Fatigue life analysis of weld ends Andréas Göransson

Fatigue life analysis of weld ends  Andréas Göransson

Fatigue life analysis of weld ends

Comparison between testing and FEM-calculations

Andréas Göransson

Master Thesis LIU-IEI-TEK-A--14/02012--SE

Department of Management and Engineering

Division of Solid Mechanics

Fatigue life analysis of weld ends

Comparison between testing and FEM-calculations

Supervisors:

Examiner:

Master Thesis in Solid Mechanics

Department of Management and Engineering

Division of Solid Mechanics

Linköping University by

Andréas Göransson

Daniel Leidermark

IEI, Linköping University

Maria Nygren

Toyota Material Handling, Mjölby

Bo Torstenfelt

IEI, Linköping University

Master Thesis LIU-IEI-TEK-A--14/02012--SE

i

Linköping University Electronic Press

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ii

Abstract

The thesis examines the fatigue life of weld ends, where very little usable research previously has been conducted, and often the weld ends are the critical parts of the weld. It is essential knowing the fatigue life of welds to be able to use them most efficiently.

The report is divided into two parts; in the first the different calculation methods used today at

Toyota Material Handling are examined and compared. Based on the results from the analysis and what is used mostly today, the effective notch approach is the method used in part two.

To validate the calculation methods and models used, fatigue testing of the welded test specimens was conducted together with a stress test. New modelling methods of the weld ends that coincide with the test results were made in the finite element software Abaqus. A new way of modelling the weld ends for the effective notch method is also proposed. By using a notch radius of 0.2 mm and rounded weld ends the calculated fatigue life better matches the life of the real weld ends. iii

iv

Preface

This master thesis was conducted at Toyota Material Handling in Mjölby during the first semester of 2014. It was the last requirement to fulfil a master’s degree in Mechanical

Engineering at Linköping University, Sweden.

I would like to extend a special thanks to my supervisor at Toyota Material Handling, Maria

Nygren for her assistance throughout the process, and to all of my colleagues at the CAEgroup who have helped me with my questions. I would also like to thank Morgan Gudding from Mechanical testing for helping me through the whole testing process and venting his thoughts about the subject.

I would also like to thank my supervisor at Linköping University, Daniel Leidermark who has thoroughly studied my work and raised good questions.

A special thanks to my family and friends, who have supported med through all these years.

It was a joy!

Andréas Göransson

Mjölby, 04/06/2014 v

vi

Table of Contents

1 Introduction ..................................................................................................................................... 1

1.1 Background ........................................................................................................................... 1

2

3

1.2

1.3

1.4

1.5

1.6

Toyota Material Handling ..................................................................................................... 1

1.2.1 Examples of trucks ................................................................................................... 2

Purpose .................................................................................................................................. 3

Research questions ................................................................................................................ 3

Delimitations ......................................................................................................................... 3

Other considerations .............................................................................................................. 3

1.7

1.8

1.9

Assumptions .......................................................................................................................... 4

Nomenclature ........................................................................................................................ 4

Methods ................................................................................................................................. 5

1.9.1

1.9.2

Simulation ................................................................................................................. 5

Testing ...................................................................................................................... 5

1.9.3 Gluing of strain gauges ............................................................................................. 5

1.10 Materials and specimen dimensions ...................................................................................... 6

1.11 Literature Review .................................................................................................................. 6

1.12 Structure ................................................................................................................................ 7

Theoretical background ................................................................................................................... 8

2.1 Weld theory ........................................................................................................................... 9

2.2

2.1.1 Definition of stress ................................................................................................. 11

Fatigue ................................................................................................................................. 12

2.2.1

2.2.2

2.2.3

2.2.4

2.2.5

FAT class ................................................................................................................ 12

Wöhler S-N-curve .................................................................................................. 12

Load spectrum ........................................................................................................ 13

Weld imperfections................................................................................................. 13

Residual stresses ..................................................................................................... 13

2.2.6 Fatigue models ........................................................................................................ 14

Nominal stress ..................................................................................................................... 17 2.3

2.4

2.5

Hot spot ............................................................................................................................... 20

Effective notch .................................................................................................................... 22

2.6 Evaluation of test data ......................................................................................................... 23

FEM analysis ................................................................................................................................. 24

3.1 FEM model .......................................................................................................................... 24

3.1.1

3.1.2

3.1.3

3.1.4

3.1.5

3.1.6

3.1.7

Load cases .............................................................................................................. 24

Boundary conditions ............................................................................................... 24

Material model ........................................................................................................ 26

FE-analysis ............................................................................................................. 26

Nominal stress ........................................................................................................ 27

Hot spot .................................................................................................................. 28

Effective notch ........................................................................................................ 28

vii

4

3.2

3.3

Parametric study .................................................................................................................. 33

Numerical analysis .............................................................................................................. 34

3.3.1

3.3.2

3.3.3

3.3.4

Nominal stress ........................................................................................................ 34

Hot spot .................................................................................................................. 35

Effective notch ........................................................................................................ 36

Comparison of the computational methods ............................................................ 37

3.3.5 Load case 2 ............................................................................................................. 38

Alternative weld modelling ................................................................................................. 40 3.4

3.5

3.4.1

3.4.2

Rounded weld end .................................................................................................. 40

Concave and convex weld profile .......................................................................... 44

3.4.3 Changed notch radii ................................................................................................ 45

Single fillet weld ................................................................................................................. 46

3.5.1 Load case 1 ............................................................................................................. 46

3.5.2 Load case 2 ............................................................................................................. 48

Testing preparation .............................................................................................................. 49 3.6

3.6.1

3.6.2

Placement of strain gauges ..................................................................................... 49

Comparative measurements from FE-analysis ....................................................... 50

Testing ........................................................................................................................................... 51

4.1

4.2

Gluing of strain gauges ........................................................................................................ 51

Measuring of specimens ...................................................................................................... 51

4.3

4.4

4.2.1 FE-model with imperfections ................................................................................. 52

Fatigue testing ..................................................................................................................... 53

4.3.1

4.3.2

4.3.3

Data......................................................................................................................... 54

Crack inspection ..................................................................................................... 56

Detection of crack initiation ................................................................................... 57

Results from testing ............................................................................................................. 58

4.5

4.4.1 Fatigue test .............................................................................................................. 58

4.4.2 Stress test ................................................................................................................ 60

Comparison FE-model and testing ...................................................................................... 61

4.5.1 Fatigue test .............................................................................................................. 61

4.5.2 Stress test ................................................................................................................ 63

Discussion ..................................................................................................................................... 65

Conclusion ..................................................................................................................................... 66

5

6

6.1

6.2

6.3

Weld calculations and parametric study .............................................................................. 66

Different types of welds ...................................................................................................... 66

Testing ................................................................................................................................. 66

6.4

6.5

Proposed modelling technique ............................................................................................ 67

Future work ......................................................................................................................... 67

References ............................................................................................................................................. 69

Appendix ............................................................................................................................................... 71

viii

1 Introduction

1.1

Background

BT Products has as many other companies, welds in their products. These welds should not fail prematurely, thus knowledge about the life of the welds has to exist. This knowledge comes from formulae and modelling techniques used to produce stresses by means of finite element software, as well as field measurements and lab tests. The methods used to assess the life of a weld are taken from handbooks for welding design and finite element modelling. There are mainly four different methods to compute and model a weld and the weld ends with FEA (Wolfgang, 2003). Those are nominal stress approach, hot-spot stress approach, effective notch stress approach and fracture mechanics.

Currently the effective notch stress approach is almost solely used, as it is the second most accurate method after fracture mechanics. The latter method require knowledge of crack length, weld defects and great knowledge about the material which most often are not known during the design of welds.

Moreover the effective notch approach works better on more complex geometries than the nominal stress and hot spot method.

The most critical areas on a weld are the weld start and end. These points become singular and this makes it hard to define stresses at those points. The above mentioned methods handle this problem differently. In the effective notch approach the stresses are measured directly in the area between the weld and material, called the weld toe and root. This transition is rounded with a fictitious radius to eliminate singularities. No method is taking the weld ends into account, but at BT Products the two most outer elements are eliminated when looking for the maximum principal stress. The magnitude of the stress is crucial for the computation of the fatigue life of the weld.

1.2

Toyota Material Handling

Toyota Material Handling (Anon., 2012) has a long history of being a big game player in the truck market. The company was founded in 1946 by Ivan Lundqvist and was then called Bygg och

Transportekonomi, which became BT in short. At the time of founding there was a baby boom in

Sweden and a lot of houses had to be built. Ivan was sent to the USA to import construction material to build houses, but he returned with another idea. He had found something he wanted in Sweden, which could solve the problem of moving material around. He started to import the Clark counterbalanced forklift trucks for the Swedish construction industry. There was a market for transportation of goods by manpower and in 1948 the first BT hand truck pallet left the factory. Since most of the transportation at this time was conducted at the railway, BT Products together with SJ designed the BT pallet, or SJ pallet which later became the Euro-pallet. The pallet still has the same dimensions as when it was designed in 1949. Some years later in 1952, BT Products moved to its current location in Mjölby, Sweden. They continued selling Clark trucks and also started exporting manual stackers in 1958. BT Products grew and sold well in Europe but the American market was almost non-existing as an export market. To solve this they bought their rival which was already well established in North America, Raymond.

