A parametric fracture mechanics study of the effect of a cold lap defect on fatigue strength

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1 Rakenteden Mekankka (Journal of Structural Mechancs) Vol. 41, No 3, 2008, pp A parametrc fracture mechancs study of the effect of a cold lap defect on fatgue strength Mkko Heskanen Summary. Several fnte element analyses were carred out to study the effect of local geometrcal varaton of weld on fatgue strength of non-load-carryng crucform jonts n as-welded condton under tensle loadng. Crucform jonts can be found n many heavy ndustral applcatons, such as n junctons of longtudnal and transverse stffeners n welded plate grders of shpyard cranes and orthotropc plates of shps. The varables were toe radus, cold lap and flank angle. The fatgue assessment was carred out wth lnear-elastc fracture mechancs n plane stran and under mxed-mode K I K condtons. The Pars crack growth law was used to predct the growth rate. An analytcal model was developed and ts accuracy was compared to the avalable expermental fatgue test results. Key words: fatgue crack growth, fnte element analyss, fracture mechancs, mxed mode fracture, welded jonts Nomenclature a A C E K I eq Crack length of cold lap Throat thckness Fatgue crack growth coeffcent Young s modulus Stress ntensty factor of mode (=I, ) K Equvalent stress ntensty factor K th Threshold stress ntensty factor m Fatgue crack growth exponent N Number of cycles r Toe radus R Stress rato T Plate thckness β Flank angle Range n cyclc loadng θ c Crack knk angle ν Posson s rato σ Normal stress σ Yeld stress y BC Boundary condton 6 FAT Fatgue strength at 2 10 cycles wth 95 % survval probablty FEA Fnte element analyss W Internatonal Insttute of Weldng 119

2 LEFM Lnear-elastc fracture mechancs LUT Lappeenranta Unversty of Technology MAG Metal Actve Gas SCF Stress concentraton factor SIF Stress ntensty factor S-N Stress-lfe curve Introducton It s well documented that welds are the weakest part of a fatgue-loaded structure due to local weld geometry and dfferent types of weld mperfectons whch strongly affect on the fatgue strength. The local geometry affects on the local stress concentratons of a structure and the weldng process can create crack-lke defects, such as cold laps and undercuts, whch durng cyclc loadng may lead to a large scatter n fatgue lfe. The conventonal fatgue desgn rules for welded jonts, whch are based on the S-N curves, only partally consder weld defects what can ntate durng fabrcaton. Usually, the S- N curves are based on the laboratory tests of welds wth normal qualty, even though, what s a normal qualty s not always clearly specfed. There s a demand for better understandng of the nfluence of macro-geometrcal effects, structural dscontnutes and weld defects that produce a hgh local stress. Typcal types of weld defects, what can be found on crucform jonts [1], are crack at the weld toe, crack at the root, nterbead crack and cold lap and are usually the consequences of mproper fabrcaton. Cold lap, Fgure 1, s a weld defect, where the weld fller materal has not properly fused wth the base metal or the prevous welds pass materal [2]. The arc has not melted the base metal suffcently and has caused a slghtly molten puddle to flow nto the base materal wthout bondng. Numerous test programs have demonstrated the detrmental effect of cold laps and ndvdual analyss results have shown nfluence of fatgue cracks growng from cold lap defects. An nvestgaton covered by Lopez and Korsgen [3], proved that 80 % of all dscovered weld defects n MAG (Metal Actve Gas) welds are cold laps. The range of a typcal cold lap sze s between mm. Moreover, there seems to be an obvous connecton between hgh speed weldng and the occurrence frequency of cold laps [4]. 120

3 Fgure 1. Typcal crack-lke defects on welded structures [5]. The objectve of ths work was to study the nfluence of cold laps on the fatgue strength of non-load-carryng fllet welded crucform jonts n as-welded condton under cyclc tensle loadng. Ths was carred out wth lnear-elastc fracture mechancs (LEFM) n plan stran. The varables were cold lap sze, toe radus and flank angle and the parametrcal nterdependence were analyzed wth 90 dfferent 2D fnte element (FE) models and non-lnear regresson analyss. As a result of ths study, an analytcal model was developed and ts valdtaton was verfed wth the comparson to expermental test results. Fracture mechancs analyss Stress ntensty factor calculaton The openng mode and the sldng mode stress ntensty factors K I and K were calculated wth FE crack growth smulaton program FRANC2D/L [6] usng the J-ntegral approach by Dodds and Vargas [7]. The nfluence of K I and K on fatgue crack growth was based on the maxmum tangental stress crteron by Erdogan and Sh [8]. It predcts that the fatgue crack propagaton path s perpendcular to the maxmum prncpal stress and the crack grows under the Mode I. The local asymptotc LEFM crack front felds can be descrbed as [9]: 1 θ 2 θ 3 θ T σ rr = cos 1 sn sn θ 2 tan + 2 2π 2 K I + + K K r 2 ( 1+ cos θ ), (1) 121

