1IntroductionThe purpose of this research work i.docx

1Introduction
The purpose of this research work is to study the fatigue related
behavior of weld toe
and weld root geometrical parameters in fillet welds based on
the effective notch stress
approach.
The fatigue tests of welded structures under fluctuating loads
shows that the crack
initiation and propagation until the final failure is carried out
mostly on the weld toe and
weld root. Since the geometrical effect on stress distribution
over a part plays a
meaningful role in respect to increasing the stress concentration
factor value and
consequently the risk of failure, in this research the geometrical
variables of welding

which can be recommended in some case of welding procedures
such as weld toe
waving and weld root penetration percentage is studied. The
fillet weld models under
special case of loading and constraint analyzed by three-
dimensional linear static
analyses of finite element method to define the maximum
principal stress distribution in
the modeled cases. The fatigue effect of analysis added to
model by utilizing the
effective notch stress approach, which models the sharp lines in
weld toe, and weld root
by determined rounded radius of 1 mm for steel material to
avoid the geometrical
singularity of numerical analysis and take into consideration the
fatigue notch factor.
The models of this study focus on the variation of stress
concentration factor due to
weld toe waving geometrical effects defining by two variables
of waving width and
waving radius in two separate set of models which the weld
flank angle has been
changed. This leads an understanding to the benefit of varying

stress concentration
factor on the weld toe between waving tips and waving depths
so that the significant
decrease of this factor in waving depths can stop the rate of
arbitrary initiated crack
propagation.
That is a crack, which initiated in a susceptible location such as
wave tips could be
controlled by the waving depths, which have a significantly
lower stress.
Meanwhile the study continued to analyze the distribution of
stress in fillet weld root in
respect of the percentage of weld penetration into the base
material by the same fatigue
9
method and numerical analyzing tools. The result of this part
depicts the usability of
analyzing models type applying the effective notch stress
approach and can be utilized

to define an optimized penetration percentage in the weld root
of fillet-welded joints
2Fatiguebasefracture
Material properties, relate to the quality control of materials
and initial material
selection by a designer and employing only a look at the stress-
strain analysis will cause
the valuable information is lost. There are factors other than
exceeding the yield stress
and causing plastic deformation, which will affect structures.
Fracture is concerned with
the initiation and propagation of a crack until the load can no
longer be held by the
structure. It is well known that most structures will contain
some crack like flaw or
defect by the manufacturing process, even after rigorous
inspection. Since it is relatively
difficult to design against crack initiation, controlling the
propagation of crack in a
material is required for most designers to consider. Crack
propagation through materials
at a high velocity is a situation of great danger. The problem of

unstable fracture first
ventured to the public scene in the mid-1930 to mid-1950. [1]
Deterioration of a component caused by the crack initiation and
followed by the growth
of a crack under a fluctuating load value is termed as fatigue.
The important parameter
in respect of fatigue effect is fatigue life, which is the number
of stress cycles of a
particular load magnitude required to cause fatigue failure in
the component.
All the components specially the structural components that
carry the periodical loads
are susceptible to the fatigue failure hence the fatigue strength
is determined as the
magnitude of stress range leading to a particular fatigue life.
Whereas the fatigue limit is
the fatigue strength under constant loading amplitude,
corresponding to a high number
of cycles large enough to be considered as infinite.

The fracture mechanics, which is dealing with the behavior and
strength of components
containing cracks, categorizes the fracture in elastic and plastic
fracture categories.
10
Linear Elastic Fracture Mechanics (LEFM) is an analytical
approach to fracture relating
the stress distribution around a crack to the parameters such as
the nominal stress
applied to the structure along with the size, shape and
orientation of the crack.
The amount of resistance against a crack as material could take
without brittle fracture
is termed as the fracture toughness (KC). Fracture toughness
depends on the material affected by the temperature, loading
rate and thickness of member so that thicker members have
lower KC. Plane strain fracture toughness (KIC) is a measure of
a material fracture resistance in the presence of a crack. [2]
The process of fatigue failure based on micro structural
phenomena (moving

