Abstract
The framework for a fatigue assessment of welded joints under service loading conditions of crane structures from the low cycle to the high cycle fatigue regime includes the consideration of elasticplastic material behavior, variable amplitude loading, and acceptable calculation times. Therefore, an integral treatment of butt joints has been developed for fatigue life estimation. The butt weld is considered in its entirety, so that it can be described by its cyclic behavior. The evaluation of the cyclic stressstrain behavior and trilinear strainlife curves of butt joints for different highstrength, finegrained structural steels, derived by straincontrolled fatigue tests, is the basis for this description. This procedure is not limited to conventionally applied gas metal arc welding only, but also the fatigue assessment of laser beam welding is possible, for example. Cyclic transient effects have been analyzed and a distinctive cyclic softening is described by linearization of RambergOsgood parameters, depending on the damage content of each cycle derived from constant amplitude, straincontrolled tests. On the basis of the cyclic behavior in combination with memory and Masing behavior, a simulation of the stressstrain paths of investigated butt welds, under constant and variable amplitude loading, has been performed. Damage parameters are used to accumulate the damage cycle by cycle in order to derive the fatigue lifetime. Finally, calculated fatigue lives were compared with experimentally determined lives, showing the impact of this procedure.
Introduction
In the design and manufacture of modern steel assemblies, permanent joining by welding is still common. The crane industry makes use of gas metal arc welding (GMAW), i.e., metal active gas welding, as a traditional and prevalent welding process, e.g., for the manufacture of truck and crawler cranes. Due to recent process developments, laser beam welding and the hybrid combination of laser beam and gas metal arc welding have appeared as expedient alternatives. However, for applications with highly stressed structures, as in the case of loading situations of the telescopic boom of truck cranes, for example, Fig. 1a, the service loads are related to the low cycle fatigue regime. Within such structures, butt joints are essential loadcarrying welds (Fig. 1b). Therefore, the following points need to be considered in the fatigue estimation:

In highly stressed areas, welded joints are limiting factors in design, e.g., butt joints in the telescopic boom

Cranespecific load scenarios result in variable amplitude loading (VAL) and elasticplastic stresses and strains (LCF)

A large number of load cases requires a method for fatigue life estimation that is easy to use
The fatigue assessment of welded joints according to recommendations and standards, Eurocode 3 [3], the crane design standard DIN EN 1300131 [4], Hobbachers IIW recommendations [5], and the FKM guideline [6], is based on fatigue classes (FAT), i.e., characteristic stress ranges Δσ_{C} at 2·10^{6} cycles to failure. These FAT classes were derived from experimental results from specimens and components. Specimens for experimental fatigue investigations of steel structures with medium sheet thickness, i.e., 5 mm to approximately 20 mm, are usually of larger scale and tested under stress control to verify the fatigue assessment and FAT classes. To date, these fatigue recommendations are mostly limited to steels with a maximum yield strength of 960 MPa and the assessment by FAT classes does not include the low cycle fatigue (LCF) regime and elasticplastic material behavior. Therefore, they are restricted to cycles to failure of N ≥ 1·10^{4}.
An overview of the fatigue design concepts, which are applied in the assessment of welded joints, is given in Fig. 2 and, in more detail, by Radaj et al. [8, 9]. The nominal stress (and strain) approach requires the definition of a nominal stress or strain, i.e., a reference crosssection, and assignment of a specific notch detail. FAT values for nominal stress and various notch details have been defined [3,4,5,6]. Even though FAT classes are defined for survival probabilities of 97.7%, analyses of fatigue results of butt welds, including data points for N_{f} < 5·10^{4} from Olivier and Ritter [10], Leitner et al. [11], Berg and Stranghöner [12], and Möller [2] have found that the assessment by FAT 90 (or even FAT 80/FAT 71) tends to be unsafe at high loading levels in and close to the LCF regime.
In the case of more complex structures, where it is not possible to define nominal stress, the structural stress (or strain) concept can be applied, as further described by the IIW recommendations of Hobbacher [5] and Fricke [13] as well as [8], where FAT classes for structural stresses can also be found. Due to the linearelastic extrapolation, which is used in most of the concept variants, the existing stress concentration at the notch and notch support effects at this location are not captured. Furthermore, structural stress and strain concepts reveal their limitations when confronted with root notches.
As a consequence and in addition to the nominal and structural stress (or strain) concepts, local concepts (cf. [5, 7,8,9, 13]) are increasingly used for the design of welded joints. FAT classes for notch stresses result in fictitious (linearelastic) stresses at the notch root. The notch stress approaches attracted wide interest and developed over recent decades, so that they are a useful assessment approach for welded joints, especially in the case of the reference radius concept (cf. [8, 13]). However, this approach cannot be applied in elasticplastic stressstrain states, as is the case in the LCF regime or, rather, in the notch root of a weld for high loading applications. In order to cover this case, the notch strain concept (cf. [5, 7,8,9, 13]) is used, where the cyclic material behavior forms the basis for the simulation and assessment of the stressstrain state in the notch, in addition to the geometry of the joint, as introduced by Lawrence et al. [14]. The effort involved in such an assessment should not be underestimated and increases further, if transient effects and microstructural differences, as given by investigations on the effect of the microstructure of the different weld zones on the fatigue strength from various authors [15,16,17,18,19,20], are taken into account. Recent work of Saiprasertkit et al. [21,22,23,24] uses an analytical approximation for the description of the effective notch strain from the notch strain concept with a reference radius of r_{ref} = 1.00 mm in the case of loadcarrying cruciform joints to show a conservative estimation of FAT 200 within the LCF and HCF regimes. On the contrary, this work aims at providing a fatigue life estimation by an integral treatment of butt welds under low to high constant and variable amplitude loading for elasticplastic stressstrain conditions with moderate effort, as described in this paper.
Finally, fracture mechanics concepts, e.g., stress intensity or crack propagation approaches, assume a preexisting cracklike defect for the life assessment, but will not be in the focus of this work.
Materials and welding process
Based on unalloyed structural steels [25] and normalized rolled finegrained structural steels (N, NL) [26] with yield strengths R_{eH} or R_{p0.2} of 235 to 460 MPa, the steel designation for highstrength, finegrained structural steels according to [27] is also based on the minimum yield strength. In a further subdivision, a distinction can be made between highstrength (R_{p0.2} ≤ 960 MPa) and ultrahighstrength (R_{p0.2} > 960 MPa) finegrained structural steels. The yield strength specification is followed in the designation by information on the manufacturing process. A basic distinction is made between water quenched and tempered (Q, QL) [28] and thermomechanically treated (M, TM) [29] steels. In the context of this work, the S960QL (material no.: 1.8933), two thermomechanically rolled products of grade S960M (manufacturer “1” and “2”) and the ultrahighstrength S1100QL (material no.: 1.8942) finegrained structural steel, suitable for welding, have been investigated. Starting from a conventional hot rolling above the recrystallization temperature of austenite, followed by normalizing annealing in normalized steels, water quenched and tempered steels are rapidly cooled in water, resulting in very good strength properties due to the bainitic and martensitic microstructure [30]. Microstructural transformations by subsequent tempering can, above all, improve their toughness properties. Thermomechanical rolling, i.e., a combined mechanicalthermal rolling process, which is partially carried out below the recrystallization temperature, comprises a large number of process variants (e.g., accelerated cooling), which, together with the alloying concept (microalloy), result in high toughness and strength [30].
The steel materials in this investigation are characterized by the mechanical properties listed in Table 1—yield strength R_{p0.2}, tensile strength R_{m}, elongation at fracture A_{5}, and impact energy KV (at three different temperatures). The characteristic values meet the requirements according to [28]:

Minimum yield strength: R_{p0.2} ≥ 960 MPa (S960), R_{p0.2} ≥ 1100 MPa (S1100)

Tensile strength: 980 ≤ R_{m} ≤ 1150 MPa (S960), 1250 ≤ R_{m} ≤ 1550 MPa (S1100)

Minimum elongation at fracture: A_{5} ≥ 10% (S960)

Notched bar impact energy: KV ≥ 40 J (S960 at − 20 °C) and KV ≥ 30 J (S960 at − 40 °C)
The specifications for the impact energy are temperaturedependent and correspond to the test carried out by the steel manufacturer.
Butt joints were manufactured, using the 8mmthick S960QL, S960M, and S1100QL steel sheets described previously, by gas metal arc welding (GMAW), i.e., metal active gas welding, applying the process parameters given in Table 2, as this is the traditionally and commonly used welding process in the crane industry and related areas. A cooling time t_{8/5} of 5 to 10 s is an essential process requirement. For the ultrahighstrength, finegrained structural steel S1100QL, the use of filler metal G 89 6 M Mn4Ni2CrMo with a minimum yield strength of R_{p0.2} = 890 MPa results in a welded joint with weld areas of lower strength (undermatching), especially in the heataffected zone (HAZ). The butt joints were created in a multilayer weld with one weld root, one backing and one or two top layers. Two overlapping top layers have been chosen for manually welded S960M and S1100QL, while a single top layer is used for manually S960QL welds, in order to compare them with a partially automated joining of the steel sheets. Welds, manufactured by manual GMAW, were executed by qualified welders from the crane industry. In the past, efforts were made to introduce automated welding and laser beam welding (LBW) or a combined LBWGMAW as a joining process, in order to reduce distorsions and increase the strength of joints, i.e., also the fatigue strength. Investigations on the fatigue behavior of these welds are still ongoing.
Stressbased fatigue life derived from forcecontrolled testing
Fatigue tests on butt joints have been performed on resonance and servohydraulic fatigue test rigs under force control at a load ratio of R_{F} = 0.1 [31, 33, 34]. The specimen was designed to have a free length between the clamping areas of 250 mm. Low test frequencies in the range of 0.1 Hz ≤ f ≤ 7.0 Hz were defined for tests based on the “Testing and Documentation Guideline for the Experimental Determination of Mechanical Properties of Steel Sheets for CAECalculations” [35] with a focus on low cycle fatigue. The test frequency was reduced with increasing force amplitude to a minimum of 0.1 Hz and was increased to 35 Hz for fatigue testing in the high cycle fatigue (HCF) regime. “Total rupture of the specimen” was defined as the final failure criterion.
The evaluation of the fatigue test results in the HCF regime, both under constant amplitude loading (Wöhler curve) and variable amplitude loading (Gaßner curve) with a random load time history derived from a Gaussianlike load spectrum [34, 36], has been carried out according to the maximum likelihood estimation (MLE) [37], Fig. 3. Both Wöhler and Gaßner curves for buttwelded S960QL, S960M, and S1100QL finegrained steels are evaluated for all steel grades together. In Fig. 3, the lines are represented for survival probabilities of P_{S} = 10, 50, and 90%. The Wöhler line is characterized by the slope k = 3.1, the nominal stress amplitude σ_{a,n} (N_{r} = 1·10^{6},P_{S} = 50%) = 60 MPa, and the scatter T_{σ} = 1:1.98—the Gaßner line is, on the other hand, described by k = 4.2, σ_{a,n} (N_{r} = 1·10^{6},P_{S} = 50%) = 184 MPa, and T_{σ} = 1:1.56. Wöhler and Gaßner lines are in good agreement with those of other evaluation methods shown in [31, 33, 34]. This is due to the fact that the evaluation is limited to the HCF and that there are no differences in applying the method of the least squares and the maximum likelihood method including just one runout. Differentiation between the various test series (combination of base material and welding process) shows a dependence of the fatigue strength on the weld quality and welding process [31, 33, 34]. It has been found that partially automated welding results in a reduced misalignment and an increase in fatigue strength. In the LCF regime, forcecontrolled fatigue testing is sensitive to plasticity and flow, so that small changes in force can have a considerable influence on the fatigue life of the welded joint [19]. This restriction can be counteracted by straincontrolled fatigue testing.
Integral treatment and cyclic behavior of butt welds
Integral treatment of welded joints
The complexity of and effort in the application of local fatigue assessment approaches increases drastically, if the elasticplastic material model of welded joints is supplemented by a local differentiation of the material behavior and the consideration of transient effects. Therefore, an integral treatment of a butt joint is introduced as a basis for the fatigue life assessment. This integral treatment uses the cyclic material behavior, evaluated from straincontrolled fatigue testing, but characterizes butt welds by the cyclic stressstrain behaviors and strainlife curves with an integral approach from the base material across the weld to the base material (Fig. 4).
Cyclic behavior of butt welds
