Vol.:(0123456789) Welding in the World (2025) 69:2293–2310 https://doi.org/10.1007/s40194-025-02018-1 RESEARCH PAPER Fatigue strength assessment of welded steel fasteners using structural stress concept with consideration of the mounting pre-load A. Jöckel1 · J. Baumgartner1 · B. Möller1 · M. Timmermann1 · H. T. Beier2 · P. Yadegari2 Received: 27 October 2023 / Accepted: 14 March 2025 / Published online: 23 April 2025 © The Author(s) 2025 Abstract The document presents a comprehensive investigation into the fatigue strength assessment of welded fasteners, specifically bolts and nuts, used in various engineering applications. A fatigue strength assessment approach using a structural stress concept is established, accounting for the influence of mounting pre-loads and residual stresses from the welding process. With the developed approach, the fatigue strength of all investigated variants can be assessed with a scatter of 1:2. The experimental investigations showed that an early decrease in pre-load forces negatively affects the fatigue strength. While pre- load forces can enhance fatigue strength, a reduction in pre-load during service loading must be avoided to ensure a safe life. Keywords  Fatigue strength assessment · Welded steel fasteners · Structural stress concept · Consideration of the mounting pre-load 1  Introduction Welded fasteners such as bolts and nuts are used in many technical applications and designs, e.g., in automotive engineering for fastening aggregates or chassis parts. The increasing use of structurally relevant and cyclically loaded fasteners, as well as the increased use of high-strength mate- rials to exploit further lightweight design potentials, poses increasing challenges for product designers. This is because no fatigue assessment approaches are available for welded steel fasteners (exception: welded head bolt anchors in steel construction, see Eurocode 3 [1]). However, the fatigue strength is a decisive design criterion for the fasteners men- tioned and therefore requires special attention [2]. Due to the subsequent assembly process of such fasteners, high residual stresses may be present in the weld areas, which on the one hand can reduce the fatigue strength (in the case of tensile pre-stresses) or increase it (in the case of compressive pre- stresses). This influence must be considered. For the process design and characterization of the weld area of welded fasteners, regulations (e.g., welding process, welding time) apply as for other welds. A good overview of the individual manufacturing parameters with a focus on welded bolts can be found in Hildebrand and Soltanzadeh [3]. A variety of evaluation concepts are available for the fatigue assessment of welded structures. These can be divided into linear-elastic (stress-based) concepts (nomi- nal, structural and notch stress concept as well as structural strain concept), elastic–plastic concepts (strain concept), and fracture mechanic–based concepts [4]. In the industrial envi- ronment, the nominal, structural, and notch stress concepts are predominantly used for a fatigue strength assessment of welded joints. These concepts, which are based on the linear-elastic material behavior, are included, for example, in the IIW recommendations [5]. The nominal stress con- cept is often the concept with the least effort. However, the prerequisite is always a clear definition of the nominal stress at the failure-determining cross-section, which is rarely the case with geometrically complex components. In the structural stress concept, on the other hand, a structural stress is used as an evaluation variable that cap- tures the influence of the geometry. The structural stress Recommended for publication by Commission XIII - Fatigue of Welded Components and Structures * A. Jöckel andre.joeckel@lbf.fraunhofer.de 1 Fraunhofer Institute for Structural Durability and System Reliability LBF, Darmstadt, Germany 2 Institute for Steel Construction and Material Mechanics IFSW, Material Mechanics Group, Technical University of Darmstadt, Darmstadt, Germany http://crossmark.crossref.org/dialog/?doi=10.1007/s40194-025-02018-1&domain=pdf 2294 Welding in the World (2025) 69:2293–2310 for weld lines is defined as either the surface stress deter- mined at a defined distance from the weld transition notch [6] or the stress extrapolated to the weld, the so-called “hot spot stress”. The latter is used for the structural stress concept in Hobbacher [5]. As an alternative to the com- putational determination of the hot-spot structural stress, a structural stress can also be determined by internal lin- earization of the calculated stress distribution over the sheet thickness [7]. For welded joints with small dimen- sions, such as spot welds, the fatigue strength assessment is based on section forces or directional stresses. As an example for the evaluation, the FESPOW concept [8] can be mentioned, which has meanwhile established itself as a standard for the evaluation of spot welds. By explicitly recording the influence of geometry on the stresses at the weld, a reduction in the number of S–N curves down to two FAT-classes [5] for hot-spot stresses and one for radial stresses [8] is achieved. However, local influences from the weld geometry cannot be recorded with the structural stress concept. If such influences occur recurrently as is typical for weld seams, they are indirectly covered within the scatter range of the structural S–N curve. In the case of the notch stress concept, the detailed shape of a weld seam is directly included in the fatigue strength assessment. For this purpose, the actual radius at the weld transition or root notches is replaced by a defined reference radius rref . The stress calculated in notches mapped in this way can be used directly as a characteristic stress value for a fatigue strength evaluation. The equivalent radius of rref = 1.0mm proposed in Olivier und Koettgen [9] for thick sheets is based on empirical investigations and coincides with a proposal in Radaj [10], which derived a fictitious equivalent radius of rref = 1.0mm based on the hypothesis of the micro-support effect according