dislocations, micro crack initiation on slip bands and further
crack growth by local slip
mechanisms at the crack tip) could be describe by a
macroscopic elastic or elastic-
plastic stress and strain analysis according to the continuum
mechanics which refers to
the cyclic deformation causing initiation and propagation of the
technical crack
including final fracture. An initial crack which is usually in the
surface of a structure is
termed the technical crack while could be detected by a common
technical instruments
for instance to have 1 mm length and 0.5 mm depth.
The fatigue study with respect to the welded structure could be
divided into two
approaches, the global and local approach. The design rules for
fatigue resistant
structures take the global approach applying the nominal stress
depend on the notch
class, detail class or fatigue class (FAT) of the welded joints.
The fatigue failure of structural members consisting of crack

initiation, crack
propagation and final fracture is a local process in respect of
the local parameters of
geometry, loading and material, which affect the fatigue
strength and service life of the
structural members.
The fatigue strength assessment concluded directly from the
external forces and
moments or from the related nominal stresses in the critical
cross-section, assuming the
constant or linearized stress distribution is termed global
approach. The critical values
11
of load or nominal stress determine the criteria of the approach,
which study the fully
plastic yielding, or total fracture of specimen.
In contrast, the study of local stress or strain parameters leads
to the local approach. The

local process of damage consists of cyclic crack initiation,
cyclic crack propagation and
final fracture is discussed in this area. Crack initiation is
covered by the notch stress or
notch strain approach, on the other hand, the crack propagation
and final fracture is
described by the initial crack propagation and fracture
mechanics approach. [3]
3Fatigueassessmentinweldedstructures
The common way of fatigue assessment for welded joints utilize
the S-N curve
approach, using S-N curves (Wőhler curves) giving the design
fatigue life for constant
amplitude loading and an appropriate damage accumulation rule
to consider the effect
of variable-amplitude loading.
Based on the different types of stress at the critical welded joint
the following
approaches would be utilized:

Nominal stress approach, based on the stress that excludes
any stress increase
due to the structural detail or the weld.
Structural hot-spot stress and other structural stress
approaches, based on the
stress [4] containing only the stress increase due to the
structure, but not due to
the local weld geometry such as weld toe.
Notch stress approach, based on the local stress at the weld
toe or the weld root,
assuming ideal-elastic material behavior and micro-structural
support effects to a
certain extent.
Notch stress intensity approach, using the notch stress
intensity factor (NSIF) at
the weld toe with zero radius as the fatigue parameter. [4]
The approaches use fracture of a specimen or structure as
failure criterion.
Alternatively, the elastic-plastic notch strain approach may be
applied, which is based
on crack initiation in the material and considers the plasticity
effect on fatigue using

relevant material properties. Additionally the crack propagation
approach is applied for
12
computing fatigue lives, up to a defined crack length. The crack
propagation approach
based on fracture mechanics principles is in widespread use as
an alternative to the S-N
curve approaches, assuming a fictitious or actual initial crack.
In comparison with the
other approaches, the notch stress approach allows the effect of
the local weld geometry
to be included directly in the stress so that different geometrical
configurations can be
compared with each other and can even be optimized. [4]
3.1Notchstressapproach
The discontinuities in the geometry of structural members,
which is unavoidable in
design process or in the joining parts such as welding seam,

increase the stress value in
comparing the whole area of the member. These stress raisers
termed as the notches,
which affect the fatigue resistance against the failure. [2]
The notched members are subject to the localized yielding
caused by the loads and the
consequence of the locally higher stresses causing fatigue
cracks to start at such
locations. [2]
To characterize the severity of a notch the elastic concentration
factor, which is the ratio
of the local notch stress to the nominal, or the average stress,
could be employed. [2]
� = (1)
The elastic stress concentration factor is determined by two
factors, the geometry and
loading of the structural component.

The fatigue notch factor characterizes the strength effective
stress concentration which
is taken from the microstructural notch support hypothesis in
the case of sharp notches,
and means that the maximum notch stress based on the theory of
elasticity dos not rule
the crack initiation and propagation, instead some lower local
stress developed by
averaging the notch stresses over a small length of material
including the area or volume
at the notch root controls the failure procedure. The micro
structural notch support
hypothesis is developed based on the grain structure, micro-
yielding and crack initiation
13
processes. The sufficiently mild notches as well as the sharp
one get supported
microstructural resistance against the rupture of material, thus
the fatigue notch factor
depends on the notch radius and a material microstructural

