FITNET FFS MK7 Section 8 CREEP MODULE. Module Coordinator: RA Ainsworth BRITISH ENERGY, UK

Transcription

1 FITNET FFS M7 Setion 8 CREEP MODULE Module Coodinato: RA Ainswoth BRITISH ENERGY, U

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3 (1 May 26) FITNET M7 Symbols a a a g ak size initial ak size ak size afte gowth a min ak size below whih the ak gowth ate is assumed to be onstant a ak gowth ate A mateial onstant (ee ak gowth) B mateial onstant (yli ak gowth) B n net seimen thikness C mateial onstant (yli ak gowth) C (t) tansient ak ti aamete C C * steady state ak ti aamete * * mean estimate of C duing tansient ealy yles d sufae ee damage aumulated in a yle suf D total sufae ee damage suf E (L J k elasti modulus f ) failue assessment uve initial value of elasti-lasti ak ti aamete fo ombined loading fato fo the weld zones stess intensity fato I id I i stess intensity fato mat ee toughness (TDFAD) maximum stess intensity fato in yle max minimum stess intensity fato in yle min s s stess intensity fato due to imay load fato fo the effet of yli stain hadening o softening stess intensity fato due to seonday loading mateial onstant (yli ak gowth) L load atio P / PL max L ut-off on TDFAD n ee stess exonent P load P L limit load mateial onstant (ee ak gowth) q q o Q fation of total load ange fo whih ak is judged to be oen mateial onstant (yli ak gowth) size of the yli lasti zone ak yli lasti zone size at the ak ti R stess intensity fato atio ( = min / max ) R * length in estimate of C R stess intensity fato atio (2CD) R stess atio (2CD) FITNET 26 All ights eseved 8-1

4 FITNET FFS M7 Cee Module S y t i minimum.2% oof stess initiation time t time to eah steady yli state y t o sevie life to date t g time equied fo the ak to oagate by an amount Δ a g t h hold time at high temeatue t m maximum allowable time at temeatue t utue time t edistibution time t ed s CD desied futue sevie life t time fo ontinuum damage failue T eene temeatue U U U U V Z e T ee aea unde load-dislaement uve elasti aea unde load-dislaement uve lasti aea unde load-dislaement uve total aea unde load-dislaement uve aamete teating inteations between imay and seonday stess elasti follow-u fato α oeffiient of themal exansion β, γ mateial onstants (ee ak initiation) δ i a i itial ak ti oening dislaement (ee ak initiation) Δ ak gowth oesonding to initiation Δ J ange of J-integal Δ ee dislaement Δ Δ e Δ T ε t elasti dislaement lasti dislaement total dislaement Δ total sufae stain ange (yli ak gowth) Δ eff stess intensity fato ange fo whih ak is oen ε ee stain ate at stess ε equivalent ee stain ate ε ee stain ε ε e elasti stain ee stain ate ε, ee stain ate at stess ε, ee stain ate at stess ε f ee dutility e ε elasti stain at stess e+ ε elasti lus lasti stain at stess 8-2 FITNET 26 All ights eseved

5 (1 May 26) FITNET M7 e+ + ε elasti lus lasti lus ee stain at stess ε elasti lus lasti stain at stess η μ ν homogeneous exeimental alibation fato stess exonent in owe law lastiity Poisson's atio shot-tem flow stess initial stess.2.2% ee stength 1. 1.% ee stength d max stess at a small distane ahead of the ak ti eak equivalent welding esidual stess nominal stess n l eene stess initial value of the total eene stess eene stess ate eene stess fo fist yle y= 1 eene stess fo imay loading homogeneous aked body eene stess R y u,hom ee utue stength yield stess ultimate tensile stess 2CD CT DMW TDFAD Two Citeia Diagam Comat Tension seimen Dissimila metal weld Time Deendent Failue Assessment Diagam FITNET 26 All ights eseved 8-3

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7 (1 May 26) FITNET M7 8 Cee module 8 Cee module Intodution Oveall Poedue Establish Cause of Caking Define Sevie Conditions Collet Mateials data Cee Rutue Data Cee Defomation Data Cee Dutility Data Cee Cak Initiation/Inubation Data Cee Cak Gowth Data Cyli Cak Gowth Data Method I Method II Othe Data Elasti and Physial Constants Stess-stain Data Fatue Toughness Data Pefom Basi Calulations Stess Intensity Fatos Refeene Stess C* Paamete Redistibution Time, t ed C(t) Paamete Chek Signifiane of Cee and Fatigue Insignifiant Cee Insignifiant Fatigue Insignifiant Cee-Fatigue Inteations Pefom Assessment Calulations Calulate Rutue Life, t CD Calulate Cak Inubation Time, t i Calulate Cak Size afte Gowth, a g Assess Signifiane of Results Sensitivity Analysis Remedial Ation Reot Results Additional Infomation Teatment of Defets in Weldments Intodution Soe Signifiane of Welding Residual Stesses Simlified Assessment Detailed Assessment Seifi Modes of Caking Teatment of Seonday Loading Failue Assessment Diagam Methods Intodution Cee Cak Initiation Assessment Poedues TDFAD Aoah Two Citeia Diagam Comaison of Paametes FITNET 26 All ights eseved 8-5

