Vetokuormitetun päittäisliitoksen väsymislujuus hitsatussa tilassa Nykykäytännön arviointia ja vaihtoehtoisia tarkastelutapoja

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2 Theme Days of the HRO Design Forum Lappeenranta University of Technology, Lappeenranta Vetokuormitetun päittäisliitoksen väsymislujuus hitsatussa tilassa Nykykäytännön arviointia ja vaihtoehtoisia tarkastelutapoja Fatigue strength of tensile loaded steel butt-welded joints in as-welded condition Evaluation of current practice and alternative considerations Timo Nykänen and Timo Björk Lappeenranta University of Technology, Laboratory of Steel Structures, P.O. Box 20, FIN Lappeenranta, Finland Friday, February 27, 2015 Design Forum of optimized welded structures (HRO)

3 The aim of the present study is to validate the fatigue strength of tensile loaded butt-welded joints by re-analysing fatigue data collected from the literature, to study the qualities (accuracy) of fatigue strength predictions, and to try to explain, at least partly, the apparent inconsistencies implicit in the results presented in the literature [5-19, ]. Tutkimuksen tarkoituksena siis: Vetokuormitetun päittäisliitoksen väsymislujuuden määrittäminen hitsatussa tilassa kirjallisuudesta kerätyn datan avulla ja sen vertaaminen nykykäytännön mukaiseen arvoon. Tutkia väsymislujuusennusteiden hyvyyttä (tarkkuutta) Yrittää ainakin osaksi selittää kirjallisuudessa esiintyviä ilmeisiä (näennäisiä) ristiriitaisuuksia väsymiskoetuloksissa ja niiden tulkinnoissa. Liittyen lähinnä jäännösjännityksen ja R-suhteen vaikutukseen Esimerkiksi as-welded (R = 0 0.1) vs. Ohtan menetelmä 3

4 Collected experimental fatigue data Ref Steel S y R m t R n n run-out K m Process Wang [11] Q235B * 30 * - 16Mn * 30 * - SS * 30 * - Remes [21] S , 18 SAW ** Hybrid LF ** Remes [22] S , 18 SAW ** , 48 Hybrid MF ** , 59 Hybrid LF ** Radziminski [23] HY * 30 * GMAW HY * 30 * SMAW HY * 30 * Nykänen [18] Optim 1100 QC , 16 GMAW ** , 32 GMAW-P ** Ohta [6,24,25,26] SP * SAW SPV * SUS304 HP * NRIM [27] SM50B SMAW NRIM [28] SM58Q SMAW NRIM [29] HT80 (A517) SMAW NRIM [30] HT80 (A517) ~727 ~ SMAW ~733 ~ GMAW SAW NRIM [31] SM50B ~488 ~ SMAW ~ GMAW ~436 ~ SAW Maddox [32] Mild steel * 30 * SMAW Harris [33] ASTM A7 ~230 ~ * 30 * SMAW AvestaPolarit [34] Duplex g * 48 GMAW ** (EN ) * 20 GTAW n For R = and N = n = 532 * Unknown K m and chosen as recommended in [2] Hybrid LF CO 2 -laser combined MAG welding, laser travels first. Hybrid MF CO 2 -laser combined MAG welding, MAG travels first. K f = , K f mean = K m mean = 1.053, mean = 30.4 o ** one-side welding (Units: MPa, mm, deg.) 4

5 Nominal stress system Ok? Collected fatigue data in the nominal stress system (Fig. 1) 5

6 Notch stress system Concentration factors Misalignments [2]: 3l e Km 1Km, 1Kme, 1, where Km, 1 and Kme, 13 2 t t The measure 2l is the distance between clamps, [rad] is the angular misalignment and e is the axial misalignment. Weld, Anthes et al. [35]: K K t m t b sin( ) t 2 3 t sin 1.968sin 0.713sin t 2 3 t sin 1.737sin sin deg. Effective notch stress method, ENS [2]: K K f m, b t m, b 1 mm The combined stress concentration, K f,was finally calculated as follows: K K K 1 K f f m m f b sin( ) 6

