aEDF-Energy Generation, Gloucester, GL4 3RS, UK. Abstract. Boiler tube to tubeplate welds are often seen in the power generation industry. In the nuclear ...
Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 130 (2015) 879 – 892
WK,QWHUQDWLRQDO&RQIHUHQFHRQ3UHVVXUH9HVVHO7HFKQRORJ\
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a0 LQLWLDOFUDFNVL]H $ WHPSHUDWXUHGHSHQGHQWSDUDPHWHU $$ PDWHULDOFRQVWDQWV F FUHHSFRQGLWLRQ &&& PDWHULDOFRQVWDQWV GF FUHHSGDPDJHSHUF\FOH GI IDWLJXHGDPDJHSHUF\FOH Dc DFFXPXODWHGFUHHSGDPDJH Df DFFXPXODWHGIDWLJXHGDPDJH Dt WRWDOFUHHSIDWLJXHGDPDJH ( @
881
882
J. (X.Y.) Tao and G. Rayner / Procedia Engineering 130 (2015) 879 – 892
7KLV SDSHU GHVFULEHV WKH GHWDLOHG SURFHGXUHV IRU DVVHVVLQJ WKH FUHHSIDWLJXH FUDFN LQLWLDWLRQ IRU WKH WXEH WR WXEHSODWHZHOGXVLQJWKHUHYLVHG5SURFHGXUH&UHHSGDPDJHSHUF\FOHLVFDOFXODWHGIRUDFUHHSGZHOOWLPHRI KRXUVDW&DQGIDWLJXHGDPDJHSHUF\FOHXQGHUD686'F\FOH7KHWRWDOGDPDJHWKHQFDQEHDFFXPXODWHG EDVHGRQWKHFUHHSGDPDJHIRUGLIIHUHQWGZHOOSHULRGVDQGWKHIDWLJXHGDPDJHIRUWKHWRWDOQXPEHURI686'F\FOHV $VVHVVPHQWLQSXWV ,QDFUHHSIDWLJXHFUDFNLQLWLDWLRQDVVHVVPHQWWKHIROORZLQJLQIRUPDWLRQLVUHTXLUHG 2.1. Geometry 7KHORFDWLRQRIVXSHUKHDWHUWXEHSODWHWRWXEHZHOGLVVFKHPDWLFDOO\VKRZQLQ)LJ7KHQRPLQDORXWHUUDGLXVRI WKHWXEHDWWKHZHOGORFDWLRQLVPPDQGWKHPD[LPXPERUHGLDPHWHULVPP7KLVJLYHVDPLQLPXPQRPLQDO WKLFNQHVVRIPP7KHWXEHSODWHKDVDQRXWHUGLDPHWHURIPPDQGWKLFNQHVVRIPP7KHPHWDOORVVGXHWR FRUURVLRQRURWKHUUHDVRQVDUHQRWFRQVLGHUHGKHUH
)LJ/RFDWLRQRI7XEHSODWHWR7XEH:HOGKLJKOLJKWHGLQEOXH
2.2. Loading conditions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
7HPSHUDWXUH
'3
0RPHQW
$[LDO)RUFH
&
03D
1P
N1
6'
68
,1123
883
J. (X.Y.) Tao and G. Rayner / Procedia Engineering 130 (2015) 879 – 892
