FATIGUE DESIGN OF WELDED STRUCTURES – SOME ASPECTS OF WELD QUALITY AND RESIDUAL STRESSES

HENRY GRANJON PRIZE COMPETITION 2010 Winner Category C: “Design and Structural Integrity” FATIGUE DESIGN OF WELDED STRUCTURES – SOME ASPECTS OF WELD QUALITY AND RESIDUAL STRESSES Z. Barsoum Dr. Zuheir BARSOUM ([email protected]) Asst Professor, is with KTH Royal Institute of Technology, Department of Aeronautical and Vehicle Engineering, Division of Lightweight Structures, Stockholm (Sweden).

ABSTRACT

The research work reported in this paper aims to increase the accuracy of fatigue life prediction of welded steel structures using local analysis methods by i) establishing a link between weld quality and fatigue life ii) developing simplified engineering methods using finite element routines for prediction of welding residual stresses iii) incorporating the residual stresses into the fatigue life predictions. Acceptance criteria were developed for the weld quality by comprehensive FE-and fracture mechanical analysis and fatigue testing. The results are the foundation for the new weld class system within the Volvo group company. Simplified FE welding simulation routines and procedures for incorporating the predicted residual stresses into crack growth analysis were developed showing good agreement with residual stress measurements and fatigue testing.

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IIW-Thesaurus keywords: Fatigue life; Quality; Residual stresses; Structures; Welded joints.

MAG

Metal Active Gas

MCAW

Metal Cored Arc Welding

NDT

Non-Destructive Testing

PWHT

Post-Weld Heat Treatment

Central Processing Unit

R

Stress ratio

Fatigue strength at 2 million cycles

SIF

[MPaMm] Stress Intensity Factor

FCAW

Flux Cored Arc Welding

ΔKeff

[MPaMm] Effective stress intensity factor range

FCG

Fatigue Crack Growth

ΔKI

FEA

Finite Element Analysis

[MPaMm] Stress intensity factor range in open Mode I

FEM

Finite Element Method

FZ

Fusion Zone

HAZ

Heat-Affected Zone

Nomenclature a

[mm]

Initial crack length in depth direction

ainital

[mm]

Initial crack length

c

[mm]

Initial crack length in width direction

CPU FAT

[MPa]

ΔKI, applied [MPaMm] Stress intensity factor range in Mode I due to applied loading ΔKII

[MPaMm] Stress intensity factor range in shearing Mode II

[MPaMm] Stress intensity factor due to residual stress

ΔKIII

[MPaMm] Stress intensity factor range in tearing Mode III

Kt

Stress concentration factor

ΔKth

LEFM

Linear Elastic Fracture Mechanics

[MPaMm] Stress intensity factor threshold value for crack growth

m

Slope of the S-N curve

Δσnom

[MPa]

KI, res

Doc. IIW-2197, recommended for publication by Commission XIII “Fatigue of Welded Components and Structures.”

Nominal stress range

FATIGUE DESIGN OF WELDED STRUCTURES – SOME ASPECTS OF WELD QUALITY AND RESIDUAL STRESSES

1 Introduction A common goal for manufacturers of welded structures, particularly transportation vehicle, is to minimize weight in order to decrease fuel consumption and at the same time to prevent fatigue failure. This will support the use of efficient and more accurate fatigue design methods which must be connected to quality requirements which can be understood and managed during production. However, welding without any improvement gives rise to local stress concentration, residual stresses and different types of defects. These features combined with complex service loading give rise to failure due to fatigue. Stress concentrations at the weld toe are caused by the geometrical discontinuities and fatigue cracks are easily initiated at these locations especially in connection with small toe radii. Fatigue crack growth may also start from weld defects; e.g. cold laps and undercuts in the weld toe, from the weld root due to incomplete fusion and small effective throat thickness. In case of fillet welds without any degree of penetration, these defect sizes can be in the order of the plate thickness. These defects behave more or less as sharp macrocracks which motivate the use of fracture mechanics as a tool to establish a link between the weld quality (e.g. local weld geometry, defects and residual stresses) for production welds and the fatigue life. Figure 1 illustrates different types of defects that could be found in fillet welds. Residual stress that arises in welded joints is another important factor which needs to be considered in the fatigue assessment of welded structures. It is well-known that tensile residual stresses in welded structures can be as high as the yield strength of the material and they have a detrimental effect on the fatigue behaviour. The combination of tensile welding residual stresses and operating stresses to which engineering structures and components are subjected can promote fatigue failure. Conversely, compressive residual stresses could have a favourable effect on the fatigue life. However, spectrum loading may relax part of the residual stress field which will affect the final fatigue life [1].

