Residual stresses in a ceramic-metal composite

HAL Id: hal-00784294

https://hal.archives-ouvertes.fr/hal-00784294

Submitted on 4 Feb 2013

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.

Residual stresses in a ceramic-metal composite

Vincent Cazajus, Sébastien Seguy, Hélène Welemane, Moussa Karama

To cite this version:

Vincent Cazajus, Sébastien Seguy, Hélène Welemane, Moussa Karama. Residual stresses in a ceramic-metal composite. Applied Mechanics and Materials, Trans Tech Publications, 2012, 146, pp.185-196. �10.4028/www.scientific.net/AMM.146.185�. �hal-00784294�

Any correspondence concerning this service should be sent to the repository administrator: staff-oatao@inp-toulouse.fr

To link to this article: DOI:10.4028/www.scientific.net/AMM.146.185 http://dx.doi.org/10.4028/www.scientific.net/AMM.146.185

This is an author-deposited version published in: http://oatao.univ-toulouse.fr/

Eprints ID: 6574

To cite this version:

Cazajus, Vincent and Seguy, Sebastien and Welemane, Hélène and Karama, Moussa Residual stresses in a ceramic-metal composite. (2011) Applied Mechanics and Materials, vol. 146 . pp. 185-196. ISSN 1662-7482

O

pen

A

rchive

T

oulouse

A

rchive

O

uverte (

OATAO

)

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible.

5HVLGXDOVWUHVVHVLQDFHUDPLFPHWDOFRPSRVLWH





_&D]DMXV9



_6HJX\6



_{+:HOHPDQH}



_.DUDPD0



_{8QLYHUVLWpGH7RXORXVH,137(1,7/*3} $YHQXHG¶$]HUHL[%3±7$5%(6&HGH[)5$1&( _{8QLYHUVLWpGH7RXORXVH,16$7*0±,&$DYHQXHGH5DQJXHLO} 7RXORXVHFHGH[ _{PRXVVDNDUDPD#HQLWIU}_{VHEDVWLHQVHJX\#LQVDWRXORXVHIU}   .H\ZRUGVWKHUPRPHFKDQLFDODQDO\VLV&HUDPLFPHWDOUHVLGXDOVWUHVVHVQXPHULFDOVLPXODWLRQV 

$EVWUDFW 7KH ZRUN RI WKLV VWXG\ FRQFHUQV WKH ILQH PRGHOOLQJ RI WKH WKHUPRPHFKDQLFDO DQG

PHWDOOXUJLFDO EHKDYLRU RI LQWHUIDFH FHUDPLFPHWDO LQ RUGHU WR GHWHUPLQH WKH UHVLGXDO PHFKDQLFDO VWDWH RI WKH VWUXFWXUHV GXULQJ EUD]LQJ SURFHVV )RU WKHVH FDVHV GLIILFXOWLHV PDLQO\ DULVH LQ WKH PRGHOOLQJ RI WKH VROLGVROLG SKDVH WUDQVIRUPDWLRQV DV ZHOO DV LQ WKH PRGHOOLQJ RI WKH PHFKDQLFDO EHKDYLRU RI WKH PXOWLSKDVLF PDWHULDO :LWKLQ DQ RULJLQDO WKHRUHWLFDO IUDPHZRUN  JHQHUDOL]HG VWDQGDUGPDWHULDOVZLWKLQWHUQDOFRQVWUDLQWV±ZHSURSRVHGPRGHOVIRUWKHEHKDYLRURIPXOWLSKDVLF PDWHULDO

7KHGHVLJQRIMRLQWVLQHQJLQHHULQJVWUXFWXUHVDQGWKHRSWLPLVDWLRQRIWKHLQGXVWULDOEUD]LQJSURFHVV UHTXLUH GHWHUPLQLQJ DQG DQDO\VLQJ VXFK D SKHQRPHQRQ ,Q WKLV ZD\ WKH SUHVHQW ZRUN DLPV DW SUHGLFWLQJWKHWKHUPDOO\LQGXFHGVWUHVVHVORFDOLVDWLRQDQGOHYHOWKURXJKQXPHULFDOVLPXODWLRQVDQG WKHQDWGHILQLQJWKHPDLQSDUDPHWHUVZKLFKLQIOXHQFHWKHLUGHYHORSPHQW