length in addition to the
parameters controlling the stress concentration factor. [3]
The different microstructural notch support hypotheses applied
for the fatigue strength
assessment are as following:
The stress gradient approach [5]
The stress averaging approach [6] [7] [8]
The critical distance approach [9]
The highly stressed volume approach [10]
The last three hypotheses have wide application in the welded
joints analysis. The stress
averaging approach is mainly used in the form of fictitious
notch rounding which is
shown in the following figure, known also as effective notch
stress approach, while the
critical distance approach employs the ratio of a material
constant and the notch radius
to reduce the elastic stress concentration factor, Kt, to the
fatigue notch factor, Kf. Further variants of the stress averaging
methods applicable to notch tips are related to a distinct area or

volume instead of the conventional line section. [3]
3.2Fictitiousnotchroundingapproach
The basic idea behind this approach is that the stress reduction
in a notch due to
averaging the stress over a certain depth can alternatively be
achieved by a fictitious
enlargement of the notch radius. The relation between actual
notch radius (ρ), factor for
stress multiaxiality and strength criterion (S) and substitute
micro-structural length (ρ*)
is as following:
� = � + � × �∗ (2)
In plane strain conditions at the roots of sharp notches
combined with the Von-Mises
multiaxial strength criterion for ductile materials for welded
joints, the strength
factor (S) is assumed 2.5. [11]. Considering typical welds in
(low strength) steel, the
14

choice of ρ* = 0.4 mm (for cast steel in the welded zone) is
appropriate. Both factors
result in an increase of the actual radius by 1 mm to obtain the
fictitious radius ρf according to Eq. (2). The rounding is applied
to both the weld toe and the weld root.
Figure 1. Fictitious notch rounding [12]
In a 'worst case' or conservative way, Radaj's approach is
applied assuming an actual
radius of zero so that the fictitious radius, now considered as
the reference radius, is

Rref = 1 mm. As the stress analysis results in the fatigue-
effective stress, the approach is
also called effective notch stress approach. [4]
The modified notch rounding developed by Seeger et al. to r = 1
mm independently of
the actual radius which varied around this value. The notch
stress was determined for
this value at both weld toes and roots without further
corrections regarding the
microstructural support effect. [4]
4Numericalanalysisofnotcheffectedmethod
The notch stress over the welded joints can be analyzed by
Finite Element Method
(FEM) or Boundary Element Method (BEM), which calculate
the stress concentration in
the fatigue critical notch under specified loads assuming linear-
elastic material
behavior. The more accurate results of stress concentration
factor due to the notch

presence require a sufficiently fine discretization of the
structure in the notch area.
Meanwhile the effects of large displacements on the structural
stress and the contact
15
problems may require a non-linear analysis, however, contact
between non-welded root
faces is not usually assumed, leading mostly to conservative
results. [4]
5Fatigueexperimentaltest
In this part, a fatigue test and results of a fatigue test, which has
been carried out in
Lappeenranta University of Technology–the fatigue laboratory
is presented. The models
in this study are based on this test, and provide the possibility
of validating the outputs
from effective notch stress approach and finite element method
analysis. The specimen
geometry is a cruciform fillet welded joint so that the weld toe

formed in waving with
waving radius and waving width of 7 mm. The sketch of waving
on the weld toe and the
dimension of weld surface over three lines measured by laser,
reported in Figs 2 and 3.
Figure 2. The fillet weld toe formed in waving shape, and the
laser measuring lines.
The laser measurement of weld toe records the Y-coordinate of
weld surface from
approximately 1.5 mm before the weld toe to 2 mm on the weld
flank.

16
Weld toe rounding
radius ≈ 0.5 mm
Figure 3. Laser measuring records the surface curvature over
the weld flank.
The fatigue test conducted on the specimen so that the
horizontal plate carries the load

and the vertical plate as a non-loading element joins by fillet
welded. The loading
system is shown in Fig. 4.
Figure 4. The loading system carried on the fillet-welded
specimen.
The loading history and the fatigue test results are listed in
Table 3.
17
Table 1. Fatigue test loading records and results.

