Fatigue strength of fillet‐welded joints at subzero temperatures

Fatigue Fract Eng Mater Struct. 2020;43:403–416. Abstract Ships and offshore structures may be operated in areas with seasonal freezing temperatures and extreme environmental conditions. While current standards state that attention should be given to the validity of fatigue design curves at subzero temperatures, studies on fatigue strength of structural steel at subzero temperatures are scarce. This study addresses the issue by analysing the fatigue strength of welded steel joints under subzero temperatures. Although critical weld details in large welded structures are mostly fillet‐welded joints, most published data are based on fatigue crack growth rate specimens cut out of butt‐welded joints. This study analyses fillet‐welded specimens at −20°C and −50°C against controls at room temperature. Significantly higher fatigue strength was measured in comparison to estimates based on international standards and data from design codes even at temperatures far below the allowed service temperature based on fracture toughness results.


| INTRODUCTION
Due to the large unexploited oil and gas reservoirs in Arctic regions, there has been a significant increase in ship traffic in Arctic regions; oil rigs and wind turbines have also been increasingly set up in areas with seasonal freezing temperatures. These structures, and their materials, must be designed to meet these environmental conditions. Although it is known that lower temperatures change the material properties of steel and their welded joints, the resulting effects are poorly understood so far; this is especially true for fatigue behaviour at subzero temperatures. 1 While detrimental effects caused by high temperatures are well covered in literature and are addressed in international standards, few publications exist on the fatigue properties of welded steel joints for subzero temperatures. [2][3][4][5][6][7][8][9][10] Moreover, most of those studies focus on fatigue crack growth (FCG) rate testing for cryogenic applications. Data for structural steels subjected to temperatures relevant for Arctic conditions are especially scarce and-except for Bridges et al 3 and Li et al, 8 who tested longitudinal stiffeners and cruciform joints, respectively-all mentioned studies are based on tests with butt-welded joints.
Although Bridges et al 3 found an increase of fatigue strength of welded specimens at subzero temperatures, the Lloyd's Register FDA ICE Fatigue Induced by Ice Loading procedure 11 did not change the fatigue design curves. Instead, it was explicitly stated that the design curves for room temperature (RT) shall be applied for fatigue assessment. The corresponding International Organization for Standardization standard ISO19906 12 states that "attention should be given to the validity of S-N curves with respect to low temperature application" for Arctic offshore structures; however, no guidance is given on how to verify the validity of S-N curves. Current standards focus almost exclusively on fracture toughness requirements to avoid brittle fracture. 13 Avoidance of brittle fracture shall be achieved by proving sufficient fracture toughness at temperatures as low as 30°C below the Lowest Anticipated Service Temperature (LAST). 14 For some Arctic locations, LAST can approach −40°C or lower; this results in hard to meet toughness requirements. 13 High-strength, thermomechanically rolled, finegrained structural steel is necessary to meet those requirements. Current ship standards are limited to S460 structural steel, however, and maritime structures are often made of normal-strength or mild-strength steel since fatigue strength of welded joints shows only minor or no influence of the base material strength. 15 By analysing large data sets of fracture toughness tests, Walters et al 16 showed that mild strength steel often fulfils the requirements for much lower temperatures than required. Fracture toughness, however, is only one parameter that has to be taken into account for subzero temperature applications (see Hauge et al 13 for an extensive summary on relevant material properties for Arctic structures; in order to develop standards for the design of fixed Arctic offshore structures, they identified fatigue strength as one of the major parameters influencing design of such structures 13 ).
