Numerical Modeling of Aluminum Alloys Fracture for Automotive Applications

Procedia Engineering 109 ( 2015 ) 17 – 26

1877-7058 © 2015 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.2015.06.203

ScienceDirect

;;,,,,WDOLDQ*URXSRI)UDFWXUH0HHWLQJ,*);;,,,

1XPHULFDOPRGHOLQJRIDOXPLQXPDOOR\VIUDFWXUHIRUDXWRPRWLYH

DSSOLFDWLRQV

/XFD&DYD]]RQL

D

_{*LXVHSSH0LVFLD}

D

_{9LQFHQ]R5RWRQGHOOD}

D

_{$QGUHD%DOGLQL}

D

_

a_{Department of Engineering "Enzo Ferrari", University of Modena and Reggio Emilia, Via P. Vivarelli 10, Modena, 41125, Italy}

$EVWUDFW

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

‹7KH$XWKRUV3XEOLVKHGE\(OVHYLHU/WG

3HHUUHYLHZXQGHUUHVSRQVLELOLW\RIWKH*UXSSR,WDOLDQR)UDWWXUD,*)

Keywords:([SHULPHQWDOQXPHULFDOFRUUHODWLRQ)DLOXUHPRGHO$OXPLQXPDOOR\V)($&UDVKZRUWKLQHVV

1RPHQFODWXUH

V  ıtrue ıeng   6WUHVVWUXHVWUHVVHQJLQHHULQJVWUHVV

H  İtrue İeng   6WUDLQWUXHVWUDLQHQJLQHHULQJVWUDLQ

Vij    &DXFK\VWUHVVWHQVRU VVM    9RQ0LVHVVWUHVV VH    +\GURVWDWLFPHDQVWUHVV   3URI$QGUHD%DOGLQL7HO E-mail address:PLOOHFKLOLODE#XQLPRUHLW

© 2015 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/).

F , G , H , L , M , N , R  +LOO¶VPDWHULDOFRQVWDQWV VHeq    +LOO¶VHTXLYDOHQWVWUHVV ij A     +LOO¶VFRQVWDQWVLQSODQHVWUHVVVWDWH  r r  r    /DQNIRUG¶VSDUDPHWHUV Veq    6WUHVVWULD[LDOLW\ Hf     (TXLYDOHQWVWUDLQWRIDLOXUH  D DD    -RKQVRQ&RRNPDWHULDOFRQVWDQWV a b     %DR:LHU]ELFNLPDWHULDOFRQVWDQWV ,QWURGXFWLRQ

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7ERWWRPVLOOVWUDQVYHUVHDQGWXQQHO $7WRSVLOOVWUDQVYHUVHDVVKRZQLQ)LJ7KHVSHFLPHQVKDYHEHHQGLUHFWO\H[WUDFWHGIURPWKHFRPSRQHQWV GHSHQGLQJ RQ WKH VSDFH DYDLODELOLW\ DV UHSUHVHQWHG LQ )LJ  6LQFH WKH\ KDYH EHHQ REWDLQHG E\ WKH H[WUXVLRQ PDQXIDFWXULQJSURFHVVWHQVLOHƒƒDQGƒKDYHEHHQFXWLQRUGHUWRHYDOXDWHWKHDQLVRWURS\VHH)LJ,QWKH FDVHLQZKLFKLWZDVQRWSRVVLEOHWRH[WUDFWWHQVLOHƒDQGƒDVZHOODQ\DQLVRWURS\LQYHVWLJDWLRQKDVEHHQGRQH DQGDQLVRWURSLFPDWHULDOFDUGKDVEHHQGHILQHG