to Neuber [11]. For the evaluation of spot welded thin sheet joints, the refer- ence radius rref = 0.05mm was successfully developed and applied in Zhang and Richter [12] and can also be justified by fracture mechanics considerations [13]. In Eibl [14], a reference S–N curve for the reference radius rref = 0.05mm was established for line welds on thin sheets. For complex geometry, notch stress can be calculated using numerical methods, such as the finite element method (FEM). The 1st principal stress �1 , to be found in Hobbacher [5] and Sonsino [15], or the equivalent stress according to von Mises �vM [15] can optionally be used as the stress hypothesis. The calculated notch stresses are then compared with permissi- ble notch stresses from standards, such as the IIW standard [5]. For reference radii rref < 1.0mm , endurable stresses are proposed in Sonsino [16] and Baumgartner [17]. Under industrial conditions, a structural stress approach with the lowest possible number of FE elements is pref- erable, since the required number of elements increases considerably when applying the notch stress concept with a reference radius rref = 0.05mm . For this reason, the notch stress concept is not considered in this work. The fatigue strength of welded bolts has been the focus of several studies in the literature. In Fricke and Tchuindjang [18], the influence of welded bolts on the fatigue strength of so- called Holland profiles was investigated. An evaluation based on the notch stress concept with rref = 1.0mm and the stress averaging approach according to Neuber [11] was considered. Agreements with the characteristic values of conventional welded joints were obtained. Similar investigations were also carried out in Bericht 5159/2011 (AiF-Nr. 16.027N) [19]. Here, the radius rref = 0.05mm was considered. Some non- conservative results were obtained from the evaluation, which could be justified by the weld quality. The fatigue strength of weld nuts was investigated experimentally in Balon and Świątoniowski [20] and Ringsberg et al. [2]. In Balon and Świątoniowski [20], the focus was on comparison with the competing clinch connections. In Ringsberg et al. [2], a total of 21 connection variants with different nuts, sheet thicknesses, and steels of different tensile strengths were investigated. An analytical model was set up to describe the fatigue strength, but this only allowed a successful evaluation of only subsets of the variants considered. Transferability of the results to other con- figurations is therefore not guaranteed. In the abovementioned investigations, however, the influence of mounting pre-load and the influence of high-strength materials were not consid- ered. The mounting-related stresses are superimposed on the welding residual stresses resulting from the welding process. Welded joints in as-welded condition are very often assumed to exhibit high tensile residual stresses. For this reason, charac- teristic values for the conservative assumption of high residual tensile stresses are usually recommended in the codes in Hob- bacher [5], AWS D1.1/D1.1M [21], British Standard BS 7608 [22], Eurocode 3 [1], and DVS Merkblatt 0905[23]. In the case of welded bolt connections, which experience additional tensile prestresses from mounting, this assumption initially appears justified. In the case of weld nuts, which are subjected to compressive prestressing during mounting, the assumption is problematic. In both cases, the residual stress fields from the welding and mounting processes overlap. Added to this are the mean stresses and stress amplitudes due to service loads, which can lead to a reduction in the mounting pre-load and a redistribution of the residual stresses. Statements about the remaining residual stress state and its effects on the fatigue strength cannot be made. Corresponding investigations are not known in the literature. To date, no valid data and concepts are available to reli- ably determine the fatigue strength of welded fasteners in loaded connections, considering the influence of mounting pre-loads. Therefore, the aim of this work is to develop a fatigue strength assessment approach for welded steel fas- teners using structural stress concept with consideration of the mounting pre-load. The assessment approach should be 2295Welding in the World (2025) 69:2293–2310 based on linear-elastic FE-analysis, as this analysis type is standard for the fatigue assessment used in the automotive industry. A structural stress approach should be developed, as it requires less modelling, calculation, and evaluation time [24], especially in large simulation models, such as of a body-in-white. All relevant joint characteristics such as structural and weld geometry, influence of high-strength steels on fatigue strength, and effects of weld residual stresses together with mounting pre-loads and their possi- ble degradation due to cyclic loading must be included in the fatigue strength assessment. The basic assumption for the investigations is the applicability of a structural stress concept for the evaluation of welded fasteners under cyclic loading. Regarding the points, the influence of the mechani- cal and statistical variables is to be considered. 2 � Basic information about the used specimens Fatigue tests were performed on two different types of specimens, bolt specimens, and nut specimens (Fig. 1). The fasteners were welded onto sheets with varying sheet thicknesses t and material grade. The zinc layer of the sheets was not removed before the welding process. The dimensions of the sheets were 150 mm × 150 mm in each case. The sheet metal specifications are plotted in Table 1. CR, Cold-rolled; BH, bake-hardening; DP, dual-phase steel; Y, minimum tensile strength; T, longitudinal direc- tion; GI, zinc coating (hot-dip galvanizing); EG, electrolytic galvanizing; U, cold-finished non-exterior skin panels. 