In 1998 BT Products cooperated with Toyota and started the manufacturing of Toyota trucks

(Introduction week, 2014). Two years later BT Products became a part of the Toyota group, Toyota

Material Handling (TMH). They are a part of Toyota Industry Corporation (TICO) that also sells

Toyota car models like Raw and Yaris. 39 % of TICO consist of trucks and the rest is based on cars, material handling, textile machinery, electronics and logistics.

1

1.2.1

Examples of trucks

Toyota Material Handling offers a wide range of trucks, from the smallest hand pallet truck to counterbalanced trucks lifting up to 8.5 tonnes. The lifting height for some of the trucks extends up to

14.8 metres. The well known BT L-series hand pallet truck has a load capacity of up to 3 tonnes,

Figure 1.

Figure 1 - BT Lifter LHM230

One of the most popular trucks is the reach truck BT Reflex, suitable for indoors stacking and transportation of loads from 1.2 to 2.7 tonnes. It has a maximum lifting height of 12.5 metres and comes in many different configurations, from multidirectional to heavy-duty and narrow chassis. As all of the trucks at Toyota Material Handling are customizable after the needs of the customer, the range of solutions for the trucks are extensive.

Figure 2 - BT Reflex B-series

All of the trucks at Toyota Material Handling contains an extensive number of welds, therefore it is of great importance that the fatigue life of the welds are known. Different welds are critical in different loading cases and due to the high loading capacities, they are all of importance.

2

1.3

Purpose

The goal of this thesis is to get a better understanding of how the computational methods used at BT

Products today agree with the fatigue life of the real welds. The modelling of the weld is the main subject of interest since it affects the fatigue life prediction of the specimen heavily. The purpose is to guarantee that the computational methods used with life assessment correspond to the life of the welds used in BT Products trucks.

1.4

Research questions

Is BT Products modelling their weld ends correctly?

Do the computations result in a fatigue life comparable to the real cases?

How should the modelling and/or calculations be altered to better correspond to the actual fatigue life?

1.5

Delimitations

To delimit the work, the specimen, Figure 3 is only to be loaded in one direction. It is subjected to a

tensile load at the bottom plate at four different load levels. The geometry is limited to one case and all the testing will be performed on specimens with the same dimensions. To statistically ensure the results during the testing, seven specimens will be tested at every load level. The focus in the thesis is not on mesh studies, thus the company’s recommendations treating mesh size and modelling techniques are followed. The material has been assumed isotropic and the material effects caused by the welding has not been analysed nor considered in the simulations. No change in material properties or plasticity has been considered. The effects of the welding are assumed to be contained within the fatigue classes.

F

F

Figure 3 - T-joint fillet weld specimen

1.6

Other considerations

No ethical or gender specific issues are raised by the work. Nor is it directly related to issues concerning the environment or sustainable development.

3

1.7

Assumptions

To make the simulation process faster and less demanding with respect to modelling and simulation time, the welds are simplified for stress analysis and simulations. Since there are a lot of welds in a truck, the weld model should also suit a broad spectrum of applications. Therefore the weld is assumed to be an isosceles triangle extruded in the direction of the weld. At the start and end of the weld no extra modifications are done. The material is assumed to be isotropic and all analyses are conducted assuming linear elastic behaviour and no plasticity is considered.

1.8

Nomenclature

E= Young’s modulus [GPa] 𝜐 𝜌

=

=

Poisson’s ratio density [ kg m

3

] π‘Ž

=throat thickness [m]

βˆ†πœŽ π‘Ÿπ‘‘

=design normal stress range (allowed stress range) [MPa]

βˆ†πœŽ π‘šπ‘Žπ‘₯

= maximum stress range [MPa] 𝜎 π‘Ÿ

=computed stress range [MPa] 𝜎 π‘›π‘œπ‘š

=nominal stress [MPa] 𝜎 β„Žπ‘  πœ€ β„Žπ‘ 

=hot spot stress [MPa]

=hot spot elongation

𝐹𝐴𝑇

=fatigue class [MPa] π‘š

= the gradient of the S-N-curve πœ‘ 𝑑 πœ‘ π‘š

=thickness factor

=material factor πœ‘ 𝑒

=stress variation factor πœ‘

𝑄 𝛾 π‘š

=coefficient for risk of failure

=failure consequence factor 𝑠 π‘š

=cumulative stress parameter

𝑅

=stress ratio

𝑁

=estimated fatigue life [cycles]

𝑁 𝑑 π‘˜ π‘š

=design life, total number of cycles [cycles]

=spectrum parameter equal unity for constant amplitude 𝑛 𝑖 𝑛 𝑑

Δ𝜎 𝑖

= number of cycles at load level 𝑖

[cycles]

= total number of cycles [cycles]

=

Δ𝜎 π‘Ÿπ‘’π‘“ stress range at load level

= 𝑖

[MPa] picked reference value for calculation of π‘˜ π‘š

, e.g. the maximum stress range measured [MPa]

4

1.9

Methods

Relevant literature, articles and former publications directly related to the subject are studied to gain the theoretical knowledge of the subject. It will also help in understanding what kind of research has been conducted in the area and what their results were.

1.9.1

Simulation

To perform the simulations of the weld a finite element method software is used, Abaqus. Different weld geometries are tested, and the results in form of stresses are then used with theory and formulas to calculate the life of the weld. Three different calculation methods are also compared. The simulations are performed with both idealized models and models with some included imperfections.

1.9.2

Testing

Testing is conducted by clamping the specimen in a hydraulic fatigue testing machine. The welded test specimens are loaded with an alternating tensile load until fracture. A fixed stress ratio is defined together with a maximum force, and the specimens are tested at several load levels. The fatigue life calculated with the help of models in Abaqus is then compared with the results from the tested specimens. A stress test with strain gauges is also performed, with the same alternating tensile load.

1.9.3

Gluing of strain gauges

To perform the stress measurements strain gauges are placed on a test specimen. The procedure includes grinding the scale until all the pores are gone and then polishing the surface until a fine and smooth surface is achieved. The exact position of the strain gauges are then measured and marked by pen. The pen makes small scratches and creates a cross where the strain gauge should be placed. When all placements are marked, the surfaces are thoroughly cleansed with isopropanol. When the surface is absolutely clean the strain gauges can be placed, firstly a small amount of glue (cyanoacrylate) is applied to the strain gauge. The glue hardens when pressure is applied and thus pressure is applied to the strain gauge when the right position has been found. After two minutes the strain gauge has been attached and the process can be repeated. All strain gauges are taped and marked with the name in both ends of the attached cable.

Figure 4 - Strain gauges glued at the weld end

5

1.10

Materials and specimen dimensions

The specimen used in this project is a T-joint with fillet welds in accordance with Figure 3. The

material is steel with the properties:

𝐸 = 210 πΊπ‘ƒπ‘Ž 𝜌 = 7850 π‘˜π‘” / π‘š

3 𝑣 = 0.3

The dimensions of the tested specimen are defined in Figure 5. The measurement of the weld is given

as the throat thickness and the length of the weld. The thickness of the weld a5, represents a weld size

of 5 mm, see 2.1.

[mm]

Figure 5 - Dimensions of the specimen

1.11

Literature Review

Wolfgang (2003) sums up the literature on fatigue analysis of welded joints that has been written in the past years, covering most techniques used. This includes the methods covered in this report. But all of the techniques only treat a continuous weld, lacking methods to model the failure-critical weld start and end. The area of weld ends is not particularly well studied. Some research has been conducted on the weld start/ends in recent years though. Kaffenberger et al. (2011) have done experimental testing on the fatigue life of weld start and end points, where they focused on both the geometry and the material of the crack initiation site. The crack initiation most often occur in the weld start or end, which is the area considered. The welds were very accurately modelled by 3D scanning and then idealised to a simpler FEM-model with the help of statistics. They also proposed a technique of modelling and meshing a weld to get a realistic fatigue life. Furthermore, they also discuss the statistical effect of changing the radii in the effective notch technique and how to compensate for using other radii’s. Even though the research found that the limit for the sheet thickness with their approach was raised to 20mm, the theory was based on thin sheet structures. Malikoutsakis et al. (2011) continues to discuss the modelling of the failure-critical weld start/end locations with respect to fatigue. They propose a different method of modelling the weld start/ends and comparing them with the analytical results gained from the guidelines of the International Institute of Welding (IIW)

(Hobbacher, 2009). They then suggest a way of assessing the local elastic stresses by means of the

Effective Notch Stress Approach, in terms of fatigue. They also mention that even though the approach of having a notch radius of 1 mm is widely used and accepted. It is based on, and limited to continuous welds, not taken macro-geometrical discontinuities into consideration.