Figure 1 – Different types of defects in fillet welds

In the case of weld root cracking several studies have shown that the weld root is under compressive residual stresses and stress relief may reduce the fatigue life [2-3]. However, the residual stress distribution for a complex welded structure is usually not known, and conservative assumptions are made for the residual stress distribution in the fatigue life assessment [4]. Hence, accurate and reliable residual stress predictions using FEM are essential for structural integrity and fatigue assessment of components containing residual stresses. Finite element simulation of residual stresses due to welding involves in general many phenomena e.g. non-linear temperature dependent material behaviour, 3D nature of the weld pool and the welding processes and microstructural phase transformation. Despite the simplification by excluding various effects, welding simulations are still CPU time demanding and complex. Hence, simplified welding simulation procedures with “good enough” accuracy are required in order to reduce the work effort and thus maintain the accuracy of the residual stress predictions.

2 Weld quality The fatigue life of welds is primarily determined by the loading conditions, weld quality and residual stresses. However, the local geometry of the welds, such as sharp transitions and different kinds of defects are the starting points for fatigue cracks. In order to control the local geometry of welds, a quality system is required which has a link to the fatigue life [5]. The weld quality is defined by the weld geometry and/or defects. A frequent type of failure from single run fillet welds is due to high Kt (> 3) and from cold laps or a combination of these, see Samuelsson [6]. Most of the investigations reported here are based on as-welded non-load carrying specimens with normal production procedures today within several Volvo units and its suppliers. Another weld parameter that affects the weld quality, particularly for load-carrying welds, is the weld penetration depth which could cause weld root fatigue in case of insufficient penetration. However, in many cases it can be difficult by “normal” NDT-methods to quantify the weld penetration. In such cases close process control combined with sample test is important. An alternative is to prescribe a larger weld penetration than required and perform a reduced sample test. The residual stress field at the root side, usually hidden for access, is complicated to measure. This motivates FEM welding simulation in order to quantify the weld penetration depth and the residual stress state at the weld root. Cold laps are a type of weld defects occurring when melted material has not fused with the cold plate surface at the weld toe. There are two types of cold laps, a line cold lap which may occur in connection with bad surface conditions and relatively high welding speed and a spatter-induced cold lap which may occur at any speed. The N° 11 12 2011 Vol. 55 WELDING IN THE WORLD

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FATIGUE DESIGN OF WELDED STRUCTURES – SOME ASPECTS OF WELD QUALITY AND RESIDUAL STRESSES

b) Line cold lap, defect along the whole weld line

a) FEA crack growth analysis from initial cold lap defect c) Spatter-induced cold lap defect Figure 2 – Typical weld toe defects, cold laps

line cold lap has an aspect ratio a/c = 0 and the spatterinduced normally are rounded with a/c = 1, see Figure 2.

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Figure 3 shows the SIF for different cold lap defects (a/c = 0) at different growth increments. The SIF reaches a fairly constant level for all cold lap sizes after ~0.1 mm of crack growth, and the cold lap will grow in the shape of a line crack in the subsequent growth increments. This is due to mixed mode crack growth (ΔKI/ΔKII) in the first crack growth increments which results in a 50° crack deflection and very quickly the cold lap is growing in Mode I. The fatigue life for different cold lap sizes tends to be more or less constant for cold lap sizes larger than a certain value, see Figure 4, and is more depending on the local weld geometry, e.g. the weld toe radius. Figure 5 shows the fatigue strength for non-load carrying fillet welds as a function of toe radius/Kt and cold lap size. FAT 80 represents the fatigue strength at 2 million cycles with a failure probability of 2.3 % for this type of joint, see Hobbacher [7]. In order to ensure the production

Based on numerical analysis.

Figure 4 – Fatigue life as function of weld toe radius and cold lap size

of welds with fatigue strength above the standard recommendation FAT 80 and normal weld quality, the weld toe radius should be larger than 1 mm. However, for welds

Kt = 2.5, Δσnom = 100 MPa. Based on numerical analysis.

Dashed lines FAT values at ΔKI < ΔKth (2 MPaMm). Based on numerical analysis.

