Fatigue design of stress relief grooves to prevent weld root fatigue in butt-welded cast steel to ultra-high-strength steel joints

Abstract

In the welded joints, fatigue failures typically originate from defects or notch-like geometries under cyclic loading. This study investigates the impact of stress relief grooves (SRG) on the fatigue performance of butt-welded cast steel to ultra-high-strength steel components using experimental fatigue tests and finite element method. The experiments examined the fatigue properties of hybrid joints between G26CrMo4 cast steel (t = 20 mm) and S960 steel plate (t = 6 mm) with and without SRG. Gas metal arc welding process was used to weld the butt joints that had a permanent root backing machined on the cast steel part, causing a crack-like defect to the weld root. Additionally, the top surfaces of the welded parts were aligned, resulting in a significant axial misalignment in the butt joint. The SRG, positioned close to the weld root, was found to have a beneficial influence on the joint’s fatigue performance by a factor of 1.2 when using the nominal stress criterion. However, the fatigue capacity was still roughly 35% lower compared to the symmetrical equivalent due to the secondary bending stress, caused by axial misalignment. The finite element analyses indicated that the SRG reduces the amount of secondary stresses at the weld root leading to lower total structural stress. The study recommends using the FAT80 (m = 3) design curve in the structural stress method, for similar butt-welds having a crack-like defect, parallel to the loading direction, at the weld root. However, for welded joints with crack-like defects, it is advisable to use linear elastic fracture mechanics rather than relying solely on stress-based local approaches.

1 Introduction

The use of ultra-high-strength steels (UHSS) has increased in recent years, especially in weight-critical structures in the transportation, heavy machinery, lifting industry and civil engineering sectors [1]. In many applications, the development has been driven by needs for lighter and more energy-efficient structures, without compromising structures’ load-carrying capacity or safety [2, 3]. However, as UHSSs allow the use of thinner material thicknesses in structures, they also increase the overall stress level of structures. Higher stresses in structures cause increased demands in the quality requirements in design and manufacturing [4]. Fatigue design aspects are especially emphasised in order to effectively utilise the higher material strength of UHSSs in structures [5].

Cast steel parts are commonly used in various steel structures, including bearing housings, pin joints, lifting lugs, and nodes of the trusses. The main advantages of using cast steel parts are their flexible geometrical designs, cost-effectiveness in serial production and aesthetical appeal [6]. Casting-enabled designs can be used to position joints away from structurally critical areas, reduce stress concentrations with smooth shapes and manufacture topology-optimised shapes with minor additional costs [7]. Cast parts are typically joined to plate components or other structures by welding, and various details can be included in the cast design to reduce the need for machining and to facilitate the positioning of the parts.

In order to enhance the productivity of welded cast steel components, various bevels and permanent root backings are often used. Nonetheless, there is always a possibility that unwelded initial cracks or defects remain on top of permanent root backings at the weld root [8, 9]. Additionally, the fatigue strength of the weld is generally lower than that of the attached cast steel component [10]. Such initial defects are considered in the fatigue design guidelines according to the nominal stress method in the International Institute of Welding (IIW) recommendations [11] and Eurocode 3: Design of steel structures (EC3) [12]. Both guidelines recommend the fatigue strength class (FAT) of FAT71 for joints with non-destructive testing (NDT), while for joints without NDT, FAT36 is recommended.

This study investigates the fatigue strength of hybrid butt-welded (BW) joints between a cast steel part and a UHSS plate, which have a crack-like defect in the weld root, parallel to the applied load direction and caused by permanent root backing. The studied hybrid BW joint has a significant difference in material thicknesses, and the axial misalignment may cause a considerable amount of secondary bending stresses in the welded joint [13]. The aim of this study is to investigate whether the fatigue capacity of joints can be enhanced by reducing stress concentration in the weld root through the implementation of a stress relief groove (SRG) design. It is worth noting that SRGs are commonly utilised in machine elements, such as shafts, to redirect stress flows away from critical details [14]. The optimal location and geometry for the SRG were approximated numerically using the finite element method (FEM). Subsequently, the effects of the developed SRG on the fatigue strength of BWs were studied experimentally using welded coupon specimens. The results were analysed using both linear elastic fracture mechanics (LEFM) and local approaches, including the effective notch stress method (ENS) and the theory of critical distances (TCD), with an idealised joint geometry of real specimens. Figure 1 provides a schematic overview of the studied BW joints, including the nominal stress method design FAT classes in the weld root, weld toe and machined SRG, according to IIW recommendations and EC3.

