Noncircular CFRP bicycle’s chainring, part II: finite element analysis

(1)

HAL Id: hal-01880446

https://hal.archives-ouvertes.fr/hal-01880446

Submitted on 16 Jan 2019

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Noncircular CFRP bicycle’s chainring, part II: finite

element analysis

Zhorachaid Thanawarothon, Abdelrahman Elmikaty, Christophe Bouvet,

Laurent Mezeix

To cite this version:

Zhorachaid Thanawarothon, Abdelrahman Elmikaty, Christophe Bouvet, Laurent Mezeix. Noncircu-lar CFRP bicycle’s chainring, part II: finite element analysis. Composites: Mechanics, Computations, Applications: An International Journal, 2018, 9 (3), pp.207-222. �10.1615/CompMechComputAp-plIntJ.2018025471�. �hal-01880446�

(2)

an author's https://oatao.univ-toulouse.fr/21631

http://doi.org/10.1615/CompMechComputApplIntJ.2018025471

Thanawarothon, Zhorachaid and Elmikaty, Abdelrahman and Bouvet, Christophe and Mezeix, Laurent Noncircular CFRP bicycle’s chainring, part II: finite element analysis. (2018) Composites: Mechanics, Computations, Applications: An International Journal, 9 (3). 207-222. ISSN 2152-2057

(3)

AUTHOR PROOF

NONCIRCULAR CFRP BICYCLE’S

CHAINRING. PART II: FINITE ELEMENT

ANALYSIS

Zhorachaid Thanawarothon,

1

Abdelrahman Elmikaty,

2

Christophe Bouvet,

2

& Laurent Mezeix

1,*

1_{Faculty of Engineering, Burapha University, 169 Long-Hard Bangsaen Road,} Chonburi 20131, Thailand

2_{Université de Toulouse, INSA, UPS, Mines d’Albi, ISAE, ICA (Institut} Clément Ader), 135 Avenue de Rangueil, 31077 Toulouse Cedex, France *Address all correspondence to: Laurent Mezeix, Faculty of Engineering,

Burapha University, 169 Long-Hard Bangsaen Road, Chonburi 20131, Thailand, E-mail: Laurent.mezeix@hotmail.com

In this paper, numerical simulation is developed in order to analyze the failure of a noncircular composite chainring, and teeth damage is especially detailed. Simulation consists of the chainring ȱȱȱȱȱȱǯȱȱȱȱ£ȱȱȱȱȱ¢ȱȱęȱŗŗȱ-ers are simulated. In order to validate the numerical simulation, the force–displacement curve is compared with the experimental results obtained on the same specimens used in the simulation. ǰȱȱěȱȱȱȱȱȱȱȱȱěȱȱǰȱȱ ȱ ȱ ȱ ȱ ǯȱ ǰȱ ȱ ěȱ ȱ ȱ ¢Ȭȱ ȱ ȱ ȱ ěȱ ¢Ȭǯȱ ȱ ȱ ȱ ȱ ȱ ȱ ȱ ȱ ȱ Ěȱ ȱ ȱ ȱ behavior, while the damage scenario depends on it. The damage consists of matrix cracking located on the teeth surface. Finally, the thickness can be reduced to 9 plies lay-up and even if the damage is larger, it is always located on the teeth surface.

K E Y W O R D S :_{noncircular chainring, CFRP, FEA, matrix cracking}

1. INTRODUCTION

7KHXVHRI&DUERQ)LEHU5HLQIRUFHG3RO\PHUV&)53KDVVLJQL¿FDQWO\LQFUHDVHGRYHU WKHSDVW\HDUVLQDHURVSDFHVWUXFWXUDOHQJLQHHULQJODQGWUDQVSRUWVDQGVSRUWLQGXV-WULHV ,QGHHG WKDQNV WR WKHLU PHFKDQLFDO SURSHUWLHV LH KLJK PRGXOXV DQG VWUHQJWK DQG ORZ GHQVLW\ JDLQ RI PDVV LV H[SHFWHG$OWKRXJK &)53 SUHVHQW EHWWHU SURSHUWLHV WKDQ DOXPLQXP LPSDFW %RXYHW DQG 5LYDOODQW 5R]\OR HW DO DQG HGJH GDPDJH2VWUpHWDO/LDQG&KHQDUHPDMRUFRQFHUQVGXHWRWKHLQÀX-HQFHRQWKHUHVLGXDOPHFKDQLFDOSURSHUWLHVRIWKHVWUXFWXUH

