A finite element simulation for orthogonal cutting of

A finite element simulation for orthogonal cutting of UD-CFRP incorporating a novel fibre - matrix interface model Abena, Alessandro; Soo, Sein; Essa, Khamis DOI: 10.1016/j.procir.2015.04.091

Citation for published version (Harvard): Abena, A, Soo, SL & Essa, K 2015, 'A finite element simulation for orthogonal cutting of UD-CFRP incorporating a novel fibre - matrix interface model' Procedia CIRP, vol 31, pp. 539-544., 10.1016/j.procir.2015.04.091

Link to publication on Research at Birmingham portal

Publisher Rights Statement: Checked for eligibility: 31/07/2015. © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

General rights When referring to this publication, please cite the published version. Copyright and associated moral rights for publications accessible in the public portal are retained by the authors and/or other copyright owners. It is a condition of accessing this publication that users abide by the legal requirements associated with these rights. • You may freely distribute the URL that is used to identify this publication. • Users may download and print one copy of the publication from the public portal for the purpose of private study or non-commercial research. • If a Creative Commons licence is associated with this publication, please consult the terms and conditions cited therein. • Unless otherwise stated, you may not further distribute the material nor use it for the purposes of commercial gain.

Take down policy If you believe that this document infringes copyright please contact [email protected] providing details and we will remove access to the work immediately and investigate.

Download date: 20. Oct. 2015

Available online at www.sciencedirect.com

ScienceDirect Procedia CIRP 31 (2015) 539 – 544

WK&,53&RQIHUHQFHRQ0RGHOOLQJRI0DFKLQLQJ2SHUDWLRQV

$ILQLWHHOHPHQWVLPXODWLRQIRURUWKRJRQDOFXWWLQJRI8'&)53 LQFRUSRUDWLQJDQRYHOILEUHPDWUL[LQWHUIDFHPRGHO $OHVVDQGUR$EHQDD6HLQ/HXQJ6RRD .KDPLV(VVDD





D

6FKRRORI0HFKDQLFDO(QJLQHHULQJ8QLYHUVLW\RI%LUPLQJKDP(GJHEDVWRQ%LUPLQJKDP%778QLWHG.LQJGRP

&RUUHVSRQGLQJDXWKRU7HOID[(PDLODGGUHVVVOVRR#EKDPDFXN

Abstract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—P LQWHUIDFHHOHPHQWVLQRUGHUWRDFFRPPRGDWH FRPSUHVVLYHIDLOXUHZKLFKLVLPSOHPHQWHGYLDDEHVSRNHXVHUVXEURXWLQH)LEUHIUDFWXUHLVEDVHGRQDPD[LPXPSULQFLSDOVWUHVVFULWHULRQZKLOH HODVWLFSODVWLFEHKDYLRXUWRIDLOXUHLVXVHGWRUHSUHVHQWPDWUL[GDPDJH7KHLQIOXHQFHRIYDU\LQJILEUHRULHQWDWLRQVƒƒƒ RQSUHGLFWHG FXWWLQJDQGWKUXVWIRUFHVZHUHYDOLGDWHGDJDLQVWSXEOLVKHGH[SHULPHQWDOGDWD:KLOHWKHIRUPHUZDVJHQHUDOO\ZLWKLQRIH[SHULPHQWDOGDWD IRUZRUNSLHFHVZLWKƒDQGƒILEUHGLUHFWLRQVSUHGLFWHGWKUXVWIRUFHVZHUHW\SLFDOO\XQGHUHVWLPDWHGE\a7KHFRUUHVSRQGLQJFKLS IRUPDWLRQ PHFKDQLVPVDQGVXEVXUIDFHGDPDJHGXHWRWKHGLIIHUHQWPDWHULDOSKDVHVZHUHDOVRLQYHVWLJDWHG 7KHSURSRVHGPRGHO ZDVDEOHWR SUHGLFWFRPSRVLWHEHKDYLRXUDQGGHIHFWIRUPDWLRQWKDWZDVFRPSDUDEOHWRH[SHULPHQWDOKLJKVSHHGFDPHUDLPDJHVRXWOLQHGLQWKHOLWHUDWXUH