 ,QWURGXFWLRQ 

 %UD]LQJ LV D ZHOGLQJ SURFHVV FXUUHQWO\ XVHG WR SURGXFH FHUDPLF WR PHWDO DVVHPEOLHV WKDW DUH LQWHUHVWLQJEHFDXVHFHUDPLFDQGPHWDOOLFPDWHULDOVKDYHGLVVLPLODUWKHUPDOPHFKDQLFDOHOHFWURQLF DQG FKHPLFDO EHKDYLRXU 6XFK DVVHPEOLHV DUH LQWHJUDWHG LQ FRPSOH[ V\VWHPV GHVLJQHG IRU KLJK WHFKQRORJ\DSSOLFDWLRQVPHGLFDODLUFUDIWVSDWLDOHOHFWURQLFRUQXFOHDU7KLVSURFHVVDOORZVWKHQ WR OLQN WZR EDVH PDWHULDOV FHUDPLF DQG PHWDO ZKLFK H[KLELW TXLWH GLIIHUHQW WKHUPRPHFKDQLFDO EHKDYLRXU7KHGLIIHUHQFHEHWZHHQWKHWKHUPDOH[SDQVLRQFRHIILFLHQW&7(RIWKHVHPDWHULDOVOHDGV WR WKH GHYHORSPHQW RI UHVLGXDO VWUHVVHV GXULQJ WKH FRROLQJ SKDVH RI WKH EUD]LQJ SURFHVV 6XFK UHVLGXDOVWUHVVHVFOHDUO\UHGXFHWKHVWUHQJWKRIWKHEUD]HGMRLQWDQGFDQOHDGWRFDWDVWURSKLFIDLOXUHDW WKH LQWHUIDFHV HYHQ GXULQJ WKH EUD]LQJ SURFHVV LWVHOI >@ ,Q RUGHU WR SHUIRUP WKH PHFKDQLFDO VWUHQJWK RI VXFK DVVHPEOLHV DQG RSWLPLVH WKH EUD]LQJ SURFHVV LW LV LPSRUWDQW WR HVWLPDWH WKHVH UHVLGXDOVWUHVVHVDQGVWXG\WKHSDUDPHWHUVWKDWLQIOXHQFHWKHLUGHYHORSPHQW



 ,QSDUWLFXODUWKHPDWHULDOVFRQVWLWXWLYHODZVWKHVWUXFWXUHJHRPHWU\DQGWKHFRROLQJFRQGLWLRQV SOD\DFUXFLDOUROHLQWKHORFDOLVDWLRQDQGWKHLQWHQVLW\OHYHORIUHVLGXDOVWUHVVHV>@0DQ\DQDO\WLFDO DQG QXPHULFDO DSSURDFKHV KDYH DOUHDG\ EHHQ FDUULHG RXW WR HVWLPDWH VXFK SKHQRPHQRQ IRU IL[HG YDOXHRIWKHVHGDWD>@,QWKLVSDSHUZHSURSRVHDVHQVLWLYLW\DQDO\VLVRIDOOWKHVHIDFWRUVRQWKH UHVLGXDO VWUHVVHV LQGXFHG ZKLFK DOORZV WR GHILQH WKH PRVW LPSRUWDQW RQHV DQG DOVR WR FKRRVH DSSURSULDWHK\SRWKHVHVIRUILQLWHHOHPHQWPRGHOV

  

 %UD]LQJSURFHVV   %UD]LQJLVDZHOGLQJSURFHVVZKLFKSURGXFHVWKHFRDOHVFHQFHRIWZRRUPRUHOLNHRUXQOLNHEDVH PDWHULDOVE\PHDQVRIDILOOHUPHWDODOOR\ZLWKDORZHUPHOWLQJSRLQW7KHDVVHPEO\LVKHDWHGWRD VXLWDEOHWHPSHUDWXUHXSSHUWKHOLTXLGXVWHPSHUDWXUHRIWKHILOOHUPHWDOZKLFKLVGUDZQLQWRWKHMRLQW E\FDSLOODU\DWWUDFWLRQ'XULQJWKHFRROLQJSKDVHWKHILOOHUPHWDOVROLGLILFDWLRQSURGXFHVWKHMRLQWRI WKHEDVHPDWHULDOV  ,QRXUFDVHDIWHUWKLVSRLQWFRROLQJIURPILOOHUPHWDOVROLGXVWHPSHUDWXUHWRURRPWHPSHUDWXUH WKHEDVHPDWHULDOVDQGWKHILOOHUPHWDODUHQRWVXEPLWWHGWRDQ\PHWDOOXUJLFDOWUDQVIRUPDWLRQ7KH WZREDVHPDWHULDOVDUHYHU\GLVVLPLODUFHUDPLFDQGPHWDOOLFSDUW$ORZWKLFNQHVVPHWDOOL]DWLRQDW WKHFHUDPLFVXUIDFHLVXVHGWRLQFUHDVHZHWWDELOLW\E\WKHILOOHUPHWDODWWKHOLTXLGVWDWHDQGDOORZ FDSLOODU\DWWUDFWLRQ7KHFDSLOODU\DWWUDFWLRQRIWKHILOOHUPHWDOE\WKHPHWDOOLFSDUWRFFXUVQDWXUDOO\ 