6

1.12

Structure

This report begins with a description of the background, introducing the reader to the problem.

Previous work in the area of weld ends, together with the aim and methods used throughout the work continues. Weld theory together with the calculation methods used follows and define the theoretical background. The main part of the report is the analysis section where the execution of the simulations and results of these are presented. Finally the report ends with a conclusion and discussion with the main findings and problems that arose during the work.

7

2 Theoretical background

When constructing a weld with respect to fatigue there are several methods describing how to perform computations to assess the fatigue life of the weld. All methods have their specific pros and cons and are also applicable to different types of problems. The hot spot and effective notch methods both have a strong connection with FE calculations. It is no guarantee that the results coincide between the cases however. The need of work that has to be put into each method also corresponds well with how

accurate the result is in accordance with Figure 6. For simple geometries, where the stress is well

defined, the nominal stress method is a good alternative that gives a good enough result considering the effort needed. When the geometries become more complex a method with higher accuracy should be used. There is every so often no answer on what is right. Instead, testing has to be performed to confirm the results from the computations, especially if the product will be produced in large quantities.

Figure 6 - The different methods for fatigue analysis of welds

8

2.1

Weld theory

There are several different types of welds, where fillet weld and butt weld are the most common. The butt weld is used for parts which are nearly parallel and do not overlap. It can be used for parts that are not in the same plane, but then chamfering is often performed in one of the sheets. Examples of butt

welds can be seen in Figure 7. The fillet weld is used to join two or more pieces which are perpendicular or at an angle, in Figure 8 some examples are represented.

Figure 7 - Butt welds in T-joints a) single-bevel butt weld b) double bevel butt weld

(Olsson, 2014)

Figure 8 - Fillet welds in different joints a) Lap joint b) T-joint c) Cross joint

(Olsson, 2014)

Welds are often the most critical point in the construction and thus has to be dimensioned in the right way. When doing computations there are three sections that are critical and therefore have to be

designed with respect to. These are displayed in Figure 9. The loading can be applied to the weld in

different directions which can be less or more critical. A load applied perpendicular to the weld is denoted

and a load applied parallel to the weld

βˆ₯

. Section III in Figure 9 corresponds to a crack

initiating from the root of the weld, and section I and II corresponds to a crack initiation from the respective weld toe.

I

III

II

II

III

I

Figure 9 - Sections of interest in a weld

The possible failure modes are shown in Figure 10, which corresponds to the computation planes in

Figure 9.

9

Toe crack

Toe crack

Root crack

Figure 10 - Possible failure modes

A fillet weld is assumed to be an isosceles triangle, where nominal throat thickness is the height of the

biggest triangle that can be fitted between the joint faces and the weld surface, see Figure 11. Since the

welds has to be easy to use in simulations the model has to be simplified compared to the very complex geometries welds in reality have. a

Figure 11 - Nominal throat thickness

There are different parts of a fillet weld that are referred to regularly and they are annotated in

Figure 12. The throat thickness

a

depends not only of the thickness of the weld but also the penetration of the weld. The penetration of the weld can be credited when doing calculations, thus reducing the material usage for the weld. The throat thickness π‘Ž

0

R is the dimension seen on drawings. a a

0

Toe

Root

Figure 12 - Parts of a fillet weld

Throat

Toe

10

2.1.1

Definition of stress

The weld toe constitutes a singularity, which makes it impossible to determine the stress by direct measuring. Therefore there are several methods that can be used to approximate the stresses in the weld toe.

Nominal stresses are stresses defined some distance away from the weld. It does not include stress concentrations caused by the weld itself. Instead, that is taken care of by the fatigue classes which are used in the calculations. Thus the nominal stresses alone do not represent the stresses in the weld toe in a good way.

Structural stress is a stress determined with the help of some reference points perpendicular to the weld. It only includes effects of the structure itself and disregards the notch effects caused by the weld profile, thus the non-linear stress peak near the weld is neglected. By doing this the stress in the weld toe can be extrapolated with a linear or quadratic method from measuring points at certain distances

from the weld, see Figure 13.

Figure 13 - Extrapolated hot spot stress

In the effective notch method, a fictitious radius is inserted in the transition between the weld and plate, to reduce the singularities in the weld toe and root. This makes it possible to measure the stress directly in the radius.

11

2.2

Fatigue

In a fatigue analysis the specimen is subjected to a cyclic load until a specified number of cycles, rupture or first crack are reached. The greater applied load, the shorter fatigue life will be obtained since the stresses and elongations will cumulate with increasing loading. Fatigue is a geometric problem, and in welds it is mostly dependant on crack growth.

The number of cycles corresponding to infinite fatigue life at BT Products is set as

𝑁

When dimensioning a design for infinite life,

2 βˆ™ 10

6

cycles is used.

= 2 βˆ™ 10

6

cycles.

There are fatigue design rules for welded structures, based on standards. These standards are intended for certain types of structures, i.e. steel structures for buildings, cranes, ships, pressure vessels. For other types of structures there are recommendations that have been thoroughly elaborated. These recommendations are published by IIW (International Institute of Welding) and AWS (American

Welding Society) and are almost used as standards in many businesses (SSAB, 2011).

2.2.1

FAT class

There are several different FAT or fatigue classes that divide different geometries into cases which are associated with design S-N curves. The library of FAT classes has been constructed through testing of specimens. They allow the fatigue life to be assessed, depending on the geometry and surface roughness of the design of interest. The quality of the material surface is a result of production quality.

The classes indicate the characteristic fatigue strength in N/mm

2

at

𝑁 = 2 βˆ™ 10

6

cycles. The survival

probability is 97.7% which corresponds to 2.3 broken units per 100 tested. Figure 14 show the

different FAT-classes as lines in an S-N or Wöhler diagram. A lower FAT-value results in a lower curve in the diagram.

Figure 14- Characteristic fatigue strength for constant amplitude loads (Olsson, 2014)

2.2.2

Wöhler

S-N

-curve

An S-N-curve show the fatigue strength of a detail and it is constructed by performing several fatigue life tests at different stress ranges. The test results are plotted in a log-log diagram, which then represent a linear relationship for the fatigue strength of one point in a construction. Usually the slope of the lines in the diagram are π‘š = 3.0

for welded joints, whereas π‘š = 5.0

for an unwelded base material. In the diagram there is a knee point which defines the transition to infinite life. This knee point is also named the fatigue limit. After this limit the slope of the Wöhler

S-N

curve decreases.

12

2.2.3

Load spectrum

Load spectrums are created from field measurements or from measurements done during lab testing.

Most fatigue assessments are made by considering a very small stress range under high loads. These full load spectrums mean that all the loading cycles have the same magnitude. In reality however, a full loading spectrum may not apply. During the life of a truck, it will lift loads with varying mass and consequently the stress range will vary. In this case stresses are of high importance thus the load spectrum used is the stress spectrum. It tells how many times a stress or stress range appears during measuring. Measuring has to be performed during at least 1/10 000 of the total life of the specimen

(SSAB, 2011).

If the design has a varying stress spectrum with a small number of maximum lifts it has to be compensated. The spectrum parameter π‘˜ π‘š

compensates for the varying stress ranges, and is equal to unity for a constant stress range. It is defined as the ratio between the maximum and minimum principal stresses in the spectrum. A varying stress range results in a lower spectrum parameter.

The cumulative stress parameter is then calculated with the help of the spectrum parameter.

2.2.4

Weld imperfections

A number of weld imperfections can arise due to welding. It is important to know how they affect the fatigue life of the weld. They can be divided into defects caused by either the material or method, and have varying effect to the fatigue. The material is always deformed due to welding, making it impossible to avoid imperfections.

Fatigue cracks often become present after a numerous of cycles and arise at a stress concentration, frequently the weld toe or root. They also grow perpendicular to the maximum principal stress. They can often be seen as they grow from the weld toe, but if they start at the weld root, they can be hard to detect. The weld root cracks grow through the throat thickness and are only seen when failure has occurred. Cracks caused by manufacturing most often grow along the joint.

A poor piece of workmanship can result in uneven welds and unnecessary stress concentrations. The start and the end of a weld are typical crack initiation spots due to their geometry.

Other factors affecting the fatigue life of the joint are misalignment between the parts of the component. Misalignment can be both axial, and angular in several directions depending on the geometry of the joint. Some allowance for misalignments are included in the tables of classified structural details, the fatigue classes.

Stress concentrations are the most important factor that affects the fatigue strength. It describes the ratio of how much the maximum stress is increased in the notch compared to the nominal stress. They are created through irregularities on the surface, holes, notches or welds. The stress concentrations in welds are very hard to define since they depend on the notch depths and the radii, which vary between all welds.

2.2.5

Residual stresses

When constructing a weld, high temperatures are present and the materials are heated very quickly.

The thermal expansion causes the material to expand, thus during cooling the weld wants to shrink, but the surrounding material resists. Both longitudinal and transverse stresses become present in the

weld and surrounding material, Figure 15.

