Volume 438, paper 1191

Transcription

1 ASME PVP High Tprtur of Structur & Mtrils August 4-8, 00, Vncouvr Volu 438, ppr 9 A SENSITIVITY STUDY OF CREEP CRACK GROWTH IN PIPES K. Wsr K. M. Nikbin G. A. Wbstr Dpt. of Mchnicl Enginring Ipril Collg London, SW7 BX, UK ABSTRACT Filur of prssur vssls nd piping systs tht oprt t high tprturs cn occur by nt sction ruptur, crp crck growth or cobintion of both procsss. Svrl dsign nd ssssnt procdurs r vilbl for dling with this sitution. Ths includ th ASME Prssur Vssl nd Piping, Frnch RCC-MR (Appndix 6) nd British R5 nd BS790 cods. Ech of ths procdurs uss cobintion of continuu chnics nd frctur chnics concpts to k n ssssnt. Although th procdurs dopt th s bsic principls, oftn diffrnt forul r ployd to k n ssssnt. Th in prtrs tht r usd r rfrnc strss, rf, strss intnsity fctor, K, nd th crp frctur chnics tr C*. In this ppr, n nlysis is prford to stit th snsitivity of th prdictions of crp crck growth in prssurisd pip to th choic of forul usd nd trils proprtis ployd. It is shown tht ost snsitivity is obtind to choic of xprssion ployd for clculting rf nd to whthr btch spcific or or gnric trils proprtis dt r slctd. KEY WORDS Dfcts, fctur chnics, crck growth, crp. NOMENCLATURE A Norton powr lw crp constnt in Eq. () C* stdy stt crp frctur chnics prtr D constnt in Eq. () F boundry-corrction fctor G j influnc cofficint for jth strss distribution I n function of n in HRR fild K, K I strss intnsity fctor, od I K M bulging fctor corrction M kb, M b strss intnsity gnifiction fctors M k, M strss intnsity gnifiction fctors M s, M T strss gnifiction fctors P pplid lod P 0 norlising lod P LC liit lod vlu of P for crckd body Q shp fctor for llipticl crck R i, R, R intrnl, n nd outr rdii of cylindr W cylindr wll thicknss dpth of surfc crck bt function of dinsions c hlf-lngth of surfc crck d/dt crp crck growth rt f w finit width corrction fctor k tb bnding strss concntrtion fctor k t brn strss concntrtion fctor l pip width in pln of flw n Norton strss indx in powr crp lw Eq. () p pplid prssur r distnc fro th crck tip r c crp procss zon siz ε f unixil crp filur ductility ε rf crp strin rt t rfrnc strss ε * f crp ductility pproprit to stt of strss ε crp strin rt φ constnt in Eq. () strss b, bnding strss, brn strss rf rfrnc strss Y norlising yild strss θ hoop strss ν Poisson s rtio ζ gotry fctor Copyright 00 by ASME

2 INTRODUCTION Mny high tprtur coponnts hv to undrgo ndtory inspction to dtrin thir suitbility for furthr us. Frquntly non-dstructiv inspction thods r ployd to dtct flws. Th incrsing snsitivity of this quipnt is nbling sllr nd sllr dfcts to b dtctd. Consquntly, thr is n incrsing nd for stblishing rlibl procdurs for dtrining th significnc of ny dfcts idntifid. Svrl dsign nd ssssnt procdurs r vilbl for dling with this sitution. Ths includ th ASME Prssur Vssl nd Piping, th Frnch A6 nd British R5 nd BS 790 cods. Ech of ths procdurs uss cobintion of continuu chnics nd frctur chnics concpts to k n ssssnt. Although th procdurs dopt th s bsic principls, oftn diffrnt forul r ployd to k n ssssnt. Th in prtrs tht r usd r rfrnc strss, rf, strss intnsity