Sequence effects on the life estimation of welded tubular structures made of S355J2H under uniaxial fatigue loading

Abstract

The use of hollow sections to form lightweight structures is widespread in common steel processing industries such as crane, commercial vehicle, steel bridge and agricultural machinery construction. The hollow sections are mainly designed as truss or frame structures, in some cases using high-strength and higher-strength steels in order to achieve optimum utilization of the component and material. A new collection of fatigue life data covering sequence effects and the accuracy of the linear damage accumulation is presented. Effects of the shape of the applied load spectra and sequence effects of different amplitudes have been investigated. This document covers tubes of 4 to 8 mm thickness made by low-carbon or mild steel S355J2H. In general, it was found that the spectrum shape and the loading sequence have an influence on the service life. Depending on the shape of the spectrum, random tests tended to lead to shorter service lives than tests with block-loading sequences. An influence of overloads was also found for the tests with interspersed overloads. Typical maximum linear damage sums taken from recommendations and codes of 0.2 or sometimes 0.5 are exceeded for all spectra investigated and in some of the cases even significantly above 1.0. Transferability of the recommendations to component-type structures like tubular joints needs revision to lift its lightweight potential. Using stress concentration factors (SCF) from finite element analysis, typical strength values for the structural and effective notch stress concepts are checked. All joints investigated show a significantly higher strength compared to the IIW recommendations using the structural stress approach or compared to the DVS 0905 with the effective notch stress approach.

1 Introduction

The use of hollow sections for tubular lightweight structures is widespread in common steel processing industries such as crane, commercial vehicle, steel bridge, and agricultural machinery design. Tubular structures mainly consist of a truss or frame-type topology. To achieve optimum utilization of the component and material the use of high-strength steels is an ecological and economical option.

The question about the sequence effects of hollow section constructions has been explored in several research projects [1, 2]. Results for thin-walled welded tubular structures made of HSS under bending from [1] have already been covered in [3]. The main findings were that the recommended critical damage sums by various codes were not exceeded by the tests conducted in the study. In addition to that, a comparison of the experimental data with the notch stress concept revealed a significantly higher fatigue strength than the code-based FAT values for the notch stress concept. An even higher difference has been found for the structural stress concept using the quadratic extrapolation method.

With the present paper, the goal is to give the results on thin- and additionally some thick-walled welded tubular structures made of S355J2H under uniaxial fatigue loading.

The fatigue strength values and SN curves for hollow section joints have so far been derived from tests with constant amplitude fatigue testing on low-strength steels for the nominal and structural stress concept [4,5,6,7,8,9]. The transfer to real operating load spectra is performed with the current design methods in mechanical engineering and crane construction as well as in the building sector [10,11,12,13,14,15]. This requires so-called damage-equivalent stress ranges on the basis of the Palmgren-Miner rule with a limit value for the damage sum of D = 1.0 [16, 17] which is independent of the strength and the shape of the spectrum.

Favorable but also unfavorable sequence effects from the real operating load spectrum remain unconsidered. Various investigations show that the simply applicable linear damage accumulation of the Miner rule is partly not very accurate, cf. [18,19,20]. In the IIW guideline [21] or the DVS 0905 [22], it is therefore already recommended to conservatively apply a damage sum of D = 0.2–0.5 as a limit in case of non-constant amplitudes and mean stresses of the respective loading cycles.

The existing inaccuracies in the LDA were already determined by Schütz [20] for tests with blocked loading. According to this, failures occurred in 348 test series with a damage sum of D = 0.2 to 10.0. The operational strength tests by Bucak [18] with different blocked spectra (VAL) on hollow section nodes showed damage sums from D = 0.3 to 20.0. A tendency showed where the higher calculated damage sums occurred in spectra with lower damage potential. Recent studies show that in certain cases, the LDA of the original Palmgren-Miner rule is less applicable. In the IIW and in the FKM guidelines [19, 20], it is therefore recommended to conservatively apply a damage sum of D = 0.5 as a limit value. The investigations in [23] on butt joints made of ultrahigh-strength steels have shown that between 10⁴ and 10⁵ load cycles to failure, a damage sum of D = 1.0 leads to very good agreements, and above 10⁵ load cycles the value of D = 1.0 is conservative in some cases.

One goal is to investigate the performance of the linear damage accumulation by providing a broad test base of different load sequences for different welded hollow sections made of typical mild steel S355J2H. The series of tests on welded X-joints in crane construction comprised a total of 108 specimens made of circular hollow sections (CHS) and square hollow sections (SHS) of different dimensional ratios. In addition to the constant amplitude loading (CAL) tests, the test series also included variable amplitude loading (VAL) using the crane spectra p(1/3), a tower crane spectrum developed on the basis of real measurements in the FOSTA P778 research project [2], the North Sea spectrum, and test series with interspersed overloads and tests with a two-step block loading.

Residual stress measurements were used to determine possible residual stress reduction as a result of operating loads and overloads. Since high residual stresses are formed in welded joints, the currently applicable standards in steel construction [10] assume a worst-case scenario. That scenario is when welded components have residual welding stresses equal to the yield strength at the critical cracking point. Even at low load levels, local plasticization can occur in the connection area of the hollow section junctions due to the high-notch effect [24].

A similar situation can be seen regarding the influence of overloads. Overloads are also frequently referred to as misuse loads in commercial vehicle design. A comparison of a large number of tests with overloads in [25, 26] shows that overloads, depending on their magnitude and type (tensile or compressive overloads), lead to a delay or an acceleration of crack growth and thus have an influence on service life. Investigations from [24] show that in many cases, individual overloads lead to an increase in service life. This is especially true for welded structures made of higher-strength structural steels [27]. The lower strains at the notch due to the larger elastic strain component of higher-strength structural steels may cause this. However, the question arises at what level and at what frequency overloads have a positive effect on service life in hollow section joints.

The first investigations on the influence of operating loads on the fatigue strength of hollow section joints were predominantly carried out as blocked load spectra [18]. Although the stresses follow the same spectrum, the fatigue life of blocked and fully random loading can be very different. It is known from previous studies [2] that the same spectrum leads to longer lifetimes in block tests than in random mixed loading. In [28], it is shown that on a conical round steel, machined and without welds, the service life of a well-mixed (random) load sequence compared to a loading with an 8-step block program can reduce by a factor of up to 5 despite high numbers of load cycles [29].

In summary, this paper aims to provide new experimental data on welded hollow section joints for a variety of test scenarios and investigate the performance of the linear damage accumulation rule for those scenarios. Besides the assessment of the limiting damage sums provided by codes, the CAL tests were evaluated with the structural and notch stress concept. The results show significantly higher endurable stresses compared to the appropriate FAT classes.

2 X-hollow section joint under uniaxial fatigue loading

2.1 Materials, specimens, and test setup

Typical joint designs used for steel and crane design can be seen in Fig. 1.

Fig. 1

Typical joint topologies for circular hollow sections: X-joint (left), K-joint (middle), N-joint (right)

For this investigation X-joints made of circular hollow sections (CHSs) and square hollow sections (SHSs) were used. All test specimens have been made from the same material S355J2H. For the test specimens made of CHS and SHS with larger wall thickness (t = 8 mm), hot-rolled tubes according to DIN EN 10210-1 [30] were used, whereas the SHS with 4-mm-thickness cold-rolled profiles according to DIN EN 10219 was used [31]. In the case of the cold-rolled specimens, no attention was paid to the position of the longitudinal weld seam to cover possible unfavorable influences due to the production process. An overview of the different specimen types and their dimensions and ratios can be found in Table 1. The total length of the chord is 800 mm for all specimens. The lengths of the braces were chosen to get a total length of the X-joint of 900 mm (except for SHS-100 specimens with 1000 mm).

