"u5o 1 ryi'rro.in?'ruurr16lfr rit,,tuoli

u:r6.:urloutrn (Tensite strengh: TS) rf,unr:ioriru:lr6'utolarlfion6ooonhJouur.lt,'lo

nll6nnutlo (Elongation at break EB) rf,unr:r-rrrirn?1tru.'l?ro.!duu.t{6'roair,r dnndo---'tv- - 4- , --.\ -,-- --i, ' , 4oQnLnIln an (01nn?1ru't?toI) nol.lyru.lilulj10 ri.tu2rufi-tliuSouavto.lnltlurr 16u rriuulntuylJ{ n'r EB = 675% uan.t't't ulituiarur:nUnoonld 6.75 Lyiuonn?luuIrdrldoufru''l.t0vt'to

!.-n15o1l!Un1:yloA0!u0y01n0{n'trJlt19lti1u ISO 37 fype L Rubber in tensite modeIouo n:oinr:roao,:uavi3nr:ynao.rfi niriohjd

3.2.1 0 nr0in'l:x6ao.!.,! '3.2.1-1 rniaworJarrrlJU!io (Two-ro[L mitt) rfi ouohiurtayrSuouavzualur.:

riuar:rni3.2.1.2 rni o{yrnaou ur,:1un r:rlonrrurafiouav6or,ltjuro{n oa [r.]oi (Mooney

Viscometer) rfi oriru'lruur:vavnarnr:outalar.rluuriavan:j.a;

3.2. 1. 3 rni0.!ouni:Uur.luac!dontolrn5o.loln.::rJurr

o = E ptt(\ - (1 - e* lt * t,(, - ! r1).$r l)

27

3.2.t.+ rnia.ryroaoua.lurt (Tensile tester) ju tnstron / 5565 14r]1uLarrn;o.l5565Q2696 Inunrlrnrud:rn:-oruriruuo'ir 6'arrf,urniariodaur:orr'rur.rlrrutriailn:nifitd:---g- =- 4- -- :, , t l' - ;

- :- .- '-', -

a'n4:uuntunluB?au'l{rnaauyta0n0,'}ntlu6lun2t!ti?ar]-tla!o n1!!1fl:stufi..n4uontrutia500 lad[!fltlulfr ar!r:nrindru:lfinnarq (Uncertainty) ld'l"riti\ + 2Vo uav6.D]1:otrAo.:dru:.:a.:aolunr:6rur.routrold uaviqrJn:nhl'aur:nio:vuv6oto.:ur,tld' i.:Hanr:aouq j .! i u d ) A-)rfluurn:o'rlau n1! [lJ:u:0{aau Lruularyl TN1-334_2009 uIor1fr 3 o'urrnrL 2552 Ioa

vriru.rruaourfiuu Dynitec co.,Ltd rardaaurfiuu 164 a:rjruanr:aaurfiuu lould Forcetransducer 500 N no.49647 jrunirrnior d.rrnrurifildaaurfiuldoo soo N rir uncertaintydo.rlilrfiu + 0.5 % anl:aaurfiuurir Uncertainty vilo 5OO tt kiryirrYu + 0.1 % lanliulsuru na 1urn flnlruoa1l]l:o [ti1!lnu lrinai1.,8drud

l.z.r.s rniorioionruuur d.rnr:i016'av16uonnd'or uacfi o arnl6'trirfi u+ 0.025 iaaunr

a.2.1.0 uuueirraiuo'odu,:run'radrl (Dies cutter) fitfituroriruunnilr.t.t0t:6.1utso 37 Type 1 n-tuaoflunrr.rni 3.12 ru.,"dr0.,rroao!et1rr!reli61u tSo 37 Type t (vniru,iaiun:) lunr:d'oilun-:adrrocfr'o{{ oi", dnu hii:ouiu *av6'ori'orrrluio,o.r Dies lfiZ-,))qri.:ornniruduurrfiovd'od'ra rfioflo.:riulriLitarurrriui::aur.riofisirvi irocrfluoounuda.llJ0.:tuytoaa! Ln

3.2.1.7 q!n:flj.ilvriuoiu6odu,rrud'rodr l riuuluriuurjulouo'nluffi uauu:{no_.j- - : ) I -1 : . ! ) e _ )alJ'ttal]0fla00!unlu L!aonuliulnflu ul.!nnuutl]Urlriourn{utfrorlolnnurltaouyaoarnq!nrfu0uuoo{na1?

