Microsoft Word - numero 14 articolo 2 In A Br Fed Bra lob AB AS 33 we par and Kw Ac cor rel rel str KE IN pro con stru cra phe con pro the esti ma Bas Th cor T nfluence ASTM A raitner Lob deral Universi asília, Brazil, batoae@gmail. BSTRACT. T STM A743 C specimens ere tested un rameters tha d its scatter wofie’s relati ccording to t rrectly the r ation are co ation makes ength. EYWORDS. F NTRODUCTIO he AST compon develop ogressive and nditions. Thi ucture, on the ack growth an enomenon is nditions of t ocedures to e e use of these imate the effe achine elemen sic relations of he fatigue life rrelated with T e of mea 743 CA6 bato da Silv ity of Brasília, 70940-910. com.br, jorge@ The objective CA6NM allo were experi nder stress at describe th bands. In th ions were te the obtained reduction ef onsistent an s it possible Fatigue; Goo ON TM A743 CA nents be desig ment and th d located pro is failure pro e presence of nd it can cul s common in these compo estimate the e e methodolog ects of mean nts subject to f load characte is described the alternat B. Lo an stres 6NM al va, Jorge L Mechanical E @unb.br, felip e of this wo oy steel. It is imentally ev ratio 0, 1/3 he fatigue be he assessmen ested in orde d results it w ffect fatigue nd the Walk to evaluate odman; Gerb A6NM alloy gned for infin e propagation ocess of struc ocess depend f residual stre lminate in fra n axes’ flaw nents indent endurance lim gies demands stress in the complex load erization by the Wöh ting stress, S obato da Silva et ss on the lloy stee Luiz de Alm Engineering D peo2@gmail.co ork is to ev s used in sev valuated und 3 and 2/3. ehavior of th nt of the me er to evaluat was possible life and pre ker’s relation in a consiste ber; Walker; steel is used nite fatigue lif n of those cr ctural degrad s strongly on esses, on the g acture of the s, blades and tified that re mit of structu s a solid char fatigue streng ds, for the us hler curve or Sa. This met alii, Frattura ed e fatigu el meida Ferr Department, Ca om, alex07@ valuate the e veral hydrog der axial load Based on t he evaluated ean stress eff te the validi to verify th esented high n presented ent way the Kwofie; AS d in several fe, fatigue cra racks are asso dation that h n the stress geometric de e structural co d rotors. Sta sidual stresse ural compone racterization gth and to ide ed material. S-N curve, S thod is a rel d Integrità Struttu ue streng reira, Felipe ampus Univer unb.br effects of m genator turbi ds with stres the obtained d material, ob fects of fatig ity of the us hat Goodman h scatter. Th d smaller sca effect of th STM A743 C hydrogenato acks usually ar ociated to th appens in a levels that a tails and on t omponent af arting from t es are fundam ents are much of the mater entify the mo Stress-life, wh lation that c urale, 14 (2010) gth of e Oliveira, rsitário Darcy mean stress o ine compon ss ratio of - d results it btain its S-N gue life, Goo se of such ru n and Gerb he prediction atter than K he presence o CA6NM. r turbine co re found at th e fatigue pro material und ctivate in the the material. T fter a certain the producti mental facto h known and rial. In that w del to be cap here the num can be well ) 17-26; DOI: 10 , José Alex Ribeiro, on the fatig ents. In ord 1 and mor was possibl N curves, its odman, Gerb ules for the er’s relation ns of Walke Kwofie’s rel of mean stre mponents. I he root of tur ocess. Fatigue der stress and e most loade These condit number of on, assembly rs to cause d relatively re way, the prese able to predic mber of cycles used to adju .3221/IGF-ESIS. xander Araú gue behavior der to achiev e 60 specim le to determ endurance li ber, Walker tested mate ns do