Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 130 (2015) 446 – 452 WK,QWHUQDWLRQDO&RQIHUHQFHRQ3UHVVXUH9HVVHO7HFKQRORJ\ (YDOXDWLRQRID3LSH)ODQJH&RQQHFWLRQ5HSODFLQJ)XVLRQ:HOGLQJ ,%DUVRXPD $0.KDODID a Department of Mechanical Engineering, The Petroleum Institute, P.O. Box 2533, Abu Dhabi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© 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license 7KH$XWKRUV3XEOLVKHGE\(OVHYLHU/WG (http://creativecommons.org/licenses/by-nc-nd/4.0/). 3HHUUHYLHZXQGHUUHVSRQVLELOLW\RIWKHRUJDQL]LQJFRPPLWWHHRI,&397 Peer-review under responsibility of the organizing committee of ICPVT-14 Keywords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mail address:LEDUVRXP#SLDFDH 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 organizing committee of ICPVT-14 doi:10.1016/j.proeng.2015.12.238 I. Barsoum and A.M. Khalaf / Procedia Engineering 130 (2015) 446 –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´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´SLSHZLWKDQRPLQDORXWHUSLSHGLDPHWHURIPPDQGDQRPLQDO LQQHUGLDPHWHURIPP 2.1. True Stress-Strain Curves 7KH8QLD[LDOWHQVLOHWHVWVDUHFRQGXFWHGRQERWKVSHFLPHQVFXWRXWIURPERWKWKHSLSHDQGWKHIODQJH,Q)LJ D WKHWUXHVWUHVVYHUVXVWUXHVWUDLQIURPWKHXQLD[LDOWHVWVDUHVKRZQIRUERWKPDWHULDOV 7KH H[SHULPHQWDO GDWD DQG WKH %ULGJPDQ GDWD ZHUH FXUYHILWWHG WR REWDLQ WKH IROORZLQJ H[SRQHQWLDO KDUGHQLQJ VWUHVVVWUDLQPRGHOJLYHQE\HTQ ZKHUHE LVWKHPRGXOXVRIHODVWLFLW\ V GHQRWHVWKHPRGHO\LHOGVWUHVVn LV WKH VWUDLQKDUGHQLQJ H[SRQHQW DQG WKHQRUPDOL]LQJ VWUDLQ H V E 7KH PRGHOSDUDPHWHUV DUH OLVWHG LQ WDEOH 7KHH[SHULPHQWDOO\REWDLQHGRIIVHW\LHOGVWUHQJWKSyIRUERWKWKHPDWHULDOVDUHDOVRUHSRUWHGLQWDEOH 448 I. Barsoum and A.M. Khalaf / Procedia Engineering 130 (2015) 446 – 452 ­ EH ° n V ® §H · °V ¨ ¸ ¯ © H ¹ H d H H ! H D E )LJ D 7UXHVWUHVVVWUDLQEHKDYLRUIRU6$ SLSH DQG6$ IODQJH DQG E GXFWLOHIDLOXUHORFXVIRU6$ SLSH 7DEOH3ODVWLFLW\PRGHOSDUDPHWHUVLQHTQ S y 0DWHULDO 03D E V0 *3D n H0 03D 6$*U% 3LSH 6$1 )ODQJH 2.2. Ductile Failure Locus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h V s ,Q > @ WKH GXFWLOH IDLOXUH ORFXV IRU 6$ *U % LV GHWHUPLQHG H[SHULPHQWDOO\ ,Q )LJ E WKH UHVXOWLQJ IDLOXUH ORFXV HJ H f YHUVXV T DW IDLOXUH REWDLQHG IURP >@ LV SORWWHG ZKHUH WKH VROLG PDUNHUV SHUWDLQ WR H[SHULPHQWDOGDWD$VZRXOGEHH[SHFWHGIURPYRLGJURZWKDQGFRDOHVFHQFHGULYHQPRGHOV>@WKHVWUDLQWR