A servohydraulic test rig with a maximum load of 100 kN has been used for straincontrolled fatigue tests of the smallscale flat specimens (Fig. 5). Although the greater sheet thickness of 8 mm does not fall within the range of thin sheets, the tests were carried out in accordance with the specifications of SEP1240 [35]. As a result of the strain ratio of R_{ε} = − 1, an antibuckling device is used. Depending on the strain level, the test frequencies were selected as 0.1 Hz (ε_{a,t} > 0.4%), 0.5 Hz (0.4% ≥ ε_{a,t} > 0.2%), and 4.0 Hz (ε_{a,t} ≤ 0.2%). From the test results, strainlife curves and cyclic stressstrain curves are derived, which describe the cyclic material behavior (base material) and the cyclic behavior of the butt weld. For this purpose, an extensometer with a 25 mm measuring length was used in the straincontrolled tests. In the case of the butt weld, this extensometer contains the entire weld area (weld metal, HAZ, and base metal on both sides).
Two approaches are used to evaluate the strainlife curve: the classical description of the BasquinCoffinMansonMorrow (BCMM) [38,39,40,41] strainlife curve and the description by the trilinear strainlife curve [42]. In the latter description, continuation of the slope of the elastic line from range 2 into 3 (b_{2} = b_{3}) is selected, since no results are available for N > 1·10^{6}. The comparison of the BCMM strainlife curves with the trilinear strainlife curves for the S1100QL butt welds (Fig. 6a) shows differences between the two estimation methods—with a more accurate description by the trilinear strainlife curve and cyclic stressstrain curve derived from compatibility equations. Therefore, the trilinear strainlife curve is preferred in describing the strainlife relation and will be used to estimate the fatigue life. There are approx. 1–2 decades in number of cycles to crack initiation between the base material and butt weld. In [19], it has also been demonstrated that a fatigue life reduction has been found for machined specimens compared with the base material state. Thus, it can be seen that the strainlife curves determined on base material specimens cannot be directly transferred to other material states, such as weld seams.
Cyclic stressstrain curves are described according to RambergOsgood [43]. In addition to the direct regression of the test results, cyclic stressstrain curves have been derived from compatibility with the strainlife curve in the form of BCMM and the trilinear strainlife curve. The three descriptions are compared for the S1100QL butt welds in Fig. 6b. The stressstrain curves from the compatibility with the BCMM strainlife curves tend to underestimate the results for lower plastic strains (0.2% < ε_{a,t} < 0.5%) and to overestimate the results for large plastic strains (ε_{a,t} > 0.6%). In contrast, the direct regression and the cyclic stressstrain curve describe the trilinear strainlife curve more accurately. This also applies in a similar way for the curves of the other base materials. All evaluated cyclic stressstrain curves are based on the results for the cyclically stabilized state and thus do not reflect any transient effects. Cyclic material parameters of the investigated highstrength, finegrained steels and buttwelded joints have been documented and analyzed in more detail in [2, 19].
Cyclic transient behavior
A first impression regarding transient effects is given by a comparison of the initial loading with the cyclic stabilized state and, especially the cyclic stressstrain curve. Distinctive cyclic softening from initial loading to cyclic stabilization can be observed for highstrength steel base materials as well as butt joints (cf. Fig. 4 (right)). However, deeper insight into the cyclic transient behavior is gained from changes in the hysteresis loops from cycle to cycle. The transient behavior is shown more clearly in the evolution of the cyclic yield strength R’_{p0.2} or the cyclic hardening coefficient K′ and the cyclic hardening exponent n′. An overview is provided by the representation of K′ and n′ in relation to the normalized number of cycles to crack initiation N/N_{i} for S960QL in Fig. 7, from which a drop in the cyclic hardening coefficient K′ can be derived as a result of softening and crack initiation. The cyclic hardening exponent n′ also shows a decreasing trend, although for S960QL steel and butt welds, it remains almost constant with increasing N/N_{i}, apart from a few minor changes. For both cyclic parameters, a linearization is performed for continuous evolution, so that (linear) functional relations for K′ = f (N/N_{i}) and n′ = f (N/N_{i}) are found. Due to the change in the characteristic values resulting from cyclic softening and crack initiation, the normalized number of cycles from straincontrolled fatigue tests can be directly interpreted as total damage, so that D = N/N_{i} follows. This definition results in the linearized descriptions for K′ and n′ depending on the damage according to Eqs. 1 and 2, where the index “0” denotes the initial state. More complex, nonlinear relationships are also conceivable, but for the following investigation, this approximation is sufficient for the description of the cyclic transient behavior.
Fatigue life estimation approach
For the fatigue life estimation from the low cycle to the high cycle fatigue regime, a strainbased approach, using damage parameters to assess simulated stressstrain paths, is used. The approach is based on the integral treatment of the butt weld already examined and its characterization by the cyclic (transient) behavior (Fig. 8). This approach includes the following steps:

1.
The starting points of the evaluation are the buttwelded specimens described before, which provide “integral characteristic values of the cyclic behavior of transverse loaded butt joints” as a result of straincontrolled fatigue tests. For the initial loading, stressstrain curves based on the initial parameters K′_{0} and n′_{0} are applied. Likewise, additional stresses (and strains) resulting from an angular misalignment are applied in the first load step.

2.
In the second step, the cyclic transient behavior of these “integral weld seams” is directly used in the analytical simulation of stressstrain paths, considering memory and Masing behavior without explicitly determining a fictitious notch stress or strain. Hysteresis loops are related to the load history. Different loading histories therefore need to be simulated computationally with this procedure. According to the forcecontrolled tests of the butt welds with R_{F} = 0, constant and variable amplitude loading is simulated in order to verify this method. The application of this method allows the inclusion of transient effects, such as cyclic softening, in the fatigue assessment with moderate effort. Based on the description of the cyclic transient behavior, the first load with stress relief is calculated using K_{0}′ and n_{0}′ from the initial RambergOsgood equation, while the following stress hystereses are calculated by damagedependent linearized parameters of K′ and n′. The RambergOsgood parameters K′ and n′ are modified cycle by cycle on the basis of the functional relationship with the damage content.

3.
The damage of every resulting hysteresis is derived by common damage parameters P_{SWT} by SmithWatsonTopper [44] (Eq. 3), P_{ε} by SonsinoWerner [45, 46] (Eq. 4), modified P_{HL,mod} by HaibachLehrke [47] (Eq. 5), and P_{J} by Vormwald [48] or the evolved P_{RAJ} by Fiedler et al. [49] (Eq. 6), which are finally compared. As a result of the analysis of these damage parameters, a generalized damage parameter P_{m} (Eq. 7) is introduced, which includes additional factors for mean stresses and mean strains as a combination of P_{ε} and the damage parameter of Bergmann P_{B} [50].

4.
With the help of the relation between damage parameter P and cycles to crack initiation Ni, the partial damage of the jth cycle d_{j} is derived and added to the damage sum of previous cycles. The accumulation is ongoing as long as the damage sum is below the theoretical damage sum of D_{th} = 1.

