Stress Effects in Cylindrical Tubes of Austenitic and Ferritic/Martensitic Steels with Oxide Scales

Transcription

1 Fchungzentum Kaluhe n de Helmhltz-Genchaft Wenchaftlche Bechte FZKA 6737 Ste ffect n Cylndcal Tube f Autentc and Fetc/Matentc Steel wth Oxde Scale - Mateal Selectn f a HPLWR - H. Stene Inttut fü Matealfchung Pgamm Nukleae Schehetfchung Fchungzentum Kaluhe GmbH, Kaluhe 22

2 Impeum de Pnt-Augabe: Al Manukpt geduckt Fü deen Becht behalten w un alle Rechte v Fchungzentum Kaluhe GmbH Ptfach 364, 7621 Kaluhe Mtgled de Hemann vn Helmhltz-Genchaft Deutche Fchungzenten (HGF) ISSN

3 Abtact In the fa f the tude f a hgh pefmance cncept f a Lght Wate React (LWR) dffeent mateal f the claddng ae nvetgated, amng them ae autentc and fetc/matentc (f/m) teel f dffeent C cntent. Due t the envaged vey extended lfe t f the fuel elent n the eact, cn pblem may ae. Thu, cackng and/ pallng effect n de cale n tallc cmpnent may play an mptant le n the cn pce a they lead, n geneal, t a datc enhancent n the datn ate. Analytcal mdel f dffeent fundantal te pblem n the cmpund de cale/ tallc ubtate have been develped and mplented n the cmpute cde. Thee mdel cncen the gwth tee n the cylndcal tube, the tee due t tempeatue change and adal tempeatue gadent and the tee due t nde and utde peue. Spannungeffekte duch Oxdchchten auf zylndchen Rhen au autentchen und fetch/matentchen Stählen Zuamnfaung Im Rahn de Studen fü en Hchletungknzept ene Lechtwaeeakt (LWR) weden vechedene Hüllmatealen auf he gnung hn unteucht, unte andeem auch autentche und fetch/matentche Stähle. Aufgund de vgeehenen eh langen Standzeten de Bennelente m Reakt können Knpble aufteten. Dabe können Rbldungen und Abplatzvgänge n den Oxdchchten zu ene datchen höhung de Oxdatnaten fühen. Dazu wuden analytche Mdelle zu Bechebung vn vechedenen fundantalen Spannungpblen m Vebund au Oxdchcht und tallchem Subtat entwckelt und n den Cmputecde engebaut. Dee Mdelle beteffen m enzelnen de Wachtumpannungen n zylndchen Rhen, de chanchen Spannungen duch Tempeatuwechel und duch adale Tempeatugadenten n den Hüllhen und de Spannungen duch nnee und äußee Dücke.

4 CONTNTS Page 1 Intductn Mateal data Mdel develpnt and dcun f te effect Gwth tee Stee upn tempeatue change Themal tee by adal tempeatue gadent Stee due t nde and utde peue Cnclun Refeence...16 Ntatn Indce Fgue 2-14

5 1 Intductn In the fa f the tude f a hgh pefmance cncept f a Lght Wate React (LWR) dffeent mateal f the claddng ae nvetgated, amng them ae autentc and fetc/matentc (f/m) teel f dffeent C cntent. Due t the envaged vey extended lfe t f the fuel elent n the eact, cn pblem may ae. Thu, cackng and pallng effect n de cale n tallc cmpnent may play an mptant le n the cn pce a they lead,n geneal, t a datc enhancent n the datn ate. The mdelng f the te/tan evlutn n the de cale and the tallc ubtate an ndpenable peequte f the undetandng f the te effect. In de t acheve th dffeent nucal thd lke fnte elent fnte dffeence lutn f the tetan equatn d ext. But thee thd demand a athe hgh nucal efft and d nt alway allw t evdence and undetand the nfluence f the bac phycal paate n an eay manne. The ue f mple analytcal mdel ha theefe advantage n th epect and wth uch mdel dffeent te effect can be nvetgated athe ealy. In th ept we have cndeed gwth tee, tee due t tempeatue change and adal tempeatue gadent, a well a tee due nde and utde ga peue. 2 Mateal data In th ectn we have cmpled the mateal data ued f the calculatn. Of cue, the eult f the mdel ae vey much nfluenced by the chce f thee data and dcun wthwhle. Data f the de C 2 O 3 and FeO, Fe 2 O 3 and Fe 3 O 4 ae athe cace, epecally f the tempeatue ange 6-65 C. A evew n chancal ppete f de gven by M. Schütze /1/. S data f de culd al be fund n a pape f H.. van /2/ and n the handbk f Gln /3/. The data ued f the fetc and autentc ally ae manly fm a ept f C. Peteen /4/. Cncenng the chancal data t upng, that the dffeence n the Yung' mdulu f the tallc ally and that f the epectve de lw, epecally f the fetc matentc ally. It huld be nted that the Yung' mdulu f the de f cndeable mptance f the te calculatn. A cncen the Pn numbe, the a value ha been taken f the de and the tallc phae n de t mplfy the te equatn a bt. Othewe at f (1 - υ )/ (1- υ ) wuld appea f the b-axal te tate. But n any cae, thee at wuld have value nt fa fm ne. 1