© 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ‹7KH$XWKRUV3XEOLVKHGE\(OVHYLHU%9 (http://creativecommons.org/licenses/by-nc-nd/4.0/). 3HHUUHYLHZXQGHUUHVSRQVLELOLW\RI7KH,QWHUQDWLRQDO6FLHQWLILF&RPPLWWHHRIWKH³WK&RQIHUHQFHRQ0RGHOOLQJRI0DFKLQLQJ2SHUDWLRQV´ Peer-review under responsibility of the International Scientific Committee of the “15th Conference on Modelling of Machining Operations .H\ZRUGV0DFKLQLQJ2UWKRJRQDOFXWWLQJ&DUERQILEUHUHLQIRUFHGSRO\PHU&)53 ,QWHUIDFHPRGHOOLQJ&RKHVLYHEHKDYLRXU

1. Introduction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

2212-8271 © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the International Scientific Committee of the “15th Conference on Modelling of Machining Operations doi:10.1016/j.procir.2015.04.091

540

Alessandro Abena et al. / Procedia CIRP 31 (2015) 539 – 544

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—P  LQWHUIDFH HOHPHQWV LQ RUGHU WR DFFRPPRGDWH FRPSUHVVLYH IDLOXUH ZKLFK ZDV LPSOHPHQWHG YLDDEHVSRNHXVHUVXEURXWLQH 2. Finite element model development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

 )LJ,QLWLDOXQGHIRUPHG)(PRGHOZLWKERXQGDU\FRQGLWLRQV

Alessandro Abena et al. / Procedia CIRP 31 (2015) 539 – 544

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ƒ ƒ DQG ƒ UHVSHFWLYHO\$WLHFRQVWUDLQWZDVGHILQHGWRLQLWLDOO\ERQGDOO RIWKHLQGLYLGXDOSKDVHV7KHZRUNSLHFHPHVKFRPSULVHGIRXU QRGHSODQHVWUHVVHOHPHQWVZLWKUHGXFHGLQWHJUDWLRQ&365  IRU WKH PDWUL[ ILEUH DQG (+0 SKDVHV ZKLOH &2+' FRKHVLYH HOHPHQWV ZHUH HPSOR\HG IRU WKH PDWUL[ILEUH LQWHUIDFH VHFWLRQV ,Q DGGLWLRQ WULDQJXODU HOHPHQWV ZHUH XWLOLVHG LQ WKH (+0 UHJLRQ IRU PHVK WUDQVLWLRQ 7KH HOHPHQW VL]H LQ WKH PLFURPHFKDQLFDO ]RQH ZDV  —P ZKLOH IRU WKH (+0 DUHDHOHPHQWGLPHQVLRQVLQFUHDVHG ZLWKGLVWDQFHIURP WKH FXWWLQJ]RQH7KH FXWWLQJSDUDPHWHUVDQGFRPSRVLWHILEUH RULHQWDWLRQVXVHGLQWKHVLPXODWLRQVDUHGHWDLOHGLQ7DEOH