13

Figure 15 - Residual stresses in weld (Olsson, 2005)

The large tensile residual stresses in and around the joint has a negative effect on the fatigue life of the specimen. Even though a crack only grows during tensile loading, the residual stresses can cause fatigue cracks anyway. In most standards the longitudinal residual stresses is assumed to be as high as the yield limit of the material.

2.2.6

Fatigue models

For fatigue life calculations there are several models applicable. When the fatigue life of the structure is estimated to be a high number of cycles, or not even occur at all, stress-based fatigue design is suitable. For high-cycle fatigue the number of stress cycles to failure could vary between tens of thousands to infinity.

For this type of calculations, material data are often determined for the material by loading the specimen with a cyclic loading with constant amplitude. The shape of the load variation is normally sinusoidal, but is considered not to influence the number of cycles to failure, which is counted. The only parameters of importance is the mean value 𝜎 π‘š amplitude 𝜎 π‘Ž

, Equation 2.1 and Equation 2.2.

, of the stress in the material, and the stress 𝜎 π‘š

=

1

2

( 𝜎 π‘šπ‘Žπ‘₯

+ 𝜎 π‘šπ‘–π‘›

)

Equation (2.1) 𝜎 π‘Ž

=

1

2

( 𝜎 π‘šπ‘Žπ‘₯

− 𝜎 π‘šπ‘–π‘›

)

Equation (2.2)

The difference between the applied loads are defined in the stress ratio

𝑅

, Equation 2.3. Also, the stress range is defined in Equation 2.4.

𝑅 = 𝜎 π‘šπ‘–π‘› 𝜎 π‘šπ‘Žπ‘₯

Equation (2.3)

βˆ†πœŽ = 2 𝜎 π‘Ž

Equation (2.4)

14

A positive stress ratio is a result of tensile stresses only, also called pulsating loading. Usually the minimum value is zero, 𝜎 π‘šπ‘–π‘›

= 0

. A negative value corresponds to a varying compressive and tensile stress, also known as alternating loading. A fully reversed loading gives a mean value of zero, 𝜎 π‘š

= 0

.

One method used to present the data is to plot a graph with the logarithm of the stress amplitude on the y-axis and the logarithm of the number of cycles to fatigue failure at the x-axis. This creates a linear relationship between the logarithm of the stress amplitude, 𝜎 π‘Ž cycles to failure,

𝑁

. This gives Equation 2.5.

and the logarithm of the total number of 𝜎 βˆ™ 𝑁 = 𝐾

Equation (2.5)

Where π‘š

and

𝐾

are material parameters to be determined from the fatigue test.

The S-N curve shows the relationship between the stress and the fatigue life of the specimen.

Normally the graph is used for 𝜎 π‘š

= 0

, thus if not so it has to be stated since a positive mean stress will result in lower fatigue life. In practice however, the mean stress have the most effect at pulsating loading. For welded joints the most significant parameter is the stress range since the local stresses at the weld transition vary from the yield point and downwards, independently of the nominal R-value

(SSAB, 2011).

When performing fatigue testing the measured data often are scattered widely. When constructing the

S-N curve it is supposed that 50 % of the specimens will fail at a life that is shorter than the curve.

Consequently 50 % will have a longer life than shown. This curve can be adjusted for other probabilities if the scatter of the data is known.

Strain based fatigue are mostly used when the stresses in the specimen reach the yield limit, or even exceeds it. At these stress levels the fatigue life of the specimen will be short; therefore this type of fatigue is called low-cycle fatigue. Due to the high stresses, it is convenient to use a strain-based fatigue model to measure the loading of the specimen. The method differs depending on if the loading is monotonically increasing or a cyclic loading. The Coffin-Manson relation characterizes the Lowcycle fatigue and describes the plastic strain amplitude, Equation 2.6.

βˆ†πœ€ 𝑝

2 = πœ€′ 𝑓

(2

𝑁

) 𝑐

Equation (2.6)

Where

βˆ†πœ€ 𝑝

⁄ 2

is the plastic strain amplitude, πœ€ ´ 𝑓

and

c

are empirical constants known as the

fatigue ductility coefficient

and the

fatigue ductility exponent,

respectively

.

2 𝑁 becomes the number of half cycles,

load reversals

to failure (Dahlberg & Ekberg, 2002).

In cyclic loading with constant stress amplitude the strain does not have to be the same in two subsequent cycles. As the stress still is the same, strain depends on if the material is work-hardening or work-softening. After a number of loading cycles, the stress-strain curve could stabilize, but this is not always the case. Due to the high stresses the material will not only undergo elastic deformation, but also plastic. This indicates that the total strain amplitude, the sum of the elastic and plastic components may correlate to life.

The cyclic stress-strain relationship is plotted in a graph with the stress on the y-axis and the strain on the x-axis.

15

The relationship according to (Osgood & Ramberg, 1943), Equation 2.7 and Equation 2.8. πœ€ π‘Ž

= πœ€ + πœ€ π‘π‘™π‘Žπ‘ π‘‘π‘–π‘ π‘Ž

= 𝜎 π‘Ž

𝐸

+ οΏ½ 𝜎 π‘Ž

𝐾′οΏ½

Equation (2.7) πœ€ π‘Ž

= 𝜎 π‘Ž

𝐸

+ πœ€′ 𝑓

οΏ½ 𝜎 𝜎′ π‘Ž 𝑓

οΏ½

Equation (2.8)

Where,

𝐸 , 𝐾

, 𝑛

, 𝜎′ 𝑓

and πœ€′ 𝑓 are material parameters to be determined from experiments performed with cyclic loading.

The energy based fatigue criterions describe the different stages of fatigue damage. The models tries to create a relationship between the energy dissipated per cycle and the fatigue life, for a constant amplitude load. They include both the stress and the strain near the crack tip.

The SWT, Smith-Watson-Topper criterion is an energy based fatigue criterion which is described by the product of the maximum stress and the strain amplitude, (Karolczuk & Macha, 2005), obtaining a simple form of damage parameter, Equation 2.9.

π‘Š π‘Ž

= 𝜎 π‘šπ‘Žπ‘₯ πœ€ π‘Ž

= 𝜎′ 𝑓

𝐸

2

(2

𝑁

)

2𝑏

+ 𝜎′ 𝑓 πœ€′ 𝑓

(2

𝑁

) 𝑏+𝑐 where 𝑏

is the

fatigue strength exponent

.

Equation (2.9)

In the case of welds the most frequently used fatigue model is the stress based.

16

2.3

Nominal stress

The nominal stress approach (SSAB, 2011) was the first method to be developed of the ones mentioned and is still today very commonly used for fatigue analysis. It disregards the local stress raisers, typically notches and local weld geometries. These effects are included into cases which contain structural details, called FAT or fatigue classes. They allow the fatigue life to be assessed.

Since it is a reasonably easy method, computations can be performed without help from a FE-analysis.

In some cases this method is possible to use when the hot spot and effective notch methods do not work, for example for longitudinally loaded welds. Since it is so well used, a lot of standards and recommendations cover the method (SSAB, 2011), and the number of FAT classes is extensive to cover most possible geometries. However, the method does not work well with more complex geometries.

For the nominal stress method to be usable it has to be possible to determine the nominal stresses in the specimen. The allowed stress range

βˆ†πœŽ π‘Ÿπ‘‘

is calculated with Equation 2.10, and refers to the difference between the maximum and minimum stresses at a specific point in a cross section. The stresses are calculated as nominal stresses without consideration of local stress concentrations (SSAB,

2011) eq.5.15.

βˆ†πœŽ π‘Ÿπ‘‘

=

𝐹𝐴𝑇 βˆ™ πœ‘ 𝛾 π‘š 𝑑

βˆ™ πœ‘ π‘š

βˆ™ �𝑆 π‘š

βˆ™ πœ‘ 𝑒

Equation (2.10)

The formula consists of several partial factors and the fatigue class, which relies on the geometry of

the specimen. The FAT value is chosen from Appendix A, and is a property of the actual design of the

weld and the weld class.

The material partial factor πœ‘ π‘š

is dependent on the yield limit and the surface roughness as seen in

Figure 16. If the material is unaffected by welding or thermal cutting the fatigue strength increases.

The material is seen as unaffected if the distance from a weld or thermal cutting is at least three times the thickness of the plate or 50 mm. The surface roughness depends on the after treatment where a higher value means a rougher surface. For a welded joint the fatigue strength is independent of the static yield limit of the material, thus the material factor πœ‘ π‘š

is equal to unity.

Figure 16 - The material partial factor πœ‘ π‘š

as a function of yield limit and surface roughness according to SSAB (Olsson, 2014)

17

The stress variation factor πœ‘ 𝑒

regards how the load is applied and is chosen with respect to the stress ratio. When applying a weld, residual stresses up to the yield strength are built into the material. To reduce the residual stresses, stress relief annealing can be used, thus it is also justified to raise the fatigue strength. The following equations, Equation 2.11 to Equation 2.13 describe how to choose the stress variation factor with respect to the stress ratio(SSAB, 2011) eq.5.12 to eq.5.14.

