Analysis of fatigue notch effect due to axial misalignment for ultra highstrength steel butt joints
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Abstract
The majority of fatigue tests of welded specimens is based on shopmade samples generally exhibiting minor misalignment. Due to the challenge of ensuring misalignmentfree joints in industrial manufacturing processes, investigations focussing on the effect of misalignment on the fatigue strength are important. Therefore, this paper deals with the influence of axial misalignment on the fatigue resistance of buttwelded ultra highstrength steel specimen. In addition, the effect of high frequency mechanical impact treatment (HFMI) on the fatigue performance is researched. In the course of the experimental investigations, specimens exhibiting three different levels of axial misalignment are manufactured. Fatigue tests at a stress ratio of R = 0.1 in aswelded condition reveal a significant drop in fatigue strength with increasing axial misalignment. Fatigue assessments of the aswelded test results based on nominal, structural and effective notch stress approach are performed taking into account the sampledependent misalignment factor. The given equations enable an improved consideration of axial misalignment regarding to fatigue strength. The HFMI treatment increases the fatigue strength compared with the aswelded state; the detrimental effect of misalignment is less pronounced. A comparison to the current IIW guideline for HFMI treatment reveals a conservative assessment if IIWrecommended FAT values for aswelded condition are applied.
Keywords
Fatigue strength Ultra highstrength steel Axial misalignment HFMI treatment1 Introduction
Within industrial manufacturing processes, weld seams usually exhibit a certain amount of angular and axial misalignment affecting the fatigue strength of welded structures in service. In contrast, the majority of welded specimens utilised for gathering fatigue test data is manufactured in workshop resulting in minor axial misalignment and angular distortion for every tested specimen. Thus, in many cases, the effect of misalignment on the fatigue strength of the weld detail is not well covered by experiment. This may be critical for applying such values without additional misalignment factors for fatigue assessment.
The offset between buttwelded sheets leads to an additional secondary bending moment significantly affecting the local stress distribution around the weld. In the IIW guideline [1], this stress magnification is captured for flat plates applying an analytical expression derived in [2]. A thorough investigation focussing on the detailed effects of weld location in the plate, its length over width ratio and load magnitude by the use of analytical approaches is published in [3]. Further studies incorporating finite element simulation runs focus on more complex assemblies such as panel structures in ships or girth welds for pipelines [4, 5].
In literature, only a limited amount of fatigue test results for buttwelds with emphasis on the effect of axial misalignment is available, see [6, 7, 8]. In [9], a summary of fatigue test results for steels is presented considering the correction factors for misalignment as suggested in [2]. Thereby, for a number of load cycles above 10^{4}, the resulting SN curve shows a rather good accordance with limited scatter. The same authors published investigations on the influence of the offset to sheet thickness ratio of butt joints in [10], clearly showing the detrimental effect of the axial misalignment. For cruciform welded joints, selected fatigue test results are listed in [11, 12, 13, 14].
The aim of this work is to investigate the effect of axial misalignment for ultra highstrength steel butt joints on the fatigue performance. Furthermore, common stressbased methods will be applied to assess different levels of axial misalignment. Finally, equations for stress magnification factors considering these geometric butt joint deviations are obtained.
2 Fatigue test samples

V0: no axial misalignment, e = 0 mm, e/t = 0

V1: moderate axial misalignment, e = 0.75 mm, e/t = 0.125

V2: high axial misalignment, e = 1.5 mm, e/t = 0.25
According to limitations for axial misalignment given in the standard EN ISO 5817 [15], the first grade V0 without any offset represents quality level B, whereas the second V1 lies in level C and the third offset V2 represents the maximum allowable quality level D.
2.1 Specimen manufacturing
Mechanical properties of base and filler material
Material  Yield strength σ_{y} (MPa)  Tensile strength σ_{u} (MPa)  Elongation A (%)  Impact work ISOV KV (J) 

Base, S1100  ≥ 1100  ≥ 1140  ≥ 8  ≥ 27 @ 20 °C 
Filler, G89  ≥ 890  ≥ 940  ≥ 16  ≥ 47 @ 60 °C 
2.2 Measurement of actual specimen misalignment
Results of distortion measurements
Misalignment level  Intended axial misalignment (mm)  Weld toe condition  Number of measured specimens  Axial misalignment (mm)  Angular misalignment (°)  