541

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

7DEOH0DFKLQLQJSDUDPHWHUVDQGPDWHULDOILEUHRULHQWDWLRQV 7RROJHRPHWU\

—PFXWWLQJHGJHUDGLXVƒ FOHDUDQFHDQJOHƒUDNHDQJOH

&XWWLQJVSHHG

PPPLQ

'HSWKRIFXW

—P

)LEUHRULHQWDWLRQV

ƒƒƒ

 )LJ0HFKDQLFDOFRQVWLWXWLYHUHVSRQVHRIFRKHVLYHHOHPHQWVXQGHUWHQVLOH DQGFRPSUHVVLYHORDGVLPSOHPHQWHGYLD980$7VXEURXWLQH

542

Alessandro Abena et al. / Procedia CIRP 31 (2015) 539 – 544

,Q FRQWUDVW VKHDU VWUHVV YDULDWLRQ ZLWK UHVSHFW WR GLVSODFHPHQW LQ WKH FRKHVLYH HOHPHQWV DFWLQJ LQ WKH SDUDOOHO GLUHFWLRQ  ZDV HTXLYDOHQW IRU ERWK SRVLWLYH DQG QHJDWLYH YDOXHVDVVKRZQLQ)LJ7KHVWUHVVUHVSRQVHRIWKHFRKHVLYH HOHPHQWVLQWHUIDFH UHJLRQ GHWDLOHG LQ )LJV  DQG  DUH IXQFWLRQVRIWKUHHSULQFLSDOSDUDPHWHUVZKLFKDUH x 3HQDOW\VWLIIQHVV  3Q  V x 6WUHVVRUGLVSODFHPHQWDWWKHGDPDJHLQLWLDWLRQ  WQR V G QR V & x )UDFWXUHHQHUJ\  *Q  V  5HJDUGOHVV RI WKH ORDGLQJ FRQGLWLRQ WKH PHFKDQLFDO VWUHVV FRQVWLWXWLYHUHVSRQVHFDQEHGLYLGHGLQWRWKUHHGLVWLQFWUHJLRQV WDNLQJLQWRDFFRXQWWKHHODVWLFEHKDYLRXUDQGPDWHULDOVWUHQJWK GHJUDGDWLRQWRIDLOXUHDVGHVFULEHGLQ(T   R 3G Q  V  G QPD[ ­  V d G Q V  ° I WQ  V ®  G Q  V 3G Q  V G QR V  G QPD[     V  G Q V  PD[ I °  G Q V t G Q V  ¯  

 

HV



GV

 

7R

 7KHPHFKDQLFDOFRQVWLWXWLYHUHVSRQVHLVLQLWLDOO\FRPSRVHG RIOLQHDUHODVWLF EHKDYLRXU SRLQWLQERWK)LJDQG)LJ   XS WR WKH PRPHQW RI GDPDJH LQLWLDWLRQ SRLQW   ZKLFK LV GHVFULEHGLQ(T   ­WQ ½ ª 3Q  º ­H Q ½  W ® ¾ « » ® ¾ 3H  Q W  F    ¯WV ¿ ¬  3V ¼ ¯H V ¿  H UHSUHVHQWWKHVWUHVVYHFWRUVWLIIQHVVPDWUL[ ZKHUH W DQG 3 DQG VWUDLQ YHFWRU UHVSHFWLYHO\ $W WKH RQVHW RI ZRUNSLHFH GDPDJHGHJUDGDWLRQRIWKHDGKHVLYHSKDVHLVUHSUHVHQWHGE\D UHGXFWLRQ RI LWV VWLIIQHVV SURSHUW\ SRLQW   DFFRUGLQJ WR UHODWLRQVKLSLQ(T     3QG V 3Q  V   GQ  V  Q W  F   $VFDODUGDPDJHYDULDEOHLVLQWURGXFHGIRUHDFKPRGH GQ V RI IDLOXUH E\ FRQVLGHULQJ D OLQHDU GDPDJH HYROXWLRQ EDVHG RQ WKHIRUPXODE\&DPDQKRDQG'DYLOD>@ZKLFKLVH[SUHVVHG E\(T   I PD[ R  G Q  V G Q  V  G Q  V G Q  V   G Q  V 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

> @

3. Results and discussion

 )LJ0HFKDQLFDOFRQVWLWXWLYHUHVSRQVHRIFRKHVLYHHOHPHQWVXQGHUVKHDU ORDGVLPSOHPHQWHGYLD980$7VXEURXWLQH

7KH IUDFWXUH HQHUJ\ UHSUHVHQWV WKH DUHD EHORZ WKH VWUHVV GLVSODFHPHQW FXUYH EHWZHHQ WKH RULJLQ DQG IDLOXUH SRLQW įI  &RUUHVSRQGLQJ VWUDLQV H WHQVLOH FRPSUHVVLYH DQG VKHDU  DUH UHODWHG WR GLVSODFHPHQW E\ PHDQV RI (T  DQG (T  ZKHUH WKH FRQVWLWXWLYH WKLFNQHVV 7R LV DVVXPHG WR EH XQLW\ ZKLOH W DQG F LQGLFDWHV WHQVLOH DQG FRPSUHVVLYH EHKDYLRXU UHVSHFWLYHO\   GQ    HQ   Q W  F 7R    