TestItems
Testrecords
Max. Force
(average value from start to fracture) [kN]
66.590
Min. Force
(average value from start to fracture) [kN]
5.192
Max. Displacement
(average value from start to fracture) [mm]
0.665
Min. Displacement
(average value from start to fracture) [mm]
0.033
Fatigue life [cycles]
1964766

The fatigue stress over cycle number diagram (S-N diagram) of
the test is shown in
Fig. 5.
N[cycles]
Figure 5. Stress vs. Life cycle Number results of test specimen.
18
The base material of the welded structure is made of high
strength material processed by
Ruukki Company under the trademark of Optim 960 QC. The
mechanical property and
chemical composition of the material are in the Tables 2 and 3.
Table 2. Mechanical property of material
Material name

Yield strength [MPa]
Tensile strength [MPa]
Elongation %
Impact strength
Temprature [C]
Charpy Test [J/cm2]
Optim 960 QC
960
1000
7
-40
34

Table 3. The chemical composition of the material
Material name
C
Si
Mn
P
S
Ti
Optim 960 QC
0.11
0.25
1.20

0.020
0.010
0.070
6Modelingoftheweldgeometry
The models of this study utilize the finite element method to
analyze the linear static
method by NX Nastran Version 10.3.1 inside the FEMAP
software (Copyright © 2012
Siemens Product Lifecycle Management Software Inc.)
modeling feature.
The study on the weld toe waving shapes is accomplished based
on the models of
cruciform fillet weld according to the dimension mentioned in
the Fig. 6.
19

Figure 6. The schematic view and dimension of cruciform fillet
weld.
To simulate the experimental fatigue test mentioned before, the
applied force value on
the model is 66590 N and the schema of force introducing on
the model is as mentioned
in Fig. 10. Since the cruciform fillet weld geometry which is
used to study on the weld
toe variables, is symmetric upon the three symmetric planes,
just 1/8 of the specimen is
analyzed under the proper symmetric boundary condition to

model the constraints, and
the applied force for this symmetric model is 16647.5 N.
Figure 7. The schematic view and dimension of one side fillet
weld.
The analysis on root weld is also carried out on a fillet weld;
however, this study
requests the welding on one side of vertical plate. The
schematic and dimension of this
20

model is depicted in Fig. 7. Since this model has two symmetric
planes, just a quarter of
whole model is analyzed, and the applied force is 33295 N in
the numerical model. The
loading schema on this case is according to Fig. 8.
Figure 8. Loading system on a fillet weld specimen, focus on
weld root effect.
6.1Weldtoestudymodels
The fillet weld models of weld toe study are analyzed based on

three variations weld toe
wave radius (WR), weld toe wave width (WW) and weld flank
angle (θ) as shown in
Fig. 9. Based on the theory of notch effective method, the sharp
edges on the waving toe
are filleted and rounded by R = 1 mm. According to the IIW
standard recommendation,
to determine the effective notch stress by FEA applying a
quadratic order of element
and shape function, the mesh size should not be less than 1/6 of
the fillet rounding
radius [13]. In order to meet the size recommendation also to
make an efficient,
optimized and accurate analysis, the mesh size around the
rounding determined
0.05 mm, and then the sizing got smoothly coarser to reach 1
mm in the farthest edges.
The analyses consist of fillet weld with flank angle 45 degrees
and 30 degrees so that in
each case set of modeling with waving variation is done. The
trends of the maximum
principal stress values and consequently the value of stress
concentration factor over the

weld line on weld toe are reported.
21
Figure 9. The schema of dimensions of fillet welds with the
flank angle of θ in the weld
toe.
The values of waving width and waving radius changes in the

weld toe waving shape
listed in Table 4, and in Fig. 10 a sample of visualized
differences in the geometry of
different waves is shown for two waving width of 7 and 20 mm.
Figure 10. The schema of weld toe waving radii in the models
with 7 mm and 20 mm
waving width.
22
Table 4. The dimension of waving radius and waving width on
models.
wavewidth(WW)

WW/WR
waveradius(WR)
Straightweld
0
∞
2
0.5
4
2
1
2
2
1.5
1.333
4
0.5
8
4

1
4
4
1.5
2.667
7
0.5
14
7
1
7
7
1.5
4.667
10
0.5
20
10

1
10
10
1.5
6.667
20
0.5
40
20
1
20
20
1.5
13.333
The value of maximum principal stress (M.P.S.) in each case of
modeling is recorded on
the rounded area through the waving line as well as the straight
line of fillet weld toe. In