8 FITNET FFS M7 Cee Module Comaison of the TDFAD and the Two Citeia Diagam The d Aoah Bibliogahy FITNET 26 All ights eseved

9 (1 May 26) FITNET M7 8.1 Intodution The oedue in this setion seifies methods fo assessing defets in stutues oeating at high temeatues and subjet to ee-fatigue loading onditions. The basi ingedients equied fo an assessment ae: (i) the oeating onditions; (ii) the natue of the defets; (iii) mateials data; and (iv) stutual alulations to oelate mateials data tests with the behaviou of omlex stutues. This infomation is then used to assess whethe a defet of a given size will gow to an unaetable size by ee-fatigue mehanisms in a given sevie life unde a given loading histoy. The oedue an eadily be adated to onside assessments of othe tyes, suh as: (a) the loadings whih give a life equal to a given sevie life; (b) the initial flaw size whih will just gow to the maximum aetable size in a given sevie life (and hene the magin fo a given flaw size); () the ombinations of mateials oeties, geomety and loadings fo whih ak ti behaviou has a negligible effet on lifetime. An altenative oedue in Setion assesses whethe o not a small, defined ak extension will ou in the equied sevie life using a failue assessment diagam aoah simila to that in Setion 6. Anothe oedue in Setion uses the alulation of a stess at a small distane ahead of the ak ti, the d aoah, to assess whethe signifiant ak extension ous in the sevie life. 8.2 Oveall Poedue In this setion, a ste-by-ste oedue is set out fo assessing a omonent ontaining a known o ostulated defet unde ee-fatigue loading. Flowhats fo the oedue ae given in Figue 8.1 to Figue 8.3. These addess a omonent that is equied to oeate fo a futhe eiod, t s, at high temeatue. Continuum damage aumulation and ak gowth ae addessed. The ases of insignifiant ee and insignifiant fatigue ae inluded as seial ases. The oedue may be alied to a omonent that has not yet seen oeation at ee temeatues, o one that has aleady oeated fo a eiod, t o, at high temeatue. In the latte ase, advie is given additionally on the effet of the time at whih the defet is assumed to fom. The stes in the oedue ae listed below. Futhe infomation on efoming the individual stes is given in Setions 8.3 to 8.1. STEP 1. Establish Cause of Caking and Chaateise Initial Defet It is fist neessay to establish the ause of the aking to ensue that the ee oedues ae aliable. This is disussed in Setion 8.3. The defet tye, osition and size should also be identified. Fo defets found in sevie, this oess may equie the advie of mateials and non-destutive testing exets, atiulaly fo the ase of defets in welds. Suitable sensitivity studies should be efomed to addess unetainties. The deteted defet should be haateised by a suitable bounding ofile amenable to analysis. Defets whih ae not of simle Mode I tye should be esolved into Mode I oientation. Note that it may also be ossible late to e-haateise a defet in the ase that the initial assessment leads to an unaetable esult. Advie on defet haateisation is ontained in Setion 5.1. Advie on methods fo deteting and measuing defets is inluded in Annex E and oves omonents oeating at high temeatue. STEP 2. Define Sevie Conditions It is neessay to esolve the load histoy into yle tyes suitable fo analysis. This inludes both histoial oeation and the assumed futue sevie onditions. Advie is ontained in Setion 5.2. The sevie life seen to date and the desied futue sevie life should be defined. FITNET 26 All ights eseved 8-7