fctor, K, nd th crp frctur chnics tr C*. In this ppr, n nlysis is prford to stit th snsitivity of th prdictions of crp crck growth in prssurisd pip to th choic of forul nd trils proprtis ployd. COMPONENT INVESTIGATED A stright pip contining longitudinl wld nd fbrictd fro 9Cr stl, dsignd s P9, with th dinsions nd coposition shown in Fig. nd Tbls nd, ws xind. Th pip hd 85 ID nd 5 OD. It hd 3 si-llipticl xil dfcts chind round its outr priphry; in th Ht-Affctd-Zon (HAZ) nd th othr in th prnt tril (PM) s shown in Fig.. Th pip ws tstd t n intrnl prssur of 5 MP, tprtur of 65 C nd th growth of ch crck ws onitord with ti by cpcitnc nd lctricl potntil tchniqus. Filur of pip occurrd by propgtion of dfct D through th wll ftr totl tst durtion of 430 h. Th initil nd finl dinsions of ch dfct r givn in Tbl. Fro this tbl, it is vidnt tht no crck growth occurrd in dfct F, dfct E only xtndd 0.7 nd th spct rtio /c rind pproxitly constnt t 0.4 during th crcking procss. Th ctul xtnsion with ti of ch of ths dfcts is shown in Fig.. An incubtion priod of bout /3 rd of lif, prior to th dtction of crck xtnsion, is pprnt for dfct D. Figur : Gotry of th pip showing loction of dfcts ini fin c ini c fin Notch D (HAZ) Notch E (PM) Not Givn Notch F (PM) Tbl : Dinsions of dfcts C Mn Si S P Cr Ni Mo V Cu N Al Tbl : Chicl coposition of P9 stl (Wight in %) Copyright 00 by ASME

3 MODEL OF CREEP CRACK GROWTH Svrl prtrs hv bn pplid to dscrib xprintl crp crck growth dt. Howvr, survys of th litrtur (Wbstr nd Ainsworth, 994) hv shown tht th ost stisfctory corrltions of crck growth rt, d/dt, r chivd with th crp frctur chnics prtr, C*, ccording to th lw φ d / dt D C * () whr D nd φ r tril constnts which cn b surd xprintlly or dtrind fro odl of th crcking chnis. [] Dfct E (Prnt) Dfct D (HAZ) Ti [h] Figur : Crp crck growth of dfct D nd E in P9 pip t 65ºC. In th odl of Nikbin, Sith nd Wbstr (NSW) (Nikbin t l., 983, 984) procss zon of siz r c is postultd t th crck tip. For tril with constnt unixil crp ductility, ε f, nd which xhibits scondry crp bhviour tht cn b dscribd by th Norton crp lw (Norton, 99): n & A () ε whr ε is crp strin rt, is strss nd A nd n r tril constnts, it cn b shown tht: nd D φ n/(n+) (3) n n+ ( n + ) * n c ε f I n ( A r ) + In Eq. (4), I n is non-dinsionl fctor which hs bn tbultd by Hutchinson (968) s function of n nd stt of strss nd ε * f is th crp ductility pproprit to th strss stt t th crck tip. Typiclly, for pln strss conditions ε * f cn b tkn to qul ε f, nd for pln strin loding to qul ε f / 30. In th prsnt invstigtion, xprintl vlus of D nd φ hv bn usd. (4) Figur 3 shows th rlvnt crp rt dt tht hv bn tkn fro two Europn projcts (HIDA nd LICON) nd British Enrgy Gnrtion Ltd. for th P9 stl xind nd Fig. 4 th corrsponding crp crck growth proprtis which wr obtind fro th HIDA invstigtion. In ch cs rsults r includd for both th PM nd HAZ tril t 65 C. It is pprnt tht th HAZ tril hs lowr crp strngth nd infrior crp crck growth rsistnc to th PM. Vlus of D nd φ for ch condition r listd in Tbl 3. Th units of D givs th crcking rt in /h for C* in MP /h. Mtril Condition D φ HAZ PM Tbl 3: Crp crck growth dt for P9 