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

 7KH ILJXUH  VKRZV WKH PLFURVWUXFWXUH RI D FHUDPLF WR PHWDO DVVHPEO\ DIWHU EUD]LQJ  :H FDQ REVHUYH WKUHH GRPDLQV PHWDO MRLQW DQG FHUDPLF 7KH MRLQW LV FRPSRVHG RI WKH ILOOHU PHWDO WKH PHWDOL]HG VXUIDFH RI WKH FHUDPLF DQG WKH LQWHUIDFHV JHQHUDWHG DW KLJK WHPSHUDWXUH E\ GLIIXVLRQ EHWZHHQWKHEDVHPDWHULDOVVXUIDFHVDQGWKHILOOHUPHWDO               )LJXUH0LFURVWUXFWXUHRIWKHFHUDPLFWRPHWDOEUD]HGDVVHPEO\ 9DFXXP FRROLQJ FRQGXFWLRQ 1LWURJHQ FRROLQJ FRQYHFWLRQ  )XUQDFH WHPSHUDWXU 7LPH KRXUV



   )LOOHUPHWDO VROLGXV   _{Dd> :K/Ed ZD/} DĞƚĂůůŝnjĞĚƐƵƌĨĂĐĞ &/>>ZDd> /ŶƚĞƌĨĂĐĞƐ

  &RPSRVLWHVWUXFWXUH   7KHDVVHPEO\JHRPHWU\VWXGLHGLQWKLVZRUNLVD'D[LV\PPHWULFF\OLQGHUFRPSRVHGRIWKUHH PDWHULDOV  DOXPLQD$O2ZLWKDSXULW\RIFHUDPLF  VWDLQOHVVVWHHOPHWDO  VLOYHUFRSSHUHXWHFWLFDOOR\ILOOHUPHWDO

DV WKH LQIOXHQFH RI RWKHU FRPSRQHQWV LV QHJOHFWHG )LJ  %HVLGHV WKH MRLQHG VXUIDFHV EHWZHHQ WKHVHPDWHULDOVDUHSHUIHFWO\SODQHVXUIDFHV               )LJXUH*HRPHWULFDOSDUDPHWHUVRIWKHFHUDPLFPHWDODVVHPEO\  7KHJHRPHWULFDOSDUDPHWHUVRIVXFKVWUXFWXUHDUHWKHKHLJKWRIHDFKFRPSRQHQWDOXPLQD+$ILOOHU

PHWDO+)0VWDLQOHVVVWHHO+66DQGWKHLQWHUQDO5LQWDQGH[WHUQDOUDGLL5H[WRIWKHF\OLQGHU)RUD

IXOOF\OLQGHUWKHLQWHUQDOUDGLXVYDOXHLVHTXDOWR]HUR5LQW 



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 0RUHRYHU WKH LPSDFW WKH HODVWRSODVWLF EHKDYLRXU W\SH RQ WKH UHVLGXDO VWUHVVHV LQGXFHG KDV DOVR EHHQ VWXGLHG E\ DFFRXQWLQJ FRQVWLWXWLYHODZVZLWKRUZLWKRXWKDUGHQLQJIRUWKHPHWDOPDWHULDO )XOO ELEOLRJUDSKLFPHFKDQLFDO DQGWKHUPDOSURSHUWLHVDUHDYDLODEOHIRUDOXPLQD$VWDLQOHVVVWHHO66DQGILOOHUPHWDO)0RQ 7DEOH   

$OXPLQD

)LOOHU0HWDO

5HYROXWLRQD[LV +$ +66 5LQW 5H[W +)0 )UHHVLGH VXUIDFH

6WDLQOHVV

VWHHO

























7HPSHUDWXUHƒ&

<

LH

OG

VW

UH

VV



0

3

D

)LOOHU0HWDO/(9<>@

)LOOHU0HWDO/29$72>@

6WDLQOHVVVWHHO

  )LJXUH0HWDOSODVWLF\LHOGVWUHVVHYROXWLRQGHSHQGLQJRQWHPSHUDWXUH                           

 7DEOH0HFKDQLFDODQGWKHUPDOSURSHUWLHVRIHDFKFRPSRQHQWDFFRUGLQJWRWHPSHUDWXUH$OXPLQD $)LOOHU0HWDO)06WDLQOHVV6WHHO66 <RXQJPRGXOXV*3D 7ƒ&        $        )0>@        66        3RLVVRQUDWLR 7ƒ&        $        )0>@        66       