(4)

AUTHOR PROOF

6SRUW LQGXVWU\ XVHV PRUH DQG PRUH FRPSRVLWH PDWHULDOV LQ RUGHU WR LQFUHDVH WKH VSHFL¿FVWUHQJWKRIWKHHTXLSPHQW&)53WHQQLVUDFNHWVDQGEDVHEDOOEDWVDUHUHSODFHG E\ZRRG%URG\&DUERQHSR[\JROIFOXEVDUHXVHGWRUHGXFHWKHZHLJKWDQG WRLQFUHDVHWKHEDOOH[LWYHORFLW\6ODWHUHWDO6QRZERDUGLQJVXU¿QJDQGRWKHU ERDUGVSRUWV WDNH DGYDQWDJH RI D FRPSRVLWH PDWHULDO WR LQFUHDVH WKH VWL൵QHVVZHLJKW UDWLR&OLIWRQHWDO3HUIRUPDQFHRISURIHVVLRQDOELNHLQFUHDVHGE\XVLQJ&)53 LQVWHDGRIDOXPLQXPWRREWDLQDKLJKVWL൵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¿UVWO\ IDLOHG/RZYHORFLW\ORZHQHUJ\LPSDFWRQWKHWHHWKZDVDOVRLQYHVWLJDWHGDQGIRUDQ HQHUJ\KLJKHUWKDQ-GHODPLQDWLRQVZHUHREVHUYHGE\&6FDQ

'XH WR WKH FRPSOH[ VKDSH RI WKH WHHWK D FRPSRVLWH GDPDJH FDQQRW EH GHWHFWHG HDVLO\H[SHULPHQWDOO\E\D1RQ'HVWUXFWLYH7HVW7KHUHIRUHQXPHULFDOVLPXODWLRQKDV EHHQGHYHORSHGLQWKLVSDSHUWRGHWHUPLQHWKHWHHWKIDLOXUHPHFKDQLVPRIQRQFLUFXODU FRPSRVLWHFKDLQULQJXQGHUTXDVLVWDWLFORDGV7KHDLPLVWRXVHWKLVPRGHODVDGHVLJQ WRRO WR RSWLPL]H QRQFLUFXODU FRPSRVLWH FKDLQULQJ ,Q RUGHU WR YDOLGDWH WKH )($ FRQ-VWUXFWLRQ WKH VLPXODWLRQ LV FRPSDUHG ZLWK H[SHULPHQWDO UHVXOWV REWDLQHG SUHYLRXVO\ E\WKHVDPHDXWKRUV7KHQQRQFLUFXODULW\H൵HFWLVLQYHVWLJDWHGWKURXJKWKUHHORDGLQJ FDVHV)LQDOO\WKDQNVWRWKHVLPXODWLRQWKHVWDFNLQJLQÀXHQFHLVSURSRVHGWR¿QGWKH EHVWOD\XS

2. MODEL CONSTRUCTION AND VALIDATION

2.1 Chainring and Chain

1RQFLUFXODUFRPSRVLWHFKDLQULQJZLWKWHHWKDUHVWXGLHGLQWKLVSDSHU)LJ7KH UDGLXVRIWKHQRQFLUFXODUFKDLQULQJGHSHQGHGRQWKHDQJOHș7DEOH7KHWHHWKGHVLJQ SURSRVHGE\:DQJLVXVHGIRUWKHFKDLQULQJ:DQJHWDO7KHFKDLQFRQVLVWHG RI UROOHUV LQQHU DQG RXWHU SODWHV )LJ DQG LW LV SURYLGHG E\ 65$0 UHIHUHQFH 3& 7KH IDLOXUH RI WKH FKDLQ LV JLYHQ IRU D IRUFH RI 1 E\ WKH PDQXIDF-WXUHU65$07KHUROOHUGLDPHWHULVPPLQDQGWKHFKDLQSLWFKLV PPLQ

7KH DLP RI WKH VLPXODWLRQ LV WR GHWHUPLQH WKH IDLOXUH VFHQDULR RI WKH QRQFLUFXODU FRPSRVLWHFKDLQULQJ7KH)(PRGHOFRQVLVWHGRIWKHFKDLQULQJDQGDSDUWRIWKHFKDLQ ZDVPRGHOOHGZLWK&'5VROLGHOHPHQWV7KHOLWHUDWXUHVKRZHGWKDWWKHORDGLQJLV