3.2.2 ntlrioudtotirlrnaau:lunr:rniultulruen.:nl: (Specimen) ovl{urls::ltrfiurn:qrurj:vrmnlma

(sTR5L) uavar:rnl'firiursralri'uur.ro::ltrfiriun-r'ort,, 7 otir.: Iouo;lril.:11unr:rir-!uln:u'r o{u

3.2.2.1 anitlfrur.:nl: (vutcanizing agent) 6o riucdu (Sutphur) riunloatio'ir s

l.Z,Z.Z n-:ri.:rJfl ffi or (Acce[erator) 6o rn n:v urBalrn g u:llnt'alv,ld(Tetramethytthiuramdisut phide) 6unlnudo.jr rlatO3.2.2.3 atzn:;du (Activator) 6o fi.:doonkri (Zinc oxide) rionloudo.ir Zno3.2.2.4 ar:rlo,:rYunr:rf, olanu (Antidegradant) 6o ar:uou6'oonfr unuri ar:

druyrruyrrttyhiruavrnfi (lsopropyt phenyt phenytene diamine) riunloudo.jr tppD3.2.2.5 a't:!fiuudi (Fiu.er) 60 a.trtrirrir (Carbon btack) Gunlnudo.ir N3ao1u.:ruiiai'ovrirnr:nrtrnaounruarLtEnr:6iur.: (Tensi[e properties) rfiorir

rirfrtdhjujiuurfiuuriurirn-r uil:luarnr:to.ruuurirao.:fir:rairr Iouovrirnr:rJiruJ6 uurJilrrudruHaluo.:ar:rnfi Iouo; uu-irfi tJnruauuGfrkiornnr:dtJfr iiur 6'.ri

22

ar:n'rriu.lfr fiSarlfiur.:nl:rJ 6o tuto ocfirnr:li!l f, uurJirLrrudruruari 3 rir-3n,lu

nr:rod l.z an:tosar:rafi drjiuuJduuGurrudxuHa! s

o'',:.od l. t an:trolar:rafifirJiuuJduuGurrudxur6tu TMTD

1'U9rd',t5rn TMTD.O TMTD.O.6 TMTD-1.5

STR5L (g) 300 300 300

ZnO (g) 15 15 15

StA (g) 6 6 6

CBS (g) 3 3

rMrD (s) 0 0.6 1.5S (g) 7.5 7.5 7.5

N330 (s) 60 60 60

PPD (c) 3 3 3

- 1.qu ,J a ' , -ia1:ylyt''l Lyulin{5! flo 5 u:!tuauuu:u1{ualurJa:J 3 01 6l{t

1'U9d1:InU s-2.4 s-6 s-7.5

STR5L (s) 300 300 300

Zno (g) 15 15 15StA (c) 6 6 6

CBS (g) 4.5 4.5 3

rMTD (g) 1.5 1.5 1.5

S (g) 2.4 6 7.5

N330 (S) 60 60 60

PPD (s) 3 3 3

I

I

I

23

a1:rairllr:r 6o ttglo rliuujduuGlrrudruaral r rir rYli

,r:rod 3.g an:ro.rar:rnfidrjiuuJduuGlrrud?ufldu N33o

tuodl:[6tr N330-0 N330-20 N330-60STR5L (c) 300 300 300

ZnO (g) 15 15 15

StA (g) 6 6 6

CBS (g) 3 3 3

TMrD (g) 1.5 1.5 1.5

S (g) 7.5 7.5 7.5

N330 (g) 0 20 60PPD (g) 3

3.2.3 n:su2unlta6nurlriauou (Compound rubber) ttacurludlounl;rJ(Vutcanized rubber)3.2.3.1 G!n1nn1:rirurruvil STR5L Lil!ul iuyi{fizu6glornr.Irur.:ao aur:ndotd'

muuyei{iirrairuuriuvi.: lnudurel'oriluiuLiiturnnoryrrrlunr:utir rnio.:rorual or-suao.ro J-- u nLunrllyt 3.J nt:ornu1.luylnL :.lllulqti0tytJ'tyLtnitri^tns0{1,otra!