not mo er and Kwof lation. Walk esses on fati n spite of th rbine blades. e is a perman d strain dyna ed points of tions can deve cycle loads. T y and operat the fatigue. eliable. Howe ent work aim ct the strengt s to failure, N ust appropria 14.02 17 újo r of ve it, mens mine imit and erial. odel fie’s ker’s igue hese The nent, amic f the elop This tion, The ever, ms to th of N, is ately http://dx.medra.org/10.3221/IGF-ESIS.14.02&auth=true http://www.gruppofrattura.it mailto: lobatoae@gmail.com.br mailto: jorge@unb.br mailto: felipeo2@gmail.com mailto: alex07@unb.br B. L 18 exp cyc Som cha min of An by Th the exp Me Ini com pro Go fati pro the In hig end sim dat wid mo stre Sy. Ex Lobato da Silva perimental da cles. This rela a AS  me practical a aracterize the nimum value the range stre mS S  mSSm  mSSa  nd to describe Eq. 5. The re ma m S S R  1 1 aS    he standard co e Eq. 1 can be perimental res ar S  ean stress effect tially, empiri mpensate the oposed a par oodman intro igue data in oposed as imp e fatigue stren order to ove gh mean stre durance limit milar to SWT, ta, Eq. 14. A despread mat odel consists i ess, Sm, on th According to a S  xpressed in fo a S  et alii, Frattura ata in the sen ation can be e bN applications a e constant am , Eq. 2. The ess is called am max minS 2 minmax S 2 minmax S e the mean str elation betwe ax in . m R S R   ondition to de e express in t sults. ' b f N  t predition Mo ic models w e effect of m rabolic repres oduced a theo the graphic provement of ngth coefficie ercome the fa esses, Smith, for the load , however usi According to thematical rel in the substit e limit of fati o this model, m rtS ar S e         orm of power m rtS ar S e           ed Integrità Stru nse to correla expressed as in and also fatig mplitude load mean stress, mplitude stre ress, a factor en Sa, Sm e R etermine the the form of E odels ere proposed mean stress in sentation of oretical line t Sa versus Sm. f the previou nt and that th ailure predicti Watson and ratio, R = -1 ing a factor  empiric con lations to des tution of the B igue strength the stress-life r series, the E 0 1 ! N i i S           utturale, 14 (201 ate the alterna n Eq. 1, wher gue tests in m ds. The stres Sm, is the ave ess, Sa, Eq. 4. used to char is expressed parameters o Eq. 7. It is call d by Gerber n the high cyc the Wöhler’s to represent Since 1960, s models. Fat he compressio ion’s problem d Topper - S 1, Sar, is expre  that makes nsiderations, scribe the effe Basquin’s equ for the rever e relation can Eq. 8 can be e i m rt S     10) 17-26; DOI: ate stress and re A and b ar materials invol ss range, S erage between These are ba racterize the d in the Eq. 6. of Wöhler cur led Basquin’s r (1874), Go cle fatigue st s limit fatigu the evaluated some mode tigue tests ind on normal m m under load SWT [3] prop essed in the E possible an a Berkovits an fect of mean s uation’s const rse load condi be presented expressed by E 10.3221/IGF-ESI d the numbe e the constan lve maximum S , is the diff n maximum v asic relations t degree of sym rve is to assum s equation. W oodman (189 trength, accor ue data on th d fatigue data els to determ dicate that the ean stress sho conditions w posed a mod Eq. 13. On th adjustment o nd Fang [5] stress on the tant, Eq. 7, fo ition, Srt, and d by Eq. 8. Eq. 9: IS.14.02 r of cycles to nt and the cur m and minimu ference betwe value and mi that character mmetry of the me alternating Where ’f e b a 9), Haigh (1 rding to Lee he graphic Sm a, Eq. 11. Ha mine the effec e tensile norm ould increase with relatively del in which his same year f the curve in and more r fatigue beha or a function on the ultim o failure betw rve exponent, um