10 FITNET FFS M7 Cee Module Fo the ase of a omonent that was known to be defet-fee at the stat of high-temeatue oeation, an estimate of the time at whih the defet fomed should also be detemined. Suitable sensitivity studies should be efomed to addess unetainty in the time of defet fomation. STEP 3. Collet Mateials Data It is fist neessay to define the mateials elevant to the assessed featue inluding, in the ase of weldments, the weld metal and heat-affeted zone stutues. Then it is neessay to ollet the mateial oeties aoiate to the tye of assessment to be efomed (yli, ee, et) ove the aoiate temeatue ange and in the oet ylially-onditioned state. Fo examle, it may be neessay to onside the effets of themal ageing and edued dutility due to intenal oxidation oduts leaking to eed fatue aths. In atie, the equiements ae influened by the outome of the tests fo signifiant ee o fatigue in Ste 6 below. Time-indeendent mateial oeties ae equied fo the stability analyses in Stes 5 and 11, noting that fatue toughness oeties may be equied fo ee-damaged mateial. STEP 4. Pefom Basi Stess Analysis Elasti stess analyses of the unaked featue should be efomed fo the extemes of the sevie yles identified unde Ste 2 assuming homogeneous oeties. The analysis should allow fo any hanges fom the stat of oeation; fo examle, ineased stess due to loss of setion by wall thinning o ineased temeatues due to edution in themal diffusivity as a esult of sufae sale. In the ase of yli loading, a shakedown assessment of the unaked featue should then be efomed. It should be detemined that the featue satisfies stit o global shakedown. If shakedown annot be demonstated, it may be neessay to emloy inelasti analysis methods. If shakedown is demonstated, the ak deth should be suh that the omliane of the stutue is not signifiantly affeted. The extent of the yli lasti zone at the sufaes of the omonent should be evaluated as this may affet the method of alulating ak gowth in Ste 9. STEP 5. Chek Stability unde Time-Indeendent Loads The omonent should be assessed against failue by time-indeendent mehanisms unde fault o oveload onditions at the initial defet size using the fatue at of this oedue. This assessment should use the initial values of any esidual stesses, not those in the shakedown state. If failue is oneded at this stage, the assumtions in the analysis should be evisited o emedial ation taken. Only if suffiient magins an be justified is it emissible to ontinue to Ste 6 to justify futue sevie life. STEP 6. Chek Signifiane of Cee and Fatigue The signifiane of ee should be assessed. If ee is insignifiant then the assessment beomes one of yli loading alone and Stes 7 and 1 below ae omitted. Convesely, if fatigue is judged to be insignifiant, then the assessment beomes one of steady ee loading alone and futhe onsideation of yli loading is not equied. A futhe test detemines if ee-fatigue inteation is signifiant. If it is not, simlified summation ules fo ombining ee and fatigue ak gowth inements may be adoted. Setion 8.7 ontains detailed advie. STEP 7. Calulate Rutue Life based on the Initial Defet Size The time to ontinuum damage failue (ee utue), t CD, is fistly alulated based on the initial ak size fom Ste 1; if this is less than the equied sevie life, then magins ae not aetable and it may not be neessay to efom ak gowth alulations. The estimate of utue life is based on a alulated limit load eene stess and, fo edominately imay loading, the mateial s ee utue data. Fo damage due to yli elaxation and due to the elaxation of welding esidual stesses, dutility exhaustion methods ae moe aoiate. The detailed alulations ae desibed in Setion 8.8. STEP 8. Calulate Initiation Time The initiation time is the time, t i, fom the stat of the assessed eiod of high-temeatue oeation io to whih no signifiant ak gowth ous. Deending on the ause of aking, its loation within a weldment and the tye of loading it may be ossible to alulate a non-zeo initiation time. It is onsevative to ignoe 8-8 FITNET 26 All ights eseved

11 (1 May 26) FITNET M7 this eiod and assume that ak gowth ous on fist loading. Calulation methods ae set out in Setion 8.8. The ause of aking influenes the detemination of an initiation time. Fo examle, a natually-ouing ee defet, suh as a Tye IV weld defet, may not exeiene an initiation eiod io to maosoi ak gowth, unless the initial defet has extended aoss the egion of extensive ee damage leading to its fomation and thus has its ti in essentially undamaged mateial. STEP 9. Calulate Cak Size afte Gowth The ak size at the end of the assessed eiod of oeation is alulated, following the advie in Setion 8.7, by integating the aoiate ee and fatigue ak gowth exessions. This integation is simlified in some ases, deending on the outomes of the signifiane tests in Ste 6. Changes in eene stess due to ak gowth should be inluded in the alulations. STEP 1. Re-Calulate Rutue Life afte Cak Gowth The time to ontinuum damage failue should be e-alulated taking into aount the ineased ak size fom Ste 9. Cak gowth alulations should not be efomed in atie beyond an aetable utue life. It is onsevative to base the estimate of utue life on the final ak size as this neglets slowe aumulation of ee damage when the ak size is smalle duing gowth. STEP 11. Chek Stability unde Time-Indeendent Loads afte Cak Gowth In atie, this ste is aied out in onjuntion with the ak size alulations of Ste 9. The ak gowth alulations of that ste should not be efomed beyond a ak size at whih failue by time-indeendent mehanisms is oneded at fault o oveload load levels using the fatue oedue. STEP 12. Assess Signifiane of Results Magins against failue ae not esibed hee and ae left to the use to set. The sensitivity of the esults of the eeding stes to ealisti vaiations in loads, initial flaw size and loation, and mateial oeties must, howeve, is assessed as at of a sensitivity study. The vaious modelling assumtions made an also be evisited with a view to eduing essimisms in the analysis if unaetable magins ae detemined. If this still fails to esult in an aetable assessment, the otions of eduing futue sevie onditions, o eai o elaement of the defetive omonent should be onsideed. This is disussed in Setion 8.9. STEP 13. Reot Results The esults of the assessment, inluding magins detemined, and the details of the mateials oeties, flaw size, loads, stess analysis alulations, et, used in the assessment should be omehensively eoted. This failitates both veifiation of the atiula assessment and eeatability in futue assessments. FITNET 26 All ights eseved 8-9