IDLOXUHLQFUHDVHVZLWKGHFUHDVHLQWULD[LDOLW\LQDQH[SRQHQWLDOPDQQHU+HQFHWKHH[SHULPHQWDOGDWDLVFXUYHILWWHG WRDQH[SRQHQWLDOIXQFWLRQJLYHQE\HTQ ZKHUHWKHSDUDPHWHUVDUHGHWHUPLQHGWREHA DQGB Hf T Ae BT $60( ERLOHU DQG SUHVVXUH YHVVHO FRGH 6HFWLRQ 9,,, 'LYLVLRQ >@ SURYLGHV D ORFDO VWUDLQ OLPLW FULWHULRQ WR SURWHFWSUHVVXUHYHVVHOVDJDLQVWORFDOIDLOXUHXQGHUDSSOLHGORDGV7KHSLSHPDWHULDO6$*U%LVDIHUULWLFFDUERQ VWHHODQGLWVFRUUHVSRQGLQJIDLOXUHORFXVGHULYHGIURP>@LVSORWWHGLQ)LJ E GDVKHGEOXHOLQH 449 I. Barsoum and A.M. Khalaf / Procedia Engineering 130 (2015) 446 – 452 +HQFHWKHIDLOXUHORFXVGHULYHGIURPHTQ LVLPSOHPHQWHGLQWKHILQLWHHOHPHQWPRGHOWRDFFRXQWIRUGXFWLOH IDLOXUHRIWKHSLSHGXULQJWKHFROGZRUNSURFHVVRIWKHSLSHIODQJHFRQQHFWLRQ 2.3. Friction Model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ª D ¬« D n º ZKHUH D ¼» § p · WDQK ¨ ¸ © Sut ¹ ZKHUHn LVWKHVWUDLQKDUGHQLQJH[SRQHQWRIWKHPHWDOJLYHQLQWDEOHpLVWKHFRQWDFWSUHVVXUHOHYHODQG Sut LVWKH XOWLPDWHVWUHQJWKRIWKHPHWDO,QWHUPVRIWUXHVWUHVVYDOXHV Sut 03DIRU6$*U% SLSH DQG Sut 03DIRU6$1 IODQJH 7KLVIULFWLRQPRGHOLVLPSOHPHQWHGLQWKHILQLWHHOHPHQWPRGHOE\SURYLGLQJDSUHVVXUH GHSHQGHQWFRHIILFLHQWRIIULFWLRQDQGZLOOJRYHUQWKHFRQWDFWLQWHUDFWLRQEHWZHHQWKHH[SDQVLRQWRROSLSHDQGIODQJH 7KH)LQLWH(OHPHQW0RGHO $GHWDLOHGWKUHHGLPHQVLRQDOPRGHOZDVEXLOWLQ$EDTXV([SOLFLWY>@WRVLPXODWHWKHLQVWDOODWLRQSURFHVVHV RI WKH SLSHIODQJH FRQQHFWLRQ DQG WR DVVHVV WKH PHFKDQLFDO LQWHJULW\ RI WKH FRQQHFWLRQ 7KH PRGHO DVVHPEO\ DV VKRZQLQ)LJFRQVLVWVRIWKHSLSHZLWK´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³ Hf dH Hf T ZKHUH Ȧ LV D SKHQRPHQRORJLFDO GDPDJH VWDWH YDULDEOH DQG H f T LV WKH IDLOXUH HQYHORSH JLYHQ E\ HTQ 7KH GDPDJH VDWH YDULDEOH Ȧ ZLOO LQFUHDVH PRQRWRQLFDOO\ ZLWK SODVWLF GHIRUPDWLRQ LQ HDFK HOHPHQW 2QFH LW DWWDLQV D YDOXH RI XQLW\ WKH GXFWLOH GDPDJH LQLWLDWLRQ FULWHULRQ LV PHW ZKLFK LQ WKLV VWXG\ LV DOVR UHJDUGHG DV WKH SRLQW DW XOWLPDWHIDLOXUH $JHQHUDOFRQWDFWLQWHUDFWLRQLVGHILQHGEHWZHHQWKHVXUIDFHVRIWKHULJLGH[SDQVLRQWRROVHJPHQWVWKHSLSHDQG WKH IODQJH 7KH IULFWLRQ FRHIILFLHQW LV DVVXPHG WR KDYH LVRWURSLF GLUHFWLRQDO SURSHUWLHV ZLWK FRQWDFWSUHVVXUH GHSHQGHQF\JLYHQE\WKHIULFWLRQPRGHOLQHTQ 7KHVLPXODWLRQLVFDUULHGRXWRYHUILYHDQDO\VLVVWHSV,QWKHILUVW VWHS WKH H[SDQVLRQ WRRO VHJPHQWV DUH H[SDQGHG UDGLDOO\ WRZDUGV WKH SLSH LQQHU GLDPHWHU DQG DUH JLYHQ D UDGLDO GLVSODFHPHQW RI PP FRUUHVSRQGLQJ WR WKH ILQDO SRVLWLRQ RI WKH WRRO VHJPHQWV LQ WKH H[SDQVLRQ SURFHVV ,Q WKH VHFRQGDQDO\VLVVWHSWKHH[SDQVLRQWRROVHJPHQWVDUHUHWUDFWHGDQGWKHSLSHH[SHULHQFHHODVWLFVSULQJEDFN,QWKH 