Procedia Engineering 109 ( 2015 ) 473 – 483
1877-7058 © 2015 The Authors. Published by Elsevier Ltd. 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 Gruppo Italiano Frattura (IGF) doi: 10.1016/j.proeng.2015.06.251
ScienceDirect
;;,,,,WDOLDQ*URXSRI)UDFWXUH0HHWLQJ,*);;,,,
&UDFNJURZWKEHKDYLRURIZHOGHGVWLIIHQHGSDQHO
5DIIDHOH6HSH
D(QULFR$UPHQWDQL
D3DVTXDOHGL/DVFLR
E5REHUWR&LWDUHOOD
EaDepartment. of Chemical, Materials and Production Engineering - University of Naples Federico II - P.le V. Tecchio, 80 - 80125 Naples, Italy bDepartment of Industrial Engineering, University of Salerno Fisciano (SA), Italy
$EVWUDFW )DWLJXHFUDFNJURZWKH[SHULPHQWDOWHVWVDQGQXPHULFDODQDO\VHVRQ)ULFWLRQ6WLU:HOGLQJ)6:ZHOGHGIODWVWLIIHQHGSDQHOVZHUH SHUIRUPHGLQRUGHUWRDVVHVVWKHLUIUDFWXUHUHVLVWDQFHFDSDELOLW\3DQHOVDQGVWLIIHQHUVDUHPDGHRIDOXPLQXPDOOR\7/LQHDU HODVWLF)(0)LQLWH(OHPHQW0HWKRGDQG'%(0'XDO%RXQGDU\(OHPHQW0HWKRGVWUHVVDQDO\VHVZHUHSHUIRUPHGWRVLPXODWH FUDFNJURZWKREWDLQLQJDVDWLVIDFWRU\FRUUHODWLRQDJDLQVWH[SHULPHQWDORXWFRPHV 7KH$XWKRUV3XEOLVKHGE\(OVHYLHU/WG 3HHUUHYLHZXQGHUUHVSRQVLELOLW\RIWKH*UXSSR,WDOLDQR)UDWWXUD,*) Keywords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mail address:UDIIVHSH#XQLQDLW
© 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
FHUWLILFDWLRQSURFHVVLVWKHIXOOVFDOHIDWLJXHWHVWZKHUHDFRPSOHWHDLUIUDPHVWUXFWXUHLVVXEMHFWHGWRUHDOLVWLFVSHFWUXP ORDGVUHSUHVHQWDWLYHRIWKRVHSUHGLFWHGWRRFFXURYHUWKHOLIHRIW\SH*HQHUDOO\WKHVHIDWLJXHWHVWVDUHF\FOHGXQWLOWKH HTXLYDOHQWRIVHYHUDOOLIHWLPHVLVDFKLHYHGRUDIDLOXUHRFFXUV
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³=´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
6FRSHRIWKHSHUIRUPHGWHVWVZDVWRHYDOXDWHIUDFWXUHDUUHVWFDSDELOLW\RIWKH)6:HOGHGVWLIIHQHUVDSSOLHGRQWKH IODWSDQHOZKHQDQDUWLILFLDOFUDFNLVLQWURGXFHGDQGSURSDJDWHGGXHWRIDWLJXHORDGV 7DEOH0HFKDQLFDOSURSHUWLHVRI7 3URSHUW\ 9DOXH <RXQJ¶VPRGXOXV >03D@ 7HQVLOH6WUHQJWK >03D@ <LHOG6WUHQJWK >03D@ &UDFNJURZWKWKUHVKROG >03DāPP@ 3RLVVRQUDWLR