Figure 3 – ΔKeff for different cold lap sizes at different crack growth increments

Figure 5 – FAT as function of toe radius (R), Kt and cold lap size

FATIGUE DESIGN OF WELDED STRUCTURES – SOME ASPECTS OF WELD QUALITY AND RESIDUAL STRESSES

deflection angle ~50˚. This is in excellent agreement with the previous crack growth analysis for a line cold lap, where the deflection angle is identical at the crack growth start. The cold lap having a/c = 1 at the beginning, now grows towards a line cold lap (a/c = 0) and results in a 2-3 times longer fatigue life [8].

Based on numerical analysis.

Figure 6 – Effect of weld defects on the fatigue strength

with high quality the cold lap size needs to be very small, < 0.1 mm, see Figure 6. The existence of cold lap in connection with good weld geometry reduces the weld quality. In the case of small toe radius the problem with cold laps is overturned by high Kt. For spatter-induced cold laps the crack growth could be different compared to line cold laps and requires 3D crack growth analysis. Figure 7 shows an example of crack growth analysis from a spatter-induced cold lap at different crack growth depths: 0 mm (Step 0), 0.3 mm (Step 2) and 2 mm (Step 5). At the start of the crack growth, Step 0 in Figure 7, along the weld toe line (0˚ and 180˚, c-direction) the crack is under mixed mode, ΔKI and ΔKIII, i.e. the ΔKI/ΔKIII deflection angle is small ~2˚. The crack growth in the c-direction along the surface will dominate and crack growth into the depth, a-direction, is small. At the bottom (90˚, a-direction) the crack growth is under mixed mode ΔKI and ΔKII leading to a much greater

Different welding methods will produce different weld qualities which will result in different fatigue strengths. In Barsoum [9] different welding methods (Laser/MAG hybrid, tandem FCAW and welding with solid wire) were investigated regarding the weld quality and the fatigue strength. The majority of the welding methods showed great scatter in the weld quality except FCAW which showed compressive residual stresses at the weld toe (40-180 MPa), almost no weld defects (cold laps < 0.03 mm) and high fatigue strength (110 MPa). The results are based on test bars which are cut out from welded panels. In Barsoum et al. [8] fatigue testing and defect assessment were carried out on specimens welded with robotic and manual welding using FCAW and MCAW. The local weld geometry showed a great scatter and cold lap defects were found, except for FCAW welds. Figure 8 shows the local weld geometry for production welds using different welding methods. It is quite clear that some welding methods will produce smaller scatter and better weld quality and vice versa. From a weld quality point of view an even transition could be defined for weld with Kt < 2.5 for high quality aswelded joints based on non-load carrying cruciform joints. This weld quality criterion among others is successfully implemented in the new Volvo weld quality system [5, 10] which is submitted to IIW to be a base for a new international weld quality system. One way to achieve high weld quality (Kt < 2.5) without employing weld improvement technique is by welding in alternative welding positions, see Figure 9.

The crack shape is seen from above from start (Step 0) to the end of the fatigue life (Step 7, a/c = 0.1).

Figure 7 – 3D crack growth from a spatter-induced cold lap defect with a/c = 1

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a) Factory A with robotic MCAW

b) Factory B with manual MCAW

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c) Factory B with manual FCAW Figure 8 – Weld quality/local geometry from different production units

a) 0°

b) 45° Figure 9 – Welding in different positions

c) 90°

FATIGUE DESIGN OF WELDED STRUCTURES – SOME ASPECTS OF WELD QUALITY AND RESIDUAL STRESSES

The welding in the upright position, 0°, shows better weld quality (lower Kt /larger toe radii and small defects) compared with other welding positions including ultrasonic peened joints, Figure 10 a). The weld toe radii measurements are carried out with silicon replica and the weld quality criteria from the new weld quality system within Volvo (normal weld quality VD, high weld quality VC and improved weld quality VB) are also included. This weld quality improvement is also reflected in the fatigue life where 0°-position showed highest fatigue strength, see Figure 10 b). Table 1 summarizes the results from the ongoing research on the weld quality for different welding positions.

Table 1 – Summarized results from study of weld positions Mean value/standard dev.

90°

45°

0°

Toe radius [mm]

0.6/0.3

0.9/0.28

2.2/0.6

Kt

3.1/0.5

2.7/0.3

2.0/0.18

m (based on linear regression)

3.62

4.55

3.87

Fatigue strength (mean) [MPa]a

119

110

163

Fatigue strength (characteristic) [MPa]b

100

70

119

a Fatigue strength at 50 % survival probability at 2 million cycles, m = 3. b Fatigue strength at 95 % survival probability at 2 million cycles, m = 3.

