1 Introduction

Friction stir welding (FSW) is a solid-state joining process performed with a non-consumable tool whose main features are a pin and a shoulder. The rotating tool is sunk in the metal to join and, after an initial short time to heat-up the metal, is fed forward to create the welds. No filler material is needed, even if examples of its use can be found [1]. The friction between pin and shoulder and workpiece together with plastic deformation generate heat that softens the materials. Pin rotation drags the softened material from its front side towards its rear side while stirring it. This generates the welding [2, 3]. This technique aroused interest because of its capacity to overcome problems related to arc-welding of highly alloyed aluminium series, e.g. alloys 2000 and 7000 [4]. Nevertheless, various papers have proven for FSW to be able to join dissimilar materials, e.g. [5,6,7], and to be suitable for many joint geometries, e.g. T joint, fillet joint and edge butt joint [4].

Laser beam welding (LBW) is a fusion welding technique that satisfies industry needs for high production speed and automation. When a laser medium is excited, a laser beam is generated. It is focused in a very narrow spot trough a delivery system, e.g. a lens system. The beam energy melts the material involved to create the weld seam [8]. LBW offers multiple advantages when compared to other fusion welding techniques: high power density focused in a very tight spot. This allows faster and deeper welding, smaller heat-affected zone, lower distortions and better mechanical properties [9].

When designing structural components, durability and reliability are of major concern. Therefore, in case of cyclically loaded structural members, a fatigue assessment needs to be carried out. Available guidelines and recommendations [10,11,12] contain methods for the assessment, e.g. nominal and local methods.

Nominal stress approach allows to perform the assessment from a macroscopic perspective requiring the knowledge of the nominal stress acting on the structural detail. As a drawback, determining the nominal stress in a complex structure can result in not being a trivial task.

Notch stress and effective stress approach are local methods. They require evaluating the maximum stress resp. the effective stress in the notch ligament. For this, a finite element analysis has to be performed developing a model in which the weld root and weld toe notches are rounded with a fictitious radius, rref = 0.05 mm typically proposed when assessing thin walled sheets [13].

In the present work, the above-mentioned approaches are applied with the aim of making a comparison between them. Based on the achieved results, it is investigated which approach better fits the task of carrying out a fatigue assessment with the addressed joints, i.e. FSW and LBW overlap welded joints and LBW butt welded joints. Purpose of the project is to better exploit the lightweight potential of the new high strength aluminium alloys and non-conventional welding processes such as friction stir and laser beam welding (FSW, LBW).

2 Specimens and test campaign

The specimens were made using 1.5-mm- thick sheets of EN AW-7075 T6 aluminium. The welding process was carried out at the Kassel University using FSW or LBW techniques. The friction stir welding was performed with rotating speed of 800 rpm, travelling speed of 1200 mm/min and a 2∘ tilt angle. LBW parameters are shown in Table 1.

Table 1 LBW overlap welded joints parameters
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Finally, ten friction stir welded and fourteen laser beam welded overlap joints were produced. The specimen dimensions were 200 mm × 50 mm × 1.5 mm, Fig. 1. Cross-section pictures from the actual specimens are shown in Fig. 2a, b.

Fig. 1
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Sketch of an overlap welded specimen

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Fig. 2
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Cross-section pictures

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The misalignment between the joined sheets was measured using a laser system. Three measurements were performed on each specimen along the dashed lines shown in Fig. 3. Figure 4 shows an example of the recorded profile of a FSW specimen. Minimum, maximum and average misalignment measured angles were respectively 0.01∘, 2.20∘ and 0.89∘. The maximum misalignment measured was smaller than three degrees. Since no correlation between misalignment and fatigue life could be identified, its effect on the fatigue life was not considered.

Fig. 3
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Along the grey dashed lines were taken the laser measure

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Fig. 4
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Plot of the misalignment angle trend in a FSW specimen

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Load controlled fatigue tests were carried out using a stress ratio R = 0.1 and a frequency in the range 30 to 50 Hz. The specimens were mounted leaving a free length of 150 mm between the clamping devices in the axial direction. The test rig had two stop criteria, i.e. specimen complete fracture or a specimen stiffness loss, under 80 % of the initial one. Figure 5 shows the experimental results in terms of the nominal stress amplitude achieved from both LBW and FSW specimens. The nominal stress is defined as force divided by the cross-section area of the plate (\(\sigma _{n}=\frac {F}{t \cdot l}= \frac {F}{{1.5}\text { mm}\cdot {50}\text { mm}}\)). Friction stir welded joints resulted in having higher endurable stresses compared to the one of laser beam joints, \(\sim {2.7}\) times at 2× 106 cycles. Although three different welding parameters were used for the LBW specimens, no remarkable differences in specimens fatigue life were observed. The results are therefore summarized.