$670 %D >@ DQG $670 % >@ KDYH EHHQ IROORZHG IRU WKH VSHFLPHQV H[WUDFWLRQ 'XH WR WKH OLPLWHGWUDQVYHUVDOVL]HRIWKHFRPSRQHQWVRQO\WKHƒVSHFLPHQVUHVSHFWWKHGLPHQVLRQVXJJHVWHGE\WKHVWDQGDUGV ,QRUGHUWRXVHWKHWHQVLOHWHVWLQJPDFKLQHIRUERWKWKHWHQVLOHDQGWKHVKHDUWHVWVWKHVKHDUVSHFLPHQVGLPHQVLRQV IROORZWKHVWDQGDUG)URPWKH)RUFH±'LVSODFHPHQWFXUYHRIWKHWHQVLOHƒWHVWWKH(QJLQHHULQJ6WUHVV6WUDLQFXUYH KDVEHHQFDOFXODWHG)LJVKRZVWKHZLGHGLVSHUVLRQRIWKHH[SHULPHQWDOUHVXOWVRIWKHWHQVLOHƒWHVWV&XWWLQJWKH VSHFLPHQV IURP GLIIHUHQWIDFHV DQGSRVLWLRQ RI WKH H[WUXGHGSDUW LW LV SRVVLEOH WRREVHUYH KRZ WKHPDQXIDFWXULQJ SURFHVVPD\GLIIHUHQWO\DIIHFWWKHPDWHULDOFKDUDFWHULVWLFV   )LJ7GRRUVLOOVLQUHG7ERWWRPVLOOVWUDQVYHUVHLQYLROHW7WXQQHOLQEOXH$7WRSVLOOVWUDQVYHUVHLQJUHHQ    )LJ([WUDFWLRQRIWKHVSHFLPHQVIURPWKHFKDVVLVFRPSRQHQWV    )LJ7HQVLOHƒƒƒVSHFLPHQV

7KHVHFXUYHVGRQRWWDNHLQWRDFFRXQWWKHUHDOWUHQGRIWKHVWUHVVGXULQJWKHQHFNLQJSKDVH7KHUHIRUH(T KDYH EHHQ XVHG WR HVWLPDWH WKH 7UXH 6WUHVV6WUDLQ FXUYH RI WKH WHQVLOH ƒ WHVW XS WR WKH PD[LPXP IRUFH FRUUHVSRQGLQJWRWKHQHFNLQJSRLQW 







true eng V V H 







true ln eng H H    )LJ(QJLQHHULQJ6WUHVV6WUDLQFXUYHRI7VSHFLPHQV1RUPDOL]HGFXUYHVDUHREWDLQHGGLYLGLQJHDFKRULJLQDOFXUYHE\DFRQVWDQW 7KHQHFNLQJSRLQWKDVEHHQGHWHUPLQHGDFFRUGLQJWR(T true true true d d V V H            $IWHUWKHQHFNLQJSRLQWWKHWUXHV H WUHQGKDVEHHQHVWLPDWHGXVLQJD)($LWHUDWLYHSURFHVV)LJVKRZVWKH OLPLWVXVHGWRGHILQHWKLVWUHQGWKHORZHUERXQGOLPLWGHILQHGE\DQXOOVORSHDQGWKHXSSHUERXQGOLPLWGHILQHGE\ WKHODVWVORSHRIWKHFXUYHEHIRUHWKHQHFNLQJSRLQW7KHFRUUHODWLRQKDVEHHQFDUULHGRQXVLQJDPPPHVKVL]HIRU WKH)(PRGHOV,QIDFWLWLVLPSRUWDQWWRDFFXUDWHO\UHDGWKHVWUHVVDQGWKHVWUDLQLQWKHPDWHULDO$VWXG\RIWKHPHVK VL]H HIIHFW LV SURSRVHG DW WKH HQG RI WKH FKDSWHU 7KH H[SHULPHQWDO )RUFH ± 'LVSODFHPHQW FXUYH KDV EHHQ ILWWHG VXSSRVLQJWKHWUHQGRIWKHWUXHVWUHVVVWUDLQFXUYHLQWKH5DGLRVVPDWHULDOFDUG7RUHVSHFWWKHSK\VLFDOEHKDYLRURI WKHPHWDODQLQFUHDVLQJWUHQGPXVWEHXVHG)LJVKRZVWKH7FRUUHODWLRQXVLQJIRUH[DPSOHRQO\WZRSRLQWV KHQFHWZRVWUDLJKWOLQHVZLWKLQFUHDVLQJVORSH 7KHWUXHVWUHVVVWUDLQFXUYHRIWKHWHQVLOHƒWHVWKDVEHHQXVHGWRVHWWKH+LOO¶VODZ>@5DGLRVV/$:+LOO GHILQHGIRUWKHDQLVRWURSLFEHKDYLRUD\LHOGVXUIDFHDVIROORZLQJ 

