One difficulty is to measure the weld toe radii associated with a large scatter. A measurement using a vision system is preferable since the radius can vary along the profile. Figure 11 shows measurements of the weld toe radius with a vision system along a weld line.

3 Procedures for predicting

welding residual stresses

Finite element simulations in order to predict temperature fields, residual stresses and deformation due to welding in 2-and 3 dimensional is used more frequently nowadays. Also 2D and 3D LEFM and FCG simulators have been developed in order to predict the fatigue life for welded joints. There are several research contributions [4, 11-13] on the incorporation of residual stress into the fracture mechanical defect assessment. However, limited work has been done on the development of reliable simulation tool in order to include all these features in the same simulation. The purpose of the developed FEM welding simulation procedure is to predict the temperatures, HAZ weld penetration and residual stresses due to welding with simplified 2D models. A sequentially coupled analysis is carried out starting with the thermal analysis and the results

a) Weld toe measurements (silicon replica) including the weld quality criteria in the Volvo standard [10]

Figure 11 – Measurement of toe radius along the weld line using vision system

from the temperature distributions are used as loads in the elastic-plasic mechanical analysis. The heat source assumes a constant distribution of volume heat flux over the cross-section of the weld filler material. The volume flux is applied simultaneously with the reactivation of the elements representing the weld filler material with a preheating melting temperature (1 500 °C). Accurate material data in the high temperature region is in general difficult to obtain and becomes at best a reasonable approximation. However, the material model and relevant properties need only to represent the real material behaviour with sufficient accuracy. The material models consider phase changes in a simplified way and 800 °C cut-off temperature is used

b) Fatigue test results for the different welding positions

Figure 10 – Results from welding position investigation

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in the elastic-plastic analysis, i.e., if the temperature from the thermal analysis is higher than 800 °C, then material properties are evaluated at the cut-off temperature. The welding simulation procedure was validated with comprehensive 3D simulation and measurements. Figure 12 shows examples of validations on fillet and butt welds. Figure 12 a) shows validation on a multi-pass butt weld, transverse and longitudinal residual stresses. It can be seen that the transverse residual stresses vary along the weld line. Figure 12 b) shows the validation on T-fillet welds. Note that the transverse and longitudinal residual stresses are constant along the weld line, except at start and stop for the fillet welds. In Barsoum et al. [14] the welding simulation procedure was used to predict the welding residual stresses in T-fillet welds in a Volvo Hauler frame box. Residual stress measurements were carried out in order to validate the

prediction. 3D and 2D simulations were carried out, using different software and modelling techniques (solid model versus contact models at the weld root gap). The objective was to study the 3D effects of fillet welding and to predict the residual stresses at the weld root with sufficient accuracy. The residual stress predictions showed good agreement with measurements. Therefore the welding simulation procedure is suitable for residual stress predictions for incorporation in further fatigue crack growth analysis from weld defects emanating from the weld toe and root. Furthermore, LEFM crack growth routines were developed together with a residual stress mapping algorithm in order to incorporate the residual stresses into the crack growth analysis [2]. The welding simulation procedure was used to predict the residual stresses in multi-pass welded tubular structures [3]. The analysis showed compressive residual stresses at

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a) Multi-pass butt welds showing the variation of the transversal residual stresses along the weld line

b) T-fillet welds where the transversal and longitudinal residual stresses are constant along the weld line, except at start and stop positions Figure 12 – Results from validation of welding simulation procedure with measurements and 3D simulations

FATIGUE DESIGN OF WELDED STRUCTURES – SOME ASPECTS OF WELD QUALITY AND RESIDUAL STRESSES

the weld root and at the weld toe between the weld and the tube. Fatigue testing of as-welded and stress relieved tubular structures were carried out in reversed torsion. Due to the stress relieve the compressive residual stresses were removed and the failure was in the tube-toe. However, when as-welded tubes were tested the failure was at the plate-toe where tensile residual stresses were predicted. Internal static pressure was used to reduce the compressive residual stresses and enable weld root cracking. This showed that the different failure locations observed in the fatigue testing were due to the residual stresses. The residual stress field was used as initial stress state in order to study any possible residual stress relaxation due to sinusoidal varying torsion moment; no severe residual stress relaxation was observed after 20 cycles [15].