Table 1 Specimen dimensions

Within the scope of the CAL tests, production optimization by different weld seam preparations was carried out on a total of four test specimens using CHS. According to DIN EN 1090-2 chapter 7.5.1.2 and chapter E.3 [32], the weld seam of the joint can be executed both as a butt weld with a weld seam preparation and as a fillet weld without weld seam preparation. The SHS specimens were butt-jointed and welded with a fillet weld. The welding process used was the MAG process with solid wire. The tubes were cut by waterjet cutting. The corresponding weld seam preparations can be seen in Fig. 2.

Fig. 2

Weld preparation for CHS specimens: weld preparation (left), no weld preparation (middle), water cuts (right)

Due to manufacturing tolerances, ovalization of the tubes can occur which might lead to a gap between the brace and the chord tube. To avoid weld seam irregularities resulting from the residual gap, these gaps must be limited and not exceed a maximum value of 2 mm [32]. During production, random checks did not reveal that this dimension was exceeded due to the relatively small chord diameter d₀.

The influence of the seam preparation on the fatigue strength was checked using four tests with and without edge preparation. Due to the very small differences in the results as shown in Fig. 3, and the significantly more cost-effective and simplified design without seam preparation, all further test specimens were manufactured using a circumferential fillet weld.

Fig. 3

Results of the CAL tests for specimens having different weld preparation

Since excessive welding-induced distortion of the test specimens can sometimes falsify the results of the fatigue tests, an attempt was made to manufacture the test specimens with as little distortion as possible. For this purpose, the welding layers were made symmetrically. The tack welds required for positioning were ground out before welding. The exact welding sequence can be seen in Fig. 4. The specimens of test specimens CHS-51.0, CHS-82.5, and SHS-50 were each welded with only one layer, since the required dimension was 4 mm. Due to the greater wall thickness and the larger welding volume required as a result, the test specimens of the SHS-100 series could not be welded in one layer but 3 layers with a weld throat thickness of 8 mm.

Fig. 4

Tack welds and welding sequence: CHS (left), SHS (right)

3 Test equipment

3.1 VAL using block-type load sequences

Different testing machines were used to perform the block tests to keep the test times short. The areas of the partial sequences that exhibited high stress amplitudes with a low number of load cycles were tested in a universal spindle machine with a maximum upper load of 250 kN from Schenck with a test frequency of 0.5 Hz. The respective blocks were connected via ramps.

A resonance testing machine from SincoTec with a maximum load of 600 kN was used for the blocks with low stress ranges but a higher number of load cycles, see Fig. 5 (right). With this type of testing machine, the load is applied by excitation of the specimen in the range of its natural frequency by unbalanced masses. The test frequency ranged from 34 to 38 Hz depending on the shape of the spectrum and the load level. The tests were stopped when a through-thickness crack could be detected. This was the case at a frequency drop of ∆f = 1.0 Hz, see Fig. 6 for typical crack lengths. Due to the mode of operation of the testing machine, the transitions between blocks could not be executed as ramps as in the spindle machine. The transitions were rather performed by a continuous increase of the frequency and thus a continuous increase of the oscillation width until the target value was reached. The cycles of these transitions were not recorded separately since they are approximately balanced out again in the block stages due to the up-down-up sequence. Nevertheless, there are usually differences in load ranges between the target and actual values, which can be explained by the swing out of the unbalanced masses. Since only a few hundred load cycles were involved in each case, these were just added to the respective final block of the partial sequence when determining the total number of load cycles. In both test rigs, hydraulic jaws were used to clamp the specimens.

Fig. 6

Typical crack size at test termination: CHS specimens (left), SHS specimens (right)

3.2 VAL using random-type load sequences

Since it had to be possible to specify any time sequence for the random tests, neither the universal spindle machine nor the resonance testing machine could be used. This is due on the one hand to the required control technology and on the other hand to the operating principle of the different test systems. Servo-hydraulic single cylinders were used for random tests, see Fig. 5 (left). The test frequency is highly dependent on the stiffness of the test specimens and the performance of the cylinders. Test frequencies between 2 and 8 Hz could be achieved. Due to the very different static strength of the specimens, two different individual cylinders were required. The SHS-50 specimens were tested with a single cylinder with a maximum load of 40 kN. The CHS series and the tests of the series with SHS-100 were carried out with a single cylinder with a maximum load of 250 kN. Due to the random load sequence, a change of displacement ∆w = 1, 0 mm related to the deformation under maximum amplitude was used as a shutdown criterion. The criterion occurred after a full wall-through crack in all cases. The connections between the single cylinder, the test frame, and the specimen were established by means of a fitting bolt connection.

Fig. 5

Specimens and test setup: CHS-82.5 hydraulic cylinder 250 kN (left), SHS-100 resonance pulsator (right)

In order to be able to exclude a possible influence of the different test machines and test frequencies, individual block program tests were carried out with the individual cylinders at the beginning of the tests. No significant difference in the number of load cycles has been seen. Consequently, an influence of the test machine itself on the test results can be neglected.

Despite the different termination criteria used for the different test rigs, the specimens exhibited approximately the same crack lengths, so that comparable test criteria can be assumed. Typical crack lengths at test break-off can be taken from Fig. 6. The crack lengths of the CHS specimens were between 80 and 120 mm regardless of the diameter of the strut, whereas the typical crack lengths of the SHS-50 specimens were 80–100 mm and of the SHS-100 specimens 140–160 mm.

3.3 Strain gage measurements

Accompanying the different test rigs, random static stress measurements were carried out in order to exclude possible influencing factors due to the different test rigs and to be able to record the occurring bending stresses due to skewing of the vertical braces. Strain gages have been applied to each type of specimen to capture secondary bending effects due to clamping.

Before clamping, the measurement was set to zero. During the clamping process, certain bending moments were generated, see Fig. 7 (left). After the elimination of the bending stresses for subsequent monotonic uniaxial fatigue loading, a homogenous axial stress of approximately 100 MPa is achieved Fig. 7 (right). Despite the elimination of bending stresses, there are still deviations from 100 MPa. The amount of these deviations depends on the amount of angular or axial misalignment and the position of the strain gages. Stress measurements in the other testing machines have shown similar results. The additional bending stresses act at the most highly stressed point at the saddle point. This occurs if the braces are slightly crooked due to angular tolerances. However, the additional bending stresses from the clamping process do not lead to larger stress ranges but rather shift the mean stress.

Fig. 7

Strain gage measurements for monotonic loading: clamping (left), subsequent monotonic loading up to nominal axial stress of 100 MPa (right)

Due to clamping, the stress ratio at the critical location of the welded joint changes. The tests are carried out using a stress ratio of R = 0.1, per definition without mean stress due to clamping. Incorporating the mean stress would yield a higher stress ratio of approximately R = 0.5 in front of the critical location for the specific joint in Fig. 8.

Fig. 8

Position of strain gages exemplary for CHS specimen

3.4 Accompanying investigations

To check the weld quality and evaluate the test results, macrosections were made on individual test specimens during the tests, and the fracture surfaces were examined more closely.

As shown in Fig. 9, the fracture surfaces of the CHS specimens are characterized by their fine-grained structure which has the same optical appearance irrespective of the test procedure, the profile dimensions, and the shape of the spectrum and does not show any zones of fast fracture in the saddle area. Fast fracture surfaces are only visible in the edge areas located at the transition to the base material. Crack initiation occurred on all CHS specimens in the saddle area at the weld seam transition to the chord tube.

Fig. 9

Typical crack faces of the CHS specimens: CHS-51.0-D-B-01 (left), CHS-82.5-D-R-04 (right)

Similar observations can be made for the fracture surfaces of the SHS specimens. Here, the crack initiation did not occur in the center, but at the section corners. However, the residual fracture surfaces extend to a significantly larger area at the edge in the SHS test specimens, see Fig. 10.