(5)

AUTHOR PROOF

3 Noncircular CFRP Bicycle’s Chainring. Part II

TABLE 1: 5DGLXV RI WKH QRQFLUFXODU FKDLQULQJ

$QJOHș>@ R>PP@ $QJOHș>@ R>PP@ $QJOHș>@ R>PP@

— — — — FIG. 1:&RPSRVLWHDQGPRGHORIQRQFLUFXODUFKDLQULQJ

(6)

AUTHOR PROOF

PDLQO\ FRQFHQWUDWHG RQ WKH ¿UVW VHYHQ WHHWK +XR HW DO 7KXV LQ WKLV SDSHU WKH¿UVWHOHYHQUROOHUVZHUHVLPXODWHGLQRUGHUWRUHGXFHWKHFRPSXWLQJWLPH)LJ 0RUHRYHUWKHPHVKDURXQGWKHVHHOHYHQUROOHUVZDVUH¿QHGWRREWDLQPRUHDFFXUDWH UHVXOWV )LJ 7R VLPXODWH WKH FKDLQULQJ EROW )LJ HQFDVWUp>Q2] boundary

con-FIG. 3:*HQHUDOYLHZDDQGGHWDLOVERIWKHFKDLQDQGFKDLQULQJRIVLPXODWLRQ

(7)

AUTHOR PROOF

GLWLRQ LV DSSOLHG )LJ 1RUPDO EHKDYLRU LV XVHG DV FRQWDFW SURSHUW\ LQ$%$486 EHWZHHQ WKH FKDLQ DQG WKH FKDLQULQJ7KH VFRSH RI WKLV ZRUN LV WKH TXDVLVWDWLF

(8)

AUTHOR PROOF

FKDQLFDOVWUHQJWKRI QRQFLUFXODUFKDLQULQJDQGVR WKHIULFWLRQEHWZHHQWKHWHHWKDQG WKH FKDLULQJ LV QRW FRQVLGHUHG 'XH WR WKH VKDSH RI WKH QRQFLUFXODU FKDLQULQJ WKUHH FKDLQSRVLWLRQVDUHLQYHVWLJDWHG)LJ7KHFKDLQLVDVVXPHGWREHVWUHWFKHGDQGWKH WDQJHQWLDOORDGLQJUHSUHVHQWLQJLWVWHQVLRQIRUFHLVDSSOLHG

2.2 Materials Properties

7KHFKDLQLVPDGHRIVWHHO7DEOHZKLOHFDUERQWZLOOZRYHQHSR[\LVXVHGIRU WKHFKDLQULQJ7DEOH7KHFKDLQULQJFRQVLVWVRISOLHVRIPPHDFKZLWKWKH IROORZLQJ VWDFNLQJ >@ JLYHQ D FKDLQULQJ WKLFNQHVV RI PPDIWHUPDQXIDFWXULQJ)LJ

$VGHODPLQDWLRQZDVQRWREVHUYHGLQSUHYLRXVH[SHULPHQWVRQO\¿EHUIDLOXUHDQG PDWUL[ FUDFNLQJ DUH PRGHOOHG WKDQNV WR WKH QRQOLQHDU PRGHOLQJ )DLOXUH FULWHULD DV-VRFLDWHGWRIDLOXUHPRGHVDUHXVHG&DPDQKR7KXV¿EHUIDLOXUHLVFDOFXODWHG WKDQNV WR WKH PD[LPXP VWUHVV FULWHULD IRU WKH ORQJLWXGLQDO DQG WUDQVYHUVH GLUHFWLRQ DQGLWLVJLYHQE\ l f t l V V

TABLE 2: 6WHHO SURSHUWLHV $]R 0DWHULDOV

Material E>*3D@ Ș ıy>03$@ ȡ>NJP3@

+666WHHO

TABLE 3: &DUERQ WZLOO ZRYHQHSR[\ SO\ SURSHUWLHV

&DUERQ(SR[\7(327(&<'/97+ 7HQVLOH<RXQJ¶VPRGXOXVLQILEHUGLUHFWLRQ *3D &RPSUHVVLYH<RXQJ¶VPRGXOXVLQILEHUGLUHFWLRQ ±*3D 7UDQVYHUVH<RXQJ¶VPRGXOXV *3D Shear modulus *3D 3RLVVRQ¶VUDWLR ȡ>NJP] Failure /RQJLWXGLQDOWHQVLOHVWUHQJWK 03D /RQJLWXGLQDOFRPSUHVVLYHVWUHQJWK ±03D 7UDQVYHUVHWHQVLOHVWUHQJWK 03D 7UDQVYHUVHFRPSUHVVLYHVWUHQJWK ±03D ,QSODQHVKHDUVWUHQJWK 03D 2XWRISODQHVKHDUVWUHQJWK 03D