5YFUHHSIDWLJXHFUDFNLPLWDWLRQDVVHVVPHQWSURFHGXUHLVEDVHGRQWKHHTXLYDOHQWVWUHVVRUVWUHVVUDQJH7KH SULPDU\DQGVHFRQGDU\VWUHVVHVDUHREWDLQHGIURPWKHHODVWLFWKHUPDODQGPHFKDQLFDOILQLWHHOHPHQWDQDO\VHVIURP ZKLFKWKHHTXLYDOHQWHODVWLFVWUHVVUDQJHVDUHFDOFXODWHGDQGOLVWHGLQ7DEOH 7DEOH(ODVWLF6WUHVV5DQJHV3ULPDU\6HFRQGDU\ 03D /RDG&DVHV
'V r
'VT
'V z
' V rT
' V Tz
' V zr
' V VM
6'68
68,1
,16'
2.3. Material properties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hysical properties @ 7KH 3RLVVRQ¶V UDWLR LV WDNHQ DV >@ 7KH HIIHFWLYH HODVWLFPRGXOXVLVGHILQHGLQ(T E
E X
2.3.2. Monotonic tensile properties 7KHORZHUERXQG\LHOGVWUHVV6\LVWDNHQIURPUHI>@ 2.3.3. Shakedown factors 7KH VKDNHGRZQ IDFWRUV .V DUH WDNHQ IURP 5 Y )LJXUH IRU 7\SH PDWHULDO .V6\ JLYHV WKH ODUJHVW VHPLVWUHVVUDQJHIRUZKLFKWKHPDWHULDOKDVQRUDWFKHWWLQJ 2.3.4. Cyclic stress-strain properties &\FOHVWUHVV±VWUDLQFXUYHIRU+SDUHQWPDWHULDOLVGHWHUPLQHGXVLQJ5DPEHUJ±2VJRRGKDUGHQLQJODZLH 'H
'V § ' V · ¨ ¸ E © A ¹
E
+HUH$DQGEDUHJLYHQLQ>@DQGVKRZQLQ7DEOHIRU+SDUHQWPDWHULDO 2.3.5. Creep rupture &UHHSUXSWXUHOLYHVDUHFDOFXODWHGXVLQJWKHIRUPXODVJLYHQLQ(TUHI>@ IRU+SDUHQWPDWHULDODQG(T IRUZHOGPHWDOUHI>@ OQtr ORJT ORJV V T T
884
J. (X.Y.) Tao and G. Rayner / Procedia Engineering 130 (2015) 879 – 892
tr
§ ORJV · ¸ ¨ H[S¨ V ¸ ¸ ¨ T T ¹ ©
2.3.6. Creep deformation &UHHSGHIRUPDWLRQVZHUHFDOFXODWHGXVLQJ5&&05FUHHSGHIRUPDWLRQODZIRU7\SHSDUHQWDQGZHOGPHWDO UHVSHFWLYHO\EDVHGRQVWUDLQKDUGHQLQJDSSURDFK7KHFUHHSGHIRUPDWLRQODZLVYDOLGXSWRVWUDLQ 3ULPDU\FUHHSVWUDLQXSWRWLPHRIWISLVJLYHQE\ Ct C V n
Hp
6HFRQGDU\FUHHSVWUDLQIRUW!WISLVFDOFXODWHGXVLQJ C t fp
Hs
C
V n C V n t t fp IRUSDUHQW
H s H p C V n t t fp IRUZHOG
+HUHHSDQGHVDUHLQIRUSDUHQWDQGEHLQJDEVROXWHIRUZHOG&&&QDQGQDUHJLYHQLQ>@DQGOLVWHGLQ 7DEOHIRUWKHWHPSHUDWXUHVRILQWHUHVW7KHKLJKHUFUHHSVWUDLQEHWZHHQSDUHQWDQGZHOGPHWDOLVXVHGLQWKHFUHHS± IDWLJXHFUDFNLQLWLDWLRQDVVHVVPHQW 7DEOH0DWHULDO3URSHUWLHVIRU7\SH .V
E
&
&
&
