18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS A PROPOSAL OF FE MODELING OF UNIDIRECTIONAL COMPOSITE CONSIDERING UNCERTAIN MICRO STRUCTURE Y.Fujit 1*, T. Kurshii 1, H.Ymtsu 1, M. Zo 2 1 Dpt. o Mngmnt o Inustry n Thnology, Os Univ., Os, Jpn 2 Cntr o Avn Crr Dvlopmnt, Os Univ., Os, Jpn * y-ujit@mit.ng.os-u..jp Kywors: multi-sl nlysis, wovn ri omposit, unrtinty, intril hvior 1 Introution This ppr sris out FE moling mtho or miro strutur o uniirtionl omposit to stimt th strngths o irous omposits onsiring unrtin miro strutur. Th gol o this stuy is to stimt th isprsion o ir unl s strngth. Sin nw onstitunt mtrils suh s thrmoplsti rsin hv n vloping, th stimtion mtho o th strngth rom th point o miro sl is ritil or th sty n rliility o omposit struturs. Th unrtinty o miro strutur oms rom th rnomnss o ir rrngmnt, th t on mhnil hviors suh s strss istriutions or strngth hv n lry isuss in svrl stuis [1][2][3]. In our prvious stuis [4], th t o rnom rrngmnt o ilmnts n th rsiul thrml strsss on th trnsvrs strngth ws stimt with FE mol o UD omposit shown in Fig.1. FE mol with ilmnts rrng hxgonlly ws lso gnrt or th omprison. In th stuy, numril rsults show goo grmnt with xprimntl rsults, whih init th importn o onsiring th rnom rrngmnt o ilmnts or th strngth stimtion n vliity o th numril mtho. Howvr, itionl moiition o th mtho will nssry us th omputtionl tim n mmory rquirmnt wr hug. To solv th prolm o omputtionl osts, w propos th stimtion mtho o strngth y simplii FE mol o UD omposit. Th isprsion o strngth is stimt y using th numril rsult o svrl FE mols. Th prour o th mtho n numril rsults r sri. 2 Propos mtho 2.1 Oliqu unit ll mol Th importnt tors o miro mol (UD omposit) r intril hvior twn ilmnt n rsin, rsiul thrml strss n rnomnss o ir rrngmnts. Consiring ths tors, FE mols o UD omposit with 5 ilmnts rrng rnomly (rnom mol) wr gnrt in our prvious stuy [4]. Intril hviors wr simult y intril lmnts insrt twn ilmnts n rsin. Fig.1. FE mols in prvious stuy [4] Fig.2. Oliqu unit ll mols
In orr to ru th omputtionl ost or FE nlysis, rnom rrngmnt o ilmnts is n to simult with smll numr o ilmnts. Thror, FE mols with 2 ilmnts in unit ll shown in Fig.2 r gnrt, whih r ll s Oliqu Unit Cll (OUC) mol. OUC mol is rott rtngl unit ll. This is or loing oliqu irtion o unit ll, whih nls ritrrily. Th unit ll siz is lult s on th ir volum rtion n spt rtio. As th rnom prmtrs, istn n ngl twn 2 ilmnts n spt rtio o unit ll r prpr. Intril lmnts r insrt twn rsin n ilmnts. Prioi ounry onitions r ppli to OUC mol. 2.2 Prioi ounry onitions In this stuy, th rltiv isplmnt vtor is us to onsir th prioiity. Fig.3 shows th onpt o rltiv isplmnt vtor. Nos n, nos n r orrsponing nos on th sur o unit ll. No is insi th unit ll. In this s, rltions twn isplmnts t nos, n t nos, r xprss y Eq. 1 n Eq. 2. whr, is rltiv isplmnt vtor. As th nos n in Eq.1 n 2, nos rrr rom othr nos r ll mstr no, othrwis, nos rrring othr no r ll slv no. Eq. 3 shows stinss qution without prioi ounry onition. Thn, Eq. 3 is trnsorm to Eq. 4 rom Eq. 1 n Eq. 2. Furthrmor th lmnts o olumn r mov to olumn n s on th prioiity n Eq. 4 is trnsorm to Eq.5. In th sm prour, olumn, row n r mov, too. Finlly stinss qution oms s shown in Eq.6. Th rows n olumns onrn with slv nos in stinss mtrix r rmov n nw row n olumn onrn with prioiity r. By th stinss qution, FE nlysis onsiring prioiity n rri out i th rltiv isplmnt vtors r trmin proprly. (3) (4) Fig.3. Dormtion o prioi sur (1) (2) (5) (6)