(9)

AUTHOR PROOF

Noncircular CFRP Bicycle’s Chainring. Part II

t f t t V V 7KHPDWUL[FUDFNLQJFULWHULRQLVFRPSXWHGWKDQNVWR tz lt f lt W W W ZKHUHılıtĲltDQGĲtzDUHUHVSHFWLYHO\WKHORQJLWXGLQDODQGWUDQVYHUVHVWUHVVWKHVKHDU

VWUHVVLQWKHl tSODQHDQGWKHVKHDUVWUHVVLQWKHt zSODQHHYDOXDWHGLQWKHQHLJK-ERULQJYROXPHHOHPHQWV f t t V LVWKHWUDQVYHUVHIDLOXUHVWUHVVLQWHQVLRQDQG f lt W LVWKH IDLOXUHVKHDUVWUHVV7KHVHFULWHULDDUHDVVHVVHGDWHDFKWLPHLQFUHPHQWDQGZKHQWKH ORQJLWXGLQDO RU WUDQVYHUVH VWUHVV UHDFKHV WKH DVVRFLDWHG VWUHQJWK WKH IROORZLQJ VWL൵-QHVV PDWUL[ SDUDPHWHU EHFRPH ]HUR 4 4 DQG 4 IRU WKH ORQJLWXGLQDO GLUHFWLRQ DQG 4 4 DQG 4 IRU WKH WUDQVYHUVH GLUHFWLRQ )RU PDWUL[ FUDFNLQJ 4 DQG 4 EHFRPH]HUR)DLOXUHPRGHVFDQEHSUHGLFWHGE\WKHVHFULWHULDDQGWKHUHIRUHDSURJUHV- VLYHGDPDJHDQDO\VLVFDQEHDGHTXDWHO\XVHG7KXVWKH)(PRGHOHPSOR\VH[SOLFLWLQ-WHJUDWLRQVFKHPHLQ$%$486([SHULPHQWDOUHVXOWVRQWKHVDPHQRQFLUFXODUFKDLQULQJ VKRZHG D OLQHDU EHKDYLRU XQWLO D IRUFH RI 1 ZKHUH WKH FKDLQ VWDUWV GDPDJLQJ 7KDQDZDURWKRQ HW DO ,Q WKH SUHVHQW SDSHU DQ DQDO\VLV LV UHDOL]HG XQWLO WKH FKDLQGDPDJHDQGWKHUHIRUHWKHFKDLQEHKDYLRULVPRGHOHGXVLQJWKHLVRWURSLFHODVWLF ODZVEHKDYLRUV&RPSRVLWHFKDLQULQJSURSHUWLHVDUHSURJUDPPHGXVLQJ)2575$1DQG LQSXWWR$%$486LQWKHIRUPRIDµXVHUPDWHULDO¶980$7VXEURXWLQH

2.3 Model Validation

,Q RUGHU WR YDOLGDWH WKH VLPXODWLRQ WKH IRUFH±GLVSODFHPHQW FXUYH REWDLQHG IURP WKH VLPXODWLRQLVFRPSDUHGWRWKHH[SHULPHQWDOUHVXOWVREWDLQHGRQWKHVDPHQRQFLUFXODU FRPSRVLWH FKDLQULQJ IRU FDVH RQO\ 7KDQDZDURWKRQ HW DO 7KH VLPLODULW\ RI WKHFXUYHVVKRZVWKDWWKHPRGHOLVDEOHWREHUHSURGXFHGXQWLOWKHFKDLQGDPDJHWKH

(10)

AUTHOR PROOF

WLQFWSKDVHVFDQEHLGHQWL¿HGIURPWKHVLPXODWLRQFXUYHV,QWKHEHJLQQLQJDQHODVWLF UHVSRQVHLVH[KLELWHGXQWLODIRUFHRI1ZKHUHWKHIRUFHGURSV7KHQWKHIRUFH LQFUHDVHVOLQHDUO\XQWLOWKHFKDLQGDPDJH'URSRIIRUFHLVREVHUYHGIRUDIRUFHRI 1