Q
Q
7HPS&
(03D
Ɯ03D
6\03D
$ 03D
3:
3:
3:
3:
3:
(
(
(
(
2.3.7. Creep ductility 7KHORZHUERXQGXQLD[LDOFUHHSGXFWLOLW\RI+SDUHQWPDWHULDOLHLVXVHGLQWKHDVVHVVPHQW)RU SDUHQWPDWHULDOWKHVWUHVVPRGLILHGGXFWLOLW\H[KDXVWLRQDSSURDFK60'( LVJLYHQLQ5Y$7KHPXOWL D[LDOFUHHSGXFWLOLW\ H f LVDIXQFWLRQRILQVWDQWDQHRXVFUHHSVWUDLQUDWH H in LH
H f H in
½ § Q · n m ° A H[S¨¨ ° ¸¸ H in V T © ¹ § V H ° ° ªV MAX ® ¾ « H[S¨¨ V © °MIN ªH A H[S§¨ Q ·¸ V m º ° ¬« V »° « L ¨ T ¸ ° © ¹ ¼» ¿ ¬« ¯
·º ¸¸» ¹¼»
ZKHUHH/LVDFRQVWDQWORZHUVKHOIGXFWLOLW\DQGWKHPDWHULDOFRQVWDQWVRIWKHORZHUERXQG60'(PRGHODUH$ $ P P Q 4 4 DQGH/ UHI>@ 7KH60'(DSSURDFKLVQRWUHFRPPHQGHGWREHXVHGIRUZHOGPHQWGXHWRSHQGLQJYDOLGDWLRQRIWKHDSSURDFK 7KHUHIRUHIRUZHOGPHWDOWKHPXOWLD[LDOHIIHFWRQFUHHSGXFWLOLW\LVFRQVLGHUHGXVLQJ6SLQGOHUIUDFWLRQIDFWRU 7KH UHODWLRQVKLS EHWZHHQ PXOWLD[LDO FUHHS GXFWLOLW\ DQG VWUHVV VWDWH LV JLYHQ LQ $SSHQGL[ $ RI 5 Y DQG SUHVHQWHGEHORZ
885
J. (X.Y.) Tao and G. Rayner / Procedia Engineering 130 (2015) 879 – 892
Hf Hf
ª § V ·º ª § V H[S « p¨ ¸» H[S «q¨ H V ¹¼ ¬ © ¬ © V
·º ¸» ¹¼
+HUHFRQVWDQWVpDQGqDUHGHULYHGIURPELD[LDOFUHHSWHVWV)RUVWHHOp DQGq DUHVXJJHVWHGLQ5 Y$DQGXVHGLQWKHFXUUHQWDVVHVVPHQW 2.3.8. Fatigue endurance 7KHPHDQIDWLJXHHQGXUDQFHGDWD(TVDQG DUHWDNHQIURP>@IRU+PDWHULDO/RZHUERXQGIDWLJXH HQGXUDQFH ZDV HVWLPDWHG E\ UHGXFLQJ WKH VWUDLQ UDQJH IRU D JLYHQ HQGXUDQFH E\ IRU PHDQ SDUHQW GDWD DQG D IDFWRURIIRUPHDQZHOGGDWD7KHORZHUYDOXHEHWZHHQERWKDUHXVHGLQWKHFXUUHQWDVVHVVPHQW Nl
A B S C S D S E S F T G T H T J T
K T S L T S M T S P T S
IRUSDUHQW
Nl
ª 'H t º «¬ »¼
IRUZHOG
+HUH S ORJ'H t T tempqC DQG N ORJ N l ZLWK SDUDPHWHUV $ WR 3 DUH GHILQHG LQ >@ LH $ % & ' ( ) * + - . / 0 3 DQG'Ht LVWKHWRWDOVWUDLQUDQJH 2.3.9. Elastic follow-up factor 7KHHODVWLFIROORZXSIDFWRU=XVHGLQWKHFXUUHQWDVVHVVPHQWIRUERWKZHOGPHWDODQGSDUHQWPDWHULDOLVDVVXPHG