STIFFNESS EVALUATION OF SOME QUASI-ISOTROPIC FIBRE- REINFORCED COMPOSITE LAMINATES

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1 The d Ieaioal Cofeee o Compuaioal Mehais ad Viual gieeig COMC OCTOBR 009 Basov Romaia STIFFSS VALUATIO OF SOM QUASI-ISOTROPIC FIBR- RIFORCD COMPOSIT LAMIATS H. Teodoesu-Daghiesu S. Vlase A. Chiu M.L. Suau I. Popa 5 A. Saiu 6 Tasilvaia Uivesiy of Basov ROMAIA daghiesu.eodoesu@uibv.o Tasilvaia Uivesiy of Basov ROMAIA svlase@uibv.o Tasilvaia Uivesiy of Basov ROMAIA ahiu@uibv.o Tasilvaia Uivesiy of Basov ROMAIA lsuau@uibv.o 5 Tasilvaia Uivesiy of Basov ROMAIA popa_ioaa@yahoo.om 6 Tasilvaia Uivesiy of Basov ROMAIA aasaiu77@yahoo.om Absa: The pape peses he siffess evaluaio of vaious uidieioal quasi-isoopi fibe-eifoed omposie lamiaes based o epoy esi. The lamiaes ae subjeed o off-ais loadig sysems. The elasi osas have bee deemied. I ode o obai equal siffess i all off-ais loadig sysems a omposie lamiae have o appoimaes isoopy by oieaio of plies i seveal o moe dieios i-plae. A ompaiso bewee he elasi popeies of hese quasi-isoopi lamiaes is peseed. Tesile-shea ieaio i a fibe-eifoed omposie lamiae ous oly if he off-ais loadig sysem does o oiide wih he mai aes of a sigle lamia o if he lamiae is o balaed. eywods : lamiaes omposies fibes siffess lamiae. ITRODUCTIO I ode o obai a omposie lamiae is eessay o bod ogehe vaious uidieioal lamiae. Fo a speifi appliaio he lamiae oieaio is fo a gea impoae sie he lamiae ehibi diffee popeies fo diffee fibes oieaios [-]. I paie he mos eoueed omposie lamiaes ae: Balaed agle-ply lamiaes; Symmei agle-ply lamiaes; Ai-symmei lamiaes; Coss-ply lamiaes; Coss ply symmei lamiaes; Quasi-isoopi lamiaes. A quasi-isoopi lamiae ehibis equal siffess ad appoimaes isoopy i all off-ais loadig sysems. Some auhos elae ha quasi-isoopi lamiaes ae o ompleely isoopi showig ha he lamiae haaeisis a diffe pepediula o he lamiae [5]. I is well kow ha omposie lamiaes wih aliged eifoeme ae vey siff alog he fibes bu also vey weak asvese o he fibes dieio. This fa is moe obvious i he ase of advaed omposie lamiaes eifoed wih aisoopi abo o aamid fibes bu his is fai auae fo glass fibe-eifoed lamiaes also [6-0].. THORTICAL BACGROUD A omposie lamiae (fig. ) fomed by a umbe of uidieioal eifoed lamiae subjeed egadig o he loadig sheme peseed i fig. is osideed. The elasiiy law fo a uidieioal lamia a be wie as followig: y y () 78

2 whee ij epese he asfomed siffess ae he mea sesses of lamia o - espeive y-ais ad y epese he mea shea sess of lamia agais he -y oodiae sysem. / / Lamia o. φ z Media sufae Lamia o. φ Lamia o. φ z Lamia o. Figue : Cosuive sheme of a omposie lamiae Media sufae of he lamiae y y y y y Off-ais loadig sysem Figue : Off-ais loadig sheme of a omposie lamiae 78

3 785 The balae equaios of he lamiae suue a be ompued as followig: ( ) () () y y y y () whee ae he omal foes o he ui legh of he lamiae o - espeive y-ais ad y epeses he shea foe i plae o he ui legh of he lamiae agais he -y oodiae sysem. ae he omal sesses o - espeive y-ais of he lamiae y epese he shea sess of he lamiae agais he -y oodiae sysem. epese he hikess of he lamia espeive he lamiae hikess ae foes o he ui legh of lamia o - espeive y-ais dieios ad y is he shea foe i plae o he ui legh of lamia agais he -y oodiae sysem. Beside he balae equaios he geomei odiios mus be also deemied o ompue he sesses. Fo omposie lamiaes hese odiios imply ha all lamias ae boded ogehe ad wihsad i a speifi poi he same sais y as well as fo he eie lamiae:. y y (5) Aodig o equaios ()-(5) he elasiiy law fo he whole lamiae a be ompued []: y y (6) whee he lamiae siffess ij ae:. ij ij (7) I ohe wods he lamiae elasiiy law beomes: y y (8) Compuig he lamiae sais as a fuio of sesses he epessios (8) beome: y y (9) whee ij epeses he lamiae asfomed ompliae eso. This eso a be ompued as a fuio of elasi osas. Thus [6 0]:. ; G ; y y υ (0) I is obvious ha he lamiae will ehibi diffee elasi osas if he loadig sysem is applied a a adomly agle Φ o he -y oodiae sysem. The ompouds of he asfomed ompliae eso a be deemied i he followig way [ ]: si G si os υ () si G os si υ ()