Although extensive subzero temperature material and fatigue tests date back to the beginning of space exploration and the storage and transport of liquefied gases, 17 it only recently regained attention from researchers. 18 Due to increased Artic transport and interest in Arctic oil and gas exploration, fatigue strength of structural materials at subzero temperatures 3,19,20 is now a critical area of study. Design standards currently assume that low temperatures have no detrimental effect on the fatigue properties of steels at typical operating temperatures. 13 This assumption is based on fatigue crack growth (FCG) rate testing of different base material steel types at temperatures down to cryogenic temperatures. [21][22][23][24][25][26][27][28][29] This assumption holds for materials that feature face-centred cubic (fcc) crystal structures. Structural steels which belong to the class of ferritic materials having a bodycentred cubic (bcc) crystal structure, however, suffer from reduced toughness below the ductile-to-brittle transition temperature (DBTT). At low temperatures (sometimes within the range of typical operating temperatures), the mechanism of stable crack growth behaviour changes from plastic blunting and tearing to cleavage-controlled brittle fracture. This transition is usually measured by fracture toughness or Charpy notch impact tests. While normal-strength steels usually show a gradual change in the governing fracture process, high strength steels have a narrow range of temperature for this transition (see Wallin 30 ). Structural design requires that the DBTT remains below the anticipated service temperatures, with a mandatory safety margin. An increase in FCG rate was found simultaneously to the decrease in fracture toughness for bcc materials in tests at DBTT-range temperatures (described by Alvaro et al 18 33 relate this behaviour to a change in striation process when ductile crack growth is superimposed by cleavage bursts, which are triggered by embrittlement of the material. For temperatures below RT but above the FTT, however, the FCG rate is significantly decreased; this extends the structure lifetime. 28,29,[31][32][33] The relation between the FTT and DBTT is better understood for different structural steel base materials due to recent effort by the aforementioned research groups; however, the effect of temperature on fatigue properties of welded structures is scarcely investigated. Fracture toughness tests show that the DBTT is usually higher in the heataffected-zone (HAZ) of welded structures than in the surrounding base material, 34 which is the reason that such tests have to be performed with the notch on the fusion line between the weld metal and the HAZ. Its implication on the fatigue properties of welded structures is, however, nonexistent due to the lack of comprehensive studies regarding the change of static and dynamic properties of welded joints at subzero temperatures. 1 In the present study, welded normal and high strength steel joints are tested to analyse the fatigue strength under subzero temperatures. The aim of the paper is to present the change in fatigue strength and to assess the effect on fatigue assessment procedures for structures experiencing low service temperatures. For this purpose, two cruciform joint weld details with the two typical failures initiation sites at weld toes and weld roots are tested at RT, −20°C, and −50°C.

| TEST SETUP AND SPECIMENS
In order to assess the temperature effect on typical weld details, cruciform joints with nonpenetrating fillet welds and two-sided transverse stiffeners-leading to weld root and weld toe failure, respectively-are chosen; these are presented in Figure 1 as polished and etched macrographs. Two-sided transverse stiffeners with weld toe failure are a typical structural detail in large welded structures containing stiffeners, while nonpenetrating cruciform joints with weld root failure are among the most critical weld details (since cracks are only visually discoverable once they have reached a significant size and have grown through the weld metal). The throat thickness of load-carrying fillet welds is usually chosen to prevent weld root failure; however, this study uses a throat thickness small enough to yield weld root failure in order to analyse the effect of low temperatures on weld root failure. To rule out material-based uncertainties of the welded joints, two series of each weld detail are tested made from different steel types; each series consists of about 10 specimens. The first is a S235 J2 + N normalized steel that is often used in ship structures and the second a S500G1 + M thermomechanically rolled, fine-grained structural steel. The chemical composition is listed in Table 1 and the measured mechanical properties in Table 2.
The Charpy V-notch test results confirm that the S500 structural steel has a high toughness, even at temperatures as low as −40°C. Although the S235J2 + N normal structural steel in this study also shows high toughness results for the base material, it is not usually used for structures exposed to Arctic conditions. As can be seen from Walters et al's 16 statistical evaluation of around 7000 data sets of S355 and S690 samples, 55% of delivered S355 structural steel plates and 72% of delivered S690 structural steel plates fulfil the toughness requirements for a design temperature of −55°C.   The specimens of this study are welded with the flux cored arc welding process. Tack welds are used during welding to limit angular distortion and are later removed. The welding direction is normal to the rolling direction of the base material, and welding is performed with a 1.2mm diameter Outershield 71E-H wire for S235 specimens and Stein Megafil 821R for S500 specimens. The welded plates are saw-cut from 1 m × 0.5 m plates into 500mm-long, 50-mm-wide, and 10-mm-thick specimens that can be seen in Figure 2A. The clock-wise welding sequence of the details are presented in Figure 2B,C. Each weld was built by one weld layer.
The geometry of all specimens was measured prior to fatigue testing; this includes angular and axial misalignment, as well as the local weld geometry. Laser triangulation was used for the local weld geometry measurements, and the point data were analysed using the curvature method developed by Jung 35 (which was verified to yield consistent results by Schubnell et al 36 ). The test specimen geometry and the local weld geometry parameter are schematically presented in Figure 2D,E. The measured throat thicknesses (a) averaged close to 5.5 and 6.4 mm for the S235 and S500 cruciform joints, respectively. For all cases, the flank angles (α) of the fillet welds were close to 135°, and the angular misalignment (φ) was below 1°; the axial misalignment (e) averaged around 7% of the plate thickness.