constant l een the maxi inimum value rize one load e load, load ra g load, null m are material co 1917) e Sode [1] and Dow max/Su versus S aigh was the ct of mean s mal mean stre it [1]. y low amplitu the equivale , Walker [4] p n relation to ecently Kwo avior of endu that will dep ate strength, ween 103 and , respectively. (1) level stresses imum value e, Eq. 3. The cycle. (2) (3) (4) atio, R, is defi (5) (6) mean stress. T onstants base (7) erberg (1930) wling [2]. Ge Smin/Su , Eq. first to plot stress have b ess should red ude and relati ent stress to presented crit the experime ofie [6] propo urance limit. S end on the m or yield stren (8) (9) d 106 . that and half fined Thus, ed in ) to rber 12. t the been duce ively the teria ental osed Such mean ngth, http://dx.medra.org/10.3221/IGF-ESIS.14.02&auth=true http://www.gruppofrattura.it Ad of Sta des MA Ma yiel Spe Th 466 for T dmitting that superior orde a a S  arting from th scribe some m ATERIAL AN aterial he mate martens strength ld strength, Sy ecimen design he specimens 6-96 [8]. The r samples A a T the argument er converge q 1 m ar rt S        his last expres models presen  ,f R   ,f R  ND METHOD erial used in t sitic. This typ h and that res Sy) of the sam of the samp ese standards nd B, Fig. 1 a B. Lo t of the expo quickly to zero    ssion, one can nted in the Ta Hypothes 1  m rt f S          , 2 rt m S    , rt m S     Table 1 DS the developm pe of steel is sist to the cor ple A and sam Table le A were de specify the m and only spec Sam A B obato da Silva et onential funct o. In this spec n verify with e ab. 1. ses m rt S      1 2 2 rt m S ln        1 2 rt m S R ln         1: Particular sol ment of this r used in the rrosion. The mple B are sh e 2: Mechanic esigned accor main dimensi cimen 2 for sa Figure 1: Spe mple E ( A 1 B 1 alii, Frattura ed tion tend to z cific conditio easiness that Resulti a ar S  a ar S   R    a S  R    a S  lutions of wide research was production o mechanical p howed in Tab cal properties rding to AST ions. In this w ample B, Fig cimen 1 for sa (GPa) Srt 198 8 198 9 d Integrità Struttu zero,  m S  n, the Eq. 9 a depending on ing Equation 1m rt S    2 1m y S         1 21 2 ar R S         1 2 ar R S          espread Kwofi the ASTM A of structural c properties (Yo b. 2. of sample A TM E 606-04 work three d 2. Tab. 3 sho ample A and B (MPa) Sy ( 890 6 918 6 urale, 14 (2010)  0 rt S  , the c assumes the f n the value of Model Goodman Gerber SWT Walker ie model. A743 CA6NM components oung modulu and B. [7] and samp different spec ows the respec . (MPa) 637 665 ) 17-26; DOI: 10 consequence following form f α, the wides Equation (11) (12) (13) (14) M alloy steel that request us, E, tensile ple B starting imens were u ctively data. .3221/IGF-ESIS. is that the te m: (10) spread model l, a stainless i high mechan strength, Srt, g from ASTM used: specime 14.02 19 erms l will inox nical and M E en 1 http://dx.medra.org/10.3221/IGF-ESIS.14.02&auth=true http://www.gruppofrattura.it B. L 20 Fa Th 90 the cur obs Th stre stre Str Th me cha equ app end and alte Lobato da Silva tigue tests he fatigue test [9] and ASTM e critical value rve, 2 specim served the tes he S-N curves ess levels. Th ess, S-N curv rategy for evalu he strategy us ean stress, Sm aracterize the uation when plication of t durance limit, d Sar Basquin sh ernating stres et alii, Frattura s under axial M 739-91 [10 es of design i mens were tes sts were repro s were obtaine he stress relat ves were desig uation of mean ed to evaluat m, alternating e mean and Sm = 0, the e he value of r , called Sar Basq hould be iden s, Sar Model. Fatigu experime data Specimen / 1 / A 1 / B 2 / B ed Integrità Stru loads