5.
The failure in the form of the crack initiation from the straincontrolled testing is achieved and the calculated number of cycles N_{calc} is returned, when the theoretical damage sum of D_{th} = 1 is reached.
A comparison between experimentally derived and simulated stressstrain paths, for a constant amplitude stresscontrolled loading situation with R_{F} = − 1 until the theoretical damage sum of D_{th} = 1 is reached, is shown in Fig. 9. Experimentally derived, simulated stressstrain paths and resulting hysteresis loops are in good agreement. Smaller differences occur at the minimum stress under compression, where cyclic creep might have an influence on the turning point. However, fatigue lives have been calculated by application of introduced damage parameters. Except for a short calculated fatigue life using P_{HL,mod}, small variations can be found for most of the damage parameters and in comparison with the experimentally determined value, in this specific example. In any case, the previously defined P_{m} seems to be a good choice. In other loading situations, advantages and disadvantages become clearer, as can be seen from [2].
This procedure offers the advantage of a simplified fatigue life estimation, based on consideration of elasticplastic stresses. Using this approach, a detailed and complex finite element simulation for the assessment of notch stresses or strains, which should additionally take transient effects into account, is avoided.
Fatigue life estimation
Constant amplitude loading (CAL)
According to the procedure described before, a fatigue life estimation under constant amplitude loading for the integral treatment of butt welds considering the cyclic transient behavior using damage parameters as defined in Eqs. 3 to 7 has been performed, where P_{m} is the introduced generalized damage parameter including mean stresses and mean strains. The results, applying the damage parameter P_{m}, are presented in Fig. 10, since P_{m} can be adjusted to the LCF regime (mean strains) and HCF regime (mean stresses) by choice of the corresponding factors in addition to the consideration of stress and strain amplitudes. In the nominal stress system, fatigue lives estimated with the help of P_{m} are compared with experimentally derived cycles to failure and fatigue classes FAT 50/71 (dotdashlines corresponding to a survival probability of P_{S} = 97.7%) derived for the different test series, which are characterized by the combination of base material and welding process execution. Figure 10a shows that the estimation results in too long fatigue lives for S960QL butt welds (green triangles), where specimens include a comparably high angular misalignment of α = 3.9° on average, if this angular misalignment is not taken into account in the fatigue life simulation(gray curve for P_{S} = 50%). Including an average angular misalignment α = 3.9° in the estimation procedure, it can be seen, from the course of the estimated fatigue life curve (cf. black curve) corresponding to a survival probability of P_{S} = 50%, that the accuracy of the fatigue life estimation is increased. Therefore, calculated fatigue lives of the other test series in Fig. 10b, c, and d already include the angular misalignment (black curves for P_{S} = 50%). It can be seen that the estimated fatigue lives coincide very well with the loadcontrolled experimental results for S960QL (Fig. 10a) and S1100QL (Fig. 10b), while more conservative fatigue lives are found for S960M (supplier 2, Fig. 10d). S960M (supplier 1) shows a good agreement at higher load levels and tends to be nonconservative at lower load amplitudes (Fig. 10c).
Variable amplitude loading (VAL)
Under variable amplitude loading, the simulated stressstrain path is more complex than the one for constant amplitude loading. Again, the fatigue life estimation is carried out for the integral treatment of butt welds with the described procedure considering cyclic transient behavior. Due to the intersection of the black curves for P_{S} = 50% with the green symbols, Fig. 11a, b, and c show that the highest stress amplitudes of loadcontrolled tests have been assessed by the approach applying the damage parameter P_{m}. For manually welded butt joints made of S960M (supplier 1, cf. Fig. 11c), there is a very good agreement between estimated and experimentally determined fatigue lives under variable amplitude loading. In the other cases, S960QL (Fig. 11a), S1100QL (Fig. 11b), and S960M (supplier 2, Fig. 11d), there is a tendency to be more conservative, when the stress amplitude decreases. Compared with the linear damage accumulation for P_{S} = 50% (here: using the allowable damage sum acc. to [5] of D_{all} = 0.5), this approach is not based on Wöhler (SN) lines derived under constant amplitude loading and is therefore independent of the slope of the Wöhler line in the HCF regime. As can be seen from Fig. 11, the transition from low cycle to high cycle fatigue is represented in a good way using this method, so that the calculated Gaßner (or Wöhler) curve is not purely linear (in doublelogarithmic scale). However, in the HCF regime, the approximation of a straight line for the Gaßner curve becomes obvious and is reasonable. At lower load levels, the estimation from the integral treatment of butt joints shows a good agreement for S960QL (cf. Fig. 11a) and S960M (supplier 1, cf. Fig. 11c), while the linear damage accumulation is closer to the experimental data for S1100QL (Fig. 11b) and S960M (supplier 2, Fig. 11d).
Discussion of the fatigue life estimation
Estimated (calculated) fatigue lives N_{calc} for the integral treatment of butt welds, considering the cyclic transient behavior using damage parameter P_{m}, are directly compared with experimentally derived fatigue lives N_{exp} for both constant and variable amplitude loading. Resulting data in the range of 1:4 from the optimum N_{calc} = N_{exp} (factor of 4) show a good agreement within the overall scatter of welded joints. In the case where N_{calc} is larger by more than a factor of 4 compared with N_{exp}, the estimation is on the unsafe side, while it is defined to be too safe, if N_{calc} = 0.25 · N_{exp}.
In Fig. 12, the direct comparison between calculated and experimentally determined fatigue lives for constant amplitude loading, applying the damage parameter P_{m}, confirms the good agreement which Fig. 10 indicates, if the angular distortion is taken into account—apart from the still very conservative estimate for the S960M (supplier 2). It can be seen that most results for S960QL (cf. Fig. 10a), S1100QL (cf. Fig. 10b), and S960M (supplier 1, Fig. 10c) are in the 1:4 range. In addition to the results of S960M (supplier 2), some of the other results at lower load amplitudes tend to be too safe. However, test results at low load levels are rare, since the focus of this investigation is set on the regime from LCF to higher load levels of the HCF. Therefore, the significance of the fatigue life estimation for very low load levels is limited, based on the results of this investigation. On the other hand, a very good agreement between estimated and experimentally derived fatigue lives at high load levels is found, at least for S960QL, S1100QL, and S960M (supplier 1) butt welds.
Figure 13 shows the comparison between calculated and experimentally determined fatigue lives for variable amplitude loading, applying the damage parameter P_{m}, again taking the angular distortion into account. For VAL, the estimation is less accurate than for CAL and leads to some results on the unsafe side—at least in a few cases of high loads for S1100QL and one result for S960M (supplier 1). For many results in the LCF regime, when elasticplastic behavior and mean strains come into play, but also at low stress amplitudes of the HCF regime, where linearelastic behavior can be assumed, the experimentally determined fatigue lives exceed the calculated ones, which gives a conservative estimation beyond the factor of 4. However, again, the same applies as for low load levels from constant amplitude loading: the significance of the estimation is low due to few test results in this regime.
Based on the integral treatment of butt welds, the cyclic behavior of the seam weld is determined and successfully used for a fatigue life estimation of corresponding joints under CAL and VAL. The estimation for CAL is in good agreement with the experiment showing some results that are too safe, while the VAL estimation tends to be very conservative, but still having some unsafe results. In both cases, consideration of the transient behavior for the fatigue life estimation is beneficial, especially at high load levels at the border to the LCF regime. The conservative estimations in the LCF regime using this method is still superior compared with the linear damage accumulation, which just gives a constant slope of the calculated Gaßner line depending on the slope of the Wöhler curve. A limitation in the LCF regime can then just be constituted by knowledge about the yield or tensile strength of the joint. Therefore, further work on this approach is expedient, in order to improve the fatigue life estimation in the regime from HCF to LCF.
Conclusions
A method for fatigue life estimation based on an integral treatment of transversely loaded butt joints has been introduced. The following conclusions can be drawn from this investigation and the developed fatigue life estimation using an integral treatment of welds:

(a)
A description of the substructure from base material to base material by its cyclic behavior (integral treatment) is the basis. The characterization by an accumulated set of parameters results in a unification and simplification, compared with locally detailed modeling of the weld. As might be seen from the hardness distribution of a section cut from the weld seam, huge variations in microhardness from one measurement point to another exist (cf. [2, 51, 52]). By implementation of a distribution of local characterization parameters in local fatigue concepts by FE modeling and simulation, calculation time increases drastically.

(b)
For the assessment from the low cycle to the high cycle fatigue regime, the cyclic elasticplastic behavior was considered. The cyclic transient behavior shows a distinctive cyclic softening of the base materials and butt welds, which is described by a damagedependent definition of the cyclic characteristic values K′ and n′ of the RambergOsgood equation. This is the main proposal to describe transient effects within this approach. Other transient effects, mean stress relaxation and cyclic creep, were not explicitly considered. In particular, cyclic creep requires further strainratedependent investigations.

(c)
Additional influences on the fatigue performance result from global geometrical factors, such as axial and angular misalignments. Axial misalignments are small and can be neglected. The angular distortion depends on the execution of the weld with respect to the boundary conditions. Furthermore, the heat input of the welding process influences the angular misalignment or residual stresses for fixed connections to the entire structure. While LBW creates a smaller angular misalignment, the increased heat input of GMAW induces a larger distortion. Therefore, the angular misalignment is considered with the help of additional stresses (and strains), which improves the fatigue life estimation.

(d)
The choice of damage parameter—P_{SWT}, P_{ε}, P_{HL,mod}, P_{J}, and P_{RAJ} were evaluated—influences the fatigue life estimation. Finally, a generalized damage parameter P_{m} (combination of P_{B} and P_{ε}) has been introduced, which can be adjusted to the regime, where damage is dominated by mean stresses (HCF) or mean strains (LCF) in addition to stress and strain amplitudes. This has been achieved by additional factors for the mean stress and mean strain in the mathematical formulation.