Fatigue testing is carried out under axial loading in the temperature chamber, with a temperature range of −180°C to +280°C on a Schenck horizontal resonance testing machine with maximum load capacity of 200 kN, at a frequency around 33 Hz and a nominal stress ratio of R = 0 (see Figure 3). Due to misalignment, however, the local stress ratio was slightly higher with R < 0.15. Failure is defined as full fracture of a specimen. Cooling is achieved using vaporized nitrogen from a liquid nitrogen tank, controlled by a chamber temperature gauge. During testing, the chamber and specimen temperatures are monitored by gauges; these are calibrated against an additional temperature gauge at RT that is positioned in the test lab and experiences only minor variations. As can be seen from Figure 3, the temperature is kept constant (within ±1°C). The spikes in max. and min. specimen temperatures are caused by nitrogen injection in the chamber.

| FATIGUE TEST RESULTS
All test results were statistically evaluated to obtain the mean stress-life (S-N) curve with where N is the endured number of cycles on the nominal stress range level Δσ n , Δσ R is the reference fatigue strength at 2 · 10 6 cycles, and k is the slope of the S-N curve. The test results, evaluated based on a fixed slope exponent k = 3 (typical for welded joints 37 ), are shown in  . The mean and reference fatigue strength for probability of survival at P s = 50% and 97.7% have been calculated and included in the figures alongside the scatter ratio (T σ ) between the fatigue strengths for P s = 90% and 10%. All cruciform joint specimens showed root cracks resulting from the small weld size; all transverse stiffeners failed from the weld toes. Generally, all test series showed a clear improvement of fatigue strength as test temperature decreased. Moreover, the fatigue strength improvement seems to be comparable for all series; no decrease in fatigue strength is found for the normal-strength steels at -50°C. Even −30°C below the certified temperature of this steel grade, the fatigue strength seems to increase; this might be related to the high Charpy impact energy measured at the certified temperatures.
The analysis of the experimental data of the four test series shows that all test specimens, at all test temperatures, fulfil the requirements according to the corresponding FAT weld detail classes. It should be remarked that the fatigue strength for a probability of survival P s = 97.7% at N = 2 · 10 6 of the S235 transverse stiffener lies below the reference fatigue strength of FAT80 due to the relatively high scatter of this test series. As expected, the results confirm the general expectation that sharply notched as-welded steel joints made of high strength steel show comparable fatigue life to mild strength steel. Furthermore, the fatigue strength of the S500 cruciform joints is lower than the corresponding S235 weld detail; this might be related to the more convex fillet weld shape of the S500 cruciform joints, which can be seen from the macrographs. Interestingly, both weld details showed similar fatigue strength in terms of applied loading, but the larger cross-sectional area of the convex S500 fillet welds caused a reduced fatigue strength (in terms of nominal stress) compared with the S235 cruciform joints.
Due to the fact that the scatter ratio (T σ ) was generally very small, a clear trend towards higher fatigue strength at subzero temperatures can be seen from the S-N curves.
The reason for the higher scatter of the S235 transverse stiffener S-N curves is caused by different numbers and locations of crack initiation sites. While the other three weld details always showed a large number of initiated cracks that grew together quickly, the S235 transverse stiffener sometimes had several cracks initiating in different planes (see Figure 5B); this can be intentionally caused with a weaving welding procedure but was not applied to the welded plates of this study. Moreover, specimens with almost no angular misalignment experienced simultaneous crack initiation at both the top and bottom side (see Figure 5B RT and −50°C).
Visual inspection of the fracture surfaces was performed to verify the fracture behaviour. As can be seen from Figure 5, large areas of the fracture surfaces of both cruciform joints and transverse stiffener specimens are dominated by fatigue crack propagation. At RT and −20°C, the fracture surfaces of the S235J2 + N transverse stiffener specimen show shear lips in the final rupture region; this indicates ductile failure. At −50°C, however, a cleavage crack perpendicular to the direction of the applied loading is visible; this is a clear sign for brittle material behaviour. In contrast, the S500G1 + M transverse stiffener specimen shows a fibrous fracture surface with some necking at both RT and −50°C, with shear lips at −20°C indicating ductile failure.