4 1 θ 2 θ 3 T σ θθ = cos cos sn θ + ( 1 cos 2θ ) 2π 2 K I K 2 2, (2) r 2 σ 1 θ T cos [ K sn θ K (3cosθ 1) ] sn θ θ 2 2πr r = I +, (3) whereσ rr, σ θθ and σ r θ are the stress components from a dstance r and angle θ from the crack tp n the cylndrcal-polar coordnate system. The T-stress s a constant component of the stress feld and actng parallel to the crack tp. Wth usng frst-order knkng theory, dfferentatng the frst term n Equaton (2) wth respect to θ and denotng θ = θ c, the crack growth drecton perpendcular to the maxmum prncpal stress can be expressed as [9]: 2 8( K ) ( ) / K I K / K I θ c = 2 tan. (4) 4 Mxed-mode nteracton can be consdered by neglectng the second term from the Equaton (2), denotng θ =, multplyng both sdes wth 2 πr and denotng the left θc sde as,.e., the tangental stress σ θθ n the Mode I s put equal to the σ θθ n the K I eq Mode I and Mode combnaton. Then, the equvalent SIF wll be: θ 3 cos 2 c θ K sn cos c I eq = K I K θ c. (5) When the loadng s a pure shear Mode wth a crack knk angle of -70.5, =1.15K. The crack growth drecton wll change f the ntal crack drecton K Ieq does not satsfy the propagaton drecton n the Mode I. The K Ieq wll be approxmately equal to K I for the followng crack propagaton steps, f the crack growth ncrement s small enough [10]. Fatgue lfe calculaton For the fatgue lfe calculaton, the Pars Erdogan relatonshp [11] was used. It has the followng form: da = C( K) m, (6) dn 122

5 where a s the crack length, N s the number of cycles, C s a materal constant, K s the openng mode SIF range and m s also a materal constant and the phase slope on log-log plot. Stress ratos R >0 can be assessed by a form of the crack propagaton equaton proposed by Forman [12]: da dn ( K ) m C =. (7) 1 R The N can be solved wth separatng the varables and ntegratng: N f = a f a (1 R) da. (8) m C( K ) For the materal constants, C char = , Cmean = and m = 3 (n Nmm -3/2 and mm unts) were used and they are recommended by Internatonal Insttute of Weldng (W) [13] for fatgue assessment of ferrte-pearlte steel welded jonts n aswelded condton. C mean s the mean crack growth rate coeffcent and C char s the characterstc crack growth coeffcent correspondng to 95 % survval probablty. The threshold K value was not used n ths study. th Fatgue analyss wth fatgue crack growth smulator Model generaton Fatgue crack growth smulatons were executed wth a typcal desktop PC wth Pentum mcroprocessor. Wth symmetry boundary condtons (BCs), only one-quarter of the structure had to be modeled. Weld throat and plate thckness were consdered to have the constant values of A = 6.5 mm and T = 10 mm, Fgure 2. For the materal model, Young s modulus E = MPa and Posson s rato ν = 0.3 was used. The heataffected zone was not consdered. For the mesh, soparametrc eght noded elements wth quadratc shape functons were used and the sngularty problem n the crack tp was solved by movng the sde nodes to the quarter-pont postons [14]. A typcal model can be seen on Fgure 3. The dmensons of the models were altered to study the parametrc relatonshp on the fatgue strength. For flank angles β = 30 o, 45 o, 60 o, toe radus r/t ratos 0.05, 0.1, 0.2, 0.4, 1 and cold lap a/t ratos 0, 0.01, 0.02, 0.04, 0.08, 0.16 were used. The crack growth smulaton started from an ntal edge crack drecton perpendcular to the global x-axs at end of the cold lap. For the ntal crack length, 0.05 mm was used. It was then ncreased wth ncrements of 0.01, 0.02, 0.05, 5 x 0.1, 5 x 0.2, and 5 x 0.5. Those models that dd not have a cold lap (a/t rato was 0), the ntal crack length was 0.05 mm and the crack began to grow at the weld toe. The fnal crack sze, Fgure 4, developed to the length wth magntude of mm, whch corresponded to 81.7 % of the double symmetrcal models plate thckness. 123