(e)
The application of the integral life estimation method has been illustrated by lifetime estimations for constant and variable amplitude loading. It has been found that the estimation is in good agreement with experimental stresscontrolled results under constant amplitude loading, while the estimated life under variable amplitude loading tends to be on the safe side for lower loading situations. In general, the (doublelogarithmic) nonlinear transition from LCF to HCF can be estimated with this method.
References
Kirschbaum M, Hamme U (2015) Einsatz von hochfesten Feinkornbaustählen im Kranbau. Stahl und Eisen 135(5):69–74
Möller B (2020) Integrale Betrachtung zur Lebensdauerabschätzung von Stumpfnähten im Bereich der Kurzzeitschwingfestigkeit. Dissertation, Technische Universität Darmstadt, Technical report FB257, Fraunhofer Verlag, Stuttgart
DIN EN 199319 (2010) Eurocode 3: design of steel structures – part 1–9: fatigue; German version EN 199319:2005 + AC:2009. Beuth Verlag GmbH, Brüssel
DIN EN 1300131 (2019) cranes – general design – part 3–1: limit states and proof competence of steel structure; German version EN 1300131:2012+A2:2018. Beuth Verlag GmbH, Berlin
Hobbacher AF (2016) Recommendations for fatigue design of welded joints and components. IIW document IIW225915 ex XIII246013/XV144013, Second Edition, International Institute of Welding, SpringerVerlag, Berlin/Heidelberg. ISBN 978–3–319–23756–5
Rennert R, Kullig E, Vormwald M, Esderts A, Siegele D (2012) FKM Richtlinie  Rechnerischer Festigkeitsnachweis für Maschinenbauteile aus Stahl, Eisenguss und Aluminiumwerkstoffen. 6th revised edition; Editor: Forschungskuratorium Maschinenbau (FKM), Frankfurt / Main
Sonsino CM Concepts and required materials data for fatigue design of PM components. Conference proceedings of the European Congress and Exhibition on Powder Metallurgy (PM 2001), 2224 Oct 2001, Nice, p 80–109s
Radaj D, Sonsino CM, Fricke W (2006) Fatigue assessment of welded joints by local approaches, 2nd edn. Woodhead Publishing, Cambridge
Radaj D, Sonsino CM, Fricke W (2009) Recent developments in local concepts of fatigue assessment of welded joints. International Journal of Fatigue 31:2–11. https://doi.org/10.1016/j.ijfatigue.2008.05.019
Olivier R, Ritter W (1979) Wöhlerlinienkatalog für Schweißverbindungen aus Baustählen – Teil 1: Stumpfstoß – Einheitliche statistische Auswertung von Ergebnissen aus Schwingfestigkeitsversuchen. Deutscher Verband für Schweißtechnik e.V., Düsseldorf, DVSreport no. 56/I
Leitner M, Stoschka M, Schanner R, Eichlseder W (2012) Influence of high frequency peening on fatigue of highstrength steels. FME Transactions 40(3):99–104
Berg J, Stranghöner N (2016) Fatigue behaviour of high frequency hammer peened ultra high strength steels. International Journal of Fatigue 82:35–48. https://doi.org/10.1016/j.ijfatigue.2015.08.012
Fricke W (2012) IIW recommendations for the fatigue assessment of welded structures by notch stress analysis: IIW200609. Woodhead Publishing. https://doi.org/10.1533/9780857098566
Lawrence FV, Ho NJ, Mazumdar PK (1981) Predicting the fatigue resistance of welds. Annual Review of Materials Science 11:401–425
Schubert R (1992) SpannungsDehnungsVerhalten von simulierten WEZGefügen und Schweißnähten unter zyklischer Belastung. Mater Werkst 23:162–170
Boroński D (2006) Cyclic material properties distribution in laserwelded joints. International Journal of Fatigue 28:346–354. https://doi.org/10.1016/j.ijfatigue.2005.07.029
Boroński D (2015) Testing lowcycle material properties with microspecimens. Materials Testing 57(2):165–170. https://doi.org/10.3139/120.110693
Sołtysiak R, Boroński D (2015) Strain analysis at notch root in laser welded samples using material properties of individual weld zones. International Journal of Fatigue 74:71–80. https://doi.org/10.1016/j.ijfatigue.2014.12.004
Möller B, Wagener R, Kaufmann H, Melz T (2015) Fatigue life and cyclic material behavior of butt welded highstrength steels in the LCF regime. Materials Testing 57(2):141–148. https://doi.org/10.3139/120.110691
Ahrend E (2018) Kurzzeitfestigkeit von Schweißverbindungen: Ein Verfahren zur Parameteridentifikation lokaler zyklischer SpannungsDehnungsKurven bei Werkstoffinhomogenitäten auf Basis digitaler Bildkorrelation. Dissertation, Technische Universität Darmstadt, TUprints, Darmstadt
Saiprasertkit K (2012) Strain based fatigue strength evaluation of beamtocolumn connections in steel bridge bents. Dissertation, Tokyo Institute of Technology
Saiprasertkit K, Hanji T, Miki C (2012) Local strain estimation method for low and highcycle fatigue strength evaluation. International Journal of Fatigue 40:1–6. https://doi.org/10.1016/j.ijfatigue.2012.01.021
Saiprasertkit K, Hanji T, Miki C (2012) Fatigue strength assessment of loadcarrying cruciform joints with material mismatching in low and highcycle fatigue regions based on the effective notch concept. International Journal of Fatigue 40:120–128. https://doi.org/10.1016/j.ijfatigue.2011.12.016
Saiprasertkit K (2013) Fatigue strength assessment of load carrying cruciform joints in low and high cycle fatigue region based on effective notch concept. IIW document XIII245613. International Institute of Welding
DIN EN 100252 (2011) Hot rolled products of structural steels – part 2: technical delivery conditions for nonalloy structural steels; German version prEN 100252:2011. Beuth Verlag GmbH, Berlin
DIN EN 100253 (2011) Hot rolled products of structural steels – part 3: technical delivery conditions for normalized/normalized rolled weldable fine grain structural steels; German version prEN 100253:2011. Beuth Verlag GmbH, Berlin
DIN EN 100271 (2017) Designation systems for steels – part 1: steel names; German version EN 100271:2016. Beuth Verlag GmbH, Berlin
DIN EN 100256 (2011) Hot rolled products of structural steels – part 6: technical delivery conditions for flat products of high yield strength structural steel in the quenched and tempered conditions; German version prEN 100256:2011. Beuth Verlag GmbH, Berlin
DIN EN 100254 (2011) Hot rolled products of structural steels – part 4: technical delivery conditions for thermomechanical rolled weldable fine grain structural steels; German version prEN 100254:2011. Beuth Verlag GmbH, Berlin