7 Notch stress system!!! FAT225, kun m = 3 Liian suuri? Collected fatigue data in the notch stress system (Fig. 3) 7

8 Statistical methods Standard fitting procedure Standardimenetelmä In the case of linear regression, the fitted mean SN-curve is of the form log N log C mlog logcchar logcmean k1stdv f where m is the slope of the curve in log-log and with the fatigue data considering log N f (the response) as a function of log (the independent variable). A design curve at 95% survival probability level is normally calculated from the mean value logc mean on the basis of two sided tolerance limits of the 75% confidence level of the logc mean : logcchar logcmean k1 Stdv, where Stdv is the standard deviation of log C [2, 36]. Minimization of the sum of squared perpendicular distances from a line (MSSPD ) Vaihtoehtoinen menetelmä, joka pitäisi antaa parempi sovitus The comparison of the perpendicular offsets approach with the traditional approach reveals that the perpendicular 2 offsets approach provides a better fit. [37] The minimization of the square of the perpendicular distances R leads to the following equations for the fitting parameters: Minimoidaan pisteiden kohtisuorien yabx log N logcmlog etäisyyksien neliön summa sovitesuorasta R R R y abx / 1b minimum, when 0 and 0 i i a b n 2 2 i [ i i ( i i) 4 ( i i) ]/2 i i where u log ( log ) / n and v log N ( log N ) / n logc mean f m v u v u uv uv n i i j i fi f j1 j1 (log N mlog ) / n log C (log N mlog ) / nk Stdv f i char f i i * Deming, W. E. (1943) Statistical adjustment of data. Wiley, NY (Dover Publications edition, 1985). ISBN n j i 1 y Vertical offsets x Perpendicular offsets Deming * regression (orthogonal). The red lines show the error in both x and y. This is different from the traditional least squares method which measures error parallel to the y axis. The case shown, with deviations measured perpendicularly, arises when x and y have equal variances. 8

9 Results of fitting procedures All broken specimen data included, R test = (n = 775): Nominal stress method m FAT mean [MPa] FAT char [MPa] r 2 Stdv of log(c) corresp. log (N) Stdv of log(c) corresp. log () Standard procedure MSSPD Vastaa IIW:n suosituksia Notch stress method m FAT mean [MPa] FAT char [MPa] r 2 Stdv of log(c) corresp. log (N) Stdv of log(c) corresp. log () Standard procedure MSSPD FAT mean vastaa IIW:n suosituksia FAT char : FAT198 < IIW FAT225 Data range for broken specimen: N = and R test = (n = 532) *) Nominal stress method m FAT mean [MPa] FAT char [MPa] r 2 Stdv of log(c) corresp. log (N) Stdv of log(c) corresp. log () Standard procedure MSSPD Hajonta pieneni!!! Notch stress method m FAT mean [MPa] FAT char [MPa] r 2 Stdv of log(c) corresp. log (N) Stdv of log(c) corresp. log () Standard procedure MSSPD *) Reduced data set, only broken specimen results in the life range were included, as recommended in [38]. 9

10 Comparison of results Reduced data set Nominal stress method SN - curve : m N C?! Sovittamalla suora test vs. pred pistejoukkoon, saadaan oheiset tulokset?! Vastaavuus sitä parempi mitä lähempänä suoraa pisteet sijaitsevat 10

11 Comparison of results All broken specimen data included Nominal stress method SN - curve : m N C?!?! 11

12 Comparison of results Reduced data set Notch stress method SN - curve : m N C k?!?!! 12

13 Comparison of results All broken specimen data included Notch stress method SN - curve : m N C k?!?!! 13

14 SN-curves nominal - standard Ok,? konservatiivinen? 14

15 SN-curves nominal - MSSPD Ok,??? R =

16 SN-curves notch - standard? Ok,? Jos FAT198? 16

17 SN-curves notch - MSSPD Ok,? Lähtökohtaisesti on edellä oletettu, että lokaali R suuri vetojäännösjännityksistä johtuen, jolloin kuormituksen R-suhteella ei pitäisi olla vaikutusta selvä vaikutus on kuitenkin nähtävissä Päätelmiä:?? R = Standardisovitus, m = 3 Nominal: FAT90 ok Notch: FAT198 < IIW FAT225 Pakottamalla m = 3 saadaan ulkoisen kuormituksen korkea R-suhde otetuksi huomioon!? Pitkällä kestoiällä ennusteet konservatiivisia MSSPD Nominal & Notch Sovitus näyttää paremmalta, Korkea R-suhde ongelmana Ilmeisesti syynä: Vähän R > 0.5 ja max = S y kokeiden tuloksia Kommentti: Usein pienillä koesauvoilla jäännösjännitykset Kuitenkin alhaisia tai jopa puristuksella, jolloin R-vaikutus johtuisi pääasiassa kuormituksen R:stä!? 17

