ELASTIC MODULUS ESTIMATION OF CHOPPED CARBON FIBER TAPE REINFORCED THERMOPLASTICS USING THE MONTE CARLO SIMULATION

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1 THE 19 TH INTERNATIONAL ONFERENE ON OMPOSITE MATERIALS ELASTI MODULUS ESTIMATION OF HOPPED ARBON FIBER TAPE REINFORED THERMOPLASTIS USING THE MONTE ARLO SIMULATION Y. Sao 1*, J. Takahash 1, T. Masuo 1, I. Ohsawa 1, K. Kryama and S. Nagoh 1 The Unversy of Tokyo, Tokyo, Japan, Toyobo o., Ld., Osaka, Japan * orrespondng auhor (y.sao0509@gmal.com Keywords: FRTP, Mone arlo mehod, Elasc modulus, UD ape 1 Inroducon Fg.1 shows energy consumpon of ranspor secor n Japan [1]. I can be seen from hs resul ha n order o solve he energy and envronmenal problems, s need o mprove fuel effcency of cars. One of he mos effecve mehods of mprovng fuel effcency s reducng wegh of producon cars usng carbon fber renforced plascs (FRP. However, cars made of FRP are no almos popular due o hgh producon coss because he moldng me of FRP s long. Therefore, reducon of moldng me s essenal n order o apply FRP o producon cars. hopped carbon fber ape renforced hermoplascs (TT s made from chopped undreconal FRTP apes (UD apes whch are lad a random (Fg.. TT s expeced o be appled o complex shaped srucural members for producon cars and o acheve a hgh-speed moldng and a sgnfcan wegh reducon of he body srucure []. However, TT has a problem n he evaluaon of parameers used n AE caused by he sze of he ape. For example, he varaon of elasc modul measured by small specmens s very large (Fgs.3- hough he varaon of elasc modul measured by srucural members s suffcenly small (Fgs.5-6. When desgnng a car, he elasc modulus of he maeral wll be as mporan as he srengh. If a car was made from a maeral havng a low elasc modulus, s wndow wll be broken by orsonal deformaon when urns he corner, or s doors wll no be opened or closed when load s appled o [3]. Therefore, when a car was made from a maeral havng a hgh average elasc modulus, bu also havng a bg varaon, s necessary o he hck body because all cars should ge he necessary rgdy. So, s mporan o measure he correc average elasc modulus and coeffcen of varaon. On he oher hand, because he elasc modulus of he srucure of TT s no vared, we wan o pu TT no praccal use, bu because dmensonal dependency of varaon would be large, he developmen of mehod o oban effecve maeral properes requred for AE s necessary. In hs sudy, we evaluaed he elasc modulus of TT usng Mone arlo mehod by focusng on he random arrangemen of he chopped UD apes. Problem of he measuremen of elasc modulus by ensle es Sandard ensle es mehod of TT does no exs ye. Therefore, n order o measure he ensle modulus, we can only use he es condons of soropc and orhoropc fber renforced plasc whch are wren o he JIS sandard []. Accordng o hs mehod, s recommended ha he specmen wdh s 50±0.5 mm and hckness s.0~10 mm, and he dsance beween he marked lnes s 50±1 mm. Also, he number of specmens s more han four. However, hs condon mgh no be approprae for TT wh he randomness n erms of he sze of specmens. Therefore, n hs sudy, we propose a new model for calculang he elasc modulus of TT, verfy he valdy of he model by comparson wh expermens wh specmens changed hckness or dsance beween he marked lnes, and dscuss he es condons ha are suable for TT usng hs model. 3 Modelng and calculaed elasc modulus of he TT specmens TT s made from UD apes approxmaely 35 mm n lengh, 15 mm n wdh, and 0.1 mm n hckness. Therefore, s consdered ha n he specmen wh a hckness of mm, 10 UD apes are lamnaed n he hckness drecon lke Fg.7. Plane drecon s consdered o approxmae UD apes o he squares of he same area lke Fg.8 and o place he squares