3. RESULTS AND DISCUSSIONS

3.1 Noncircularity Effect

$VWKHFKDLQULQJLVQRWFLUFXODUH൵HFWRIWKHORDGLQJSRVLWLRQLVVWXGLHG)LJ+RZ-HYHUORDGLQJSRVLWLRQGRHVQRWVKRZWKHLQÀXHQFHRQWKHFKDLQULQJEHKDYLRU)LJ 7KHFXUYHVLQGLFDWHD¿UVWOLQHDUGRPDLQFRUUHVSRQGLQJWRWKHFRQWDFWEHWZHHQWKH ¿UVWUROOHUDQGWKH¿UVWWRRWK7KHQWKHIRUFHRVFLOODWHVGXHWRWKHVXFFHVVLYHFRQWDFW EHWZHHQ WKH ¿UVW ¿YH UROOHUV DQG WKH DVVRFLDWHG WHHWK 'URS RI IRUFH REVHUYHG H[SHULPHQWDOO\)LJLVGXHWRWKHFRQWDFWRIUROOHUVIURPWKHWKWRWKZLWKWKH FKDLQULQJ

'XH WR WKH SUHVVXUH RI WKH UROOHUV RQ WKH WHHWK WHHWK IDLOXUH FRQVLVWV RQO\ RI PD-WUL[FUDFNLQJJLYHQE\(T7KHUHIRUH¿UVWIDLOXUHDSSHDUVLQWKHWRRWKZKHUHWKH VKHDU VWUHVV LV WKH PD[LPXP )RU FDVH IDLOXUH LQLWLDWHV RQ WKH WK WRRWK DQG WKHQ SURSDJDWHVWRWKH¿UVWWRRWK7KH¿UVWIDLOXUHIRUFDVHDSSHDUVLQWKHQGWRRWKWKHQ WKH VW RQH IDLOV IROORZHG E\ WKH WK RQH )RU ERWK FDVHV IDLOXUH VHHPV WR VWDUW LQ

(11)

AUTHOR PROOF

WKHVDPHDUHD,QGHHGWKHWKDQGQGWRRWKRIFDVHVDQGUHVSHFWLYHO\DUHERWK ORFDWHGDWWKHEHJLQQLQJRIWKHFXUYHSDUWRIWKHQRQFLUFXODUFKDLQULQJ)LJ&DVH SUHVHQWVDGL൵HUHQWEHKDYLRUZKHUHWKHWKWRRWK¿UVWO\IDLOV7KHQWKHIDLOXUHSURJ-UHVVIURPWKHVWWRWKHWK&DVHVDQGVKRZD¿UVWIDLOXUHIRUDVLPLODUORDGZKLOH IRUFDVHWKHIDLOXUHDSSHDUVIRUDORZHUYDOXH7DEOH+RZHYHUORDGLQJSRVLWLRQ GRHVQRWKDYHLQÀXHQFHRQWKHQH[WWHHWKORDGIDLOXUH0DWUL[FUDFNLQJLVORFDWHGRQO\ RQWKHVXUIDFHRIWKHWHHWKZKHUHFRQWDFWVDUHPDGHZLWKUROOHUV)LJ)LQDOO\)($ VKRZVWKDWXQWLOWKHFKDLQVWDUWVGDPDJLQJLHIRUDORDGRI17KDQDZDURWKRQ HWDOWHHWKSUHVHQWRQO\ORFDOPDWUL[FUDFNV ),*)RUFH±GLVSODFHPHQWFXUYHVIRUGL൵HUHQWORDGLQJFDVHVREWDLQHGE\WKHVLPXODWLRQ

TABLE 4: )DLOXUH VFHQDULR DQG DVVRFLDWHG IRUFH

Failure Scenario Case 1 Case 2 Case 3 )LUVWWRRWKIDLOXUH ₁ ₁ ₁ 6HFRQGWRRWKIDLOXUH ₁ ₁ ₁ 7KLUGWRRWKIDLOXUH ₁ ₁ ₁

(12)