The fracture surfaces of the cruciform joints show similar behaviour. At RT, the fracture surfaces are characterized by a long crack propagation phase, and the final fracture is caused by plastic collapse (again, indicated by small shear lips). At −20°C, large areas of brittle fracture can be easily seen especially for the S500G1 + M cruciform joint in Figure 6. At −50°C, the shear lips are much smaller than at RT and −20°C (even for the S500 steel specimens), while they were still quite large for the transverse stiffener at −50°C. Both confirm that the DBTT temperature (and thus the FTT) is lower in the weld metal than in the base material. Although the cruciform joints failed by brittle fracture, the fatigue life was significantly longer at subzero temperatures compared with RT.

| FURTHER TEST EVALUATION AND INFLUENCING FACTORS
From fatigue testing of full-scale and small-scale specimens, it is known that the residual stress level in small-scale fatigue test specimens is often lower than in full-scale structures. This fact has led to the conservative assumption of design codes that no residual stresses are present in small-scale specimens (see Hobbacher 37 ). Consequently, fatigue test results of small-scale test specimens shall be corrected to a high stress ratio of R = 0.5, since fatigue design curves of welded joints are defined for that value, 37 in order to achieve comparable results for full-scale structures. When correcting results tested at a stress ratio of R = 0, a reduction of fatigue strength of 20% shall be applied according to IIW recommendations. 37 In recent years, this topic has gained new attention; alterations to the bonus-factor concept of the IIW recommendations for low residual stresses have been proposed, taking into account the mean-stress sensitivity dependent on joint type, residual stress level, and postweld treatment (see Hensel et al 38 ). Despite huge progress in the field of residual stress measurements, in-depth measurements based on neutron diffractionwhich is the preferred method for such applicationsare still costly. Consequently, residual stresses at weld roots in cruciform joints are difficult to measure. In order to investigate the mean stress sensitivity, additional tests at RT with a stress ratio of R = 0.5 were performed for three of the weld details. The results are presented as a comparison of the test series at R = 0.5 and R = 0 in Figure 6; these are summarized in Table 3.
Based on the results at R = 0.5 and R = 0, the mean stress sensitivity for the three compared cases can be calculated as the mean stress correction factor f (R) by the ratio of mean fatigue strength (σ R,mean ) at R = 0.5 and R = 0 according to Equation (2).
As can be seen from the summarized correction factors f (R) in Table 3, the mean stress sensitivity is the same for the S500 cruciform joint and transverse stiffener, while it is smaller for the S235 cruciform joint weld detail. Moreover, the factors are smaller than the factor of f (R) = 1.2 recommended by IIW. The difference between the fatigue strength between R = 0.5 and R = 0 of the S235 cruciform joint is very small. Thus, the residual stress level is probably close to the yield stress of the material in this case. A larger difference was found in the S500 test series. Consequently, the residual stress is smaller relative to the higher yield stress. The same mean stress correction factor was found for the S500 cruciform joint and transverse stiffener weld detail. Therefore, a similar level of residual stresses at weld toe and root can be expected. Since the same welding procedure was applied to the cruciform joint and transverse stiffener weld detail, it is assumed that the residual stress level at the weld toes of the S235 transverse stiffeners is also similar to the weld roots. Thus, the same correction factor as for the cruciform joints seems applicable.
To illustrate the increase of fatigue strength at subzero temperatures compared with RT, the results-in terms of the mean fatigue strength (Δσ R,50% (T))-are normalized by the corresponding mean fatigue strength at 20°C Δσ R,50% (T = 20°C). The fatigue strength ratio V R is calculated according to Equation (3) and is shown in Figure 7A for the two different weld details and steel types.
The assessed fatigue strength ratio increase is not constant for both weld details and steel types but shows a clear trend of higher fatigue strength at subzero temperatures. At −50°C, an almost identical increase for cruciform joints of both steels was measured, while the increase was different at −20°C. Moreover, a higher increase in fatigue strength was measured for the cruciform weld details than for transverse stiffener. The smallest increase of fatigue strength was found for the S500 transverse stiffener weld detail. It is important to note that more testing is required to completely rule out statistical uncertainty.
To illustrate the difference between fatigue strength at subzero temperatures and the IIW design recommendations, 37 the results in terms of the fatigue strength Δσ R,97.7% at N = 2 · 10 6 cycles for a probability of survival of P s = 97.7% are normalized by the corresponding IIW design fatigue strength Δσ R,FAT . The so calculated fatigue strength ratio V R according to Equation (4) is shown in Figure 7B corrected to R = 0.5 with the mean stress correction factor f (R) according to Table 3.