Weld: πœ‘ 𝑒

Base material: πœ‘ 𝑒

= 1

= 1 − 0.3

𝑅�

0 ≤ 𝑅 ≤ 0.5, 𝜎 π‘šπ‘Žπ‘₯

> 0

Equation (2.11)

Weld: πœ‘ 𝑒

Base material: πœ‘ 𝑒

= 1

= 1

0.2

𝑅

0.25

𝑅�

− 1 ≤ 𝑅 ≤ 0

Equation (2.12) πœ‘ 𝑒

= 1.3

𝜎 π‘šπ‘Žπ‘₯

< 0

Equation (2.13)

When there are unknown parameters, πœ‘ 𝑒

is set to unity which gives a conservative result.

The fatigue strength is dependent on the dimensions of the material, where a thinner material has higher fatigue strength than a thicker material, Equation 2.14. It is used when the loading is perpendicular to the welds extension and the weld toe is the most stressed area. This could be taken into account by multiplying the fatigue strength with a thickness factor πœ‘ 𝑑

(SSAB, 2011) eq.5.11. πœ‘ 𝑑

= οΏ½ 𝑑

0 𝑑 οΏ½ 𝑛

Equation (2.14) 𝑑

= thickness of the material 𝑑

0

= reference thickness; 15mm

Depending on the joint type, different exponents 𝑛

are used according to Table 1.

Table 1 - Table for determination of thickness factor πœ‘ 𝑑

(SSAB, 2011) – table 5.9

Joint type

Fillet weld, transverse T-weld, sheets with transverse junction, longitudinal stiffeners

Fillet weld, transverse T-weld, sheets with transverse junction, longitudinal stiffeners

Transverse butt weld

Treated butt rye, transverse welds or weld junctions

Non welded material

Class

Untreated weld

Treated weld

Untreated weld

All

All

n

0.14

0.10

0.10

0

0

For sheets thinner than 4 mm, πœ‘ 𝑑

are set to the value of a sheet of thickness 4 mm. When doing computations with the hot spot and effective notch method, πœ‘ 𝑑

is set to unity.

The partial 𝛾 π‘š

is a failure impact factor with regard to the Safety Class, and is chosen based on the consequences a failure could have. The acceptable risk of failure is also a variable in the choice of the partial coefficient 𝛾 π‘š

. Usually an acceptable risk of failure is set to 2.3 %, which would correspond to

2.3 failures per 100 units. This risk is accepted since in most failures the load is distributed between other welds and thus not leads to total failure. In some cases it is necessary knowing the mean fatigue limit instead of the characteristic fatigue limit. In those cases it is practical to use the coefficient for

18

risk of failure πœ‘

𝑄

, rather than the partial coefficient 𝛾 π‘š

. The coefficients and accepted risks of failure

can be seen in Table 2.

Table 2 – Partial coefficient and accepted risk of failure (SSAB, 2011) – table 5.11

Consequence of failure Approximated risk of failure

Testing

Negligible

Less severe

Severe

Very severe

50 %

2.3 %

0.1

%

0.01

%

0.001

%

Partial coefficient 𝛾 π‘š

0.77

1.0

1.15

1.25

1.34

Coefficient for risk of failure πœ‘

𝑄

1.3

1.0

0.87

0.8

0.74

Depending on how well defined the load is, the partial 𝛾 𝑓

is used. It defines the insecurity in the load applied. For loads based on field measurements 𝛾 𝑓

is set to unity.

Cumulative stress parameter s m

, Equation 2.15

(SSAB, 2011) eq.5.10 – eq.5.8. 𝑠 π‘š

=

2 βˆ™

𝑁 𝑑

10

6

βˆ™ π‘˜ π‘š

Equation (2.15) π‘˜ π‘š

= οΏ½ οΏ½ 𝑖

βˆ†πœŽ

βˆ†πœŽ 𝑖 π‘Ÿπ‘’π‘“

οΏ½ π‘š

βˆ™ 𝑛 𝑛 𝑖 𝑑

Equation (2.16)

Equation 2.16 compares the stress

βˆ†πœŽ stress range

βˆ†πœŽ π‘Ÿπ‘’π‘“

and the total number of cycles 𝑛 𝑑

When a constant stress range is present 𝑖 and number of cycles 𝑛 𝑖 π‘˜ π‘š

at load level

i,

with the maximum

. For an alternating stress range

= 1

, which yields a conservative result. π‘˜ π‘š

< 1

is used.

Then the maximal stress range is calculated with Equation 2.17(SSAB, 2011) eq.5.19.

βˆ†πœŽ π‘šπ‘Žπ‘₯

= 𝜎 π‘šπ‘Žπ‘₯

− 𝜎 π‘šπ‘–π‘›

Equation (2.17)

For the construction to be accepted for the designed life, Equation 2.18 has to be fulfilled.

βˆ†πœŽ π‘šπ‘Žπ‘₯

βˆ™ 𝛾 𝑓

< βˆ†πœŽ π‘Ÿπ‘‘

Equation (2.18)

The calculated life of the specimen has to be bigger than the designed life according to Equation 2.19

𝑁 ≥ 𝑁 𝑑

Equation (2.19)

Where N is the fatigue life of the specimen, and is calculated with Equation 2.20 (SSAB, 2011), eq.5.22.

𝑁 = 𝑁 𝑑

οΏ½

βˆ†πœŽ π‘Ÿπ‘‘

βˆ†πœŽ οΏ½ π‘š

Equation (2.20)

19

2.4

Hot spot

The hot spot method (SSAB, 2011) was developed for the off-shore industry and includes all notch effects of the structural detail but not the effects caused by the weld profile itself. It was developed to evaluate elongations with strain gauges but has since been applied to finite element modelling. Two reference points at a specified distance from the toe are used for evaluation; the values are then extrapolated to produce the geometric hot spot stress. This stress is used together with the FAT class specific for the hot spot method to calculate the fatigue life of the specimen.

The hot spot method is especially useful when there are no clearly defined nominal stresses and also when the FAT class is missing in the nominal method. It also gives a good connection between strain gauges and FE-analysis.

The most applied method is linear extrapolation where the elongation is measured in two points according to Equation 2.21 (SSAB, 2011) eq.5.26. πœ€ β„Žπ‘ 

= 1.67

βˆ™ πœ€

0 .

4𝑑

− 0.67

βˆ™ πœ€

1 .

0𝑑

Equation (2.21)

If the stress diverges nonlinearly towards the weld toe, quadratic extrapolation can be used where the elongation is measured in three points according to Equation 2.22 (SSAB, 2011) eq.5.27. πœ€ β„Žπ‘ 

= 2.52

βˆ™ πœ€

0 .

4𝑑

− 2.24

βˆ™ πœ€

0 .

9𝑑

Both of the methods are illustrated in Figure 17.

+ 0.72 βˆ™ πœ€

1 .

4𝑑

Equation (2.22)

Figure 17 - The measuring points in the hot-spot method illustrated.

Since the stress state in the analysis can be approximated to a uniaxial stress state Hooke’s law can be used to approximate the hot spot stresses by means of Equation 2.23. 𝜎 β„Žπ‘ 

= 𝐸 βˆ™ πœ€ β„Žπ‘ 

Equation (2.23)

The main stresses used in the calculations are the maximum or minimum principal stress, as long as its direction is within

±60°

perpendicular from the weld toe.

When the hot spot stress has been calculated, the computations are done as in the nominal method with some simplifications. πœ‘ π‘š

, πœ‘ 𝑒

, πœ‘ 𝑑

are all set to unity since the calculations are done on untreated welds.

20

Equation 2.10 is used together with Equation 2.15, which results in Equation 2.24.

βˆ†πœŽ π‘Ÿπ‘‘

= πœ‘

𝑄

3

βˆ™ 𝐹𝐴𝑇

2 βˆ™ 𝑑

10

6

Equation (2.24)

The fatigue life is then computed with Equation 2.25.

𝑁 = 𝑁 𝑑

οΏ½

βˆ†πœŽ π‘Ÿπ‘‘

βˆ†πœŽ οΏ½ π‘š

Equation 2.25 together with Equation 2.24 results in the formula:

Equation (2.25)

𝑁 = 2 βˆ™ 10

6

βˆ™ οΏ½ πœ‘

𝑄 𝜎

βˆ™ 𝐹𝐴𝑇

οΏ½

3 β„Žπ‘ 

For a risk of failure, πœ‘

𝑄

at 2.3% and with a design life of

𝑁 𝑑

= 2

Equation (2.26)

βˆ™ 10

6

cycles Equation 2.26 can be simplified to Equation 2.28 with the help of Equation 2.27.

βˆ†πœŽ π‘Ÿπ‘‘

= 𝐹𝐴𝑇

Equation (2.27) and

𝑁 = 2 βˆ™ 10

6

βˆ™ οΏ½

𝐹𝐴𝑇 𝜎 β„Žπ‘ 

οΏ½

3

Equation (2.28)

According to the hot spot method a design passes if Equation 2.29 and Equation 2.30 are fulfilled.