6 Fgure 2. A double symmetrc model wth boundary condtons and loadng. Fgure 3. Typcal mesh sze. Fgure 4. Fnal deformed mesh. 124

7 Fatgue strength calculaton Fatgue strength of a welded jont s characterzed by a fatgue class, FAT [13], whch 6 dentfes the stress range correspondng to 2 10 cycles to falure wth a 95 % survval probablty calculated from a mean value of a two-sded 75 % confdence level. In ths study, The Pars-Erdogan relatonshp, Equaton (6) and Equaton (8) was used wth equvalent Mode I values of the SIF range to obtan the cycles to falure. To convert the cycles to falure to a characterstc fatgue class were carred out as follows [15]: N ref FAT = σ 3 ref, (9) where σ ref was the adapted tensle load of 100 MPa and N ref was the predcted fatgue lfe of the gven model. To compare the results from the crack growth smulaton wth 50 % survval probablty to the expermental fatgue test results, a converson was made: FAT mean Cchar = 3 FAT FAT, (10) C mean where 6 FAT s the mean fatgue strength at 2 10 cycles. mean Results Non-lnear regresson analyss The results from the crack growth smulaton for each model are represented n Appendces. For the ntal crack, the stress ntensty factor ranges for K I and K along wth the crack knk angles c were obtaned from the smulator. Then, the equvalent stress ntensty factors K Ieq were calculated separately. The FAT, relatve toe radus r/t, relatve cold lap sze a/t and flank angle were curve-ftted wth non-lnear regresson analyss [16]. The parametrc Equaton (11) along wth the adjuncton functons, Equatons (12, 13 and 14), are presented below. The parameters for the parametrc equaton and adjuncton functons are presented n the Table 1. Furthermore, the average devaton and the maxmum devaton from the predcted FAT of the parametrc Equaton (11) are presented lastly. a FAT T where, r T m, β =, (11) r f3, β 2 r r a T r r f1, β + f 2, β + p + q T T T T T 125

8 r 1 f1, β =, (12) c T r a + b T f h r r r T 2, β = d g, (13) T T l r r f 3, β = k, (14) T T = 1, 2, 3. Table 1. Parameters for the Equatons (11), (12), (13) and (14) β 30 o 45 o 60 o a -0,2436 1,936 1,985 b 4,551 2,527 2,408 c 0, ,070 0,9115 d 0,4131 2,083 1,189 g 0,3871 0, ,1687 h 0,5511 1,309 1,130 k 0,4274 0,3803 0,3629 l 0, ,1524 0,1473 m 24,34 36,24 34,92 p -0, , ,08232 q 0, , , Average devaton Max. devaton Data plots The results from the crack growth smulaton (Appendces: Table 1, 2 and 3) are represented as the 3D surface plots below to each flank angle. Lastly, all the 3D flank angle plots are represented together along wth the correspondng W fatgue class 80 [13]. 126

9 Fgure 5. Flank angles of 30 degrees. Fgure 6. Flank angles of 45 degrees. Fgure 7. Flank angles of 60 degrees. Fgure 8. Results from the study plotted jontly wth the W recommendaton (FAT 80) to nonload-carryng fllet welded crucform jonts Comparson to test results The FAT results from the FEA were compared wth the avalable test results of nonload-carryng crucform jonts from three dfferent sources; Martnsson [1] examned specmens wth the yeld strength of 380 MPa, thckness of 12 mm and welded wth tandem arc MAG; Barsoum [17] examned as well also specmens wth 12 mm of thckness, but they were welded wth hybrd Nd:YAG-laser/MAG and MAG; Sehadr [18], nvestgated at the Lappeenranta Unversty of Technology (LUT), specmens wth 6 mm of thckness and wth two dfferent yeld strength, 355 MPa and 650 MPa. Sehadr classfed weld defects from the test specmens and all test specmens were mcrographed, Fgure 9. Martnsson and Barsoum used R = 0 for the stress rato whle LUT [18] used varyng stress rato wth R = 0.10 to R = The specmens and batches are lsted n the Table

