Keywords:steel wire reinforced aluminum; MMC; failure; fracture; maximum shear stress criterion. 1. .... At pure tension in wire direction, a low yield strain of.
Available online at www.sciencedirect.com
ScienceDirect Procedia CIRP 18 (2014) 144 – 149
,QWHUQDWLRQDO&RQIHUHQFHRQ0DQXIDFWXUHRI/LJKWZHLJKW&RPSRQHQWV±0DQX/LJKW
7KHUPRPHFKDQLFDOEHKDYLRUDQGPDWHULDOIDLOXUH RIVWHHOZLUHUHLQIRUFHGDOXPLQXP $0RUDVFK 0:HGHNLQG'0DWLDV+%DLHU ,QVWLWXWHRI/LJKWZHLJKW6WUXFWXUHV780QFKHQ*HUPDQ\
&RUUHVSRQGLQJDXWKRU7HO ID[ E-mail address PRUDVFK#OOEPZWXPGH
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© 2014 Elsevier B.V. This is an open access article under the CC BY-NC-ND license 7KH$XWKRUV3XEOLVKHGE\(OVHYLHU%9 (http://creativecommons.org/licenses/by-nc-nd/3.0/). 6HOHFWLRQ DQG SHHUUHYLHZ XQGHU UHVSRQVLELOLW\ RI WKH ,QWHUQDWLRQDO 6FLHQWLILF &RPPLWWHH RI WKH ³,QWHUQDWLRQDO &RQIHUHQFH RQ Peer-review under responsibility of the International Scientific Committee of the “International Conference on Manufacture 0DQXIDFWXUHRI/LJKWZHLJKW&RPSRQHQWV±0DQX/LJKW´LQWKHSHUVRQRIWKH&RQIHUHQFH&KDLU3URI$(UPDQ7HNND\D of Lightweight Components – ManuLight 2014” Keywords:VWHHOZLUHUHLQIRUFHGDOXPLQXP 00& IDLOXUH IUDFWXUH PD[LPXPVKHDUVWUHVVFULWHULRQ
,QWURGXFWLRQ ,Q WKH FROODERUDWLYH UHVHDUFK SURMHFW 6)% 7UDQVUHJLR DQ H[WUXVLRQ SURFHVV IRU FRPSRVLWH VHFWLRQV LV EHLQJ LQYHVWLJDWHG 2QH DSSOLFDWLRQ LV WKH LQWHJUDWLRQ RI VWHHO ZLUHV DV UHLQIRUFHPHQW WR DQ DOXPLQXP PDWUL[ RI H[WUXGHG VHFWLRQV %\ LQWURGXFLQJ WKH ZLUHV PHFKDQLFDO SURSHUWLHV VXFK DV VWLIIQHVV DQG VWUHQJWK FDQ EH DGMXVWHG ORFDOO\ DOORZLQJ IRU WDLORUHG UHLQIRUFHPHQWV )RU DQ DSSOLFDWLRQ RI WKH PDWHULDO LQ ORDGEHDULQJ VWUXFWXUHV LWV RUWKRWURSLF VWLIIQHVV DQG VWUHQJWKV PXVW EH NQRZQ 6WLIIQHVV DQG VWUHQJWK DUH DIIHFWHGE\WKHUPDOO\LQGXFHGUHVLGXDOVWUHVVHVWKDWDULVH E\ MRLQLQJ VWHHO ZLUHV DQG DOXPLQXP PDWUL[ DW KLJK WHPSHUDWXUHVDQGKDYHWREHWDNHQLQWRDFFRXQW ,Q WKH VHFRQG FKDSWHU WKH PHFKDQLFDO SURSHUWLHV RI VWHHOZLUHUHLQIRUFHGDOXPLQXP VKRZQLQ)LJXUH DUH GLVFXVVHG IRU D ZLUH FRQWHQW RI ZLWK UHVSHFW WR UHVLGXDOVWUHVVHV)RUHIILFLHQWFRPSXWDWLRQDODQDO\VLVD KRPRJHQL]HGVKHOOPRGHORIWKHPDWHULDOLVSUHVHQWHG 8VLQJKLJKVWUHQJWKVWHHOZLUHVDVUHLQIRUFHPHQWVRID