Fig. 10

Typical crack faces of the SHS specimens: SHS-50-D-B-04 (left), (c) SHS-100-D-B-03

Tests with overloads show significant marking lines due to overloads. These are clearly visible at regular intervals in the incipient crack area, especially with the more frequently interspersed overloads (every 10,000 LW), cf. Fig. 11(a). Due to the significantly less frequently interspersed overloads (every 100,000 LW) in the block tests, these marking lines are not so clearly visible in Fig. 11(b). It is noticeable that these marking lines can only be seen in the first third of the wall thickness. With respect to the test procedure, the fracture surfaces differed significantly in the random tests. Thus, although marking lines can also be glimpsed, these are only visible from the half of the wall thickness, cf. Fig. 11(c).

Fig. 11

Typical crack faces of the CHS specimens with overloads

Figure 12 shows an example of the macrosections produced, which allow conclusions to be drawn about the weld seam quality during the destructive tests. In the case of the CHS test specimens, crack initiation occurred in all test specimens in the saddle area at the weld transition to the chord tube, similar to that shown in Fig. 12 (left). Several sections showed weld seam irregularities in the form of pores and non-melted weld seam roots, so-called root defects. According to DIN EN 5817 [33], insufficient penetration welding as seen in the sections is not permissible. The welds would therefore be classified in group D according to DIN EN 5817 [33]. However, this does not seem to have any influence on the fatigue strength since the test results of the different test series show relatively low scatter and no cracks starting from the root could be detected.

Fig. 12

Macrosection, CHS specimens (left), SHS specimens (right)

4 SN curves

Using specimens from the same production lot as the later variable amplitude tests, at first, SN curves for the structure were obtained. The resulting raw data can be found in Table 21 of the Appendix.

Crack initiation and through-thickness cracking were checked visually by inspection and recording of cycles at frequency drops of Df = ± 0.2, ± 0.4, ± 0.6, ± 0.8, ± 1.0, and ± 1.2 Hz. Some tests have stopped before reaching the higher drop values because of significant crack lengths. All SHS sections showed visible cracks at ± 0.2 Hz and through-cracks at ± 0.4 Hz. Most CHS-51.0 showed through-cracks at ± 0.6Hz frequency drops, except at ± 0.4 Hz. CHS-82.5 also showed through-cracks at a drop of ± 0.6 Hz and one at ± 0.2 Hz. The SN curves are evaluated using the through-cracked state.

As a basis for the evaluation of the test results, the tests with CAL were first evaluated and compared with the test results from [18] to check the comparability of existing test results for the further intended joint evaluation. As can be seen in Fig. 13 (right), there is a very good agreement for the SHS-50 tests. For this reason, the basic SN curve was also determined using both results from new tests as well as results from [18]. For the CHS specimens, however, there is a clear difference of the new results to CAL as can be seen in Fig. 13 (left). One explanation for these deviations could be the technological advances in welding technology, which have led to better control of the welding process and thus to welds with a lower number of weld seam defects and better weld seam quality, which also has a positive effect on the service life of the test specimens. However, due to the weld quality from [18], which is no longer traceable, this remains only an assumption. Due to these differences, the number of tests by CAL was significantly increased to validate the baseline. Additional tests were also carried out for the specimen dimensions with larger wall thicknesses, since no comparative results were available for the SHS-100, and strong deviations in the results were found for the CHS-82.5, similar to the smaller dimensions.

Fig. 13

Comparison of the test results with the results of [2]: CHS-51 (left), SHS-50 (right)

Nominal stress was calculated by a linear transfer coefficient for the applied load DF of c_N. Nominal stresses in the cross-section of the brace can be derived by

$$\varDelta S=\frac{\varDelta F}{A}=\varDelta F\cdot {c}_N$$

(1)

Due to the definition of the nominal stress, range axial or angular misalignment is not covered in the linear transfer coefficients. The individual linear transfer coefficients c_N are given in Table 2.

Table 2 Data for evaluation of nominal stresses

Regression of the SN curves was done using the equations from DIN 50100 [34] since the project is focused on steel construction and crane design which usually use this procedure. According to this rule, especially for small sample numbers (n < 10), the logarithmic standard deviation s_lg,N tends to be underestimated and must therefore be corrected according to

$${s}_{\lg, \mathrm{N},\mathrm{corr}}={s}_{\lg, \mathrm{N}}\frac{n-1.74}{n-2}$$

(2)

The scatter factor T_N is the ratio of the 90% quantile and the 10% quantile based on a standardized normal distribution and calculated by

$${T}_N=1{0}^{2.564\cdot {s}_{\mathit{\lg},\mathrm{N},\mathrm{corr}}}$$

(3)

T _N covers 80% of the sample data. Since it strongly depends on the sample size n, the values of T_N are significantly higher if the sample size is small compared to a higher sample size, see Table 3. This table also shows the results from regression using a fixed slope exponent of m = 5 and a free slope exponent, while the slope exponent of m = 5 is based on the notch stress concept for thin-walled structures with sheet thicknesses t < 7 mm. Also, the EC3 [35] suggests to use m = 5 for welded hollow section joints.

Table 3 Parameters of SN curves

5 Load spectra for variable amplitude testing

Various test sequences were used to determine the influence of the sequence. On the one hand, tests were carried out as two-block tests with a high-low or low-high sequence. On the other hand, test series were tested as block tests. Finally, test series were also tested with a random load time sequence.

The load spectra used refer to crane structures in accordance with the area of application. For comparative purposes, tests were also carried out with less damaging spectra in order to quantify any influences from the shape of the spectrum applied. For this purpose, the North Sea spectrum was used, which is also called linear spectrum due to its linear distribution. Its specification was developed in the context of off-shore research by measurements on ships and off-shore platforms in order to be able to design the structures for stresses due to sea states [36]. The distribution function and the corresponding stair-stepping of the North Sea collective were carried out analogously to [18, 36] and [36], see Fig. 14.

Fig. 14

Load spectra

For the operational loadings within the scope of the project, the tower crane spectrum based on measurements was used as the load sequence. Due to its shape, the spectrum will be referred to as q-spectrum in the following.

One hundred eight welded X-joint specimens were tested. The tests using block-type spectra serve as a control or reference for the random loading. By varying the wall thickness and the dimensional ratios, the effects of size influence on the fatigue strength were investigated. In another series of tests, the influence of tensile and compressive overloads on the service life estimation was investigated.

For the variable amplitude testing, different spectra have been defined. The naming of the test type and number of tests for variable amplitude loading can be seen in Tables 4 and 5.

Table 4 Naming convention for load type and no tests performed using CHS specimen

Table 5 Naming convention for load type and no tests performed using SHS specimen

The naming of the specimens depends on the respective type of section, the diameters of the brace tubes, the shape of the spectrum, and the type of sequential application. An overview is given in Table 6. The results of the individual series is given in the compilation of the test results in Table 21.

Table 6 Naming convention for each test series

Using the SN curves, the following spectra have been defined using analytical linear damage accumulation for an allowable damage of D = 1.0 for the respective specimen and loading.

6 High-low vs. low-high-spectra

Two-level–two-block load spectra have an analytical damage of the initial block to be D = 0.5. After application of the first block in the test, the second one was applied until failure occurred.

In the low-high tests, this procedure led to failure in all test specimens. For about 50% of the high-low tests, no cracking or fracture could be detected in the low block, even at load cycles of up to 10⁸. For this reason, these specimens were subsequently loaded again with the high block until failure occurred. The load levels used have a ratio of 2.0 from the low to the high load cycle.

6.1 Multilevel block-type application of VAL spectra

Multilevel block tests were carried out as a Gassner-type up-down-up sequence with Markov transitions. This means that in the test sequence, only the next higher or lower load cycle was applied directly after one another. The tests were started in the medium-sized load cycle of the spectrum. The individual blocks were specified in such a way that, on the basis of the determined characteristic fatigue strength of the SN curves, the partial sequences can be repeated 6 to 8 times up to a calculated theoretical damage sum of D = 1.0. This should ensure a good mixing of the block-type test sequences. Due to the different load levels, this resulted in different partial block lengths for the respective spectrum and tubular joint. Table 22 in the Appendix contains the spectra definition normalized by the maximum range as used.