)LJVKRZV WKHSUHGLFWHGFXWWLQJIRUFHV IURPWKHFXUUHQW )( VLPXODWLRQ LQFRUSRUDWLQJ WKH QRYHO FRKHVLYH ]RQH UHODWLRQVKLS FRPSDUHG DJDLQVW FRUUHVSRQGLQJ H[SHULPHQWDO DQG QXPHULFDO )( UHVXOWV UHSRUWHG E\ &DO]DGD HW DO >@ 7KH H[SHULPHQWDOGDWD UHYHDOHGD UHGXFWLRQLQFXWWLQJIRUFHV ZLWK LQFUHDVLQJ ILEUH RULHQWDWLRQ IURP ƒ WR ƒ 7KH SUHGLFWHG FXWWLQJ IRUFHV REWDLQHG IURP ERWK WKH SUHVHQW VLPXODWLRQ DQG QXPHULFDO )( UHVXOWV LQ WKH OLWHUDWXUH >@ VKRZHG HTXLYDOHQW WUHQGV DQG H[KLELWHG FORVH DJUHHPHQW WR WKH H[SHULPHQWDO YDOXHV IRU ILEUH DQJOHV RI ƒ DQG ƒ EXW ZHUH XQGHUHVWLPDWHGIRUWKRVHRULHQWHGDWƒ,QFRQWUDVWWKHWUHQG LQ SUHGLFWHG WKUXVW IRUFH XVLQJ WKH QHZ FRKHVLYH ]RQH PRGHO VKRZHG D PLQLPXP IRU WKH ƒ RULHQWHG &)53 ZRUNSLHFH ZKLFKFRQWUDGLFWHGERWKWKHH[SHULPHQWDODQGQXPHULFDOGDWD RXWOLQHG E\ &DO]DGD HW DO >@ ZKHUH IRUFHV GHFUHDVHG ZLWK ODUJHU ILEUH RULHQWDWLRQV VHH )LJ  +RZHYHU WKUXVW IRUFHV ZHUHXQGHUSUHGLFWHGE\XSWRaLQERWK)(PRGHOVZKHQ FXWWLQJZRUNSLHFHVZLWKƒDQGƒILEUHGLUHFWLRQV7KLVZDV

543

Alessandro Abena et al. / Procedia CIRP 31 (2015) 539 – 544

PRVWOLNHO\DWWULEXWHGWRWKHIDLOXUHDQGVXEVHTXHQWGHOHWLRQRI HOHPHQWV GXULQJ WKH DQDO\VLV DORQJ WKH FXWWLQJ SDWK WKHUHE\ FDXVLQJDUHOD[DWLRQLQWKHIRUFHFRPSRQHQWGXHWRWKHORVVRI FRQWDFWEHWZHHQWKHWRRODQGZRUNSLHFH 

GHSWK RI FXW UHJLRQ ZKLFK LQLWLDWHG DW WKH SRLQW RI FRQWDFW EHWZHHQ WKH WRRO DQG ZRUNSLHFH $V PDFKLQLQJ SURJUHVVHG WKH IUDFWXUHFRQWLQXHGWRSURSDJDWH WKURXJK VXFFHVVLYH ILEUHV DKHDG RI WKH WRRO DORQJ WKH FXWWLQJ SODQH 7KH VHFRQG FUDFN FRPPHQFHG EHORZ WKH FXWWLQJ SDWK GXH WR EHQGLQJ VWUHVVHV IURPWKHFXWWLQJRSHUDWLRQ+HUHGDPDJHSURSDJDWHGWRZDUGV WKHFXWWLQJSODQHDORQJWKH ILEUHV $VWKH PDWUL[UHSUHVHQWVD ZHDNHU SKDVH RI WKH PDWHULDO IDLOXUH ZDV SULPDULO\ GXH WR FRPSUHVVLYHVWUHVVHVIURPWKHVXUURXQGLQJILEUHV :LWK UHJDUG WR WKH ƒ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