7KH WHVWLQJ PDFKLQH )LJ D LV FRPSRVHG E\ D K\GUDXOLF DFWXDWRU PD[ ORDG Pmax N1 FRQQHFWHG WR DQ
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
$VWUDLQURVHWWH)LJFW\SH&($85RI009LVKD\ZDVERQGHGRQHDFKSDQHOVLGHLQRUGHUWR YHULI\WKHDEVHQFHRIVHFRQGDU\EHQGLQJDQGDVVHVVWKHFRQVLVWHQF\RIPHDVXUHGORFDOVWUHVVDJDLQVWWKRVHIRUHFDVWHG LQWKHGHVLJQSKDVH7KHIDWLJXHWHVWVZHUHFDUULHGRXWXQGHUFRQVWDQWDPSOLWXGHORDGFRQWUROR Pmax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model 7KHSDQHOZDVPRGHOHGXVLQJWZRGLPHQVLRQDOHLJKWQRGHVKHOOHOHPHQWV6+(//ZLWKHDFKQRGHKDYLQJVL[ GHJUHHV RI IUHHGRP DQG WZRGLPHQVLRQDO HLJKWQRGHV SODQH HOHPHQWV 3/$1( ZLWK HDFK QRGH KDYLQJ WZR GHJUHHVRIIUHHGRP7KHILQLWHHOHPHQWPHVK)LJDFRQVLVWVRIHOHPHQWVDQGQRGHVGLIIHUHQWFRORUVDUH DVVRFLDWHGWRGLIIHUHQWW\SHRIHOHPHQWV6KHOODQGSODQHHOHPHQWVZHUHXVHGWRPRGHOVWULQJHUVDQGVNLQUHVSHFWLYHO\
)LJD')(PRGHORIWKHSDQHOEERXQGDU\FRQGLWLRQVDSSOLHGWRWKHSDQHO
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p 03DP N1ZDVDSSOLHGLQ<GLUHFWLRQPRUHRYHUWRVLPXODWHWKHJULSIL[WXUHULJLGFRQVWUDLQVZHUHDSSOLHG DORQJDVWULSPPZLGH,Q)LJEWKHERXQGDU\FRQGLWLRQVDSSOLHGWRWKHSDQHODUHVKRZQ
3.2. DBEM model 7KHWZRGLPHQVLRQDO'%(0PRGHOUHDOL]HGE\WKHFRPPHUFLDOVRIWZDUH%($6<>@LVVKRZQLQ)LJDZLWK KLJKOLJKWRIHDFKVLQJOHFRPSRQHQWSDQHOVWLIIHQHUVJULSIL[WXUHQRWFK7KHPRGHOLVGLYLGHGLQIRXU]RQHV)LJ EWKHVNLQLVPRGHOHGDV]RQHZLWKDWKLFNQHVVHTXDOWRPPDQGUHODWHGPDWHULDOSURSHUWLHVDVUHSRUWHGLQ 7DEOHWKHJULSSODWHLVPRGHOOHGDV]RQHWKHWZRVWULQJHUVDUHPRGHOHGDV]RQHDQG7KHODWWHUDUHWREHVSOLW LQWZRGLIIHUHQW]RQHVLQRUGHUWRDOORZWKHFUDFNWRSURSDJDWHLQWKHVNLQZLWKRXW³DIIHFWLQJ´WKHDSSURDFKLQJVWLIIHQHU WKDWIDLOVRQO\DIWHUWKDWWKHFUDFNKDVRYHUFRPHLWWKH PRGHOLQJSURFHGXUHLVGHWDLOHGLQ>@,QSDUWLFXODUWZR OD\HUVRYHUODSSHGLQFRUUHVSRQGHQFHRIWKHVWLIIHQHUDUHDDUHPRGHOHGWKHILUVWUHSUHVHQWDWLYHRIWKHVNLQDQGDIIHFWHG E\WKHFUDFNSURSDJDWLRQDQGWKHVHFRQGWRPRGHOWKHVWLIIHQHU )LJD''%(0PRGHORIWKHSDQHOZLWKFORVHXSRILQLWLDOFUDFNDQGLQWHUIDFHOLQHWRFRQQHFW]RQHDQG]RQHEKLJKOLJKWRI]RQHV ZLWKGLIIHUHQWWKLFNQHVV
