The fatigue behavior of bus frame components consisting of thin-walled tube beams joined together by fillet welding has been investigated. Numerical analysis by means of finite elements and experimental stress analysis by means of strain gages explored the failure-critical locations at the weld toe. In addition, a proposal for finite element modeling in particular of the welded area, and evaluation of hot spot stresses to be used for fatigue life calculations of such thin-walled structures has been developed. The calculation results have been verified based on experimentally determined fatigue lives of the components under constant amplitude loading. A satisfactory agreement between experimental and theoretical results has been observed

Athanassios FOKILIDIS

Georgios SAVAIDIS

The Annals of “Dunarea de Jos” University of Galati Fascicle IX Metallurgy and Materials Science

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THE ANNALS OF “DUNAREA DE JOS” UNIVERSITY OF GALATI. 
FASCICLE IX. METALLURGY AND MATERIALS SCIENCE 
N0. 2 – 2007, ISSN 1453 – 083X 
 
 
 
 
EXPERIMENTAL INVESTIGATION OF FATIGUE OF  
THIN-WALLED WELDED STRUCTURES OF  
COMMERCIAL VEHICLE FRAMES 
 
Athanassios FOKILIDIS, Georgios SAVAIDIS 
Aristotle University of Thessaloniki, Dept. of Mechanical Engineering, Greece 
email: gsavaidis@meng.auth.gr 
 
ABSTRACT 
 
The fatigue behavior of bus frame components consisting of thin-walled tube 
beams joined together by fillet welding has been investigated. Numerical analysis 
by means of finite elements and experimental stress analysis by means of strain 
gages explored the failure-critical locations at the weld toe. In addition, a proposal 
for finite element modeling in particular of the welded area, and evaluation of hot 
spot stresses to be used for fatigue life calculations of such thin-walled structures 
has been developed. The calculation results have been verified based on 
experimentally determined fatigue lives of the components under constant 
amplitude loading. A satisfactory agreement between experimental and theoretical 
results has been observed.  
 
KEYWORDS: Fatigue, welds, finite elements, hot spot stress, experimental 
analysis 
 
1. Introduction 
 
Calculation methods for the investigation of 
fatigue behavior of welded structures under 
operational loading are gaining increasing importance 
in many technical applications, since they contribute 
in decreasing developmental costs and time. 
Extensive research activities over the last decade 
especially in the fields of crane and marine 
construction led to various calculating procedures, 
which differ fundamentally in their type of evaluation 
(based on nominal, local or structural hot spot 
stresses). Radaj et al. [5] and Maddox [12] give an 
overview and a systematic survey of the existing 
methodologies and concepts dealing with fatigue 
evaluation of welds. Details for numerical analyses 
by means of finite elements are given in [13]. In 
addition, fracture mechanics based approaches have 
been also elaborated [2, 11]. A state of the art has 
been recently reported by Tovo and Livieri [16] and 
Fricke [9]. 
Valuable recommendations for fatigue 
assessment of welds engineering applications are also 
given in international guidelines, e.g. the one of the 
International Institute of Welding (IIW) [9], Eurocode 
[6], as well as [4] and [1]. However, all these 
recommendations deal mainly with quite thick 
structures.  
In the automotive sector, there is an increasing 
interest for computer-aided methods to shorten the 
development time. In the last years developments on 
theoretical assessment of welded automotive 
components with low thicknesses have been achieved 
in conjunction with the hot spot stress approach, see 
e.g. Boven-Griffon et al. [3], Fayard et al. [7] and 
Fermér and Svenson [8]. Own initial experience [14, 
15] revealed that fatigue analysis based on hot spot 
stresses might be capable for handling such thin 
components.  
However, nowadays it still lacks of experiment-
ally verified guidelines for the calculation of fatigue 
life. Therefore, the assessment of thin-walled welded 
components under operational loading is still domina-
ted by experimental methods.  
Taking new generation bus frame components 
consisting of thin-walled tube beams with thickness 
t=2mm joined together by fillet welds as examples, 
the investigation focuses to: 
a) the investigation of the mechanical behavior 
of the components, in particular of structural stresses 
acting at the failure critical welds 
b) the determination of the fatigue live curves 
under bend loading 
c) the development and assessment of the 
reliability of a finite element meshing and calculation 
procedure that can be applied for the fatigue life 
prediction based on hot spot stresses. 
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FASCICLE IX. METALLURGY AND MATERIALS SCIENCE 
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2. Hot spot stress approach 
 
The so-called “structural” stress at the hot spot 
(HSS), i.e. at the failure-critical point of the weld, is a 
fictitious stress. In many applications, this point 
corresponds to the weld toe. The HSS value can be 
determined using reference points in certain distances 
from the weld toe by extrapolating the surface stress 
values measured or calculated at the reference points 
at the weld toe [10]. The reference points are set 
dependent on the thickness t of the welded 
components and the extrapolation method used. 
Depending on the shape of the stress distribution 
acting perpendicular to the weld toe a linear or 
quadratic stress extrapolation at the weld toe is 
recommended as depicted in fig. 1 and 2, 
respectively.  
 