2 whou gaps. And s consdered how much each square s ncluded n he area of he sze correspondng o he wdh of he specmen and he dsance beween he marked lnes. To make he model of specmen, usng he Mone arlo mehod, each UD ape s gven a drecon ( a random usng random number. We calculaed he elasc modulus of each square (E n by nroducng lamnae heory n he hckness drecon [5]. Equaons (1 o (5 are calculaon formula of lamnae heory and Table1 s he elasc properes of UD apes whch was used when calculang lamnae heory. Afer calculang he elasc modulus of each square, we synheszed he modulus n he wdh drecon (E m by he superposon prncple. E' m a1e1 ae Afer synheszng he modulus n he wdh drecon, we synheszed he modulus n he longudnal drecon by he superposon prncple n order o ge he elasc modulus of he measuremen range (E. a n E n (6 c s 16 6 E ( ( ( 1 E E G cos sn c ( c s /(1 _ /(1 /(1 E s s ( c 1 1 ( ( xy _ 1 s 3 s 3 ( ( / _ s xy /(1 s s s 16 ( c 1 s s 6_ 3 3 s 6_ (1 ( (3 ( b1 b b E E' E' m E' 1 omparson of expermenal and calculaed resuls.1 Expermen We obaned he average elasc modulus and coeffcen of varaon based on sandard es condons of JIS and by performng ensle ess n each of four ypes of specmens wh dfferen hckness (:mm and dsance beween he marked lnes (L:mm and wh he same wdh (W:mm. Table shows he condons of he ensle es specmens. And we calculaed average elasc modulus and coeffcen of varaon usng he model based on he same condons. The resuls of hese expermens are from Fgs.9-. In Fgs.9 and, 10 lnes are no sragh bu wave, so s a queson hese expermenal resuls are correc. Therefore, we dd ensle es of same specmens of W35L5 usng he conac exensomeer (Fg.13. Fg.1 s he resul of he ensle es and shows ha lnes are sragh and he slopes of he 10 lnes are almos he same as he slopes of he lnes of Fg.9, so cause of he waves of he lnes n Fgs.9 and s usng he vdeo exensomeer o measure he oo small measurng range. Also we found ha he waves do no affec measurng he correc value of he elasc modulus. m (7 E n /( 6_ (5. alculaon Fgs.15 and 16 show he comparsons of expermenal and calculaed resuls. Each blue bar shows he average elasc modulus or coeffcen of

3 varaon of he 10 or 6 specmens obaned from he expermen, so each error bar of he blue bar n Fg.15 shows he varaon n he elasc modulus of he 10 or 6 specmens. On he oher hand, each green bar shows he average of he 1000 averages of he elasc modulus whch are obaned by 1000 mes smulaons of a ensle es of 10 or 6 specmens. The reason ha he number of smulaons s 1000 mes s because was found from Fg.17 ha values are suffcenly converged. Therefore, each error bar of he green bar n Fg.15 shows he varaon n he 1000 averages of he elasc modulus of he 10 or 6 specmens and n Fg.16 shows he varaon n he 1000 coeffcens of varaon. Fgs.15 and 16 ndcae ha he model of he Mone arlo mehod can represen he expermenal resuls wh he excepon of he coeffcen of varaon of W35L5. The reason why he dfference of calculaon resuls wh expermenal resuls of W35L5 occurs may be some facors ha are no descrbed n hs model and become larger when he measuremen range s oo small. However, hs model was found o be applcable enough f he sze of he measuremen range o be calculaed s close o he sze of he acual srucure or s he sze ha could be a new es condons. varaon decreases as he number of specmens becomes large. 5. Effec of cu lengh of UD apes TT, whch has been reaed ever, s made of UD apes whch are cu o 35mm, bu s possble o make TT from UD apes of varyng lengh o cu. Fg.1 shows comparson of he coeffcen of varaon of TT made from UD apes wh dfferen cu lengh. From hese resuls, can be seen ha he shorer he cu lengh of UD apes s, he smaller he varaon of he elasc modulus s. So, n he fuure, we wll verfy he effec of he cu lengh n he expermen. 6 oncluson The proposed model usng lamnae heory and he Mone arlo mehod were successfully able o represen he elasc modulus and her varaon of ensle TT specmens. I was found ha he varaon of he elasc modulus depends on he sze of specmen. Therefore, hs model enable us o fnd reasonable es condons o evaluae an nrnsc elasc modulus and s varaon of TT. 5 Influence on he varaon of elasc modulus 5.1 Effec of he sze and he number of specmen Fg.18 shows he coeffcen of varaon when changng L and. From hese resuls, can be seen ha he coeffcen of varaon s reduced by ncreasng or L. In oher words, n TT, s mporan ha sze of specmen s se so ha doesn' overesmae he varaon n he mechancal properes of he acual srucure. Fg.19 shows he comparson of he coeffcen of varaon of L5W5 and he coeffcens of varaon of he specmen whch were doubled each L, and W. Each coeffcen of varaon was deermned from specmens. From hese resuls, f specmen s made n he same volume, should ncrease he hckness han he wdh or dsance beween he marked lnes. Ths s also rue from he fac ha here s a lm of he specmen sze on laboraory nsrumen. Fg.0 shows effec of he number of specmens n an expermen. From hese resuls, n he expermen usng 10 or more specmens, he average coeffcen of varaon converges subsanally. On he oher hand, he sandard devaon of he coeffcen of Fg.1 Energy consumpon of ranspor secor n Japan