GXFWLOHDOXPLQXPPDWUL[WKHUHLQIRUFHGDOXPLQXPRIIHUV VLJQLILFDQWO\ LQFUHDVHG VWUHQJWK LQ ZLUH GLUHFWLRQ ZKLOH PDLQWDLQLQJ JRRG GXFWLOLW\ 7KLV DVSHFW VKRZV SRWHQWLDO IRUWKHDSSOLFDWLRQLQFUDVKHQHUJ\DEVRUELQJVWUXFWXUHV $ PDWHULDO PRGHO LQFOXGLQJ WKH GHVFULSWLRQ RI PDWHULDO IUDFWXUH LV GHULYHG DQG WHVWHG LQ D WKUHHSRLQW EHQGLQJ WHVWRIUHLQIRUFHGUHFWDQJXODUVHFWLRQV )LJXUH
)LJ+\EULGPDWHULDOZLWKZLUHYROXPHFRQWHQWRI
7KHUPRHODVWLFSURSHUWLHVRIVWHHOZLUHUHLQIRUFHG DOXPLQXP 7KH HODVWLF SURSHUWLHV RI VWHHO ZLUH UHLQIRUFHG DOXPLQXP DUH VWURQJO\ LQIOXHQFHG E\ WKH ZLUHV 7KH ZLUHV KDYH D VWLIIHQLQJ HIIHFW DOWKRXJK WKH\ LQWURGXFH UHVLGXDO VWUHVVHV GXH WR D GLIIHUHQFH LQ FRHIILFLHQWV RI WKHUPDO H[SDQVLRQ &7( 6LPXODWLRQV RI WKH PDWHULDO
2212-8271 © 2014 Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Peer-review under responsibility of the International Scientific Committee of the “International Conference on Manufacture of Lightweight Components – ManuLight 2014” doi:10.1016/j.procir.2014.06.122
A. Morasch et al. / Procedia CIRP 18 (2014) 144 – 149
VXEMHFWHG WR D WKHUPDO ORDG DV LQ WKH H[WUXVLRQ SURFHVV IROORZHG E\ D PHFKDQLFDO ORDGLQJ DOORZ IRU DQ DVVHVVPHQWRIVWLIIQHVVDQG\LHOGVWUHQJWKZLWKUHVSHFWWR UHVLGXDO VWUHVVHV 7KLV PHWKRGRORJ\ LV GHVFULEHG LQ WKH IROORZLQJDQGYHULILHGZLWKH[SHULPHQWV 2.1. Thermo-elastic properties of the constituents $VDQLQSXWIRUDQDO\VHVWKHHODVWLFSURSHUWLHVDQGWKH &7( RI DOXPLQXP PDWUL[ DQG VWHHO ZLUH DUH QHHGHG ([HPSODU\ D GXFWLOH DOXPLQXP DOOR\ (1$: DQGKLJKVWUHQJWKVWHHOZLUHV ;&U1L DUHFKRVHQ 0DWUL[ DQG ZLUH ZHUH WHVWHG LQ WHQVLOH WHVWV JLYLQJ WKH HODVWLF SURSHUWLHV OLVWHG LQ 7DEOH )RU WKDW WHVW VSHFLPHQV IRU WKH DOXPLQXP PDWUL[ ZHUH FXW IURP H[WUXGHGIODWEDUVKDYLQJWKHVDPHJHRPHWU\DQGWHPSHU FRQGLWLRQ ) DV WKH UHLQIRUFHG EDUV PHDQLQJ WKDW QR VSHFLDOWHPSHULQJZDVSHUIRUPHG