2.1 � Bolt specimens The bolt specimens were welded onto the prefabricated sheets using the arc bolt welding method. Twenty-millime- ter-long M6 threaded bolts of strength class 8.8 (SWB130.10 SM6 × 20.8.8) were welded onto the prefabricated sheets. The welds are very irregular in the outer contour (Fig. 2). For clarification, a CT-scan of 210–08 is also shown. For a more detailed characterization of the bolt speci- mens, the local geometry of the seam weld was visualized by cross-sections of each of the three variants of the bolt speci- mens (Fig. 3). In some cases, air inclusions were found in the welding areas, which, however, occurred predominantly Fig. 1   Bolt specimen on the left and nut specimen on the right Table 1   Materials used for specimens manufacturing Sheet description Material Rm Rp0.2 Thickness t 210–08 CR210BH-GI50/50-U 320–400 MPa 210–270 MPa 0.8 mm 210–16 CR210BH-GI50/50-U 320–400 MPa 210–270 MPa 1.6 mm 700–16 CR700Y980T-DP-EG50/50-U 980–1130 MPa 700–850 MPa 1.6 mm 2296 Welding in the World (2025) 69:2293–2310 in the center. Despite the inclusions, the weld quality was rated as standard and subsequently satisfactory by supplier of the automotive industry and OEM that accompanied the research project. 2.2 � Nut specimens For the nut specimens, nuts (thread M8, geometry similar to DIN EN ISO 21670 [25]) were welded onto the prefab- ricated sheets using resistance projection welding. Circular welds and spot welds with three segments were manufac- tured (Fig. 4). For the variants of the nut specimens, cross-sections were taken to evaluate the weld seam area and analyze the local notch geometry (Fig. 5). Satisfactory weld quality was found in each case. As main quality criteria, the melted cross sec- tion with good metallurgical connection between nut and sheet needs to be fulfilled. Sharp notches at the end of the weld zone cannot be avoided and pose, therefore, no quality issue. 3 � Fatigue testing For the bolts and nut specimens, fatigue tests were carried out in each case under axial tensile load without mount- ing pre-load and under oblique tensile load (at an angle of 45° and 90° to the center axis of the fastener) with pre-load (Fig. 6). One adapter (bolt specimen: “bolt adapter”, nut specimen: “nut adapter”) each was used to apply the pre-load forces FP and perform the oblique tensile tests. For the nut specimens with three segments welding, two different positions P1 and P2, related to the load axis, were additionally set (Fig. 6). The sheets with fasteners welded-on were fixed in each case by means of a clamping plate with Fig. 2   Typical weld seams of the bolt specimens Fig. 3   Local geometry of the seam weld of the bolt specimens 2297Welding in the World (2025) 69:2293–2310 an inside diameter of di = 90mm that is bolted with eight screws to the base plate. The base plate itself has also a hole with a diameter of 90 mm, so the plate can move freely. In the case of axial loading, the load was applied with the aid of a screwed-in rod end. In contrast, additional bolt and nut adapters were used to apply defined torques M or mount- ing pre-load forces FP with the aid of a mechanical torque wrench. These adapters and relevant dimensions are shown in Fig. 7. The bolt specimens were tested up to a limiting number of cycles of N = 5 ∙ 106 and the nut specimens up to N = 2 ∙ 106 . Specimens that reached the limiting number of cycles were considered as run outs. The limit number of cycles was chosen to keep the testing time at an acceptable level. All fatigue tests were performed on servo-hydraulic test- ing machines, force-controlled, under room temperature, at test frequencies between f = Hz , with constant force amplitudes Fa , with load ratios of RF = 0.1 , RF = 0.5 , and RF = 10 up to a defined failure criterion. For this purpose, an increase in the max. displacement of the cylinder of the test machines of Δxmax. ≥ 3mm (bolt axial tensile load), Δxmax. ≥ 5mm (nut axial tensile load), Δxmax. ≥ 3mm (bolt oblique tensile load) and Δxmax. ≥ 8mm (nut oblique tensile load) was used in each case. The achieved number of cycles N up to the increase in the max. displacement of the cylinder of the test machines is referred to as the number of cycles to failure Nf  , at which the stiffness reduced significantly (cf. Figure 9). 3.1 � Mounting pre‑load One objective of this study is to identify the influence of pre-load forces FP resulting from the mounting process on the fatigue strength of welded fasteners. For this reason, it is necessary to determine the pre-load force FP resulting from the mounting process in order to take it into account when assessing the fatigue strength using the structural stress con- cept. In the case of the bolt specimens 210–08, plasticization (“cup formation”) of the sheet occurred at a fastening torque of M ≥ 2Nm using the bolt adapter. To limit this cup forma- tion, only torques in the range of 1Nm ≤ M ≤ 2Nm were used for these specimens. These are significantly below the maximum possible torque of M = 8.8Nm typically used for M6 screws. Such plastic deformations during the mounting process do not correspond to a realistic industrial applica- tion and cannot be simulated with a linear-elastic material behavior. Therefore, the range of possible pre-loads/torques in this study is limited for the bolt specimens 210–08 under oblique tensile load. If plastic deformation could be ruled out, e.g., by changing the design of the adapter or others approaches, increasing the tightening torque would lead to an increase in the mounting stresses. If it can be shown that there are no or only small residual welding stresses in the fasteners to be evaluated, these could have a negative effect on the fatigue strength and would have to be consid- ered in the fatigue strength assessment. On the other hand, increasing the pre-load forces could also prevent an early reduction of the existing or acting preload forces due to Fig. 4   Typical weld seams of the nut specimen Fig. 5   Local geometry of the seam weld of the nut specimen, circular 210–16 (1) and 3 segments 210–08 (2) 2298 Welding in the World (2025) 69:2293–2310 cyclical load effects. This in turn could lead to an increase in fatigue strength, as, for example, one-sided lifting of the adapter used here is avoided. Such one-sided lift-off can lead to accelerated specimen failure, as this increases the local bending stresses on the adapter lift-off