Fig. 1. Determination of HSS by linear 
extrapolation 
 
Fig. 2. Determination of HSS by quadratic 
extrapolation 
 
Note that the HSS includes all stress raising 
effects of the structural detail except the stress 
concentration due to the local weld profile itself.  
 
3. Specimens and loading 
 
Figure 3 illustrates the geometry of the 
specimens and the load configuration applied in the 
present investigation.  
Two longitudinal tube beams with dimensions 
50x50x2 [mm] are jointed to a vertical tube beam 
with dimensions 50x50x2 [mm] by fillet welds. The 
thickness of the weld amounts to 4mm.The ends of 
the longitudinal beams are fixed while the load is 
introduced at the one end of the vertical beam.  
The specimens were subjected to force-
controlled, fully reversed loading with constant 
amplitudes. Therewith, mainly normal stresses due to 
bend loading are acting at the weld toes.  
 
Fig. 3. Specimen’s geometry and load 
configuration 
 
4. Finite element meshing 
 
Figure 4 shows schematically the procedure 
followed here to model the weld and to calculate the 
HHS value at the weld toes in the longitudinal and the 
vertical beam. The origin of this procedure goes back 
to Fayard et al. [7].  
 
Fig. 4. Specimen’s geometry and load 
configuration 
 
The vertical and longitudinal beams of the 
component are shown in fig. 4. Their thickness 
amounts to t=2mm. The fillet weld triangle is 
illustrated with side lengths lw. Two rectangular 
surfaces consisting of intermediate shell elements 
have been used to model the beams shown in fig. 4 
with bold lines. In accordance with Fayard’s et al. [7] 
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FASCICLE IX. METALLURGY AND MATERIALS SCIENCE 
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suggestion, the fillet weld itself has been modeled by 
an additional surface of shell elements, whereby the 
dimensions of the rectangular sides of the fillet weld 
triangle amount to (t+lw)/2 on both the longitudinal 
and the vertical beam, respectively. The stiffness of 
the shell elements of the fillet weld is assigned to 
replicate the stiffness of the real weld. 
A servo-hydraulic actuator introduces the load 
into the end of the vertical beam. The longitudinal 
beams are beard to the test rig traverse and the table 
using two bearing elements. The bearing elements are 
designed to compensate possible misalignments 
between the vertical and the longitudinal arms due to 
residual stresses induced by the weld-heat as well as 
possible deviations of the real geometrical 
dimensions of the beams from the nominal ones. 
Differing from Fayard’s initial suggestion, the 
finite element mesh has been created to explore nodal 
stresses at the distances of 0.4t, 0.9t and 1.4t from the 
weld toe. These distances correspond to the principal 
recommendation of the IIW guideline [10] when a 
fine mesh with quadratic surface stress extrapolation 
is to be applied.   
Three batches of specimens with equal 
dimensions of the beams and the welds but made up 
of three different constructive steels have been tested, 
named as T1, T2 and T3. However, the steels provide 
similar mechanical behavior and fatigue properties so 
that no influence is expecting due to the different 
steel material. 
Figure 5 shows the finite element mesh detail of 
the welded area used for the theoretical analysis.  
The specimens were tested under force-
controlled, fully reversed cyclic loading (force ratio 
RF=-1) with constant amplitudes vs. time. Thereby, 
various force amplitudes were applied in order to 
determine secured knowledge of the component’s 
Woehler curves. The specimens were tested in the as-
welded condition, at room temperature with a 
frequency of 4 Hz.  
  
Fig. 5. Finite element mesh detail of the weld 6. Results 
  
The stress values at the reference points 0.4t, 
0.9t and 1.4t from the weld toe will be used to 
calculate the HSS values at the weld toe using 
Equation (1) [10]: 
Fatigue cracks were initiated at the weld toe 
very near to the edges of the beams, where the highest 
stresses arise, during the applied force-time 
sequences.  
= ⋅σ − ⋅σ + ⋅σ0.4t 0.9t 1.4tHSS 2.52 2.24 0.72     (1) The cracks propagated along the weld toe 
perpendicular to the direction of the normal stresses. 
Thereby, both weld toes, the one in the vertical and 
the one in the longitudinal beam, have been found out 
to be failure-critical. The initiation of fatigue cracks 
with lengths of approximately 3mm to 4mm at the 
surface of the components has been defined as failure 
criterion.  
 