ntrd g.a nr:n'our{uvi.r'Ififi ruroxon4urc'lunr:rrirrnio.ruoe.rarr

3.2.3.2 d1u'r.: ua y ar: rnfiur t-.: u3ryrin q rl ar,: zual tr'rir n r: oo nan:'[ior I n r: r r r'!tu3.1 fir 3.3 o'.:uan{unud 3.4 nr:rirurluacar:rnl'lrt'.:riryrinnlrLan: 61t

24

n1ild 3.4 n1ld1u1{ STR5L uasdrrlniiurd'.:itarinnuan:lau

3.2.3.3 riald'url$av ar:rafiflrr.tan:narLfi lqriull{u;'r 6rirrr rrilnio.:lnr.ral:vrrrtln (Two-rolt miLt) rfioun ttayfi6lurlfiiar:rni ,iunouioyld Compound rubber n-.1nur,rirrur"',rn'',nfi a.s lniuld'ruzualar:uniouan:fi riryuo

nrnfi l.s rn3uudruaarar:rnfi nruasr:fi ritauo

nr:uoralur,:rYunr:rfi uar:rnfl,urn6owol.rar:vuurilo (Two+ott mttt)1- v qv , a :u 0y0r0.: Ltn?ir: vrlo:u1-{ adt.utn tlol lr nan n6.:tyyltuuo u.t.l na ao rrar uavt:r6'ol1d

. d a t qr ,1 !4 4i Z - ., .j )uonnrn0:n:nlflot?u tynl:!oHa! LnLsx[Lasdd.iiu d.:uaollunrnfr 3.6 drur lur]r rn5o.:louavrualar:tni

aI

-

25

J .. e an1 3.6u1u1.lli1t65A{U6UAJHd:.ld'lt16n

3.2.3.4 rio16lar:rniol!6m:n:!ui'r uavlozuarhJrsoulourioen,:nirolalfiua e, a a - "-".;ov a - aa1:Lnlouriur ordurriuudr idrur.:lrrinlirfra lriurlr0r.rd'r rf,o.:n1nn1:uorJarJui inurilf i

- i i ," ;du1! LrrRooruyn!ai{xnouiL:royleiur,:fr[5uniT u.tiiiououni:! (Compound rubber ) rfia, a y 4. e J - 4 - a, ! . Ju'r.tuufl'ta.r0un{0fuynr!nnual nu.ul1tu1rn50{Fto Lr!0f40t!utunl!!6ondl uanllunr1\yt-

3.7 n1:er'nriluiusr1l..lueonuri!u't.lriououRn:! (Compound rubber)

n1nfi 3.7 nr:f,nrfludunruu6onuduurlriouauR.:: (Compound rubber)

3.2.3.5 u"r.!ueiav(nidkiri'Frriuduudr 6rjurr{rrnio,!ytodolrBl{un1:ion?1uviouav6oratjur;o{roatlroi (Mooney viscometer) rdoo'rurrurar:cuyrla{unriouul{'tuusiacan: fi-iudoflunrnyrJ 3.8 rjrurlr{rtnCo.: Mooney viscometer

l_

-[

a'

f4\\'I

26

nTirfi 3.8 rirur.:ritaios Mooney vtscometer

3.2.3.0 rfio16:cuvrrar1unr:orurrudr fidr urrrr l{ru5 o n rfio lmi uuoc rdrJ,"idioLn5o.ioun{i u1.l drur,:fruqSu!Li nlrln:- otol LuoruynfiU: yrti iu 150 oifilr{arfiua q.u

:vuvrrarfirirurzu'tiluuoiavao: riruanrlunrnfi 3.9 uao.:drur.trrrrrirlSonrfiorniulovrrirLn:a.la!n{:! u1.!

ntrvrt a.g rirurlrnrriru6onrdorn,:'uuo:rrirrado.:oun.r.:rjt r.r

a! .iJ.z.J./ .!0auu1t Lnnl:l:yuyL'ta1rn0.:.r:uar frdroo"r:rornrni o.: LLaurLnsoon

