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1 Introduction .......................................................................................................................................... 2

1.1 Background ................................................................................................................................... 2

1.2 Scope of the work ......................................................................................................................... 3

2 Method ................................................................................................................................................. 4

2.1 Geometry and meshing ................................................................................................................. 4

2.2 Extra Test: smaller bead + smaller undercut ................................................................................ 7

3 Results ................................................................................................................................................... 7

4 Further calculations ............................................................................................................................ 14

5 References .......................................................................................................................................... 16

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1 Introduction1.1 BackgroundEffective notch stress (ENS) is a method to calculate the fatigue strength of structures. As shown in [1]

and [2], this method is based on considering a fictitious radius in the location of the notch to eliminate

the singularity and yield a finite stress value which could be read directly as the or as would bepresented here . The fictitious radius is based on a concept which is called microstructural notchsupport hypotheses. According to Radaj [3] The term microstructural notch support means that the

maximum notch stress according to the theory of elasticity is not decisive for crack initiation and

propagation but instead some lower local stress gained by averaging the notch stresses over a material-

characteristic small length, area or volume at the notch root (explicable from grain structure,

microyielding and crack initiation processes). [3]

There are a couple of approaches to take into effect the microstructural notch support. Here Neuber

method is used which is based on fictitious radius:

(1)Where = Fictitious radius

Actual notch radiusS= Factor for stress multiaxiality and strength criterion

Substitute micro-structural length

By considering , and [2], the fictitious radius would be 1 mm which is inaccordance with [1] as well. The life cycles of the structure then can be calculated as below:

[ ]

Where,

= cycles to failure = load safety factor = notch stress rangePresumably the thickness of the base plate is not less than 5mm. It is suggested [4] that, for thinner base

plate, a fictitious radius of 0.05 mm should be considered and then an analogous formula could be used

as below:

[ ]

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These cases are compared to each other inFigure 1.1.

Figure 1.1 Different fictitious radii [4]

Mentioned formulae suggest that there should be a stress ratio of 2.8 between models with fictitious

radius 0.05 mm and 1 mm. This matter has been studied in this works and such ratio has been calculated

and compared for different models inTable 2

1.2 Scope of the workIn this work these formulae would be tested for a simple butt welded structure including some undercut

effect in the weld root. The effect of having weld bead on both side of the baseplate is studied as well.

All together 4 tests have been done which include two different fictitious radii for a full model (welded

on both sides of the baseplate) and one-side-welded as shown below:

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Figure 1.2 on the left, both sides are welded (double V). On the right, one side is welded (single V).

Case 1: root undercut = 1 mm, two-sided weld (double V), fictitious radius = 1 mm Case 2: root undercut = 1 mm , two-sided weld (double V) , fictitious radius = 0.05 mm Case 3: root undercut = 1 mm, two-sided weld (single V), , fictitious radius = 1 mm Case 4: root undercut = 1 mm , two-sided weld (single V) , , fictitious radius = 0.05 mm

2 Method2.1 Geometry and meshingThe model used for cases 1 and 3 was based on a plate (thk=10mm) welded on both sides as shown in

the following figure. The model shown inFigure 2.2 includes a fictitious radius of whereas themodel shown inFigure 2.3 has a fictitious radius of .

Figure 2.1 The 3D presentation of the case 1

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Figure 2.2Dimensions of the case 1

Figure 2.3 Dimensions for the case 2

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For both case 1 and case 2, analysis was done for a symmetric model.

Cases 3 and 4 are analogous to cases 1 and 2 respectively with the exception that they model one-sided

welds (single V). Therefore these cases were modeled using a symmetry boundary condition (Figure

2.5).

Steel with modulus of elasticity of and Poisson ratio of was used for this model.Plane strain was presumed for the mesh property of this model. In both case parabolic elements were

used and the element size in the both area is around 0.1r, which r is the fictitious radius. An amount of

tension force was used to generate a nominal stress of 1MP in the base plate. Load and boundary

conditions are shown for the symmetry model of case 1-case 3 and case2-case 4 in Figure 2.4 and

Figure 2.5 respectively.