6 Table 1: Mateal data ued f the te calculatn α [1/K] 1,8 1-5 (autente) 1, (fete) α [1/K], [MPa] 1,5 1 5 (autente) 1,7 1 5 (fete) [MPa] 2,6 1 5 (autente) 2,1 1 5 (fete) ν [-],3 K I [M/M 3/2 ] 1,7 γ [J/m 2 ] 6 Data f ceep and datn f fetc/matentc and autentc ally have been tanmtted by L. Heknhem /5/ and M. Scha /6/. The celatn f the tal l thckne wee gven n the fllwng fm: (t) = A e B / T t 1/ 2 + p t (1) The value f the paate A, B, and p ae t be fund n table 2. Table 2: Paate value f the tal l celatn f dffeent elected ally Ally C cntent (%) A (µm/h ½ ) B (K) p (T=65 C) (µm/h) ST22 TP91 HCM12A TP347HFG <4 1-4 <2 1-4 <2 1-4 Baed n thee data celatn f the de cale thckne value f the tal l thckne wee btaned ung: = 1/ 2 (2) a the Pllng-Bedwth at have value f abut 2. F the ceep ate f the tallc ubtate ε, the fllwng celatn vald f tempeatue aund 65 C have been etablhed baed n the data tanmtted n /6/: 2

7 ST wt% C ε& (,T) = exp( 5543 / T) TP91 9 wt% C ε& (,T) = NF616 1 wt% C 5.5 ε& (,T) = HCM12A wt% C ε& (,T) = ε& (,T) = exp( 868/ T) exp( 722 / T) exp( / T) exp( 5687 / T) ε& n 1/ n Mpa T n K 3 Mdel develpnt and dcun f te effect In th ectn mple analytcal mdel f dffeent te effect due t the peence f de cale ae develped and dcued. Thee cncen the tee due t the gwth f the de cale, the te effect f tempeatue change and that f adal tempeatue gadent, and the tee due t nde and utde (ga) peue. All thee effect ae dcued epaately n de t etablh clealy the epectve mptance. But accdng t the ccumtance, f thee effect may act cncmtantly, and a ceep effect n the tallc ubtate may play a le, the eal tuatn can be athe cmplcated. All the mdel peented and dcued n the fllwng ectn ae mplented n the ecently develped cde, whch un n a penal cmpute. The dffeent mdel can be elected wth the help f a teeng paate. 3.1 Gwth tee Gwth tee ae due t the vlu nceae caued by the ygen uptake. The te tate depend n the detal f the gwth pce, that an whethe the de cale gw n t utde n t nde whethe gwth tpc ge nly n adal dectn /7/. In autentc teel t pedmnantly the C 3+ n whch ae mgatng /8/, theefe the de cale gwng at the utde. In fetc/matentc ally the de cale cnt f eveal ublaye /9/. A thee ygen dffun bede that f Fe 2+/3* and C 3+ n we have nde and utde gwth n the de cale. Thu, the tuatn athe cmplcated f f/m ally. 3

8 The man aumptn that the gwth f the de cale ge nly n adal dectn and that f autentc a well a f fetc ally. On a flat plate thee wuld be n th cae n gwth tee, but n a cuved uface, a f a cylndcal tube, gwth tee ae. Thu, we have a puely getcal effect. By the gwth f the cale a pnt P, whch wa gnally lcated at the adu a dplaced by the amunt u (ee fg. 1): befe datn afte datn P a u h Q Fg. 1: Schematc vew f the getcal change due t de cale fmatn h = thckne f cnud tal laye u = h (3) The hp tan at th lcatn then gven a: and wth: u ε = (4) a = hϕ (5) ϕ = Pllng-Bedwth at we btan f the hp tan at the utde f the cale: ε ϕ 1 = (6) ϕ a F a flat plate the adu f cuvatue a wuld g t nfnty and the hp tan wuld be ze. Wth ϕ = 1 th wuld al be the cae. 4