145
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ǻ7 . 7KH HTXLYDOHQW FRROLQJ LV ORZHU WKDQ WKH DFWXDO FRROLQJ ǻ7§& EHFDXVH ORZHU PDWHULDO VWUHQJWKV DW KLJK WHPSHUDWXUHV DUH QRW FRQVLGHUHG &RPSDULQJ WKH H[SHULPHQWDO VWUHVV VWUDLQFXUYHWRDVLPXODWHGRQHZLWKRXWUHVLGXDOVWUHVVHV VKRZVWKDWRQFHPDWUL[DQGZLUHEHKDYHSODVWLFDOO\WKH UHVLGXDO VWUHVVHV DUH UHOHDVHG DQG UHJLRQ ,,, LV DOPRVW XQDIIHFWHG
7DEOH3URSHUWLHVRIDOXPLQXPPDWUL[DQGVWHHOZLUH 3URSHUW\
6WHHOZLUH
$OXPLQXP
@ ZDV FKRVHQIRUWKHGHVFULSWLRQRIPDWUL[IDLOXUHDQGWKHHIIRUW LVDVIROORZV Eff matrix
§ V __ ¨ ¨V © __PD[
· ¸ ¸ ¹
§ VA ¨ ¨V © APD[
· ¸ ¸ ¹
V __V A
V __PD[
§ W A__ ¨ ¨W © A__PD[
· ¸ ¸ ¹
$WSXUHWHQVLRQLQZLUHGLUHFWLRQDORZ\LHOGVWUDLQRI WKHZLUHFDQLQLWLDWHSODVWLFEHKDYLRXU
Eff wire
§ H __wire · ¨ ¸ ¨H ¸ © __wirePD[ ¹
'HERQGLQJRIWKHLQWHUIDFHPDLQO\RFFXUVGXHWRQRUPDO WHQVLOH VWUHVVHV DW WKH LQWHUIDFH 7KHUHIRUH WKH HIIRUW RI WKHLQWHUIDFHLV Eff Interface
§ V ¨ A ¨ ¨ V InterfacePD[ ©
V
6WUDLQKDUGHQLQJDQGIUDFWXUHRIVWHHOZLUH UHLQIRUFHGDOXPLQXP )RU KLJK SODVWLF VWUDLQV İS! DV W\SLFDOO\ RFFXUULQJ GXULQJ LPSDFW SURFHVVHV UHVLGXDO VWUHVVHV SOD\ RQO\ D PLQRU UROH $ KLJK HQHUJ\ DEVRUSWLRQ FDQ EH UHDFKHG ZLWKKLJKIORZVWUHVVHV'XHWRWKHKLJK\LHOGVWUHQJWKRI WKH ZLUHV WKH IORZ VWUHVVHV RI WKH UHLQIRUFHG DOXPLQXP LQ ZLUH GLUHFWLRQ DUH LQFUHDVHG VLJQLILFDQWO\ DOUHDG\ DW ORZZLUHYROXPHFRQWHQWV>@5DGLDOO\VXSSRUWHGE\WKH DOXPLQXPPDWUL[QHFNLQJLVSRVWSRQHGDQGORZIUDFWXUH VWUDLQV İI RI WKH ZLUHV DUH LQFUHDVHG WR D[LDO VWUDLQVRIDERXW,QFUHDVHGIORZVWUHVVHVPDNHVVWHHO ZLUH UHLQIRUFHG DOXPLQXP LQWHUHVWLQJ IRU HQHUJ\ DEVRUSWLRQ IRU ORDG FDVHV ZLWK GRPLQDWLQJ WHQVLRQ LQ ZLUHGLUHFWLRQ$VWKHVWUDLQKDUGHQLQJLQIRUPDWLRQIURP WHQVLOH WHVWV LV OLPLWHG WR WKH XOWLPDWH VWUDLQ DW QHFNLQJ FD IRU WKH ZLUH IRU WKH DOXPLQXP PDWUL[ VWUDLQKDUGHQLQJGDWDKDVWREHH[WUDSRODWHG
