The participants of the study were asked to evaluate the fatigue strength of the box configurations based on the nominal stress method. They presented their calculations together with information regarding which design code and representative detail they implemented. Their results are discussed and compared in the following section. Six participants took part in the fatigue strength assessment using the nominal stress method.
Implemented design codes
The design codes implemented by the participants in the nominal stress method assessment are presented in Table 3 together with information on the applied geometrical detail, the FAT values used, and the failure probability implemented by the standards.
Table 3 Summary of the different approaches by the participants for the nominal stress method Participant 1 and participant 2 have implemented the same detail from two different design codes: a single-sided V-butt weld with full penetration in the form of either a cruciform joint or a T-joint that is load carrying. It should however be noted that the structural details in the SSAB Design Handbook [13] are primarily based on the IIW recommendation [12], which is the case for the chosen detail. Both codes state that the FAT value of the chosen detail is 71 and potential failure from the weld toe might be expected provided that the full penetration is checked by inspection of the root. If no inspection is carried out, then root failure is expected, and the FAT value is representatively lowered to 36. Both participants have chosen to utilise FAT 71 for the box specimens with full penetration (A, D, F) and FAT 36 when the weld is partially penetrated.
The detail implemented by participant 3 represents a cylindrical hollow tube welded to a flange using a circumferential groove weld with a FAT-value of 63. The tube can be subjected to both axial and bending stresses, and the nominal stresses shall be calculated in the tube. The same detail has the option of utilizing the more representative case of square tube welded onto the flange which would decrease the FAT value to 45. The basic conditions specified for detail 3.33 states that it is governed by a fully penetrated grove weld and is therefore only applicable for box specimens A, D and F. In addition, it is stated that the flange thickness must be greater than two times the thickness of the tube which is true for all cases investigated [16].
Participant 4 and participant 5 have both chosen to implement details representing splices of rectangular hollow sections with an intermediate plate. One of the details, 424, is governed by a single-sided butt weld with potential failure from the weld toe, whereas detail 425 is governed by a single sided fillet weld where potential weld root failure would be expected. FAT values of both details are dependent on if the wall thickness of the hollow section is larger or smaller than 8 mm. If the thickness is above the threshold value, then the FAT values are 50/40 (detail 424/425) and if they are below the FAT values becomes 45/36 (detail 424/425). Participant 4 investigated and compared both details and concluded that weld root failure (detail 425) is to be regarded as the limiting failure mode in fatigue strength assessment for the presented box specimen. As this participant only presented calculations for box specimens A, B and C in the nominal stress method the FAT value of 40 was exclusively used as these cases all have web thicknesses of 10 mm. Participant 5 implemented detail 424 for the specimens with full penetration and detail 425 for the specimens with partial penetration considering the reduction of FAT based on the web thickness.
Participant 6 implemented detail 7.9 in the British Standard 7608:2014 [17] represented by a single-sided fillet weld as a corner or T-joint with either a full penetration or a partially penetrated weld that is subjected to both normal and bending stresses. The location of the potential crack initiation is prescribed to the weld root and the associated class for the nominal stress method is class G. A comparable FAT value for class G at 2·106 cycles and a nominal probability of failure that is 2.3 % (two standard deviations from mean) is 50.
Four out of six participants have chosen to implement details with little to no bending stress over the throat section of the weld. This could potentially overestimate the fatigue life of the component as detrimental bending stresses can be expected over the throat section due to bending in the flange. Three of the four participants are in extension using details for the full penetration cases which either state that weld toe failure is the most plausible failure type or that root and toe failure can be regarded as equally plausible. Participant 3 and participant 6 are the only ones who implemented details where the bending contribution of the applied load over the throat of the weld is considered.
Nominal stress evaluation
Both analytical hand calculations as well as FE-based simulations were used to derive the nominal stress for each box configuration. The methods ranged from simple models considering only the membrane stresses as the ratio between the applied load and the nominal area to FEM simulations with stresses calculated over the weld throat. The approaches used by the participants are presented in Table 4. Participant 2 and participant 6 chose to include calculation results using both analytical models and numerical simulations.