6.2 Random-type application of VAL spectra

The corresponding partial block sequences of the block-type tests were used to define the randomized load sequences. A detailed description of the procedure for generating randomized load time sequences can be found in [37] and [29]. To facilitate the evaluation, the time sequences were constructed in such a way that each maximum of a load cycle was followed by the corresponding minimum. The advantage of this approach lies in the evaluation, since the maximum values had to be counted only to determine the corresponding load range of the cycle. Due to the control software, the tests were performed at a constant frequency, resulting in different speeds for the different amplitudes. Depending on the load level of the peak values and thus the corresponding amplitudes, the maximum values could not be approached exactly in some cases. This circumstance was taken into account in the evaluation by minimally shifting (2 kN which is equivalent to a maximum difference of the stress cycles of 3.4 MPa) the limit values of the respective cycle in order to avoid incorrect assignments of the load ranges. An exception is the test sequence with q-spectrum and the SHS-50 specimens because these have smaller distances in the low load steps and were therefore shifted by only 1 kN. Due to the continuous data recording, all cycles could be recorded and subsequently evaluated via a maximum value count. Table 22 in the Appendix contains the spectra definition normalized by the maximum range as used in the project.

The p(1/3) spectrum has a very high value in the lowest block level due to the stress amplitude of 1/3 of the maximum amplitude. The minimum stress range for all types of specimen is therefore above the fatigue limit.

The situation is different for the other spectra. Here, lower ranges are partly below the fatigue limit and therefore have to be considered according to the applied standard. However, a comparison of the calculated damage sums for selected test specimens showed that the deviations of the total damage sums are very small due to the low damage in the lower blocks and can only lead to somewhat larger deviations for test specimens with extremely long lifetimes. For comparison, Table 7 shows the corresponding values for damage sums based on Miner original and Miner elementary and different codes. In order to consider the maximum damage sum in the evaluation, all tests were therefore evaluated on the basis of the Miner elementary rule Table 8.

Table 7 Comparison of knee-points and cut-off limits from different codes

Table 8 Comparison of damage sum calculations according to different methods

For the evaluation of the test results, the conversion to damage-equivalent stress ranges was also performed. This conversion is suitable for comparing the block and random tests with the tests from CAL and is available in various standards, like [21]. The background of this conversion is to obtain a damage-equivalent CAL spectrum and thus to verify the fatigue strength. When applying the damage-equivalent stress range, a conversion of cycles below the fatigue limit is also performed with the corresponding slope m₂ according to the standard used. Analogous to the determination of the damage sums, the determination of the damage-equivalent stress ranges was carried out on the basis of Miner elementary.

6.3 Spectra with overloads

In those tests, overloads were interspersed at regular intervals (10,000 or 100,000 cycles) as block or random tests on the basis of the p(1/3) spectra. The block tests were performed exclusively with tensile overloads, whereas the random tests were performed with both tensile and compressive overloads. In each case, the tensile overloads corresponded to 1.2 times the maximum load of the corresponding spectrum. To reduce the risk of buckling, for the compression overloads, only − 1.0 times and once − 1.2 times of the maximum load of the spectrum was used. Due to the test setup and the connection of the specimens to the testing machine, transition ramps had to be provided for the compression overloads, since the bolt connection would otherwise have led to abrupt loading and unloading during the test and control by the software would not have been possible. A typical test sequence with the corresponding transition ramps for the tests with compression overloads (left) and for the tensile overloads can be taken from Fig. 15 (right).

Fig. 15

Schedule of the tests with overloads: compression overloads (left), tension overloads (right)

7 Test results from variable amplitude testing

The following section evaluates and summarizes the test results for different influencing factors. These are presented separately from each other. For a better comparison of the results, the ∆S_2E6,50% values of the respective test series are tabulated below the diagrams. The separate evaluation of the individual test series and the compilation of the test results can be taken from Tables 23, 24, 25, 26, 27, 28 and 29 of the Appendix.

7.1 Shape of spectrum

Figure 16 summarizes the influence of the different spectra applied. Here, the results of the random tests on the CHS-51 (left) and SHS-50 (right) tubes are shown as an example in a Gassner-type diagram, i.e., fatigue life plotted for the maximum range of load cycles. Characteristic values of Gassner-type SN curves are given in Table 9. The same observations can also be noted when comparing the block-type application of these spectra. The corresponding schematic representation of the different spectra with an indication of the damage potential n is placed between the two diagrams. The CAL tests with a damage potential of n = 1.0 represent the test series with the lowest fatigue life. As can be seen from the arrangement of the graphs, a decreasing damage potential leads to an extension of the fatigue life. The influence of the shape of the spectrum could be observed in the tests carried out and is independent of the shape of the tubular cross-sections, since this could be determined both in the tests with CHS and with SHS. Thus, the damage potential can also be used as a factor for an adapted fatigue strength analysis.

Fig. 16

Influence of the shape of the load spectrum

Table 9 Characteristic values of Gassner-type SN curves

7.2 Multilevel application sequences of VAL spectra

When considering the different test executions and thus the load sequence, it was observed that the block-type testing led to significantly longer running times and thus to longer fatigue lives compared to the random-type application sequence. The block tests thus seem to overestimate the fatigue life somewhat. The random tests, on the other hand, seem to be better able to represent real operating conditions. This influence can be seen for both application sequences and all dimensional ratios in Figs. 17 and 18. It is noticeable that the influence of the shape of the spectrum can also be seen. With increasing damage potential of a spectrum, the distance between the two test runs becomes significantly smaller as can be seen in Fig. 17. In the SHS tests, on the other hand, this influence does not appear to be so pronounced, see Fig. 18.

Fig. 17

Typical crane spectrum of CHS: CHS-51—p(1/3) spectrum (left), CHS-51—q spectrum (right)

Fig. 18

Typical crane spectrum of SHS: SHS-50—p(1/3) spectrum (left), SHS-50—q spectrum (right)

From regression analysis of the different test series, the characteristic strength values for 50% probability of failure and 2 ×·10⁶ cycles DS_2E6,50% are given in Table 10.

Table 10 Characteristic values of Gassner-type SN curves: CHS (left) and SHS (right)

7.3 Spectra with overloads

As described in chapter 4.4, both tensile and compressive overloads were interspersed in intervals in block type as well as in pure random tests. Overloads in tension have been 1.2 times the maximum load range of the applied spectrum for all geometries, see Fig. 19. The plots are marked at the maximum stress range of the spectrum, not the overload level.

Fig. 19

Tests conducted with overloads in tension: CHS-51 (left), CHS-82.5 (right)

For the applied compressive overloads, the magnitude of the applied compressive overloads varies; that is why they are included in Fig. 20 for the p(1/3) spectrum. The results were compared with the corresponding SN curves and the corresponding results of the block or random tests with the p(1/3) spectrum.

Fig. 20

Tests conducted with compressive overloads

As can be seen from Fig. 19 (left), the interspersed tensile overloads lead to a smaller reduction in service life when performed as block tests compared to the test results of the p(1/3) spectrum. However, since the block tests tend to be subject to larger scatter, the results of the tests with tensile overloads are in the range of the typical scatter of the block tests. The few test results suggest that tensile overloads do not lead to a significant shortening of the service life.

For the results of the tests with tensile overloads and random sequence, see Fig. 19 (right), the test results are slightly above those of the tests carried out for the p(1/3) spectrum applied in random sequence. Similar to the overload tests performed as block tests, these results lie within the typical scatter of the test results without overloads. Thus, for the tests with tensile overloads, no influence on the service life can be determined. This could also be due to the too-small difference of the overloads to the maximum range value of the spectrum. Such overload could not be selected higher due to the already very high maximum loads of about the static load capacity of the X-nodes.