4 Case study: Welded diesel engine frame box

The objective of this case study was to carry out welding simulation and LEFM FCG analysis on a welded frame box in a MAN B&W diesel engine, see Figure 13. In Hansen and Agerskov [16] fatigue testing was carried out on the welded engine part. The stress relieving by PWHT reduced the fatigue resistance due to the relieving of the beneficial compressive residual stresses at the weld root. The welding simulation was carried out using the developed welding simulation procedure. The engine frame box was welded with two welds, Weld A and Weld B, and each weld with four passes, respectively. For the nonpenetrated weld root (5 mm for Weld A and 8 mm for Weld B) contact elements were used in order to prevent penetration of the main plates during the welding simulation. Figure 13 shows the FE model used for the welding simulation and the subsequent crack growth analysis by incorporating the residual stresses. The residual stress predictions were in qualitative good agreement with the Neutron diffraction measurements.

Welding simulation of engine frame box: FEM mesh, welds, dimensions and remote loading during fatigue testing.

Figure 13 – MAN B&W two stroke diesel engine and welded frame box part analysed

The predicted residual stresses in the normal direction of the assumed crack path are shown in Figure 14 for Weld A and B respectively. It can be seen that the weld lack of fusion are under favourable compressive residual stresses. The fatigue testing was carried out in constant amplitude loading with R = 0. A set of the welded components was stress relieved by PWHT before fatigue testing. The compressive residual stress is relieved with PWHT and is clearly seen in Figure 15 where the predicted and experimentally fatigue lives are compared. The fatigue life

Figure 14 – Predicted residual stress in Welds A and B

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researchers for compilation of residual stress distribution for welded joints. Two of the important issues regarding welding simulation, besides the complexity and high degree of non-linearity of the problem, are the quantification of net heat input supplied by the welding arc and the modelling of material behaviour at higher temperatures. Both are important in order to have an accurate model in successful welding simulations. As a general rule, it can be stated that all production components and structures contain residual stresses that influence fatigue strength and need to be accounted for in the design. A major challenge for the future is the development of general models for residual stress relaxation due to service loading, particularly for spectrum loading. Figure 15 – Fatigue life prediction compared with experiments for a welded engine frame box

predictions for the as-welded and the PWHT specimens show good agreement with experiments. The threshold value (ΔKth) is predicted to 6 MPaMm. Hobbacher [7] states a conservative regression curve for structural C-and CM-steels is for the threshold value with Kth = 6 MPaMm at external R = 0. The suggestion is

ΔKth = 6.0 − 4.6 · R 10

In Table 2 the SIFs for the initial root crack defects are summarized for Weld A and Weld B, respectively. The root crack in Weld B is under compression and will remain closed for the as-welded specimens, consequently all the specimens, as-welded and PWHT, failed in the weld root in Weld A.

5 Discussion A weld quality system based on local fatigue assessment methods is developed and is nowadays introduced as a corporate standard within AB Volvo. Within the framework of this research work many aspects of fatigue design and manufacturing of welded joints have been studied and introduced into the industrial environment. It is clear that residual stress prediction and welding simulation in complex structures is elusive and employs many Table 2 – Predicted threshold values in (MPaMm) for welds in the frame box As-welded

PWHT

Weld A

Weld B

KI, res

− 2.3

− 15

–

–

ΔKI, applied*

13.05

6.8

5.98

3.1

ΔKI

10.75

− 8.2

5.98

3.1

5

8

5

8

ainital [mm]

ΔKth * Minimum value.

10.75 (24 kN)

− (46 kN)

Weld A

5.980 (11 kN)

Weld B

− (21 kN)

Another aspect of the design of welded structures against fatigue is the introduction of post weld improvement techniques e.g. ultrasonic peening. Improvement methods will also support the use of higher strength materials, an alternative which traditionally has been limited by older design and weld quality rules. Following effective improvement of the weld toe, failure tends to move to other locations such as the weld root. Hence, assessment of the weld root will be more important in connection with weld improvement techniques.

6 Conclusions

1. The majority of weld defects found in high speed single run MAG welding are cold laps in connection with spatter. The existence of cold lap in connection with good weld geometry reduces the weld quality. In the case of small toe radius the problem with cold laps is overturned by high Kt. 2. It is indicated that spatter-induced cold laps could be expected to have 2-3 times longer fatigue life than line cold laps. By welding in alternative position a high weld quality is achievable (with large toe radius and no / or small defects) without employing improvement techniques. 3. The lack of weld root penetration has a major influence on the fatigue life of fillet welded joints. The weld root is, in most cases, under favourable compressive residual stresses and this will enhance the fatigue life. The residual stress at the vicinity of the weld root is at present difficult to measure hence welding simulations are used to quantify these. 4. The developed welding simulation procedures tend to predict residual stresses with sufficient accuracy and with 30-100 times shorter computational time compared with 3D welding analysis. The developed welding simulation procedure is a valid tool for residual stress prediction for further accurate fatigue life assessment. 5. The fatigue life prediction for the diesel engine welded frame box using the developed procedures confirms the fatigue life enhancement observed in the fatigue testing of the as-welded specimens compared with the stress relieved. This illustrates the significant effect of residual stress on the fatigue life and hence should be included in the fatigue life assessment.