7KLV FDQ EH LQWURGXFHG WR WKH ILWWLQJ DV D VHW RI WZR FRQVWUDLQWV fit dV fit _H H V H u G d u dH
· ¸ ¸ ¸ ¹
$V WKH IDLOXUH PRGHV GHVFULEH WKH RQVHW RI SODVWLFLW\ WKHUHLVDSSDUHQWO\QRLQWHUDFWLRQEHWZHHQWKHPDQGWKH FRPSOHWHIDLOXUHFULWHULRQLV Eff total PD[ Eff matrix Eff wire Eff Interface
VKRXOG EH FKRVHQ DV WKH VWUDLQ KDUGHQLQJ IXQFWLRQ RI PRVWDOXPLQXPDOOR\VLVNQRZQWRVDWXUDWH$JRRGILWWR WKH H[SHULPHQWDO GDWD LV REWDLQHG XVLQJ WKH +RFNHWW 6KHUE\IXQFWLRQ>@ )LJXUH ı\ LV WKH XQLD[LDO \LHOG VWUHQJWK ı6 S DQG 1 DUH ILWWLQJ SDUDPHWHUV p V V s V s V y H[S N H 7KHTXDOLW\RIWKHH[WUDSRODWHGVWUDLQKDUGHQLQJFXUYH FDQEHLPSURYHGE\LQWURGXFLQJ&RQVLGqUHVFULWHULRQ>@ WRWKHILWWLQJSURFHGXUH&RQVLGqUHVFULWHULRQVWDWHVWKDW QHFNLQJLQXQLD[LDOWHQVLRQVHWVLQDWPD[LPXPIRUFHDQG WKXV SURYLGHV DGGLWLRQDO NQRZOHGJH WR WKH ILWWLQJ SURFHGXUH 7UDQVODWHG LQWR WKH UHJLPH RI WUXH VWUHVVHV DQGWUXHVWUDLQV&RQVLGqUHVFULWHULRQLV dV _H H V H u u dH
H[S
H u V fit H u G d
&RQVWUDLQW HQVXUHVWKDWDWWKHSRLQWRIXOWLPDWHVWUDLQ &RQVLGqUHVFULWHULRQLVIXOILOOHGZLWKLQDFHUWDLQOLPLWį &RQVWUDLQW HQVXUHV WKDW WKH XOWLPDWH VWUHVV RI WKH ILWWHG IXQFWLRQ HTXDOV WKH H[SHULPHQWDO XOWLPDWH VWUHVV ZLWKLQ WKH OLPLW į 7HQVLOH WHVWV RI WKH KLJKVWUHQJWK VWHHO ZLUHV ZHUH SHUIRUPHG JLYLQJ YDOXHV RI 7DEOH 'XHWRORZSODVWLFKDUGHQLQJFDSDELOLWLHVLWLVUHDVRQDEOH WRPRGHOWKHZLUHDVHODVWLFSHUIHFWO\SODVWLF 3.2. Strain rate hardening 'XULQJLPSDFWSURFHVVHVVWUDLQUDWHVLQKLJKO\ORDGHG UHJLRQV FDQ EH DV KLJK DV VHYHUDO H V ,I D PDWHULDOH[KLELWVDVWUDLQUDWHVHQVLWLYHVWUDLQKDUGHQLQJ WKLV KDV D QRQQHJOLJLEOH LQIOXHQFH RQ WKH VWUXFWXUDO UHVSRQVH +RZHYHU PRVW DOXPLQXP DOOR\V RQO\ VKRZ OLWWOHVWUDLQUDWHVHQVLWLYLW\ZKLFKFDQRIWHQEHQHJOHFWHG $VLPLODUDOXPLQXPDOOR\(1$: 7 ZDVWHVWHG LQDKLJKVSHHGWHQVLOHWHVWLQJPDFKLQHDWGLIIHUHQWVWUDLQ UDWHV GRQH E\ ,$0±.DUOVUXKHU ,QVWLWXW IU 7HFKQRORJLH 7KH VWUDLQ KDUGHQLQJ FXUYHV LQ )LJXUH FRQILUP D VPDOO VWUDLQ UDWH GHSHQGHQFH ZKLFK LV FRQVLGHUHGQHJOLJLEOHIRUIXUWKHUUHVHDUFK ([SHULPHQWDOGDWDIRUVWHHOZLUHVLVQRWDYDLODEOHIRU KLJKVWUDLQUDWHV+RZHYHUWHVWVRIVLPLODUKLJKVWUHQJWK VWHHODOOR\VVXJJHVWWKDWVWUDLQUDWHHIIHFWVDUHVPDOODQG FDQDOVREHQHJOHFWHG>@ 0RGHOLQJRIIDLOXUHDQGIUDFWXUH