12 FITNET FFS M7 Cee Module 8.3 Establish Cause of Caking Befoe efoming alulations, an investigation should be aied out to detemine the most likely ause of aking. At least, this should involve a ombination of non-destutive testing, visual examination and metallugial examination. If it is ossible to identify the mode of aking, this an ovide qualitative infomation on the elative ontibutions of ee and fatigue to the oveall oess; ee ak gowth is geneally integanula wheeas fatigue ak gowth tends to be tansganula. Also, whee ossible, a dimensional hek should be aied out to establish whethe thee has been any signifiant distotion. When a defet has been disoveed in a omonent that has been in sevie, the onsevative assumtion fo the alulation of ontinuum damage is that the ak initiated ealy in life. This should be assumed unless thee is evidene to the ontay. Whee the defet an be eliably justified to have fomed afte the stat of high-temeatue oeation, then it is emissible to use an estimate of the oesonding time in the alulations of ak gowth and ontinuum damage. The eene stess aoiate to this eiod is then detemined on the basis of the unaked body. Suitable sensitivity studies should be efomed to addess the effet of the assumtion on the obustness of the assessment. Patiula aution should be taken if the defet fomed in sevie by ee mehanisms, noting the omments in the next aagah onening the effets of ee damage on ak gowth oeties. Signifiant ee damage, away fom the ak ti, obably indiates that thee has been loal ove-heating o ove-stessing. In these iumstanes, all ak gowth alulations should take aount of the mateial in its damaged state. In addition, whee aks ae disoveed in mateial that has exeiened extensive ee damage, it is essential fo end-of-life assessment that mateial data ae used whih ae fully eesentative of mateial in its damaged state. Data on fatue toughness and emaining ee utue life ae atiulaly sensitive in this eset. Whee thee is evidene of envionmentally assisted aking (multile aking without avitations), the methods equied ae disussed in Setion Define Sevie Conditions This oedue is aliable to omonents whih oeate fo long eiods at steady o steady yli onditions of load (stess), o dislaement, and temeatue. Eah loading and temeatue must be defined fo the loations of inteest. In making an assessment, it is onsevative to assume that all the loading is load-ontolled and ignoe stess elaxation; it may also be assumed that infequent shot-tem oveloads will not modify the ak ti onditions signifiantly. Seifiation of the sevie onditions must define the load, temeatue and life seen to date. In addition to histoial oeation, futue sevie onditions must also be defined. The loading must inlude all time indeendent, tansient and fault loading. In many iumstanes, the sevie load and temeatue histoy an be boken down into a numbe of bloks duing whih stess and temeatue ae sensibly onstant. This will simlify the analysis. Whee tansient loading ous, duing eithe stat-u o shutdown, the numbe of load and temeatue yles and thei magnitude should be established. In defining the futue life that is equied fom lant, onsevative editions have to be made about the likely tansient onditions that will be exeiened. 8.5 Collet Mateials data This setion outlines the mateial oeties data equied to follow the stes in the oedue set out in Setion 8.2. Futhe disussion is ontained in Setion 5.4 and samle mateials data ae esented in Annex M. Some of the mateial oeties may be inte-elated and it is neessay to use onsistent mateial oeties data in diffeent stes of the oedue. This is of atiula imotane when mateial oeties data ae obtained fom a numbe of diffeent soue eenes. Whee ossible, mateials oeties data should be obtained by following testing standads. Howeve, standads ae not available fo measuing all oeties fo efoming a omehensive ee-fatigue ak initiation analysis and Setion 8.11 inludes guidane set out in, fo examle, odes of atie in these ases. 8-1 FITNET 26 All ights eseved

13 (1 May 26) FITNET M Cee Rutue Data Cee utue data ae equied to alulate the utue life of the emaining ligament and to estimate the uent ontinuum damage level in the ligament as the defet gows Cee Defomation Data Cee defomation data ae equied fo steady loadings to estimate the ee ak inubation time and subsequent ee ak gowth ates using eene stess tehniques. Fo ases with steady imay load o lage elasti follow-u, fowad ee data olleted unde onstant load onditions ae aoiate. Fo essentially stain-ontolled onditions, in the absene of follow-u, stess elaxation data may be moe aoiate than fowad ee data. Reliable onstitutive equations ae needed to ovide a smooth tansition between these extemes. Fo ee-fatigue loadings, a desition is equied of the ee defomation of the mateial in the elevant yli ondition in ode to estimate ee ak gowth ates duing the dwell eiods. Cee defomation data may also be equied to alulate the time fo failue by ontinuum damage using a dutility exhaustion aoah o to estimate ee damage at the sufae fo use in a ee-fatigue ak gowth law. Often a simle owe law exession o ( ) n ε ε = (8.1) o is used to desibe ee stain ate. Moe geneally, ee defomation is desibed by thee stages: imay, seonday and tetiay. Equation (8.1) desibes the seonday stage wheeas some othe laws onside only an ineasing stain ate afte the imay stage. Rathe than desibing the ee stain ate, ee defomation data ae often eesented by isohonous stess-stain uves, see Figue 8.4, o tables giving, fo examle, the stess equied to give a total stain of 1% afte a seified time at a seified temeatue. Examles of ee stain ate equations and isohonous data ae ontained in Annex M Cee Dutility Data Cee dutility data may be equied to alulate the time fo failue by ontinuum damage using a dutility exhaustion aoah o to estimate ee damage at the sufae. In addition, ee dutility data may be used to estimate ee ak gowth ates fo situations in whih exliit ak gowth data ae not available Cee Cak Initiation/Inubation Data Fo situations whee fatigue is insignifiant, it may be ossible to take aount of an inubation eiod io to ak extension. Cee ak inubation data may be exessed in tems of a itial ak ti oening dislaement, δ i, o, fo widesead ee onditions, by a elationshi of the fom: * β t(c i ) =γ (8.2) whee t i is the inubation time and β and γ ae mateial onstants. In situations whee exliit inubation data ae not available, it is ossible to estimate the inubation time fo widesead ee onditions using aoximate exessions given late. In addition, two altenative aoahes fo editing inubation times ae given in Setion Cee Cak Gowth Data Cee ak gowth data ae equied to alulate ak gowth unde steady loading onditions o to estimate the ak extension duing dwell eiods fo ee-fatigue onditions. Cee ak gowth data ae geneally esented as a simle elationshi of the fom: * q a= A(C ) (8.3) FITNET 26 All ights eseved 8-11