10 Fgure 9. Mcrograph from a test specmen [18]. Only those specmens that were n the range of ths parametrc study,.e. r/t wthn , a/t wthn and bound to 30 o - 60 o, were selected to the comparson; e.g. from Martnsson and Sehadr, only the above-mentoned geometrcal constrants satsfyng ndvdual specmens were selected. However, because of the absence of a more detaled descrpton, four batches were selected from Barsoum and FATexp were estmated wth the average value of all specmens n the certan batch. Values for the flank angle were estmated from the LUT s test specmens by subtractng the measured toe angles from 180 degrees [18]. Comparson was made wth the followng way: frstly, the geometrcal dmensons from the specmens and batches were converted to the ratos wth the respect of plate thckness, Table 3. Secondly, a predcton from the parametrc Equaton (11) was calculated wth a gven geometrcal rato and converted to mean fatgue strength wth the Equaton (10). Thrdly, f the flank angles on the specmens were not occurred to be 30, 45 or 60 degrees, the correspondng mean fatgue strength wth a gven flank angle was lnearly nterpolated [19]. Fnally, the average, maxmum and standard devaton were calculated from the comparson. 128

11 Specmen / Batch Weldng method Table 2.Test specmens. T [mm] σ y Remarks [MPa] C1 [1] MAG Tandem arc C2 MAG C3 MAG C5 MAG C6 MAG D2 MAG D5 MAG L [17] YAGlaser/MAG C MAG Tandem arc, sold wre E MAG Flux cored wre F MAG Tandem wre, flux cored A1 MAG Manual weldng A2 MAG Robotc weldng B MAG Manual weldng 01 [18] MAG MAG MAG MAG Specmen/ Batch Table 3. Comparson to test results of non-load-carryng crucform jonts r T a T β [deg] FAT exp [MPa] FAT cal [MPa] FAT mean 30 deg FAT mean 45 deg FAT mean 60 deg SCF Mean/ Std.dev. C1 [1] C C C C D D L [17] / 0.5 C / 0.3 E < / 0.6 F < / 0.1 A / 1.2 A / 0.5 B / [18] Avg.dev % Max.dev. % Std.dev. %

12 6 FAT exp s the expermental fatgue strength at 2 10 cycles and FAT cal s the mean 6 fatgue strength at 2 10 calculated from the Equatons (10) and (11). To examne the accordance and conformty of the FAT exp and FAT cal, they were plotted wth an deal reference lne along wth + 20 % and 20 % lnes, Fgure 10. If the correspondence would be perfect, the ponts would subsde to the reference lne n the mddle. Fgure 10. Comparson of fatgue strength wth specmens and FEA The Fgure 10 llustrates that there was scatter between the test results and FEA. Moreover, when the ponts seemed to settle under the reference lne, t meant that, the FEA allows more conservatve fatgue strength and lfe predctons than what was perceved from the expermental endurance test results wth real specmens. The trend wth the comparsons, Fgure 10, seemed to be that the FEA allocates more conservatve fatgue strength and lfe predctons n pluralty of the cases than what was observed expermentally from the real test specmens on the endurance tests. Dscussons The objectve of ths work was to study the nfluence of cold laps on the non-loadcarryng fllet welded crucform jonts fatgue strength n as-welded condton under cyclc tensle loadng. The fatgue analyss data from the crack growth smulator ndcated that there was a sgnfcant dfference n FAT for a gven flank angle when the local geometry was vared; e.g. wth the 45 o models, the FAT wth 95 % survval probablty ncreased from 70.4 MPa to MPa by smoothng the toe radus and elmnatng the cold lap. Comparable values from the models wth 30 o and 60 o flank angles were 71.1 MPa to MPa and 71.4 MPa to MPa. When the r/t rato was ncreased from 0.05 to 1.0 and wthn the a/t rato of 0.16 to models wth 30 o, 45 o and 60 o flank angles, 130