Fig. 1

Schematic picture of the studied BW joints with stress-flow curves, with and without SRG, along with nominal stress method design S–N curves [11, 12, 15]

2 Materials and methods

2.1 Materials

For the experimental study, two structural steel plates were selected: UHSS S960 MC (t = 6 mm) and S355 (t = 20 mm). These plates were welded to G26CrMo4 QT2 cast steel slabs. The materials were chosen based on an existing structure where a cast steel component is butt-welded to the S355 plate, with both welded materials having a 20 mm thickness. By replacing mild steel with higher strength grade steel (S960), a 70% weight reduction in the plate structure can be achieved, while still maintaining good weldability. Although thinner S960 has an ultimate load-carrying capacity approximately 40% lower than S355, it still reliably represents the fatigue strength of the joint detail under study. The specimens were produced using the gas metal arc welding (GMAW) process with filler materials that match the strength of the steel plates. A preliminary welding procedure specification, also known as pWPS, was created to ensure the quality of the welds. Tables 1 and 2 present the mechanical properties and chemical compositions of the steels and filler materials used, respectively.

Table 1 Mechanical properties of the studied materials (nominal and material certificate values). Where, f_y and f_u are the yield and ultimate tensile strengths of the material, respectively, A is the elongation at the fracture and KV is the Charpy V-notch impact strength energy

Table 2 Chemical composition of the studied materials in wt.-% (nominal, material certificate and measured values)

2.2 Geometrical design of stress relief grooves and specimens

The SRG’s optimal location was numerically approximated using FEM. FEM models were created using quadratic plane-strain elements, and meshing at the notches was based on the mesh convergence study [16]. In these analyses, a U-notch type reference radius of r_ref = 0.05 mm [17] was applied to the initial crack caused by permanent root backing, and the weld root was modelled in a worst case when there is no weld penetration to the backing at all. The ENS approach with r_ref = 0.05 mm is recommended to be used on thin plates (t < 5 mm). However, in this case, the use of the smaller reference radius was deemed to be more appropriate than the reference radius of r_ref = 1 mm [17], which would have resulted in a significant material reduction at the weld root. The SRG was modelled as a simple cut with rounding of 1 mm, and a circular zone with a diameter of 6 mm was left untouched around the weld root. This area ensures sufficient conditions for welding with proper conduction away from the weld root, and root backing remains infusible after welding. A schematic overview of the FEM analysis with boundary conditions and loads is presented in Fig. 2.

Fig. 2

The ENS model was utilised to estimate the optimal position of the stress relief groove. The point p, located at the centre of the modelled stress relief groove, was varied in relation to the coordinate system applied in the weld root. The area surrounding the weld root that was not modified is shaded with red

Seven iterations were performed with varying distances (x-parameter in Fig. 2) and depth (y-parameter) of the centre (p-point) of the circular SRG arc in relation to the weld root. The analyses were conducted separately for membrane and bending loading. Stress concentration factors (SCFs) were collected separately for both axial and bending load cases at the weld root using the major principal stress criterion. SCFs were collected from the bottom of the applied groove with only membrane loading. The results of the rough analysis of the SRG location are presented in Fig. 3. Based on the obtained SCF results, the SRG variation ID no. 5 was chosen for the experimental testing, having a good compromise between SCFs in the root and the groove. The geometry was smoothened, and the groove radius was increased from 1 to 5 mm. This change did not significantly affect SCFs in the weld root (< 5% change), but it decreased SCF in the SRG and made parts easier to manufacture.