t 65 o C Mt. Cst Crp N of A n Cond. rt tsts PM All ε in.e PM LICON ε in 3 5.7E-3 3. PM HIDA ε in 9.38E PM All ε v 37.0E PM LICON ε v E PM HIDA ε v 9 6.9E HAZ LICON ε in.6e HAZ LICON ε v.e WM All ε in.55e WM All ε v 4.4E Tbl 4: Vlus of A nd n usd to dscrib unixil crp proprtis of for P9 t 65ºC Miniun crp strin rt [h - ].0E-0.0E-0.0E-03.0E X P9_HAZ.0E-05 P9_PM P9_WM.0E-06 n_p9_haz n_p9_pm n_p9_wm.0e no [MP] Figur 3: Scondry crp proprtis for P9 t 65ºC tkn fro th LICON, HIDA nd British Enrgy studis. 3 Copyright 00 by ASME

4 In Tbl 4, vlus of A nd n r givn for individul tril conditions nd for diffrnt btchs of tril to corrspond with both th iniu nd vrg crp rts (whr th vrg strin rt is siply th filur strin dividd by th ruptur lif to rprsnt th ntir crp curv by scondry crp lw). Also includd r vlus whn ll th PM dt r cobind. In th tbl th units of A r chosn to giv th strin rt in h - with strss in MP. Th rng of vlus of A nd n llow th ffcts of vritions in tril crp proprtis on crck growth bhviour to b xind. d/dt [/h].0e+0.0e+0.0e+00.0e-0.0e-0.0e-03 P9 - HAZ P9 - PM Pln Strin Pln Strss Powr (P9 - HAZ) Powr (P9 - PM) HAZ 0.786C* 0.47 PM.484C* E-04.0E-06.0E-05.0E-04.0E-03.0E-0 C* [MP/h] Figur 4: Crp crck growth proprtis of P9 t 65ºC tkn fro HIDA DETERMINATION OF C* C* cn b obtind xprintlly, by nuricl nlysis or rfrnc strss thods. In this invstigtion th rfrnc strss pproch hs bn doptd (Ainsworth, 98, 984). Th rfrnc strss of crckd body cn b dfind s: P rf Y (5) PLC whr P LC is th liit lod vlutd for yild strss Y, for th crckd body. Sinc P LC is proportionl to yild strss, rf is indpndnt of Y. By using Ainsworth s pproch, C* cn b xprssd pproxitly in trs of th rfrnc strss by: * K C & rf ε (6) rf rf whr ε rf is th crp strin rt t th rfrnc strss nd K is th strss intnsity fctor corrsponding to th lod P. Using Eq. (), Eq. (6) cn b writtn s: C* A K n rf (7) Th vlu obtind for C* will dpnd on th forul usd to dtrin K nd rf. Diffrnt procdurs nd cods oftn ploy diffrnt qutions for ths trs. Sinc φ in Eq. () is clos to on, th crck growth rt will vry pproxitly proportionlly to K nd rf n-. Grtr snsitivity to rfrnc strss thn K will thrfor b xpctd. For xpl, 0% chng in K will giv % chng in crcking rt nd siilr chng in rf will giv or thn 00% chng in crck growth rt for ost vlus of n. Exprssions for vluting ths trs for n xil sillipticl dfct in pip will now b xind. EXPRESSIONS FOR STRESS INTENSITY FACTOR A survy in th litrtur (Rju nd Nwn, 98, Dubry t l., 995, Andrsson t l., 996, Lh, 999, British Enrgy Gnrtion Ltd., 000, nd British Stndrd, 999) shows tht thr r svrl forul to dtrin th strss intnsity fctor. Howvr, ll of th r bsd on Rju nd Nwn (98). Dubry t l. (995), Andrsson t l. (996), Lh (999) nd British Enrgy Gnrtion Ltd. (000) ll us xctly th s forul. Thrfor, only, Rju nd Nwn (98) nd British Stndrd (BS 790) forul r coprd in this ppr. Forul du to Rju nd Nwn (98) This strss intnsity fctor for surfc crck ws obtind by using thr-dinsionl finit-lnt strss nlysis nd is dfind s: R i W K p π F,, (8) I Rju W Q c W Ri whr Q is pproxitd by: Q (9) c nd F is th boundry-corrction fctor of n xtrnl surfc crck, which cn b writtn s: 3 W R