&RHIILFLHQWRI7KHUPDO([SDQVLRQuuuuƒ&

7ƒ&        $        )0>@        66        <LHOGVWUHVV03D 7ƒ&        )0>@        )0>@        66        7HQVLOH6WUHQJWK03D 66        7HQVLOHIDLOXUHVWUDLQ 66           1XPHULFDOPRGHO   1XPHULFDOVLPXODWLRQVKDYHEHHQSHUIRUPHGZLWKWKHILQLWHHOHPHQW$%$486FRGH7KHPRGHO LVGHILQHGLQDFFRUGDQFHZLWKWKHJHRPHWU\FKRVHQDQGWKHEUD]LQJSURFHVVGHVFULEHGSUHYLRXVO\  WKHVWUXFWXUHLV'D[LV\PPHWULF  WKHPHVKRIWKHDVVHPEO\KDVEHHQGRQHZLWKDQQRGHTXDGUDWLFD[LV\PPHWULFTXDGULODWHUDO HOHPHQW7KHHOHPHQWVL]HLVORZHVWQHDUWKHLQWHUIDFHVDQGWKHIUHHVLGHVXUIDFHEHFDXVHWKH UHVLGXDO VWUHVVHV DUH HVVHQWLDOO\ ORFDOLVHG LQ WKHVHV ]RQHV )LJ  $ FRQYHUJLQJ VWXG\ RQ 9RQ 0LVHV VWUHVVHV KDV IL[HG WKH QRGHV QXPEHU DW  LQ RXU FDVH WR HVWLPDWH UHVLGXDO VWUHVVHVZLWKDJRRGSUHFLVLRQ

 WKHULJLGERG\GLVSODFHPHQWKDVEHHQIL[HG)LJ

 WKHVWDUWLQJSRLQWRIWKHVLPXODWLRQLVWKHVROLGLILFDWLRQRIWKHILOOHUPHWDOGXULQJWKHFRROLQJ SKDVH RI WKH EUD]LQJ SURFHVV )LJ  DQG WKH VLPXODWLRQ HQGV ZKHQ WKH FHUDPLF PHWDO DVVHPEO\WHPSHUDWXUHLVHTXDOWRWKHURRPWHPSHUDWXUH  WKHUHLVQRPHFKDQLFDOORDGLQJRQWKHFHUDPLFPHWDODVVHPEO\  WKHWKHUPDOORDGLQJLVWKHFRROLQJF\FOH)LJIURPWKHILOOHUPHWDOVROLGXVWHPSHUDWXUHWR URRPWHPSHUDWXUH                )LJXUH0HVKRIWKHFHUDPLFPHWDODVVHPEO\IRUWKHIXOOF\OLQGHUGHVLJQ5LQW     0RUHRYHUWZRK\SRWKHVHVKDYHEHHQVWXGLHGRXWWRJHWWKHQRGHVWHPSHUDWXUHDFFRUGLQJWRWLPH LQWKHDVVHPEO\

L 8QLIRUP FRROLQJ K\SRWKHVLV WKH WHPSHUDWXUH RI DOO WKH QRGHV LV DVVLPLODWH WR WKH IXUQDFH WHPSHUDWXUHDFFRUGLQJWRWLPH

LL 7KHUPDODQDO\VLVWZRSKDVHVFRUUHVSRQGLQJWRWKHFRROLQJSURFHVVKDYHEHHQVLPXODWHG)LJ  )LUVW WKH DVVHPEO\ LV LQ YDFXXP DWPRVSKHUH XQWLO D ORZ FRROLQJ WHPSHUDWXUH WKH ERXQGDU\ FRQGLWLRQ DSSOLHG WR LWV H[WHUQDO VXUIDFH LV WKHQ WKH IXUQDFH WHPSHUDWXUH FRQGXFWLRQ7KHQLQDVHFRQGSDUWWKHERXQGDU\FRQGLWLRQDSSOLHGWRWKHH[WHUQDOVXUIDFH RIWKHDVVHPEO\WXUQVLQWRWKHFRQYHFWLRQIORZ

7KHQRGHWHPSHUDWXUHVREWDLQHGDUHILQDOO\LQWURGXFHGLQWKHPHFKDQLFDODQDO\VLVWRJHWWKHVWUHVV VWUDLQ UHVSRQVH DQG WKH UHVLGXDO VWUHVVHV 1RWH WKDW WKH WKHUPDO DQG PHFKDQLFDO DQDO\VHV DUH XQFRXSOHG    5HVLGXDOVWUHVVHVDQDO\VLV   $OOUHVXOWVVKRZWKDWPD[LPXPVWUHVVFRQFHQWUDWLRQRFFXUVLQWKHFHUDPLFQHDUWKHLQWHUIDFHZLWK WKHILOOHUPHWDOZKLFKFRUURERUDWHVH[SHULPHQWDOREVHUYDWLRQV>@ ,QIOXHQFHRIWKHFRQVWLWXWLYHODZV  ,QWKLVSDUWWKHLQIOXHQFHRIWKHPHWDOOLFPDWHULDOVILOOHUPHWDODQGPHWDO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