 )LJ&RPSDULVRQEHWZHHQH[SHULPHQWDODQGSUHGLFWHGFXWWLQJIRUFHVDW GLIIHUHQWILEUHRULHQWDWLRQVƒƒƒ 

 )LJ)DLOXUHPRGHIRUD ƒE ƒDQGF ƒILEUHRULHQWDWLRQV

 )LJ&RPSDULVRQEHWZHHQH[SHULPHQWDODQGSUHGLFWHGWKUXVWIRUFHVDW GLIIHUHQWILEUHRULHQWDWLRQVƒƒƒ 

)LJ VKRZV WKHSUHGLFWHGIDLOXUH PRGHVREVHUYHGIRU WKH GLIIHUHQW &)53 ILEUH RULHQWDWLRQV IROORZLQJ RUWKRJRQDO PDFKLQLQJ )RU WKH ƒ ILEUH RULHQWDWLRQ VKRZQ LQ )LJ D  WKH IDLOXUH PRGH FRPSULVHG RQO\ D VLQJOH IUDFWXUH VLWXDWHG DKHDGRIWKHWRROZLWKGDPDJHSULQFLSDOO\FDXVHGE\VKHDULQJ UDWKHU WKDQ EHQGLQJ VWUHVVHV 6XEVXUIDFH GDPDJH LQ WHUPV RI GHERQGLQJ DQG PDWUL[ IDLOXUH ZDV DOVR HYLGHQW &RQYHUVHO\ ILEUHV LQ WKH ƒ GLUHFWLRQ ZHUH VXEMHFW WR PXOWLIUDFWXUH GDPDJH ZKLFKRFFXUUHGSULPDULO\LQWZRGLIIHUHQW ORFDWLRQV VHH)LJE 7KHILUVWIUDFWXUHRFFXUUHGDWDSSUR[LPDWHO\WKH

)LJ  VKRZV WKH VLPXODWHG GHERQGLQJ GDPDJH XVLQJ WKH QHZLQWHUIDFHPRGHOZKHQPDFKLQLQJWKHƒRULHQWHGILEUHV &RKHVLYH HOHPHQW GHOHWLRQ ZDV SULPDULO\ WULJJHUHG E\ FRPSUHVVLYH ORDGLQJ DW WKH LQWHUIDFH GXULQJ FXWWLQJ 7KH WRRO SXVKHGWKHILEUHWRZDUGVWKHPDWUL[OHDGLQJWRDFRPSUHVVLYH IRUFHZKLFKDFWVRQWKHLQWHUIDFLDOHOHPHQWVDVVKRZQLQ)LJ  7KH UHVXOW GHPRQVWUDWHV WKDW DQ LQWHUIDFLDO PRGHO FRQVLGHULQJRQO\WHQVLOHDQGVKHDUEHKDYLRXULVQRWVXIILFLHQW WRDFFXUDWHO\VLPXODWHZRUNSLHFHVXEVXUIDFHGDPDJH 

 )LJ'HERQGLQJVLPXODWLRQIRUƒILEUHRULHQWDWLRQ

544

Alessandro Abena et al. / Procedia CIRP 31 (2015) 539 – 544

4. Conclusions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eferences >@

'DQGHNDU &5 6KLQ @ 6DQWLXVWH&6ROGDQL;0LJXpOH]0+0DFKLQLQJ)(0PRGHORIORQJ ILEHU FRPSRVLWHV IRU DHURQDXWLFDO FRPSRQHQWV &RPSRV 6WUXFW   >@ &DQWHUR-/6DQWLXVWH&0DUtQ16ROGDQL;0LJXpOH]+'DQG' DSSURDFKHV WR VLPXODWLRQ RI PHWDO DQG FRPSRVLWH FXWWLQJ ,Q $,3 &RQIHUHQFH3UHRFHHGLQJV$,33XEOLVKLQJS >@ 5DR *9* 0DKDMDQ 3 %KDWQDJDU 1 0LFURPHFKDQLFDO PRGHOLQJ RI PDFKLQLQJ RI )53 FRPSRVLWHV ±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

>@ =KRX