i F + + G0 + G 3 G 4 G3 Ri R Ri R R R (0) whr th G j r dpndnt on /c, /W nd W/R i nd r givn in th litrtur (Rju nd Nwn, 98). Th G j rlvnt to this invstigtion wr vlus r obtind fro intrpoltion or xtrpoltion nd r s follow: G o.93, G 0.738, G nd G Forul fro BS 790 (999) Th qutions in th British Stndrd diffr in pprnc fro thos to b found in th publiction of Rju nd Nwn (98) nd in th originl BS PD For surfc flws, on st of qutions is pplid to ll gotris nd th strss intnsity fctor cn b writtn s: whr for Lvl nd 3 ssssnts K ( Y ).65 I BS 790 p π () 4 Copyright 00 by ASME

5 ( Y ) M f [ k M M + k M M ] p () w t k In Eq. (), M is bulging fctor corrction, f w is finit width corrction fctor, M k, M, M kb nd M b r strss intnsity gnifiction fctors, k tb nd k t r th bnding nd brn strss gnifiction fctors, rspctivly nd b nd r th bnding nd brn strsss. In th cs studid in this ppr, M, f w, M k, M, M kb, k tb, nd k t ll qul. By substituting ths vlus into Eqs () nd (), K I BS 790 bcos: K ( M + M ) tb I BS 790 b b π (3) whr M b nd M r obtind fro intrpoltion or xtrpoltion nd in th cs xind r qul to 0.58 nd.00, rspctivly. Clcultions hv bn d for constnt spct rtio with /c 0.4 to corrspond with th dinsions of dfcts D nd E. Th rsults for diffrnt rltiv crck dpths r prsntd in Fig. 5. Thr is xiu diffrnc of bout 5% in K for th shllowst dfct. K [MP / ] K Rju - A6 - R5 - R6 K BS /W Figur 5: Dpndnc of K on /W for si-llipticl dfct in pip with /c 0.4 EXPRESSIONS FOR REFERENCE STRESS Millr (988) hs rviwd svrl rfrnc strss solutions tht hv bn drivd for n xtrnl si-llipticl dfct. Both globl nd locl solutions hv bn producd. Globl solutions corrspond to filur of n ntir cross-sction whrs locl solutions r for filur of th lignt hd of crck only. As consqunc locl stits of rfrnc strss will lwys b grtr thn or qul to globl vlus. Globl solutions Assuing globl collps, th procdurs A6, R5 nd R6 (Connors, 998) giv th s rfrnc strss solution. This solution ssus th Trsc yild critrion bsd on burst prssur, p nd is s follows (Kifnr t l., 973): kb b b p (4) rf R6 Globl R ( ) bt, c + ln R Ri whr bt(, c) is: bt(, c) (5) c +.6 R [( ) ] An ltrntiv forul hs bn proposd by Millr (988) who clis tht thr is not dqut xprintl vidnc to judg ny ffct btwn hving n intrnl or xtrnl dfct. Thrfor, h suggsts tht th piricl xprssion, du to Chll (984), for intrnl dfcts cn lso b pplid to xtrnl flws so tht: p R c η + ( η).6 + (6) rf Chll Globl W R W whr η is dfind s η (7) W Locl solutions Thr r or locl solutions for rfrnc strss thn globl solutions. Th forul usd in R6 is bsd on Sttri- Fr (994) nd cn b xprssd s: whr rf R6 Locl g 3 9 b b ( ζ ) + g ( ζ ) + ( ζ ) ( ) ( ζ ) (8) g ζ ζ (9) c c ζ (0) W ( c + W ) In this cs, th brn strss hs bn tkn s th hoop strss t th n rdius nd th bnding strss tht xists t th crck tip. British Stndrd BS 790 dfins th rfrnc strss for cylindr with n xil xtrnl flw s idnticl to tht for cylindr with n xil intrnl flw. Th ltst forul is bsd on th originl Folis (965) (rprintd in 984) solution for thin-wlld cylindrs nd is dfind s: b. M + () rf BS 790 s 3 ( ") 5 Copyright 00 by ASME