Average  Standard deviation  Average  Standard deviation  
V0  0  Aswelded  32  0.17  0.12  0.29  0.19 
V1  0.75  Aswelded  29  0.65  0.18  0.56  0.28 
V2  1.5  Aswelded  27  1.51  0.15  0.29  0.20 
V0  0  HFMItreated  30  0.25  0.21  0.20  0.23 
V1  0.75  HFMItreated  8  0.65  0.32  − 0.05  0.41 
V2  1.5  HFMItreated  8  1.53  0.2  0.09  0.36 
3 Fatigue tests
At this point, it should be noted that the actual cross section at the weld toe is used as basis for calculation of the load to achieve the desired nominal stress level. Therefore, the sheet thickness is measured near the weld toe exhibiting the lowest cross section (see Fig. 3b and c). This has a considerable influence especially for the specimen exhibiting moderate misalignment due to the grinding process of the weld root significantly reducing sheet thickness on the ‘critical’ side of the weld. The average sheet thickness in this critical region for all tested specimens of series V1 is t = 5.83 mm.
Summary of fatigue test results in aswelded condition
Misalignment level  Weld toe treatment  Inverse slope k (−)  Scatter index 1:T_{σ} (−)  Transition knee point N_{k} (−) (P_{S} = 97.7%)  FAT value  Δσ_{runout} (P_{S} = 97.7%)  

(MPa)  (%)  (MPa)  (%)  
V0  Aswelded  4.8  1.18  315,000  229  100  288  100 
V1  Aswelded  4.7  1.16  1,390,000  191  83  194  67 
V2  Aswelded  4.3  1.35  680,000  123  54  146  51 
4 Numerical analysis
The clamping is modelled to comply with the testing facilities for the conducted fatigue tests using rigid clamping. This method assumes a very high stiffness of the rest rig compared with the specimen, otherwise the influence of the specimens secondary bending is not assessed properly. In [27], a holistic study on the effect of secondary bending including a strain gauge measurements and subsequent comparison to numerical results was performed using specimens of similar stiffness and the same testing facilities. The investigations show the use of rigid clamping is sufficient for the present test rig and specimen combination. Therefore, the sheet surface at the clamping jaws is fully clamped including rotational degrees of freedom, only movement in load direction is allowed on one side. At first, a unity load leading to a nominal stress of 1 MPa is applied in order to assess the stress concentration factors. Subsequently, the nominal load is increased to 1000 MPa to study the effect of very high loads. For a proper assessment of these nonlinear geometric effects due to high deformations properly, the large deformation theory has to be enabled.
Stress concentration factors for various misalignment values derived from numerical analysis
Axial misalignment e (mm)  Unity load (σ_{N} = 1 MPa)  σ_{N} = 1000 MPa  

K_{hs} (−) (weld toe)  K_{t} (−) (weld toe)  K_{t} (−) (ground weld root)  Hotspot stress σ_{hs} (MPa) (weld toe)  Effective notch stress σ_{notch} (MPa) (weld toe)  
0  1.025  1.708  –  1061.3  1771.3 
0.75  1.371  2.327  1.978  1360.0  2319.3 
1.5  1.719  2.895  2.717  1660.6  2816.9 
5 Fatigue assessment of aswelded specimen
This section deals with an assessment of the effect of axial misalignment on the fatigue strength of welded ultra highstrength steel butt joints in aswelded condition. Thereby, commonly applied stressbased fatigue assessment methods as suggested in [1] are applied.
5.1 Nominal stress approach
Thereby, the parameter λ stands for a factor dependent on the restraint of the specimen. This equation is initially derived for cruciform and butt joints in [2]. In the case of cruciform joints, restraining of the stiffeners allows several levels of restraint. For butt joints, on the other hand, only two boundary conditions are feasible which are related to the clamping situation of the specimen. If the clamping allows a rotational degree of freedom, λ = 6 is applied, if not, then λ = 6.75. As the test rig does not allow any rotation and its stiffness is far higher compared with the specimen, the latter value applies for the present case. The weld of the investigated specimens is in the middle between the clamping jaws leading to l_{1} = l_{2} = L/2. Therefore, the stress magnification factor is according to this analytical expression not dependent on the length of the specimen.
Stress magnification and stress concentration factors
Axial misalignment e (mm)  k_{m,axial} [−] λ = 6  k_{m,axial} [−] λ = 6.75  k_{m,eff} [−] λ = 6.75  Numerical analysis  