Fig. 3

Results of the groove location iteration and SCFs from applied groove (r_ref = 1 mm) and weld root (r_ref = 0.05 mm) along with the control which did not have the groove

Four series of the coupon test specimen were used in the experimental research. The first series (35BW) served as a control group and did not have any axial misalignment. The remaining three series utilised S960 UHSS and had axial misalignment. The first of these (96BW-A) did not have the SRG, while the second (96BW-B) had the designed SRG. The third variation (96BW-C) had a deeper groove to highlight the effect of the groove by removing an additional 1 mm of material. The test matrix can be seen in Table 3, and schematics of the designed specimens are presented in Fig. 4. All specimens were tested in the as-welded condition (AW), except a few 96BW-C specimens that underwent high-frequency impact (HFMI) treatment from the bottom of the groove. In the first AW specimens of the series 96BW-C, the failure location shifted from the weld root to the bottom of the groove (Sect. 3). To maintain the weld root critical for the fatigue failure, HFMI treatment was employed to increase the fatigue strength of the machined surface of the groove, by inducing compressive residual stress and slightly improving the surface quality [17].

Table 3 Fatigue specimen matrix

Fig. 4

Fatigue test specimens weld detail geometries: a) 35BW, b) 96BW-A, c) 96BW-B and d) 96BW-C. Dimensions of the specimens: e) 35BW and f) all 96BW variations. Dimensions in mm

2.3 Manufacturing and measurements of the specimens

The plate parts were cut using nitrogen as cutting gas with a fiber laser parallel to the rolling direction. The cast steel parts with bevels, for weld configuration, were machined from cast steel slabs. Before welding, all steel parts underwent cleaning in a 10% citric acid bath. During the welding process, the cast steel and plate parts were clamped into the welding jig, and welding was performed with robotised GMAW in flat position (PA). Mixed shielding gas (8% CO₂ + Ar) was used during welding. Figure 5a presents the welding setup, where the specimen is attached to the welding jig with four clamps. Details on the weld configuration and welding sequence are illustrated in Fig. 5b, c. After welding, the start and end points of the weld were cut, and the cut surfaces were machined and ground to flush. The used welding parameters corresponding to Fig. 5 are presented in Table 4.

Fig. 5

a) The welding setup, weld groove dimensions and welding order of b) 35BW and c) all 96BW variations. Dimensions in mm

Table 4 Welding parameters, where U and I are welding voltage and current, v_w is wire feed speed, v_t is welding torch speed, T₀ is the interpass temperature and Q_avg is the calculated average heat input

The quality of the welds was verified through hardness measurements from macrographs and quasi-static tensile tests. The hardness measurements were performed with the Struers DuraScan 70 micro/macro hardness tester using the 5 kgf Vickers hardness (HV5) procedure. The measurement lines were taken roughly 1 mm below the surface at the weld face and the weld root. The results of the hardness measurements can be seen in Fig. 6. Both specimens show a significant increase in the hardness in the heat-affected-zone (HAZ) of the cast steel, which may be attributed to the higher carbon content of the studied cast steel, as seen in Table 2. The typical softening of the S960 microstructure was also detected in the HAZ, as previously reported in Refs. [19, 20].

Fig. 6

Hardness measurements in a) 35BW and b) 96BW-A specimens

Quasi-static tensile tests were performed on 35BW and 96BW-A specimens. The specimen shapes and dimensions of the tensile test specimens were identical to those presented in Fig. 4, except for a reduced width from 50 to 40 mm. The quasi-static tensile test were conducted using a Galdabini Quasar 600 material testing machine. The elongation in the vicinity of the weld area was measured using a digital image correlation (DIC) system [21]. The Aramis DIC setup used two 12-megapixel cameras, each with an 85 × 65 mm capturing area. The stress values were obtained using the rig’s force transducer data and measured cross-sectional values. Strain values were extracted using a 50-mm-long virtual extensometer in the DIC system measuring distance over the weld. The engineering stress–strain curves for both specimens are shown in Fig. 7, along with DIC images at the point reaching ultimate tensile loading. The 35BW specimen experienced final rupture outside of the DIC capturing area in the S355 base material, while the 96BW-A specimen failed at the softened HAZ on the S960 plate.

Fig. 7

Stress–strain curves and ultimate capacities of the studied 35BW and 96BW-A welded joints

2.4 Fatigue testing

Fatigue tests were conducted mainly using a 750 kN servo-hydraulic fatigue test rig at around 1 Hz frequency. Because there was no axial misalignment in 35BW specimens, the fatigue tests at a frequency of 100 Hz frequency were conducted on Rumul Vibroforte 700 resonance test rig. Both fatigue testing rigs can be seen in Fig. 8. The experiments were performed with stress ratio of R = 0.1, and a few additional fatigue tests were carried out with an applied stress ratio of R = 0.5.