18 R-effect simplified consideration Asumption: Residual stress res 0 Smith, Watson, and Topper (SWT) [4] If the plastic strains are small : 2 2 ref 1Rref maxa ref, if Rref =0 2E 1 R 1R 1R R R 0 2E1Rref The mean stress correction factor is also : f 1R => Pelkästään kuormituksen R-suhteeseen perustuva tarkastelu SWT R-vaikutus Oletetaan: Ei jäännösjännityksiä Plastiset venymät pieniä => R R local Fitted stress range vs. N f Nominal stress method: = test [(1-R ref )/(1-R test )] 1/2 Notch stress method: = k fmax test [(1-R ref )/(1-R test )] 1/2 All broken specimen data included, R test = (n = 775): Nominal stress method R test = m FAT mean [MPa] FAT char [MPa] r 2 Stdv of log(c) corresp. log (N) Stdv of log(c) corresp. log () Standard procedure MSSPD Notch stress method R test = m FAT mean [MPa] FAT char [MPa] r 2 Stdv of log(c) corresp. log (N) Stdv of log(c) corresp. log () Standard procedure MSSPD Vastaa IIW:n suosituksia R = 0 tulos?!!! FAT mean vastaa IIW:n suosituksia FAT201 < IIW FAT225 R = 0 tulos?!!! 18

19 Comparison of results Nominal stress method SN - curve : m m N 1 R C, R 0 2 ref 19

20 Comparison of results Notch stress method SN - curve : m m N k 1 R C, R 0 2 ref 20

21 Reference SN-curves notch stress method R ref = 0 Lovijännitykset muunnettu SWT:lla vastaamaan R = 0 ja sovitettu referenssikäyrät (master-käyrät) 21

22 SN-curves notch stress method R-effects, standard fitting, m = 3 SN-käyrät vastaten R = -1, 0 ja 0.5 m = 3 Kommentti: R > 0 muuttuu konservatiiviseksi Sitä konservatiivisempi mitä suurempi R Pitkällä kestoiällä konservatiivinen 22

23 SN-curves notch stress method R-effects, standard fitting, m = 3, comparison with IIW!? SN-käyrät vastaten R = -1, 0 ja 0.5 m = 3 Vertailu IIW -suosituksiin Kommentti: IIW high RS vastaa suunnilleen tapausta R = 0?!? 23

24 SN-curves notch stress method Standard fitting, m = 3, no SWT Kommentti: Käyrä edellä vastaten R = 0 käytännössä sama kuin ilman SWT:a 24

25 SN-curves notch stress method R-effects, MSSPD, m = 4.43 SN-käyrät vastaten R = -1, 0 ja 0.5 m = 4.43 R = Kommentti: R > 0 hieman konservatiivinen Sitä konservatiivisempi mitä suurempi R Ennuste kuitenkin selvästi parempi kuin jos m = 3 Pitkällä kestoiällä konservatiivinen 25

26 SN-curves notch stress method R-effects, MSSPD, comparisons Kommentti: Jotainhan tästäkin näkee, kun jaksaa tutkiskella! 26

27 SN-curves notch stress method MSSPD, m = 4.28, no SWT Kommentti: Käyrä edellä vastaten R = 0 hieman ylempänä kuin ilman SWT:a 27

28 SN-curves nominal stress method R-effects, MSSPD, comparisons Nominal Vertailu ainoastaan Ohtan tuloksiin Huom! Vastaavuus on vielä parempi, jos referenssikäyrä määritetään pelkästään Ohtan tulosten perusteella! For R > 0 the correction factors are the conservative the higher R-ratio. Comparison of the MSSPD-fitted SN-curves, which include the applied stress ratio effect, with the results of Ohta et al. [6, 24-26] using the nominal stress system. 28

29 SN-curves notch stress method R-effects, MSSPD, comparisons Notch Vertailu Ohtan ja Kranz & Sonsino tuloksiin Selvää yhtenevyyttä ennustekäyrien ja Kranz & Sonsino käyrien kanssa Kranz & Sonsino: Comparison of the MSSPD-fitted SN-curves, which include the applied stress ratio effect, with the results of Ohta et al. [6, 24-26] and Kranz and Sonsino [16] using the notch stress system. 29