0HWDO

&HUDPLF

)LOOHU0HWDO

5HYROXWLRQD[LV

)UHHVLGH

VXUIDFH

5LJLGERG\

GLVSODFHPHQW

'D[LV\PPHWULF

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  &HUDPLF 0HWDO _0HWDO)LOOHU

'LVWDQFHDORQJWKHIUHHVLGHVXUIDFHPP  )LJXUH5HVLGXDOVWUHVVGLVWULEXWLRQDORQJWKHDVVHPEO\IUHHVLGHVXUIDFH DFFRUGLQJWRWKHPHWDOOLFPDWHULDOVFRQVWLWXWLYHODZV  

 /HW H[DPLQH QRZ WKH HYROXWLRQ RI VWUHVV GXULQJ WKH FRROLQJ SKDVH DFFRUGLQJ WR WKH WZR ELEOLRJUDSKLFSODVWLF\LHOGVWUHVVJLYHQIRUWKHILOOHUPHWDOE\/HY\>@DQG/RYDWR>@)LJ)RU ERWKFDVHVWKHILOOHUPHWDOH[KLELWVDORZ\LHOGVWUHVVYDOXHLQWKHKLJKWHPSHUDWXUHVUDQJHƒ& ƒ&DQGFRQVHTXHQWO\WKHSODVWLFEHKDYLRXU TXLFNO\RFFXUV7KH VWUDLQ LQGXFHGE\ WKH WKHUPDO H[SDQVLRQFRHIILFLHQWGLIIHUHQFHEHWZHHQWKHDOXPLQDDQGWKHVWDLQOHVVVWHHOSDUWDUHWKHQELJJHULQ WKHILOOHUPHWDOSDUWWKDQLQWKHRWKHUFRPSRQHQWV&RQVHTXHQWO\WKHUHVLGXDOVWUHVVHVDUHTXLWHVPDOO ZLWKLQ WKH DVVHPEO\ DW KLJK WHPSHUDWXUH EHFDXVH WKH\ DUH OLPLWHG WR WKH \LHOG VWUHVV LQ WKH ILOOHU PHWDODQGDVVRFLDWHGWRORZVWUDLQVYDOXHVLQPHWDODQGFHUDPLF)LJ

                   )LOOHU0HWDO/(9<>@ )LOOHU0HWDO/29$72>@    )LJXUH0D[LPXP9RQ0LVHVVWUHVVRQWKHIUHHVLGHVXUIDFHDFFRUGLQJWRIXUQDFHWHPSHUDWXUHDQG ILOOHUPHWDOPHFKDQLFDOSURSHUWLHV   

 ,Q WKH ORZ WHPSHUDWXUHV UDQJH XQGHU ƒ& WKH \LHOG VWUHVV YDOXH IRU ERWK GDWD LQFUHDVH VLJQLILFDQWO\DQGLQGXFHELJJHUVWUHVVHVGXULQJFRROLQJ)LJ+RZHYHUWKHEHKDYLRXUGHSHQGVRQ WKH\LHOGVWUHVVFKRVHQ)RUWKHGDWDJLYHQE\/RYDWR>@ZHREVHUYHWKHVDPHIHDWXUHVDVIRUKLJK WHPSHUDWXUH DV WKH ILOOHU \LHOG VWUHVV UHPDLQV WKH VLJQLILFDQW SDUDPHWHU HYHQ LI LWV YDOXH LQFUHDVH ZLWK WHPSHUDWXUH 7KH ILOOHU PHWDO \LHOG VWUHVV JLYHQ E\ /HY\ >@ JHWV XSSHU WKDQ WKH PHWDO RQH EHWZHHQDQGƒ&)LJVRIURPWKDWSRLQWWKHVWUHVVHVHYROXWLRQIROORZVWKHSDWWHUQRIWKH PHWDOPDWHULDO7KXVZHFDQFRQFOXGHWKDWPHWDOOLFPDWHULDOVZLWK\LHOGVWUHVVDVORZDVSRVVLEOH VKRXOGEHXVHGLQRUGHUWROLPLWUHVLGXDOVWUHVVHVYDOXHVRQWKHFHUDPLFPHWDODVVHPEOLHV