5. Test rig 
 
Figure 6 shows the test rig used for the 
experimental investigation. Note that the adjustment 
of the specimen in the test rig is rotated by an angle 
of 90° in comparison to the illustration shown in fig. 
3.  
Longitudinal 
H
SS
 ra
ng
e,
 Δ
σ H
SS
   
[M
Pa
]  
 
 Number of cycles to failure, N
 
Fig. 7. Fatigue life results for failure at the 
longitudinal beam  
 
Fig. 6. Test rig 
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FASCICLE IX. METALLURGY AND MATERIALS SCIENCE 
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A crack length of this size causes a reduction of 
the component’s stiffness of approximately 5%, 
which can be measured reliably by the electronic 
devices of the test rig. Figures 7 and 8 contain the 
experimentally determined fatigue life results plotted 
vs. the range of the HSS, ΔσHSS, calculated by means 
of finite elements for failure detected in the 
longitudinal and the vertical beam, respectively.  
 
 
 
 
Fig. 8. Fatigue life results for failure at the 
vertical beam  
 
The different marker symbols in fig. 7 and 8 
stand for the different specimen batches. The Woehler 
lines for the various probabilities of survival PÜ have 
been determined by means of regression analysis of 
the corresponding results.  
The characteristic scatter band TN can be 
derived from the Woehler curves for the probabilities 
of survival of 10% and 90%. It is defined as 
=
=
= P 10%N
P 90%
N
T
N
.                           (2) 
It amounts to TN=1:3,7 for the cases with failure 
at the longitudinal beam, and TN=1:7 for those with 
failure at the vertical beam.  
The slopes of the Woehler curves for the two 
failure cases do not deviate significantly from each 
other. They amount to k=4.2 (failure at the longitu-
dinal beam) and k=4.36 (failure at the vertical beam). 
These k-values are slightly higher than the one 
reported in the IIW-guideline (k=3).  
Furthermore, a general comparison of the 
fatigue life results determined according to the 
procedure described in section 4 with the hot spot 
stress-life curves suggested by the IIW-guideline [10] 
is shown in fig. 7 and 8 for the two failure cases, 
respectively. The latter are to be used for the design 
of fillet welds in an as-welded condition if no 
experimental results are available.  
They are based on several fatigue tests and 
assigned with a probability of survival of 90% within 
a confidence belt of 75%, which results in an overall 
probability of survival of PÜ=97.5%. 
To determine the Woehler curves according to 
the IIW guideline, the so-called FAT value for this 
weld configuration, i.e. the HSS range at a lifetime of 
2000000 cycles, has been used as reference value. 
The reference FAT value for the weld configuration 
under investigation amounts to FAT=100 MPa. This 
value considers wall thicknesses of approximately 
25mm and stress ratios of R>0.5. Therewith, the 
benign thinness effect due to the reduced thickness of 
the beams investigated here (t=2mm) has been taken 
into account explicitly, using the correction thickness 
factor reported in the IIW guideline. Finally, an 
additional correction factor due to the acting stress 
ratio Rσ=RF=-1 has been considered. To determine 
fatigue lives at lower N-values, IIW recommends a 
unique Woehler curve slope of k=3 for all types of 
welds. 
Vertical 
H
SS
 ra
ng
e,
 Δ
σ H
SS
   
[M
Pa
]  
In both failure cases noticed in the present 
investigation, a satisfactory agreement between the 
Woehler curves determined according to the IIW 
guideline and the corresponding ones determined by 
the presented calculation procedure for the probability 
of survival 97.5% can be observed. 
Number of cycles to failure, N
 
7. Conclusions 
 
The fatigue behavior of thin-walled, fillet-
welded components made from various ductile steels 
used for bus frames have been investigated theore-
tically and experimentally under fully reversed con-
stant amplitude cyclic loading. The following remarks 
are made in conclusion: 
The test results identified the weld toes at the 
edges of the horizontal arm to be the failure critical 
locations. Few specimens failed at the corresponding 
weld toe of the vertical arm. The finite element 
analysis unraveled the locations, which were 
identified experimentally as failure-critical. 
A finite element meshing procedure according 
to Fayard’s et al. proposal for weld modeling by 
means of shell elements in conjunction with the 
recommendations of the IIW guideline has been 
applied. In addition, a quadratic surface stress 
extrapolation at the hot spot of the modeled weld has 
been proposed.  
The HSS-Woehler curves determined by the 
suggested calculation procedure have been found out 
to be in satisfactory agreement with the 
corresponding ones determined according to the IIW 
guideline. These results confirm the accuracy and 
efficiency of the so-calculated hot spot stresses for 
fatigue design of thin-walled components such as the 
ones investigated here. 
Though the experimental database used here for 
the verification of the calculation procedure is 
certainly narrow for generalizations, the results 
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THE ANNALS OF “DUNAREA DE JOS” UNIVERSITY OF GALATI. 
FASCICLE IX. METALLURGY AND MATERIALS SCIENCE 
N0. 2 – 2007, ISSN 1453 – 083X 
 
 
encourage to apply and verify this procedure to thin-
walled structures such as the one investigated.  
 
References 
 
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[12]. Maddox S.J., Fatigue strength of welded structures, 2nd 
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Experimental Investigation of Fatigue of Thin-Walled Welded Structures of Commercial Vehicle Frames

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Experimental Investigation of Fatigue of Thin-Walled Welded Structures of Commercial Vehicle Frames

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