Mean Stress Related Tests on the Fatigue Strength of Welded Tubular Joints Made from Mild and High-Strength Steels

19th International Symposium on Tubular Structures (ISTS 19) Hong Kong, China, December 1st – 3rd, 2025 Edited by Tak-Ming CHAN Mean Stress Related Tests on the Fatigue Strength of Welded Tubular Joints Made from Mild and High-Strength Steels A. DÜRR a, M. WINKLER a, S. KNEFELKAMP a, K. ROTHER a and M. KLING a a Institute for Material and Building Research, University of Applied Sciences Munich, Germany E-mails: [email protected], [email protected], [email protected], [email protected], [email protected] Keywords fatigue strength; mean stress effect; high-strength steel; welded tubular joints Abstract The subject of this paper is the investigation of the fatigue strength for welded tubular section joints with special consideration on the mean stress. Existing standards for welded tubular section joints, such as CIDECT or EN 1993-1-9, do not consider the influence of mean stress on the fatigue strength in the as-welded condition due to the high residual stresses which are generated in the component as a result of the welding process. However, test results at the University of Applied Sciences Munich showed a considerable influence of the mean stress on the fatigue strength of welded steel structures with tubular section joints. Neglecting the influence of mean stress in the fatigue design of tubular structures can lead on the one hand to a safety risk or can lead in the other hand to an uneconomical design. Therefore, within the research project FOSTA P 1603 fatigue tests on welded tubular section joints were to investigate the mean stress effects on the fatigue strength systematically. The results of the experimental tests on thick-walled tubular joints are summarised within this paper. 1 INTRODUCTION In the fatigue verification of welded joints current design standards like EN 1993-1-9 [1] do not consider the mean stress effect on fatigue strength unless the structure was subjected to thermal stress relief. However, fatigue tests on tubular joints in the as-welded condition at the University of Applied Sciences showed a non-negligible mean stress effect. Thus, within the research project FOSTA P 1603 [2] 146 fatigue tests on welded tubular joints were performed with up to 4 different load ratios, different wall thicknesses, sections shapes, loading types and steel grades. In this paper the results of the fatigue tests of tubular joints with wall thicknesses t ≥ 4.0 mm and the accompanying strain gauge measurements are presented. Previous fatigue tests on thin-walled tubular joints are presented in [3]. 2 EXPERIMENTAL INVESTIGATIONS 2.1 Test program To systematically investigate the mean stress effect on the fatigue strength of welded tubular joints different specimen types were tested with up to 4 different load ratios. These ratios are typically described with the Rvalue defined as the ratio of the minimal stress 𝜎𝜎𝑚𝑚𝑚𝑚𝑚𝑚 and the maximum stress 𝜎𝜎𝑚𝑚𝑚𝑚𝑚𝑚 of the stress range, see (1). 