In the evaluation of the tests with compressive overloads, Fig. 20, a shortening of fatigue life compared to the random tests without overloads can be stated. Due to the different magnitudes of interspersed compressive overloads, a joint evaluation is not possible. Further tests are necessary to be able to make a qualified statement about the influence of pressure overloads on the service life.

7.4 Evaluation by damage-equivalent stress ranges

As an alternative to Gasser-type diagrams, the results can be reformulated in damage-equivalent stress cycles. The following figures, Figs. 21 and 22, contain those values as plotted in a SN diagram together with the SN curves in the typical scatter band of failure probability obtained from fatigue testing by CAL for each specimen dimension. The design fatigue curve for the respective geometry from DIN EN 13001-3-1 [11] is also added in these figures.

Fig. 21

Evaluation of the CHS test series by conversion to equivalent stress ranges: CHS-51 (left), CHS-82.5 (right)

Fig. 22

Evaluation of the SHS test series by conversion to equivalent stress ranges: SHS-50 (left), SHS-100 (right)

Most of the test results are within the scatter band of the experimentally obtained SN curves. Similar to the results in the Gassner diagrams before, the block tests are at the upper edge or outside the upper scatter band, which indicates that the block tests could overestimate the service life of the structures. The block tests carried out by Bucak [18] lie at the upper edge or even above the scatter range of the SN tests as well. The results of the random tests, on the other hand, are in the vicinity of the lower scatter limit. Sufficient distance to the reference lines according to DIN EN 13001-3-1, however, is present for all tube dimensions, which suggests a safe design. For the larger dimensions (CHS-82.5 and SHS-100), the scatter of the test results is larger. This shortens the distance of the lower scatter band compared to the reference line from the standard.

7.5 Evaluation of relative damage sums

The relative Mine sums in Table 11 as given by D_V = D_calc / D_test reflect the prognosis quality of the linear damage accumulation as calculated using the corresponding SN curves. D_test is the damage by testing the specimen using the spectrum loading until failure and sets the reference level of 100% damage or D_test = 1.0 for all cases. The respective total number of cycles as applied until failure is then checked analytically using Miner elementary to get a theoretical damage D_calc of the spectra using the SN curves from CAL for mean failure probability. D_V > 1.0 refers to an analytical damage higher than physical and indicates a very conservative value for using the Miner rule for such cases. Vice versa, values below 1.0 result in an underestimation of the analytical fatigue life using the Miner rule if compared to the experiments.

Table 11 Relative damage sums D_V for each specimen including mean values and standard deviations

Table 11 contains the results for circular hollow sections (CHSs) as well as square hollow sections (SHSs) for each type of loading and each test performed. Since the number of repeated tests is low for all cases, statistical evaluation is restricted to arithmetic mean and standard deviations. In case multiple tests using (a) the same load spectrum, (b) the same load sequence (block or random), and (c) the same tube dimensions have been performed, D_V,mean,1, s₁, n_1, and D_V,10%,1 in Table 11 represent the mean, standard deviation, number of such specimens, and the value of the 10% quantile involved. Due to the low number of samples, those statistical data are not sound ones but give an indication of tendency.

D _V,mean,2, s₂, and n₂ in Table 11 provide the mean, standard deviation, and number of specimens involved for using (a) all specimens for a specific load spectrum, (b) the same type of application (block or random), and (c) all available dimensions for such loadings.

The results from Table 11 for the three spectra p(1/3), q, and North Sea are also shown in the box plots in Fig. 23 by a limited range of D_V < 10.0 (left) and full range (right). The style of the boxes is kept the same for all plots, and the sequence of boxes and the graphical style is identical for all graphs shown to simplify comparability. The four boxes in red/orange on the left relate to CHS joints and the 4 gray on the right to the SHS joints. Filled colored blocks represent block-load sequences and crosshatched ones random type load sequences. Because the two-level block loadings and the p(1/3) spectra with overloads have been done with a very small number of specimen n, those are not contained as box plots. Values at D_V = 0 indicate that no test result is available for those specifications. The boxes contain 50% of the samples. The whiskers define the full range of data but without considering run-outs. Run-outs are defined as values above 1.5 times the interquartile distance (box width) and can be seen as dots outside the whiskers, e.g., see CHS-51.0-D-B and q spectrum.

Fig. 23

Box plots of DV values as listed in Table 11: D_V < 10 (left) and full range (right)

When evaluating the damage sums, it can be clearly seen that block-type load sequences and p(1/3) spectrum as well as the North Sea spectrum lead to large D_V > 1.0 which represents a high overestimation of Miner elementary for such loading.

Underestimation by applying Miner elementary can be seen for q spectra in a few cases down to worst case D_V = 0.3 and for random type sequences of North Sea spectra D_V = 0.5 as minimum.

Furthermore, it can be observed that the block tests show a significantly larger scatter in the test results compared to the random tests.

Specimen dimensions do not show a unique tendency. For p(1/3) spectra, there is a slight tendency toward more conservative results for CHS and SHS specimens as well as block and random loading sequences. For q spectra, the minimum D_V values are almost the same for both specimen sizes, but the scatter is much lower for larger dimensions.

8 Residual stress measurements

To get a first impression about residual stresses and relaxation due to service loads, measurements of longitudinal stresses have been taken on one specimen.

For CHS tubes, the measurements were taken initially on the chord as well as the brace tubes, see Fig. 24 (left). Due to accessibility and spatter from welding, the distances in the diagrams might vary a little for the different quadrants. Because due to service loading, the residual stresses will change only in the vicinity of the weld toes, and subsequent measurements have been taken only at two points at the respective weld toes, see Fig. 24 (middle).

Fig. 24

Path, location, and quadrant definitions for residual stress measurements: initial (left) and subsequent (middle) measurements on CHS and measuring positions on SHS specimens (right)

Measurements for SHS were taken at the critical locations at the corners of the weld seams using parallel paths along the chord, like the CHS tubes again in all quadrants.

For measurement, X-ray diffraction was used. For the initial measurements, an X-ray diffractometer X3000 from StressTech was used and switched to a μX360s from Pulstec for subsequent testing. For the latter, see the parameters in Table 12. This device captures the full diffraction cone in the form of the Debey-Scherer ring, which allows an additional evaluation of the microstructure. Thus, a closed ring reflects a fine-grained material, cf. Fig. 25f. Furthermore, by exchanging the measuring instruments, the irradiated area could be reduced, so that the results could be evaluated even more selectively. This work was performed by University of Kassel, Germany.

Table 12 Data and parameters for X-ray diffraction

Fig. 25

Impressions of the residual stress measurements: a–c measurements with the StressTech device, d, e measurements with the Pulstec device, f closed Debey-Scherer-ring

The specimens were tested before loading and after application of a load as can be seen in Table 13. Measurements have been taken after 0 and 1 or 100 repetitions of monotonic load level S_o and after block testing of spectra for specimen Nos. 5 and 6 with a maximum stress range DS_max.

Table 13 Overview of scenarios used for residual stress measurement

Residual stresses for the SHS specimen in all four quadrants can be seen in Fig. 26. The results of the measurements in the unloaded condition between the different quadrants already show clear differences in the course and level of the residual stresses. For example, the opposite sectors 1 and 4 in the immediate vicinity of the weld transition show very high tensile residual stresses in the yield strength range, which, on the other hand, decrease with increasing distance from the weld. The residual stresses in areas 2 and 3, however, exhibit significantly lower tensile residual stresses, which in part also decrease to compressive residual stresses with greater distance. Due to the applied tensile load of S_o = 60 MPa, the high tensile residual stresses in the area of the weld in quadrants 1 and 4 reduce very strongly and become compressive. With increasing distance to the weld, the residual stresses are significantly below the residual stresses in the unloaded state. In some cases, the residual stresses even reach the compressive range. The results of the residual stress measurements in sector 3 show a similar pattern except for the measurements after loading in sector 2. There, the residual stresses in the weld area hardly change due to the single load. With increasing distance to the weld seam transition, however, the tensile residual stresses increase more and more. In conclusion, it can be said that residual stresses are reduced in the area of the weld seam. With increasing distance to the weld transition, significant scatter occurs in the results, so that only a tendency statement can be made about the influence of a single load on the residual stress reduction at a greater distance to the weld.