A PROPOSAL OF FE MODELING OF UNIDIRECTIONAL COMPOSITE CONSIDERING UNCERTAIN MICRO STRUCTURE 2.3 Enor isplmnt vlu Thr r 3 prioi surs to whih pproprit isplmnt shoul ppli. Fig.4 shows th ormtion o OUC mol whn loing to x irtion. In th igur, 1 n 2 r prioi vtors n 1 n 2 r isplmnts to 1 n 2. moulus o th nighor lmnt is lso ru. Finlly, i ny lmnts on t il t this point (B), th nlysis is progrss into th nxt stp. An, th sm lultion is rri out t th point (C), (D) n (E). Tl 1 shows mhnil proprtis o polystr rsin, intril lmnt twn ilmnt n rsin n glss ilmnt us in th nlysis. Expt omprssiv strngth, rsin n intr hv ommon proprtis. Homn s ritrion is ppli s mg ritrion to onsir th irn o tnsil n omprssiv strngth. Fig.4. Dormtion o OUC mol 1 n 2 whn proviing strin to x irtion r xprss y Eq.7 n 8, lult s on th uniorm rtio o r xpnsion. L1 os( ) L 1 1 L2 os( ) (7) 2 L1 os( ) L 2 1 L2 os( ) (8) 2 Poisson s t is lso onsir whn y irtion o prioi sur is r. Whn provi out o pln shr lo, 1, 2 n 3 whih is prioiity in z irtion r n to lult. Th sm mtho s ling Eq.7 n 8 n ppli to lult ths vlus. 2.4 FE nlysis s on mg mhnis FE nlysis s on mg mhnis is rri out with 1 numrs o OUC mols. Fig.5 shows th mtho o mg vlopmnt nlysis. Th til o th mtho is sri in rrn [5]. Whn th initil ilur ours t this point (A), th moulus o mg lmnt is ru. I th nighor lmnt is ron y th strss onntrtion u to th rls o strss, th Fig.5. Dmg vlopmnt nlysis mtho Tl 1 Mhnil proprtis ()Polystr rsin n intril lmnt Proprty Symol Dt Young's moulus[gp] E m 2.614 Shr moulus[gp] G m 972.7 Poisson's rtio n m.3866 Coiint o thrml Expnsion[1-6 / ] m 15 Tnsil strngth[mp] F T 8 Shr strngth[mp] F s 8 omprssiv strngth[mp] F rsin : 16 intr : 25 3 Rsults o nlysis ()Glss ilmnt Proprty Symol Dt Young's moulus[gp] E 74.75 Shr moulus[gp] G 28.75 Poisson's rtio n.3 Coiint o thrml Expnsion[1-6 / ] 5 Tnsil strngth[mp] F 1857 1 OUC mols with th volum rtion o ir 3, 3
4, 5, 6 n 7% rsptivly r gnrt n FE nlyss r rri out. Fig.6 shows strss istriutions o x irtion in hxgonl mol n OUC mol with n without rsiul thrml strss. Filmnts r invisil in th igur. Th strss in OUC mol is highr thn hxgonl mol or th short istn o ilmnts n strsss on nr =18 gr is high without thrml strsss on th othr hn =15 gr is high with thrml strsss or th t o strss rlxtion. Fig.8. Dmg vlopmnts (x strin=.55%) Howvr, th tnny ws ppr in s strngth without thrml strss is low, th mol o istn twn 2 ilmnts is short. In s th istn is long, strngth rss. Thror, th vrg o th strngths ws lowr whn onsiring rsiul thrml strsss. Fig.9 shows rltionship twn strngth n volum rtion o ir (V ) otin rom 1 numr o OUC mols t h V rsptivly. Th istriution is hrtriz y Wiull s istriution n sttr r shows.1 n.99 o umultiv istriution untion. For th rson sri ov, isprsion o strngth in miro sl is smllr whn rsiul thrml strsss r onsir. Fig.6. Distriution o x strss Fig.7 shows rution o stinss n Fig.8 shows mg vlopmnt o OUC mol. Bl lmnts r trt s mg n th stinss is ru. As shown in igurs, th toughnss will highr with onsiring thrml strsss, us mg our n vlop in lrgr strin thn th numril rsults without thrml strsss. Fig.9. Trnsvrs strngth Strngths n mg vlopmnts unr shr n omprssiv los r lso l to stimt y th mtho. Fig.1 shows xmpls o th mg vlopmnts unr omprssiv n shr lo. Fig.7. Rution o stinss