      G   H   L  M  N    V V  V V  V V   V  V  V     

F  G  H  L  M  N DUH WKH PDWHULDO FRQVWDQWV DQG WKH VWUHVVVIJDUH  H[SUHVVHG LQ WKH &DUWHVLDQ UHIHUHQFH

SDUDOOHOWRWKHWKUHHSODQHVRIDQLVRWURS\(TFDQEHVLPSOLILHGXVLQJWKHDVVXPSWLRQRISODQHVWUHVV              Heq A A A A V V  V  V V  V    7KHFRHIILFLHQWVA DUHGHWHUPLQHGXVLQJ/DQNIRUG¶VDQLVRWURS\SDUDPHWHU ri D  

     A H r § ·  ¨ ¸ © ¹       A H r § ·  ¨ ¸ © ¹    A H  





         A H r r r § ·  ¨  ¸ © ¹    R H R       r r r R      )LJ'HILQLWLRQRIWKHSRVWQHFNLQJWUHQGRIWKH5DGLRVVPDWHULDOFDUG  7KH/DQNIRUGSDUDPHWHUVFDQEHVHWLQRUGHUWRREWDLQWKHVSHFLPHQFRUUHODWLRQLQWHUPVRIORDGV,QIDFW+LOO¶V FULWHULRQ GRHV QRW FRQVLGHU WKH DQLVRWURS\ HIIHFWV RQ WKH VWUDLQ 7KH /DQNIRUG SDUDPHWHUV GHILQHG IRU WKH PDWHULDO VWXGLHGDUHOLVWHGLQ7DE$VVKRZQIRUWKH$7WKHLVRWURSLFFRQGLWLRQKDVEHHQVHWQRVSHFLPHQVLQƒDQG ƒZHUHFXWGXHWRWKHOLPLWHGVSDFHDYDLODEOHRQWKHFRPSRQHQW 'XHWRWKHFRPSOH[LW\RI(TD'HVLJQ2I([SHULPHQWVKDVEHHQSHUIRUPHGWRVXSSRUWWKH)RUFH'LVSODFHPHQW ILWWLQJ'R(DOORZVWKHVDPSOHRIWKHGHVLJQGRPDLQDQGDOVRWKHHVWLPDWLRQRIWKHLQIOXHQFHDQGLQWHUDFWLRQVRIWKH YDULDEOHVRQWKHFRQWUROOHGUHVSRQVHV$IXOOIDFWRULDOPHWKRGKDVEHHQXVHGLPSRVLQJWKHFRHIILFLHQWVܣ௜DVYDULDEOHV DQGWKH/DQNIRUGSDUDPHWHUVDVUHVSRQVHV7KLVSUHOLPLQDU\VFUHHQLQJKDVEHHQXVHIXOWRGHWHUPLQHDUHOLDEOHVHWRI VROXWLRQLQWHUPVRIPDWHULDOFRHIILFLHQWVܣ௜)LJVKRZVWKHUHVXOWVRIWKH7DIWHUWXQLQJWKH+LOO¶VPDWHULDO