side of the weld seam of the bolt specimens. For this reason, all possible scenarios must be considered when assessing the fatigue strength. Fo r t h e t h i cke r s h e e t s , t o rqu e s i n t h e r a n g e o f 3.5Nm ≤ M ≤ 5Nm   ( 2 1 0 – 1 6 ) a n d 4Nm ≤ M ≤ 8Nm (700–16) have been used. Unlike the bolt specimens, the welded nut is bolted against the adapter in Fig. 6   Load introduction for axial and oblique tensile loads of bolt and nut specimens 2299Welding in the World (2025) 69:2293–2310 the case of nut specimens. For this reason, undesirable plas- ticizing cannot occur in the sheet metal. As a result, torques in the range of 19Nm ≤ M ≤ 30Nm (210–08, 210–16, and 700–16) could be used. For the investigation of the bolt specimens, a special adapter with applied strain gauges was manufactured (Fig. 7). Four uniformly distributed strain gauges for local strain measurement are attached to the cylindrical inner and outer walls of the adapter surface in the clamping area. Based on the measurement signals, conclusions can be drawn about the stresses and loading of the adapter and thus about the pre-load forces FP . The strain gauges are numbered consecutively, with the inner strain gauges being assigned numbers 1–4 and the outer strain gauges number 5–8. In the case of the weld nut specimens, a modified M8 bolt with internal strain gauges was used to determine the pre-load forces FP. The pre-load forces FP of the bolt specimens were deter- mined using the strain gauge adapter. A validation of the strain gauge adapter was carried out before the fatigue tests have been started. The adapter was loaded using the bolt specimens and a quasi-static testing machine, which allowed the force values F of the quasi-static testing machine to be correlated with the measured and averaged strains �exp on the inside of the adapter. The correlation between the measured and averaged strains �exp and forces F is as follows: Prior to fatigue testing the strain gauge adapter was bolted against the bolt specimens. The defined tightening torques M were applied by means of mechanical torque tools and the resulting strains �exp on the inside of the strain gauge adapter (1)F=13.5N⋅𝜀𝑒𝑥𝑝 𝑚 𝜇𝑚 were determined and subsequently averaged. The pre-load forces FP required for the FE simulation (chapter 4) were determined using Eq. (1). In the case of the nut specimens, mounting tests were carried out using the modified M8 bolt with internal strain gauges. The pre-load force FP was determined based on the measured strains, which were subsequently correlated with the torques M . Nonlinear correlations between tightening torques M and pre-load forces FP can be seen below tighten- ing torques of M < 4Nm . For this reason, a linear regression was performed in a range of 4Nm ≤ M ≤ 30Nm , which was composed as follows: The nut specimens were predominantly carried out with a pre-load force of with FP = 14kN . Just one test series with three segments welded nut with the material 210–16 was also tested with a pre-load force of FP = 10kN. 3.2 � Fatigue failure behavior In all nut specimens and the bolt specimens with the materi- als 210–16 and 700–16, crack initiation occurred starting at the weld seam on the sheet surface of the welded fasteners and propagated through the sheet. Thus, when the stop cri- terion was reached, clearly visible technical crack initiation lengths a on the surface of the back side of a > 5mm can be seen (Fig. 8). Only in a few cases of the bolt specimens 210–08 under oblique tensile load, crack initiation occurred starting from the edge inside of the adapter (Fig. 8) (1). These tests were not considered in the evaluation of the S–N (2)FP = 510 1 m ∙M − 818N Fig. 7   Bolt and nut adapters used 2300 Welding in the World (2025) 69:2293–2310 curves. The exact reason for this type of failure could not be clarified in detail during the investigation. However, mate- rial plasticization of the specimen due to too high pre-load forces and force amplitudes was identified as a possible main reason. The failure location of all specimens used for the evalu- ation of the S–N curves corresponded to the location with the highest stress (hot-spot location) in the notch of the weld seam. Despite the low tightening torque in the range of 1Nm ≤ M ≤ 2Nm (bolt specimen: 210–08), a slight plasti- cization (“cup formation”) can be seen (Fig. 8). During the fatigue tests, the cyclic stiffness of the speci- mens was recorded. In the case of a force-controlled fatigue test, the cyclic stiffness kcyc can be used to describe the dis- placement amplitude of the cylinder xa that results to gener- ate the force amplitude Fa . This is defined as follows: In addition, the cyclic stiffness kcyc can be mapped as a relative value to allow comparability between different stress levels. For this purpose, the so-called initial stiff- ness k0 is used. This describes the existing cyclic stiffness kcyc after transient processes as well as occurring effects such as settling processes and hardening of the material. The cyclic stiffness decrease Δkcyc is therefore calculated as follows: (3)kcyc = Fa xa In the case of the bolt specimens with the material 210–08 under axial tensile load, first visible technical cracking lengths of a ≥ 1mm are visible on the surface of the back side at a cyclic stiffness decrease of Δkcyc = 5% . On the other hand, for specimens with the materials 210–16 and 700–16, especially in the case of low force amplitude Fa , no visible technical cracks can be seen yet. For the failure criterion, the number of cycles N was therefore determined with a cyclic stiffness decrease of Δkcyc = 8% . This is continuously referred to as NΔkcyc=8%. In the case of the bolt and nut specimens, different types of stiffness curves can be observed (Fig. 9). The typical and predominant stiffness curve shows a nearly constant stabilized curve and then an accelerated cyclic stiffness decrease in Δkcyc . In contrast, some of the speci- mens, but especially the bolt specimens with the materials 210–08 and 210–16 with very high load amplitudes Fa , show steadily increasing cyclic stiffnesses kcyc until Nf is reached. A possible reason for this could be plasticization, but this could not be proven in the course of this work. Due to the possible plasticization leading to stiffness increase and, hence, impossible evaluation of the cyclic stiffness drops of Δkcyc = 8% , these specimens were not considered further in this investigation and have been excluded from evaluated S–N curves for this failure criterion. (4)Δkcyc = kcyc k0 − 1 Fig. 8   Typical failure mode images of the backside of bolt and nut specimens under oblique tensile loading 2301Welding in the World (2025) 69:2293–2310 3.3 � Test results In this chapter, the results of the fatigue tests of bolt and nut specimens under axial tensile load without pre-load and under oblique tensile load (with 45° and 90° to the center axis of the fastener) with pre-load are presented and dis- cussed. Here, the respective force amplitudes Fa are plotted against Nf (Fig. 10) and NΔkcyc=8% (Fig. 11). 