27

n11{fi 3.10 n't:un:u1{aano,tnu6ofl

3.2.3.8 riokiurlolnl:rludt6rirlrn'oriu8'ulru ufl ugrJ6'l rlari (Dumb be[t- -:shape) louliulldry:nfi'oiu.:rud'rotjrl (Dies cutter) 6lituroriryuotutrn:orunr:vnaor rriorirr{rrnio.rloaolnr:6lu1l (Tensite test) q-rrao lnrnfi 3. t t uaron..,iyoaol6.:rr.r nr:roaoufi'u.:rru.',orrr.,dldriryuoan:n6rurrti ounr:rrfi 3.t, 3.2 uav 3.3 firfiarrralr',rr, 9 an: [qiacao:0, rriul,dro.,u (Specimen) li: 6'u rvr'olirnr:yrnaotlr]1rr.l'reriflru l5O 37 Type 1 riol!

nrnfi 3.t1 nr:yoaauilur.r (Tensite test)

28

nt^rd 3.12 !u1adu{'ru naaunlllrln:ilu tSO 37 Type 1 (urjrtr: ia6ura:)

rdorirnr:uoaorRd:ocldr.ranr:raoaoudu.:ruuriavan:Ha! 6rusiacao:i e durirti'td r rir iirovrorrirroda (Mean) luuoiayan:urlfl,unr:irn:rvdrGuurfiou d.rocn.ir?tuuvrqiohl

u?rd4fl an1:ytaao{uayn1:il1d'1fl 1:,1fi rnafluuuudlao{

o1n!yfi 3 L:l'[d'riaraaura.]a!n1ruasaafl 1:yrofi oldu.:ruudr 6rsdr!rrirnr:irn:rcriivtla3!:c lauar!:uljtyruLnu Lou0y t5!o?un1: ttao: anl:yo aa I t 1:iu[t: r6tta.!u1{ 1un: fi

i -e & - .frorrl- 5lrrutora1:Lnfrufln0i1.! n"un1nuun.:yt1n't:y1n1fl1tit rnoflurr!!iiraol tuayaofr'ruovirn:rvr.inrrufiuuUtro.:yl1:lfiLnaiuriavoir rfiofircr:ru.irflr:rfirmoi usiavd'rluatnr:fiil a qia r,i q A n:: ! $a !:"u u:.r 6.: o d r.r1:

4.1 Hafl1:UOaO{-- i,.. :.:ruid'ufrkirirnr:roao!6x.r1!u1: nrlfildrir vuo6n:r{a! u1lli n^!n1lrifi 3.1, 3.2

rac 3.3 i.iian:rlalyi.ryr:n 9 aqt uoiavan:oytrriariuor, (Specimen) '[i : dufi'roejrl rdorirnr:uoaotqu!]iFtil'11/ ISO 37 Type 1 Rubber in tensile mode louovdrzuayoaolrir rad a (uean)druaarto.rdr:

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' J , I -. -^ 4 j.n-(5trnness) !1ntu [el14tnrr! TM]D !1nouLRl,/ [rJovlir Lv:cuvEofrfir lytroioua lfl'r r do avd < i . !-!n?'luttlj':u''tn1!ua8r.ln't1!l!'tc!1niuolu

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30

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37

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39

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[2J Sopakayang, R and et aL. "Elastic and viscoetastic properties of a type I collagenfiber", Journal of Theoreticat Biotogy. 293: 197-205,20t2.

t3J orlo:ol #.:drJru. nr:irn:r:dauri6ialalauJoi6ara6ntalur.:algrJvrtoolr.r4fiunndr.:nu. lytu1u v0rj5 t!,1,tfl1nttufl 1an:lj}t1utufl9l: a0luutyln[ul,aufl:voaltn6tn:vun:rufio, zssol

[4] Goktepe, S and Miehe, C. 'A micro-macro approach to rubber-tikemateriats. partlll: The micro-sphere mode[ of anisotropic Muttins-type damage,,, Journalof the Mechanics and Physics of Sotids. 53: 2259-2283, 2005.

tsl fiin: rarjr aurihrilna{ntro.:ur.rrfirennriuousr'rnrutdnr:rilduu:rJurnviqrura4iunnd1.:i"u. ivrurinuriilirptplJitsgrnufruirufin: anluYurylnlula6n:voolrndr?i:cun:ryio, 2547.