Fig. 5
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S-N curves of LBW and FSW overlap joints

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3 Literature research

During literature research, forty-three papers focusing on the fatigue life of FSW joints were collected with the aim of creating a database containing the available experimental S-N data found in each paper. Additionally, the provided information, i.e. material, type of joint, welding parameters and testing conditions were stored.

Table 2 shows the list of papers providing S-N data that were included in the above-mentioned database. Weld types, different from butt joint and overlap joint, were gathered but not taken into account since they lie outside the scope of the present work.

Table 2 Table containing the list of the paper addressed
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In some cases, data from some papers had to be excluded. One recurrent reason was that some experimental results appeared to be oddly scattered, e.g. data from [41]. Other reason was the use of a so-called anti-bending systems when testing, e.g. in [42].

From the data collected, test series, used in the performed assessments, were isolated, Table 3. Although many papers focused on FSW butt welded joined specimen, they have been identified as not eligible for the local methods. The reasons are either the lack of cross-section pictures in the correspondent paper that did not allow developing a finite element model or the use of specimens subjected to surface imperfections grinding, thus entailing no relevant geometrical notches to address in a finite element analysis.

Table 3 Isolated test series shown with paper reference and number of data set (No.)
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4 Finite elements analysis

Based on the isolated test series, a model for each of the available cross-sections was created to exactly represent their geometry. In the end, four different main geometries distinguished the models as they are shown in Fig. 6a, b, c and d.

Fig. 6
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a–d Model cross-section samples

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It was necessary to design two different geometries for the FSW overlap welded joints since cross-sections taken from the paper were symmetric as shown in Fig. 7 [29] in comparison to the “asymmetric” joints tested within the current project, Fig. 2b.

Fig. 7
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Overlap cross-section [29]

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Figure 8 shows the applied load and constraint. In the FE model, two partition were created to recreate the interfaces between the clamping device of the test rig and the specimen. Thus, in the left end of the specimen, the upper and lower edges were picked and all degrees of freedom were fixed. On the other end, all the degree of freedom of the upper and lower edges were coupled with a reference point using a kinematic coupling condition. The reference point was constrained in all directions besides the x-direction in which the load was applied.

Fig. 8
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Model section showing an overview of load, coupling and constraints

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All the dimensions used to develop the geometry of the sections were taken from the cross-sections, e.g. Fig. 2a. Since the maximum misalignment angle was smaller than three degrees, no misalignment of the sheet was included in the simulation.

Finally, maximum equivalent stress at the notch was derived to perform the notch stress assessment. To derive the effective stress, a 1-mm path perpendicular to the notch tip edge and entailing the maximum effective stress is chosen, as shown in Fig. 9.

Fig. 9
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Contour plot showing the path with 65∘ inclination and its stress gradient plotted on the side. ρ∗ = 0.125 mm [50] and ρ∗ = 4 ⋅ a [51]

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5 Parametric study on FSW joints

The difference between the symmetric and asymmetric FSW geometries was addressed to find out if it was affecting the resulting maximum stress. Thus, two models were designed that differed only for the direction of one notch and they were repeatedly simulated while making the notches inclination steeper with the same angle α on both sides. Figures 10 and 11 show the results of the maximum stress divided by the nominal stress plotted over the angle of the notch curvature. In each plot, a sketch is available showing how the geometry was changing.

Fig. 10
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Local stress normalized over nominal stress plotted over the increasing angle of the defect. Symmetric geometry

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Fig. 11
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Local stress normalized over nominal stress plotted over the increasing angle of the defect. Asymmetric geometry

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What is significant is the opposite behaviour that emerged. Hence, while in the symmetric model, the maximum stress was increasing because, on the loaded side, a steeper “defect” was entailing a reduction of the effective sheet thickness (EST), in the asymmetric one the maximum stress was decreasing. This is because no EST reduction is reported in this case; moreover, as can be observed by focusing on the given contour plots, in the asymmetric model, the flow of the stress does not need to go around the “defect” on the loaded side with smaller stress intensification.

6 Fatigue assessment

The main focus of this work is to carry out two fatigue assessments of FSW and LBW welded joint, the first one of butt welded geometry and the other for overlap welded geometry. Hence, three approaches were used, the nominal stress approach and two local approaches, i.e. notch stress and effective stress approach. All of them are elastic methods thus requiring a linear elastic material law when carrying out finite element analysis.