Fig. 11, a graphical schema of the modeling, mesh size and
mesh transition type along
with the value of M.P.S. for weld toe model with waving width
and waving radius of
7 mm is depicted. Also in Fig. 12, a trend of M.P.S. values on
the weld toe line in the
same model as in Fig. 11 is recorded.
These graphical results and trends are the base of post-
processing and analyzing the
numerical output of models. The same path has been surveyed
in the modeling of root
study, which will be presented in Section 6.3.
23
Min. Stress on
weld toe wave
Max. Stress on

weld toe wave
Figure 11. The maximum principle stress on the weld toe line
with waving width and
waving radius of 7 mm.
Weld Width
Figure 12. The maximum principle stress variation on the weld
toe over the weld line
width with waving width and waving radius of 7 mm.

6.2Notchstressfatiguestrength
Based on the notch effective stress method with R = 1 mm, and
according to the
recommendation of IIW [13] and test of Oliver et al. [4], the
fatigue strength for welds
24
of steel material, characteristic fatigue strength with survival
probability of Ps = 97.7% and endurance cycle of N=2×106
cycle is FAT 225. The mean fatigue strength with
Ps = 50% is applied for the normal weld fatigue life estimation
by FAT 309 [3].
The original endurance limit approach subsequently converted
to S-N curves based so
that such curves should be in the form of Eq. (3):
∆� ∗ � = � (3)

Where Δσ is the notch stress range and the constant C = 2×106
(FAT)m. As generally
assumed for welded joints, the slope exponent of m = 3 is
selected.
Since stress for waving toe with WW = 7 mm and WR = 7 mm is
504 MPa and for
straight weld is 489 MPa the failure cycles respectively would
be calculated as the
characteristic life:
NWave = 2×106 × (309 / 504)3 = 1226190 cycles NStraight
= 2×106 × (309 / 489)3 = 1263803 cycles
6.3Weldrootmodeling
To model the weld root based on the notch effective method, the
root steep and singular
angle is modeled with a rounded semi-circle with R = 1 mm.
The mesh size concerning
the IIW recommendation [13] is utilized to be 0.05 mm. the
study on root weld is
divided to three state of penetration from zero penetration to
full penetration through the

vertical element of welded joint, which in this modeling does
not carry the load.
6.3.1No-penetrationmodel
This model is to prepare the situation that a fillet weld cannot
penetrate in the root weld
area depending on the situation of welding. The model shape
and dimension is shown in
Fig. 13 and the graphical view of maximum principal stress
value over the root area is
in Fig. 14.
25

Figure 13. Sketch and dimension of no-penetration model.
Figure 14. The maximum principal stress variation on the root
area in no-penetration
model.
6.3.2Half-penetrationmodel

This model refers to the situation that the weld penetrates half
in the root area
depending on the welding situation.
26
Figure 15. Sketch and dimension of half-penetration model.

Figure 16. The maximum principal stress variation on the root
area in half-penetration
model.
6.3.3Full-penetration,model-1
The full-penetration model is that the weld penetrated
thoroughly through the thickness
of vertical plate. This situation provides two choice of rounding
to apply the notch
effective method to obtain the notch stress. Here the first model
is presented.
27

Figure 17. Sketch and dimension of full-penetration model-1.

Figure 18. The maximum principal stress on the root area in
full-penetration model-1.
6.3.4Full-penetration,model-2
The second choice of rounding the weld root in the full-
penetration model is to make a
simple rounding with radius of 1 mm in the sharp corner on the
back of the weld.
28

Figure 19. Sketch and dimension of full-penetration model-2.
Figure 20. The maximum principal stress on the root area in
full-penetration model-2.
7Results

In this section the fatigue strength and stress based results
extracted from the various
modeling of fillet welds analyzed by Finite Element Method is
introduced.
The results of modeling in the fillet weld with 45 degrees and
30 degrees flank angle
which was analyzed by Finite Element Method, based on the
notch effective stress
method are summarized in the tables and charts presented in
Section 7.1.
29
7.1Stressvaluesresultsbasedonnotcheffectiveanalysisinweldtoe
The results consist of maximum principal stress value in the tip
and depth of a weld
wave consequently since the linear static analysis have been
done, the value of Stress
concentration factor in these points are calculated to make the
analyses and comparisons

of the models independent to the value of force. The related
chart for the fillet weld with
45 degrees flank angle is presented the values of Stress
concentration factor varying
against a normalized parameter as waving width to waving
radius ratio in Table 5 and
Fig. 21.
Table 5. The results of waving dimension variation on weld toe
with 1 mm rounded and
45 degrees flank angle.
waving
width[mm]
wavingradius
[mm]
wavingwidth/
radiusratio
M.P.S.in
tip[MPa]
M.P.S.in
depth[MPa]
S.C.F.in
tip