AUTHOR PROOF

'DPDJHSURSDJDWLRQLQWHHWKFDQEHVWXGLHG(YROXWLRQLVWKHVDPHIRUDOOWHHWKDQG WKHQGWRRWKRIFDVHLVSURSRVHGDVDQH[DPSOHLQ)LJ0DWUL[FUDFNLQJDOZD\V VWDUWVLQWKHQGDQGWKSOLHVDQGWKHQWKHGDPDJHSURSDJDWHVPDLQO\WR WKHDGMDFHQWLQWHULRUSOLHV FIG. 9:0DWUL[FUDFNLQJJLYHQE\(TIRUWKUHHORDGLQJSRVLWLRQVDQGIRUDIRUFHRI1

(13)

AUTHOR PROOF

3.2 Stacking Effect

(൵HFW RI WKH OD\XS LV LQYHVWLJDWHG WKURXJK D VHFRQG SOLHV VWDFNLQJ >@ 6LPLODU EHKDYLRU DV WKH SUHYLRXV VWDFNLQJ LV REVHUYHG )LJ DQG PRUHRYHU ORDGLQJ SRVLWLRQ GRHV QRW VKRZ LQÀXHQFH ,QGHHG DV WKH

),*(YROXWLRQRIWKHPDWUL[FUDFNLQJLQWKHQGWRRWKRIFDVH

(14)

AUTHOR PROOF

PDWUL[ FUDFNLQJ LV REVHUYHG RQO\ RQ WKH VXUIDFH RI WKH WHHWK LW LV WRR VPDOO WR KDYH DQH൵HFW+RZHYHUGDPDJHVHHPVWREHOLJKWO\UHGXFHGFRPSDUHGWRWKH¿UVWOD\XS )LJ)RUORDGLQJFDVHQRPDWUL[FUDFNVDUHREVHUYHGLQWKHWKWRRWK7DEOH

FIG. 12:0DWUL[FUDFNLQJJLYHQE\(TIRUWKUHHORDGLQJSRVLWLRQVIRU>] OD\XSDQGIRUDIRUFHRI1

(15)

AUTHOR PROOF

TABLE 5: )DLOXUH VFHQDULR DQG DVVRFLDWHG IRUFH IRU >@ OD\XS Failure Scenario Case 1 Case 2 Case 3 )LUVWWRRWKIDLOXUH ₁ ₁ ₁ 6HFRQGWRRWKIDLOXUH ₁ ₁ ₁ 7KLUGWRRWKIDLOXUH ₁ ₁ ₁ )RXUWKWRRWKIDLOXUH ₁ — — (YROXWLRQRIWKHPDWUL[FUDFNLQJLVVLPLODUWRWKRVHREVHUYHIRUWKHSUHYLRXVSOLHV OD\XS)LJ 3.3 Thickness Effect (OHYHQSOLHVFRPSRVLWHFKDLQULQJVKRZHGRQO\PDWUL[FUDFNLQJORFDWHGRQWKHWHHWKVXU-IDFH7KHUHIRUHWKHQXPEHURISOLHVFDQEHUHGXFHGLQRUGHUWRPLQLPL]HWKHFKDLQULQJ FRVW 'XH WR WKH FKDLQ VL]H UHGXFWLRQ RI SOLHV QXPEHU LV OLPLWHG 7KXV H൵HFW RI WKH QXPEHURISOLHVLVVWXGLHGWKURXJKDSOLHVVWDFNLQJ>@0RUHRYHUDV WKHORDGLQJFDVHGRHVQRWVKRZLQÀXHQFHRQO\ORDGLQJFDVHLVLQYHVWLJDWHG)LJ $VLPLODUEHKDYLRUDVWKHSUHYLRXVVWDFNLQJLVREVHUYHG+RZHYHUPDWUL[FUDFNLQJLV

FIG. 13:)RUFH±GLVSODFHPHQWFXUYHVIRUORDGLQJFDVHZLWKDQGSOLHVVWDFNLQJREWDLQHG E\VLPXODWLRQ

(16)

AUTHOR PROOF

REVHUYHGIRUDORZHUIRUFHDQGGXHWRWKHORZHUQXPEHURISOLHVWKHWHHWKGDPDJHLV ELJJHU )LJ ,QGHHG IRU WKH SOLHV VWDFNLQJ WKH IRXUWK ¿UVWV WHHWK DUH GDPDJHG ZKLOHIRUWKHSOLHVVWDFNLQJRQO\WKHWKUHH¿UVWVVKRZPDWUL[FUDFNLQJ