3.3.1 � Axial tensile loading without pre‑load The nut specimens with spot welds with three segments under axial tensile load show the highest cyclic load capacities with respect to Nf (Fig. 10). Clear influences on the fatigue strength, caused by the material or the load ratio RF used, are not evident. The circular welded nut specimens under axial tensile loading show similar but slightly lower cycles to Nf at identical force amplitudes Fig. 9   Typical decreasing and atypical increasing cyclic stiff- ness curves of a bolt specimen under oblique tensile loading Fig. 10   Results of fatigue tests of bolt and nut specimens, force amplitude Fa plotted against Nf 2302 Welding in the World (2025) 69:2293–2310 Fa in each case compared the nut specimens with three segments spot welds (Fig. 10). This can be explained by an earlier crack initiation and thus longer crack propaga- tion phase of the nut specimens with spot welds compared to the circular welded nut specimens. This has a signifi- cant effect on the sum of the achieved number of cycles to Nf  . With reference to NΔkcyc=8% , it can be seen that the circular welded nut specimens achieve a higher num- ber of cycles to NΔkcyc=8% at similar force amplitudes Fa compared to the nut specimens with spot welds (Fig. 11). This can be explained by more homogeneous local stress distributions leading to a longer crack initiation phase. The bolt specimen test series show lower cyclic loading capacities with respect to Nf compared with the nut speci- men test series (Fig. 10). However, these show compara- ble cyclic load capacities when plotted against NΔkcyc=8% (Fig. 11). The lowest cyclic load capacities of specimens under axial tensile loading are shown by bolt specimens of the specimen test series B_210-08_ax using mild steel sheets, which can be attributed to the low sheet thickness of t = 0.8mm . Here, the cyclic load capacity is approx. a factor of 2 to 3 lower than of bolt specimens of the speci- men test series B_210-16_ax (mild steel: t = 1.6mm). 3.3.2 � Oblique tensile load In the case of the oblique tensile tests and with reference to Nf  , the bolt specimens 700–16 and nut specimens 700–16 and 210–16 exhibit similar fatigue strengths (Fig. 10). Due to the oblique tensile loading of 90°, between the load axis and the center axis of the fastener, the cyclic load capacities are below the specimens with axial tensile loading. The lowest cyclic load capacities are exhibited by bolt specimens 210–08, which can be attributed to the low sheet thickness t . The specimens also exhibit the lowest tighten- ing torques M , which are significantly below the maximum possible torque of M = 8.8Nm. Particularly noticeable are the cyclic load capacities of the bolt specimen test series B-A_210-16_90 (bolt speci- men; mild steel; t = 1.6mm ), which are about a factor of 2 lower than those of B-A_700-16_90 (bolt specimen; high-strength steel; t = 1.6mm ). This can be explained by the present or acting pre-load forces FP during the fatigue tests. In the case of the bolt specimens of test series B-A_210-16_90, changes in the strain amplitudes �a dur- ing the fatigue tests could be determined with the aid of the strain gauge adapter (Fig. 12). The evaluated values of Fig. 11   Results of fatigue tests of bolt and nut specimens, force amplitude Fa plotted against NΔkcyc=8% 2303Welding in the World (2025) 69:2293–2310 strain gauges 1–4 represent the pre-load force FP present. If these show a constant value, a constant pre-load force FP can be assumed. However, this behavior was observed only in the case of the highest torques of M = 5Nm com- bined with low force amplitudes of Fa ≤ 165N (Fig. 12). In this example, an almost constant course of the strain amplitudes �a until N = 5 ∙ 105 cycles can be seen. The decrease in the measured values of strain gauge 2 results in increases in the values of strain gauge 1, strain gauge 3 and strain gauge 4. Shortly after reaching NΔkcyc=8% , the values of strain gauge 2 drop to approx. zero. This means that the adapter lifts off completely on one side. This one- sided lifting subsequently leads to accelerated specimen failure, because of an increase in local bending stresses at the adapter lifting side of the weld seam of the bolt specimens. In the tests with high force amplitudes of Fa > 170N , the values of strain gauges 1–3 and therefore also the pre-load force FP tend to be approx. zero after only a few cycles N (Fig. 13). In these tests, the assumption of a constant pre- load force FP during the fatigue tests cannot be made, which must be considered in a fatigue assessment. The drop in strain gauge 2 values could be caused by plastic effects, by crack formation and crack propagation, or others. A differentiation between the possible influ- ences mentioned was not possible within the scope of Fig. 12   Strain amplitudes vs. number of cycles of specimen 011, test series: B-A_210-16_90 Fig. 13   Strain amplitudes vs. number of cycles of specimen 037, test series: B-A_210-16_90 2304 Welding in the World (2025) 69:2293–2310 this investigation. However, it can be stated that an early decrease of the pre-load force FP led to significantly lower fatigue strengths in the specimens examined here. In addi- tion, it can be assumed that the bolt specimens of test series B-A_210-08_90 also exhibit premature pre-load decrease due to the small sheet thickness of t = 0.8mm and the low torque M , which must be considered in the fatigue strength evaluation. 