| REVIEW OF TEMPERATURE EFFECT ON DESIGN CURVES
As initially mentioned, data on fatigue strength of welded steel joints at subzero temperatures are scarce; however, more data are available for notched and unnotched base material specimens. To the authors' best knowledge, the oldest studies date back to the 1930s, with the first extensive data collection by Hempel and Luce. 39 Probably, the most comprehensive collection of the temperature effect on fatigue strength dates back to the 1960s and 1980s. Forrest 40

FIGURE 7 (A) Ratio of measured mean
(P s = 50.0%, N = 2 · 10 6 ) to mean fatigue strength at room temperature and (B) ratio of measured to corresponding fatigue strength class (P s = 97.7%, N = 2 · 10 6 ) corrected to R = 0.5 with the mean stress correction factor f(R) according to This formula seems to be based on BS 7910, 48 where Equation (50) relates the threshold stress intensity factor K 0 of nonferrous metals to the threshold stress intensity factor of steels via the Young's modulus of steel, see Equation (6).
Here, no comment is given regarding the applicability of this formula for changing Young's modulus with temperature. However, since the same formula for the changing intersection point A of the simplified FCG curve is used for the calibration for nonferrous metals (Equation 7) and high temperatures (Equation 8), it can be assumed that Equation (6) is valid for changing Young's modulus at high temperatures E HT as well.
A  44 while the change from 25°C to −50°C is comparably low with 4 GPa.
Based on a Young's modulus of approximately 205 GPa at 25°C, considered here as comparable to RT, an increase of about 1% in fatigue strength would be expected for a temperature of −20°C and 2% for −50°C. The increase found in this study was, however, much higher, leading to the conclusion that the Young's modulus might increase more at subzero temperatures than expected by ASME BPVC. 45 Moreover, measurements of Young's modulus are already highly scattered at RT, making it difficult to accurately measure it at low temperatures. Since the formula given by the IIW recommendations 37 is actually meant for high temperatures and not validated for low temperatures, it does not seem applicable to subzero temperatures.
The German FKM guideline is another standard that include a correction factor based on service temperature. 49 Although the guideline states that low temperatures are outside its scope and that no correction shall be applied in the range of −40°C to 60°C, the given empirical formula for temperatures above 100°C might, due to its formulation, yield reasonable results for subzero temperatures as well. As in the IIW recommendations, 37 a linear relation between fatigue strength and temperature is assumed according to Equation (9), with the correction factor K T,D from Equation (10): Setting the reference to 20°C, an increase of fatigue strength of 5.6% would be expected compared with RT and 9.8% from RT to −50°C. Compared with the IIW recommendations, 37 a much higher increase is calculated at subzero temperatures. Moreover, the measured increase in fatigue strength based on Equation (9) would be conservative for all test series except the S500 transverse stiffener.

| DISCUSSION
The study has shown that there is a clear fatigue strength dependence on low temperatures for welded joints, which confirms the results of earlier studies on FCG rate testing of base materials (eg, Walters et al, 29 Alvaro et al 31 ) as well as on fatigue strength of longitudinal stiffeners at subzero temperatures (see Bridges et al 3 ). The increase in fatigue strength of the tested weld details was found to be in the same order of magnitude for both steels. Most importantly, no decrease of fatigue strength was found for the normal strength steel with a nominal lowest design temperature of −20°C, even at a test temperature of −50°C. Consequently, welded joints with weld toe and weld root failure made of a normal strength steel are assumed to be safe even at the lowest design temperatures defined by Hauge et al, 13 being −40°C. Thereby, the findings of Walters et al 16 regarding fracture toughness requirement over fulfilment at subzero temperatures are supported for fatigue strength of welded joints. Interestingly, a larger increase in fatigue strength was found for cruciform joints with root failure compared with transverse stiffener with weld toe failure. Although transverse stiffener specimens show a longer crack initiation period for which higher temperature effect would be expected, the increase in fatigue strength for this weld detail was smaller than for the cruciform joint detail. From FCG rate measurements by Walters et al 29 and Alvaro et al, 31 a stronger decrease in FCG rate was found in the low stress-intensity factor range than in the intermediate and higher region of the Paris-curve. Further investigation is required to explain the smaller increase observed for the transverse stiffener's fatigue strength. Although, the mean fatigue strength of the transverse stiffener at RT is almost the same as the S235 transverse stiffener specimens, the latter experienced a higher fatigue strength increase at subzero temperatures. While fatigue cracks initiate in the weld metal in case of the cruciform joint weld detail, they initiate in the HAZ for the transverse stiffener.