Schröter F (2003) Höherfeste Stähle für den Stahlbau – Auswahl und Anwendung. Bauingenieur no 9, p. 420–432
Melz T, Möller B, Baumgartner J, Ummenhofer T, Herion S, Hrabowski J, Henkel J, Boos B, Baier E (2015) Erweiterung des örtlichen Konzeptes zur Bemessung von LCFbeanspruchten geschweißten Kranstrukturen aus hochfesten Stählen. Forschungsbericht P 900, Forschungsvereinigung Stahlanwendungen e.V., Düsseldorf
Voestalpine Steel Division: alform® – Hotrolled cut sheets alform® xtreme: Data sheet. August 2013
Möller B, Baumgartner J, Wagener R, Kaufmann H, Melz T (2015) Bemessung zyklisch beanspruchter Schweißverbindungen aus höchst und ultrahochfesten Stählen. Stahlbau 84(9):620–628. https://doi.org/10.1002/stab.201510303
Möller B, Baumgartner J, Wagener R, Kaufmann H, Melz T (2017) Low cycle fatigue life assessment of welded highstrength structural steels based on nominal and local design concepts. International Journal of Fatigue 101:192–208. https://doi.org/10.1016/j.ijfatigue.2017.02.014
StahlEisenPrüfblatt (SEP) 1240 (2006) Testing and documentation guideline for the experimental determination of mechanical properties of steel sheets for CAEcalculations, Stahlinstitut VDEh, 1st Edition
Möller B, Wagener R, Hrabowski J, Ummenhofer T, Melz T (2015) Fatigue life of welded highstrength steels under Gaussian loads. Procedia Engineering 101:293–301. https://doi.org/10.1016/j.proeng.2015.02.035
Spindel JE, Haibach E The method of maximum likelihood applied to the statistical analysis of fatigue data including runouts. S. E. E. International Conference 3–6 April 1978; Special print from the lecture volume “Applications of Computers in Fatigue”, p. 7.1–7.23
Basquin OH (1910) The exponential law of endurance tests, American society test. Materials Proc 10:625–630
Coffin LA (1954) A study of the effects of cyclic thermal stress on a ductile metal. Transactions ASME (76):931–950
Manson SS (1965) Fatigue: a complex subject – some simple approximations. Exp Mech 5(7):193–226
Morrow JD (1965) Cyclic plastic strain energy and fatigue of metals, Internal Friction, Damping and Cyclic Plasticity. Special Technical Publication No. 378, ASTM, 45–87
Wagener R (2007) Zyklisches Werkstoffverhalten bei konstanter und variabler Beanspruchungsamplitude. Dissertation Technische Universität Clausthal, Papierflieger Verlag, ClausthalZellerfeld
Ramberg W, Osgood WR (1943) Description of stressstrain curves by three parameters, Technical Report Technical Note No. 902, NACA
Smith KN, Watson P, Topper TH (1970) A stressstrain function for the fatigue of metals. Journal of Materials 5(4):767–778
BacherHöchst M, Werner S, Sonsino CM (2001) Schwingfestigkeit kaltumgeformter Fügestellen von Aluminiumgehäusen für Bremsregelsysteme. DVM report 128 „Fertigungsverfahren und Betriebsfestigkeit“, Schaffhausen, 85–104
Werner S (1999) Zur betriebsfesten Auslegung von Bauteilen aus AlMgSi 1 unter Berücksichtigung von hohen Mitteldehnungen und Spannungskonzentrationen. Dissertation, Technische Universität Darmstadt, Technical report FB217, Darmstadt
Haibach E, Lehrke HP (1975) Das Verfahren der AmplitudenTransformation. Fraunhofer LBF, Darmstadt, Technical report FB125
Vormwald M (1989) Anrißlebensdauervorhersage auf Basis der Schwingbruchmechanik für kurze Risse. Dissertation, Technische Hochschule Darmstadt, Darmstadt
Fiedler M, Wächter M, Varfolomeev I, Vormwald M, Esderts A (2019) Richtlinie Nichtlinear  Rechnerischer Festigkeitsnachweis für Maschinenbauteile unter expliziter Erfassung nichtlinearen Werkstoffverformungsverhaltens – Für Bauteile aus Stahl, Stahlguss und Aluminiumknetlegierungen. FKMRichtlinie, VDMA, 1st Edition, Frankfurt/Main
Bergmann J (1983) Zur Betriebsfestigkeitsmessung gekerbter Bauteile auf Grundlage der örtlichen Beanspruchungen. Dissertation, Technische Universität Darmstadt
Seyfried B, Möller B, Knödel P, Wagener R, Ummenhofer T, Melz T (2018) Anwendungspotential von Laserstrahl und Laserhybridschweißnähten für Stumpfstoßverbindungen ultrahochfester Feinkornbaustähle. DVS report 344:376–384
Möller B Seyfried B, Wagener R, Knödel P, Melz T, Ummenhofer T (2019) Fatigue strength of laser welded butt joints made of highstrength finegrained structural steels for the application in crane structures. Proceedings der European Steel Technology and Application Days (ESTAD), Düsseldorf, 335
Acknowledgments
Open Access funding enabled and organized by Projekt DEAL. The basis for this work was established during my time as a research assistant at the Research Group System Reliability, Adaptive Structures, and Machine Acoustics of the Technische Universität Darmstadt and the Fraunhofer LBF. For their support, the author would like to thank Prof. C.M. Sonsino, Prof. T. Melz, Prof. M. Vormwald, Dr.Ing. H. Kaufmann, Dr.Ing. R. Wagener, and the colleagues at the corresponding institutes. The related research projects “Enhancement of the Local Concept of Fatigue Assessment of Welded Crane Structures of High Strength Steels in the Low Cycle Fatigue Regime”, IGFprojectno. 17102 N, and “Fatigue Life Assessment of Laser Beam and Laser Hybrid Welded Crane Structures made of HighStrength Steels“, IGFprojectno. 19272 N, of the Research Association for Steel Application (FOSTA—Forschungsvereinigung Stahlanwendung e.V.) are funded by the AiF as part of the program for »Joint Industrial Research (IGF)« by the German Federal Ministry of Economic Affairs and Energy (BMWi) by decision of the German Bundestag.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Recommended for publication by Commission XIII  Fatigue of Welded Components and Structures
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, 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/.
About this article
Cite this article
Möller, B. Integral treatment of butt joints for the fatigue life assessment in the low cycle fatigue regime. Weld World 65, 275–288 (2021). https://doi.org/10.1007/s4019402001006x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s4019402001006x
Keywords
 Integral treatment
 Welded joint
 Butt weld
 Cyclic behavior
 Damage parameter
 Fatigue life estimation