4 � FEA 4.1 � Bolt and nut specimens, meshing specification FE-models with linear elastic material behavior for the bolt and nut specimens were built with the software Abaqus 2018, Fig. 14 and Fig. 15, using steel with a Young’s modu- lus of E = 210GPa and a Poisson’s ratio of v = 0.3 for the fasteners and the sheets. These models are used for the development of reference S–N curves that can be used for the fatigue assessment of welded steel fasteners with consid- eration of mounting pre-load force FP by means of a struc- tural stress concept. The sheet metal in the failure-critical region is meshed in each case with 16 shell elements over 360° (element type: S4R) and three elements in the radial direction with the element length of lrad = 2mm . The con- nection elements are modeled using beam elements (ele- ment type: B31), adapting them to the real geometry. The connection of shell elements to beam elements is done by using rigid elements (kinematic coupling) following the real local weld geometry. 4.2 � Bolt and nut specimens, oblique loading For the representation of the oblique tensile loads, the adapter is additionally implemented as a solid FE representation consisting of tetrahedral elements (ele- ment type: C3D10) and hexahedral elements (element type: C3D20), with an element edge length of lel = 1.6mm (Fig. 16). For this purpose, the contact between adapter and shell elements is simulated using the contact definition “surface to surface contact” (tangential behavior: penalty, isotropic, friction coeff. of 0.1, normal behavior: “hard” con- tact). The force application point is connected to the adapter using rigid elements (kinematic coupling). These are also used for the connection between the nut or screw head con- tact surface of the adapter and the beam element. In the first calculation step (step 1), the boundary condi- tions are modeled and the pre-load force FP is applied (bolt load-method: “apply force”). In the second calculation step (step 2), the bolt is fixed at its current length (bolt load- method: “fix at current length”), and the force amplitude Fa is applied. Geometric non-linearities were considered due to the contact definition in the simulation. Thus, all speci- mens were simulated and evaluated with the present applied pre-load force and experimentally tested force amplitude. In the case that the contact between adapter and sheet is not opening, the stresses caused by the applied force amplitudes showed an almost linear behavior for all load level. This was true for all specimen with an assumed constant pre- load force during fatigue testing. An early loss of the pre- load force, as observed for B-A_210-16_90 or assumed for B-A_210-08_90, could be considered in the simulation by a very low preload force of FP ≤ 10N , so that a one-sided lift- ing of the adapter was simulated as realistically as possible. In this case, a non-linear load-stress relationship resulted. 4.3 � Determining the structural stress (post‑processing) The structural stress is determined based on the idea behind the FESPOW concept [8]. For this purpose, a cylindrical Fig. 14   FE model bolt speci- men, axial loading 2305Welding in the World (2025) 69:2293–2310 coordinate system (CSYS) is created in the center axis of the fastener (Fig. 17). Subsequently, the results are transformed to this coordinate system and the maximum radial stresses �rad in second element row are extracted at the integration point, Fig. 17. In contrast to FESPOW, not the section load or section moments are used for the evaluation, but the stresses in a certain, fixed distance from the weld, such as it is proposed by Haibach [6] for welded thick plates. The Fig. 15   FE-models of the nut specimens with circular weld and spot welds with three segments, axial loading Fig. 16   FE-models bolt and nut specimens, oblique loading 2306 Welding in the World (2025) 69:2293–2310 determination of the element radial stress amplitude �rad,a is then performed according to: Subsequently, the radial stress amplitude �rad,a is corrected by a sheet thickness factor K according to Rupp et al. [8], which is determined as follows: The structural stress amplitude �S,a is thus given by: (5)�rad,a = �rad,step2 − �rad,step1 (6)K = 0.6 ∙ √ t (7)�S,a = K ∙ �rad,a 5 � Fatigue strength assessment Figure 18 shows the structural stress amplitudes �S,a plot- ted against Nf including both results for nut and for bolt specimens, whereby all simulations were carried out with consideration of the “theoretically” applied pre-load force FP caused by the mounting process. This means that the observed early decrease of pre-load force FP of the two test series B-A_210-16_90 and B-A_210-08_90 were not taken into account (simulated “incorrectly”). No additional mean stress transformation was deliberately performed since no significant influence by the investigated load ratios RF on the fatigue strength could be detected during the analysis of the fatigue results. Predominantly, the test series of the bolts and nut speci- mens show similar cyclic stress capacities, with the nut spec- imens of test series N-A-3S_210-16_45_0.1_P2 showing the highest cyclic stress capacity (Fig. 18). In direct comparison with the other test series, the test series B-A_210-16_90 and B-A_210-08_90 exhibit cyclic stress capacities that are too low by a factor of approx. 