9 The pnt Q at the nde f the cale undplaced and ha theefe n hp tan. Between Q and P the hp tan nceae lnealy wth the adal ptn. Due t u aumptn that the vlu nceae ge entely nt the adal dectn, thee n axal tan n the cale and the tallc ubtate. Theefe we have a mn-axal te tate n the claddng, naly a tenle hp te n the cale and a cmpeve hp te n the tallc ubtate. Theefe the tallc ubtate expeence a cntactn ε : Θ = an hp te n the tallc ubtate ε = (7) If th taken nt accunt, we btan f the dan hp tan n the de cale: ϕ 1 ε = 1 / 2 + ε (8) ϕ a The an hp tee n the de cale calculated wth the help f: x and n the tallc ubtate ae then = ε / (9) + = (1), = Yung mdule f tal and de phae = thckne f the tallc ubtate we btan: and: ϕ 1 = 1 / 2 (11) ϕ a 1 + = (12) If thee ceep n the tallc ubtate, due t the mn-axal te tate the equvalent te and ceep tan ncent ae gven a: eq = ε = ε eq,c (13) (14) and the ceep ncent n the t tep t then calculated wth the help f the ceep celatn: 5

10 ε,c = t ε(,t) (15) In th cae, n cled fm lutn f can be gven but th quantty can then be detemned wth the help f an teatve pcedue tatng at t = and takng nt accunt the accumulated ceep defmatn f the tallc ubtate n the cntactn ε : ε = + ε, c (16) t The teatve pcedue dne wth the help f the equatn (8), (15) and (16). In the de cale telf we d nt cnde ceep effect, a the maxmum degn tempeatue (65 C) dtnctly belw.4t m. It huld al be nted that the hp tee at the nde and the utde f the cale ae gven a:, = ε (17) 1, ϕ = ( + ε ) (18) ϕ a The fegng devatn f tee and tan baed n the aumptn that the vlu nceae due t datn pefectly antpc and ge nt the adal dectn. Wth th aumptn we hpe t appmate the eal cae athe well, but thee may, f cue, be tpc cmpnent n the vlu change. If ne take th tpc cmpnent nt accunt the hp te n the de cale a upeptn f an antpc and an tpc cmpnent: =, an +, (19) wth thee cmpnent gven a:, an f ϕ 1 = 1/ 2 a f ϕ 1 + (2), ε = w 1 ν 1. + (21) wth:,, z = (22) 6

11 f ϕ = ϕ 3 ε w ϕ = ε an w + ε w (23) (24) If the vlu change cmpletely tpc, ε an wuld be ze and equatn (21) pvde the well-knwn expen f the hp te n th cae. It huld be nted that the tpc vlu change gve a cmpeve hp te nt dependng n the adal lcatn. The tpc cmpnent f the te huld have a benefcal effect n the chancal tablty f the de cale. Up t a cetan value f the thckne the de cale eman entely n a cmpeve te tate due t the upeptn f the tpc and the antpc cmpnent f the hp te. It wuld be vey nteetng t check whethe f cetan ally we culd btan a maked effect. The tpc cntbutn culd be detemned by bendng expent wth a flat plate makng ue f the fmula f Stney/1/:, = (25) 6R R = adu f cuvatue F the t beng n uch bendng tet have been dne. Theefe, n data n the tpc cmpnent ae avalable. Thu, f the t beng we have t tck t u bac aumptn f a pefectly antpc vlu nceae gng entely nt the adal dectn. Calculatn have been dne wth f the f/m ally ST22, TP91, and HCM12A wth 2, 9, and 11 wt% C and f the autentc ally 1.491, a datn and ceep celatn wee avable f thee ally. Only the paablc cntbutn f the datn celatn have been ued n the celatn. S f the eult ae t be fund n fg. 2 t 7. The gwth tee ae mt mptant n the hgh tempeatue egn f the claddng, a the claddng cn nceae expnentally wth the tempeatue. Theefe the tempeatue ange between 5 and 65 C ha been nvetgated. Calculatn have been dne wth and wthut takng nt accunt the ceep f the tallc ubtate. The eult hwn n fg. 2 t 7 wee all btaned f a tempeatue f 6 C. In cae f n ceep effect taken nt accunt, the an and utde hp tee n the cale hw a paablc nceae, wheea the elatc cntactn f the tallc ubtate lead t cntnuu deceae f the nne hp te f the de cale. In the nne pat f the cale and n the tallc ubtate the hp tee ae cmpeve, wheea the ute pat f the cale n a tenle te tate. The hghe the datn ate, the hghe and fate e the tenle hp tee. A n a ceep n the tallc ubtate c nt play the utde and the an hp te n the de cale n lnge e paablcally, but the an hp te even eache a maxmum and then deceae gadually theeafte. Tenle tee lead t cackng n the cale when the maxmum hp te abve the factue te. We can lean fm u calculatn f gwth tee that n the nne pat f the cale thee huld be n cackng and the ally wth hgh datn ate huld hw me cackng than that wth lw datn ate. We wuld expect that f the ally ST22 and TP91 cackng tat athe ealy, wheea f HCM12A t vey much late and le evee. It huld be nted that the autentc ally ha pactcally the a datn ate a the f/m ally HCM12A and theefe al abut the a te evlutn. The factue te n the de cale detemned by the flaw ze c. Wth K I beng the factue tughne, we have the fllwng equatn f the factue te f : 7