were p 0] , the minim is 12 specime sted for each oduced, guara ed considerin ted to the in gned for the f n stress models te models’ ad stress, Sa, an alternating s equivalent fa resulting life, quin Then, if th ntical statistic Figure 3: St ue ental a  ,a m   N / Sample a A 15 B 15 B 15 utturale, 14 (201 Figure 2: S Tab erformed in t mum number ens with repr h one of the anteeing at le ng the total cr finite life is d following rati s’ adherence dherence con nd the resulti stress in one atigue strength N, in the Ba he prediction cally. Tab. 4 trategy for eval Extrapol    arS   ar   arS   a (mm) b (mm 51.42 63.7 51.13 61.5 52.40 58.8 10) 17-26; DOI: Specimen 2 for ble 3: Specimen the MTS 810, of necessary roduction of 5 chosen str ast 58% of re rack growth u defined as lim o loads, R, -1 nsists in the u ing life, N. A mean stress h according asquin’s equa model was ad shows a resu luation of mea late data N Sm   ,a m  m) c (mm) 71 24.00 57 28.00 87 34.66 10.3221/IGF-ESI r sample B. n data , universal tes specimens to 50 to 75%. T ress levels. In eproduction. under dynami mit of fatigue 1, 0, 1/3 and 2 use of three p According to s model allow to specific m ation allows t dherent to th ume of the e an stress model Cycle numbe mS  Experimental d d (mm) e 10.00 12.00 12.50 IS.14.02 sting machine o obtain a cur Then, for a pr n the three le ic loads, repe e. In order to 2/3. parameters th Fig. 3, the a ws to evalua model, called to estimate a e experiment equations use ls’ adherence er S     ata e (mm) f (m 6.00 48. 7.00 28. 7.00 56. e. According rve S-N in or reliminary an evels where la ating the pro o evaluate th hat characteri application o ate, through Sar Model. In a new value fo tal results, the ed to estimat Statistical analysis Modelar S Basquinar S mm) g(mm) 00 50.00 00 50.00 00 to ASTM E 4 rder to determ nalysis of the arger scatter cess for diffe e effect of m ize a fatigue f the data wh extrapolation a similar way, or the equiva e values of Sar te the equiva 468- mine S-N was erent mean test: hich n of , the alent r Model alent http://dx.medra.org/10.3221/IGF-ESIS.14.02&auth=true http://www.gruppofrattura.it To res Th obt RE Tes F estimate the pectively. 1 ' Ra f S    2 1 a R         he estimate of tained results ESULTS AND sts with ratio l or the ra 7 show t F e exponents o   m rtSe N          1 1 ' R f S N         f parameters s. P D DISCUSSIO loading, -1 atio loading e the statistic b Sa ( Sa / M Dev CV Mod Goodm Gerb Walk Kwo B. Lo Table 4: Equ of the Kwofi  1Rb  1R b   and  was Parameter E   Table 5: Par NS equal -1, 11 sp ehavior of th (MPa) 4 Srt (%) 4 Mean 9.63 viation 5.46 V (%) 5 Table 6: S del Equat man ber ker ofie obato da Silva et uations used to fie and Walke s accomplish Expected Estimate Sta 0.407 1.453 rameters that c pecimens wer he estimated f 417 4 46.9 4 3 e+05 3.51 6 e+05 5.73 56.7 1 Statistic behavi tion to estima S S ar S alii, Frattura ed o estimate the e er’s models,  ed using the d value andard error 0.019 0.084 characterize Kw re used of sam fatigue lives fo 440 4 49.4 52 e+05 1.99 3 e+04 4.92 6.3 0 ior of fatigue li ate the equiva 1 a ar m rt S S        1 a ar m rt S S        2 1 r a R       S ar a S e        d Integrità Struttu equivalent alter  and  , resp Levenberg-M Confiden Estimate 0.346 1.187 wofie and Wal mple A and 2 or such stress 463 5 2.1 57 e+05 8.03 e+02 2.63 0.2 32 ives (R = -1) - alent alternatin m t    2    1 R     m rt S     urale, 14 (2010) rnating stress. pectively, the Marquardt m nce intervals Standard erro 0.468 1.720 ker’s models. 22 specimens s level. 