30 SN-curves notch stress method R-effects, comparison with experimental results R = 200, 268, 368 Hobbacher, A. (2013) The notch stress method for fatigue assessment of welded joints. Presentation in Theme Days of the HRO Design Forum , Holiday Club Tampere Spa, Tampere, Finland. MSSPD, all data included, SWT m 4.43, FAT = 266 R1 R0.0 R0.4 R0.5 R0 char 1R R ( 1) (0.0) (0.4) (0.) MSSPD, reduced data, no S WT m 4.08 R 0.5?? Standard, all data included, SWT m 3 1R R R1 R0.0 R0.4 R0.5 R ( 1) (0.0) (0.4) ( 0.5) Standard, reduced data, no SWT m ?? 211? MSSPD, all data included, no SWT m 4.28 R 0.5?? R ?? 198 Standard, all data included, no SWT m 3 R Kommentti: MSSPS + SWT näyttää toimivan, kun m = 4.43 Standard + SWT ei näytä toimivan, kun m = 3 Yleinen kommentti SWT:sta: Kun res = 0, SWT näyttäisi toimivan MSSPS kanssa, tosin muuttuu konservatiiviseksi, kun R > 0 sitä enemmän mitä suurempi R johtuu plastisista venymistä 30

31 R-effect more comprehensive consideration Lokaaliin R-suhteeseen perustuva tarkastelu We may try to take the plasticity effect (and thus the local stress ratio) into the account by introducing a plasticity correction factor fpl, Rs,, where s = res /R m. The corrected mean stress correction factor is then f(, R, s) f (, R, s) f ( R) 1R pl SWT This is quite complicated relation that depends on the applied stress range, applied stress ratio, R, residual stress level and material. Simplifying asumptions: Ramberg-Osgood relationship with the typical material parameter estimates for steels based on ultimate strength are used (n = 0.15, H = 1.65R m ) [1] An ideal kinematic hardening behavior was assumed for simplicity Neuber s rule for plasticity local Määritetään R local paikallisen venymän menetelmällä [1] In order to demonstrate the method, the plasticity correction factor is calculated only for local stress ranges = 225 and 304 MPa, corresponding ultimate strengths of R m = 400, 600, 800 and 1000 MPa. The coefficients for the fitted plasticity correction factor equation and the corresponding correlation coefficients r, are presented in Table below, when R = and s = b crdr es fs gsr hsr fpl, R, s a/1 e R m a b c d e f g h r n max max max E K nom 1 K f maxmax res E 1R 1 n 1 2 2E 2K K 2 f nom E min max min R local max 31 2

32 Comparisons s = res /R m Keskijännityksen korjauskerroin f, R, s 1Rlocal res = 0 R0 m 2 m N (1 R ) C local C m 1 Rlocal, joten N FAT FAT 1R local res >> 0 Kommentti: Kun vetojäännösjännitys suuri, on kuorman R-suhteen vaikutus vähäinen Ääritapauksissa lähes sama korjauskerroin kuin IIW-suosituksissa " Predicted mean stress correction factors (R m = 600 MPa) and comparisons with scaled (to correspond R ref = 0) fatigue enhancement factor f(r) by IIW [2] and Kranz & Sonsino [16]. R ref = 0 32

33 Effects on SN-curves (relative) Mielivaltaisesti valitulla referenssikäyrällä (vastaten R = 0, s = 0), ktso alla. $ R suuri res >> 0 # Notch stress method SN - curve : R ref 0 m k N f, R, s C or m 2 m N 1R C k local m R suuri res = 0 # # R = 0 res >> 0 Kommentti: # Erot suhteellisen pieniä Lujemmilla teräksillä puristusjäännösjännitys (suhteellinen) parantaa väsymislujuutta varsinkin suuremmilla kuormanvaihtojen lukumäärällä Predicted effects of R-ratio and residual stress level on SN-curves The slope for base SN-curve was arbitrary chosen (to give m = 3, when R = 0.5, s = 0.5 and R m = 1000 MPa) 33

34 Effects on SN-curves (relative) Mielivaltaisesti valitulla referenssikäyrällä (vastaten R = 0, s = 0), ktso alla. & $! Kommentti: Lujemmilla teräksillä puristusjäännösjännitys (suhteellinen) parantaa väsymislujuutta varsinkin suuremmilla kuormanvaihtojen lukumäärällä Etu kuitenkin menetetään, jos R suuri % #! Kommentti: Ennustettu R local vaikutus Lujempi teräs korkeampi keskijännitys Predicted effects of R-ratio and residual stress level on SN-curves The slope for base SN-curve was arbitrary chosen (to give m = 3, when R = 0.5, s = 0.5 and R m = 1000 MPa) 34