12 K I = f Π c (26) f F a penny-haped flaw the getcal fact f exactly 1, f the flaw gete f a bt dffeent fm 1. Thu, th paate ha nt a decve nfluence. F a factue tughne value f 1,7 MN/m 3/2, we have calculated the factue te f the flaw adu c vayng between 1 and 1 µm. The eult ae t be fund n table 3. Thu the factue te vae between abut 1 and 9 MPa. The flaw ze huld what be celated t the thckne f the cale. It, f example, nt pble t have a flaw ze f 1 µm n a cale f abut 1 µm. If thee a gwth f vd and/ pe n the de cale due t mgatn f vacance, then the flaw ze a functn f t and theefe the factue te huld deceae n the cue f the datn pce. Table 3: Factue te value n n de f penny-haped flaw f dffeent ze (K I = 1,7 MN/m 3/2 ) Radu f penny-haped flaw [µm] Factue Ste [MPa] In /1/ value f tenle factue tan f C 2 O 3 cale gwn n ally 8H and f bulk chma ae gven. The value ange fm abut.1% t abut.4%. F tempeatue between 6 and 65 C the value ae between.2 and.4%. Wth a value f 2.6e5 Mpa f Yung mdulu we btan factue te value between 52 and 14 Mpa. In /11/ the fllwng celatn f the de falue tan n dependence n the de cale thckne pvded: γ c 1/ 2 ε fac = ( ) (27) 2p wth p epeentng the factn f the effectve flaw ze t the de cale thckne and γ c beng the cheve factue enegy. A uggeted n /11/ the value p =.25 and γ c / = wee ued t detemne the de factue te n dependence n the de cale thckne. The factue te gven by th empcal mdel hwn n fg. 8. F vey mall de cale we btan factue te value f me than 2 Mpa. F de cale abve 1 µm the factue te fall belw 2 Mpa. In fg. 3 t 5 the evlutn f the factue te hwn tgethe wth the nde, an, and utde hp tee n the de cale f the thee f/m ally, whch we have nvetgated. Accdng t thee eult the f/m ally ST22 and TP91 wuld be much eale affected by de cale cackng than the f/m ally HCM12A. F th ally the utde hp te n the de cale ce the factue te cuve but nt the an hp te. Th wuld an that le than half f the de cale huld be affected by cackng. The te calculatn peented and dcued n the fegng ae,f cue, nly vald n the lnea elatc cae, that an befe cackng f the cale. Wth the ccuence f cackng the tee n the cale ae eleaed t a gd extent and wth futhe gwth f the cale a new te cycle evlve. We gue that the gwth f the cale cntnue at the utde f the ntact pat (autentc ally) at t utde and nde (f/m ally), and that the cacked pat f the cale ely dplaced ahead f the ntact pat. Wth a new cackng event pat f the newly fd ntact cale cacked. The data ugget that cackng 8