09 56 7.2 63 e+04 9.38 e+04 * 2.7 * Sample A. ng stress Eq ) 17-26; DOI: 10 e Eqns. 21 an ethod [11]. T or of sample B 66 3.3 e+03 * * quation (17) (18) (19) (20) .3221/IGF-ESIS. nd 22 were u (21) (22) Tab. 5 shows B. The Tab. 6 14.02 21 used, the and http://dx.medra.org/10.3221/IGF-ESIS.14.02&auth=true http://www.gruppofrattura.it B. L 22 Tes For stat Tes For the Tes For fati Lobato da Silva sts with ratio l r the ratio loa tistic behavio sts with ratio l r the ratio loa e statistic beh Sa (M Sa / S Me Devia CV sts with ratio l r the ratio lo igue lives esti et alii, Frattura Sa ( Sa / M Dev CV loading, 0 ading, R = 0, or of fatigue li Sa (MP Sa / Srt Mea Deviat CV (% Sa (MP Sa / Srt Mea Deviat CV (% loading, 1/3 ading, R = 1/ avior of the f MPa) 19 Srt (%) 29. ean 4.9 e+ ation 1.1 e+ (%) 22. Ta loading, 2/3 oading, R = 2 imated for su Sa (MP Sa / Su Médi Desv CV (% ed Integrità Stru (MPa) 3 Srt (%) 3 Mean 1.73 viation 5.49 V (%) 3 Table 7: S 13 specimen ives estimated Pa) 260 (%) 29.2 an 6.2 e+ tion 5.5 e+ %) 88.9 Table 8: St Pa) 260 (%) 29.2 an 7.9 e+ tion 3.5 e+ %) 44.7 Table 9: St /3, 7 specime fatigue lives e 7 200 .2 29.8 +05 3.5 e+ +05 * .7 * able 10: Statisti 2/3, 19 spec ch stress leve Pa) 133 (%) 14.7 ia 8.7 e+0 vio 3.7 e+0 %) 42.3 Table 11: Sta utturale, 14 (201 353 3 38.4 3 3 e+06 1.13 9 e+05 8.82 31.6 7 Statistic behavi ns were used d for such str 265 2 29.8 05 5.3 e+05 05 * * tatistic behavio 265 2 29.8 05 1.7 e+05 05 * * tatistic behavio ens were used estimated for 211 33.7 05 4.0 e+05 1.4 e+05 35.7 ic behavior of cimens of the el. 135 14.8 05 7.8 e+05 05 4.1 e+05 52.2 atistic behavior 10) 17-26; DOI: 364 4 39.6 43 3 e+06 4.53 2 e+05 8.32 78.1 1 ior of fatigue li of sample A ress level. 300 33.7 5 1.8 e+05 4.4 e+04 24.6 or of the fatigue 300 33.7 5 2.0 e+05 1.5 e+03 0.8 or of the fatigue d of the samp such stress le 216 37.3 5 2.7 e+05 5 * * the fatigue live e sample B w 140 15.5 5 4.4 e+05 5 1.5 e+05 33.8 r of the fatigue 10.3221/IGF-ESI 400 4 3.6 47 e+05 2.61 e+02 1.09 8.4 0 ives (R = -1) - and 14 specim 332 37.3 9.3 e+04 4.1 e+04 43.7 e lives (R = 0) 332 37.3 8.8 e+04 3.8 e+04 42.7 e lives (R = 0) ple A and 7 s evel. 223 38.9 1.5 e+04 * * es (R = 1/3) - were used. Ta 141 15.6 3.7 e+05 4.0 e+04 10.6 e lives (R = 2/3 IS.14.02 40 50 7.9 55 e+05 5.75 e+03 9.74 0.4 16 Sample B. mens of samp 347 38.9 7.0 e+04 1 1.0 e+04 2 14.3 - Sample A. 347 38.9 9.7 e+04 2 3.8 e+04 3 38.8 - Sample B. specimens of 228 44.0 1.3 e+04 7 * * Samples A and ab. 11 shows 143 15.8 2.0 e+03 6 * * 3) - Sample B. 09 5.5 e+04 e+03 6.9 ple B. Tabs. 8 391 44.0 1,9 e+04 2.4 e+03 12.4 391 44.0 2.7 e+04 3.2 e+03 11.7 f the sample B 235 26.0 7.1 e+04 3.4 * * d B s the statistic 148 16.4 6.2 e+01 * * 8 and 9 show B. Tab. 10 sh 270 29.0 4 e+04 * * behavior of w the hows f the http://dx.medra.org/10.3221/IGF-ESIS.14.02&auth=true http://www.gruppofrattura.it Bas Eff Th cha the end Mo Fig adh arri lev sed on the ob ffect of the mea he experiment aracterize the e parallel proj durance limit odels’s adheren g. 5 shows th herence. The ives to 300 M vels around 34 F 1E 2 3 4 5 6 7 8 9 100 1000 S ar ( M P a) btained result an stress tal data and i e fatigue stren ection metho considering a R M -1 14 0 99 1/3 72 2/3 15 nce to experime he fatigue ex trend line a MPa. In addi 4% upper tha Figure 5: Good E+2 1E+3 1E Numb R = -1 R = 0 R = 1/3 R = 2/3 Trend Lin Confiden Trend Lin Confiden B. Lo ts it is possibl its respective ngth are summ od [12]. Basic an extrapolati Figu Basquin’s co (A) [MP Mean Stand 406.9 1 96.8 1 29.8 9 52.3 Table ental results: xperimental d adjusts to Bas tion, for ratio an real failure dman’s predicti 1E+4 100 1000 S a (M P a) E+4 1E+5 1E+ ber of cycle (N) ne - Goodman Eq. nce Interval - Goodman ne - Basquin Eq. nce Interval - Basquin obato da Silva et le to verify a