13 t produced a dfference of 11.3 MPa, 12 MPa and 10.7 MPa n the FAT. Wth that knd of dfference, the theoretcal FAT could be rased by one fatgue class [13]. Cold laps also proved to have a serous effect on the fatgue strength; e.g. wth the 60 o models wth 1.0 r/t rato, the FAT decreased from MPa to 82.1 MPa, creatng a dfference of 28.4 MPa, when the a/t rato was ncreased from 0 to Wth the 30 o and 45 o flank angles equvalent prolepses were 27.4 MPa and 26.7 MPa. The dfference wth that knd of magntude nflcts proceedng to the two step hgher fatgue class. However, wth a sharper toe radus, the dfference dd not mount as much and the nfluence of the r/t rato,.e. local notch, on the fatgue strength s self-evdent. Also, compared to the models wthout a cold lap, the FAT decreased more wth a smoother toe radus. Ths seemed to be n correspondence wth numerous studes [1, 4, 17], that wth hgh SCF (stress concentraton factor) values, cold laps effect on the fatgue strength wll become almost mperceptble and a sharp toe radus,.e. small r/t rato, s the prmary contrbutor to the hgh stress concentratons, thus the most nfluental factor on the fatgue strength. Varaton on the flank angle seemed to have only mnmal effects on the fatgue strength wth examned flank angle range and that can be observed from Fgures 5, 6 and 7. The 3D surface plots from the results seemed to be almost dentcal. However, the fatgue strength s usually greater wth a gently slopng flank angle, Table 1, and t s documented that the effect of flank angle on the fatgue strength s mnmal when the r/t rato s large and ncreases when the toe radus decreases [15]. Ths study supports those conclusons. When comparng the FEA results to the test results, the correlaton seemed to be satsfyng and occasonally scatterng; e.g. when compared to the batches and specmens that were n the examned range wth ther geometrcal parameters, the largest devaton was - 31 % wth specmen C2, Table 6, from Martnsson and the smallest devaton of 2 % wth specmen 77 from LUT, whle the mean of the specmens was -12 %. Three of the largest devatons came from the specmens and batches wth thckness of 6-12 mm, r/t ratos of 0.083, and 0.075, a/t ratos of 0.025, and The flank angles were 48 o, 30 o and 48 o, the yeld strength vared from 355 MPa to 380 MPa and the weldng processes were smlar. They all had SCFs from 2.2 to It was notable that the correlaton between FAT exp and FAT cal was more unsubstantal wth 12 mm specmens when they all had a small SCF, whle wth the LUT s specmens wth 6 mm of thckness, the correlaton was better the more lower the SCF went. Best correlaton came from the 50 o and 60 o flank angles. Only three specmens proved to last less than the correspondng FAT cal and that can be observed on Fgure 10. The reason of the dfference between FEA and test results could be explaned wth the nature of LEFM and FEM; t s well documented [15], that the predctons wth 2D LEFM n plan stran wll be more conservatve than the expermental test data from the real case, because the crack wll grow sem-ellptcally n the real structure [20]. Furthermore, the compressve resdual stresses n weld toe on Batch E [17] and the nonexstent cold laps, wll affect defntely on the dvergence between the conservatve planar LEFM analyss and the expermental tests. Moreover, the nfluence of throat thckness varaton on the fatgue strength has not been consdered n ths paper and the study was carred out wth constant throat thckness of 6.5 mm. However, there s evdence [21] that the varaton of throat thckness wll only have small effect on the fatgue strength. It can also be observed from the Fgure 9, that the determnaton of the flank angle from the real specmens for FEA s rather dffcult because the welds usually have a certan convexty. Furthermore, the LEFM approach was conducted wth usng C char = [13] as the materal parameter, but W (2004) [22] and Brtsh Stan- 131