[6] Tomita, Y and et at- " Numerical evatuation of micro- to macroscopic mechanicalbehavior of carbon btack-fitted rubber", lnternationaI journaI ofmechanical sciences. 48: 108-116, 2006.

[7] Marckmanna, G and et at. "A theory of network alteraflon for the Muttins effect,,,Journal of the Mechanics and physics of Sotids. 50: 201I-2028,2002.

[8] Tezopoutos, D and Fteiseher, K "Modeting inetastic deformation: Viscoetasticityplasticity fracture", Computer Graphics. 22: 269-27 8, 199g.

[9J Yang, L and et at. "A visco-hyperetastic approach to model.ting the constitutivebehaviour of rubber", lnternationaI Journat of lmpact Engineering.24: 545-560,2000.

[10] r:rn:oi ro:hula. ryralulaaur.r (RUBBER TECHNOLOGY). nlnLrflr:deuonarun::uurl anrriuio'uurl nirJirinltrnumi, 2541.

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Th€ 6.n d !rl! r€.eardt |t b t irr.aat. a math€.naDc.t nrodd bos€d m dbbclbr strrturo olvrrcDurd rvDD€r undd tari.o, Lrr!. tn ql'.r.t, Ea fiofrg. c! pdrdc. chart in tubt€. cii !adas!fi.d .r lH (llllcrr lnrrgrr: pnyri.al ,rhr. and cierica{ Lat! r^ h. i6t regioo ot iho l6n3rbb.htvs, aI pltysl.t lrlt 6r. s.lrrrn€d b b..cUvG b.{or6 lh.y grad.,any tad. tn lh. yoh rcgirl. Ol.9nyt|cal ll*a all sll Liirg r,tyta tlle charrlrd hI! a.€ asarr.riad to gradually b.cdna,cb,o. tn olelrrdcrurg ra{iri, q$t dal7El kraga rt aslurad b gtay ara mport nt ,ota 0lr h. tari$€ b€hay1or, totf, clEricd hrra b Fograary.ry drya dr thb rcgbfl ln dEl6|o.t, gr garsyEiers ,.r modet aradctalrtnld br trnlt l[no O]a nEdcl r$rh tE rrranlrl.otd Oata l can b€ srroin !,tat tE .r€

44

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u!ud1ao.rn1rhnin6'1f,n{oT nIc:!nir,rr;ilfrranara,rur,rcurrlzru;ilu.l,re'lA rnathamatical model besed on molecular structurs ot vulcanized rubber under

tensilo tests

uturltrn'nrni rmulo' Lrn: ar.i'net lanro:f.r

.,rrrllnj0rri !,,-rLrF!o1.1 tri a u.ao,.ii. -r^0)riLnr u i!.:id!d !r ; 1.reo'ir.i En, dD.id€Fto r' rrcflr,;r'i oaa,sr6rs.

J ruiiuililunrrEilr ruui raarr'rrorina-rni rrrlr:rni_, r::i.-rl r r n n ntir.r u.t rn.:) Jr !L:1'u,r.r I6r bo!

45

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at8ua0 I o.titltrua:tta' |rnttna llJitaJnna.l!1n rllo,rtlnulJx'ttltrtult!u!T1n] uil uimi-'llt!11n nnJ ullJ 11a0,rn't Jn rrr, nti ntii1!_looiu.ruuR:n1cn:runq;n)run.riunl::urJ!o.JU-1.!'lf trl sn:rdnrrliilulsrrt ealAii0tontfia HaiHFsncr.ru l I Li n.lrJUtmrral0tir/|.rr]6r fturi trl rbilnr,|fir,ui ri:nslia-ix1iantlu

ttnJllltiunmu:JlolJll't100.tyt'] Jfl tut!t,tArinI nEfir1ljnnonr:!itrla&!aJU'r Jo.tt trlruulJ1160lt1 Ollrru rqintl! rllnaooju-ltPhemfllendog,cal mo&r) drd'rur}nlr:lqr.,luttaot uJ!u)1!ltmul,l:ln1Lntft y,nLfi 1rtn!Io:rairnrullrtor!1-r ri,,r uuui,nat6an,cuiosden n'odel) us:laiiyliu (Mc'oney,Rivtn