s trend lines, marized in th cally, this met ion of the fat ure 4: S-N curv onstant Pa] ard error M 02.9 -0 46.8 -0 91.2 -0 7.4 -0 e 12: Paramete Goodman’s m data and the squin’s curve o loading of condition. ion. 1E +6 1E+7 n Eq. Eq. alii, Frattura ed significant dis for such ratio he Tab. 12. T thod consists tigue curve fo ves about the ef Basquin’s ex (b) Mean Stan 0.0941 0 0.0962 0 0.0987 0 0.0077 0 ers that charact model predictions e but reveal b 2/3, the mo E+5 N (number of c d Integrità Struttu spersion of fa o loading, are The enduranc in achieving or life identifi ffect of mean s xponent dard error M 0.0059 0.0125 2 0.0101 0.0039 terize the S-N based on G big scatter, a del predicts t Figure 1E+6 cycle) Experim 100 2 3 4 5 6 7 8 9 100 1000 S ar G o o d m an ( M P a) urale, 14 (2010) atigue life for e shown in F ce limit, S`f, c S-N curve fo ed as infinite stress. Enduranc (S`f) [M Mean Stand 383.2 2 263.9 186.7 136.9 curves Goodman’s m as shown in F the possibilit e 6: Goodman 1E+7 mental Data R = -1 R = 0 R = 1/3 R = 2/3 Trend Line Sar Bas R = -1 R = 0 R = 1/3 R = 2 ) 17-26; DOI: 10 all stress rati Fig. 4 and the an be easily o or the steel an fatigue life. ce limit MPa] dard error 28. 0 28.0 23.3 6.7 model. The re Fig. 6. The c ty to apply, o n’s scatter diagr squin (MPa) 0 2/3 Trend .3221/IGF-ESIS. os tested. e parameters obtained thro nd estimating esults reveal confidence lim on average, st ram. 1000 d Line 14.02 23 that ough g the low mits tress http://dx.medra.org/10.3221/IGF-ESIS.14.02&auth=true http://www.gruppofrattura.it B. L 24 Mo Fig res out lev Mo Th obt we ord Mo Th res exp are adh Lobato da Silva odels’s adheren gs. 7 and 8 sh ults, it is veri t of the conf vels around 72 odels’s adheren he fatigue exp tained results re adjusted v der of size, ap odels’s adheren he Figs. 11 an ults presente pressively hig e around 100 herent. 1E 2 3 4 5 6 7 8 9 100 1000 S ar ( M P a) 1E 2 3 4 5 6 7 8 9 100 1000 S ar ( M P a) et alii, Frattura nce to experime how the fatig ified a relative fidence limits 2% lower than Figure 7: Ger nce to experime perimental da s indicate that very well to B pproximately Figure 9: Wa nce to experime nd 12 show d it is verifie gh. The obtai MPa, twice E+2 1E+3 1E Num Trend Li Confiden Trend Li Confiden E+2 1E+3 1E Num R = -1 R = 0 R = 1/3 R = 2/3 Trend Li Confiden Trend Li Confiden ed Integrità Stru ental results: G gue experimen ely high scatte s of the Basq n real failure rber’s predictio ental results: W ata and the p t this model h asquin’s curv 50 MPa. alker’s predictio ental results: K the fatigue e d that in a w ned results w larger than t E+4 1E+5 1 mber of cycle (N) R = -1 R = 0 ine - Gerber Eq. nce Interval - Gerber ine - Basquin Eq. nce Interval - Basqui E+4 1E+5 1 mber of cycle (N) ine - Walker Eq. nce Interval - Walker ine - Basquin Eq. nce Interval - Basqui utturale, 14 (201 Gerber’s model ntal data and er, approxima quin’s equatio conditions an on. Walker’s mode predictions b has a level of ve. In addition on Kwofie’s model experimental way similar to were adjusted the value pre E+6 1E+7 R = 1/3 R = 2/3 r Eq. in Eq. E+6 1E+7 r Eq. in Eq. 10) 17-26; DOI: l d the predictio ately 300 MP on. This mod nd it is extrem del based on Wa adherence sig n, the confide l data and the Walker’s mo well by the esented by W 10.3221/IGF-ESI ons based on Pa. The trend del predicts t mely conserva Figu alker’s model gnificantly hig ence intervals Figu e predictions odel, Kwofie’s Basquin’s tre Walker’s mode 100 2 3 4 5 6 7 8 9 100 1000 S ar G er b er ( M P a) 100 2 3 4 5 6 7 8 9 100 1000 S ar W al k er ( M P a) IS.14.02 n Gerber’s m line of the pr the possibility ative. ure 8: Gerber’s l are showed gh to the exp s associated t ure 10: Walker’ based on K s model also end line. How el. In other w Sar Ba R = -1 R = R = 1/3 R = Sar Ba R = -1 R = R = 1/3 R = model. Based o redict results y to apply, o s scatter diagra d in the Figs erimental res to both mode ’s scatter diagr Kwofie’s mod presents a le wever, its con words, Kwofi squin (MPa) 0 2/3 Tre squin (MPa) 0 2/3 Tre on the presen for this mod on average, st am. . 