βˆ†πœŽ β„Žπ‘ 

βˆ™ 𝛾 𝑓

≤ βˆ†πœŽ

𝑅𝑑

Equation (2.29)

𝑁 ≥ 𝑁 𝑑

Equation (2.30)

In this case, with a T-joint specimen, a FAT-value of 100 is used in the calculations.

21

2.5

Effective notch

When applying the effective notch method (SSAB, 2011), the maximum stress in a notch with a linear elastic material is considered. This stress is obtained by modelling the whole design of the detail and taking into consideration all transition radii and fillets. It is very useful when different weld geometries are to be compared and neither the nominal stress nor the hot-spot method is possible to use. It is also well suited for examination of crack propagating from the weld root. The assessment is done using a single Wöhler S-N curve given by FAT=225 for steel.

Since the method uses the stresses in the transition between the weld and the base material, uncertainties arise at what the exact geometry look like. The difference between the maximum and minimum principal stress for the present load case is used and it should be angled within

±60° perpendicular to the weld. The maximum principal stress is to be found in the root or the transition between weld and base material, the toe of the weld.

The calculation steps are basically the same as previous methods where the stress range and life are based on Equation 2.10 and Equation 2.24.

The life of the weld is then computed with Equation 2.31. The stress 𝜎 π‘Ÿ maximum and minimum principal stresses, taken from the FE-model.

is the difference between the

𝑁 = 𝑁 𝑑

οΏ½

βˆ†πœŽ π‘Ÿπ‘‘ 𝜎 π‘Ÿ

οΏ½ π‘š

Equation (2.31)

By inserting Equation 2.24 in Equation 2.31 and simplifying the result, Equation 2.32 is yielded. This is used to calculate the life of the weld.

𝑁 = 2 βˆ™ 10

6

βˆ™ οΏ½ πœ‘

𝑄

βˆ™ 𝐹𝐴𝑇 𝜎 π‘Ÿ

οΏ½

3

This equation results in Equation 2.33 if the design life is

𝑁 𝑑

2.3%, which corresponds to πœ‘

𝑄

= 1

.

= 2

Equation (2.32)

βˆ™ 10

6

cycles and the risk of failure is

𝑁 = 2 βˆ™ 10

6

βˆ™ οΏ½

𝐹𝐴𝑇 𝜎 π‘Ÿ

οΏ½

3

Equation (2.33)

A design passes according to the effective notch method if Equation 2.34 and Equation 2.35 are fulfilled.

βˆ†πœŽ π‘Ÿ

βˆ™ 𝛾 𝑓

≤ βˆ†πœŽ π‘Ÿπ‘‘

Equation (2.34)

𝑁 ≥ 𝑁 𝑑

Equation (2.35)

The FAT classes for the effective notch approach are chosen to 225 if the thickness of the metal sheet is greater or equal to 5 mm, otherwise 625 is used if the metal sheet is less than 5 mm in thickness. For the thicker metal sheets an effective notch radius of 1 mm is used, respectively 0.05 mm for the thinner plate.

22

2.6

Evaluation of test data

For evaluation of test data characteristic values are calculated. The goal is to derive an S-N curve to be able to compare the fatigue lives of the testing results and the computations.

The test data gathered,

βˆ†πœŽ

and the number of cycles

𝑁

is recalculated to log

10

values. log 𝑁 = log 𝐢 − π‘š βˆ™ log βˆ†πœŽ

By the use of Equation 2.36, the exponents π‘š

and the constant log 𝐢

can be calculated.

Equation (2.36)

The constant log 𝐢

are called π‘₯ 𝑖

, and the mean value are denoted π‘₯ π‘š

, Equation 2.37. The standard deviation can be calculated with Equation 2.38. π‘₯ π‘š

=

∑ π‘₯ 𝑖 𝑛

Equation (2.37)

𝑆𝑑𝑑𝑣 =

οΏ½∑

( π‘₯ π‘š 𝑛 −

− π‘₯ 𝑖

1

)

2

The characteristic value π‘₯ π‘˜

is calculated by Equation 2.39. π‘₯ π‘˜

= π‘₯ π‘š

+ π‘˜ βˆ™ 𝑆𝑑𝑑𝑣

The value for π‘˜

are chosen from Table 3.

Table 3 - Values of

k

for the calculation of the characteristic values 𝑛 π‘˜

10

2.7

15

2.4

20

2.3

25

2.2

30

2.15

40

2.05

50

2.0

100

1.9

Equation (2.38)

Equation (2.39)

With the help of these values the data can be plotted in a Wöhler diagram for further comparison.

If the number of test objects, 𝑛 < 10

more calculations have to be done. Refer to, (Hobbacher, 2008)

Appendix 6.4.1.

23

3 FEM analysis

3.1

FEM model

The specimen is a T-junction fillet weld steel design as can be seen in Figure 18. The model is

modelled in Abaqus where the FE-analysis is carried out. The weld and weld end are modelled as an isosceles triangle extruded in the direction of the weld, no modifications are done at the weld end. This weld end model will be called normal weld end. Depending on the method used for computations,

different modelling techniques have been used. The modelling effort needed, represented by Figure 6

corresponds well to the size of mesh and time needed to be put into the modelling and meshing. The elements used for analysis is a 10-node quadratic tetrahedron element with improved surface stress formulation, C3D10I. The integration points in this element are placed at the corner nodes, thus the stresses are calculated at the surface, removing extrapolation issues.

3.1.1

Load cases

Two different load cases are considered where the load is applied differently. In the first case the welds are unloaded.

F

F F

Figure 18 - Load case 1 to the left and load case 2 to the right

Both load cases are analysed with two different boundary conditions, one case with fixed ends and one where the ends are free to rotate around the direction of the edge, the x-direction.

3.1.2

Boundary conditions

Symmetry constraints are used to simplify the model as in Figure 19.

Figure 19 - Specimen with symmetry constraints, quarter of a model

24

The mid plane surface in the YZ-plane and the mid plane surface in the YX-plane have symmetry

conditions according to Table 4. The reference point is tied to a rigid body constraint to the whole end surface as can be seen in Figure 20. It is then constrained according to Table 4 in the U2 direction; and also constrained to no rotation around the x-axis, see Figure 21. These constraints are then applied to

the entire rigid surface due to the tie constraint. The force is applied to the reference point. Two different types of boundary conditions were specified, compare fixed end and simply supported.

Table 4 - Boundary conditions fixed end, boundary condition case 1

Symmetry

YZ-plane

YX-plane -

Reference point -

U1 U2 U3

0 - -

-

0

0

-

Figure 20 - Load and rigid body constraint at specimen end

Figure 21 - Reference point constraints, fixed end

25

The force is applied perpendicular to the surface and is directed in positive U3-direction. Three load levels, 100 kN, 200 kN and 300 kN are used in the simulations.

The second variant of the boundary condition was used to see how big the difference would be if the end of the specimen could move more freely. The reference point where the force is applied is able to rotate freely around the x-axle, a simply supported boundary condition. From now on the two cases will be named case 1 and case 2.

3.1.3

Material model

The material in the simulations is isotropic and elastic with the properties:

𝐸 = 210 πΊπ‘ƒπ‘Ž 𝜌 = 7850 π‘˜π‘” / π‘š

3 𝑣 = 0.3

3.1.4

FE-analysis

The FE-analysis is a standard static implicit analysis. Due to the relatively high forces in some of the analysis there could be a risk of large displacements. Therefore the

Nlgeom

option was used. It takes into consideration the nonlinear effects the large displacements and deformations could have on the geometry. The solution technique is the Full Newton.

26

3.1.5

Nominal stress

In the nominal stress method the stresses are taken from an area where the stress field is even and no stress concentrations are present.

Measuring points, 𝜎 π‘›π‘œπ‘š , 1

, 𝜎 π‘›π‘œπ‘š , 2

, 𝜎 π‘›π‘œπ‘š , 3

~90 mm

50 mm

Figure 22 - Nominal stress measure points

The stresses are read at the corner nodes of the elements at the points marked in Figure 22, at both

sides of the specimen. The maximum three are denoted 𝜎 π‘›π‘œπ‘š , 1

, 𝜎 π‘›π‘œπ‘š , 2

, 𝜎 π‘›π‘œπ‘š , 3

. The mesh has a global size of 10 mm with a single bias technique used at the weld ranging from 10 mm to 5 mm at the weld

end, as seen in Figure 23.

Figure 23 - Weld modelling nominal stress approach

27

3.1.6

Hot spot

The hot spot method uses the stresses or strains at specific reference distances from the weld toe based on the thickness of the material. Depending on which extrapolation method is used, linear or quadratic, different amounts of reference points are used and at different distances from the weld end. The mesh around the weld, especially in front of the weld toe has a mesh that corresponds to

0.1

𝑑

. The result is a

mesh with much more elements than in the nominal method, Figure 24.