13 nceae lnealy wth t, that an the lape f t needed t each a te level uffcent f cackng huld be ughly cntant ve the whle expue t. An expental pgam wuld be needed f the valdatn f the mdel f the gwth tee peented and dcued n th ectn. In the fa f uch a pgam ne huld ty t detemne the net f cackng n the de cale and the evclutn f the factued pat. The ceep f the tallc ubtate n the the hand lead t ceep tan, whch culd eventually be aued. 3.2 Stee upn tempeatue change Thee tee ae due t the dffeence n the themal expann f the de cale and the tallc ubtate. Fce equlbum: + = (28) and cntnuty f hp tan at the nteface de/tal: 1 ν 1 ν + α T = + α T lead t the fllwng equatn f the hp tee n the de cale and the tallc ubtate: (29) ( α α = 1 ν 1 + ) T (3) = (31) Due t the tpc natue f the themal expann we have a b-axal te tate n the claddng wth:,,, z (32) It undetd that the claddng n a hmgeneu tempeatue dtbutn befe and afte the tempeatue amp T. If th nt the cae the tem T α ha t be eplaced by ntegal ve the clad wall thckne. 9

14 The cectn fact 1 + ae due t the fnte thckne f the tallc ubtate. Wth an nfntely thck ubtate th fact wuld be 1 and we wuld btan an expen f the hp te n the de cale knwn fm the lteatue. Calculatn have been dne f autentc and fetc ally and dwnwad tempeatue amp f -1 K, - 3 K, and - 6 K wth the mateal data taken fm table 1. The eult f the hp te ae pltted n fg. 9 and 1 a a functn f the de cale thckne. A the themal expann ceffcent n the de cale malle than that n the tallc ubtate, we btan cmpeve hp tee n the de cale and tenle tee n the tallc ubtate. F f/m ally the dffeence f themal expann ceffcent abut 5 % malle than f autentc ally. Th eflected n the hp te value. It ha been aud, that we have the a themal expann ceffcent n the whle de cale. But the data fund n the lteatue /3/ ugget that thee ae dffeence f the ublaye n the cale f fetc teel. Th wuld lead t dffeence n the hp tee n the ublaye. N expental data f the n de culd be fund f tempeatue abve 1 C. Thu, we have taken f α the a value a f C2O 3. It culd well be that the themal expann ceffcent f n de n the elevant tempeatue ange (3-5 C) a bt hghe than, /K. Th wuld then an that the hp te value n cae f fetc matentc ally ae what lwe than that hwn n fg. 9. Wth cmpeve tee n the de cale thee ae tw ute f cale cackng and pallng naly a wedgng and a bucklng chanm dependng n the chancal ppete f the cale and the nteface (ee f example ef. /2/). The bucklng chanm nly mptant f cack-lke defect n the nteface wth a adu much lage than the cale thckne/12/. Thu, the chanm elevant n u cae huld be the wedgng pce, a we d nt expect lage defect n the nteface. If W* the elatc tan enegy pe unt vlu, then the fllwng ctea f the cackng f the cale ha been pped by U.R. van /13/. W* γ (33) whee γ the factue enegy pe unt aea f the nteface. F a b-axal te tate the elatc enegy W* gven a: 2 W* = ( 1 ν ) (34) c Thu, we btan the fllwng expen f the ctcal tempeatue amp Τ 2 c γ ( 1 ν ) 1 1 ( 1 ) τ = + (35) 2 ( α ) Wth the data lted n table 1 we wuld btan f a cale thckne f 1 µm a ctcal tempeatue amp f abut -39 K f fetc ally and abut -13 K f autentc ally. 1

15 3.3 Themal tee by adal tempeatue gadent A n the fegng ectn we have a b-axal te tate ang due t the dffeence n themal expann, but n th cae due t the tempeatue gadent n each mateal. Thu we have f the tallc ubtate and the de cale the fllwng hp te ncent between nde and utde lcatn: α T = 1 ν α T = 1 ν (36) (37) whee T, ae the tempeatue dffeence between nde and utde f each laye. T a gd appmatn we have n bth mateal lnea te dtbutn. They can be detemned wth the help f the cntnuty cndtn f the hp tan at the nteface., whch lead t the fllwng equatn: Wth the help f the fce balance:, =, (38) + = (39) we btan the fllwng equatn f the aveage hp te n the tallc ubtate: + = (4) 2( + ) Thu, the nde and utde hp tee n the tallc ubtate and n the de cale ae gven a:,, = 1/ 2 = + 1/ 2 (41) (42), =, (43) and:, =, +, (44) 11