WREHIROORZLQJWKHDGYLFHJLYHQLQ6HFWLRQRI5Y 5YROXPHDVVHVVPHQW 3.1. Elastic stress analysis 7KHHODVWLFVWUHVVUDQJHVDUHFDOFXODWHGEDVHGRQWKHWKHUPDODQGPHFKDQLFDO)(DQDO\VHVDQGDUHVKRZQLQ7DEOH 3.2. Margin against plastic collapse 3ODVWLF FROODSVH ZDV FKHFNHG IRU WKH SULPDU\ PHPEUDQH HTXLYDOHQW VWUHVV 3P WKH VXP RI WKH ORFDO SULPDU\ PHPEUDQH HTXLYDOHQW VWUHVV 3/ DQG SULPDU\ EHQGLQJ HTXLYDOHQW VWUHVV 3% DQG WKH HTXLYDOHQW VWUHVV UDQJH '3/3%4 DJDLQVWWKHUHTXLUHGPDUJLQVJLYHQLQ6HFWLRQRI5YDQGVKRZQLQ7DEOH 7DEOH3ODVWLF&ROODSVH&KHFN
,WHPV
6WUHVV 03D
5 &ULWHULD
03D
@DQGGHPRQVWUDWHGWKHFRPSRQHQWUHPDLQVZLWKLQWKHOLPLWVRI YDOLGLW\E\WKHHQGRIVWDWLRQOLIH 3.5. Assessment methodologies and cycle construction 7KHORDGF\FOHFRQVWUXFWLRQIROORZVWKHJXLGHOLQHVJLYHQLQ$SSHQGL[HV$DQG$RI5Y$W\SLFDOF\FOHLV VKRZQLQ)LJ7KHGHWDLOHGPHWKRGRORJLHVDQGFRQVWUXFWLRQSURFHVVHVDUHGHVFULEHGEHORZ 3.5.1. Determination of strain range 7KHVWUDLQUDQJHRIWKHILUVWKDOIF\FOHZLWKRXWFUHHSIURPSRLQWV$WR& DQGWKHVWUHVVDQGVWUDLQUDQJHVRIWKH VHFRQGKDOIF\FOHIURPSRLQWV(DQG$ƍH[FHSWIRU3RLQW) DUHGHWHUPLQHGE\VROYLQJWKHIROORZLQJHTXDWLRQV )RU 'V el t V D
'V el E
'H N
E ª§ V V §V · D V N V D «¨ N ¨ N ¸ ¨ E ©A ¹ ¬«©
VN VD E
§V · ¨ N ¸ © A ¹
·º ¸» ¸» ¹¼
E
887
J. (X.Y.) Tao and G. Rayner / Procedia Engineering 130 (2015) 879 – 892
)RU 'V el V D
VN 'H N
'V el a V D 'V el a E
ZKHUH'VHOLVWKHHODVWLFVWUHVVUDQJHJLYHQLQ7DEOHV'LVWKHGDWXPVWUHVVDVWUHVVRIIVHWDIWHUSRVLWLRQLQJLHWKH VWUHVVUDQJHLVDGMXVWHGVRWKDWWKHH[FXUVLRQVEH\RQGHDFKRIWKH.V6\OLPLWDUHHTXDODWERWK.V6\ FDQG.V6\ QF HQGV QRWLQJWKDWV'LV]HURIRUWKHKDOIF\FOHZLWKRXWFUHHSV1LVWKHVWUHVVDWWKHLQWHUVHFWLRQVDQG$ LVHTXDOWR $DQG$IRUWKHKDOIF\FOHZLWKRXWDQGZLWKFUHHSUHVSHFWLYHO\
)LJ+\VWHUHVLV&\FOH&RQVWUXFWLRQ
3.5.2. Strain volumetric correction 7KHVWUDLQUDQJHLVHQKDQFHGE\ 'Hvol DFFRXQWLQJIRUWKHVWUDLQUDQJHGXHWR3RLVVRQ¶VUDWLRFKDQJHQRWDFFRXQWHG IRUGXULQJWKHHYDOXDWLRQRIWKHHODVWLFSODVWLFVWUDLQUDQJH7KHYROXPHFRUUHFWLRQLVHYDOXDWHGE\ 'H vol