𝑅𝑅= 𝜎𝜎 𝑚𝑚𝑚𝑚𝑚𝑚 𝜎𝜎𝑚𝑚𝑚𝑚𝑚𝑚 (1) However, if load cycle-normalized results of fatigue tests are compared with the R -value on the abscissa, fully compressive stress ranges would result in high positive R - ratios and therefore cannot be plotted in a meaningful manner with results of alternating or fully tensile fatigue tests. Therefore, the stress ratios are described with the ρ - value defined as the ratio of the mean stress 𝜎𝜎𝑚𝑚 and the stress range Δ𝜎𝜎 i.e. 2∙𝜎𝜎𝑚𝑚, see (2). 𝜌𝜌= 𝜎𝜎𝑚𝑚 Δ𝜎𝜎=𝜎𝜎𝑚𝑚 2∙𝜎𝜎𝑚𝑚 (2) The investigated stress ratios with the ρ -value and the R-value are given in Figure 1. Figure 1: Investigated load ratios σ[MPa] σm R = 10 compression tension t [s] + - R = -1 R = 0.1 R = 0.5 Δσ= 2*σa All specimens were welded as X-joints which are divided into 4 different test series (latin letter) depending on the profile type or steel grade. All test series are divided into sub-series (roman numeral) depending on the load ratio, see Table 1 and Figure 2. The tests were conducted in the as-welded condition without thermal stress relief. Table 1: Test program Series ρ σm/Δσ R σmin/σmax Material Loading Dimensions β b1/b0 γ b0/2t0 τ t1/t0 Number of specimens E-I -0.67 10 S335J2H Axial Chord SHS 100x4 EN 10219 Brace SHS 50x4 EN 10219 0.5 12.5 9.1 7 E-II 0 -1 7 E-III 0.67 0.1 2+61) E-IV 1.5 0.5 7 F-II 0 -1 Chord S620QH Brace S700MH Axial 0.5 12.5 9.1 7 F-III 0.67 0.1 7 F-IV 1.5 0.5 7 G-II 0 -1 S335J2H Axial Chord SHS 200x8 EN 10210 Brace SHS 100x8 EN 10210 0.5 12.5 9.1 3 G-III 0.67 0.1 31) G-IV 1.5 0.5 3 H-I -0.67 10 S335J2H Axial Chord CHS 101.6x5.6 EN 10210 Brace CHS 51x4 EN 10210 0.5 11.2 0.7 4 H-II 0 -1 4 H-III 0.67 0.1 3+91) H-IV 1.5 0.5 4 1)results taken from [4] Figure 2: Specimens 2.2 Test results The fatigue tests were aborted when the failure criterion through thickness cracking (N3) was reached. For comparability and due to the small number of tests per series the fatigue strengths Δσ𝐶𝐶,50% were evaluated at 2∙106 load cycles with fixed slope of m = 5 and a survival probability of 50 %. Tests with more than 5∙106 load cycles are declared as run-outs and neglected in the evaluation.The test results of the different test series are summarised in S-N curves in Figure 4 and Figure 5. In the test series E, F and G with square hollow sections (SHS) all cracks initiated at the weld toe on the chord profile. In the test series H with circular hollow sections (CHS) cracks initiated at the weld toe both on the chord and brace profile, see Figure 3. The test results show that even without thermal stress relief an increasing mean stress leads to decreasing fatigue strength. Especially tests with a high mean stress with the stress ratio R = 0.5 showed an overall very low fatigue strength. On the other hand, the tests with fully compressive stress ranges are less damaging than alternating or fully tensile stresses and showed a very high fatigue strength. Figure 3: Failure location of specimens 800 Brace: SHS 50x4 - EN 10219 800 Brace: SHS 100x8 - EN 10210 Chord: SHS 200x8 - EN 10210 Chord: SHS100x4EN10219(seriesE) / 10210(seriesF) 800 Chord: CHS 101.6x5.6 - EN 10210 Brace: CHS 51x4.0 EN 10210 44 8 4 8 4 series E/F series Gseries H [mm] Figure 4: Results of fatigue tests – left) series E, right) series F Figure 5: Results of fatigue tests – left) series G, right) series H 3 STRAIN GAUGE MEASUREMENTS 3.1 Test setup Distortion occurs in the specimens