16 =, + 1/ 2 (45) If thee n de cale peent, then the expen mplfy t:, = 1/ 2 (46), = 1/ 2 (47) F mplcty we au that the heat pedmnantly pduced n the fuel. If the lnea d pwe χ, we have the fllwng tempeatue gadent n bth laye: χ T = ln(, /, ) (48) 2Πλ χ T = ln(, /, ) (49) 2Πλ Wth the paate lted n table 1 we btan the te dtbutn hwn n fg. 11. Thu, f a lnea d pwe f 4 W/cm we wuld f autentc ally btan an utde hp te n the de cale f abut 185 Mpa, a te level whch culd lead t cackng. F fetc ally the utde hp te wuld amunt t abut 145 MPa. If the tallc ubtate can ceep, tee n th mateal can elax t a cetan extent; and the te level n the de cale can be cndeably educed. But the calculatn f the ceep elaxatn pce n th cae beynd the cpe f the cde, a we have te and tempeatue gadent n the tal phae. N value f the themal cnductvty f C 2 O 3 culd be fund n the lteatue. A a ft eanable gue t wa aud that λ = 1/5 λ, baed n data f ZO Stee due t nde and utde peue The peence f ntact de cale nceae the tength f the claddng. The man pupe f th ectn t nvetgate the cnequence f th effect n fuel d degn. Thu, the epectve calculatn ae f nde and utde peue value a btaned fm degn calculatn f the taget bun-up. Tw dffeent lutn ae mplented n the cde. The ft lutn baed n a fnte dffeence appmatn f the te equlbum cndtn n the tube and the ecnd lutn baed n the La equatn. We tat wth the ft lutn. The fllwng equlbum cndtn vald f cylndcal tube: d d = (5) The fnte dffeence appmatn t th equatn, appled f a cetan laye n the claddng ead a fllw: 12

17 wth : = (51) = 1/ 2( + ) (52) 1/ 2(, = + ) (53),, Wth the bunday cndtn:, = p, (54) we btan: ( p ) 1/ 2( p p = p + ) (55) wth = - and p and p beng the nde and utde peue. The equatn (55) can be appled t the tallc ubtate and the de cale: nt = ( p p ) + (56) nt = ( p p ) + (57) The unknwn peue at the nteface p nt can be detemned wth the help f the cntnuty cndtn f the hp tan, whch lead t: that we fnally btan: = (58) p nt = (p ( + 1) + p ( 1)) /( + ) (59) The thckne f the tallc ubtate can be calculated accdng t: = (6) ϕ = the a-fabcated clad wall thckne Reult f calculatn f the fetc ally HCM12A ae hwn n fg. 12 t 13 wth and wthut takng nt accunt the tengthenng effect f the de cale n the te calculatn. The value f the paablc de cale thckne at a tempeatue f 65 C 13

18 and the nne pn peue at dffeent t f peatn ae lted n table 4,a they wee btaned fm the datn celatn f th ally and fm degn calculatn f the fn ga peue /14/. The datn celatn f the autentc ally gve ughly the a value f the de cale thckne, f example at an peatnal t f 45 h we btan a value f 133 µm f th autentc ally. Th nly lghtly lwe than the epectve value f 136 µm f the fetc ally HCM12A. Theefe the te eult btaned f the fetc ally HCM12A ae t a gd appmatn al vald f the autentc ally If ne take the tengthenng effect f the de cale nt accunt, Yung mdul f the tal and f the de play a le and th make that bth ally have lghtly dffeent te value. Unde nmal peatnal cndtn the clant peue 25 Mpa but n cae f an accdent we have t take a value f Mpa f the ute peue. Ste calculatn have been dne n each cae f bth value f ute d peue. Theefe we have n each fgue fu te cuve. F degn cndeatn the hp te n the tallc ubtate decve. Theefe we have cncentated n th apect. Unde nmal peatn we btan cmpeve hp tee and unde afety cndtn tenle tee n the claddng. If ne take the tengthenng effect f the de cale nt accunt the ladng f the tallc ubtate educed. An mptant paate cnttute al the a-fabcated clad wall thckne. A ange f.4 t.7 mm ha been taken n the calculatn f th paate. The hghe the a-fabcated clad wall thckne the lwe the chancal ladng f the claddng. The nceae f the n pn ga peue unde nmal peatn benefcal f the chancal ladng f the claddng, a the dffeence between nne and ute peue deceae. If the chancal effect f the de cale neglected, the deceae f the tallc laye thckne cuntebalance the peue effect t extent up t an peatnal t f abut 1 h. Aftewad the benefcal effect f the n pn ga peue nceae dmnate n any cae. Table 4: Value f the de cale thckne at 65 C f the fetc ally HCM12A and f the n pn ga peue at dffeent peatnal t t (h) (um) p n (Mpa) When the peue n the clant channel hghe than the nde ga peue, we btan cmpeve hp tee n the de cale and n th cae thee may be n dubt abut the tengthenng effect f the de cale. In the LOCA cae (p = Mpa) we btan tenle hp tee n the de cale and dependng n the value f the factue te thee can be cackng f the cale and the tengthenng effect wll be lt. The fegng appmate lutn f the te pblem wa baed n a fnte dffeence expen f the equlbum cndtn f the tee n the cylndcal tube, and an value can uccefully be appled nly f thn-walled tube. F thck-walled tube ne mut take ecue t the La te equatn /15/. Thee ae n the elatc cae the exact lutn f the te pblem n a cylndcal tube wth nde and utde peue. The La lutn can,f cue, be ued t check the valdty f the appmate lutn. 14