! -, J. , Jmooer) luucrl 16l ruliultuutr!Jt!.$nt:in1triuuiraoJrmlndcarsa{ drirurlrnrululiuui-raD.r!611!n!Illltnuin9tu:rNn_unln1Jorlnr:ai.:n_ulur: (Srnjctural modcD':n'r!'rrnDi!run1tr iu."r.Urr,ro r[fl r Jnr''].Jnr!1.rni1atuna.!rnJo.Jr niEtLur.r6.:li lcull'uu,6otin.,rutiu (rot Elastr: *d /iscodaslicprop€rties o, a tyr I collagen rber l3l 4$ilsmritnolnr:r!6uuurJarnrtnrrrl arlo:lri.ln-rolutEnliitnnsi!urJ[!unn1uoi1! tr:lr (Retaxalion)IEEA[lJlUnnantUG)ilOAa.AAnuE:0R]na1n0looerrrru!{rr:of

z. nqr!nlno,)na,lrlnn'lt;inuli ltuJ1fi rii,1uitriasrilumrcu

n.lrJ r:ll&g.rtrqairr!ti.lnnLuiaunilriaeialn6r,nin luto.:dLnua_:o!,oJr 0:unr.rc, r!rLL'liifl0a1nfln$0u(N iuulJnl Jl.rJ-u,ttLl^R'tg.lnr\dtr' rLr:.:lT o r rn r rorjccr rq ila!rur;,Li01Ja.:rLi!n alfi ,J U.arii.i!16u1:;1or rl al,6 r- ainz.t fcrr lirl ua: irg ur ar:rnn'di r a i oa!ri6to,rmlal:J

i^rd::i!itn, r:,riFnlia)^irr", n,""iJt.,rrr1"r rir; tr!&,8 '"ax' 255d i,' L i:.;yr!!i

,deJr1nu1J6u lNahrral Rub3l)!i.rrrrnonlar'nialdi'LiLnur:rufir:i, \ liJ1s lounlt tJtlllrsrr0l!ot:u1un]I 1tJJIlonrrllilnunrrrmr ru6rn_rm:roidrr "1 riobiu_lufll}str!itll1\!r:d!n!nr rJ)ufi r)1 nl!Iriolnr: mra'':rir (F,Ier) Li]umrdlia a! n-lrurra!L;oiluin;un)r (RontorcemenD rilr $i!fl 11!r-lnn-l].t,1JnJ ltt!i1.trunan1)imDlDL iirlltrnr J ntr l u t|l fl lll IlJulllJlrranl t lj till J u:t 0 e:nl'r!icndlrn D..ro-t.rn,Jr! i',Jizr.t nrrirln-ur.r al rrJ lvulcaniz.fion)

r::u )un]tl11l9 1Ja,!:tl l atr ltr--.rr: nlr|it iJtutrrL'.rrlJtrtr nl!:nr"t:11^lrulTtrrul)uetur:nir.rrirLil lrannt olrr.rua:nrriliu:niurilunT :urunrrnn_.:l.rrn-rfl nq fl r !r"!ni!m:io!raqd.urll oue::U d^ l: riu r: n I e aLiri r rLi1!rdne10:0^Inatittauna yj)L$u],1!n)llJuiouro{u rur.ua.nr-,riou,ro:n::fi nnias irrirruui 15 trln^Ratu lu l9n, tull I nrrr:nllt:'.i:':r iuori'.n: :ol'u rAclrvarort un:n'1ri)rillAc.ereratorl 3't11:alrntrs ) tUna S Jrru0nlrriJn:'lronL,ruin i ti,yr..iilirJll.a'tulrlrr:,f !r1l

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46

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1Ji 2 nrnairu SEM iS.annirrg EtectronMicroscope) narU^.r{;!fl .iuauri, ZO pr', 1r;

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(tlonlinea behavor) dirrrrr!T rnuritdnuir:nltuno.:fi nrntt!rt Jnfi 10 :tn.ll,nr:IUu1r9.t Itrilu: irr 6o irr6!r'u (Firn legk)n) ii-)rnlrniY€ld rsgon) ua:irloriernuiJ ltrarden,ng,esion) t-.,rlatJlurJi 3

t Utr I t!qOntlrr LIIlrJtrllrt,IJraUla.!U1t

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48

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6^ 5a arrr:roigi inrrriarLdari'u n,rntunenuatrtaaantt n6'u

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49

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