Fig. 26

Residual stress measurements at SHS specimens

For the residual stress measurements on CHS specimens, the residual stresses were measured both on the chord tube and on the brace tube because in some cases cracks could be detected at the weld toe to the brace in the initial tests by CAL. Those initial measurements revealed similar distributions of residual stresses, cf. Fig. 27. Very high compressive residual stresses occurred in the area of the weld seam, which, however, change to tensile residual stresses with increasing distance from the weld seam transition. The greater the weld seam distance, the more the residual stresses approached a constant level, which was around 50 MPa for the measurements on the brace tube and around approx. 100 MPa for the measurements on the chord tube. In contrast to the measurements on the SHS tube, the results in all sectors show almost identical curves. Change of the residual stresses is due to single loads. Figure 28 shows an extract of the changes in residual stresses caused by the application of a single tensile load in sectors 1 and 2, which is about the same in the remaining 2 sectors. As can be seen from the diagram, a relaxation in residual stresses as a result of an applied load only occurs in the direct vicinity of the weld seam or the heat-affected zone. The applied load had no effect on areas at greater distances.

Fig. 27

Comparison of the results of the measurements at brace and chord CHS

Fig. 28

Change of the residual stresses due to single loads, CHS

Figure 29 shows the influence of CAL with different amplitudes on the residual stresses on the chord tube at the measuring points MP01 and MP02, grouped according to sectors 1 to 4. The loads were applied according to the definitions in Table 13. It is noticeable that only compressive residual stresses are present in the weld seam area of specimens subjected to tensile forces. In contrast, the picture is not clear for compressive loads.

Fig. 29

Residual stress measurements CHS before/after CAL: a, b tension loading with 100% of S_o, c, d tension loading with 50% of S_o, e, f compression load, LW means cycles

The results for the tension loading with 100% of S_o show a uniform increase in the residual compressive stresses in the area of the weld with an increasing number of load cycles with the largest change after the first cycle. However, this is contradicted by the results of residual stress measurements on the specimen loaded with half the maximum tensile force. There, the application of a single load leads to a reduction of the residual compressive stresses. An exception are the measurements at point MP01 in sector 3 and at point MP02 in sector 4, whose residual stresses also shift further into the compression range after loading. The amount of tensile load thus seems to have an influence on the residual stress state.

The measurements of the specimen subjected to compressive loading, on the other hand, do not show a uniform picture. For example, a single compressive load leads in part to a reduction of the existing residual compressive stresses and in some cases even significantly into the tensile range. However, this does not apply to measuring point MP2 in sector 1 as an exception. However, when further compressive loads are applied, the residual stresses shift back into the compressive range, and tensile residual stresses are relieved. Assuming that tensile residual stresses favor crack growth under alternating loads, the residual stress measurements can be used to draw conclusions about the results of the tests with compressive overloads. Due to the applied compressive overloads, the existing compressive residual stresses are relieved, and crack growth is promoted, so that this could lead to a shortened service life.

Both p(1/3) spectrum and q spectrum yield compressive residual stresses of comparable magnitude after applying a single pass of tensile loading at position MP01, which is located directly in the weld toe, see Fig. 30.

Fig. 30

Residual stress measurements before/after application of a, b p(1/3) spectrum and c, d q spectrum

However, the reduction of residual stresses is irregular, so that no quantifiable conclusion can be drawn about the influence of the type of spectrum on the change of the residual stress state. At the slightly more distant measuring point MP02, even opposite tendencies are evident. It should be noted, however, that the measurements are subject to scatter. As an example of the scatter, an excerpt from the measurement data can be taken from Table 14.

Table 14 Extract from the residual stress measurement data

9 Stress concentration factors

Finite element analysis is state of the art for analytical assessment of deformation, stresses, and strains as well as for welded structures [38]. Besides the experiments, notch factors to evaluate structural and notch stresses were determined for all specimen geometries by finite element analysis in this project as well. Using those stress concentration factors, the SN curves based on nominal stresses can be transferred to structural stresses and effective notch stresses. For finite element analysis, ANSYS Workbench 2021 R2¹ was used.

The nominal dimensions of the tubular joints as described in chapter 2 have been used to model the geometry. Due to the symmetry of geometry and loading, 1/8 of the total structure was modeled by applying symmetry boundary conditions in the cutting planes. This means that angular or axial misalignment of the vertical brace is not covered in the numerical analysis. Loading is applied by tension or compressive forces on the top face of the vertical brace.

To reduce computational effort, submodeling was used. The domains of the submodels for SHS and CHS can be seen in Fig. 31. These models include the stiffening effect of the weld seam with angular, i.e., discontinuous transitions for the analysis of structural stresses and in case of notch stress analysis of the fictitious radii at weld root and weld toe. The flank angle is set to 45° for SHS and at the crown position of the CHS.

Fig. 31

Displacement under loading and submodel domain: SHS-50.0 (left) and CHS-1.0 (right)

Only solid elements with quadratic shape functions have been used. For mesh refinement in weld root and weld toes for the effective notch stress concept, the DVS 0905 code of practice recommends at least 24 elements along a 360° arc in the notch radius and also the corresponding element edge length normal to the notch surface for quadratic approach functions of the finite elements. A convergence study on our model confirms this recommendation as seen in Fig. 32 (right).

Fig. 32

Mesh detail of root and weld toes (left), convergence behavior of mesh refinement (right)

To determine the structural stresses, the methods according to Haibach (1 mm and 2 mm stresses) [29], as well as the linear and quadratic extrapolation methods according to [21], were applied. For this purpose, the notch area was modeled without filleting the weld toe. To determine the stress curves, the required evaluation points were defined by means of several evaluation paths and sections perpendicular to the notch on the component surface. The path with the highest resulting stress was used for further evaluation. Figure 33 shows the maximum principal stress ending at the hot spot along the tube flange in tension. The structural stress values can be seen on the right.

Fig. 33

Structural stress evaluation for path with maximum principal structural stress

It can be seen from this figure that the Haibach structural stress is underestimated, and thus, this definition should not be taken for thin-walled structures. This pragmatic method performs much better for thicker welds.

For SHS, notch stress analysis results in maximum stresses in the weld toe at the section corners only. For CHS, the critical location is at the weld to the saddle point, see Fig. 34.

Fig. 34

Notch stress distribution, maximum principal structural stress, and at the weld toe of maximum stress r = 0.3 mm for CHS (left) and SHS (right)

Stresses in the weld root are lower compared to the maximum stressed weld toes in all cases. Therefore, they can be excluded as failure-critical locations.

Stress concentration factors (SCF) represent the ratio between the determined structural or notch stresses and the previously defined nominal stresses. Nominal, structural, and notch stress concepts always refer to linear-elastically determined stresses. For this reason, structural and notch stresses can be obtained simply by linear scaling of the applied nominal maximum principal stress as shown in Table 15. For better comparison, the wall thicknesses of chord t₀ and brace t₁ are also given in the table.

Table 15 Stress concentration factors, SCF for structural, and notch stress

For CHS, the maximum notch stress is at the weld toe on the brace. The weld root and the weld toe at the chord have shown smaller values not shown here.

$${K}_t=\frac{\sigma_k\ \mathrm{or}\ {\sigma}_{hs}}{S}$$

(7.1)

Taking the SCF from quadratic extrapolation to obtain structural stresses as a reference, the SCF derived for the two Haibach methods show an underestimation of the structural stress for specimens with thinner wall thicknesses. For the thicker SHS-100.0, the results from the different structural stress methods are very similar. For stress fields showing nonlinear distributions in front of the hot spot, the quadratic extrapolation should be used for hot-spot stress evaluation.