14 FITNET FFS M7 Cee Module whee A and q ae mateial onstants. Annex M gives some tyial values of these onstants fo a numbe of mateials. The onstants A and q may deend on the test seimen geomety used to obtain ee ak gowth data. Fo a onsevative assessment, it is eommended that omat o deely aked bend seimens ae hosen and that data satisfy validity iteia seified in standads. Howeve, if use of moe seifi data an be justified, to allow fo loss of onstaint fo examle, altenative test seimens an be used as desibed in the CRETE ode of atie [8.18] Cyli Cak Gowth Data The tye of yli ak gowth data equied deends on the size of the defet elative to the yli lasti zone at the sufae of the omonent. Fo small defets embedded in the yli lasti zone, a stain based method fo alulation of ak gowth is set out in Setion (A). This uses the stain based ak gowth law temed Method II that is desibed in Setion Fo aks lage than the yli lasti zone, a Pais law modified fo ak losue is used. This is temed Method I and is desibed in Setion Deending on the aliation, it may not be neessay to ollet both Method I and Method II data Method I The yli omonent of ee-fatigue ak gowth equied fo a Method I ak gowth ate law is desibed by da dn f =CΔ l eff (8.4) whee C and l ae mateial and temeatue deendent onstants. Δ eff is the stess intensity fato ange fo whih the ak is judged to be oen, as evaluated fo omonent aliations by equation (8.6) below. In situations whee yli ak gowth data have been obtained fom tests with signifiant lastiity, it is eable to evaluate Δ fom exeimental estimates of ΔJ. Howeve, it will be essimisti to use data eff whih have been oelated with elastially alulated Δ eff values. Futhe infomation on the use of fatigue ak gowth data is given in Setion 7, whih inludes altenative exessions to equation (8.4) Method II The yli omonent of ee-fatigue ak gowth equied fo a Method II ak gowth ate law is desibed by a high stain fatigue ak gowth law of the fom: da dn f =Ba Q a a (8.5) min a min whee =.2mm is the ak deth below whih the ak gowth ate is assumed to be onstant. B and Q deend on mateial, stain ange and envionment and an be detemined exeimentally. These laws aly fo a total sufae stain ange Δε t, while the defet is embedded in the yli lasti zone of size at the sufae of the omonent. Futhe infomation on stain based methods fo fatigue ak gowth assessment is ontained in Setion Othe Data In addition to the ee data desibed in Setions , it may be neessay to have othe data to efom an assessment. These ae listed below. In addition, fo the altenative methods in Setion 8.1, some seial equiements ae needed when altenative aoahes ae followed and these equiements ae disussed in the aoiate at of Setion FITNET 26 All ights eseved