Figure 2.4 Load and boundary conditions for case 1 and case 2 (double V)

Figure 2.5 BC for case 3 and case 4 (single V)

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2.2 Extra Test: smaller bead + smaller undercutSince the eccentricity in the model caused by weld bead and undercut leads to a bending moment (as

shown in Figure 4.1), the amount of major principal stress is not uniform across the thickness of the

baseplate (beside the effect that notch has on stress distribution). To reduce the effect of this

eccentricity, some extra tests were done. In these tests, as shown in the following figure a smaller bead

was used. The depth of undercut in the weld root was supposed to be 0.5mm whereas the fictitious

radius maintained to be 1mm. The baseplate thickness has not changed (thk = 10 mm for double V and

thk = 5 mm for single V). As before there are two boundary conditions according to the double V (two-

sided) and single V (one-sided) weld.

These extra cases are listed as below:

Case 5: root undercut = 0.5 mm, two-sided weld (double V), fictitious radius = 1 mm Case 6: root undercut = 0.5 mm , two-sided weld (double V) , fictitious radius = 0.05 mm

Case 7: root undercut = 0.5 mm, two-sided weld (single V), fictitious radius = 1 mm Case 8: root undercut = 0.5 mm , two-sided weld (single V) , fictitious radius = 0.05 mm

Figure 2.6 Test 1, smaller bead and shallower undercut

3 ResultsAll together 16 different values of major principal stresses are reported here which are correlated to theweld toe and weld root of the models with factious radius of 1mm and 0.05 mm for the full model and

half model with large weld bead and small weld bead.

Major Principal Stress contours have been shown for all cases throughFigure 3.1 -Figure 3.11.

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Figure 3.1 Major Principal Stress at root = 3.06 for case 1

Figure 3.2 Major Principal Stress at root = 10.07 for case 2

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Figure 3.3 Major Principal Stress at root = 4.18 for case 3

Figure 3.4 Major Principal Stress at root = 15.01 for case 4

For a better understanding of stress distribution, especially for cases 2 and 4 which include high stress

gradients, stress contours in the vicinity of the weld toe and weld root have been shown in more details

inFigure 3.5 andFigure 3.6.

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Figure 3.5 Major Prinipal stress in weld toe. Case 2 on the left, case 4 on the right. Element size around 0.005 mm

Figure 3.6 Major Principal stress in weld root. Case 2 on the left, case 4 on the right. Element size around 0.005 mm

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Figure 3.7 Major Principal Stress at root = 2.47 MPa for case 5

Figure 3.8 Major Principal Stress at root = 7.48 MPa for case 6

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Figure 3.9 Major Principal Stress at root = 2.94 MPa for case 7

Figure 3.10 Major Principal Stress at root = 9.56 MPa for case 8

The stress in the weld root for cases 6 and 8 is shown in more detail in theFigure 3.11.

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Figure 3.11 Major Principal Stress in the root, case 6 on the left, case 8 on the right

All the results for peak values of major principal stresses at weld toe and weld root are summarized in

Table 1.

Table 1 Summary of all the results

Case Number Stress in the weld toe stress in the weld root

1 2.24 3.06

2 5.33 10.07

3 1.55 4.184 3.70 15.01

5 1.86 2.47

6 3.93 7.48

7 1.52 2.94

8 3.23 9.55

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5 References[1] A. Hobbacher, Recommendations for Fatigue Design of Welded Joints and Components,

International Institute of Welding, XIII-2151-07/XV-1127r18-03, 2008.

[2] W. Fricke, Guideline for the Fatigue Assessment by Notch Stress Analysis for Welded Structures, The

International Institute of Welding, 2010.

[3] D. Radaj, C. M. Sonsino ja W. Fricke, Fatigue assessment of welded joints by local approaches,

Woodhead Publishing Limited, 2006.

[4] T. Bjrk, Kirjoittaja, Lectures on Steel Structures (TERSRAKENTEET II). [Performance]. Lappeenranta

University of Technology, 2013.