FDUG ,W LV SRVVLEOH WR QRWLFH WKH VORSHV LQ WHQVLOH ƒƒ DQG VKHDU DUH GLIIHUHQW EHWZHHQ QXPHULFDO DQG H[SHULPHQWDO 7KLV LV GXH WR D ODFN RI D VXLWDEOH H[WHQVRPHWHU GXULQJ WKH H[SHULPHQWDO WHVWV IRU WKLV NLQG RI VSHFLPHQV+RZHYHUWKHIDLOXUHFULWHULDXVHGGRQRWFRQVLGHUWKHDQLVRWURS\HIIHFW+HQFHWKHHTXLYDOHQWVWUDLQWR IDLOXUHLQWHQVLOHƒDIIHFWVWKHƒDQGƒFDVHVDVZHOOWKHFRUUHODWLRQLQWHUPVRIGLVSODFHPHQWVLVQRWUHTXLUHG )XUWKHUK\SRWKHVLVIRUWKHGLVSODFHPHQWVFRUUHODWLRQDUHH[SODLQHGLQWKHQH[WSDUWVRIWKHSDSHU 7DEOH/DQNIRUGSDUDPHWHUVIRU77DQG$7  _ r_  r  r 7    7    $7     7KHIROORZLQJSKDVHGHDOVZLWKWKHILWWLQJRIWKHORDGGURS$IDLOXUHFDUGKDVEHHQDGGHGWRFRQVLGHUWKHVKHOO HOHPHQWVGHOHWLQJDFFRUGLQJWRWKHIUDFWXUHFULWHULD,QWKLVZRUNWZRGLIIHUHQWIDLOXUHPRGHOVKDYHEHHQFRQVLGHUHG %DR:LHU]ELFNL>@DQG-RKQVRQ&RRN>@IDLOXUHPRGHOV7KHVHFULWHULDGHILQHWKHWUHQGRIWKHHTXLYDOHQWVWUDLQWR IDLOXUHGHSHQGLQJRQWKHVWUHVVWULD[LDOLW\ 150 200 250 300 350 400 0,00 0,05 0,10 0,15 0,20 0,25 0,30 TRUE_stress [MPa] TRUE_plastic_strain[] experimentaltrue stress_strain lastslope ToRadioss nullslope neckingpoint

  )LJ5HVXOWVRIWKH7DIWHUWXQLQJWKH+LOO¶VPDWHULDOFDUG





   f D D exp D eq H ª _ V º ¬ ¼  





          _             V V V V V V H V V V V V V ­ f d ° ° ° _{  d  } °  ° ® ° _{  d d} ° ° ° d d °¯ eq I II III eq eq f eq VM eq eq eq eq a b a a b   

ZKHUHVI VII DQGVIIIDUH WKH SULQFLSDO VWUHVV DQG VVMLV WKH 9RQ 0LVHV VWUHVVD  D  D  a  bDUH WKH

PDWHULDOFRQVWDQWV,QWKH-&HTXDWLRQQRWHPSHUDWXUHDQGVWUDLQUDWHHIIHFWKDYHEHHQFRQVLGHUHG

7KHPD[LPXPGLVSODFHPHQWVUHDFKHGGXULQJWKHH[SHULPHQWDOWHVWVKDYHEHHQXVHGWRGHILQHWKHHTXLYDOHQWVWUDLQ WRIDLOXUHRIWKHIUDFWXUHPRGHOVUXQQLQJWKH)(PRGHOVRIWHQVLOHƒ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