'DPDJH SURSDJDWLRQ LQ WHHWK FDQ EH VWXGLHG IRU WKH SOLHV OD\XS$V IRU WKH SOLHV HYROXWLRQ LV WKH VDPH IRU DOO WHHWK DQG WKH WK WRRWK RI FDVH LV SURSRVHG DV H[DPSOH)LJ0DWUL[FUDFNLQJVWDUWVDOZD\VLQWKHUGDQGWKSOLHVDQG WKHQWKHGDPDJHSURSDJDWHVV\PPHWULFDOO\WRWKHVHSOLHV

FIG. 14:0DWUL[FUDFNLQJJLYHQE\(TIRUORDGLQJFDVHZLWKDVWDFNLQJRIDQGSOLHV

(17)

AUTHOR PROOF

4. CONCLUSIONS

,QRUGHUWRGHVLJQDQGRSWLPL]HQRQFLUFXODUFRPSRVLWHFKDLQULQJDQXPHULFDOVLPXOD-WLRQKDVEHHQSURSRVHGWRGHWHUPLQHWKHIDLOXUHVFHQDULRRIWHHWK7KHFKDLQULQJDQG UROOHUV RI WKH FKDLQ KDYH EHHQ PRGHOHG XVLQJ DQ H[SOLFLW VLPXODWLRQ7KUHH ORDG-LQJSRVLWLRQVZHUHSHUIRUPHGLQRUGHUWRVWXG\WKHH൵HFWRIWKHQRQFLUFXODUFKDLQULQJ VKDSH &)53 PDGH RI SOLHV RI FDUERQ ZRYHQHSR[\ ZDV LQYHVWLJDWHG DQG PD[L-PXPVWUHVVKDVEHHQXVHGDVIDLOXUHFULWHULDIRUWKHFRPSRVLWHPDWHULDO$FFRUGLQJWR WKHQXPHULFDOVLPXODWLRQWKHPHFKDQLFDOEHKDYLRURIWKHQRQFLUFXODUFKDLQULQJFDQEH FRQFOXGHGDVIROORZV

y7KHQRQFLUFXODULW\KDVQRLQÀXHQFHRQWKHPHFKDQLFDOEHKDYLRU

y7KHGDPDJHVFHQDULRKDVEHHQGHWHUPLQHGDQGLWGHSHQGVRIWKHORDGLQJSRVLWLRQ +RZHYHU XQWLO WKH FKDLQ GDPDJH LH 1 WHHWK GDPDJH FRQVLVWV RQO\ RI PDWUL[FUDFNLQJORFDWHGRQWKHWHHWKVXUIDFH

y$VWKHGDPDJHLVRQO\ORFDWHGRQWHHWKVXUIDFHWKHFKDLQULQJEHKDYLRULVQRWLQ-ÀXHQFHGE\WKHOD\XSXQWLOWKHFKDLQGDPDJH

y7KHWKLFNQHVVFDQEHUHGXFHGWRSOLHV(YHQLIWKHPDWULFFUDFNLQJLVODUJHUWKDQ RQSOLHVFKDLQULQJWKHGDPDJHLVDOZD\VORFDWHGRQWKHWHHWKVXUIDFH

8QGHU TXDVLVWDWLF FRQGLWLRQ QRQFLUFXODU FRPSRVLWH FKDLQULQJ PDGH RI SOLHV GRHVQRWIDLO,QGHHGRQO\ORFDOPDWUL[FUDFNLQJDUHREVHUYHGRQWKHFRQWDFWVXUIDFH ZLWKWKHUROOHU7KHUHIRUHWKLFNQHVVFDQEHOLJKWO\UHGXFHGWRSOLHVLQRUGHUWRPLQL-PL]HWKHFKDLQULQJFRVW+RZHYHUH[SHULPHQWVVKRZHGWKDW-ORZYHORFLW\LPSDFW ORFDWHG RQ D WRRWK FUHDWHV GHODPLQDWLRQ WKDW FRXOG UHGXFH WKH ¿QDO VWUHQJWK RI WKH QRQFLUFXODU FRPSRVLWH FKDLQULQJ 7KH ORZYHORFLW\ LPSDFW KDV WR EH LQYHVWLJDWHG RQ SOLHVVWDFNLQJWRGHWHUPLQHWKHGDPDJH7KHSURSRVHGQXPHULFDOPRGHOLVFXUUHQWO\ XQGHUGHYHORSPHQWWRVLPXODWHDORZYHORFLW\LPSDFWHVSHFLDOO\WRREWDLQGHODPLQD-WLRQVLQRUGHUWRGHWHUPLQHWKHLULQÀXHQFHRQWKHUHVLGXDOFKDLQULQJVWUHQJWK REFERENCES $]R0DWHULDOV)URPKWWSZZZD]RPFRP %LQL55DQG'DJRHVH)1RQFLUFXODU&KDLQULQJVDQG3HGDOWR&UDQN,QWHUIDFHLQ&\FOLQJ$/LWHUDWXUH 5HYLHZBraz. J. Kinantropom. Hum. Perform.YRO14SS±