Fig. 8

Test specimen installed to a) the high-capacity resonant- and b) the servo-hydraulic test rig

The specimens were fitted with a single strain gage (SG) according to the IIW recommendations [11], i.e. using the grid sizes of 3 mm and 0.6 mm for the t = 20 mm (S355) and t = 6 mm (S960) specimens, respectively. The SGs were installed at 0.4t distance from the weld toe to the steel plate. The nominal stress in each specimen was calculated using the test rig’s force data and the net cross-section of fatigue failure location, excluding the weld reinforcement. In addition to the test rig’s force data, SG measurements were used to determine structural stress at the steel plate. Structural stress in the bottom of the SRG was estimated analytically over the weld with the following equation:

$${\sigma }_{s,{\text{SRG}}}={\sigma }_{\text{m}}\frac{{t}_{1}}{{t}_{2}}+{\sigma }_{\text{b}}{\left(\frac{{t}_{1}}{{t}_{2}}\right)}^{2},$$

(1)

where, σ_m/b are membrane and bending stress components that form the structural stress at the weld root, t₁ is the thickness of the plate at the SG location and t₂ is the material thickness at the SRGs location, excluding the additional thickness brought by the weld reinforcement (Fig. 9).

Fig. 9

Schematic picture about on the determination of structural stress analytically in SRG

3 Fatigue test results

The fatigue test results were analysed using the standard statistical method [11], which utilises the least square linear regression to calculate the mean fatigue (Δσ_c,50%) at 2 × 10⁶ cycles, with a fixed slope parameter m = 3. The specimens from the 96BW-C series, which had the fatigue failure occurring from the bottom of the SRG, were also analysed with the slope parameter of m = 5 that is recommended for machined surfaces. The characteristic fatigue strength (Δσ_c,97.7%) was determined from Δσ_c,50% using the standard deviation of the data set and survival probability of 97.7% [11]. Table 5 presents the mean fatigue strength of each test series, using both the nominal and structural stress systems. One 96BW-B specimen was excluded from the statistical analysis due to an overload (> 1.5F_max) caused by an error in a hydraulic pressure source, during the experiment. The complete fatigue test data is presented in the Appendix: Table 7.

Table 5 The mean fatigue strength of each test series using the nominal and structural stress criteria at 2 × 10⁶ cycles

The fatigue test data points are presented in Fig. 10a according to the nominal stress criterion, along with the previously mentioned fatigue design curves (Fig. 1). In Fig. 10b, data points are shown in the structural stress system, with S–N curves fitted according to the fatigue failure location. A total number of 18 specimens failed from the weld root, and the sample size was sufficient to present the design S–N curve, Δσ_c,s,97.7% = 84 MPa, corresponding to Δσ_c,s,50% = 98 MPa (m = 3). The natural slope parameter correlated well with the recommended value slope parameter being m = 3.06. The HFMI treatment at the bottom of the groove increased the fatigue strength of 96BW-C specimens from Δσ_c,s,50% = 149 MPa to Δσ_c,s,50% = 192 MPa (m = 5).

Fig. 10

a) Data points with a nominal stress criterion with design S–N curves and b) data points with structural stress criteria and fitted S–N curves according failure location of the weld

The cross-sectional macrographs were created from the failed specimen in each test series, as presented in Fig. 11. It can be observed that in the 35BW, 96BW-A and 96BW-B test series, the crack initiated from the weld root, except for one specimen in the 96BW-B series, which failed from the bottom of the SRG. Upon further examination of this specimen, a competing fatigue crack from the weld root, measuring approximately 1 mm long, was discovered. The fatigue failure initiated from the bottom of the SRG in both machined and HFMI-treated conditions, in the 96BW-C series, where the SRG effect was emphasised with a deeper groove.