 1RWHILQDOO\WKDWIRUWKHWZRGLIIHUHQWHYROXWLRQVWKHUHVLGXDOVWUHVVHVDWURRPWHPSHUDWXUHDUH TXLWH WKH VDPH PD[LPXP VWUHVV GLIIHUHQFH RI  03D 7KH \LHOG VWUHVV HYROXWLRQ DFFRUGLQJ WR WHPSHUDWXUHVHHPVWKHQWRKDYHDVLJQLILFDQWLPSDFWRQVWUHVVHVHYROXWLRQGXULQJWKHEUD]LQJSURFHVV EXWQRWRQWKHLUILQDOYDOXHVUHVLGXDOVWUHVVHV  ,QIOXHQFHRIFRROLQJFRQGLWLRQV  ,QWKLVSDUWZHFRPSDUHWKHUHVXOWVREWDLQHGIRUWKHWZRWKHUPDOORDGLQJK\SRWKHVHVXQLIRUP FRROLQJFRQGXFWLRQDQGFRQYHFWLRQIORZ

)LJXUH  SUHVHQWV WKH PD[LPXP WKHUPDO JUDGLHQW LQGXFHG LQ WKH FHUDPLF PHWDO DVVHPEO\ IRU WKH VHFRQG K\SRWKHVLV ZKLFK LV REWDLQHG DW WKH EHJLQQLQJ RI WKH FRROLQJ SKDVH IXUQDFH WHPSHUDWXUH HTXDO WR ƒ& $V WKLV JUDGLHQW UHPDLQV TXLWH QHJOLJLEOH ƒ& DOO DORQJ WKH FRROLQJ VWUHVVHV UHVSRQVHVZLWKERWKK\SRWKHVHVDUHTXLWHVLPLODUGXULQJWKHSURFHVV)LJDQGDWWKHILQDOVWDJH UHVLGXDO VWUHVVHV RQ )LJ  7KH XQLIRUP FRROLQJ K\SRWKHVLV VHHPV WKHQ VXIILFLHQW IRU WKH QXPHULFDOWKHUPDODQDO\VLV  0 D[LPXP 9RQ0 LVHV VW UHVV 0 3D  7HPSHUDWXUHƒ&

  )LJXUH0D[LPDOWHPSHUDWXUHJUDGLHQWLQWKHFHUDPLFPHWDO DVVHPEO\IURPWKHWKHUPDODQDO\VLV                 8QLIRUPFRROLQJ 7KHUPDODQDO\VLV  0 D[L P XP 9RQ 0 LVH V VW UH VV 0 3D  7HPSHUDWXUHƒ&   )LJXUH0D[LPDOVWUHVVHYROXWLRQDFFRUGLQJWRIXUQDFHWHPSHUDWXUHDQGFRROLQJFRQGLWLRQV  5HYROXWLRQD[LV /HJHQGƒ& 0HWDO &HUDPLF )LOOHU 0HWDO 6WDQG 7KHUPDOORDGLQJ

                                   8QLIRUPFRROLQJ 7KHUPDODQDO\VLV 9RQ 0L VHV VW UH VV 0 3 D  'LVWDQFHDORQJWKHIUHHVLGHVXUIDFHPP &HUDPLF

0HWDO _0HWDO)LOOHU

 )LJXUH5HVLGXDOVWUHVVGLVWULEXWLRQDORQJWKHIUHHVLGHVXUIDFH GHSHQGLQJRQFRROLQJFRQGLWLRQV    ,QIOXHQFHRIJHRPHWU\ *HRPHWULFDOHIIHFWVRQUHVLGXDOVWUHVVHVDUHFDUULHGRXWZLWKWZROHYHOIDFWRULDODQDO\VHV

)LUVW D VWXG\ KDV EHHQ SHUIRUPHG IRU WKH IXOO F\OLQGHU GHVLJQ 5LQW  ZKHUH WKH PD[LPXP 9RQ

0LVHV VWUHVV YDOXH LQ WKH FHUDPLFPHWDO DVVHPEO\ LV FDOFXODWHG IRU VL[WHHQ GLIIHUHQW DVVHPEO\ PRGHOV ZKHUH IRXU IDFWRUV KHLJKWV RI HDFK FRPSRQHQW +$ +)0 +66 H[WHUQDO UDGLXV RI WKH

F\OLQGHU5H[WDUHHDFKDVVLJQHGWRWZROHYHOV7DE2Q)LJXUHZHREVHUYHWKDWLIWKH

DOXPLQD KHLJKW +$ DQG WKH H[WHUQDO UDGLXV 5H[W DUH LQFUHDVHG WKH VWUHVVHV LQ WKH DVVHPEO\

LQFUHDVH VLJQLILFDQWO\ 2Q WKH RWKHU KDQG DQ LQFUHDVH RI WKH ILOOHU PHWDO +)0 DQG VWDLQOHVV VWHHO

+66KHLJKWVLQGXFHDVPDOOGHFUHDVHRIWKHVWUHVVHV                  )LJXUH*HRPHWULFDOIDFWRUVHIIHFWVRQPD[LPDOVWUHVVRIWKHIXOOF\OLQGHUGHVLJQ             0HDQYDOXH $OXPLQD+HLJKW+$ ([WHUQDO5DGLXV5H[W 6WDLQOHVV6WHHO+HLJKW+66 )LOOHU0HWDO+HLJKW+)0 *HRPHWULFDOIDFWRUVOHYHO7DE  9 RQ0 LVHV V WU HVV 0 3D   