Each assessment was performed in two stages. Initially, a comparison was made between design S-N curve and the S-N data. Later, data stress ratio was transformed to R = 0.5 following the recommendations for aluminium, and category I case in [10]. Thus, the stress amplitude σa(Rt) was evaluated with Eq. 1 where \(\bar {R}\) stand for initial stress ratio and Rt for target stress ratio. The mean stress σm was not affected by variation of the R.

$$ \sigma_{a}(R_{t})=\frac{1.2 - 0.4\cdot R_{t}}{1.2 - 0.4\cdot\frac{ \sigma_{m, \bar{R}}-\sigma_{a, \bar{R}}}{\sigma_{m, \bar{R}}+\sigma_{a, \bar{R}}}} \cdot\sigma_{a, \bar{R}} \qquad-1 \leq \bar{R} \leq 0.5 $$
(1)

Then, for each assessments, a S-N curve is evaluated using maximum likelihood method as proposed by Spindel and Haiback [52]. To perform the evaluation, some assumptions were made: low residual stresses, a fixed inverse slope of k = 5 and knee point set to 1× 107 cycles. Finally, the endurable stress at 2× 106 cycles with Pσ = 97.7% is evaluated and rounded to the nearest FAT value in [10]. Using this stress should lead to a conservative assessment. Table 4 shows the FAT class and inverse slope used for each design S-N curve in the assessments and the source. For the effective stress approach, a microstructural length of ρ∗ = 0.125 mm [50] was used.

Table 4 Design S-N curve with Pσ = 97.7% and knee point at 1 × 107 cycles, used in each approach. (1) only butt welded joints; (2) only overlap welded joints; (3) ρ∗ = 0.125 mm
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6.1 Nominal stress assessment

In the nominal stress assessment, FAT classes were chosen from the IIW recommendations [10], although they are not meant for either FSW or LBW joints. Hence, for the butt welded joints, detail 216 was chosen which recommend a FAT 28 for butt welded joint with no defects spotted with NDT inspections such as a visual one. No structural detail was matching the addressed overlap welds. Therefore, the detail number 614 (overlap joint with failure form the root, FAT 12) which reassembles the loading of the joint closely was chosen.

It is worth mentioning that no FSW butt joint S-N data were included in the evaluation with the nominal stress approach, since this data could not be used for evaluation with the linear-elastic local methods. In order to allow a comparison of the different approaches, the dataset should be the same.

Figure 12 shows the comparison between the nomial S-N data and the correspondent design S-N curve. The LBW butt joints showed a high fatigue strength in comparison to the considered design S-N curve, thus resulting in a conservative assessment. In case of overlap welded joints, the curve was partly non-conservative. Overlap welded joints emerged as a critical detail due to their typical crack like notches that weakens the joint section.

Fig. 12
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Nominal stress approach, comparison between considered data and designed curve

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Figure 13 shows the S-N curves evaluated with the maximum likelihood criterion as described at the beginning of Section 6 and in the box, the conservative endurable stress is documented for each plot. The allowable stress of the butt welded joints can be increased up to 40 MPa, circa 1.4 times the FAT 28. The overlap welds, partly due to the big scatter of data, requires instead an endurable stress of 8 MPa lower than the chosen FAT 12 which is furthermore the lowest FAT class recommended in [10].

Fig. 13
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Nominal stress approach, evaluation of Pσ = 97.7% endurable stresses at 2× 106 cycles

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6.2 Notch stress assessment

The notch stress approach requires a finite element analysis as described in Section 4 in order to derive the maximum local stress resp. notch factors Kt, Eq. 2. The aim of the analysis is to derive endurable notch stresses for each specimen type. These endurable notch stresses are compared to the proposed design S-N curve in [50], suggesting a FAT 160 and k = 5 together with von Mises criterion, Fig. 14.

$$ K_{t}=\frac{\sigma_{loc, a}}{\sigma_{N, a}} $$
(2)

As a consequence of not having included any correction factor for the LBW butt welded joint, characterized by a mild notch [53], the assessment led to a partly non-conservative result. Indeed, data contributing to this result all belong to the above-mentioned joint type whose maximum stress is located at the weld toe which has a wide opening angle thus referred to as a mild notch. This matched a Kt of circa 1.6 resulted from the finite element analysis of this welds.

Fig. 14
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Notch stress approach, comparison between considered data and designed curve (left), evaluation of Pσ = 97.7% endurable stresses at 2× 106 cycles (right)

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In [13] is specified that for rref = 0.05 mm notch stress assessment, lower FAT classes are to be chosen in case of crack initiating at the weld toe. Thus, including mild notches leads to a borderline condition for the assessment. If the LBW butt welded joints are excluded, a slightly conservative assessment is achieved.

For this method, a conservative endurable stress, derived as described at the beginning of Section 6, is 80 MPa, Fig. 15. When the same procedure is carried out while taking into account only the FSW overlap welded joints a 220 MPa endurable stress is derived that is even higher than the FAT 160 recommended. This can be explained with the Kt > 20, usually resulting from the FE analysis of FSW overlap joint models, that were entailing a very high stress peak.