Figure 24 - Hot spot model

The linear extrapolation approach has reference points at

0.4

𝑑

and

1.0

𝑑

from the weld toe, marked

with red in Figure 25. The corresponding points in the quadratic extrapolation approach are

0.4

𝑑

,

0.9

𝑑 and

1.4

𝑑

, which are marked with black in Figure 25. The maximum or minimum principal stress at the

distance of

0.4

𝑑

along the weld toe is used to find at what distance from the weld end the reference points are to be placed.

Figure 25 - Hot spot stress measuring points

3.1.7

Effective notch

In the effective notch approach the stress is assessed directly in the problematic areas. To be able to do this, a fictive radius is inserted in all transitions and notches. At the weld root a circular fillet is

inserted in accordance with Figure 26.

28

r

ref

Figure 26 - Effective radius

Depending on the thickness of the material, π‘Ÿ π‘Ÿπ‘’π‘“ material is less than 5 mm π‘Ÿ π‘Ÿπ‘’π‘“

is set to 1 mm or 0.05 mm. If thickness of the

is set to 0.05 mm, otherwise 1 mm. It is recommended that the element size in the notches are π‘Ÿ ⁄ 4

(Wolfgang, 2013), which yields an element size of 0.25 mm. To obtain a good mesh, partitions are created around the fillets and partitions are also created around the area of the weld toe and root to get a successive transition to coarser mesh.

Due to the small element sizes used, a sub modelling technique was used. The global model has a coarse mesh with a size of 10 mm. At the weld a single bias function was used to make the mesh finer

near the weld end. The mesh can be seen in Figure 27.

Figure 27 - Global model for the effective notch approach

29

A sub model was created of the weld whose surfaces were coupled to the displacements of the global model. All loads and boundary conditions are specified in the global model which drives the sub

model via the sub model boundary condition. The surfaces in Figure 28 have this coupling to the

global model.

Figure 28 - Sub model boundary conditions

An element size of 0.25 mm is used at the most important areas, the fillets, around the weld toe and the root. The weld toe and root have an element size along the weld at a length of 3-throat thicknesses.

Outside the fine mesh a larger element size of 1.25 mm, in an area 5 mm around the weld is used

which transits to an element size of 5 mm at the edges, Figure 29.

Figure 29 - Sub model mesh

30

Figure 30 – Procedure of finding the maximum principal stress in the weld toe

The fine mesh at the weld toe is displayed in Figure 30, which is where, together with the weld root, the stresses are examined. The procedure can be seen in Figure 30, where the two outer most elements

at the weld toe are removed. The stress field limits are adjusted so that the maximum or minimum stress can be seen at the corner of a few elements. If the weld is subjected to a tensile force the maximum stress is used, and the minimum stress if the weld is subjected to a compressive force. By measuring the principal stress in the corner of these elements, the highest or lowest of these stresses can be found. This principal stress has to be perpendicular to the weld and the value is to be used in the fatigue life calculations. The stress are denoted as 𝜎 π‘‘π‘œπ‘’

.

The fillet hole at the root of the weld can be modelled in different ways. Depending on the modelling technique the maximum stress appear at different locations and the magnitude of the stress also differs.

The standard (BSK99 , 2003) covers the first and second modelling technique, as seen in Figure 31.

The one to the right is frequently used at BT Products since the results are considered not to differ between the modelling techniques.

Figure 31 - Different ways of modelling the effective radius at the weld root, centred,

U-shaped and eccentric

31

When evaluating the weld root the procedure is much the same as in the weld toe. The root is isolated

and the two elements nearest the weld end are removed, see Figure 32. The stress field limits are

adjusted so that the highest or lowest stress can be seen at the corner nodes of a few elements. The principal stress is measured in the corner nodes of the elements and the maximum or minimum stress are then used in the calculations. 𝜎 π‘Ÿπ‘œπ‘œπ‘‘ , 𝐼

Figure 32 - Procedure of finding the maximum principal stress in the weld root

Failure in the weld can occur either through the base material, the plate, or through the weld. In Figure

9 the failure modes were described. Failure can not only occur as described through the base material

but also through the weld. Therefore two stresses are measured in the weld root. One stress corresponds to failure in section I and the other, through the weld corresponding to section III. The stresses will be denoted as 𝜎 π‘Ÿπ‘œπ‘œπ‘‘ , 𝐼

and 𝜎 π‘Ÿπ‘œπ‘œπ‘‘ , 𝐼𝐼𝐼

. In Figure 33

𝜎 π‘Ÿπ‘œπ‘œπ‘‘ , 𝐼𝐼𝐼

can be seen in the top right of the root. 𝜎 π‘Ÿπ‘œπ‘œπ‘‘ , 𝐼𝐼𝐼

Figure 33 - Maximum principal stress towards the weld, corresponding to section III failure

32

3.2

Parametric study

The dimensions of the specimen affects the fatigue life, by doing a parametric study the critical dimension can be isolated. The dimensions that are changed include the thickness of the plate

t

1

, the throat thickness of the weld

a

, and the thickness of the bottom plate,

t

2

. The values used in the parametric study are chosen based on the dimensions of plates and welds that are present in the production. Future studies should cover more dimensions.

Table 5 - Parameters of the parametric study

Model

1

2

3

4

5

t

1

8

8 mm

10

10

10

t

2

mm

10

10

8

8

10

a

mm

5

4

5

5

5

300

200 y = 15827x

-0.329

y = 16321x

-0.33

Model 1

Model 2 y = 14093x

-0.326

Model 3 y = 14472x

-0.327

Model 4 y = 16171x

-0.329

Model 5

100

10000 100000 1000000 10000000

Cycles

Figure 34 - Curve for the parametric study showing applied force plotted against fatigue life

The thickness of the transverse plate does not seem to affect the fatigue life, but a thinner base plate

causes higher stresses in the weld and as a result lower fatigue life, Figure 34. The stresses chooses the

stiffer path. A smaller throat thickness in this case causes lower stresses in the weld and thus higher fatigue life. The equations seen to the left of the legend belong to respective model.

33

3.3

Numerical analysis

The numerical analysis and all other analysis following is performed on the specimen with plate thicknesses 10 mm and the throat thickness 5 mm. The choice of plate and throat thickness is based on common material that is used in the company’s products, other dimensions are to be considered, but not in this report.

The three commonly used calculation methods are to be compared in load case 1 to be able to see the differences and which is most accurate when weld ends are present in the specimen.

3.3.1

Nominal stress

The analytical values for the nominal stresses are computed with Equation 3.1. 𝜎 π‘›π‘œπ‘š

=

𝐹

𝐴

=

𝐹 𝑀 βˆ™ 𝑑

2

Equation (3.1)

The results from the numerical analysis for boundary condition case 1 are displayed in Table 6. Only

three of the measured six values are shown. The number of cycles is computed with the maximum

nominal stress found in Table 6.

Table 6 - Nominal stresses and cycles to rupture for boundary condition case 1

F kN

100

200

300

Analytical

σ nom

MPa

100

200

300

FE-analysis

σ nom,1

MPa

σ nom,2

MPa

101 99

202

302

197

306

σ nom,3

MPa

98

198

297

Cycles

461 000

58 000

17 000

Corresponding results from boundary condition case 2 can be seen in Table 7. The results vary

depending on the maximum nominal stress that is found. Sometimes a local peak is captured at the point of measuring.

Table 7 - Nominal stresses and cycles to rupture for boundary condition case 2

F kN

100

200

300

Analytical

σ nom

MPa

100

200

300

FE-analysis

σ nom,1

MPa

σ nom,2

MPa

101 100

204

305

200

300

σ nom,3

MPa

99

196

296

Cycles

461 000

56 000

17 000

34

3.3.2

Hot spot

The results from the finite element analysis can be seen in Table 8. It includes both the linear and

quadratic extrapolation method for comparison. Since the stress behaviour towards the weld root should be linear, there are no big differences in the results.

Table 8 - Hot spot stresses and cycles to rupture for boundary condition case 1

F kN

100

200

300

F kN

100

200

300

σ

0.4t

MPa

108

217

327

σ

0.9t

MPa

105

212

319

σ

1.0t

MPa

105

211

319

σ

1.4t

MPa

104

210

316

Linear

σ hs

MPa

110

221

333

Quadratic

σ hs

MPa

111

223

337

Linear

Cycles

3 334 000

408 000

119 000

Quadratic

Cycles

3 220 000

394 000

115 000

Corresponding results from boundary condition case 2 can be seen in Table 9. The outcome is a higher

fatigue limit than for the fixed edge boundary condition.

Table 9 - Hot spot stresses and cycles to rupture for boundary condition case 2

σ

0.4t

MPa

107

217

327

σ

0.9t

MPa

105

211

319

σ

1.0t

MPa

105

211

318

σ

1.4t

MPa

104

209

316

Linear

σ hs

MPa

109

220

333

Quadratic

σ hs

MPa

110

223

337

Linear

Cycles

3 390 000

411 000

119 000

Quadratic

Cycles

3 274 000

397 000

115 000

35

3.3.3

Effective notch

For the effective notch approach the results from the FE-analysis are displayed in Table 10. The

results from the different modelling techniques of the weld root are also compared. The U-shape could lead to higher stresses in the weld toe due to the decreased stiffness and as can be seen it does here too.