 7KHVH UHVXOWV DUH FRUUHODWHG E\ H[LVWLQJ GDWD >@ ,Q RUGHU WR UHGXFH WKH UHVLGXDO VWUHVVHV LQ FHUDPLFPHWDODVVHPEOLHVLWLVWKHQUHFRPPHQGHGWRWDNH+$DQG5H[WDVVPDOODVSRVVLEOHDQG+66 DVELJDVSRVVLEOHDVWKHILOOHUPHWDOKHLJKW+)0LVXVXDOO\OLPLWHGE\WKHEUD]LQJSURFHVV   $VHFRQGIDFWRULDODQDO\VLVKDVEHHQGRQHIRUWKHSLSHGHVLJQ5LQWZLWKDIL[HGILOOHUPHWDO KHLJKW+)0 PP7KHIDFWRUVFRQVLGHUHGLQWKLVFDVHDUHWKHKHLJKWVRIEDVHPDWHULDOV+$+66 DQGWKHSLSHWKLFNQHVV5H[W5LQWRIWKHF\OLQGHU7DE  7DEOH*HRPHWULFDOIDFWRUVOHYHOPPDIXOOF\OLQGHUGHVLJQ±ESLSHGHVLJQ  D    E   5H[W    5LQW   +66    5H[W   +)0    +66   +$    +$     )LJXUHVKRZVWKDWWKHODWWHUSDUDPHWHULVWKHPRVWLPSRUWDQWIDFWRUZKLFKFRQWUROVWKHUHVLGXDO VWUHVVHVOHYHOLQWKHDVVHPEO\,QGHHGWKHLQIOXHQFHRIDOXPLQDDQGVWDLQOHVVVWHHOKHLJKWVLVTXLWH QHJOLJLEOH)RUWKLVJHRPHWU\LWLVWKHQQHFHVVDU\WROLPLWDVPXFKDVSRVVLEOHWKHSLSHWKLFNQHVVRI WKHF\OLQGHU                     )LJXUH*HRPHWULFDOIDFWRUVHIIHFWVRQPD[LPDOVWUHVVRIWKHSLSHGHVLJQ   &RQFOXVLRQ 

 7KLV SDSHU KDV VWXGLHG WKURXJK D QXPHULFDO DSSURDFK WKH GLIIHUHQW IDFWRUV WKDW LQIOXHQFH WKH VWUHVV GHYHORSPHQW DQG WKHLU ILQDO YDOXH RQ FHUDPLF PHWDO EUD]HG DVVHPEOLHV 7KHVH QXPHULFDO UHVXOWVDUHLQDFFRUGDQFHZLWKH[SHULPHQWDOREVHUYDWLRQVRQVXFKSLHFHVE\SUHGLFWLQJIRUH[DPSOH WKHORFDOLVDWLRQRIWKHPD[LPXPVWUHVVLQWKHFHUDPLFQHDUWKHLQWHUIDFHZLWKWKHILOOHUPHWDO

 ,QFHUDPLFPHWDODVVHPEOLHVWKHWKHUPRPHFKDQLFDOEHKDYLRXURIWKHFRPSRQHQWVDQGHVSHFLDOO\ WKH SODVWLF FRQWULEXWLRQ RI PHWDOOLF PDWHULDOV KDYH D VLJQLILFDQW LQIOXHQFH RQ WKH UHVLGXDO VWUHVVHV UHSDUWLWLRQ DQG WKHLU PD[LPXP YDOXHV 6WUHVVHV HYROXWLRQ GXULQJ WKH FRROLQJ LV FRQWUROOHG E\ WKH

      0HDQYDOXH 3LSHWKLFNQHVV5H[W5LQW $OXPLQD+HLJKW+$ 6WDLQOHVV6WHHO+HLJKW+66  *HRPHWULFDOIDFWRUVOHYHO7DE  9RQ 0L VHV VW UHVV  0 3 D 

PHWDOOLFPDWHULDOILOOHUPHWDORUPHWDOWKDWH[KLELWWKHORZHVW\LHOGVWUHVVYDOXH,QRUGHUWRUHGXFH WKH UHVLGXDO VWUHVVHV LQ FHUDPLF PHWDO DVVHPEOLHV LW LV WKHQ UHFRPPHQGHG WR FKRRVH PHWDOOLF PDWHULDOVZLWKWKHKLJKHVWGXFWLOLW\