19 The te functn have the fllwng geneal fm n the tallc ubtate and n the de cale: B ( ) A = + (61) 2 B ( ) = A (62) 2 B ( ) A = + (63) 2 B ( ) = A (64) 2 Thu, thee lutn depend n 4 fee paate, whch have t be detemned wth the help f 4 bunday cndtn: p ( ) = (65) p ( ) = (66) ε ( nt ) = nt ( ) = ε ( ( nt nt ) (67) ) (68) The lutn f thee equatn a lengthy tak and hall nt be epeated hee. But we can nte that the 4 paate A / and B / depend n the 3 ad,, and nt, the nde and utde peue p and p and the Yung mdul and and the Pn numbe υ. The eult f a calculatn f the fetc ally HCM12A ae t be fund n fg. 14. In th fgue ae al nted the paate whch have been ued f the calculatn, naly an afabcated clad wall thckne f.4 mm, f example. The tee depend n th cae n the adal ptn wth a nealy lnea dependence. The an value f the hp te n the tallc ubtate abut 112 MPa, wheea wth the appmate lutn we btaned a value f abut 115 MPa. 4 Cnclun Smple analytcal mdel f lutn f dffeent te pblem n cylndcal tube f autentc and fetc/matentc ally wth de cale have been develped and mplented n the cde. They allw t gan dect nght nt the tuatn and t dcen the man phycal paate, whch detemne the behav f the cmpund de cale/ tallc ubtate and ae theefe mt valuable f degn cndeatn. 15

20 5 Refeence [1] M. Schütze: Mechancal Ppete f Oxde Scale, Ox. Of Met., Vl. 44, pp 29-61, 1995 [2] H.. van: Mdelng de pallatn, Mat. Hgh Temp., Vl. 12, pp , 1994 [3] Gln Handbuch de Anganchen Cheme, Velag Cheme, Wenhem, 197 [4] C. Peteen: Lteatuübecht chanche und phykalche genchaften vn Hüllwektffen fü Ftgechttene Duckwaeeakten (FDWR) be hhe Tempeatu, KfK 3469, 1983 [5] L. Heknhem: pvate cmmuncatn [6] M. Scha: pvate cmmuncatn [7] M. I. Mannng: Getcal ffect n Scale Integty, C. Scence, Vl. 21, pp , 1981 [8] S. pevk, et al: Oxdatn f N-C-W Tenay ally, Oxdatn f Metal, Vl. 14 pp , 198 [9] G. Mülle: Knvehalten vn Stählen n flügem Ble nach Behandlung mt hchenegetchen gepulten lektntahlen, FZKA 6422, 2 [1] G. C. Stney, Pc. R. Sc., Lndn A82, p.172, 199 [11] M.I. Mannng and D.B. Meadwcft, unpublhed [12] H. Stene, M. Heck: Stee n an Oxdzed Zcaly Claddng unde Quench Cndtn, Nucl. Techn. Vl. 123, pp , 1998 [13] U.R. van: An Intductn t Metallc Cn, dwad Anld, Lndn, 1948 [14] K. hlch, pvate cmmuncatn [15] J. Chakabaty: They f Platcty, Mcgaw-Hll Inten. dt.,n.y., p.316,