K v 'H el
+HUH .Y LV D IDFWRU UHODWHG WKH 3RLVVRQ¶V UDWLR DQG WKH VHFDQW PRGXOXV PHDVXUHG IURP WKH F\FOLF VWUHVVVWUDLQ FXUYHDQGGHILQHGLQ$SSHQGL[$RI5YROXPH
888
J. (X.Y.) Tao and G. Rayner / Procedia Engineering 130 (2015) 879 – 892
3.5.3. Enhancement of strain range for weldment :KHQXVLQJWKHSDUHQWF\FOLFVWUHVVVWUDLQGDWDIRUWKHZHOGPHQWWKHFDOFXODWHGVWUDLQIROORZLQJWKHYROXPHWULF VWUDLQ FRUUHFWLRQ ZDV HQKDQFHG E\ DSSO\LQJ WKH :6() )RU WKH ZHOGLQJ JHRPHWU\ SURILOH FRQVLGHUHG LQ WKLV DVVHVVPHQWWKHZHOGZDVIXOO\SHQHWUDWHGVRWKDW5:HOG7\SHLVDSSOLHG7KLVFRUUHVSRQGVWRD:6()RI )LJXUHVKRZVVFKHPDWLFDOO\GHWHUPLQDWLRQRIHQKDQFHGVWUDLQUDQJHRIZHOGPHQWIURPWKHSDUHQWVWUDVVVWUDLQ F\FOLFFXUYH7KH:6()LVDSSOLHGWR'HWDIWHUYROXPHFRUUHFWLRQZLWKRXWWDNLQJDFFRXQWRIFUHHSVWUDLQLH 'H t
WSEF 'H t 'H c ǻı
6&)ǻV3/3%4 1HXEHU FRQVWUXFWLRQ
&\FOLF6WUHVV6WUDLQ&XUYHV :HOG 3DUHQW
ǻı Z ǻı 3
:6()
:(5
ǻİ YRO
2/')65)
ǻİ W
ǻİ
)LJ6FKHPDWLF,OOXVWUDWLRQRI:HOGPHQW$VVHVVPHQW3URFHGXUH8VLQJ:6()UHI>@
3.5.4. Stress relaxation during creep dwell $WSRLQW(WKHVWDUWRIGZHOOVWUHVVVUHOD[HVGXULQJWKHFUHHSGZHOOSHULRG7KHVWUHVVUHOD[DWLRQ'VIURPSRLQW (WR) DQGWKHFRUUHVSRQGLQJFUHHSVWUDLQ'HFDUHFDOFXODWHGXVLQJ$SSHQGL[RI5Y(T DQGWKH5&& 05FUHHSGHIRUPDWLRQODZ(TVWR
Z dV E dt
Hc V H c T t Hc V R ref H c T t
+HUH Hc V H c T t LVWKHFUHHSVWUDLQUDWHDWWKHLQVWDQWDQHRXVHTXLYDOHQWFUHHSVWUDLQ H c HTXLYDOHQWVWUHVV V WKHWLPH tDQGWKHWHPSHUDWXUHT Hc V R ref H c T t LVWKHVDPHDV Hc V H c T t EXWDWWKHFRQVWDQWFUHHSUXSWXUHUHIHUHQFHVWUHVV V R ref RU D VWHDG\ VWDWH FUHHS VWUHVV ,Q WKH FDOFXODWLRQ LI WKH VWDUW RI GZHOO VWUHVV LV EHORZ WKH UXSWXUH UHIHUHQFH VWUHVV WKH FUHHS GHIRUPDWLRQ LV FRQVHUYDWLYHO\ DVVXPHG WR RFFXU DW WKH UXSWXUH UHIHUHQFH VWUHVV &UHHS UHOD[DWLRQ GXULQJWKHVWHDG\VWDWHRSHUDWLRQLVFRYHUHGE\WKHLQVWDELOLW\FRQGLWLRQZKLFKLVFRQVLGHUHGWREHFRQVHUYDWLYH