15 (1 May 26) FITNET M Elasti and Physial Constants Values fo Young s modulus, E, Poisson s atio, ν, and the instantaneous o mean oeffiient of themal exansion, α, ae equied to efom the basi stess analysis and may also be equied if a detailed shakedown analysis has to be efomed Stess-stain Data Values fo the minimum monotoni.2% oof stess ae equied to hek ak stability fo timeindeendent loadings and to efom a shakedown analysis. Cyli stess-stain data ae equied to detemine the stess intensity fato ange when yli lasti defomation ous and to detemine defomation stess-stain loos. Cyli stess-stain data may be desibed by a elationshi between the total stess ange and the total stain ange of the hysteesis loos though the use of the Rambeg-Osgood equation. Fo ylially stable mateials, the stess-stain hysteesis loo an be eonstituted fom this equation but the oess is less suessful fo hadening and softening mateials. Fo situations in whih stit shakedown is ahieved, these data will not be equied as the shottem esonse will be elasti. Howeve, yli stess-stain data will be equied fo moe sevee loading. The fato s is an exeimentally deived fato whih an be alied to the minimum.2% oof stess of the mateial to give a level, S s y, whih is the lagest semi-stess ange fo whih the mateial has stable i.e. exhibits non-athetting, yli stess-stain behaviou. s is theoe equied to efom a shakedown analysis. s with temeatue fo Tye 316 and wought feiti steels is given in R5 Volume 2/3. The vaiation of Additional details on the deivation of Fatue Toughness Data s ae given in Setion A1.3 of R5 Volume 2/3. Values of the fatue toughness ae equied to hek ak stability fo time-indeendent loadings. In geneal, data elate to mateials whih have exeiened no io global (ligament) o loal (ak ti) ee damage. It is theoe neessay to onfim that the fatue toughness values used fo assessing ak stability unde time indeendent loadings ae aoiate fo the mateial ondition ahead of the ak ti. 8.6 Pefom Basi Calulations Stess Intensity Fatos The linea elasti stess intensity fato,, deends on the loading and the ak size and may vay with osition aound a ak font. Fo yli loading, it is neessay to evaluate the stess intensity fato ange and the atio, R, of minimum min to maximum stess intensity fato, max. The value of R should be alulated fom a shakedown analysis athe than a simle elasti analysis. This is beause ee duing a yle tends to lead to a yli stess state whih gives a lowe value of R than the initial elasti esonse. The shakedown analysis only affets the value of R and not the total stess intensity fato ange, as the esidual stess is indeendent of osition in the yle. In the absene of yli lastiity in the unaked body, the effetive stess intensity fato ange defined by: Δ eff is Δ =q Δ (8.6) eff o FITNET 26 All ights eseved 8-13

16 FITNET FFS M7 Cee Module whee Δ=max - min and q o is the fation of the total load ange fo whih a ak is judged to be oen. This may be estimated onsevatively fom: q = 1 R q o o = ( 1 -.5R)/(1- R) R < (8.7) whee R = min / max Refeene Stess Fo ee ak gowth evaluation, it is neessay to evaluate the eene stess at the stat of the dwell. The eene stess fo simle imay loading is detemined by the methods of limit analysis and is defined by: = P /P (,a) (8.8) y L y In ases whee yli loading is esent the load P is evaluated fom the stess, odued by the shakedown analysis, at the time in the yle oesonding to the ee dwell. It should be noted that this is not neessaily at the eak stess in the yle. P L is the value of P oesonding to lasti ollase assuming a yield stess y. The effet of the flaw must be inluded in evaluating the lasti ollase load. When ee ak gowth is being onsideed, the elevant flaw size is the size of the oiginal flaw lus the amount of ak gowth. Fo the uoses of initial alulation of the time fo failue by ontinuum damage mehanis and alulation of inubation time, the elevant flaw size is that of the oiginal defet C* Paamete Fo steady state ee, the ak ti stess and stain ate fields (and hene ee ak gowth ates) may be * haateised by the C aamete. This is the ee equivalent of the J-ontou integal used to desibe elasti-lasti fatue. It may be evaluated by finite element analysis but a eene stess based estimate of * C is often used. This is (8.9) C = ε [ (a),ε ]R * Hee, ε is the ee stain ate at the uent eene stess and ee stain, ε, aumulated unde the eene stess histoy u to time t; that is, a stain hadening ule is used to define ee stain ates unde ineasing stess duing the ak inubation and gowth stages. This is aliable to omlex time-vaying ee laws. The haateisti length, R is defined by (8.1) R=( / ) 2 whee is the stess intensity fato due to imay load only. As both and ae dietly ootional to the loading P, the value of R is indeendent of the magnitude of P. Howeve, R does vay with ak size and, when ee ak gowth is being onsideed, both and should be alulated fo the defet size equal to the size of the oiginal ak lus the amount of ee ak gowth. The value of R is also diffeent at the sufae and deeest oints of a semi-ellitial sufae defet due to diffeenes in the values of. Fo othe than simle imay loadings, estimates of * C ae given in Setion FITNET 26 All ights eseved

17 (1 May 26) FITNET M Redistibution Time, t ed This alulation is only equied when yli loading is insignifiant. Time is equied fo stess edistibution due to ee fom the initial elasti state at the stat of a ee dwell. The equiement fo the stess edistibution to be omlete and widesead ee onditions to be established may be exessed in tems of a edistibution time, t ed. This may be exessed onveniently in tems of the eene stess fo ases of imay load only as ε [ (a),t ] = (a) E (8.11) ed whee ε [ (a),t] is the aumulated ee stain at the eene stess fo time, t, and ak length, a, fom uniaxial ee data. Equation (8.11) alies fo steady ee loading unde imay stesses. When alulating ak gowth unde signifiant yli loading (see Setion 8.7), it may be neessay to onside the ealy yles befoe the steady yli state is eahed. Time is equied fo the mateial esonse to the yli loading to eah a steady yli state o shakedown. This time, t y, an be estimated in tems of the eene stess fo the fist yle, y=1, and the eene stess unde steady yli onditions fo ombined imay and seonday loading,, as: y=1 y=1 ( + ) ( - ) ε [,t y]=z 2 E (8.12) whee Z is an elasti follow-u fato, whih ontols the ate of stess elaxation to steady state ee. Futhe details of the teatment of seonday loading ae given in Setion C(t) Paamete Fo times less than the edistibution time, it may be neessay to alulate the tansient ak ti aamete C() t. An inteolation fomula fo C() t duing the tansition between initial elasti loading and steady state seonday ee is C(t) (1 + ε /ε ) C 1/(1-q) e = * (1 + ε 1/(1-q) /ε e ) - 1 (8.13) ε is the aumulated ee stain at time t, ε e is the elasti stain and q is the exonent in the ee whee ak gowth law of equation (8.3) with q-n/(n+1) whee n is the exonent in equation (8.1). Fo times in * exess of the edistibution time, C() t aoahes C. 8.7 Chek Signifiane of Cee and Fatigue In many ases the omlexity of a ee-fatigue ak gowth assessment an be avoided by efoming simle alulations to demonstate the insignifiane of ee and/o fatigue. In the event of both ee and fatigue being shown to be signifiant, simle tests an also be used to demonstate insignifiant ee-fatigue inteations, and thus emove the oneous equiement to geneate mateial fatigue data inooating the effets of ee holds. The test fo insignifiant ee alies when both Method I and Method II data of Setions and ae used. The tests fo insignifiant fatigue and ee-fatigue inteation only aly to Method I. FITNET 26 All ights eseved 8-15