6 whr th ultiplir of. is introducd to giv siilr lvls of consrvtis to thos for flt plts. nd b r th brn nd bnding strsss, rspctivly, rsulting fro th pplid intrnl prssur. M s is strss gnifiction fctor which is givn s: W M T M s () W nd is non-dinsionl crck lngth. rf [MP] rf R6 000 Globl solution rf R6 000 Locl solution rf BS Locl solution rf Kifnr Locl solution rf Chll Globl solution rf Chll Locl solution nd " for l ( c + W ) (3) W W + c M T c +.6 (4) R W i A locl rfrnc strss solution hs bn drivd by Kifnr t l. (973) using n piricl Bttll xprssion p R c ( ) rf Kifnr η +.6 (5) W η R W Anothr solution du to Chll (984) givs rf Chll Locl p R W η ( η) +.6 ( η) c R W (6) Prdictions of rfrnc strss fro th vrious forul for crck with /c0.4, siilr to th dinsions of dfcts D nd E in th pip, r shown in Fig. 6. It is clr tht th vlus obtind or thn spn th rng of th unixil dt prsntd in Fig. 3. Although ll th solutions for dfct dinsion /W0.4 r brodly in grnt, it cn b sn tht for lrgr dpths (/W0.8) locl stits of rf cn b up to bout 70% grtr thn globl vlus which cn rport in substntilly diffrnt prdiction in crck growth whn incorportd into Eqs () nd (7) /W Figur 6: Dpndnc of rf on /W for si-llipticl dfct in pip with /c 0.4 PREDICTIONS OF CRACK GROWTH It is pprnt fro Eqs () nd (7) tht th prdiction of crck growth in th pip will dpnd on th tril proprtis usd nd th forul pplid for clculting K nd rf. Ths coprisons r shown in Figs 7-9 for dfct E which ws loctd in PM. Also includd in ths figurs r th xprintl rsults. In Figs 7 nd 8 btch spcific tril iniu crp rt dt tkn fro th HIDA projct hv bn usd. This is th s btch of tril fro which th pip ws d. In ll css clos corrltion with th xprintl rsults is obtind for th short ount of crck xtnsion surd. Figur 7 donstrts tht only sll diffrnc in crck growth is prdictd whn diffrnt forul for K r usd nd rf is clcultd fro Eq. (8). This is to b xpctd fro Eq. (7) nd Fig. 5. In contrst, Fig. 8 illustrts tht substntil diffrncs r obtind whn diffrnt forul for rf r usd nd Eq. (8) is ployd for clculting K. Ths howvr only bco pprnt for lrg crck xtnsions. A fctor of diffrnc in ti for crck growth of 8 cn b prdictd. As nticiptd locl solutions of rf usully produc fstr growth rts thn globl solutions. In Fig. 9, coprisons r d with prdictions bsd on diffrnt tril proprtis dt whn K ws clcultd fro Eq. (8) nd rf fro Eq. (8). In this cs, prdictions of th ti tkn for th crck to xtnd 8 cn vry by fctor of up to bout 5. Thr is or sprd in prdictions bsd on vrg rthr thn iniu crp strin rts. Avrg crp strin rts, s xpctd, giv th fstst crcking rts. A coprison hs bn d in Fig. 0 btwn th xprintlly surd crck growth of dfct D in th HAZ nd prdictions obtind fro Eqs (8) nd (8) for K nd rf, rspctivly, using diffrnt trils proprtis dt. Whn ll th prtrs r tkn fro prnt tril (PM) too slow crck rt is prdictd nd whn thy r ll tkn fro th HAZ tril too rpid growth is obtind. Rsonbl 6 Copyright 00 by ASME