3.6. Assessment results 7KHDVVHVVPHQWUHVXOWVIURPHDFKVWHSEDVHGRQWKHPHWKRGRORJLHVGHVFULEHGLQVHFWLRQDUHVXPPDUL]HGDV IROORZ
J. (X.Y.) Tao and G. Rayner / Procedia Engineering 130 (2015) 879 – 892 7DEOH&RQVWUXFWLRQRIWKHKDOIF\FOHZLWKRXWFUHHS$%& ,WHPV
5HVXOWV
8QLW
ORDGLQJF\FOH
6'68
WHPSHUDWXUHDWWHQVLRQ
&
WHPSHUDWXUHDWFRPSUHVVLRQ HQKDQFHGVWUDLQUDQJH 'H
ABC ep
HQKDQFHGVWUHVVUDQJH 'V YROXPHWULFFRUUHFWLRQ 'H
ABC ep
ABC vol
&
03D
7DEOH3RVLWLRQLQJWKHUHYHUVHVWUHVVGDWXP ,WHPV
5HVXOWV
8QLW
HTXLYDOHQWVWUHVVDWSRLQW$
03D
HTXLYDOHQWVWUHVVDWSRLQW&V'
03D
HTXLYDOHQWVWUDLQDWSRLQW$
HTXLYDOHQWVWUDLQDWSRLQW&
7DEOH&RQVWUXFWWKHF\FOHVHJPHQWEHIRUHGZHOO&'( ,WHPV
5HVXOWV
8QLW
ORDGLQJF\FOH
68,1
&
WHPSHUDWXUH HQKDQFHGVWUDLQUDQJH 'H
CDE ep
HQKDQFHGVWDUWRIGZHOOVWUHVVV YROXPHWULFFRUUHFWLRQ 'H
CDE vol
03D
7DEOH&DOFXODWLRQRIFUHHSVWUHVVGURSGXULQJGZHOO() ,WHPV
5HVXOWV
8QLW
ORDGLQJF\FOH
,1
WHPSHUDWXUH
&
FUHHSVWUDLQLQFUHPHQW 'H C
6WUHVVGURSUHOD[DWLRQ 'V
03D
C
7DEOH&DOFXODWLRQRIWKHKDOIF\FOHZLWKFUHHS&)$¶ ,WHPV
5HVXOWV
8QLW
ORDGLQJF\FOH
686'
WHPSHUDWXUH
&
HQKDQFHGVWUDLQUDQJH 'H CFA
03D
ep
HQKDQFHGVWUHVVUDQJH ' V YROXPHWULFFRUUHFWLRQ 'H
CFA ep
CFA
vol
7DEOH6XPPDU\RIWKHFUHHSDQGIDWLJXHVWUDLQV ,WHPV
5HVXOWV
WRWDOVWUDLQUDQJHIRUWKHKDOIF\FOHZLWKRXWFUHHS
WRWDOVWUDLQUDQJHIRUWKHKDOIF\FOHZLWKFUHHS
FUHHSVWUDLQ
889
890
J. (X.Y.) Tao and G. Rayner / Procedia Engineering 130 (2015) 879 – 892
3.7. Calculation of creep and fatigue damage 3.7.1. Creep damage &UHHSGDPDJHSHUF\FOHLVFDOFXODWHGEDVHGRQWKHGXFWLOLW\H[KDXVWLRQDSSURDFK7KHFUHHSVWUDLQ IURP WKHF\FOHFRQVWUXFWLRQLVXVHGWRFDOFXODWHWKHFUHHSGDPDJHSHUF\FOHXVLQJWKHIRUPXODEHORZ th
dc
Hc
³H
f
Hc Hf