3.1. Extrapolation of the material´s strain hardening $Q H[WUDSRODWLRQ IXQFWLRQ RIIHULQJ D VDWXUDWLRQ VWUHVV
0RGHOLQJ WKH PDWHULDOV IDLOXUH DQG IUDFWXUH WKH
147
A. Morasch et al. / Procedia CIRP 18 (2014) 144 – 149
IRUPLQJ OLPLWV RI WKH PDWUL[ DUH XVHG DV D FULWHULRQ IRU RQVHW QHFNLQJ DV GXFWLOH IDLOXUH ,Q RUGHU WR DOVR FRYHU VKHDU GRPLQDWHG IUDFWXUH WKH PD[LPXP VKHDU VWUHVV FULWHULRQLVXVHG)RUWKHWKLQZLUHVZLWKPRVWO\XQLD[LDO WHQVLRQ VWUHVVHV D PD[LPXP VWUDLQ FULWHULRQ LV XVHG $OVR IDLOXUH RI WKH LQWHUIDFH HJ ZLUH GHERQGLQJ FDQ DFFHOHUDWHWKHIUDFWXUHSURFHVVDQGQHHGVWREHDVVHVVHG
VWDWLVWLFDO YDULDWLRQ RI WKH VKHHW WKLFNQHVV IROORZLQJ D *DXVVLDQ GLVWULEXWLRQ ZKLFK ZDV ILUVW VXJJHVWHG E\ /DGHPR >@ 7KH PDJQLWXGH RI WKH GLIIHUHQFH LQ VKHHW WKLFNQHVVǻWLVFDOLEUDWHGDFFRUGLQJWRWKHQHFNLQJVWUDLQ IURP XQLD[LDO WHQVLOH WHVW JLYLQJ ǻW W 7KH VWDQGDUG GHYLDWLRQ ı LV FKRVHQ DV ı ǻW 7KH VR GHWHUPLQHG QHFNLQJ VWUDLQV DUH VKRZQ LQ )LJXUH DQG DUHLPSOHPHQWHGLQWRWKHVLPXODWLRQSURJUDP/6' @
)LJ6WUDLQUDWHGHSHQGHQWVWUDLQKDUGHQLQJRI(1$:7
4.1 Fracture model for the aluminum matrix based on forming limits and the maximum shear stress criterion
)LJXUH6LPXODWLRQPRGHOIRUWKHGHWHUPLQDWLRQRIIRUPLQJOLPLWV VWUHWFKHGDWDJOREDOVWUDLQUDWLRRIİPLQİPDM
6WUDLQ VWDWH GHSHQGHQW IRUPLQJ OLPLWV DUH GHWHUPLQHG ZLWKDVLPXODWLRQPRGHORIDQDOXPLQXPVKHHWZKLFKLV VWUHWFKHG DW GLIIHUHQW JOREDO VWUDLQ UDWLRV )LJXUH 1HFNLQJLVGHWHUPLQHGRQFHWKHPD[LPXPVWUDLQUDWHLQ WKLFNQHVV GLUHFWLRQ LQ WKH PRGHO H[FHHGV WKH PLQLPXP VWUDLQUDWHE\DIDFWRUEHWD E
HPD[ HPLQ
&KRRVLQJ WKH YDOXH IRU EHWD WRR KLJK UHVXOWV LQ RYHUSUHGLFWHGIRUPLQJOLPLWVFKRRVLQJEHWDWRRFORVHWR XQLW\ VPDOO VWUDLQ UDWH IOXFWXDWLRQV LQ WKH PRGHO DUH PLVLQWHUSUHWHG DV QHFNLQJ :LWK EHWD QHFNLQJ ZDV GHWHUPLQHGVKRUWO\DIWHURQVHW )RUPLQJOLPLWVIXUWKHUPDLQO\GHSHQGRQ x 6WUDLQKDUGHQLQJ x @ m m m ) V V V V V V V y 7KH\LHOGH[SRQHQWPLVUHODWHGWRWKHODWWLFHVWUXFWXUH DQGLVFKRVHQDVP IRUIDFHFHQWHUHGFXELFDOXPLQXP 0DWHULDO DQG JHRPHWULF LPSHUIHFWLRQV DUH PRGHOHG DV D