14 dard 7910: 1999 [23] have recommended slghtly hgher values wth C char = and C char = , whch reduces the predcted FAT wth 95 % survval probablty by 15.6 % and 16.8 %. Ths leads nto more conservatve fatgue strength predctons. Fnally, a concluson could be made that the parametrc Equaton (11) predcts effectvely credble and slghtly conservatve FAT values that can be used on fatgue analyss and desgn. The study was made wth steel as the materal, but the parametrc equaton can be also used to alumnum, when the FAT s reduced to one-thrd from the orgnal value [20]. LEFM works most accurately to welds wth lower qualty than welds wth smooth toe radus and wthout any sgnfcant defects due to neglgence of crack ntaton perod, whch s proporton of total fatgue lfe ncreases wth hgh qualty welds [20, 24]. Conclusons The objectve of ths work was to study the nfluence of cold laps on the fatgue strength of non-load-carryng fllet welded crucform jonts under cyclc tensle loadng. The assumpton of as-welded condton made the fatgue crack ntaton perod to be consdered non-exstent. LEFM n plan stran was used for fatgue analyss wth several FE models and dfferent weld geometry varatons. The rato of cold lap sze and toe radus to the plate thckness and the flank angle were systematcally altered and analyzed and the parametrc relatonshps between those varables were formulated wth the respect of FAT wth 95% survval probablty and curve-ftted to a parametrc Equaton (11). Steel was used as the materal and the FAT predctons wll cover also alumnum when the FAT value s reduced to one-thrd. The FAT predctons from the parametrc equaton were converted to mean fatgue strength, FAT mean, and compared to numerous test results wth dfferent nvestgatons of non-load-carryng fllet welded crucform jonts. Based on these proceedngs, the followng conclusons can be made: 1) Cold laps effect sgnfcantly on the fatgue strength. 2) Wth a small toe radus, cold laps wll not effect on the fatgue strength nearly as much as wth a large toe radus. 3) Varaton n the flank angle from 30 to 60 degrees wll not produce a consderable fluctuaton on the fatgue strength. 4) The predctons from the analytcal model are correspondng wth the test results from smlar structure detals and weld defects. 5) Cold laps substantal effect on the fatgue strength s evdent and should be consd ered crtcally n desgnng, fabrcaton and qualty nspectng stages. 6) LEFM n plane stran works well for ths knd of problem and allocates credtable predctons that are most accurate on welds wth lower qualty due to non-exstent crack ntaton perod. 132

15 Acknowledgements Ths work was conducted n the Department of Mechancal Engneerng at the Lappeenranta Unversty of Technology as the part of the LAATU weld qualty project, funded by Fnnsh ndustry and the Natonal Technology Agency of Fnland. Acknowledgements go to Professor Gary Marqus and Dr. Tmo Nykänen, who supervsed ths study and to Dr. Tmo Björk, who was the Project Coordnator. References [1] Martnsson, J. Fatgue Strength of Welded Crucform Jonts wth Cold Laps. De sgn and Analyss of Welded Hgh Strength Steel Structures EMAS ltd. ISBN X. [2] NDT Resource center. [On-Lne]. Retreved January 3 rd 2007 from: [3] Lopez Martnez, L. and Korsgen, S. Characterzaton of Welded Defect Dstrbuton and Weld Geometry n Welded Fatgue Test Specmens. Fatgue Under Spectrum Loadng an n Corrosve Envronments EMAS ltd. Warley, UK. [4] Samuelsson, J. Cold Laps and Weld Qualty Acceptance Lmts. Desgn and Analyss of Welded Hgh Strength Steel Structures EMAS ltd. ISBN X. [5] Martnsson, J. Fatgue Assessment of Complex Welded Structures. Doctoral Thess ISBN [On-Lne]. Retreved December 25 th 2006 from: fulltext.pdf [6] James M. and Swenson D. FRANC2D/L: A Crack Propagaton Smulator for Plane Structures. Avalable from: [7] Dodds RH and Vargas PM, Numercal evaluaton of doman and contour ntegral for nonlnear fracture mechancs: formulaton and mplementaton aspects. Report from Unversty of Illnos at Urbana-Champagn, Dept. of Cvl Engneerng, [8] Erdogan F. and Sh GC. ASME J Basc Engng 1963; 85: [9] Ingraffea, A., Wawrzynek, P. Fnte Element Methods for Lnear Elastc Fracture Mechancs.Chapter 3.1 n Comprehensve Structural Integrty Elsever Scence Ltd., Oxford, England.[On-Lne]. Retreved November 1 st 2008 from: [10] Nykänen, Tmo. Fatgue crack growth smulatons n laser welded lap jonts. W- Document XI [11] Pars, P.C and Erdogan, F. A crtcal analyss of crack propagaton law, Trans ASME, J Basc Eng, 1963, 85, [12] Forman, R. G., Kearney, V.E. and Engle, R.M. Numercal analyss of crack propagaton n cyclc loaded structures, Trans ASME, J Basc Eng, 1967, 89, 459. [13] Hoppacher, A. Fatgue Desgn of Welded Jonts and Components, Recommendatons of W Jont Workng Group XI-XV, doc. XI /XV , Abngton Publshng, [14] Bathe, K-J. Fnte Element Procedures, Prentce-Hall, Inc. A Smon & Schuster Company, Eaglewood Clffs, New Jersey 07632,