FATIGUE DESIGN OF WELDED STRUCTURES – SOME ASPECTS OF WELD QUALITY AND RESIDUAL STRESSES

Acknowledgements The author would like to thank Professor Jack Samuelsson at KTH for supervising and mentorship. Mr. Bertil Jonsson at Volvo CE is greatly acknowledged for fruitful collaborative research. Dr. Imad Barsoum at The Petroleum Institute Abu Dhabi is acknowledged for programming support. Dr. Fethi Abdul-Wahab at Volvo material lab is acknowledged for assisting with some of the analysis work. Vinnova and Volvo CE are acknowledged for financing the research project.

[8] Barsoum Z. and Jonsson B.: Fatigue assessment and LEFM analysis of cruciform joints fabricated with different welding processes, Doc. IIW-2175, Welding in the World, 2008, vol. 52, no. 7/8, pp. 93-105 (Research Supplement). [9] Barsoum Z. and Samuelsson J.: Fatigue assessment of cruciform joints welded with different methods, Steel Research International, 2006, vol. 77, no. 12, pp. 882888. [10] Volvo Group weld quality standard, STD 181-0004, 2008.

References [1] Barsoum Z. and Gustafsson M.: Fatigue of high strength steel joints welded with low transformation consumables, Engineering Failure Analysis, 2009, vol. 16, no. 7, pp. 2186-2194. [2] Barsoum Z. and Barsoum I.: Residual stress effects on fatigue life of welded structures using LEFM, Engineering Failure Analysis, January 2009, vol. 16, no. 1, pp. 449-467. [3] Barsoum Z.: Residual stress analysis and fatigue of multi-pass welded tubular structures, Engineering Failure Analysis, 2008, vol. 15, no. 7, pp. 863-874. [4] Finch D.: Effect of welding residual stresses on significance of defects in various types of welded joint-II, Engineering Fracture Mechanics, 1992, vol. 42, no. 3, pp. 479-500. [5] Jonsson B., Samuelsson J. and Marquis G.B.: Development of weld quality criteria based on fatigue performance, Doc. IIW-2200, Welding in the World, 2011, vol. 55, no. 11/12, pp. 79-88. [6] Samuelsson J.: Cold laps and weld quality acceptance limits, Design and Analysis of Welded High Strength Steel Structures, pp.151-163, Stockholm, EMAS, 2002. [7] Hobbacher A.: IIW Recommendations for fatigue design of welded joints and components, Doc. IIW-1823, WRC Bulletin 520, Welding Research Council, Inc., New York, 2009.

[11] Finch D. and Burdekin F.M.: Effect of welding residual stress on significance of defects in various types of welded joints-II, Engineering Fracture Mechanics, 1992, vol. 42, no. 3, pp. 479-500. [12] Michaleris P., Kirk M., Mohr W. and McGaughy T.: Incorporation of residual stress effects into fracture assessment via the finite element method, Fatigue and Fracture Mechanics: vol. 28, ASTM STP 1321, J.H. Underwood and B.D. Macdonald, M.R. Mitchell, Eds., American Society for Testing and Materials, 1997. [13] Stacey A., Barthelemy J.-Y., Leggatt R.H. and Ainsworth R.A.: Incorporation of residual stresses into the SINTAP defect assessment procedure, Engineering Fracture Mechanics, 2000, vol. 67, no. 6, pp. 573-611. [14] Barsoum Z. and Lundbäck A.: Simplified FE welding simulation of fillet welds – 3D effects on the formation of residual stresses, Engineering Failure Analysis, 2009, vol. 16, no. 7, pp. 2281-2289. [15] Barsoum Z.: Residual stress prediction and relaxation in welded tubular joint, Doc. IIW-1773, Welding in the World, 2007, vol. 51, no. 1/2, pp. 23-30. [16] Hansen J.L. and Agerskov H.: Fatigue assessment of root defects in the welded structure of a diesel engine, Design and Analysis of Welded High Strength Steel Structures, pp. 373-390, Ed. J. Samulesson, EMAS, Stockholm, 2002.

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