From literature, it is known that the fracture toughness-and thereby the DBTT and FDBT-are often least favourable in the HAZ and at the fusion line. 34 In their FCG tests of S460 structural steel, Walters et al 29 found a FTT which was approximately 18°C higher than the T 27J DBTT from Charpy notch impact testing. More recently, Alvaro et al 32 found a difference of 15°C between the FTT and DBTT in weld simulated 420 MPa steel. It might therefore be possible that temperatures below the FTT of the HAZ cause the increases in fatigue strength to be smaller for transverse stiffeners than for cruciform joints. Walters et al 29 and Alvaro et al, 31,32 however, measured only a slight increase of the threshold stress intensity factor range below the FTT; this would explain why the fatigue strength at −50°C is still above the fatigue strength at −20°C. Although, S-N tests are not well suited to measure the FTT due to the large number of specimens needed for each curve, the constant increase in fatigue strength at subzero temperatures verifies that the fatigue strength of welded joints seems to stay above the fatigue strength at RT for temperatures corresponding to Arctic conditions.
In summary, a high fatigue strength increase at 50°C was found for the cruciform joint weld detail, with an increase of about 20% when comparing the S235 J2 + N normal strength and the S500G1 + M high-strength steel with RT. The transverse stiffener weld detail, in contrast, showed an increase of about 12% for the S235J2 + N and 6% for the S500G1 + M steel at this temperature. Comparing this increase to the empirical formulas by the German FKM guideline, 49 the increase would be correctly estimated for the S500G1 + M transverse stiffener, while being conservative in all other cases. Assuming a change of Young's modulus of 4 GPa from RT to −50°C (based on BS7910 48 and ASME BPVC 45 ) and applying the formula given by the IIW design recommendations 37 leads to overly conservative results; however, those formulas are only meant for high temperature fatigue. Applicability to subzero temperatures was investigated in this study since no correction formulas for subzero temperatures currently exist. Additionally, Young's modulus is a varying quantity due to factors such as rolling of plate material, thickness effects, sensing technology, etc. Thus, it might not be particularly suitable to describe the temperature effect on fatigue strength.

| CONCLUSIONS
This study investigated the fatigue strength of fillet welded joints of a normal and a high strength steel at room and at subzero temperatures by means of S-N tests; experimental results were compared with estimates based on international standards. The following conclusions can be drawn from the investigation: • Compared with RT, the fatigue strength of fillet welded joints of normal and high strength steel seems to increase constantly with decreasing temperature throughout the tested range. The average fatigue strength increases by 8% at −20°C and 15% at −50°C. • The highest increases in fatigue strength, of approximately 22%, have been found at −50°C for a normalstrength steel grade that is only qualified for −20°C (based on fracture toughness properties). This extends the findings of Walters et al 16  = Fatigue strength at 2 · 10 6 cycles for a probability of survival 95% and a confidence level of 75% at 20°C e = Axial misalignment e f = Elongation at fracture f (R) = Mean stress correction factor k = Slope exponent of the stress-life curve K T,D = Fatigue strength correction factor acc. to the FKM guideline N = Number of cycles to failure P s = Probability of survival r = Weld toe radius R = Stress ratio between lower and upper stress T = Temperature T σ = Scatter ratio (1/ (Δσ R,10% /Δσ R,90% )) V R = Fatigue strength ratio α = Weld flank angle K 0 = Threshold stress intensity factor of nonferrous metals K 0,steel = Threshold stress intensity factor of steel Δσ n = Nominal stress range Δσ R,FAT = Reference fatigue strength at 2 · 10 6 corresponding to the IIW FAT class Δσ R,i = Reference fatigue strength at 2 · 10 6 cycles for a probability of survival i Δσ R,i, R = 0.5 = Reference fatigue strength at 2 · 10 6 cycles for a probability of survival i and a stress ratio R = 0.5 Δσ R,mean = Mean fatigue strength at 2 · 10 6 cycles for a probability of survival of 50% σ w,T = Fatigue strength acc. to the FKM guideline at a temperature T σ w,T = 20°C = Fatigue strength acc. to the FKM guideline at a temperature of 20°C σ UTS = Ultimate tensile strength σ YS = Yield strength φ = Angular misalignment