450 I. Barsoum and A.M. Khalaf / Procedia Engineering 130 (2015) 446 –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óRIWKHHQWLUHDVVHPEO\FDQ EHPRGHOHGDVVKRZQLQ)LJ6\PPHWU\ERXQGDU\FRQGLWLRQVDUHDVVLJQHGWRWKHxySODQHDQGWKHxzSODQHDQGDQ D[LDOORDGLVDSSOLHGRQWKHIUHHHQGRIWKHSLSH$WRWDORI'OLQHDUQRGHLVRSDUDPHWULFEULFNHOHPHQWV ZLWKUHGXFHGLQWHJUDWLRQ &'5 ZHUHXVHGLQWKHH[WHUQDOD[LDOORDGFDVH 3LSH )ODQJH z y ([SDQVLRQWRRO VHJPHQWV x )ODQJHJURRYHV )LJ$VVHPEO\RIWKH)(PRGHO 3HUIRUPDQFH$FFHSWDQFH&ULWHULD 7KH SHUIRUPDQFH RI WKH SLSHIODQJH FRQQHFWLRQ LV HYDOXDWHG EDVHG RQ DQ H[WHUQDO D[LDO ORDG FULWHULRQ $60( %>@JLYHVDEDVLFDOORZDEOHVWUHVVLQWHQVLRQIRUSLSHPDWHULDOVDQGGHVLJQVWUHVVYDOXHVIRUIODQJHPDWHULDO 7KHVHVKDOOQRWEHH[FHHGHGDVSHU$60(%FRGHUHTXLUHPHQWV)RU6$*U%WKHDOORZDEOHVWUHVVLVSall 03DZKLFKLPSOLHVDVDIHW\IDFWRUDJDLQVW\LHOGLQJ Sy 03D DQGDJDLQVWXOWLPDWHIDLOXUH Sut 03D +HQFHWKHDFFHSWDQFHFULWHULRQIRUD[LDOORDGEDVHGRQ>@LVGHILQHGDVWKHDOORZDEOHIRUFHLQWHQVLRQLQ WKHWUDQVYHUVHFURVVVHFWLRQRIWKHSLSHFall N1ZKLFKLVHVVHQWLDOO\REWDLQHGE\PXOWLSO\LQJSallZLWKWKHFURVV VHFWLRQDODUHDRIWKHSLSH)RUFRPSDUDWLYHUHDVRQVWKHIRUFHFDXVLQJLQLWLDO\LHOGDQGXOWLPDWHIDLOXUHLQWKHSLSHDUH DOVRGHWHUPLQHGFy N1 DQG Fut N1 UHVSHFWLYHO\ 7KH FDSDFLW\ RI WKHSLSHIODQJH FRQQHFWLRQZLOO EH DVVHVVHGLQYLHZRIWKHVHOLPLWLQJIRUFHV 5HVXOWV 7KUHHGLIIHUHQWJURRYHJHRPHWULHVZKHUHFRQVLGHUHGDVVKRZQLQ)LJDQGDUHUHIHUUHGWRDVPRGHODQG 7KHILUVWURZRI)LJVLQ)LJVKRZVWKHLQLWLDOVWDJHSULRUWRWRROH[SDQVLRQZKHUHDVWKHVHFRQGURZVKRZVWKHHQG RIWKHFROGZRUNSURFHVVZKHUHWKHH[SDQVLRQWRROLVUHWUDFWHG7KHH[SDQVLRQWRWDOIRUFHUHTXLUHGIRUHDFKRIWKH WKUHHFDVHVYDULHV)RUPRGHODQGWKHWRWDOH[SDQVLRQIRUFHUHTXLUHGLVN1N1DQGN1 451 ,QLWLDO I. Barsoum and A.M. Khalaf / Procedia Engineering 130 (2015) 446 – 452 ([SDQVLRQ 3XOO2XW 0RGHO 0RGHO 0RGHO )LJ&RQWRXUSORWVDWWKHLQLWLDOVWDJHHQGRIWKHH[SDQVLRQVWDJHDQGDWWKHSXOORXWVWDJHRIWKHSLSH Futαʹͺ 270kN 260kN 250kN Fyαͳ Fallαͻͷ ʹ ͳ D E ͵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arsoum and A.M. Khalaf / Procedia Engineering 130 (2015) 446 – 452 WKDQ WKH DOORZDEOHIRUFH FallDQG \LHOGLQJ IRUFH Fy DV SHU$60( %>@EXW VPDOOHU WKDQ WKHXOWLPDWH WHQVLOH IRUFH Fut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all N1 )RUPRGHORQWKHRWKHUKDQGLWFDQEHVHHQWKDWORDGFDUU\LQJFDSDFLW\LVN1ZKLFKLVFORVHWRWKHXOWLPDWH WHQVLOHIRUFHFut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qPHV6LPXOLD $60(3URFHVV3LSLQJ&RGH$60(%