)LJXUH6LPXODWHGIRUPLQJOLPLWGLDJUDPZLWKFDOLEUDWLRQSRLQWIURP WHQVLOHWHVW
4.2 Evolution of necking failure (VSHFLDOO\ WKLFN VKHHW KDV D KLJK UHPDLQLQJ IRUPLQJ FDSDELOLW\DIWHURQVHWRIQHFNLQJZKLFKGRHVQRWOHDGWR VXGGHQ IUDFWXUH 7KXV WKH IRUPLQJ OLPLWV DUH XVHG DV D FULWHULRQIRURQVHWRIIDLOXUHZKLFKHYROYHVDFFRUGLQJWR D IDLOXUH HYROXWLRQ XQWLO ILQDO IUDFWXUH 7KH DSSOLHG IDLOXUHHYROXWLRQZDVSURSRVHGE\%RUYDOOHWDO>@DQG LV DYDLODEOH LQ /6'@XVLQJWKH+ROORPRQVWUDLQKDUGHQLQJ IXQFWLRQ ILWWHGWRH[SHULPHQWDOVWUDLQKDUGHQLQJGDWD Hf
° C® °¯
Hf
° C® °¯
D D
D D D D
n
½° ¾ °¿
for
D D
n
½° ¾ °¿
for D
E
Į LV WKH VWUDLQ UDWLR İPLQİPDM DQG Q LV WKH +ROORPRQ KDUGHQLQJ H[SRQHQW 7KH FDOLEUDWLRQ FRQVWDQW & LV GHILQHG IURP WKH IUDFWXUH VWUDLQ RI D VKHDU WHVW RI D IODW VKHDU VSHFLPHQ VKRZQ LQ )LJXUH ZKLFK SURYLGHV D VWUHVV VWDWH FORVH WR SXUH VKHDU >@ )RU VKHDU IUDFWXUH WKH VDPH HYROXWLRQ IXQFWLRQV DUH XVHG DV IRU QHFNLQJ IDLOXUH\HWZLWKDORZHUXOWLPDWHGHIRUPDWLRQDIWHURQVHW RI IUDFWXUHXIS LQRUGHU WR DFFRXQW IRUFUDFNJURZWK WKURXJKWKHIUDFWXULQJHOHPHQW 4.4 Maximum strain criterion for the steel wires )RU WKLQ VWHHO ZLUHV DQG PRVWO\ WHQVLRQ LQ ZLUH GLUHFWLRQDIUDFWXUHFULWHULRQDFFRUGLQJWRWKHPD[LPXP SODVWLFVWUDLQLQWKHZLUHLVFKRVHQ H f H p PD[ 7KHIUDFWXUHVWUDLQZDVWDNHQIURPWKHWHQVLOHWHVWVRI WKHUHLQIRUFHGDOXPLQXPDV H p PD[
)LJXUH6KHDUVSHFLPHQDQGIUDFWXUHVWUDLQVSUHGLFWHGIURPPD[LPXP VKHDUVWUHVVFULWHULRQDQGIURPVLPXODWHGIRUPLQJOLPLWV
4.5 Interface failure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
)LJXUH5HLQIRUFHGVSHFLPHQIRUWKUHHSRLQWEHQGLQJ