According to DVS 0905 [22], checking against a SN curve for the base material in addition to the check with respect to the SN curve according to the FAT class is mandatory for mild notches having low-stress concentration factors [39]. To exclude such cases, minimum values of the seam shape factor K_w must be achieved, which is defined by the ratio of notch stress to structural stress and is depending on the reference radius. The minimum value of K_w for r = 0.3 mm to use the FAT class–based SN curve for the fatigue assessment only is K_w,min = 2.13 and for r = 1.0 mm K_w,min = 1.6 [22]. The ratios for the respective reference radii are given in Table 15 as well. In case of the thin-walled circular section CHS-82.5, the ratios are slightly below those limits.

10 Discussion

10.1 Constant amplitude loading (CAL) testing

First, the SN curves are compared to FAT classes taken from DVS 0905 for the effective notch stress concept and from the IIW recommendations for structural stresses, both applied to maximum principal stress. For load-carrying welds, FAT90 is recommended for structural stresses, FAT300 is recommended for r = 0.3 mm for the effective notch stress concept and weld toe failure, and FAT is recommended 225 for r = 1.0 mm. The recommended slope exponent is m = 5 for thin-walled structures (t < 7 mm) and m = 3 for thicker welds t ≥ 7 mm. The latter rule complies well with the SN curve for SHS-100. The other section types show slope exponents between 3 and 5 as can be seen in Table 16.

Table 16 Structural stress concept: characteristic values for 2E6 cycles

FAT classes are given for a low probability of failure as typical in many standards of 2.3% (about equal to a probability of survival of 95% of the mean together with either a two-sided 75% or a one-sided 95% confidence limit or alternatively mean minus two times standard deviation [22]). Transferring the FAT classes to a failure probability of 50%, multiplication by 1.3 as a pragmatic approach is used. FAT classes are valid for a stress ratio R = 0.5 to minimize the effect of residual stresses from welding. According to DVS 0905 [22], a transformation to R = 0.1 requires an additional factor of f(R) = 1.073 in case of conservatively assuming residual stresses. For comparison with mean values from regression DS_2E6,50%, the FAT class has to be multiplied by an assumed 1.4 to obtain comparable characteristic values. We consider this as an upper bound value for the code-based SN data for 50% probability. If mean stresses from clamping of the specimens were additionally taken into account, stress ratios at the critical locations would be even higher. Then, a beneficial factor of f(R) would not be multiplied with the FAT class, and the following differences in the characteristic values would be even higher.

The modified FAT classes and the stress ranges from constant amplitude testing multiplied by the corresponding stress concentration factors can be seen in Table 16 for characteristic values of structural stress Ds_hs,2E6 and Table 17 for the effective notch stresses Ds_ns,2E6, both valid for a failure probability of 50%. A significant difference can be seen in both tables. For structural stresses, the stress concentration factor from quadratic extrapolation only is used for this evaluation.

Table 17 Effective notch stress concept, characteristic values for 2E6 cycles for r_ref = 0.3 mm (top) and 1.0 mm (bottom)

To get a better view on the full range of the SN curves, the ratios of characteristic values can be seen in Tables 18 and 19. The values for 10⁴ cycles have been calculated using the respective slope exponents for each approach from Tables 18 and 19 (note the value for the “thick-walled” SHS-100). Also, the K_t-values are applied with the same magnitudes as for 2 ×·10⁶ cycles. The ratios between characteristic values from the experimental SN curves and the code-based values are given for 10⁴ and 2·× 10⁶ cycles in the last two columns of these tables.

Table 18 Structural stress concept: comparison of characteristic values

Table 19 Effective notch stress concept: comparison of characteristic values for r_ref = 0.3 mm (top) and 1.0 mm (bottom)

The results demonstrate an increased fatigue strength for all specimens for the full SN curve, except the one with a wall thickness of 8 mm (SHS-100) if comparing the data to the transferred FAT classes and standardized slope exponents from the codes. This gives an indication that—due to wall thicknesses of t < 6 mm and tested components (not just weld details)—the application of the cited technical recommendations is too conservative for such cases.

A visual representation of the comparison of the CAL test in terms of notch stress ranges with FAT300 for r_ref = 0.3 mm is given in Fig. 35. It can be clearly seen that all test results are covered by the notch stress design curve FAT300 for a low failure probability of P_A = 2.3% and R = 0.1. Comparing the dashed mean line showing FAT300 for P_A = 50% and R = 0.1 shows good agreement between experimental data and the mean design curve for the thick-walled SHS-100 specimens (Fig. 35 right). However, for the thin-walled specimens (Fig. 35 left), a clear difference between the experimental data and the dashed line is visible.

Fig. 35

Notch stress ranges of CAL tests: maximum principal stress at the weld toe for r_ref = 0.3 mm (FAT300) for thin-walled specimens (m = 5) (left) and thick-walled specimens (m = 3) (right)

The difference in strength between experiment and code-based strength by using the structural stress is even higher compared to the notch stresses. Because the experimental obtained characteristic values are based on the same nominal stress but different stress concentration factors, this difference can only be due to wrong FAT classes. The FAT classes from IIW recommendations for the structural stress concept apply to any load-carrying weld geometry, and thus, those FAT values might be more conservative than the corresponding FAT class for the effective notch stress concept. A single master SN curve is used by the effective stress concept as well, but very local stress concentrations at the critical section corners are captured by this concept only. This might be the reason for this difference.

10.2 Variable amplitude loading (VAL)

Tests for CAL and VAL were all done using specimens. Most of the load specifications have been done using only few specimens which limits statistical evaluations. The resulting data can only give an indication of tendencies. A conclusion for an improvement of the linear damage accumulation cannot be drawn by these tests alone.

Important findings regarding the relative damage sums D_V are as follows.

Effects as observed by fracture mechanics on speed up or slow down of crack propagation due to varying mean stress and varying amplitudes in two-step loadings can be seen for the fatigue of welded specimens investigated here as well. Change from high to low in-phase slows down crack propagation temporarily and speeds up from low- to high stress cycles. Change from negative high stress cycles to positive low ones (reversed mean stress) also yields a speed up. This can be seen in the experimental results obtained. Since the linear damage accumulation does not consider those physical-based sequence effects, this—besides other reasons—is reflected by the relative damage sums D_V > 1.0 or D_V < 1.0.

Apart from reversed overloads, median values of all relative damage are in general well above 0.84, and all 10% values are above 0.51 up to 1.0. For reversed overloads, the damage accumulation is underestimated by D_V = 0.35 in minimum.

Block-type load sequences tend to have larger scatter compared to random-type load application of the spectrum data.

IIW recommendations [21] suggest a critical damage sum of 0.2 for fluctuating mean stresses. This criterion is fulfilled by all tests performed. Median relative damage sums of most of the tests performed are safely above 0.5. However, it is difficult to differentiate the load sequences to be used for this purpose. In case of in-phase tensional loadings, i.e., mean stress remains positive for all stress ranges, the critical damage sum could be modified to higher values. An allowable value of 0.5 seems reasonable as recommended by DVS 0905 [22]. If the load spectra comply with the ones used in this program, even higher values could be taken but require additional tests for qualification. A few more comments about the specific spectra are summarized.

10.2.1 Two-level high-low and low-high spectra

Only a few specimens have been tested for such loadings. The findings cannot be evaluated statistically and thus the results or just aiming a few trends. See [3] for a more detailed analysis on two-level block loadings. For all two-level sequences tested here, the relative damage is above 0.5.

10.2.2 p(1/3) Spectra

Block-type sequences show the most conservative relative damage sums D_V > 2.5 up to 10.0 but also the most scatter of all test series.