2 to fall within the scatter range of the other test series. This is due, among other things, to the early decrease the of pre-load force FP mentioned in chap- ter 3.3.2, which shows a relevant negative influence on the fatigue strength. This is caused by the one-sided lifting of the adapter, which subsequently leads to accelerated speci- men failure, because of an increase in local bending stresses at the weld seam of the bolt specimens. For this reason, Fig. 17   Determination of structural stress based on FESPOW concept [8] Fig. 18   Structural stress amplitudes �S,a plotted versus Nf 2307Welding in the World (2025) 69:2293–2310 to correctly simulate the one-sided lifting of the adapter, specimens of test series B-A_210-16_90 and B-A_210- 08_90 were simulated only with a very low pre-load force of FP ≤ 10N for the development of the reference S–N curve (Figs. 19 and 20). Since the evaluation without considera- tion of the pre-load force FP leads to a more conservative Fig. 19   Reference S–N curves, for fatigue assessment of welded steel fasteners with consideration of mounting pre-load by means of structural stress concept, Nf Fig. 20   Reference S–N curves, for fatigue assessment of welded steel fasteners with consideration of mounting pre-load by means of structural stress concept, NΔkcyc=8% 2308 Welding in the World (2025) 69:2293–2310 fatigue strength assessment, the procedure is recommended for an industrial application. This applies to the case where plasticizing or pre-load degradation cannot be ruled out for the planned service life. Figure 19 shows the reference S–N curves evaluated using the maximum likelihood method [26] with reference to Nf and consideration of the present applied pre-load force FP . The following parameters result referring to a stress ratio of Rs = 0.1, which has been applied to the majority of fatigue tests: Slope before the knee point, k: 4.4 Slope after the knee point according to [27], k∗: 22 (specified) Cycles at the knee point according to [27], Nk: 107 (specified) Stress amplitude at the knee point, �S,a,PS=50%,Nk : 59 MPa Stress amplitude at the knee point, �S,a,PS=97.7%,Nk : 35 MPa Scatter in stress direction, Tσ: 1:1.9 Figure 20 shows the reference S–N curves evaluated using the maximum likelihood method [26] with reference to NΔkcyc=8% and consideration of the present applied pre- load force FP . The following parameters result referring to a stress ratio of Rs = 0.1, which has been applied to the major- ity of fatigue tests: Slope before the knee point, k: 4.5 Slope after the knee point according to [27], k∗: 22 (specified) Cycles at the knee point according to [27], Nk: 107 (specified) Stress amplitude at the knee point, �S,a,PS=50%,Nk : 46 MPa Stress amplitude at the knee point, �S,a,PS=97.7%,Nk : 26 MPa Scatter in stress direction, Tσ: 1:2.0 For industrial application, the reference S–N curve is recommended at a survival probability PS = 97.7% . In the literature, the scatter Tσ of reference S–N curves of welded joints can be found in the range of 1 ∶ 1.7 to 1 ∶ 2.03 [28]. Thus, the scatter values of the reference S–N curves of Tσ = 1 ∶ 1.9 (reference to Nf  ) and Tσ = 1 ∶ 2.0 (reference to NΔkcyc=8% ) are in a typical range for welded joints. Due to the scatter values Tσ of the reference S–N curves, which are typical for welded joints, the fatigue strength assessment, limited to the materials, fasteners, and test conditions used, is rated as good and goal-oriented. 6 � Consideration of the load ratio and pre‑load force Based on the bolt and nut specimens investigated under axial tensile load without pre-load and under oblique tensile load with mounting pre-load, no significant influence of the inves- tigated load ratios RF ( RF = 0.1 , RF = 0.5 , and RF = 10 ) on the fatigue strength could be determined. Similar behavior was also observed in Fricke and Tchuindjang [18] and was attributed to weld residual stresses, which were also identi- fied in Bericht 5159/2011 (AiF-Nr. 16.027N) [19] on welded bolt specimens. For this reason, it is reasonable to assume that weld residual stresses are also present in the bolt and nut specimens investigated here. On that basis, no mean stress transformation was delib- erately carried out, since no significant influence of the investigated load ratios RF on the fatigue strength could be determined and the results already showed a scatter Tσ typi- cal for welded joints. For practical application, the reference S–N curves by means of the structural stress concept with reference to Nf and NΔkcyc=8% , and for survival probabilities of PS = 97.7% are recommended. Based on this, the fatigue strength assessment, limited to the materials, fasteners, and test conditions used, is rated as good and goal-oriented. When analyzing the fatigue tests of the bolt specimens under oblique tensile load with mounting pre-load, early and significant decreases of the pre-load force FP could be detected. These led to significantly lower fatigue strengths in the investigated specimens. The exact reason for the early decreases of the pre-load force FP could not be clari- fied within the scope of this work. However, it is assumed that it might be explained by a plastic deformation of the plate in combination with a reduction of roughness in the contact areas, as it typically occurs at bolted connections. In addition, early crack formation and crack propagation under cyclic loading conditions may have occurred. A differentia- tion between the possible influences mentioned was not pos- sible within the scope of this investigation. In extreme cases, the decrease of the pre-load force FP leads to a one-sided lifting of the adapter, which in turn leads to an increase in local bending stresses at the weld seam of the bolt specimens and consequently has a negative influence on the fatigue strength. No negative influence on the fatigue strength was found when increasing the pre-load forces FP . On the con- trary, it was observed that with increasing pre-load forces FP , the force amplitude Fa that can be applied increased or, applying the same force amplitude Fa , the fatigue strength increased. This can be attributed to the adapter used, since the one-sided lifting of the adapter and thus local bending stresses at the weld seam of the bolt specimens are reduced as the pre-load force FP increases. The significant influence of the early decrease of pre- load force FP on the fatigue strength is illustrated when considering the tolerable structural stress amplitudes �S,a plotted against Nf  . In direct comparison with the remaining specimen test series, the welded bolt specimen test series B-A_210-16_90 and B-A_210-08_90 exhibit cyclic stress capacities that are too low by a factor of approx. 