S.C.F.in
depth
S.C.F.
deviation
Straight Weld
Straight Weld
Straight Weld
489
460
2.350
2.211
0.139
2
1.333
1.5
501

447
2.408
2.148
0.259
2
2
1
498
460
2.393
2.211
0.183
2
4
0.5
494
473
2.374

2.273
0.101
4
2.667
1.5
505
418
2.427
2.009
0.418
4
4
1
499
442
2.398
2.124
0.274

4
8
0.5
494
468
2.374
2.249
0.125
7
4.667
1.5
511
382
2.456
1.836
0.620
7
7

1
504
422
2.422
2.028
0.394
7
14
0.5
496
453
2.384
2.177
0.207
10
6.667
1.5
510

361
2.451
1.735
0.716
10
10
1
503
406
2.417
1.951
0.466
10
20
0.5
494
442
2.374

2.124
0.250
20
13.333
1.5
501
295
2.408
1.418
0.990
20
20
1
492
364
2.364
1.749
0.615

20
40
0.5
487
417
2.340
2.004
0.336
30
S.C.F.variationoverW.W./W.R.in45degreesflnkangleweldmodels
2,5
2,4
2,3

2,2
WW2 Tip
2,1 WW2 Depth
WW4 Tip
S.C.F.
2 WW4 Depth
1,9 WW7 Tip WW7 Depth
1,8 WW10 Tip
WW10 Depth 1,7 WW20 Tip
1,6 WW20 Depth
1,5
1,4
0 0,5 1 1,5
W.W.overW.R.Ratio
Figure 21. The variation of the waving width over waving
radius ratio against the stress
concentration factor for models in 45-degrees flank angle.

The results for the situation of welding with 30 degrees flank
angle are also summarized
in Table 6 and the related charts in Fig. 22. The values of Stress
concentration factor
give an overall view about the position and the range of stress
over the various models.
31
Table 6. The results of waving dimension variation on weld toe
with 1 mm rounded and
30 degrees flank angle.
waving
width[mm]
wavingradius
[mm]
wavingwidth/
radiusratio
M.P.S.in
tip[MPa]
M.P.S.in
depth[MPa]

S.C.F.in
tip
S.C.F.in
depth
S.C.F.
deviation
Straight Weld
Straight Weld
Straight Weld
455
429
2,187
2,062
0,125
2
1.333

1.5
466
421
2,239
2,023
0,216
2
2
1
461
433
2,215
2,081
0,135
2
4
0.5
459

442
2,206
2,124
0,082
4
2.667
1.5
473
400
2,273
1,922
0,351
4
4
1
466
422
2,239

2,028
0,211
4
8
0.5
461
441
2,215
2,119
0,096
7
4.667
1.5
483
372
2,321
1,788
0,533

7
7
1
474
405
2,278
1,946
0,332
7
14
0.5
463
428
2,225
2,057
0,168
10
6.667

1.5
486
355
2,335
1,706
0,630
10
10
1
475
395
2,283
1,898
0,384
10
20
0.5
464

424
2,230
2,038
0,192
20
13.333
1.5
486
295
2,335
1,418
0,918
20
20
1
473
362
2,273

1,740
0,533
20
40
0.5
374
338
1,797
1,624
0,173
Regarding the symmetric models of weld toe and weld root, the
geometry is so that the
nominal stress in all cases is kept 208 MPa. This will make an
easier comparison among
the model cases.
32

S.C.FvariationoverW.W./W.R.in30degreesflankangleweldmodel
s
2,5
2,4
2,3
2,2 WW2Tip
2,1 WW2 Depth
WW4 Tip
S.C.F.
2 WW4 Depth
1,9 WW7 Tip WW7 Depth
1,8 WW10 Tip
WW10 Depth 1,7 WW20 Tip
1,6 WW20 Depth
1,5
1,4