21 Ntatn = te є = tan T = tempeatue t = t = Yung' mdulu ν = Pn-numbe φ = Pllng/Bedwth-at α = themal expann ceff. K I = factue tughne γ = factue enegy = adu = cale thckne = wall thckne a = gnal clad ute adu c = flaw ze w = tan enegy Indce = de = tallc = nne = ute = azmuthal z = axal = adal eq = equvalent f = factue c = ctcal w = wellng V = vlu 17

22 de cale thckne [µm] T = 6 C ST22 TP91 HCM12A t [h] Fg. 2: vlutn f the paablc cntbutn t the de cale thckne f thee f/m ally T = 6 C ST22 n ceep T = 6 C ST22 wth ceep 1 5 S 1 5 S hp te [M/Pa] Sm Sfac S Sm Sfac S t [h] t [h] Fg. 3: vlutn f the hp tee n the de cale f the f/m ally ST22 wth and wthut ceep n the tallc ubtate and the factue te acc. t ef. [11] 18

23 hp te [M/Pa] Fg. 4: T = 6 C TP91 n ceep S Sm Sfac S T = 6 C Sm t [h] t [h] vlutn f the hp tee n the de cale f the f/m ally TP91 wth and wthut ceep n the tallc ubtate and the factue te acc. t ef. [11] S TP91 wth ceep Sfac S T = 6 C HCM12A n ceep T = 6 C HCM12A wth ceep hp te [M/Pa] Sfac S Sfac S 2 Sm 2 Sm Fg. 5: -2 S t [h] -2 S t [h] vlutn f the hp tee n the de cale f the f/m ally HCM12A wth and wthut ceep n the tallc ubtate and the factue te acc. t ef. [11] 19

24 1 1 1 T = 6 C n ceep T = 6 C wth ceep 9 9 an hp te [M/Pa] ST22 TP91 HCM12A ST22 TP91 HCM12A 1 1 Fg.6: t [h] t [h] vlutn f the an hp te n the de cale f thee f/m ally wth and wthut ceep n the tallc ubtate T = 6 C n ceep T = 6 C wth ceep utde hp te [M/Pa] ST22 TP91 HCM12A ST22 TP91 HCM12A t [h] t [h] Fg. 7: vlutn f utde hp te n the de cale f thee f/m ally wth and wthut ceep n the tallc ubtate taken nt accunt 2

25 2 5 factue te [MPa] de cale thckne [µm] Fg. 8: Factue te n the de cale veu the de cale thckne acc. t ef. [11] hp te [MPa] Fg. 9: S (1) S (2) S (3) fetc / matentc ally S (3) S (1) S (2) (1) : t = -1 K (2) : t = - 3 K (3) : t = - 6K,,1,2,3,4,5,6,7,8,9,1. cale [mm] Hp te n the. cale and the t. ubtate f dffeent temp. amp h p t e [MPa ] Fg. 1: autentc ally S (1) S (2) S (3) S (3) S (2) S (1) (1) : t = -1 K (2) : t = - 3 K (3) : t = - 6K,,1,2,3,4,5,6,7,8,9,1. cale [mm] Hp te n the. cale and the t. ubtate f dffeent temp. Ramp 21

26 hp te [M/Pa] d =.1 mm =.4 mm P = 4 W/cm autentc teel fetc teel 3,6 3,65 3,7 3,75 3,8 3,85 3,9 3,95 4, 4,5 4,1 adu [mm] Fg. 11 Radal hp te dtbutn n an dzed claddng due t a adal temp. gadent HCM12A T = 65 C p = 25 MPa 2 HCM12A T = 65 C p = MPa an t. hp te [M/Pa] (1) =.4 mm wth. cale (2) =.4 mm wthut. cale (3) =.7 mm wth. cale (4) =.7 mm wthut. cale (3) (4) (1) (2) 2 4 t [h] (2) (1) (3) (4) (1) =.4 mm wth. cale (2) =.4 mm wthut. cale (3) =.7 mm wth. cale (4) =.7 mm wthut. cale 2 4 t [h] Fg : vlutn f the an hp te n the t. ubtate f tw value f the afab. clad wall thckne wth and wthut takng nt accunt the tengthenng effect f the de cale 22

27 te [M/Pa] hp te HCM12A p = 17.9 MPa p = MPa d = 271 µm adal te 3,6 3,7 3,8 3,9 4, 4,1 adu [mm] Fg. 14: Radal dtbutn f tee n an dzed claddng acc. t the la lutn 23