4 os υ si () G si υ si os G () υ υ si os os si G G (5) υ os si G υ si os. G (6). RSULTS The oupu daa have bee geeaed usig he sofwae developed by Hull ad Clye fom Maeials Siee Depame a Cambidge Uivesiy U [6]. The quasi-isoopi lamiaes ake io aou i he umeial aalysis pese followig plies sequee: [0/-0/90] [0/5/-5/90] ad [0/8/6/5/7/90/-8/-6/-5/-7]. Geeal ipu daa ae: fibes volume faio φ 0.5 i all ases plies hikess 0.5 mm ad off-ais loadig sysems vaies bewee 0 ad 90. Fo he glass fibe-eifoed lamiaes followig daa have bee used []: M.9 GPa; F 7 GPa; υ M 0.8; υ F 0.5; G M < 0 GPa; G F < 5 GPa. Fo HM abo fibes-eifoed lamiaes followig daa have bee used []: M.9 GPa; > 00 GPa; < 00 GPa; υ M < 0.5; υ F < 0.; G M < 5 GPa; G F < 50 GPa. The elasi osas G y as well as he Poisso aio υ y ae peseed i figs. 5. [GPa] Off-ais loadig agle Glass fibes HM Cabo fibes Figue : Disibuio of Youg moduli ad of hee epoy based fibe-eifoed quasi-isoopi omposie lamiaes: [0/-0/90] [0/5/-5/90] ad [0/8/6/5/7/90/-8/-6/-5/-7] 786

5 0 5 0 Gy [GPa] Off-ais loadig agle Glass fibes HM Cabo fibes Figue : Disibuio of shea modulus G y of hee epoy based fibe-eifoed quasi-isoopi omposie lamiaes: [0/-0/90] [0/5/-5/90] ad [0/8/6/5/7/90/-8/-6/-5/-7] Poisso aio [-] Off-ais loadig agle Glass fibes HM Cabo fibes Figue 5: Disibuio of Poisso aio υ y of hee epoy based fibe-eifoed quasi-isoopi omposie lamiaes: [0/-0/90] [0/5/-5/90] ad [0/8/6/5/7/90/-8/-6/-5/-7]. COCLUSIOS Ude off-ais loadig omal sesses podue shea sais ad of ouse omal sais. Shea sesses podue omal sais as well as shea sais. Usually esile-shea ieaio is also pese i ommo lamiaes bu does o ou if he loadig sysem is applied alog he mai aes of a sigle lamia o if a lamiae is a quasi-isoopi oe. Fom he siffess poi of view hee is o diffeee if a quasi-isoopi omposie lamiae is desiged wih hee layes (fo isae [0/-0/90]) fou layes (e.g. [0/5/-5/90]) o e layes (fo isae [0/8/6/5/7/90/-8/-6/- 5/-7]). 787

6 Fo he segh poi of view he quasi-isoopi omposie lamiae wih plies sequee [0/8/6/5/7/90/-8/-6/- 5/-7] a wihsad a ieased loadigs ha he quasi-isoopi omposie lamiae wih plies sequee [0/-0/90]. The values of Youg moduli ad as well as he shea modulus G y fo HM abo fibes lamiaes ae moe ha fou imes geae ha he Youg moduli ad shea modulus of he glass fibes oes. The disibuio of Poisso aio υ y ae lose i boh ases of eifoeme. RFRCS [] Teodoesu-Daghiesu H.: Basis ad mehais of polyme mai omposie maeials Tasilvaia Uivesiy of Basov Publishig House 007 (i Romaia). [] Vlase S. Goia I. Teodoesu-Daghiesu H. Modea A. Suau L.: Composie maeials. Compuig mehods Tasilvaia Uivesiy of Basov Publishig House 007 (i Romaia). [] Goia I. Vlase S. Tieea M. Dimiiu S. Teodoesu-Daghiesu H. Pop O. Plamadeala R.: Colleio of poblems of segh of maeials Lu Libis 007 (i Romaia). [] Vlase S. Teodoesu-Daghiesu H. Puaea R. Modea A.: Mehais of fibe-eifoed omposie maeials Ifomake 008 (i Romaia). [5] Va Oeloo D.L. Dayal V.: How isoopi ae quasi-isoopi lamiaes Composies Pa A: Applied Siee ad Maufauig Vol. o. Ja. 00 lsevie pp [6] Hull D. Clye T.W.: A Ioduio o Composie Maeials Cambidge Uivesiy Pess d ediio 996. [7] Miale D.B. Doaldso R.L.: ASM Hadbook Volume : Composies ASM Ieaioal 00. [8] Daiel I.M. Ishai O.: gieeig of Composie Maeials d ed. Ofod Uivesiy Pess 005. [9] Viso J.R. Sieakovski R.L.: The Behavio of Suues Composed of Composie Maeials Spige 008. [0] Clye T.W. Wihes P.J.: A Ioduio o Meal Mai Composies Maeials Cambidge Uivesiy Pess 99. [] ops M.: Aalysis of Failue i Fibe Polyme Lamiaes: The Theoy of Alfed Puk Spige 008. [] Teodoesu-Daghiesu H. Vlase S. Chiu A. Suau M.L. Moo D.L.: O he lasi Cosas of a Fibe- Reifoed Composie Lamiae. Poeedigs of he d WSAS Ieaioal Cofeee o GIRIG MCHAICS STRUCTURS ad GIRIG GOLOGY (MSG 09) Rodos Geee July WSAS Pess pp