x Hf tensileB Hf shearB Æ-&IDLOXUHPRGHO)LJ

x Hf tensileB !Hf shearB Æ%:IDLOXUHPRGHO)LJ

IDLOXUHLQWKH)(VDPSOHV2QWKHOHIWLVVKRZQWKHUXQZLWKRXWIDLOXUHFDUGQRUXSWXUHVRFFXUDQGWKHHTXLYDOHQW VWUDLQ WR IDLOXUH KDV EHHQ H[WUDFWHG DFFRUGLQJ WR WKH H[SHULPHQWDO GDWD 7KH SLFWXUHV DOVR VKRZ WKH GLIIHUHQFHV LQ WHUPV RI IDLOXUH RQ WKH ULJKW ,Q WKH 7 VKHDU VDPSOH WKH FUDFN IRUPDWLRQ RFFXUV FORVH WR WKH HGJH RI WKH FHQWUDOVHFWLRQKLJKWULD[LDOLW\VWDWH,QIDFWXVLQJD-&PRGHOWKHWHQVLOHVWUDLQWRIDLOXUHLVORZHUWKDQWKHVKHDU RQH   )LJ7-&IDLOXUHPRGHO   )LJ7%:IDLOXUHPRGHO 7KHQXPHULFDO)RUFH'LVSODFHPHQWFXUYHVKDYHEHHQFRPSDUHGZLWKWKHH[SHULPHQWDORQHV)RULQVWDQFH)LJ VKRZVWKHFRPSDULVRQIRUWKH7DOOR\,QWKHFDVHRIWKHWHQVLOHƒWHVWVRQO\RQHFXUYHZDVWDNHQDVUHIHUHQFH IRUWKHFRUUHODWLRQGXHWRWKHGLIIHUHQWWKLFNQHVVHVRIWKHVDPSOHVWHVWHG7KHORDGDQGWKHPD[LPXPGLVSODFHPHQWV DUH ZHOO SUHGLFWHG &RQFHUQLQJ WKH WHQVLOH ƒ DQG ƒ FDVHV RQO\ WKH ORDG FDQ EH ILWWHG DV H[SODLQHG EHIRUH WKH IUDFWXUHFULWHULDGRHVQRWFRQVLGHUWKHDQLVRWURS\HIIHFW7KHFRPSDULVRQRIWKHVKHDUWHVWVKRZVGLIIHUHQFHVLQWHUPV RIERWKIRUFHVDQGGLVSODFHPHQWV,QSDUWLFXODUWKHIRUFHVKDYHEHHQXQGHUHVWLPDWHGDQGWKHPD[LPXPGLVSODFHPHQW KDVEHHQRYHUHVWLPDWHG6LQFHWKHH[WHQVRPHWHUZDVQRWVXLWDEOHRQWKHVKHDUVDPSOHVWKHPHDVXUHPHQWVKDYHEHHQ

GLUHFWO\SHUIRUPHGE\WKHFURVVEDURIWKHWHQVLOHPDFKLQHWKLVH[SODLQVWKHVWLIIQHVVGLIIHUHQFHLQWKHILUVWSDUWRI WKHFXUYH   )LJOHIW7ULD[LDOLW\VWUHVVLQWKHVKHDUWHVWVD7ZLWKRXWIDLOXUHE7ZLWKIDLOXUHF7ZLWKRXWIDLOXUH G7ZLWKIDLOXUHULJKW(TXLYDOHQWVWUDLQLQWKHVKHDUWHVWVH7ZLWKRXWIDLOXUHI7ZLWKIDLOXUHJ7ZLWKRXWIDLOXUH K7ZLWKIDLOXUH  )LJOHIW7ULD[LDOLW\VWUHVVLQWKHWHQVLOHWHVWVD7ZLWKRXWIDLOXUHE7ZLWKIDLOXUHF7ZLWKRXWIDLOXUH G7ZLWKIDLOXUHULJKW(TXLYDOHQWVWUDLQLQWKHWHQVLOHWHVWVH7ZLWKRXWIDLOXUHI7ZLWKIDLOXUHJ7ZLWKRXWIDLOXUH K7ZLWKIDLOXUH $VDOUHDG\PHQWLRQHGDPPPHVKVL]HKDVEHHQXVHGLQWKHLQLWLDOFRUUHODWLRQWREHWWHUFDOFXODWHWKHVWUHVVDQG VWUDLQ YDOXHV LQ )($ ,Q D IXOO YHKLFOH PRGHO D FRDUVH PHVKVL]H LV QHHGHG WR UHGXFH WKH FRPSXWDWLRQDO WLPH  PP 7RREWDLQ FRKHUHQWUHVXOWVEHWZHHQ D  PP DQG D  PPPHVKVL]HV PRGHO LW LV QHFHVVDU\ WR GHILQH D PHVKVFDOLQJIXQFWLRQ7KHVFDOLQJIDFWRUGLUHFWO\DIIHFWVWKHIDLOXUHIXQFWLRQWKHJUHDWHULVWKHPHVKVL]HDQGWKH ORZHULVWKHVFDOLQJIDFWRU7KHWHQVLOHƒVSHFLPHQKDVEHHQPRGHOHGZLWKGLIIHUHQWPHVKVL]HV,Q)LJLVVKRZQ WKHPHVKVFDOLQJIXQFWLRQRIWKH7DOOR\,QJHQHUDOLWYDULHVGHSHQGLQJRQWKHPDWHULDOVWXGLHG