A PROPOSAL OF FE MODELING OF UNIDIRECTIONAL COMPOSITE CONSIDERING UNCERTAIN MICRO STRUCTURE n isprsion rss s shown in Fig.12. Th rltion is importnt to stimt strngth t ir unl sl s on th rsult o OUC mol. Th rltion is lrly u to th mg initition is th wst prt whn th numr o ilmnts is lrg suh s th mol shown in Fig.1. Fig.1. Dmg vlopmnts Fig.11 shows th strngths in miro sl whn out o pln shr lo n tnsil or omprssiv lo r omin. This urv is lso l y som in o mg ritrion suh s Homn s ritrion. In s o th unit lls with svrl ilmnts, it spns too muh omputtionl osts. Howvr, OUC mol nls to ru.1% o th omputtionl tim ompr with th unit ll mols with 5 ilmnts. Fig.11. Dmg nvlop 4 Estimtion o strngth t ir unl sl Tl 2 is sl n shp prmtrs o mhnil proprtis o trnsvrs irtion in miro sl otin rom OUC mols without onsiring rsiul thrml strsss. Two mg mos, whih r th mg o intr n rsin, is onsir us stinss rss to out hl whn intr mg n whn rsin mg, stinss rops signiintly. Disprsions r hrtriz s on Wiull s istriution. Tl 2 Mhnil proprtis o trnsvrs irtion ()Sl prmtr Volum rtion o ir [%] 3 4 5 6 7 Young's moulus[gp] 5.6 6.24 8.12 1.6 15.5 Strss[MP] : intr mg 34.6 34.3 32.7 33.3 32.5 Strin [%]: rsin mg.75.69.68.65.53 ()Shp prmtr Volum rtion o ir [%] 3 4 5 6 7 Young's moulus 31. 19.9 15.4 12.3 8.4 Strss: intr mg 8.61 7.6 7.68 7.61 8.36 Strin: rsin mg 7.2 5.9 4.1 3.5 3.3 Fig.13. FE mol o UD Fig.12. Rltionship twn numr o ilmnts in unit ll n strngth. Thr r rltion twn th numr o ilmnt in unit ll n istriution o strngth tht whn th numr o ilmnts inrss, vrg o strngth Ths mhnil proprtis r ppli to FE mol shown in Fig.13 whih is ompos o 1 lmnts with th proprtis o OUC, ssums out 5 to 1 ilmnts in mol. Mhnil proprtis o lmnts r trmin y rnom numr s on istriution shown in Tl 2. Th volum rtion (V ) o lmnts r trmin rnomly, iming th 5
vrg V is trgt vlu. Fig.14 shows th rsult o nlysis, ompring th rsult o rnom mol with 5 ilmnts shown in Fig.1. Both th s with n without thrml strss, th rsults o propos mol in Fig.9 gr with th rsults o rnom mol. Though th strngths o OUC mol r out 3MP, th strngths o UD r smllr. This is us o th isprsion o strngth (w lmnt mg) n th t o vrin o lol volum rtion o ir. trnsvrsly lo UD-CFRP rom viwpoint o ilur initition. Composits Sin n Thnology, Composits Sin n Thnology, vol. 69, 11-12, pp. 1726-1734, 29. [3] A. J. Flthr, J. L. Oshott Thrml rsiul mirostrss gnrtion uring th prossing o uniirtionl ron ir/poxy rsin omposits: rnom ir rrys. Composits, vol. 25, 8, pp. 86-813, 1994. [4] Y. Fujit, T. Kurshii, M. Zo, On th Trnsvrs strngth o uniirtionl omposit, Proings o 14th Europn Conrn on Composit Mtrils (ECCM14), Bupst, 497, 21. [5] M. Zo, Y. Utsuji, T. Kurshii Finit lmnt nlysis o mg wovn ri omposit mtrils. Composits Sin n Thnology, vol. 63, 3-4, pp. 57-516, 23. Fig.14. Rsult o nlysis By using th propos mtho, shr strngth n omprssiv strngth might stimt s wll. In th utur stuis, th isprsion o mhnil proprtis o UD is ppli to mso sl mol to rry out multi-sl nlysis. 5 Conlusions 1) FE nlysis o oliqu unit ll (OCU) mol hs n propos to stimt mhnil proprtis o uniirtionl omposit t miro sl. 2) Mhnil proprtis o miro sl r hrtriz s on Wiull s istriution rom 1 numr o OUC mols. 3) From th rsult o OUC mols, mhnil proprtis t ir unl sl n stimt. Rrns [1] Y. Hung, K. K. Jin, S. K. H Ets o Fir Arrngmnt on Mhnil Bhvior o Uniirtionl Composits. Journl o Composit Mtrils, vol.42, 18, pp. 1851-1871, 28. [2] M. Hojo, M. Mizuno, T. Hoirunn, T. Ahi, M. Tn, S. K. H Et o ir rry irrgulritis on mirosopi intril norml strss stts o