Random load sequences reduce scatter and conservatism of the miner accumulation. D_V clusters around 1.0 for those load sequences.

For SHS, the specimens with larger dimensions have given reduced scatter but also reduced conservativity in the damage accumulation. This might be explained by the lower number of specimens (6 vs. 3) used.

10.2.3 q Spectra

All specimens tested using q spectra, no matter if using block-type or random load sequence, give values of D_V between 0.5 and 2.5 (excluding outliers to very high relative damage values). Also, scatter is low in most of those cases. Non-conservative estimation of the fatigue life cannot be assigned to a specific type of loading, load application, specimen geometry, or tube dimensions. Because these load spectra—due to the high damage potential—are close to CAL, the differences might be lowest for such load specifications.

10.2.4 North Sea spectra

The North Sea spectrum has the lowest damage potential of all spectra tested. Only a few specimens made of CHS were tested. Block-type load application has yielded very conservative relative damage sums ranging from about 3.5 to 10. Random loading on the other side has yielded values above 0.5.

10.2.5 Overloads + p(1/3) spectra

For p(1/3) spectra with interspersed overloads 20% above the maximum spectrum value and applied in-phase in tension, all specifications have led to highly conservative results D_V > 1.5. A slow down as expected from fracture mechanical observations can be confirmed. The sample sizes have been very small for such tests which reduce the statistical confidence of this data of course.

A few tests using reversed overloads of − 1.0 or − 1.2 times the maximum spectrum value and random load sequence also confirm the observations from fracture mechanics to show a speed up of the crack propagation in such cases. For our findings, a non-conservative estimation of fatigue damage can be seen in those results.

10.3 Plausibility checks according to ISO 14347

ISO 14347 [40] is a specific standard for the design of joints made of welded hollow section. Although this code is limited to a minimum of 4 mm, it was used to check the plausibility of the experimental results from constant amplitude testing. Based on the stress resultants acting on each brace of a welded joint, this method uses stress concentration factors for many different designs to estimate fatigue life as a structural stress concept at different critical positions along the welds. ISO 14347 provides SN curves with different “FAT classes” and different slope exponents m_ISO dependent on the wall thickness of the tubes.

Table 20 summarizes the results for comparing the experimentally obtained life for the characteristic values at 2·× 10⁶ cycles and 50% probability, DS_2E6,50%. Remarkable are slightly different slope exponents m_ISO and m_Exp. The following check thus is only valid for the stress range used. Due to the steeper SN curves of the ISO, the results for higher stress ranges are different.

Table 20 Fatigue life evaluation using ISO 14347

The fatigue strength as given in ISO 14347 is valid for low failure probability. For comparison with the mean values from the constant amplitude testing, a factor of 1.3 was applied also for this analysis. D_V,1 relates the 2·× 10⁶ cycles from the experimental tests to the cycle to failure number as obtained using the modified characteristic value from the ISO. A high additional safety distance of about a magnitude in life for these materials and wall thickness can be observed for this stress level. Since ISO is not focusing on high-strength steels either, this might be an additional reason for this result.

No factor of mean stress correction is included in D_V,1, because ISO 14347 does not contain a procedure for it. D_V,2 gives an idea about this effect by using an assumed correction factor of 1.15 to increase the fatigue strength toward R = 0.1. Looking at the different results from D_V,1 and D_V,2, a potential for improving the ISO by adding a correction function for mean stress effects can be concluded.

Finally, the ISO is also checked with the given SN curves taken from this code without modification, i.e., low failure probability and no mean stress correction. D_V,3 represents this number.

11 Conclusion

Welded X-type circular and square hollow section joints made of a manually welded low alloy mild steel S355J2H have been tested under uniaxial fatigue loading on the braces all with stress ratio R = 0.1. SN curves as well as fatigue lives for different variable amplitude spectra were obtained by the experiments. All raw data of the tests can be found in the Appendix.

Fatigue strength of the steel joints tested for CAL at 2·× 10⁶ cycles gives a conservative underestimation of fatigue life compared to analytical estimations using ISO 14347 by a factor D_V > 3.3 for all specimen dimensions tested except the large SHS joint, where the underestimation is D_V = 1.8. Except the largest specimen dimensions (SHS-100 for which m = 3 were obtained from regression analysis), the slope exponents of the SN curves are around m = 4. The resulting differences in fatigue life estimation are thus addressed in the component testing. The differences might also be associated with the size effect which is not contained in the ISO. Such an effect requires further investigations.

Finite element models were used to calculate corresponding stress concentration factors for structural as well as the effective notch stress concept using a fictitious radius in the weld toe and root or a fictitious radius of r = 0.3 mm. Comparing the numerically calculated notch stresses to FAT values from the IIW recommendations and DVS 0905 has shown a significant difference, while the numerical values are significantly higher than the allowable stresses. The difference is higher for the structural concept. Thin-walled design and component characteristics by a strong local stress concentration in the welds at the section corners might be responsible, for the two stress-based concepts differ.

X-ray diffraction was used to get an idea about the residual stresses in the structure before and after applying CAL or VAL loads. High compressive residual stresses have been observed after welding at the critical weld toes but changing to tensional mean stresses away from the toes. After load application, those compressive residual stresses at the weld toes relaxed after tensional loading and remained unchanged at greater distances to the weld toes. Compressive loads have not given a clear result.

Variable amplitude testing was done for a few different two-level block spectra and mainly for VAL spectra (p(1/3) spectra with and without interspersed overloads in tension and compression (q spectra, North Sea spectra, all with blocked type and random type load sequences). Those spectra after specimen failure define a reference value of D_test = 1.0 using the experimental obtained SN curves. Constant and variable amplitude testing was performed for specimens taken from the same manufacturing lots. The effects obtained from the experiments thus can be considered as of high quality. Many samples for a single configuration tested used 4–7 specimens to get minimum statistical confidence. The results are on a sound basis but will require further tests on different materials and test scenarios to get enough data to improve rules for damage accumulation. Alternatively, such high experimental effort could be reduced by combining experimental with high-level analytical means based on computational fracture mechanics. From the results obtained, the following findings can be summarized:

• DVS 0905 recommends not to exceed a partial damage sum of 0.5 for variable amplitude loading. This is fulfilled by all tests except the case with reversed mean stresses and considering this mean stress effect.

• IIW recommendations suggest a critical damage sum of 0.2 for fluctuating mean stresses. As can be seen in Table 11 and Fig. 23, these recommendations are fulfilled by all tests performed.

• Median relative damage sums of most of the tests performed are above 1.0. Block-type loading sequences yielded the most conservative relative damage sums and the maximum increase in life compared to random-type load application of the respective spectrum.

• q Spectra, which have the highest damage potential of the VAL spectra tested, show the lowest level of uncertainty for the damage accumulation used. A significant increase or decrease of the uncertainty in damage accumulation for such spectra cannot be found in the results with respect to section type and dimensions but also not with respect to the strategy of load application.

• If the load spectra comply with the ones used in this program, even higher values could be taken but require additional tests for qualification.

This paper covers a contribution to a database of tests on welded hollow sections using constant amplitude testing and variable amplitude testing using different spectra in pure uniaxial fatigue loading of the braces.

It has been demonstrated, that applying selected codes leads to highly safe results for the SN curves of the welded hollow sections and materials tested. Further research and modification of the technical rules are recommended.

Appendix

Table 21 Test results SN curves

Table 22 Definition of load spectra

Table 23 Test results variable amplitude testing two-level block loadings

Table 24 Test results variable amplitude testing p(1/3) spectra, CHS

Table 25 Test results variable amplitude testing p(1/3) spectra, SHS

Table 26 Test results variable amplitude testing q-spectra, CHS

Table 27 Test results variable amplitude testing q-spectra, SHS

Table 28 Test results variable amplitude testing North Sea spectra, CHS

Table 29 Test results variable amplitude testing p(1/3)-spectra with overloads