Fig. 15
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Notch stress approach, comparison between considered data and designed curve (left), evaluation of Pσ = 97.7% endurable stresses at 2× 106 cycles (right)

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6.3 Effective stress assessment

The effective stress requires to address the stress in the notch ligament and can be evaluated using two different methods, i.e. microstructural length ρ∗ and critical distance a and using respectively the formulation in Eq. 3 from [54] and Eq. 4 from [55]. The effective stress was evaluated along a hundred paths spreading in radial direction from the rounded notch tip. Later on, the maximum effective stress achieved was chosen instead of the effective stress occurring on the same path including the maximum notch stress.

$$ \sigma_{eff} = \frac{1}{\rho^{*}} {\int}_{0}^{\rho^{*}}\sigma(x) dx $$
(3)
$$ \sigma_{eff}=\sigma(x=a) $$
(4)

In [50], a design S-N curve with a FAT 80 and a slope k = 5 was derived for the data using the von Mises stress. Moreover, ρ∗ = 0.125 mm was evaluated to fit data addressed in the above-mentioned paper. It was decided to carry out the assessment both using this microstructural length and the one evaluated for the data addressed.

Thus, an iterative procedure using the maximum likelihood criteria was used to evaluate the scatter of the S-N curve while increasing ρ∗ stepwise, see [56]. At the end, the scatter was evaluated over the microstructural length with the result that ρ∗ = 0.280mm was leading to the smallest scatter, Fig. 16. The effect of bigger ρ∗ was to mitigate the stress peaks thus decreasing the difference in the effects of severe and mild notches.

Fig. 16
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Scatter in the load direction plotted versus the ρ∗. The minimum value is specified on the side of the black dot

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In the left plot in Fig. 17, a comparison between the design S-N curve FAT80 and the data derived with the microstructural length ρ∗ = 0.125 mm is plotted. The assessment leads, in this case, to a partly non-conservative result. In the right plot in Fig. 17, the effective stress of data for ρ∗ = 0.280 mm is plotted that leads to a slightly smaller scatter. Since no FAT class for such a microstructural length was derived in literature, no comparison with a design curve was achieved.

Fig. 17
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Effective stress approach, comparison between considered data and designed curve for a microstructural length ρ∗ = 0.125 mm (left). Effective stress evaluated for a microstructural length ρ∗ = 0.280 mm (right)

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Next to the assessment with the stress averaging approach, evaluation of effective stresses by the critical distance approach was carried out. The ρ∗ = 4 ⋅ a formulation from [51] allowed the evaluation of a critical length each microstructural length; thus, an assessment each was performed. However, assessments performed with the critical distance were always leading to slightly higher effective stress values so the other method was preferred for the sake of conservativeness.

Finally, as shown in Fig. 18, a conservative endurable stress (PS = 97.7%, R = 0.5) was evaluated for both values of ρ∗, as described at the beginning of Section 6, resulting in FAT40MPa for ρ∗ = 0.125 mm and FAT36MPa for ρ∗ = 0.280 mm.

Fig. 18
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Effective stress approach, evaluation of Pσ = 97.7% endurable stresses at 2 × 106 cycles

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7 Conclusion

Following main results have been achieved in this work:

  • The FEM analysis of asymmetric geometry of the crack-like roots encountered in the Allegro FSW overlap welded specimens led to smaller stress concentration factors Kt, Section 5. This was indirectly confirmed from the resulting higher fatigue strength achieved in the test. No similar cases of such an asymmetric geometry were found in other papers

  • Given the remarkable difference in the nominal endurable stresses of butt welded joints and overlap welded joints, a structural detail for each weld geometry was chosen, Section 6.1. The nominal assessment of butt welded joints led to a remarkable conservative result thus suggesting that a higher FAT class could be designed. The nominal assessment of overlap welded joints led to a partly non-conservative result. However, it is advisable to highlight the facts that up to now, no specific FAT-classes exists for FSW joints.

  • FAT class addressed in the notch stress assessment led again to a partly non-conservative result. Beside the fact that no specific FAT-classes exist for FSW joints, it is worth mentioning that, in the application of the notch stress approach, the influence of mild notches has not been considered.

  • The combination of FAT class and microstructural length, addressed in the effective stress approach, led to a non-conservative result. For the data considered, a microstructural length entailing the smallest scatter in load direction was achieved (ρ∗ = 0.280 mm) and a 97.7% safe endurable effective stress at 2 × 106 cycles was evaluated.

  • Based on results achieved in this work, the effective stress approach seemed to provide a more reliable evaluation of the addressed data among the performed approaches:

    • It offers the smallest scatter in load direction for the addressed data;

    • In contrast to the notch stress approach, the stress gradients need to be considered thus leading to a slightly higher effort in application.