9 and 10. ults because t els have the s am el. Based on evel of adhere nfidence inter ie’s model is 1000 end Line 1000 end Line nted del is tress The they ame the ence rvals less http://dx.medra.org/10.3221/IGF-ESIS.14.02&auth=true http://www.gruppofrattura.it CO bet we lim sup des goo to d AC RE [1] [2] [3] [4] [5] [6] [7] [8] T T ONCLUSION he aim o alloy ste results w tween Basqui re used to pr mit for this all perior reducti scribe the me od prediction describe the e CKNOWLEDG his proje are grate EFERENCES Y-L. Lee, J Butterworth N. E. Dowl K. N. Smith K. Walker, Testing and A. Berkovit S. Kwofie, I ASTM / E 6 ASTM / E 4 1.0E+3 2 3 4 5 6 7 8 9 100 1000 S ar [ M P a] T T Figure 11: Kw NS of this resear eel. In that se were used to in’s alternatin edict the mea loy steel is 38 tion around 5 ean stress effe n for the pres effect of the m GEMENTS ect was suppo efully acknow S J. Pan, R. H h-Heinemann ling, Mechani h, P. Watson, Effect of E d Materials, W ts, D. Fang, In Int. J. Fatigue 606-04 - Stand 466-96 - Stand 3 1.0E+4 Num R = -1 R = 0 R = 1/3 R = 2/3 Trend Line - Kw Basquin Eq. Bas Confidence Inte B. Lo wofie’s predicti ch was to eva nse, S-N curv o determine t ng stress and an stress effec 83 MPa; b) th 50% in the e fect on the fa ence of mean mean stress o orted by Cen wledged. We a Hathaway, M n, USA (2005) ical Behaviou , T. H. Toppe Environment West Conshoh nt. J. Fatigue, e, 23 (2001) 8 dard Practice fo dard Practice fo 1.0E+5 1.0 mber of Cycle (N) wofie Eq. sed on Experimental Da rval Limits - Basquin Eq Confidence Interval Limits obato da Silva et ion. aluate the eff ves were exp the enduranc predictions o cts. By means he fatigue lif endurance lim atigue strength n stress but p on the fatigue trais Elétricas are thankful t M. E. Barkey ). ur of Material er, Journal of and Comple hocken, PA, ( , 15 (1993) 17 829. for Strain - Con for Conducting 0E+6 1.0E+7 ta . - Kwofie Eq. alii, Frattura ed fect of mean erimentally d ce limit of th of such mode s of the obtai fe is strongly mit; c) Good h, turning its presents relativ e strength of A s do Norte do o God for th y, Fatigue T s, 2nd edition, f Materials, AS ex Load Hist (1970) 1. 73. ntrolled Fatigu g Constant Am d Integrità Struttu Figu stress of the determined fo he material a el. The Good ined results it influenced b dman and G s use non-rec vely high scat ASTM A743 o Brasil S. A. he blessing of Testing and A , Prentice-Ha STM, 5(4) (19 tory on Fatig ue Testing, (20 mplitude Axial 0 1 0 100 200 300 400 500 600 700 800 900 1000 S a r [M P a ] K w o fi e urale, 14 (2010) ure 12: Kwofie’ fatigue behav or loading rati and to evalua dman, Gerber t is possible t by the presen erber’s mode ommended; d tter; e) Walke CA6NM allo - Eletronorte to live, to pro Analysis (Th all, Englewood 970) 99.767. gue Life, AST 004). l Fatigue Tests 100 200 300 400 Sar [MP R = -1 R = 0 R = 1/3 R = 2/3 Trend Line ) 17-26; DOI: 10 ’s scatter diagra vior of ASTM ios of -1, 0, 1 ate the comp r, Walker and o infer: a) the ce of mean s el were show d) Kwofie’s m er’s model wa oy steel. e and Finatec oduce and to heory and Pr d Cliffs, NJ, ( TM STP 462 s of Metallic M 500 600 700 80 Pa] - Eq (2.2.1) .3221/IGF-ESIS. am. M A743 CA6 1/3 and 2/3. parative diagr d Kowfie’s mo e fatigue stren stresses, havin wn inadequate model presen as the best mo c. These supp develop scie ractice), Else (1998). 