Table 4 Model types used in the nominal stress method by the participants Analytical methods
Two types of analytical methods were presented by the participants, those who only considered the membrane stresses and those who also accounted for bending stresses. The method for calculating the membrane stresses is similar for all participants, the applied force is equally distributed onto a reference area. The source of variation for the calculated membrane stresses is therefore given by the magnitude of the applied load and the size of the load carrying area, which in a simplified form can be expressed as
$$ {\sigma}_{\mathrm{m}}=\frac{F}{4{\mathrm{l}}_{weld}\alpha \left(\mathrm{a},\mathrm{p},{\mathrm{t}}_{\mathrm{web}}\right)}. $$
(1)
F is here the applied force, lweld is the length of the weld along one of the web plates and α is a function describing the equivalent load carrying thickness. This latter parameter is by some used as either the total cross-sectional area of the web plates, or as a percentage of this area while other participants have used an effective throat thickness. The effective throat thickness is governed by the penetration depth and throat thickness (the definition of these two can be seen in Fig. 2b). The number of ways that this effective throat thickness was calculated equals the number participants who implemented this approach, all different versions are presented in Fig. 3. The parameters used by participants in the implementation of Eq. (1) are presented in Table 5.
Table 5 Effective cross-sectional properties used by the participants Participant 4 and participant 6 have added analytical calculations of the bending stresses to capture a more complete stress state. Both have calculated these stresses by assuming that half of the box section resists half of the load applied at the load surfaces. The bending stresses were calculated using the area moment of inertia and the bending moment, both of which were calculated differently by the two participants. The estimation of the bending stresses thereby differs considerably between the two participants, with the method by participant 4 giving stresses around 37 MPa whereas the method by participant 6 gave stresses of 128 MPa. Both participants state that they are unsure on validity of the methods that they used. This shows the uncertainty in analytical models when the complexity of the problem studied exceeds that of typical textbook examples.
Simulation methods
Participants 1, 2 and 6 have all performed numerical simulations to derive the nominal stress. Both participants 1 and 2 investigated the far field stresses by looking at how the stresses in the web change along the load direction. They chose a stress path mid centre of the load surfaces to analyse, the same path on which the maximum principal surface stress was found. The far field stress was taken by both participants as the local minima along this line, as presented in Fig. 4.
Participant 6 chose to implement the nominal stress method and fatigue class G found in the British Standard [17] with linearised stresses in the weld throat. The stress distribution over a path from the weld root to the weld toe on the web side was extracted from simulations with a refined mesh at the weld and around its close proximity. A linear fit was manually estimated to the stress distribution along the path from which the stresses at the weld root was extrapolated. This extrapolation of stresses at the weld toe shares resemblance to methods proposed by Søreensen et al.[18] and Fricke et al. [19], the FAT classes used by the participant are however not the same as in the mentioned methods.
Assessed fatigue strength
The critical stress levels determined by the participants for each box specimen are presented in Fig. 5. Almost no dependency of the penetration depth is seen for the participants, who only considered the nominal membrane stresses. The same is seen for the simulation results of participants 1 and 2 who also have a high level of agreement with each other. The analytical methods considering the bending stresses by participants 4 and 6 shows a clear dependency of the penetration depth; they do however not coheir well with each other as a factor of two separates them.
All participants were asked present the mean fatigue life for each box configuration using the nominal stress method. The recalculations of the results from the probability level given by the codes to the mean level prove to introduce some variations in the fatigue assessment. Participant 3 stood out the most with a scaling factor on the fatigue life that was approximately 10% lower than the rest of the group that lay within 2% of each other. The mean fatigue life for the specimens investigated by the nominal stress method is presented in Fig. 6. Large scatter is seen for all specimen configurations when comparing both the analytical results and the FEM results.
The numerical results of participant 6 estimate the lowest number of cycles, as can be expected with their approach of implementing local stress extrapolation over the throat. Little to no variation is seen between participant 1 and participant 2 who both used a numerical approach to derive the far field stress in contrast to the participants that utilised analytical approaches. This shows that numerical simulations are to recommend in situations where either a complex geometry or stress distribution gives rise to local bending effects that are hard to capture analytically.