35 Preliminary comparisons Muodostetaan master-käyrä (base line) alla olevin oletuksin ja verrataan koetuloksiin Siis olettaen, että pienissä koesauvoissa res 0 The curves are assumed to be based on R = 0, s = 0 and R m = 600 MPa data!! Data points: R m = MPa!!! Mean base line estimate : Mean base line estimate : (Based on IIW mean curve) N f f,0,0 N f 3.7 (Based on MSSPD mean curve) N f f, 0, 0 N f 5.4 Muodostetaan siten, että kumpikin käyrä antaa likipitäen saman tuloksen, kun R = 0, s = 0 ja R m = 600 MPa Käytännössä joudutaan tekemään käyränsovitus pistejoukkoon, joka ei ole tarkalleen suoralla (ero pieni) muunnoksesta johtuen s = 0 s = 0 Kommentti: Tämä tapaus näyttäisi vastaavan paremmin koetuloksia 35

36 Preliminary comparisons Sama kuin edellä vertailu ainoastaan Kranz & Sonsino ja Ohta et al. tuloksiin Ensin perustuen IIW:n käyrään The curves are assumed to be based on R = 0, s = 0 and R m = 600 MPa data!! Data points: R m = MPa!!! Most ~630 MPa! s = 0 Base line estimate : (Based on IIW mean curve) N f f,0,0 N f Effect of R + res s R FAT mean As a comparison, also the scaled (to correspond R ref = 0) factors of Kranz and Sonsino [16] are presented for fully penetrated welds (A) and for fully and nonfully penetrated welds, and with non-fully penetrated welds with circular and long holes (A, B, C, D). 36

37 Preliminary comparisons Sama kuin edellä vertailu ainoastaan Kranz & Sonsino ja Ohta et al. tuloksiin Sitten perustuen MSSPD sovituksella saatuun käyrään The curves are assumed to be based on R = 0, s = 0 and R m = 600 MPa data!! Data points: R m = !!! s = 0 Base line estimate : (Based on MSSPD mean curve) N f f,0,0 N f Effect of R + res s R FAT mean Kommentti: Ennusteen mukaan väsymislujuus pienenee edelleen, jos korkea R-suhde ja suuret vetojäännösjännitykset! Kommentti: Tämä tapaus näyttäisi vastaavan paremmin koetuloksia kuin edellinen Kun R > 0 ennuste parempi kuin lineaarisessa tapauksessa Kun R = -1 ennuste huonompi kuin lineaarisessa tapauksessa As a comparison, also the scaled (to correspond R ref = 0) factors of Kranz and Sonsino [16] are presented for fully penetrated welds (A) and for fully and nonfully penetrated welds, and with non-fully penetrated welds with circular and long holes (A, B, C, D). 37

38 Example Real base line for Optim 1100 QC based on as-welded data An attempt was also made to predict the fatigue strength of UP treated joints (red) based on the base line of the as-welded state (blue). MAG welding. R m = 1055 MPa, which is used in the following analysis. The measured mean residual stress gives s = in as-welded condition. For the UP treated joints, the residual stress varied from 132 to 315 MPa. The mean value of 240 gives s = , when the ultimate strength was assumed to remain the same as in as-welded condition. MSSPD Rough estimate: Assuming that the ENS works for UP treated joints as well! Mean weld notch (toe) radius, mm As-welded After UP Surface 0.39 Surface 0.81 Root 0.5 Root 0.99 Kommentti: Tässä jäännösjännitykset mitattu pinnalta ei yhteismitallinen ENS-jännityksen kanssa NB: UP, R = 0.38 Crack initiation site: Surface, unsuccessful UP treatment, specimen failed from reinforcement side of groove! Base line for ultra-high strength steel based on as-welded state test results and MSSPD-fitting procedure, and comparison of predictions with test results [18]. 38