7 prdictions r producd whn D nd φ r tkn for th HAZ nd A nd n fro th PM tril Exprintl Dt K Rju - A6 - R5 - R6 K BS 790 [] Exprintl All prtrs fro PM D nd ф fro HAZ, A nd n fro PM All prtrs fro HAZ [] [] [] Ti [h] Figur 7: Dpndnc of crck growth in P9 t 65ºC on forul usd for K Exprintl Dt rf R6 000 Globl solution rf R6 000 Locl solution rf BS 790 Locl solution rf Kifnr Locl solution rf Chll Globl solution rf Chll Locl solution Ti [h] Figur 8: Dpndnc of crck growth in P9 t 65ºC on forul usd for rf Exprintl Dt 0.0 LICON nd HIDA - in Cst LICON - in Cst HIDA - in 9.0 All Csts - v Cst LICON - v Cst HIDA - v Ti [h] Figur 9: Dpndnc of crck growth on vrition in tril proprtis Ti [h] Figur 0: Coprison of xprintl nd prdictd crp crck growth of th dfct D (HAZ). DISCUSSION Prdictions of th growth of llipticl dfcts in prssurisd pip hv bn d using Eqs () nd (7). Th prdictions dpnd on th tril crp dfortion nd crck growths proprtis usd nd th forul ployd for clculting K nd rf. For givn tril proprtis, it hs bn found tht th ount of crck growth prdictd is ost snsitiv to th choic of qutions usd to clcult rf. Nvrthlss, whn pplid to th growth of crck (dfct E) in PM, stisfctory prdictions wr obtind fro ll th forul for th sll xtnt of crcking surd whn iniu crp strin rt dt wr usd (Figs 7 nd 8). Crck growth ws lwys ovrstitd whn vrg crp rt dt wr ployd (Fig. 9). Coprison of Figs 8 nd 9 indict tht siilr dvitions in prdictions of crcking cn b obtind fro choic of forul for rf or fro ppliction of diffrnt vrg crp strin rt dt. Prdictions of crck growth in th HAZ r uch or difficult to dtrin. Th thin lyr of HAZ is sndwichd btwn wld tl (WM) nd prnt tril (PM). Figur 3 shows tht th HAZ tril iniu crp rt is or or lss 000 tis fstr thn in th PM or WM t th s strss so tht it is unlikly tht it cn sustin th s strss s th trils on ithr sid. Prdictions bsd purly on HAZ or PM proprtis r thus not xpctd to produc rlibl prdictions s indictd in Fig. 0. A rsonbl corrltion is obtind whn th crck growth proprtis fro th HAZ r usd in conjunction with PM crp strin rt proprtis. It should b pointd out tht this invstigtion hs highlightd th snsitivity of crcking to th choic of forul nd trils proprtis dt ployd to k prdictions. No ccount hs bn tkn of diffrnt odls of th crcking procss. It is vidnt fro Fig. tht dfct D xhibitd n incubtion priod prior to th onst of crcking whrs dfct E did not. Th odl doptd ssud tht stdy stt distribution of dg hd dvlopd round th crck tip fro 7 Copyright 00 by ASME

8 th strt. It is possibl to dl with n incubtion priod by llowing th dg to build up hd of th crck prior to th onst of crcking (Wbstr nd Ainsworth, 994), but this ws not th purpos of th invstigtion. CONCLUSION A Modl for prdicting crp crck growth fro dfcts in high tprtur plnt hs bn prsntd in trs of th crp frctur chnics prtr C*. Th crp prtr, C*, hs bn stitd fro rfrnc strss forultions dvlopd by Ainsworth (98). It hs bn stblishd tht diffrnt strss intnsity fctor, K, nd rfrnc strss, rf, solutions r vilbl for prforing ssssnts. Consquntly, it hs bn found tht diffrnt prdictions r obtind whn ths solutions r pplid to si-llipticl surfc dfct in pip subjctd to n intrnl prssur, vn whn th s tril crp proprtis r ssud. Vritions in crck growth ti of up to fctor of hv bn found fro diffrnt rfrnc strss solutions. Howvr it hs bn dtrind tht btch to btch vritions in tril proprty dt cn cus crck growth tis to diffr by up to fctor of 5 dpnding on whthr iniu or vrg crp strin