as a result of the welding process. During the clamping process the specimens are straightened causing clamping stresses that affect both the stress range and the mean stress. To evaluate the fatigue tests considering the clamping stresses strain gauge measurements were performed. Therefore, strain gauges were applied on the brace walls parallel to the chord member at a distance of 100 mm to the chord wall, see Figure 6. Figure 6: Location of strain gauges In the second step the specimens were clamped, precycled and unclamped. Then, the gauges were tared to zero to correctly quantify the clamping stresses. The measured strains were converted into stresses by multiplication with the modulus of elasticity ( E = 210,000 MPa). For the evaluation only the stresses on the side of the first crack initiation were considered. 3.2 Evaluation of the mean stress effect considering strain gauge measurements To consider the clamping stresses in the evaluation of the fatigue tests the measured stress range Δ𝜎𝜎𝑆𝑆𝑆𝑆(SG = strain gauge) was normalized to 2∙106 load cycles, see (3). The normalized Δ𝜎𝜎𝑆𝑆𝑆𝑆,𝑚𝑚𝑛𝑛𝑛𝑛𝑚𝑚was then plotted in a scatter plot with the measured stress ratio 𝜌𝜌𝑆𝑆𝑆𝑆 as abscissa. 𝜌𝜌𝑆𝑆𝑆𝑆 is calculated by dividing the measured mean stress 𝜎𝜎𝑚𝑚,𝑆𝑆𝑆𝑆 by the measured stress range Δ𝜎𝜎𝑆𝑆𝑆𝑆, see (4). A linear regression was then performed to calculate Δ𝜎𝜎𝐶𝐶 (𝜌𝜌= 0) i.e. the average normalized fatigue strength at ρSG = 0 ( R = -1) for each series, see Figure 7 and Figure 8. Δ𝜎𝜎𝑆𝑆𝑆𝑆,𝑚𝑚𝑛𝑛𝑛𝑛𝑚𝑚=Δ𝜎𝜎𝑆𝑆𝑆𝑆∙�𝑁𝑁3 2∙106 5 (3) 𝜌𝜌𝑆𝑆𝑆𝑆 = 𝜎𝜎 𝑚𝑚,𝑆𝑆𝑆𝑆 Δ𝜎𝜎𝑆𝑆𝑆𝑆 (4) 10 4 10 5 10 6 2*10 6 5*10 6 10 7 load cycles [-] 10 20 30 50 70 100 stress range [MPa] E-I: ρ = -0.61 (R = 10) E-II: ρ = 0 (R = -1) E-III: ρ = 0.61 (R = 0.1) E-IV: ρ = 1.5 (R = 0.5) steel grade: S355J2H failure criterion = N 3 t = 4 mm m = 5 Δσ C,50% [MPa] series 18.3E-I 13.1E-II 12.3E-III 9.5E-IV 10 4 10 5 10 6 2*10 6 5*10 6 10 7 load cycles [-] 10 20 30 50 70 100 stress range [MPa] F-II: ρ = 0 (R = -1) F-III: ρ = 0.61 (R = 0.1) F-IV: ρ = 1.5 (R = 0.5) 0 steel grade: S620QH/ S700MH (braces) failure criterion = N 3 t = 4 mm m = 5 Δσ C,50% [MPa]series 11.4F-II 11.2F-III 9.7F-IV 10 4 10 5 10 6 2*10 6 5*10 6 10 7 load cycles [-] 10 20 30 50 70 100 stress range [MPa] G-II: ρ = 0 (R = -1) G-III: ρ = 0.61 (R = 0.1) G-IV: ρ = 1.5 (R = 0.5) steel grade: S355J2H failure criterion = N 3 t = 8 mm m = 5 Δσ C,50% [MPa]series 13.1G-II 10.6G-III 9.3G-IV 10 4 10 5 10 6 2*10 6 5*10 6 10 7 load cycles [-] 10 20 30 50 70 100 150 200 300 500 stress range [MPa] H-I: ρ = -0.61 (R = 10) H-II: ρ = 0 (R = -1) H-III: ρ = 0.61 (R = 0.1) H-IV: ρ = 1.5 (R = 0.5) steel grade: S355J2H failure criterion = N 3 t = 5.6 / 4 mm m = 5 Δσ C,50% [MPa]series 74.0H-I 63.8H-II 41.5H-III 31.8H-IV 100 mm strain gauge measuring grid length = 3 mm Figure 7: Calculation of ΔσSG,norm at ρ = 0 – series E-G Figure 8: Calculation of ΔσSG,norm at ρ = 0 – series H In the next step the values of ΔσSG,norm were normalized to the value of ΔσC ( ρ = 0), see Figure 9. Then a another “normalized” regression was performed. To maintain clarity only the regression of series H is plotted in Figure 9. The resulting slope x reflects the mean stress sensitivity for each series, see Figure 10. x can