+HUH H c LVWKHDFFXPXODWHGFUHHSVWUDLQGXULQJWKHGZHOOWLPHWK,IWKHVWDUWRIGZHOOVWUHVVLVFRPSUHVVLYHFUHHS GDPDJHVKRXOGEH]HUR 7KH ORZHUERXQG PXOWLD[LDO GXFWLOLW\ PRGHO LV XVHGIRUZHOG PHWDO XVLQJ WKH 6SLQGOHU IUDFWLRQIDFWRUJLYHQ LQ (T 7KH 60'( PRGHO (T LV XVHG WR FDOFXODWH WKH SDUHQW FUHHS GDPDJH 7KH FUHHS GDPDJH SHU F\FOH LV ZKLFKHYHULVKLJKHU7KHUHVXOWVEHORZVKRZWKHFUHHSGDPDJHSHUF\FOHIRUZHOGPHWDOLVERXQGLQJ ,WHPV
&UHHSGDPDJH
FUHHSGDPDJHSHUF\FOHIRUZHOGPHWDO
(
FUHHSGDPDJHSHUF\FOHIRUSDUHQWPDWHULDO
(
3.7.2. Fatigue damage )DWLJXHGDPDJHSHUF\FOHLVFDOFXODWHGE\
df
N
+HUH N0 LV WKH IDWLJXH HQGXUDQFH WR LQLWLDWH D GHIHFW RI VL]H a0 DW F\FOLF VWUDLQ UDQJH 'H t 7KH VWUDLQ UDQJH IRU IDWLJXHLVGHWHUPLQHGE\WKHODUJHUVWUDLQRIWKHKDOIF\FOHVZLWKDQGZLWKRXWFUHHS,QWKLVDVVHVVPHQWWKHIDWLJXH GDPDJHLVGRPLQDWHGE\WKHKDOIF\FOHZLWKRXWFUHHS(TLVXVHGWRFDOFXODWHN0
N
N i N g
+HUH Ni LV WKH QXPEHU RI F\FOHV IRU FUDFN QXFOHDWLRQ D GHIHFW OHQJWK RI ai DQG LV FDOFXODWHG XVLQJ WKH IDWLJXH HQGXUDQFHGDWD(TVDQGIRUSDUHQWDQGZHOGUHVSHFWLYHO\ JLYHQLQ(T OQN i OQ N l N l
NgƍLVWKHQXPEHURIF\FOHVWRJURZWKHFUDFNIURPVL]HaiWRa0N’gLVDIXQFWLRQRIWKHQXPEHURIF\FOHVIRUFUDFN JURZWK NgDQGSDUDPHWHU0ZKLFKLVJLYHQLQ6HFWLRQRI5YLH N g
Ng
M N g
Nl Ni
NiLVLJQRUHGIRUZHOGPHQWDVVHVVPHQWZKHQSDUHQWGDWDLVXVHGLHN0=N’gDQGNg=Nl, LPSOLFLWO\DQHIIHFWRIWKH :(57KHIDWLJXHGDPDJHSHUF\FOHRIWKHZHOGPHQWLVWKHERXQGLQJGDPDJHFDOFXODWHGIRUERWKSDUHQWDQGZHOG PDWHULDOVDQGHTXDOVWRî
891
J. (X.Y.) Tao and G. Rayner / Procedia Engineering 130 (2015) 879 – 892
3.7.3. Total creep and fatigue damage for crack initiation 7KH WRWDO FUHHSIDWLJXH GDPDJH Dt FDQ EH FDOFXODWHG E\ DFFXPXODWLQJ WKH FUHHS GDPDJHV Dc IRU HDFK ERLOHU LQVWDELOLW\PRGHVDVHULHVRILQVWDELOLW\WHPSHUDWXUHVDQGGZHOOSHULRGV DQGWKHIDWLJXHGDPDJHVDf IRUHDFKVHUYLFH F\FOHLH Dt
D f Dc
nj
H ck
¦n d ¦n d ¦ N ¦ H j fj
j
k ck
k
j
j
k
f