K_{hs} [−] (weld toe)  k_{m,hs} [−]  K_{t} [−] (weld toe)  k_{m,t} [−]  
0  1  1  1  1.025  1  1.708  1 
0.65  1.325  1.366  1.188  1.324*  1.292  2.244*  1.314 
0.75  1.375  1.421  1.236  1.371  1.338  2.327  1.362 
1.5  1.750  1.844  1.603  1.719  1.677  2.895  1.695 
Based on these effective stress magnification factors, the recommended FAT class for butt joints considering the effective sheet thickness FAT106 is adjusted to FAT89 for moderate and FAT66 for high offset values. The result is plotted in Fig. 7. All fatigue tests for axial misalignment level V1 are above FAT106; therefore, further adjustment would not have been required. But for specimens V2 exhibiting high offset values, the use of k_{m,eff} is necessary in order to assess the axial misalignment properly.
Comparison of fatigue assessment methods, combined evaluation
Nominal stress approach  Structural stress approach  Effective notch stress approach  

Misalignment  V0  V1  V2  Comb.  V0  V1  V2  Comb.  V0  V1  V2  Comb. 
k [−]  4.5  4.2  4.4  4.4  4.6  4.3  4.4  4.5  4.6  4.3  4.4  4.5 
1:T_{σ} [−]  1.21  1.33  1.39  1.30  1.19  1.28  1.38  1.25  1.19  1.29  1.38  1.26 
FAT value [MPa]  240  227  231  233  247  229  215  234  411  383  364  392 
Δσ_{Runout} [MPa]  284  –  –  240  287  –  –  228  498  –  –  387 
1:T_{σ,Runout}[−]  1.27  –  –  1.42  1.29  –  –  1.43  1.26  –  –  1.41 
5.2 Structural stress approach
Fatigue assessment using structural hotspot stresses [29] applies basically the same stress magnification factors k_{m} as nominal stress approaches. However, assessment is also possible using the results of numerical studies. Both, the analytical k_{m} and the numerically determined values K_{hs} are listed in Table 5. According to these results, a restraint factor λ = 6 is more consistent with the numerical results than λ = 6.75. As already stated, this could be traced back to a comparably high L/tratio of the specimens reducing the restraint noticeably. Based on these findings, the length between the clamps does influence the stress magnification of the joint in terms of secondary bending in contrast to the analytical expression.
The calculation of every fatigue test results’ structural stress is performed using Eq. 2, the individual specimen misalignment value e and the respective nominal stress range. Figure 12b shows the consequential SN curve in terms of structural stress range, the related values of the statistical evaluation are listed in Table 6. This evaluation method leads to a reduced scatter band for all three individual misalignment levels as well as the combined evaluation in comparison to the nominal stress approach in Section 5.1. Furthermore, the mean P_{S} = 50%lines are almost congruent in the finite life domain showing a sound estimation of the notch effect in this region. However, the structural stress approach is not suitable to describe the shift of the knee point N_{k} to a higher number of load cycles with increasing offset. Thus, a proper assessment of the highcycle fatigue regime is not feasible with this approach.
5.3 Effective notch stress approach
The assessment of the fatigue test results on the basis of the effective notch stress approach is performed by the aid of the stress concentration factor analysis of each specimen type using a reference radius of r_{ref} = 1 mm, see Section 4. Therefore, each data point acquired during the fatigue tests is multiplied by the respective stress concentration factor determined by the use of Eq. 3 and the individual specimen misalignment e. The resulting effective notch SN curve is displayed in Fig. 12c; Table 6 lists the related values. Here, the statistical parameters are almost identical to the results of the structural stress approach. However, the scatter band in the highcycle fatigue regime is still on a high level.
6 Discussion
All three investigated fatigue assessment approaches are within the finite life domain suitable to consider axial specimen misalignment. If the stress concentration is considered separately for every single specimen, a shift up to the fatigue performance of nominally offsetfree specimens is observed. In the case of nominally offsetfree welded specimens, the separate consideration of each specimen’s axial misalignment e results in a minor increase of the FAT value and a decreased scatter band with a slightly reduced value of the inverse slope k. Therefore, even the comparably small offsets of technically plain specimens have a slight influence on the fatigue strength.
For the nominal stress approach, the P_{S} = 97.7%lines of each misalignment fatigue strength level are almost congruent in the finite life domain suggesting a reasonably good agreement. However, the mean P_{S} = 50%lines show a slight rise in fatigue strength with axial misalignment indicating a slight overestimation of the stress magnification. The congruency can be therefore traced back to this overestimation with a simultaneous increase in scatter band.
Structural and effective notch stress approach leads to a very good approximation of the 50% survival probability in the finite life domain. The scatter bands of each misalignment level are similar and lower compared to the nominal stress approach. However, a rise with increasing offset value is still observable. This could be traced back to a quite strong dependency of the local weld topography on the axial misalignment, which is not covered within these investigations.
Each of these linear elastic approaches is based on a multiplication of the nominal stress with a cycletofailure independent misalignment factor. Therefore, a shift of the SN curve’s knee point N_{k} cannot be covered by this means. Therefore, none of the methods is thoroughly suitable for the assessment of the highcycle fatigue domain. It is known that a shallow notch leads to a shift of the SN curve’s transition knee points towards lower cycles [30, 31], but the IIW recommendations suggest a fixed knee point of ten million cycles. Hence, the evaluated data points match quite well in the finite life region, but exhibit some deviations in regions above two million load cycles.
7 Effect of HFMI postweld treatment on fatigue performance
For the investigation of the effect of HFMI treatment on axially misaligned specimens, 16 specimens of offsetfree and eight specimens per misalignment grade V1 and V2 are tested. Thereby, the same test setup and data evaluation procedure as presented in Section 3 is used.
Summary of the fatigue test results in HFMItreated condition
Misalignment level  Weld toe treatment  Inverse slope k [−]  Scatter index 1:T_{σ}[−]  Transition knee point N_{k} [−] (P_{S} = 97.7%)  FAT value  Δσ_{runout} (P_{S} = 97.7%)  