16 [15] Nykänen, T., Marqus, G. and Björk, T. Fatgue analyss of non-load-carryng fllet welded crucform jonts. Engneerng Fracture Mechancs, Volume 74, Issue 3, pp , February [16] Sherrod PH. NLREG. Nonlnear Regresson Analyss Program. Avalable from: [17] Barsoum, Z. Fatgue Strength of Crucform Jonts Welded wth Dfferent Weldng Processes. Internatonal Symposum on Integrated Desgn and Manufacturng of Welded Structures. March 13-14, 2007, Esklstuna, Sweden. [18] Sehadr, A. Statstcal Varaton of Weld Profles and Ther Expected Influence on Fatgue Strength. Master s Thess Lappeenranta Unversty of Technology. [19] Hyams, D. CurveExpert 1.3. A comprehensve curve fttng system for Wndows. Avalablefrom: [20] Radaj, D. and Sonsno, C-M. Fatgue assessment of welded jonts by local approaches, Woodhead Publshng Ltd, [21] Nykänen, T., Marqus, G., Björk, T. Approxmatve master curve for fatgue assessment of crucform jonts wth non-load-carryng welds. Fnnsh Weldng Socety Desgn Forum , Laht. [22] Hobbacher, A. Recommendatons for Fatgue Desgn of Welded Jonts and Components. WDocument XI /XV Update July [23] Gude on methods for assessng the acceptablty of flaws n metallc structures, Brtsh Standard BS 7910:1999, [24] Björk, T., Marqus, G., Qualty Assessment of Welds for Fatgue Loaded Structures. Internatonal Symposum on Integrated Desgn and Manufacturng of Welded Structures. March 13-14, 2007, Esklstuna, Sweden. Mkko Heskanen Konecranes Heavy Lftng Corporaton P.O. Box 662 FIN Hyvnkää FINLAND e-mal: Mkko.Heskanen@konecranes.com 134

17 Appendx Results from fracture mechancs analyss Table A1. Results for the models wth flank angle of 30 degrees Model β r/t a/t FAT K I K θ c K I eq ,05 0,0 78,8 87,2-6,7 8,7 87, ,05 0,01 76,1 91,1-28,9 30,3 103, ,05 0,02 75,4 91,1-31,2 31,9 104, ,05 0,04 74,2 96,1-29,2 29,4 108, ,05 0,08 72,7 103,9-35,4 31,8 119, ,05 0,16 71,1 116,2-42,5 33,3 135, ,1 0,0 88,7 72,5-7,7 11,9 73, ,1 0,01 78,8 68,1-15,4 23,4 73, ,1 0,02 76,9 69,1-20,1 28,4 76, ,1 0,04 76,1 75,4-23,1 29,5 84, ,1 0,08 73,9 88,7-18,8 22,1 94, ,1 0,16 72,1 108,2-38,6 32,8 125, ,2 0,0 88,7 67,9-1,9 3,3 68, ,2 0,01 88,7 47,4-15,8 38,8 59, ,2 0,02 81,6 53, ,3 65, ,2 0,04 79,3 61,2-26,8 37,3 75, ,2 0,08 75,7 72,2-35,9 40,1 92, ,2 0,16 73,1 77,1-39,4 40,6 99, ,4 0, ,1-4,5 9,1 57, ,4 0,01 89,8 34,5-15,8 38,3 43, ,4 0,02 85,4 47,6-22,4 38,9 59, ,4 0,04 82,4 52,4-18,2 32,2 60, ,4 0,08 79,8 51,8-28,8 42,4 69, ,4 0,16 74,5 62,7-35,4 42,8 84, ,0 0,0 109,8 50,2-2,1 4,7 50, ,0 0,01 100,6 36,7-16,1 37,3 45, ,0 0,02 95,1 53,4-14,4 26,9 58, ,0 0,04 93,2 55,9-13,6 24,8 60, ,0 0,08 88,7 63,6-14,5 23,5 68, ,0 0,16 82,4 68,7-21,7 30,2 77,6 Table A2. Results for the models wth flank angle of 45 degrees. Model β r/t a/t FAT K I K θ c K I eq ,05 0,0 74,2 97,6-9,3 10,7 98, ,05 0,01 72,4 101,2-32,9 30,8 115, ,05 0,02 71,4 111,3-30,1 26,9 122, ,05 0,04 71,1 106,1-35,6 31,5 121, ,05 0,08 70,4 108,3-35,1 30,7 123, ,05 0,16 70,4 125,3-42,0 31,5 143, ,1 0,0 78,2 82,6-4,9 6,8 83, ,1 0,01 74,2 95,6-30,1 30,1 107, ,1 0,02 73,1 96,9-30,8 30,3 109, ,1 0,04 71,4 105,1-27,1 25,9 114, ,1 0,08 70,8 106,7-32,7 29,5 119, ,1 0,16 70,8 109,0-40,7 33,8 128, ,2 0,0 84,3 71,1-2,6 4,2 71, ,2 0,01 78,5 63,7-27,4 36,9 77, ,2 0,02 76,6 82,2-28,8 32,4 95,1 135