rt dt r chosn. Furthr diffrncs in prdictions cn b xpctd if llownc for n incubtion priod prior to th onst of crcking is includd in th nlysis. ACKNOWLEDGMENTS Th uthors would lik to cknowldg th provision of dt fro th Brit/Eur HIDA ( ) nd LICON (997-00) projct prtnrs, nd to British Enrgy Gnrtion Ltd. for thir finncil support. REFERENCES Ainsworth, R.A. So Obsrvtions on Crp Crck Growth. Intrntionl Journl of Frctur, Vol. 0, pp (98) Ainsworth, R. A. Th Assssnt of Dfcts in Structurs of Strin Hrdning Mtril. Enginring Frctur Mchnic, Vol. 9, pp (984) Andrsson, P., Brgn, M., Brickstd, B., Dhlbrg. L., Nilsson, F. nd Sttri-Fr, I. A Procdur for Sfty Assssnt of Coponnts with Crcks - Hndbook. SAQ, (996) British Stndrd. BS 790: Guid on Mthods for Assssing th Accptbility of Flws in Mtllic Structurs. BSi,, (999). Chll, G. G. A Coputr Progr for Assssing Dfcts in Sphrs nd Cylindrs. ADISC, TPRD/L/MT037/M84, (984) Connors, D. C. A Copndiu of Liit Lods. BNFL Mgnox Gnrtion, M/TE/GEN/REP/0054/98, (998). Druby, B., Moulin, D. nd Chpuliot, S. A6: Guid for Dfct Assssnt nd Lk Bfor Brk, Third Drft. Coissrit l'enrgi Atoiqu (CEA), DMT , (995) Ellison, E. G. nd Hrpr, M. P. Crp Bhviour of Coponnts Contining Crcks - Criticl Rviw. Journl of Strin Anlysis, Vol. 3, pp (978) Folis, E. S. An Axil Crck in Prssurisd Cylindricl Shll. Intrntionl Journl of Frctur Mchnics, Vol., pp (965) Hutchinson, J. W. Singulr Bhviour t th nd of Tnsil Crck in Hrdning Mtril. Journl of th Mchnics nd Physics, of Solids, Vol. 6, pp (968) Kifnr, J. F., Mxy, W. A., Eibr, A. nd Duffy, A. R. Filur Strss Lvls of Flws in Prssurisd Cylindrs. Progrss in Flow Growth nd Grctur Toughnss Tsting, Vol. ASTM STP 536, pp (973) Lh, S. Al. Strss Intnsity Fctor nd Liit Lod - Hndbook. British Engry, EPD/GEN/REP/036/98, (999). Millr, A.G. Rviw of Liit Lods of Structurs Contining Dfcts. Intrntionl Journl of Prssur Vssl nd Piping, Vol. 3, pp (988) Nikbin, K. M., Sith, D. J. nd Wbstr, G. A. Influnc of Crp Ductility nd Stt of Strss on Crp Crck Growth. Advncs in Lif Prdiction Mthods t Elvtd Tprturs, Vol., pp (983) Nikbin, K. M., Sith, D. J. nd Wbstr, G. A. Prdiction of Crp Crck Growth fro Unixil Crp Dt. Procdings of th Royl Socity, Vol. A396, pp (984) Nikbin, K.M., Sith, D. J. nd Wbstr, G.A.,. An Enginring Approch to th Prdiction of Crp Crck Growth. Journl of Enginring Mtrils nd Tchnology, Vol. 08, no. Arpil 986, pp (986) Norton, F.H. "Th Crp of Stl t High Tprturs". Editd by McGrw nd Hill. London, (99) British Enrgy Gnrtion Ltd. R5: Assssnt Procdur for th High Tprtur Rspons of Structurs. British Enrgy Gnrtion Ltd. Uk, Rport R5, (000) British Enrgy Gnrtion Ltd. R6: Assssnt of th Intgrity of Structurs Contining Dfcts. British Enrgy Gnrtion Ltd. Uk, Rport R6, (00) Rju, I. S. nd Nwn, J. C. Strss-Intnsity Fctors for Intrnl nd Extrnl Surfc Crcks in Cylindricl Vssls. Journl of Prssur Vssl Tchnology, Vol. 04, pp (98) Sttri-Fr, I. Finit Elnt Anlysis of Liit Lods for Surfc Crcks in Plt. Intrntionl Journl of Prssur Vssl nd Piping, Vol. 57, pp (994) Wbstr, G.A. nd Ainsworth, R.A. "High Tprtur Coponnt Lif Assssnt". st d. Cbridg: Chpn nd Hll, (994) 8 Copyright 00 by ASME