18 FITNET FFS M7 Cee Module Insignifiant Cee The signifiane of ee stains should be detemined fo the assessed loading and temeatue histoy. Cee may be signifiant fo some tyes of loading histoy but not fo othes. The effets of ee may be negleted if the sum of the atios of the hold time t to the maximum allowable time t m, at the eene temeatue, T, fo the total numbe of yles is less than one: N t/t m(t ) < 1 (8.14) j j=1 The values of t m deend on mateial, ak size and temeatue. R5 ontains uves in Figues A6.6 and A6.7 fo austeniti Tye 316 and Tye 34 mateials. Fo othe mateials, guidane on ee exemtion may be taken fom BS 791. In BS 791, t m, fo mateials with ee utue dutilities > 1%, is taken as the time equied to ahieve an aumulated ee stain of.2% at a stess level equal to the eene stess. Fo dutilities < 1%, t m should be detemined on the basis of ee stains with a magnitude equal to 1/5 th of the ee utue dutility. Howeve, it should be noted that fo onsisteny with the insignifiant ee tests fo unaked stutues, values of t m should not be geate than those allowed in design odes Insignifiant Fatigue It should fist be detemined whethe o not ee behaviou is unetubed by yli behaviou. This test should be efomed both fo the oveall stutual esonse and fo stesses loal to the ak ti. Sine Ste 4 of the oedue of Setion 8.2 equies that the ak deth is suh that the omliane of the stutue is not signifiantly affeted, the test fo the oveall stutual esonse may be demonstated by showing that the elasti stess ange does not exeed the sum of the steady state ee stess and the stess to ause yield at the othe exteme of the yle. Futhe infomation is ontained in R5. The test fo stesses loal to the ak ti may be made by demonstating that, fo the most sevee fatigue yle, the yli lasti zone at the ak ti is small. Unde yli loading, the allowable elasti stess ange is 2 y in the absene of yli hadening o softening, and the yli lasti zone size at the ak ti, ak 2 = β(δ/2 y ), whee β is tyially 1/2π in lane stess and 1/6π in lane stain. Moe geneally, the yli lasti zone size at the ak ti should be alulated using the yli yield o.2% offset stess. This yli lasti zone size should be shown to be muh less than the ak size o any othe dimension haateisti of the stutue, suh as setion thikness o emaining ligament ahead of the ak. If the above tests ae satisfied, yli loading effets on ee ak gowth an be negleted. Futhe, fatigue is insignifiant, ovided that estimated fatigue ak gowth does not exeed 1/1 th of the estimated ee ak gowth. At the stat of an assessment only aoximate estimates of gowth ae equied and bestestimate data fo both ee and fatigue ak gowth should be used to alulate this atio. These aoximate alulations an be ined when esults of a detailed assessment beome available Insignifiant Cee-Fatigue Inteations When both ee and yli loading ae shown to be signifiant, the signifiane of ee-fatigue inteation should be detemined. In geneal, the effet of ee damage on fatigue ak gowth ates has little influene on the total ak gowth e yle ovided the latte inludes an exliit alulation of ee ak gowth. Hene, ee-fatigue inteation is insignifiant and mateial data that allow fo inteations, whih lead to enhaned fatigue ak gowth ates, ae not equied. It is adequate, theoe, in Ste 9 of Setion 8.2 to sum ee ak gowth with ontinuous yle fatigue ak gowth estimates. Thee ae two exetions to this geneal ule: 8-16 FITNET 26 All ights eseved