Fig. 11

Fatigue crack paths in crack test series. a) 35BW, b) 96BW-A, c) 96BW-B, d) 96BW-C (AW) and e) 96BW-C (HFMI)

The SGs were used to monitor the crack growth behaviour during the fatigue test. It has been shown that SGs installed a few millimetres away from the weld toe can be used to measure a 0.5 to 1 mm long fatigue crack, indicating the transition from the crack initiation (CI) to the crack propagation (CP) phase [22]. In this study, a recommended 5% change in the measured strain values was used as a threshold from CI to CP. The normalised strain behaviour in all 96BW variations related to the total fatigue life is presented in Fig. 12 along with ratio of CI to total fatigue live. It can be observed that SRG has a clear effect on the CI trends. However, it is likely that the shift from CI to CP was not detected reliably in 96BW-C specimens and is not comparable to A and B variations. The reason being, SG was far from the fatigue failure location it responded with a delay to the crack growth. Similarly, AW and HFMI-treated specimens could not be distinguished, although the fatigue results indicate a significant difference.

Fig. 12

The normalised strain behaviours in relation to the total fatigue life in all 96BW variations, along with average CI to CP transition points. AW and HFMI-treated specimens could not be distinguished in 96BW-C variation

4 Application of local approaches

The fatigue strength of joints 96BW-A and 96BW-B was evaluated using various local approaches, including TCD, ENS and LEFM analyses. In order to conduct a more detailed analysis, plane strain FE models were created based on 96BW-A and BW96-B specimens, in comparison to the rough SRG iteration models used in Sect. 2.2. The boundary conditions were adjusted to closely resemble those produced by the fatigue test rig. However, it should be noted that measuring the stiffness of the test rig would have to be a challenging task to measure and incorporate into the FEM analysis. To compensate for this unknown boundary condition, an additional external moment was included in the calculations based on the SG measurements. The FE models were created using an idealised version of the real geometry, which was based on 3D scanned specimens and macrographs. Schematic figure from the idealised FEM model creation can be seen in Fig. 13.

Fig. 13

The idealised real geometry of the finite element model was created based on the scanned experimental specimens. The initial crack length was measured from multiple macrographs, and the average length was used

The study utilised the point method (PM) amongst various TCD criteria, as proposed by Baumgartner et al. [23], using a critical distance of a = 0.1 mm with the design S–N curve FAT160. A radius of 0.05 mm was used at the weld root when creating FE models for TCD. The same model was also used in the ENS method (r_ref = 0.05 mm) with a corresponding FAT630 design curve [24], and in LEFM (with an inserted initial crack). Furthermore, the ENS models with a fillet-type reference radius (r_ref = 1 mm) were created, which have a corresponding FAT225 curve [25]. The design S–N curves, according to both IIW and EC3 guidelines, include a characteristic survival probability of P_s = 97.7%. However, it has been suggested by Radaj et al. [26] that a statistical factor of j_σ = 1.37 can be used to estimate the mean fatigue strength (P_s = 50%), which should correlate with experimental results. The stress distributions with TCD and ENS, with a smaller reference radius, can be seen in Fig. 14 along with location where structural stress was collected.

Fig. 14

SCFs obtained from the same model in the TCD_PM and ENS method (r_ref = 0.05 mm)

In order to conduct the LEFM FEM analysis, an initial crack with length of a_i = 0.01 mm was introduced at the weld root in location, more specifically at the location where the maximum principal peak stress occurs. To model the crack, five additional elements were included along its length. The crack growth was executed with small increments to simulate the crack growth, and the J-integral approach was used to calculate stress intensity factors (SIF). The fatigue life estimation in the crack propagation phase was calculated with Paris’ power law using numerical integration with the following equation [27]:

$${N}_{{\text{f}},{\text{LEFM}}}\text{=}\underset{{a}_{\text{i}}}{\overset{{a}_{\text{f}}}{\int }}\frac{1}{C\cdot \Delta K{\left(a\right)}^{{m}_{\text{p}}}}\cdot da,$$

(2)

where, N_f,LEFM is the estimated fatigue life, a_i is the initial crack length, a_f is the final crack length, C is the crack propagation coefficient, ΔK(a) is the SIF range as a function of the crack length and m_p is exponent of Paris power law. The nominal fatigue strength based on the S–N curve can be calculated from the LEFM analysis results using the following equation:

$$\Delta {\sigma }_{\text{nom}}={\left(\frac{{N}_{{\text{f}},{\text{LEFM}}}}{2\cdot {10}^{6}}\right)}^\frac{1}{m}\cdot\Delta {\sigma }_{\text{LEFM}},$$

(3)

where m is the slope parameter of the S–N curve, and Δσ_LEFM is the stress range corresponding with N_f,LEFM. For crack propagation, coefficient values are proposed: C_mean = 1.5∙10⁻¹³ mm/cycle [28] and C_char = 5.21∙10⁻¹³ mm/cycle for weld root failure and exponent m_p = 3 [11].