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
)LJVKRZVWKHVWUHVVVFHQDULRHYDOXDWHGE\)(0DQG'%(0PRGHOVDIWHUF\FOHVRIFUDFNSURSDJDWLRQ a PP WKH '%(0 FRORU PDS DSSHDUV URXJK EHFDXVH RI D OLPLWHG QXPEHU RI LQWHUQDO SRLQWV DYDLODEOH IRU WULDQJXODWLRQ 7KHFUDFNJURZWKODZDGRSWHGIRUWKHSURSDJDWLRQLQWKHDOXPLQXPOD\HULVWKH1$6*52HTXDWLRQ(T q crit p th n K K K K K R f C dN da ¸¸ ¹ · ¨¨ © § ¸ ¹ · ¨ © § ' ' » ¼ º « ¬ ª ' ¸ ¹ · ¨ © § PD[ ZKRVHFDOLEUDWLRQSDUDPHWHUVDUHWKRVHUHODWHGWR$/77DEOH DE
)LJ'LUHFWVWUHVVHVV\\>03D@HYDOXDWHGE\)(0DQG'%(0DFRYHUDOOYLHZVEGGHWDLOYLHZVQHDUE\FUDFNWLS 7DEOH)LWWLQJSDUDPHWHUVIRUWKH$/7IURP1$6*52OLEUDU\6,)LQ>MPa*mm0.5@DQGOHQJWKLQ>mm@ 3DUDPHWHU 9DOXH 3DUWWKURXJKIUDFWXUHWRXJKQHVV.( 3ODQHVWUDLQIUDFWXUHWRXJKQHVV.& $.&RHIILFLHQW$. %.&RHIILFLHQW%. &UDFNJURZWKUDWHFRHIILFLHQW& ā( 1&RHIILFLHQW1 3&RHIILFLHQW3 4&RHIILFLHQW4 7KUHVKROG6,)DW5 '. &7KUHVKROGSRVLWLYHYDOXH&37+ 3ODQHVWUHVVVWUDLQFRQVWUDLQWIDFWRU$/)$ 655DWLR65 ,QWULQVLFFUDFNOHQJWK$ D E
)URP)(DQG'%(0DQDO\VHVLWFRPHVRXWWKDWWKHWZRFUDFNWLSVSURFHHGVZLWKQHDUO\WKHVDPHJURZWKUDWHEXW GXHWRWKHGLIIHUHQWLQLWLDOGLVWDQFHIURPWKHVWLIIHQHUVWKHOHIWWLSUHDFKHVWKHVWLIIHQHUEHIRUHWKDQWKHULJKWWLS)LJ D$WWKLVVWDJHWKHWZRVWLIIHQHUVDUHVWLOOERWKLQWDFWSURYLGLQJDUHOHYDQW³EULGJHHIIHFW´DVYLVLEOHIURPWKHVWUHVV VFHQDULRLQ)LJE )LJDGHIRUPHGSORWEGLUHFWVWUHVVı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
)LJD'%(0GHIRUPHGSORWRIWKHSDQHOZKHQa PPE'%(0GLUHFWVWUHVVV\\>03D@LQ<GLUHFWLRQ
D E
)LJ&UDFNVL]H>PP@YVQXPEHURIF\FOHVIRUWKHWZRFUDFNV 7KHH[SHULPHQWDOSURSDJDWLRQUHFRUGLQJSURFHHGVXSWRDQXPEHURIF\FOHVHTXDOWRDWWKLVVWDJHWKHSDQHO EUHDNVGRZQ)LJ$V)LJVKRZVWKHH[WHQVLRQRISODVWLF]RQHVXUURXQGLQJWKHFUDFNWLSLVVWLOOQRWDIIHFWLQJ WKHPDLQSDUWRIWKHUHVLGXDOOLJDPHQWVRWKDWDSDQHOIDLOXUHIRUSODVWLFFROODSVHFDQEHH[FOXGHGFRQVHTXHQWO\WKH SDQHOVIDLOVGXHWRIUDFWXUHLQVWDELOLW\7KLVLVFRQILUPHGE\WKHKIYDOXHVLQWKHILQDOVWDJHRIFUDFNSURSDJDWLRQ)LJ JHWWLQJFORVHWRWKHSODQHVWUHVVIUDFWXUHWRXJKQHVVQHDUO\03DāPPFDOFXODWHGIRUWKHPDWHULDOXQGHU DQDO\VLVDQGLQFRUUHVSRQGHQFHRIWKHUHODWHGVNLQWKLFNQHVV(T )LJDGHIRUPHGVFDOHEGLUHFWVWUHVVVFHQDULRı\\>03D@DIWHUIDWLJXHWHVW )(0DQG'%(06WUHVV,QWHQVLW\)DFWRUV6,)¶VFDOFXODWHGLQFRUUHVSRQGHQFHRIGLIIHUHQWFUDFNVL]HVDUHVKRZQ LQ)LJDQGWXUQRXWWREHLQDVDWLVIDFWRU\DJUHHPHQW 1XPEHURIF\FOHV & UD FN VL ]H >PP @ ([S )(0 '%(0 /()767,))(1(5 5,*+767,))(1(5 D E
)LJ6,)¶VYVFUDFNVL]HIRUWKHWZRFUDFNVDOHIWVLGHEULJKWVLGH ¸¸ ¸ ¸ ¸ ¸ ¸ ¹ · ¨¨ ¨ ¨ ¨ ¨ ¨ © § ¸ ¸ ¹ · ¨ ¨ © § y IC K t AK IC C BK e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
5HIHUHQFHV >@ 5-+:DQKLOO/0ROHQW6$%DUWHU)UDFWXUHPHFKDQLFVLQDLUFUDIWIDLOXUHDQDO\VLV8VHVDQGOLPLWDWLRQV(QJ)DLO$QDO±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± >@ ($UPHQWDQL5&LWDUHOOD56HSH)0/)XOO6FDOH$HURQDXWLF3DQHO8QGHU0XOWLD[LDO)DWLJXH([SHULPHQWDO7HVWDQG'%(06LPXODWLRQ (QJ)UDFW0HFK >@ ($UPHQWDQL)&DSXWR5(VSRVLWR**RGRQR$1HZ7KUHH/RDGLQJ$[HV0DFKLQHIRU6WDWLFDQG)DWLJXHWHVWV3URFHHGLQJVRIWKH6L[WK ,QWHUQDWLRQDO&RQIHUHQFHRQ%LD[LDO0XOWLD[LDO)DWLJXH )UDFWXUH/LVERD3RUWXJDO >@ 5LJE\5+$OLDEDGL0+0L[HGPRGH-LQWHJUDOPHWKRGIRUDQDO\VLVRI'IUDFWXUHSUREOHPVXVLQJ%(0(QJ$QDO%RXQGDU\(OHP ±
>@ & &DOu 5 &LWDUHOOD 0 3HUUHOOD 7KUHHGLPHQVLRQDO FUDFN JURZWK QXPHULFDO HYDOXDWLRQV DQG H[SHULPHQWDO WHVWV (XURSHDQ 6WUXFWXUDO ,QWHJULW\6RFLHW\%LD[LDO0XOWLD[LDO)DWLJXHDQG)UDFWXUH(GLWHGE\$QGUHD&DUSLQWHUL0DQXHOGH)UHLWDVDQG$QGUHD6SDJQROL >@ &&DOu5&LWDUHOOD5HVLGXDOVWUHQJWKDVVHVVPHQWIRUDEXWWMRLQWLQ06'FRQGLWLRQ$GY(QJ6RIWZ >@ 5&LWDUHOOD03HUUHOOD0XOWLSOHVXUIDFHFUDFNSURSDJDWLRQQXPHULFDOVLPXODWLRQVDQGH[SHULPHQWDOWHVWV)DWLJXH)UDFW(QJ0 >@ ($UPHQWDQL5&LWDUHOOD'%(0DQG)(0DQDO\VLVRQQRQOLQHDUPXOWLSOHFUDFNSURSDJDWLRQLQDQDHURQDXWLFGRXEOHUVNLQDVVHPEO\,QW -)DWLJXH± >@ 5&LWDUHOOD1RQ/LQHDU06'FUDFNJURZWKE\'%(0IRUDULYHWHGDHURQDXWLFUHLQIRUFHPHQW$GY(QJ6RIWZ± >@ 5&LWDUHOOD06'&UDFNSURSDJDWLRQRQDUHSDLUHGDHURQDXWLFSDQHOE\'%(0$GY(QJ6RIWZ >@ 5&LWDUHOOD*&ULFUu($UPHQWDQL0XOWLSOHFUDFNSURSDJDWLRQZLWK'XDO%RXQGDU\(OHPHQW0HWKRGLQVWLIIHQHGDQGUHLQIRUFHGIXOOVFDOH DHURQDXWLFSDQHOV.H\(QJ0DW >@ %($6<9U'RFXPHQWDWLRQ&0%($6</WG