19 (1 May 26) FITNET M7 (i) (ii) In ases whee the tests fo insignifiant yli loading and fatigue indiate that ee is etubed by yli behaviou, but fatigue ak gowth is shown to be only a small fation of the total ak gowth e yle (i.e. fatigue ak gowth does not exeed 1/1 th of the ee ak gowth), the enhanement of fatigue ak gowth by ee damage may be lage. In these iumstanes the onstants in equation (8.4) should be obtained fom tests at hold times elevant to the sevie aliation being assessed. In ases whee aks ae oagated by fatigue though mateial heavily damaged by io ee, oagation ates ae likely to be ineased. In these iumstanes, a fato should be alied to the fatigue data, deending on the amount of io ee damage. BS 791 eommends that this fato should be detemined exeimentally, and elates heavy io ee damage to a value of damage fato D geate than about Pefom Assessment Calulations Calulate Rutue Life, t CD Both stess-based and dutility-based aoahes may be used fo assessing ee damage. Fo loadings whih ae edominantly onstant and imay, the stess is well known and it is aoiate to use stess/time-to-utue elationshis fo assessment. Fo damage due to yli elaxation, the stain aumulated is limited in eah yle and dutility methods ae aoiate. Fo edominately imay loading the time, t CD, fo ee damage to oagate though a stutue and lead to failue is taken as t CD =t [ (a)] (8.15) is the utue time at stess,, fom onventional stess/time-to-utue data and the eene stess is alulated fo the imay loads only fo the uent ak size, a. Pio to ak gowth the utue time is alulated fo the initial defet size, a. If t CD is less than the emaining assessment time then emedial ation must be taken. Fo ombined and yli loading, it may be neessay to evaluate t CD fom a dutility exhaustion aoah; futhe details ae given in Setion 8.1. whee t ( ) Calulate Cak Inubation Time, t i The inubation time, t i, is defined as the time duing whih the initial ak blunts without any signifiant ak extension. Inubation is defined fo engineeing uoses as oesonding to.2mm ak extension. The method fo eesenting inubation data then deends on obseved seimen esonse. Fo steady state ee onditions with an essentially onstant dislaement ate, the inubation time in test seimens is * oelated with exeimental estimates of the ak ti aamete C by equation (8.2). Use of the estimate of fom equation (8.9) fo the initial ak size a, then ovides an estimate of t i. Moe geneally, inubation times an be elated to measuements of a itial ak oening dislaement, δ i, whih an then be used to alulate a itial eene stain as ε [ (a ),t ] = [δ /R (a )] - (a )/E (8.16) n/(n+1) i i If fatigue is signifiant it is onsevative to set the inubation time to zeo. Howeve, a ee-fatigue ak inubation time (o yles) may be alulated using the FAD o sigma-d aoahes outlined in Setion 8.1. Fo ellitial o semi-ellitial defets, the inubation time should be taken as the lowe of the values obtained fom equation (8.16) at oints oesonding to the majo and mino axes of the ellise o semi-ellise. FITNET 26 All ights eseved 8-17

20 FITNET FFS M7 Cee Module Calulate Cak Size afte Gowth, a g The extent to whih ak gowth alulations ae equied deends on the elative magnitudes of the sevie life to date, t o, the desied futue sevie life, t, s and the inubation time, t i ; this may be summaised as follows. If t o+ t s < t i, the ak will not inubate and a g = a. If the ak inubates duing the assessment time, then it is neessay to alulate the ak size, a g, afte gowth in time t o + t s - t. i If the ak has inubated io to the assessment, then it is neessay to alulate the ak size, a g, afte gowth in time t s. The time equied fo the ak to oagate by an amount Δa g is denoted t g. Thee ae a numbe of diffeent egimes fo alulations of ak gowth and these ae set out below. (A) Caks gowing inside the yli lasti zone,, at the sufae of the omonent. In this egime the Method II high stain ee-fatigue ak gowth law should be used. This is eqn (8.5) fo insignifiant ee. When ee is signifiant, the ee-fatigue ak gowth e yle is given by: da da suf = (1 - D ) dn dn f -2 (8.17) suf whee (da/dn) f is the fatigue ak gowth e yle fom eqn (8.5) and D is the total sufae ee damage (taking aount of stess state, if neessay) aumulated u to the uent time fom evey yle and is: suf N D = (d ) (8.18) j=1 suf j suf whee (d ) is the ee damage aumulated in the j th yle and the summation is aied out u to the j suf uent time. The tem (d ) is evaluated at the sufae of the unaked omonent and is given by the dutility exhaustion method as j t h, j suf ε (d ) j= dt ε f(ε ) (8.19) whee t th, j is the j th ee dwell eiod, ε is the instantaneous equivalent ee stain ate duing the dwell and ε f (ε ) is the ee dutility at that stain ate, aounting fo stess state. The stain ate ε is evaluated at the instantaneous stess duing the dwell obtained fom stess elaxation data. The elaxation data should oesond to a stating stess equal to the unaked-body stat-of-dwell stess at the sufae,. In atie, many yles will be of a simila tye, in whih ase the summation in equation (8.16) is simlified. When D 1 suf, equation (8.17) edits an infinite ak gowth ate. Howeve, this should not be inteeted as editing the failue of the omonent. This oesonds to the exhaustion of ee dutility at the sufae of the omonent and the instantaneous ak deth, a, should be set to the deth of the yli 8-18 FITNET 26 All ights eseved