2, Am. Soc. Materials, (200 00 900 1000 14.02 25 NM The rams odel ngth ng a e to nts a odel ports ence. evier For 02). http://dx.medra.org/10.3221/IGF-ESIS.14.02&auth=true http://www.gruppofrattura.it B. L 26 [9] [10 [11 [12 RE T Lobato da Silva ASTM / E (1990). 0] ASTM / E (-N), (1991 1] P. R. Gill, W Press, (1981 2] S-K. Lin, Y ESPONSIBILI he autho T et alii, Frattura E 468-90 - Sta 739-91 - Stan 1). W.Murray, M 1) 136. Y-L. Lee, M-W ITY NOTICE ors are the on ed Integrità Stru andard Practi ndard Practic M. H.Wright, T W.Lu, Int. J. o E nly responsibl utturale, 14 (201 ice for Presen ce for Statistic The Levenbe of Fatigue, 23 le for the prin 10) 17-26; DOI: ntation of Co cal Analysis o erg-Marquard (2001) 75. nted material 10.3221/IGF-ESI onstant Amp of Linear or L dt Method in included in th IS.14.02 plitude Fatigu Linearized Str Practical Oti his paper. ue Test for M ress-Life (S-N imization, Lo Metallic Mater N) and Strain- ondon: Acade rials, -Life emic http://dx.medra.org/10.3221/IGF-ESIS.14.02&auth=true http://www.gruppofrattura.it << /ASCII85EncodePages false /AllowTransparency false /AutoPositionEPSFiles true /AutoRotatePages /None /Binding /Left /CalGrayProfile (Dot Gain 20%) /CalRGBProfile (sRGB IEC61966-2.1) /CalCMYKProfile (U.S. Web Coated \050SWOP\051 v2) /sRGBProfile (sRGB IEC61966-2.1) /CannotEmbedFontPolicy /Error /CompatibilityLevel 1.4 /CompressObjects /Tags /CompressPages true /ConvertImagesToIndexed true /PassThroughJPEGImages true /CreateJobTicket false /DefaultRenderingIntent /Default /DetectBlends true /DetectCurves 0.0000 /ColorConversionStrategy /CMYK /DoThumbnails false /EmbedAllFonts true /EmbedOpenType false /ParseICCProfilesInComments true /EmbedJobOptions true /DSCReportingLevel 0 /EmitDSCWarnings false /EndPage -1 /ImageMemory 1048576 /LockDistillerParams false /MaxSubsetPct 100 /Optimize true /OPM 1 /ParseDSCComments true /ParseDSCCommentsForDocInfo true /PreserveCopyPage true /PreserveDICMYKValues true /PreserveEPSInfo true /PreserveFlatness true /PreserveHalftoneInfo false /PreserveOPIComments true /PreserveOverprintSettings true /StartPage 1 /SubsetFonts true /TransferFunctionInfo /Apply /UCRandBGInfo /Preserve /UsePrologue false /ColorSettingsFile () /AlwaysEmbed [ true ] /NeverEmbed [ true ] /AntiAliasColorImages false /CropColorImages true /ColorImageMinResolution 300 /ColorImageMinResolutionPolicy /OK /DownsampleColorImages true /ColorImageDownsampleType /Bicubic /ColorImageResolution 300 /ColorImageDepth -1 /ColorImageMinDownsampleDepth 1 /ColorImageDownsampleThreshold 1.50000 /EncodeColorImages true /ColorImageFilter /DCTEncode /AutoFilterColorImages true /ColorImageAutoFilterStrategy /JPEG /ColorACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /ColorImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000ColorACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000ColorImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 300 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /GrayImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000GrayACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000GrayImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 1200 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict << /K -1 >> /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile () /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False /CreateJDFFile false /Description << /ARA /BGR /CHS /CHT /CZE /DAN /DEU /ESP /ETI /FRA /GRE /HEB /HRV (Za stvaranje Adobe PDF dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. 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