39 Example Real base line for Optim 1100 QC based on as-welded data An attempt was also made to predict the fatigue strength of UP treated joints (red) based on the base line of the as-welded state (blue). MAG welding. R m = 1055 MPa, which is used in the following analysis. The measured mean residual stress gives s = in as-welded condition. For the UP treated joints, the residual stress varied from 132 to 315 MPa. The mean value of 240 gives s = , when the ultimate strength was assumed to remain the same as in as-welded condition. Standard Rough estimate: Assuming that the ENS works for UP treated joints as well!! After prediction model NB: UP, R = 0.38 Crack initiation site: Surface, unsuccessful UP treatment, specimen failed from reinforcement side of groove! Base line for ultra-high strength steel based on as-welded state test results and standard fitting procedure with free slope, and comparison of predictions with test results [18]. 39

40 Päätelmiä Nimellisen jännityksen menetelmän mukaiset FAT char = 89 ja FAT mean = 141 (vastaten K m mean 1.05 ja mean 30 o ), jotka saatiin standardisovituksella käyttäen kiinteää kaltevuutta m = 3, vastaavat hyvin normien arvoja Tehollisen lovijännityksen menetelmän mukaisiksi vastaaviksi arvoiksi saatiin FAT char = 198 ja FAT mean = 304. Karakteristinen arvo on selvästi pienempi kuin IIW:n ilmoittama 225 MSSPD sovitus antaa paremman korrelaation sekä väsymislujuuden, että kestoiän suhteen Kun jäännösjännitykset on pieniä, lineaariseen materiaalikäyttäytymiseen perustuva SWT-parametri näyttäisi toimivan. Korkeilla R-suhteilla se osoittautui sitä konservatiivisemmaksi mitä korkeampi R-suhde on Lokaalisen R-suhteen käyttö näyttäisi ottavan keskijännityksen paremmin huomioon Alustavien SWT-parametriin perustuvien arviointien mukaan korkealla R-suhteella ja pienillä koesauvoilla saatuihin tuloksiin perustuva väsymislujuus ei välttämättä takaa todellisten hitsattujen rakenteiden väsymislujuutta Parempaan ennusteeseen voitaisiin päästä, jos esitetyn menetelmän mukaista masterkäyrää muodostettaessa voitaisiin ottaa kunkin koesauvan jäännösjännitys/lujuus, lujuus,, huomioon. Hieman yleisempi masterkäyrä olisi voitu muodostaa ottamalla lujuus huomioon ja olettamalla res = 0. Laskennassa käytettävän jäännösjännityksen suuruus pitäisi ilmeisestikin määrittää samoin perustein kuin tehollisen lovijännityksen suuruus. Sopiva laskenta-arvo voisi olla 0.4 mm syvyyteen ulottuvan jäännösjännitysjakauman keskiarvo Multiaxiality factor s 2.5 * 0.4 mm, 0 mm mm 1 mm f

41 Conclusions The following conclusions are drawn based on re-analysis of a large amount of fatigue data: The derived results in the nominal stress system FAT char = 89 and FAT mean = 141 (corresponding to K m mean 1.05 and q mean 30 o ) with standard fitting procedure and fixed m = 3 are in a good agreement with codes. The corresponding fitting using the notch stress system gives FAT char = 198 and FAT mean = 304. The characteristic value is clearly lower than the recommended design fatigue class 225. Use of FAT198 might harmonize the nominal and notch stress fatigue assessment methods. The perpendicular offsets approach gives more reasonable correlation between the predicted and experimental values for both the fatigue life and the fatigue strength than the standard procedure, at least from the designer s viewpoint. For joints with negligible residual stresses, the SWT-parameter based on linear material behavior appears to give good results, except for high applied R-ratios where it seems to be a little conservative. Use of the local stress ratio instead of the applied stress ratio takes the mean stress effect better into consideration and seems to explain some of the apparent inconsistencies that seem to exist between different investigations. Preliminary calculations with the SWT-approach, based on the comparisons made and assuming that the approach is applicable and effective in this context, indicate that high applied R-ratio in small size specimen tests might not inherently guarantee safe fatigue strength for welded joints that are loaded with high applied R- ratio and contain high tensile residual stresses as found in real welded structures. The R local based method seems to be quite promising. In order to test and verify the method more properly we should be able to determine the base line first. 41

42 Thank you Acknowledgements The authors wish to thank Rautaruukki Corporation, FIMECC Ltd. and the Finnish Funding Agency for Innovation (TEKES) for the founding this BSA-project, which enabled to complete this research work. Project, which is a part of the Breakthrough Steels and Applications (BSA) programme..

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