2 to fall within the scatter range of the other test series. This can be attributed to the mentioned early decrease of the pre-load force FP . Therefore, for the development of the reference 2309Welding in the World (2025) 69:2293–2310 S–N curves, specimens from test series B-A_210-16_90 and B-A_210-08_90 were simulated and evaluated only with a very low pre-load force of FP ≤ 10N . This approach leads to a more conservative fatigue strength assessment, which is especially recommended for an industrial application, if no further information about the joint and its behavior during service is available. This applies if plasticizing or an early decrease of pre-load force FP cannot be ruled out for the planned service life. 7 � Conclusions and outlook These main conclusions can be drawn from the presented investigation: • Based on the welded bolt and nut specimens examined, no significant influence of the load ratios RF examined on the fatigue strength could be determined. • When analyzing the fatigue tests of the bolt specimens under oblique tensile loading with mounting pre-load, early and significant decreases of the pre-load force FP were found, which showed a negative influence on the fatigue strength. Therefore, a possible strong reduction of the pre-tension of bolts in real structures due to service loads must be avoided. • In principle, no negative influence on the fatigue strength was found when increasing the pre-load forces FP . On the contrary, it was observed that the applied force amplitude Fa increased with increasing pre-load force FP , or, conse- quently, the fatigue strength increased for the same force amplitude Fa. • It could be shown that specimens with demonstrably early decrease of the pre-load force FP exhibit cyclic stress capacities that are too low by a factor of approx. 2 to fall within the scatter range of the other test series, if these are incorrectly simulated from the mounting force. When these specimens are simulated and evaluated with only a very low pre-load force of FP ≤ 10N , they show similar endurable structural stress amplitudes �S,a com- pared with the rest of the specimens. In the case that a pre-load reduction due to yielding or self-loosening cannot be ruled out, this approach is recommended for industrial application. • For a fatigue assessment, limited to the materials and fasteners used as well as the test conditions, a reference S–N curve by means of the structural stress concept with reference to NΔkcyc=8% and survival probabilities of PS = 97.7% , a tolerable stress amplitude �S,a = 26MPa at N = 107 cycles and a slope of k = 4.5 are recommended. For a less conservative failure criterion related to Nf  , this reference S–N curve refers to the structural stress amplitude �S,a = 35MPa at N = 107 cycles and a slope of k = 4.4. The scatter values of Tσ = 1 ∶ 2.0 (reference to NΔkcyc=8% ) and Tσ = 1 ∶ 1.9 (reference to Nf  ) are in a typical range of these for welded joints. • If it can be shown that there are no or only small residual weld stresses in the fasteners to be evaluated or that the stress ratios Rσ deviate significantly, a mean stress trans- formation should also be performed. Based on the extensive tests, a reliable fatigue assessment approach for pre-loaded welded fasteners was developed. Further test with additional conditions can be performed to identify influences such as varying sheet thicknesses, materi- als, welding parameters, variable amplitudes, and different sizes of fasteners on the fatigue strength. This will allow the developed reference S–N curves to be validated, or to give evidence, how the method should be further developed or modified, if required. In addition, the structural stress concept should be extended to with further joining and specimen types as well as complete assemblies or structural components to verify its applicability in the industry. Author contribution  All authors contributed to the conception and design of the study. The planning, preparation, testing and evaluation of the fatigue strength tests were carried out by B. Möller, M. Tim- mermann and H. T. Beier. The numerical investigations were carried out by A. Jöckel, J. Baumgartner and P. Yadegari. The first draft of the manuscript was prepared by A. Jöckel and reviewed and corrected by all authors. All authors have read and approved the final manuscript. Funding  Open Access funding enabled and organized by Projekt DEAL. This report is the scientific result of the research project “Fatigue assessment of welded fasteners under mounting pre-load”, IGF-project-no. 20818 N, funded by the Forschungsvereinigung Auto- mobiltechnik e.V.—FAT via the AiF as part of the program to pro- mote joint industrial research (IGF) by the German Federal Ministry of Economic Affairs and Climate Action (BMWK) by decision of the German Bundestag. Data availability  The data that support the findings of this study are available from the corresponding author upon reasonable request. Declarations  Ethical approval  Not applicable. Competing interests  The authors declare no competing interests. Open Access  This article is licensed under a Creative Commons Attri- bution 4.0 International License, which permits use, sharing, adapta- tion, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. http://creativecommons.org/licenses/by/4.0/ 2310 Welding in the World (2025) 69:2293–2310 References 1. DIN EN 1993-1-9:2010-12. 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Fatigue strength assessment of welded steel fasteners using structural stress concept with consideration of the mounting pre-load Abstract 1 Introduction 2 Basic information about the used specimens 2.1 Bolt specimens 2.2 Nut specimens 3 Fatigue testing 3.1 Mounting pre-load 3.2 Fatigue failure behavior 3.3 Test results 3.3.1 Axial tensile loading without pre-load 3.3.2 Oblique tensile load 4 FEA 4.1 Bolt and nut specimens, meshing specification 4.2 Bolt and nut specimens, oblique loading 4.3 Determining the structural stress (post-processing) 5 Fatigue strength assessment 6 Consideration of the load ratio and pre-load force 7 Conclusions and outlook References