(MPa)  (%)  (MPa)  (%)  
V0  HFMI  4.8  1.14  1,100,000  314  100  332  100 
V1  HFMI  6.4  1.16  1,700,000  347  111  339  102 
V2  HFMI  5.4  1.10  4,200,000  226  72  196  59 
The majority of HFMItreated specimens reveal failure from weld toe. However, for these postweld treated ultra highstrength steel joints, crack initiation is also observed from the weld root, sheet edges, pores or small weld splashes, even in case of specimens without misalignment.
In [32], recommendations regarding to upgrades of the fatigue strength resistance for HFMI posttreated highstrength steel joints are given. The guideline provides design proposals for the improvement in terms of numbers of FAT classes. Thereby, a benefit of one FAT class corresponds to an increase of 12.5% in FAT value. These upgrades are dependent on the yield strength of the base material stepwise starting with σ_{y} = 355 MPa up to the top level above σ_{y} = 950 MPa. Furthermore, the inverse slope k is set to a value of five for all postweld treated joints. For the present S1100 butt joints assessed in nominal stresses, the guideline proposes an increase of eight FAT classes corresponding to a factor of about 2.57.
Assessment of the improvement of the fatigue strength by HFMI postweld treatment
Misalignment level  FAT value aswelded  FAT value HFMI  Improvement  FAT value aswelded according to IIW  Suggested upgrade for HFMI according to IIW  