be used to calculate the fatigue strength ΔσC for any load ratio ρ , see (5). Figure 9: Calculation of the mean stress sensitivity x It can be seen that except for series F the mean stress sensitivities are similar. The specimens of series F are geometrically equal to series E but made from a highstrength steel S620QH/S700MH instead of a mild steel S355J2H. It appears that the higher yield strength mitigates the mean stress sensitivity. Δ𝜎𝜎 𝐶𝐶 (𝜌𝜌)=Δ𝜎𝜎 𝐶𝐶 (𝜌𝜌= 0)−𝑥𝑥∙𝜌𝜌∙Δ𝜎𝜎 𝐶𝐶 (𝜌𝜌= 0) (5) Figure 10: Mean stress sensitivity x and ΔσC (ρ=0) 4 CONCLUSIONS The fatigue tests on welded tubular joints showed a non-negligible mean stress effect in as-welded condition. Clamping stresses were considered with strain gauge measurements. It could be shown that increasing mean stresses correlate with decreasing fatigue strength. Especially the tests with fully compressive stress ranges showed a very high increase in fatigue strength compared to the tests under alternating or fully tensile stresses. In addition, residual stress measurements will be performed to see whether the residual stresses could be the reason for the differences on the mean stress sensitivity between the high-strength steel (series F) and the mild steel (series E). ACKNOWLEDGEMENTS The research project FOSTA P1603 [4] from the Research Association for steel Application (FOSTA) is supported by the German Federal Ministry for Economic Affairs and Climate Action as part of the programme for promoting industrial cooperative research (IGF). The project is carried out at University of Applied Sciences Munich. The authors would like to thank the project committee and the supporting companies for providing material and fabricating specimens. REFERENCES [1] ‘EN 1993-1-9:2009, Eurocode 3: Design of steel structures - Part 1-9: Fatigue. [2] Dürr A., et al.., “Final report (in progress): Berücksichtigung des Mittelspannungseinflusses bei Hohlprofilkonstruktionen aus niedrigund hochfesten Stählen zur verbesserten Lebensdauerabschätzung“, FOSTA P1603/IGF-Nr.: 22258N, Publication expected in 2025. [3] Winkler M., et al., “Fatigue tests on tubular joints with different load ratios to quantify the mean stress effect“, Sweden, June 2024, doi: 10.5281/ZENODO.12123097. [4] Dürr A., Rother K., Roth J., Neuhäusler J. and Oswald M., “Berücksichtigung von Reihenfolgeeffekten bei der Lebensdauerabschätzung von Hohlprofilkonstruktionen“, Final Report FOSTA P1195/IGF-Nr.: 19410 N, 2022. 0.16 0.05 0.12 0.17 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 1 2 3 4 series GFE H mean stress sensitivity x [-] ΔσC(ρ=0) [MPa] Series 16.2 E 12.3 F 12.6G 63.2 H 0.0 5.0 10.0 15.0 20.0 25.0 -2.0 0.0 2.0 4.0 6.0 8.0 Δσ SG,norm [MPa] ρ SG [-] series E series F series G regression - series E regression - series F regression - series G Δσ C (ρ= 0) = Δσ SG,norm at ρ= 0 with P = 50% 0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 -2.0 0.0 2.0 4.0 Δσ SG,norm [MPa] ρ SG [-] series H regression - series H Δσ C (ρ= 0) = Δσ SG,norm at ρ= 0 with P = 50% 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 -3,0 -1,0 1,0 3,0 5,0 normalized Δσ SG,norm [-] ρ SG [-] series E series F series G series H exemplary „normalized“ regression (series H) 1 x 1) 1)