18 ,2 0,04 74,6 93,9-31,4 31,4 107, ,2 0,08 72,1 95,9-35,5 33,6 112, ,2 0,16 71,1 107,2-34,6 30,6 121, ,4 0,0 99,3 55,9-4,2 8,5 56, ,4 0,01 86,1 54,3-21,2 34,8 64, ,4 0,02 82,9 67,5-16,8 25,3 73, ,4 0,04 80,9 67,5-19,7 28,5 75, ,4 0,08 76,1 84,4-25,3 29,1 94, ,4 0,16 71,7 98,8-37,6 34,2 116, ,0 0, , ,0 0,01 96,5 49,0-17,6 33,0 57, ,0 0,02 96,1 49,3-16,4 31,3 56, ,0 0,04 93,5 53,2-9,9 19,8 55, ,0 0,08 88,7 61,1-15,2 25, 66, ,0 0,16 82,4 65,8-22,6 32,0 75,8 Table A3. Results for the models wth flank angle of 60 degrees Model β r/t a/t FAT K I K θ c K I eq ,05 0,0 73,6 97,7-7,7 8,9 98, ,05 0,01 72,1 107,5-35,6 31,2 122, ,05 0,02 71,4 111,9-35,8 30,4 126, ,05 0,04 71,4 120,9-36,5 29,2 135, ,05 0,08 71,4 121,3-37,5 27,3 136, ,05 0,16 71,4 125,2-37,2 28,9 140, ,1 0,0 77,7 83,9-4,4 6,0 84, ,1 0,01 74,8 66,8-33,3 40,1 85, ,1 0,02 73,6 77,8-37,5 39,4 98, ,1 0,04 72,4 85,3-37,0 37,1 104, ,1 0,08 71,7 95,6-42,5 37,6 118, ,1 0,16 71,7 126,7-35,4 27,6 139, ,2 0,0 87,0 69,2-3,0 5,0 69, ,2 0,01 77,7 75,9-20,4 26,7 83, ,2 0,02 76,0 87,3-22,6 26,0 95, ,2 0,04 74,5 80,2-33,0 35,9 96, ,2 0,08 72,4 85,5-46,6 42,0 113, ,2 0,16 71,7 112,9-25,6 23,4 120, ,4 0,0 94,3 59,3-1,9 3,7 59, ,4 0,01 86,1 61,6-15,1 24,9 66, ,4 0,02 82,9 68,5-17,7 26,0 74, ,4 0,04 80,4 75,0-19,8 26,4 82, ,4 0,08 76,0 91,1-23,5 25,9 99, ,4 0,16 72,1 87,8-34,0 34,6 104, ,0 0,0 110,5 49,1-0,6 1,4 49, ,0 0,01 96,1 45,1-16,6 33,6 52, ,0 0,02 95,0 51,6-9,3 19,3 54, ,0 0,04 92,8 56,7-11,7 21,7 60, ,0 0,08 88,7 64,7-14,6 23,3 69, ,0 0,16 82,1 71,1-23,2 30,9 80,9 136