5.1 Comparison of simulated and experimental bending test &RPSDULQJ H[SHULPHQWDO DQG VLPXODWHG IRUFH GLVSODFHPHQW FXUYH LQ )LJXUH E VKRZV D JRRG DJUHHPHQWXQWLOSHDNIRUFH$WWKLVIRUFHWKHPDWUL[KDV WR EHDU KLJK VWUDLQV İS! VR WKDW PDWFKLQJ WKH H[SHULPHQWDOPD[LPXPIRUFHDUJXHVIRUWKHGHWHUPLQHG VWUDLQKDUGHQLQJH[WUDSRODWLRQ )LJXUHDVKRZVVLPXODWHGDQGH[SHULPHQWDOSULQFLSDO VWUDLQ LQ WKH VLGH RI WKH VHFWLRQ DQG IUDFWXUH DW D SXQFK GLVSODFHPHQW RI PP 7KH VHFWLRQV GHIRUPDWLRQ DQG WKH VWUDLQ GLVWULEXWLRQ DJUHH UHDVRQDEO\ ZHOO @ )RUWKHSUHGLFWLRQRIIUDFWXUHDPDWHULDOPRGHOIRUD VKHOOEHDP UHSUHVHQWDWLRQ LV FDOLEUDWHG DQG WHVWHG LQ WKUHHSRLQW EHQGLQJ WHVWV 7KH VWUDLQ KDUGHQLQJ
149
SURSHUWLHV DUH GHWHUPLQHG IURP WHQVLOH WHVWV DQG H[WUDSRODWHGZLWKDFRQVWUDLQHGILWWLQJDSSURDFK $ IUDFWXUH PRGHO EDVHG RQ IRUPLQJ OLPLWV DQG WKH PD[LPXPVKHDUVWUHVVFULWHULRQLVSUHVHQWHGDQGWHVWHGLQ D WKUHHSRLQW EHQGLQJ WHVW RI D UHLQIRUFHG VHFWLRQ VKRZLQJJRRGDJUHHPHQWRIH[SHULPHQWDQGVLPXODWLRQ +RZHYHU SRVVLEOH OLPLWDWLRQV WR WKH VKHOOEHDP PRGHO ZHUHLGHQWLILHG)RUWKHVHFDVHVDYROXPHPRGHOZLWKD PRUHFRPSOH[GHVFULSWLRQRIIUDFWXUH IRULQVWDQFHE\WKH *XUVRQ PRGHO DQG DOVR WDNLQJ LQWR DFFRXQW LQWHUIDFH IDLOXUHKDVWREHFKRVHQ $FNQRZOHGJHPHQWV 7KH UHVHDUFK SUHVHQWHG LQ WKLV SDSHU ZDV FDUULHG RXW ZLWKLQ WKH 7UDQVUHJLRQDO &ROODERUDWLYH 5HVHDUFK &HQWHU 6)%7UDQVUHJLR VXESURMHFW & ZKLFK LV NLQGO\ VXSSRUWHGE\WKH*HUPDQ5HVHDUFK)RXQGDWLRQ ')* 5HIHUHQFHV >@ ) =DHK $ ( 7HNND\D 0 /DQJKRUVW 0 5XKVWRUIHU $ 6FKREHU ' 3LHW]ND ([SHULPHQWDO DQG QXPHULFDO LQYHVWLJDWLRQ RI WKH SURFHVV FKDLQ IURP FRPSRVLWH H[WUXVLRQ WR IULFWLRQ VWLU ZHOGLQJ UHJDUGLQJ WKH UHVLGXDO VWUHVVHV LQ FRPSRVLWH H[WUXGHGSURILOHV3URG(QJ5HV'HYHO9ROSS >@ 0 :HGHNLQG &KDUDNWHULVLHUXQJ YRQ 6WHLILJNHLW XQG )HVWLJNHLWKHWHURJHQYHUVWl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± 7UDQV $60(SS >@ 2 * /DGHPR 7 %HUVWDG 2 6 +RSSHUVWDG . 2 3HGHUVHQ $ QXPHULFDO WRRO IRU IRUPDELOLW\ DQDO\VLV RI DOXPLQXP DOOR\V3DUW, 7KHRU\6WHHO*ULSV6XSSO0DWHULDO)RUPLQJ > @ : 0VFKHQERUQ + 0 6RQQH (LQIOX GHV )RUPlQGHUXQJVZHJHV DXI GLH *UHQ]IRUPlQGHUXQJHQ GHV )HLQEOHFKHV$UFK(LVHQKWWHQZHVHQ9ROSS >@ 7 %RUYDOO 7 -RKDQVVRQ 0 6FKLOO $ *HQHUDO 'DPDJH ,QLWLDWLRQ DQG (YROXWLRQ 0RGHO ',(0 LQ /6'