FAT value (%)  FAT classes  FAT classes  FAT value (MPa)  
V0  229  314  37  2.7  106  8  273 
V1  191  347  82  5.1  89  8  229 
V2  123  226  84  5.2  66  8  170 
The suggestions for improvement due to HFMI postweld treatment in [32] are intended to be based on the initial FAT values suggested in the IIW guideline. Here, the proposed increase of eight FAT classes upgrades FAT106 to FAT273. This value is in very good accordance with the fatigue test results of the specimens without misalignment. The upgrades for misaligned specimens from FAT89 to FAT229 and FAT66 to FAT170 are clearly below the test results. This circumstance definitely confirms the proposed improvements in [32] for the present case. The consequential fatigue resistance SN curves are illustrated in Fig. 13 enabling direct comparison to the fatigue test results; the data is again provided in Table 8.
8 Conclusions
Ultra highstrength steel butt joint specimens are manufactured exhibiting different amounts of axial misalignment. Subsequent measurements confirm three significantly varying axial misalignment values; in detail 0, 10 and 25% of sheet thickness. The angular distortion of the aswelded specimens naturally shows positive values corresponding to a bending towards the weld reinforcement. An additional HFMI treatment leads to a slight negative shift of the angular specimen distortion.
Fatigue tests in aswelded condition reveal a significant influence of axial misalignment on both finite life domain as well as highcycle fatigue region. This can be traced back to secondary bending introduced by the axial offset. The effect is supported by the detrimental change of the local weld topography due to sheet offset. Specimens exhibiting a high offset at about 25% of sheet thickness cannot be treated using the nominal, IIWrecommended FAT values without special consideration of the misalignment.
Numerical investigations based on the effective notch stress concept utilising a fictitious reference radius of r_{ref} = 1 mm are carried out additionally. The geometric shape deviations of the joint are taken into account by individual numerical studies per specimen. These linear elastic finite element simulations show a linear increase of stress concentration factor with the axial offset value. In numbers, an offset of about a quarter of sheet thickness leads to a distinctive increase of local stresses at about 68 %. Furthermore, the numerical results are used to calculate the structural hotspot stress magnification of each specimen type. A comparison of these values to analytical results indicates that the IIWrecommended restraint factor λ for fully restrained clamps may overestimate the stress concentration. Especially for high ratios between clamping jaw distance and sheet thickness a deviation is observable. In such cases, the use of the restraint factor for unrestrained clamps leads to more coinciding results.
The fatigue assessments based on nominal, structural and effective notch stress approach taking into account the sampledependent misalignment factor as stress magnifier are performed. The evaluation based on nominal stresses in combination with the suggested stress magnification factors for axially misaligned joints slightly overestimates the stress magnification of the misaligned joints in the finite life domain. The scatter range of the combined evaluation of all specimens gets narrower with a value of 1:T_{σ} = 1.30. Structural and effective notch stress approaches according to IIW lead to an even more improved scatter range of 1:T_{σ} = 1.26.
Summing up, the axial misalignment results in increased local stress concentration factors due to a change in geometry and additional secondary bending under loading. This affects the scatter band with nominal, structural and notch stressbased evaluation. The proposed equations for structural and notch stresses support an improved fatigue strength assessment of axially misaligned highstrength steel joints referencing a seam without alignment errors.
Fatigue tests with HFMI postweld treated specimens of various misalignment levels indicate that due to the applied posttreatment method, a certain amount of axial misalignment may be tolerated without any reduction in fatigue strength compared to offsetfree HFMI postweld treated specimen. In numbers, for specimens exhibiting an axial misalignment up to 15% of sheet thickness no considerable deviation regarding to fatigue strength compared to the offsetfree specimens is observed. The assessment of these fatigue test results reveals that the IIW recommendations for HFMI treatment lead to satisfactory conservative results if recommended FAT values are used. If the improvement from the actual aswelded to the HFMI fatigue test results is considered, the upgrade is far less pronounced compared with the proposal in the guideline.
Notes
Acknowledgements
Special thanks are given to industry partner for the supply of material and the fabrication work done.
Funding information
This study was financially supported by the Austrian Research Promotion Agency (FFG), who founded the research project by funds of the Austrian Ministry for Transport, Innovation and Technology (bmvit) and the Federal Ministry of Science, Research and Economy (bmwfw).
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