The structural stress values, obtained from the SG measurements and FEM models, showed differences, and this disparity can be attributed to the flexibility of the test rig, which was not taken into account in the FEM analysis. However, it was factored into analyses by calculating the difference in bending moment between structural stress and FEM analysis. This additional bending was incorporated, e.g. in the determination of the ENS stress range (Δσ_ENS) with the following equations:

$$\Delta {\sigma }_{\text{b}}=\Delta {\sigma }_{\text{s,SG}}-\Delta {\sigma }_{\text{s,FEM}},$$

(4)

$$\Delta {\sigma }_{\text{ENS}}={K}_{f,{\text{m}}}\Delta {\sigma }_{s,{\text{FEM}}}+{K}_{f,{\text{b}}}\Delta {\sigma }_{\text{b}},$$

(5)

where, Δσ_s,SG is the structural stress range determined by SG, Δσ_s,FEM is the structural stress range from FEM model at the SG location, Δσ_b is additional bending caused by boundary conditions and K_f,m/b are fatigue stress concentration factors for bending and membrane load, respectively. SCF values with used local approaches are presented in Table 6, from which can be observed that SRG should influence the stress concentration caused by the initial defect in the weld root and thus affect the fatigue life of the specimen.

Table 6 SCFs with local approaches. Separate SCFs for the membrane and bending were obtained with cantilever boundary conditions with corresponding membrane and bending unit loads

The experimental fatigue test results were compared with the presented local approaches. Figure 15 shows that, whether or not the specimen had SRG, TCD and ENS methods yield non-conservative fatigue life estimates. Among the tested methods, LEFM provided the most accurate estimation of the experimental results.

Fig. 15

Fatigue life estimations (N_f,est) compared to experiments (N_f,exp) with different approaches. a) 96BW-A with a survival probability P_s = 50%, b) 96BW-A with P_s = 97.7%, c) 96BW-B with P_s = 50% and d) 96BW-B P_s = 97.7%

5 Discussion

The study experimentally investigated the applications of the SRGs to enhance the fatigue capacity of the root critical butt-weld between the cast steel part and UHSS plate. The SRG was placed with an objective to reduce the stress concentration at the weld root by re-directing the stress flow away from the initial defect at the weld root, thereby improving the fatigue capacity of the weld. The results of fatigue tests showed that SRG improved the fatigue capacity by approximately 20% in axially misaligned BWs when examined using the nominal stress method. Additionally, with SRG specimens, the crack initiation phase accounted for a comparatively longer portion of the total lifetime (Fig. 12). Based on these findings, it is possible to conclude that SRG improves the BW’s fatigue strength, even though the fatigue resistance is still roughly 35% lower than it is for the control series.

The SRG was expected to have an influence on the SCFs, as indicated by preliminary FEM analyses (Fig. 3) and further studies in Sect. 4 (Table 6). This influence, approximately 10–15%, should have been reflected of the experimental results in the structural stress system. However, the control series (35BW) and the series with and without SRG (96BW-A/B) exhibited essentially the same mean fatigue strength (96–99 MPa) and showed a linear correlation in the structural stress system (Fig. 10b), which contradicts the numerical analyses. Due to this observation, additional experiments were conducted with a groove that was 1 mm deeper (96BW-C) to highlight the influence of the SRG. However, this modification resulted in a shift of the fatigue failure location from the weld root to the bottom of the SRG, which was not desired. To address this issue, HFMI treatment was applied to the bottom of the groove with the aim of ensuring that the weld root remained in the critical location for fatigue failure. The fatigue strength of the treated specimens improved, but the failure location remained at the bottom of the SRG.