4 Fg. hopped carbon fber ape renforced hermoplascs (TT. Fg.5 Three-pon bendng es. oeffcen of varaon.6% Fg.3 Tensle es usng he vdeo exensomeer. Fg.6 Resuls of hree-pon bendng es usng large frame members. oeffcen of varaon 13% Fg. Resuls of he ensle es usng small specmens. Fg.7 Modelng mehod of hckness.

5 Table ondons of he ensle es specmens. Name of specmens (mm L (mm W (mm ondon of JIS N Dsance beween he marked lnes (L W35L W35L W35L W35L Wdh (W L Modelng W Fg.8 Modelng mehod of wdh and dsance beween he marked lnes. Fg.9 Resuls of ensle es of W35L5. Table1 Elasc properes used n hs sudy. Elasc modulus (Fber drecon E 1 (GPa 105 Elasc modulus (vercal drecon E (GPa Posson's rao (conracon n he 0.3 vercal drecon Posson's rao (conracon n he fber drecon Shear modulus G (GPa 1. Fg.10 Resuls of ensle es of W35L100.

6 Fg. Resuls of ensle es of W35L5. Fg.1 Resul of ensle es of W35L5 usng he conac exensomeer. Fg. Resuls of ensle es of W35L100. Fg.15 omparson of he expermenal resuls and calculaed resuls n he average elasc modulus. Fg.16 omparson of he expermenal resuls and calculaed resuls n he coeffcen of varaon. Fg.13 Tensle es usng he conac exensomeer.

7 Fg.17 Dfferences beween he number of smulaons of ensle es of W35L5n10. Fg.0 Effec of he number of specmens n an expermen. Fg.18 Relaonshp beween he coeffcen of varaon and he specmen sze. Fg.1 Effec of he cu lengh of UD apes. Acknowledgmen Ths sudy was conduced as a par of Japanese METI-NEDO projec "Developmen of susanable hyper compose echnology" snce 008fy. Auhors would lke o express sncerely apprecaon o he projec members who have provded valuable nformaon and useful dscussons. Fg.19 Effec of he sze of specmen whou changes n volume. References [1] The ENERGY DATA AND MODELLING ENTER, "EDM, Energy & Economc Sascs 0". pp 8-9, 0.

8 [] NEDO: Developmen of Susanable Hyper ompose Maerals Technology hp:// [3] M. Shkda, and Y. Kanayama, "The Srengh of The ar". SANKAIDO PUBLISHING o.,ld., Japan, [] Japanese Sandards Assocaon, "JIS Handbook 6 plasc 1 Tes". pp , 010. [5] D. Hull, and T. W. lyne, "An Inroducon o ompose Maerals Second Edon". ambrdge Unversy Press., Uned Kngdom, 1996.