0 0,5 1 1,5
W.W.overW.R.Ratio
Figure 22. The graphs of stress concentration factor in the tip
and depth of waving toe
of models with 30 degrees flank angle in weld toe.
Just the curves in the waving width of 20 mm are not
comparable with the other curves
because there is only one waving all over the width of the weld
line and some
information at the end rounding of weld might be missing.
7.2Stressvaluesresultsbasedonnotcheffectiveanalysisinweldroot
In this part the stress results on the weld toe varying the
measure of weld penetration is
presented in the form of Table 7 and the related chart in Fig. 23.
33

Table 7. The summarized results of stress in weld root studies
with nominal stress
208 MPa.
M.P.Sinweldroot[MPa]
S.C.F.inweldroot
Nopenetration
367
1.764
Halfpenetration
381
1.831
Fullpenetration#1
380
1.826
Fullpenetration#2
373
1.792

S.C.F.valuesintheroundedareaofweldrootoverthepercentageofpen
etration
2
1,9
1,8
1,7
1,6
S.C.F.
1,5
1,4 S.C.F. in weld root
1,3
1,2
1,1
1
0 50 100
PercentageofPenetration[%]
Figure 23. The results of stress concentration factor over the
welding penetration

percentage.
8Conclusion
Since the study covers the fillet weld stress study in two
separate areas, weld toe and
weld root, the result is concluded in these zones accordingly.
Referring the analysis results of fillet weld models in weld toe,
the dimension of models
has been calculated to keep the measure of weld throat constant
(approximately 5 mm).
34
The clear observation is that the stress concentration factor in
the tip of weld toe waves
increases by decreasing the value of wave radius in a constant
weld width. Meanwhile
the increase of wave width in the models directly increases the
value of stress
concentration factor. From the other hand the decrease in wave

radius and increase in
wave width; significantly decrease the value of stress
concentration factor in the depth
point of weld toe waving line.
The major deviation between the values of stress concentration
factor in tip and depth of
the weld toe waving line effectively play a role of crack
propagation obstacle. That is an
arbitrary crack initiated in the tip of the weld toe wave can get a
lower speed of
propagation by the effect of significantly lower stress value in
the weld depth.
Comparing with a straight weld, if a crack starts in the straight
weld toe line can be
propagated easily in the direction of constant stress value. The
result of the lower stress
concentration factor in the depth of the waving on weld toe is to
obtain a longer fatigue
life.
The other aspect of stress consideration in the waving weld toe
is that the stress

concentration factor in the tip points increases slightly
comparing with a straight weld
toe, which can higher the probability of crack initiation in these
susceptible points.
However, the significant decrease in this factor on the depth
points (even less than the
S.C.F. value in the equivalent straight weld) can guarantee the
part to be visually
checked before vast and huge crack propagation.
Based on the results of weld root analysis, this is inferred that
the stress concentration
factor in the rounded root area increases by the increase in the
penetration percentage,
however the stiffness of weld structure will rise up by a bigger
penetration. Since the
increase in stress concentration factor, increase very slightly,
the effect stress increase in
the weld root of half penetration weld can be neglected before
the effect of strength
increase in the structure.
35

9Futureworks
In Section 6.2, a sample calculation of fatigue strength of a
fillet weld waving toe model
with waving width and waving radius of 7 mm calculated. This
example is similar to the
model, which experimentally tested in fatigue library.
Comparing the results of the
effective notch method based on numerically analyzed model
with the experimental test
shows difference in fatigue strength results. The reason can be
referred to the difference
of weld toe rounded radius in the actual experimental specimen
shown in Fig. 3 and the
assumption of effective notch stress approach applied in this
study. Since the assumed
rounded radius in weld toe based on effective notch stress
method is for the worst case,
the conservative rounding is calculated to be sharp and the
radius is zero millimeter, but
in the real case the radius is 0.5 mm. In future the modeled weld
geometries can follow

the approach to apply the original geometry of weld in the root
or toe area and set a
proper curve and element size in that area to obtain a precise
stress value by calculation
of effective notch stress approach.
The other stress analyzing approach can be based on the
modeling of fillet-welded toe
rounding with the original radius as mentioned in Fig. 3. The
finite element analysis of
the original rounded radius model can be compared with the
result of the effective notch
approach presented in this study to figure out whether there is a
better estimation of
stress analysis over the fillet-welded model.
s

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