%RXYHW&DQG5LYDOODQW6'DPDJH7ROHUDQFHRI&RPSRVLWH6WUXFWXUHVXQGHU/RZ9HORFLW\,PSDFWLQ 9 6LOEHUVFKPLGW (G Dynamic Deformation, Damage and Fracture in Composite Matererials and

Structures,:RRGKHDG3XEOLVKLQJSS±

%URG\+7KH3K\VLFVRI7HQQLV,,,7KH%DOO±5DFNHW,QWHUDFWLRQAm. J. Phys.YRO65SS±

&DPDQKR 33 Failure Criteria for Fiber-Reinforced Polymer Composites IURP KWWSVZHEIHXS SWaVWSLQKRWHDFKLQJIHXS\IFULWHULDSGI

&OLIWRQ36XELF$DQG0RXULW]$6QRZERDUG6WL൵QHVV3UHGLFWLRQ0RGHOIRUDQ\&RPSRVLWH6DQG-ZLFK&RQVWUXFWLRQProced. Eng.YRO2SS±

+XR-<X6<DQJ-DQG/L76WDWLFDQG'\QDPLF&KDUDFWHULVWLFVRIWKH&KDLQ'ULYH6\VWHPRID +HDY\'XW\$SURQ)HHGHUOpen Mech. Eng. J.YROSS±

(18)

AUTHOR PROOF

-LQ&KHH/LX7DQG:X+&)LEHU'LUHFWLRQDQG6WDFNLQJ6HTXHQFH'HVLJQIRU%LF\FOH)UDPHPDGH RI&DUERQ(SR[\&RPSRVLWH/DPLQDWHMater. Des.YRO31SS±

/L 1 DQG &KHQ 3+ ([SHULPHQWDO ,QYHVWLJDWLRQ RQ (GJH ,PSDFW 'DPDJH DQG &RPSUHVVLRQ$IWHU ,PSDFW &$, %HKDYLRU RI 6WL൵HQHG &RPSRVLWH 3DQHOV Compos. Struct. YRO SS ±

2VWUp % %RXYHW & 0LQRW & DQG$ERLVVLqUH - )LQLWH (OHPHQW$QDO\VLV RI &)53 /DPLQDWHV 6XE-MHFWHGWR&RPSUHVVLRQDIWHU(GJH,PSDFWCompos. Struct.YRO153SS±

3HWHUCarbon Fiber Bikes vs. Aluminum Bikes. Which Should You Buy?)URPKWWSZZZRYHUF\FOLVW FRPFDUERQ¿EHUELNHVYVDOXPLQXPELNHV

5R]\OR3'HEVNL+DQG.XELDN7$0RGHORI/RZ9HORFLW\,PSDFW'DPDJHRI&RPSRVLWH3ODWHV VXEMHFWHG WR &RPSUHVVLRQ$IWHU,PSDFW &$, 7HVWLQJ Compos. Struct. YRO SS ±

6ODWHU & 2WWR 65 DQG 6WUDQJZRRG 0 7KH 4XDVL6WDWLF DQG '\QDPLF 7HVWLQJ RI 'DPSLQJ LQ *ROI&OXEV6KDIWV)DEULFDWHGIURP&DUERQ)LEHU&RPSRVLWHVProced. Eng.YRO2SS± 65$03&&KDLQKWWSVZZZVUDPFRP 7KDQDZDURWKRQ=3DLUDW3%RXYHW&DQG0H]HL[/1RQFLUFXODU&)53%LF\FOH¶V&KDLQULQJ3DUW, 6WDWLFDQG/RZ9HORFLW\,PSDFW$QDO\VLVVXEPLWWHGLQCMCA :DQJ<-L'DQG=KDQ.0RGL¿HG6SURFNHW7RRWK3UR¿OHRI5ROOHU&KDLQ'ULYHVMech. Theor. YROSS±