The linear correlation in the structural stress system enabled the grouping and analysis of all 18 test specimens in which weld root fatigue failure occurred. The mean and characteristic fatigue strengths for these were 98 MPa and 84 MPa (m = 3), respectively (Fig. 10b), and the natural slope parameter of m = 3.06 indicated a good fit to the experimental data. Failures occurring at the bottom of the SRG followed closely slope parameter m = 5, with and without SRG. However, a small sample size of SRG failures must be noted. Based on the nominal stress method (Fig. 10a), it can be concluded that the FAT36 design curve is safe to use for all investigated BW geometries, and the FAT71 design curve is safe to use in the case of negligible secondary bending moment.

The calculation of the degree of bending (DOB), which indicates the ratio between the bending stress and total structural stress, was performed for each specimen. This was done by using the nominal stress (determined from the specimen cross-section and the force sensor data on the rig) and the strain gage data. The results showed that, instead of the SCF, the SRG had an influence on the DOB, which can be found in the Appendix: Table 7 along with other experimental data. This observation suggests that SRG reduced the amount of the secondary bending moment, which in turn lowers the overall structural stress at the weld root.

The fatigue strengths of joint geometries used in the 96BW-A and 96BW-B specimens, one with SRG and the other without, were estimated using stress-based local approaches TCD_PM and two ENS variations, as well as LEFM. The estimations were compared with the experimental results which can be seen in Fig. 15. The stress-based approaches resulted in non-conservative estimations, as the experiments showed good agreement with the P_s = 97.7% design curves (FAT225, FAT630 and FAT160, depending on the approach). Ahola et al. [25] have also reported similar results regarding the ENS method for evaluating the weld root fatigue strength. LEFM performed well in the determination of the fatigue strength in specimens with or without SRG and estimated fatigue performance better than other approaches used. Similar results, regarding use of LEFM, were reported by Peng and Zhu [8] for a similar welded hybrid joint. Lipiäinen et al. [29] compared LEFM with local approaches and found that LEFM was conservative for specimens with an initial crack length of 0.3 mm at the bottom of the notched geometry, which was significantly shorter than in the present study.

6 Conclusions

This study experimentally and numerically investigated the fatigue capacity of axially misaligned butt-welds, with an initial defect in the weld root caused by permanent root backing. The experimental results were compared to the IIW recommendations and EC3 standard, and computational fatigue life estimations were obtained based on the local approaches. The following conclusions can be drawn based on the results of the experimental research, and evaluation of local approaches and LEFM:

• Axial misalignment significantly reduces the fatigue capacity of the studied joints from the mean fatigue strength of 99 to 53 MPa in the nominal stress system. However, the stress relief groove increases the fatigue strength by a factor of 1.2 compared to the similar joint without the groove. Nevertheless, the fatigue capacity is still approximately 35% lower compared to the control S355 test specimens that did not have any axial misalignment.

• In butt-welds where a weld root defect may arise, it is recommended to use the design curve FAT36 (m = 3) as suggested in both the IIW recommendations and EC3, which also aligns with the findings of the study. However, according to both design guidelines, FAT71 (m = 3) should not be used if the weld root is uninspected or has any defects. Nevertheless, it could be used conditionally in the absence of secondary stresses as found in this study.

• The experimental study shows that the stress relief groove affects the amount of secondary bending moment in the joint, leading to a decrease in total structural stress in the weld root. The results of this study suggest that the structural stress method with FAT80 (m = 3) design curve could be recommended for butt-welded joints that have a weld root defect or crack caused by permanent root backing, parallel to the loading direction, regardless of whether the joint has axial misalignment or geometry modifications.

• LEFM is found to be the most suitable method for evaluating the fatigue capacity of the welded joint under investigation with a crack-like defect in the weld root. In terms of fatigue life, the safety factors for specimens with and without stress relief groove are roughly 4.5 and 3, respectively. The fatigue strength assessment with other local approaches, TCD_PM and two ENS variations, resulted in non-conservative estimations, and the experimental results closely followed P_s = 97.7% design curves, indicating that the safety factor in life was close to one.

• The experimental results did not indicate the reduction of stress concentration factors due to the stress relief groove, despite the FEM analyses suggesting a reduction of approximately 10–15%. The study did not cover the reason for this phenomenon, and further research may be necessary.

Appendix

Table 7 Fatigue test data