&RQFOXVLRQV

7KLV SDSHU DLPV DW GHILQLQJ D PHWKRGRORJ\ LQ RUGHU WR SUHGLFW WKH DOXPLQXP IDLOXUH LQ DXWRPRWLYH FUDVK DSSOLFDWLRQV7KHDFWLYLW\KDVEHHQGHYHORSHGLQFROODERUDWLRQZLWK)HUUDUL6SDDQGLWLVDSUHOLPLQDU\SKDVHRID ZLGHSURMHFWWKDWDLPVDWUHILQLQJWKH)(PRGHOVXVHGLQFUDVKDQDO\VLV

3UHGLFWLYLW\ LQ WKH IDLOXUH RI WKH DOXPLQXP DOOR\V XVXDOO\ UHTXLUHV D KXJH DQG GHWDLOHG H[SHULPHQWDO FDPSDLJQ 7KH SUHVHQW ZRUN WULHV WR SURYLGH D VLPSOLILHG PHWKRGRORJ\ EDVHG RQ D OLPLWHG QXPEHU RI H[SHULPHQWDO WHVWV ,Q H[WUDFWLQJWKHVSHFLPHQGLUHFWO\IURPWKHILQDOFRPSRQHQWVLWLVSRVVLEOHWRFRQVLGHUWKHPDQXIDFWXULQJHIIHFWGXULQJ WKHFRUUHODWLRQV,WKDVEHHQDOVRQRWLFHGWKDWH[WUXGHGFRPSRQHQWVPDGHE\WKHVDPHDOXPLQXPDOOR\EXWVXEMHFWHG

WR GLIIHUHQW H[WUXVLRQ PDWUL[ VKRZ GLIIHUHQW PHFKDQLFDO SURSHUWLHV 7KHUHIRUH GXULQJ WKH QXPHULFDO FRUUHODWLRQ LW FRXOGEHQHFHVVDU\WRGHILQHDVSHFLILFPDWHULDOFDUGIRUHDFKFRPSRQHQWDQGQRWRQO\IRUWKHDOXPLQXPDOOR\FODVV   )LJ&RUUHODWLRQUHVXOWVRI7DOOR\   )LJ'HILQLWLRQRIWKHPHVKVFDOLQJIXQFWLRQRQWKHWHQVLOHƒ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ƒƒDQGƒLWKDVEHHQSRVVLEOHWRLQFOXGHWKHDQLVRWURS\RIWKH PDWHULDOLQWKH)(DQDO\VLVDVZHOO

7KH)(DQDO\VHVRQVDPSOHVKDYHEHHQSHUIRUPHGZLWKDPHVKVL]HRIPPDQG-&DQG%:IDLOXUHFULWHULD KDYH EHHQ QXPHULFDOO\ YDOLGDWHG %RWK FULWHULD DUH SRWHQWLDOO\ FRQYHQLHQW IRU QXPHULFDO VLPXODWLRQ LQ DXWRPRWLYH