+HUHnjLVWKHQXPEHURIVHUYLFHF\FOHVRIW\SHjDQGdfjDQG1MDUHWKHYDOXHVRIdfDQGN0FRUUHVSRQGLQJWRWKDW W\SH F\FOH nk LV WKH QXPEHU RI ERLOHU LQVWDELOLW\ HYHQWV RI W\SH k DQG dck DQG H ck DUH WKH YDOXHV RI dc DQG H c FRUUHVSRQGLQJWRWKDWW\SHRIHYHQW'XHWRWKHFRPSOLFLW\RIWKHERLOHULQVWDELOLWLHVDQGVHUYLFHFRQGLWLRQVWKHWRWDO GDPDJHLVQRWSUHVHQWHGKHUH 'LVFXVVLRQ 4.1. Effect of cyclically enhanced creep 7R OLPLW FUHHS GHIRUPDWLRQ UHVXOWLQJ IURP WKH HQKDQFHPHQW RI FUHHS VWUDLQV E\ F\FOLF WKHUPDO ORDGV WKH FUHHS XVDJHIDFWRU:VKRXOGEHFKHFNHGDQGLVOHVVWKDQXQLW\UHI>@ :LVDIXQFWLRQRIWKHFRUHVWUHVVVFRUH5Y 6HFWLRQ SURYLGHV DQ DSSURDFK WR GHILQH WKH FRUH VWUHVV EXW LW LV RQO\ VXLWDEOH IRU WKH VLWXDWLRQV LQYROYLQJ FRQVWDQW SULPDU\ ORDGV FRPELQHG ZLWK VHFRQGDU\ ORDGV ZKLFK DUH ]HUR GXULQJ VWHDG\ RSHUDWLRQ 7KLV SURGXFHV HVVHQWLDOO\WKURXJK@ KZDOOEHQGLQJVWUHVVHVDFURVVWKHVHFWLRQRILQWHUHVWGXULQJWUDQVLHQWV7KHUHIRUH)(DQDO\VLV VKRXOGEHFDUULHGRXWIRUWKHVWHDG\VWDWHFRQGLWLRQWRREWDLQWKHFRUHVWUHVVDQGWKLVZRUNLVVWLOORQJRLQJ 4.2. Effect of elastic follow-up ,QWKLVDVVHVVPHQWDQHODVWLFIROORZXS=RIZDVWDNHQDVSHUWKHDGYLFHJLYHQLQ5Y,QSUDFWLFHWKLVFRXOG EHHLWKHURYHUO\RUQRQFRQVHUYDWLYH$VHQVLWLYLW\VWXG\KDVEHHQFRQGXFWHGDQGVKRZQWKHHIIHFWRI=RQWRWDOFUHHS GDPDJHLVLQVLJQLILFDQW 4.3. Creep strain re-priming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
892
J. (X.Y.) Tao and G. Rayner / Procedia Engineering 130 (2015) 879 – 892
LQVWDELOLW\ 7KH FDOFXODWLRQV GHPRQVWUDWH WKH ZHOGV FDQ VXVWDLQ WKH VXEMHFWHG ORDGV ZLWKRXW SODVWLF FROODSVH FUHHS UXSWXUHDQGUDWFKHWLQJ7KHFUHHSGDPDJHSHUF\FOHRIWKHZHOGPHQWLVîIRUDGZHOOSHULRGRIKRXUVDW WHPSHUDWXUH&DQGWKHIDWLJXHGDPDJHLVî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ÿ'RQQHOO$*53RZHU6WDWLRQV8VHRIIRUZDUGFUHHSGHIRUPDWLRQWRHVWLPDWHWKHF\FOLFVWUHVVUHOD[DWLRQEHKDYLRXULQW\SH VWDLQOHVVVWHHODWWHPSHUDWXUHVIURPe&WRe&(')(QHUJ\LQWHUQDOWHFKQLFDOUHSRUW(5(3$7(&$*55HYLVLRQ 2FWREHU