 2QWKHQXPHULFDOSRLQWRIYLHZWKHXQLIRUPFRROLQJLVWKHPRVWDSSURSULDWHK\SRWKHVLVIRUWKH WKHUPDODQDO\VLVRIWKHEUD]LQJSURFHVVDVWKHWKHUPDOJUDGLHQWEHWZHHQWKHH[WHUQDOVXUIDFHDQGWKH FHQWUHRIWKHDVVHPEO\LVTXLWHQHJOLJLEOH

)LQDOO\ ZH KDYH VKRZQ WKDW WKH RSWLPLVDWLRQ RI FHUDPLF PHWDO DVVHPEOLHV UHTXLUHV PLQLPXP DOXPLQD KHLJKW DQG H[WHUQDO UDGLXV IRU IXOO F\OLQGHUV DQG PLQLPXP SLSH WKLFNQHVV IRU WKH SLSH GHVLJQ



 1XPHULFDOVLPXODWLRQRIWKHEUD]LQJSURFHVVFRXOGEHLPSURYHGZLWKDPRUHFRPSOHWHPRGHOOLQJ RI WKH LQWHUIDFHV EHWZHHQ WKH EDVH PDWHULDOV DQG WKH ILOOHU PHWDO ,W PD\ EH DOVR LQWHUHVWLQJ WR DFFRXQWIRUWKHEULWWOHGDPDJHWKDWDIIHFWVWKHFHUDPLFPDWHULDODQGWKHFUHHSEHKDYLRXURIWKHILOOHU PHWDOWKDWRFFXUVDWKLJKWHPSHUDWXUH    5HIHUHQFHV 

>@ =KDQJ -; &KDQGHO 56 &KHQ <= 6HRZ +3  ³(IIHFW RI UHVLGXDO VWUHVV RQ WKH VWUHQJWKRIDQDOXPLQDVWHHOMRLQWE\SDUWLDOWUDQVLHQWOLTXLGSKDVH37/3EUD]LQJ´-RXUQDORI

0DWHULDOV3URFHVVLQJ7HFKQRORJ\SS

>@ &KDUOHV <  ,GHQWLILFDWLRQ GXQ PRGH GH YLHLOOLVVHPHQW GDQV XQ DVVHPEODJH FpUDPLTXH

PpWDO3K'7KHVLV(FROH1RUPDOH6XSpULHXUHGH&DFKDQ

>@ +VXHFK&+(YDQV$*³5HVLGXDOVWUHVVHVLQPHWDOFHUDPLFERQGHGVWULSV´-RXUQDORI

WKH$PHULFDQ&HUDPLF6RFLHW\YQRSS

>@ <X+<6DQGD\6&5DWK%%³5HVLGXDOVWUHVVHVLQFHUDPLFLQWHUOD\HUPHWDOMRLQWV´

-RXUQDORIWKH$PHULFDQ&HUDPLF6RFLHW\YQRSS

>@ ,DQFX 27 0XQ] '  ³5HVLGXDO VWUHVV VWDWH RI EUD]HG FHUDPLFPHWDO FRPSRXQGV´

-RXUQDORIWKH$PHULFDQ&HUDPLF6RFLHW\YQRSS

>@ 6DQWDFUHX 32  6XU OD PpFDQLTXH GHV DVVHPEODJHV FDOFXO GHV FRQWUDLQWHV UpVLGXHOOHV

GDQV OHV DVVHPEODJHV FpUDPLTXHPpWDO REWHQXV SDU EUDVDJH UpDFWLI HW FDUDFWpULVDWLRQ PpFDQLTXHGHVLQWHUIDFHV3K'7KHVLV(FROH3RO\WHFKQLTXH

>@ 0XQ] ' 6FNXKU 0$ <DQJ <  ³7KHUPDO VWUHVVHV LQ FHUDPLFPHWDO MRLQWV ZLWK DQ LQWHUOD\HU´-RXUQDORIWKH$PHULFDQ&HUDPLF6RFLHW\YQRSS

>@ /HY\ $  ³7KHUPDO UHVLGXDO VWUHVVHV LQ FHUDPLF WR PHWDO EUD]HG MRLQWV´ -RXUQDO RI WKH

$PHULFDQ&HUDPLF6RFLHW\SS

>@ /RYDWR *  5KpRORJLH GHV MRLQWV EUDVpV  pWXGH H[SpULPHQWDOH HW GpWHUPLQDWLRQ SDU

PpWKRGHLQYHUVH3K'7KHVLV(FROH1DWLRQDOH6XSpULHXUHGHV0LQHVGH3DULV