ILHOG DOVR EHFDXVH WKH\DUH LQWHJUDWHG LQ WKH PRVW RI WKH H[SOLFLW VROYHUV 7KHVXJJHVWHG PHWKRGRORJ\ WKDQNV WR D GHILQLWLRQRIDPHVKVFDOLQJIXQFWLRQLVPHVKVL]HLQGHSHQGHQWDQGLWFRXOGEHDSSOLHGWRWKH)XOO9HKLFOHPRGHOV WKDWXVXDOO\SUHVHQWDPHGLXPPHVKVL]HJUHDWHUWKDQPP7KHPHVKVL]HHIIHFWKDVEHHQHYDOXDWHGRQWKHWHQVLOH ƒ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

$FNQRZOHGJHPHQWV

$FNQRZOHGJPHQWV WR )HUUDUL 6SD DQG LQ SDUWLFXODU WR (QJ $QGUHD 0HUXOOD DQG (QJ /XFD '¶$JRVWLQR IRU VXSSRUWLQJWKHUHVHDUFKDFWLYLW\

5HIHUHQFHV

>@ $*$WNLQV)UDFWXUH PHFKDQLFVDQG PHWDOIRUPLQJGDPDJH PHFKDQLFV DQGWKHORFDODSSURDFKRI\HVWHUGD\DQGWRGD\+35RVVPDQLWK (G)UDFWXUH5HVHDUFKLQ5HWURVSHFW$Q$QQLYHUVDU\9ROXPHLQ+RQRXURI*HRUJH5,UZLQVWK%LUWKGD\$$%DONHPD5RWWHUGDP %URRNILHOGSS± >@ )$0F&OLQWRFN6OLSOLQHIUDFWXUHPHFKDQLFV$QHZUHJLPHRIIUDFWXUHPHFKDQLFV)DWLJXHDQG)UDFWXUH0HFKDQLFV$670673 :HVW&RQVKRKRFNHQ3$ >@ 7:LHU]ELFNL<%DR<:/HH<%DL&DOLEUDWLRQDQGHYDOXDWLRQRIVHYHQIUDFWXUHPRGHOV,QW-0HFK6FL± >@ <%DL(IIHFWRI/RDGLQJ+LVWRU\RQ1HFNLQJDQG)UDFWXUH0DVVDFKXVHWWV,QVWLWXWHRI7HFKQRORJ\3K'WKHVLV

>@ $670 %D 6WDQGDUG 7HVW 0HWKRGV RI 7HQVLRQ 7HVWLQJ :URXJKW DQG &DVW $OXPLQXP DQG 0DJQHVLXP$OOR\ 3URGXFWV $670 ,QWHUQDWLRQDO:HVW&RQVKRKRFNHQ3$ >@ $670%6WDQGDUG7HVW0HWKRGIRU6KHDU7HVWLQJRI7KLQ$OXPLQXP$OOR\3URGXFWV$670,QWHUQDWLRQDO:HVW&RQVKRKRFNHQ 3$ >@ $OWDLU(QJLQHHULQJ,QF$OWDLU+\SHU:RUNV5$',2668VHU¶V*XLGH7UR\0LFKLJDQ86$ >@ *5-RKQVRQ:+&RRN)UDFWXUHFKDUDFWHULVWLFVRIWKUHHPHWDOVVXEMHFWHGWRYDULRXVVWUDLQVVWUDLQUDWHVWHPSHUDWXUHVDQGSUHVVXUHV (QJLQHHULQJ)UDFWXUH0HFKDQLFV >@ <:/HH)UDFWXUH3UHGLFWLRQLQ0HWDO6KHHWV0DVVDFKXVHWWV,QVWLWXWHRI7HFKQRORJ\3K'WKHVLV