But, the stresses in the weld toe show very small differences between the modelling techniques. In the weld root however the stresses are varying. In case 1, the stresses in the root are lower than at the weld toe, not affecting the analysis and consequently the fatigue life. The number of cycles are computed for the eccentric hole modelling method.

Table 10 – Maximum stress and cycles to rupture for boundary condition case 1

F kN

100

200

300

σ toe

MPa

Eccentric

σ root,I

MPa

217 172

437 346

660 520

σ toe

MPa

U-shaped

σ root,I

MPa

217 150

438 300

662 367

σ

toe

MPa

Centered

σ root,I

MPa

217 160

438 322

661 484

Cycles

4 910 000

599 000

174 000

Corresponding results from case 2 can be seen in Table 11, without the weld root modelling

comparison. Since the differences are so small, the technique used here and onwards will be the eccentric hole modelling technique. The

σ root,III value at load level 200 kN is missing due to lost data.

Table 11 – Stress ranges and cycles to rupture for boundary condition case 2 with eccentric hole modelling in the weld root

F kN

100

200

300

σ toe

MPa

216

436

659

σ root,I

MPa

170

342

515

σ root,III

MPa

153

-

464

Cycles

4 910 000

599 000

174 000

36

3.3.4

Comparison of the computational methods

In Figure 35 the differences between the computed fatigue lives amongst the different methods are

displayed. The differences are big and the nominal method is predicting a clearly lower fatigue life than the other two methods. The two hot spot methods, linear and quadratic extrapolation showed no big dissimilarities. The equations describing the S-N curve for the welds are correct seen to the theory, and all of them have a slope of around three.

300

200 y = 14135x

-0.33

y = 7466.7x

-0.33

100

10,000 100,000 1,000,000

Cycles to rupture

Figure 35 - Comparison between the computation methods y = 15827x

-0.329

10,000,000

Hot spot

Nominal

Effective notch

37

3.3.5

Load case 2

The differences between the two boundary condition cases can be magnified by a simulation of the same specimen as used earlier but with a load transmitting weld. The load and the boundary conditions

are applied according to Figure 36. Two cases for the boundary conditions were tested, fixed and

simply supported.

F

Figure 36 - Load case 2 with load and fixed boundary conditions

Three different load levels where used, 100, 200 and 300 kN for both boundary conditions. Results are

shown in Table 12 for the hot spot method and Table 13 for the effective notch method. The nominal

stress method cannot be used in this load case since there are no fatigue classes applicable.

Table 12 - Fillet weld load case 2 with fixed ends, hot spot method

F kN

100

200

300

σ

0.4t

MPa

σ

0.9t

MPa

σ

1.0t

MPa

σ

1.4t

MPa

Linear Quadratic Linear Quadratic

σ hs

MPa

2 116 1 932 1 900 1 776 2 261

σ hs

MPa

2 259

Cycles

380

Cycles

368

3 334 3 015 2 961 2 750 3 583

4 282 3 844 3 770 3 484 4 624

3 627

4 686

95

44

92

43

Table 13 - Fillet weld load case 2 with fixed ends, effective notch method

F kN

100

200

300

σ toe

MPa

4 724

7 533

9 798

σ root,I

MPa

2 089

3 395

4 425

σ root,III

MPa

1 916

-

4 412

Cycles

475

117

53

Results from the other boundary condition case are shown in Table 14 and Table 15.

38

Table 14 - Fillet weld load case 2 with simply supported ends, hot spot method

F kN

100

200

300

σ

0.4t

MPa

2 171

3 309

4 227

σ

0.9t

MPa

1 995

3 004

3 807

σ

1.0t

MPa

1 965

2 953

3 736

σ

1.4t

MPa

1 851

2 755

3 464

Linear

σ hs

MPa

2 309

3 547

4 555

Quadratic

σ hs

MPa

2 336

3 592

4 618

Linear

Cycles

357

98

46

Quadratic

Cycles

345

95

45

Table 15 - Fillet weld load case 2 with simply supported ends, effective notch

F kN

100

200

300

σ toe

MPa

4 884

7 496

9 621

σ root,I

MPa

2 050

3 204

4 149

σ root,III

MPa

1 577

2 494

3 260

Cycles

430

119

56

The stresses in the welds are much higher than in load case 1, since the welds are transferring loads in

this case. The life of the weld dramatically decreases as a result of the higher stresses. In Figure 37 the

results are visualized in an S-N scatter diagram which shows the decreasing life due to the higher stresses present in load case 2.

10000

1000

Load case 1

Load case 1 - fix

Load case 2

Load case 2 - fix

100

10 1000

Cycles

100000 10000000

Figure 37 - Comparison between load case 1 and 2 with simply supported and fixed ends

The differences between the two boundary conditions, fixed ends and simply supported ends are small in both load cases. The fixed ends boundary condition causes slightly higher stresses in the weld toe, leading to a lower fatigue life. They are however on a straight line.

The highest stresses are not present at the weld ends as in load case 1, but in the middle of the weld.

39

3.4

Alternative weld modelling

3.4.1

Rounded weld end

The existing method of modelling the weld ends are greatly idealized and does not represent the geometry of a real weld. The method used also assumes that the stresses taken two elements from the weld end are usable stresses in the effective notch approach. If the singular weld end was to be rounded to look more like a real weld, maybe the stresses and ultimately the life would better match the testing. The weld is modelled with a sweep action and the throat thickness is unchanged, the

geometry can be seen in Figure 38.

Figure 38 - Overall geometry of the rounded weld

The model is simulated with three different radii of the curvature at the weld end, Figure 39. The

roundings are chosen with a radius starting from the length of the catheter

5

2

mm of the weld, denoted as 7.07 mm from here on, followed by 10 mm and 12 mm. The numbers are based on measurements of real welds, which are within this range. The mesh of the global model and sub model

can be seen in Appendix F.

Figure 39 - The different radii compared,

7.07, 10 π‘Žπ‘›π‘‘ 12 π‘šπ‘š

40

The hot spot stress method evaluates the stresses at reference distances from the weld toe. To find at what point along the weld the maximum stress appear, the maximum principal stress along the weld

toe are plotted in Figure 40, the stresses are read at the distance of 4 mm perpendicular to the weld toe.

The figure shows the stress starting from the weld end for the different modelling techniques.

335

330

325

320

315

310

305

300

295

290

285

0

Rounded r7

Rounded r10

Rounded r12

Normal weld end

10 20 30

Distance from weld end [mm]

40

Figure 40 - Stress distribution parallel to the weld toe, 4 mm from the toe

The distance from the weld end where the maximum stresses are measured define where the hot spot

stresses will be evaluated, perpendicular to the weld. In Table 16, Table 17 and Table 18 the linear and

quadratic hot spot stresses and the life computation are shown. These data are based on the maximum principal stresses. For comparison the stress increase compared to the normal weld model can also be seen. The rounded weld ends result in slightly higher stresses and lower life, but the increase is very small.

Table 16 - Rounded weld comparison hot spot approach, load level 100 kN

Model

Normal weld end

Rounded 7.07 mm

Rounded 10 mm

Rounded 12 mm

Linear Quadratic Linear

Stress increase

σ hs

MPa

- - 110

1 %

1 %

2 %

2%

3%

3%

111

111

111

Quadratic

σ hs

MPa

111

112

113

113

Linear

Cycles

3 334 000

3 245 000

3 208 000

3 180 000

Quadratic

Cycles

3 220 000

3 116 000

3 086 000

3 056 000

41

Table 17 - Rounded weld comparison hot spot approach, load level 200 kN

Model

Normal weld end

Rounded 12 mm

Linear Quadratic Linear

Stress increase

σ hs

MPa

- - 221

Rounded 7.07 mm 1 %

Rounded 10 mm 1 %

2 %

2%

3%

3%

223

223

224

Quadratic

σ hs

MPa

223

226

225

227

Linear

Cycles

Quadratic

Cycles

408 000 394 000

398 000 382 000

395 000 385 000

390 000 375 000

Table 18 - Rounded weld comparison hot spot approach, load level 300 kN

Model

Normal weld end

Rounded 12 mm

Linear Quadratic Linear

Stress increase

σ hs

MPa

- - 333

Rounded 7.07 mm 1 %

Rounded 10 mm 1 %

2 %

2%

3%

3%

336

337

338

Quadratic Linear

σ hs

MPa

Cycles

337

Quadratic

Cycles

119 000 115 000

341

342

343

116 000 111 000

115 000 110 000

114 000 109 000

For the effective notch approach the stresses are compared between the rounded cases and the original weld end modelling technique. The stress range measured in the radius of the root and weld toe are

displayed in Table 19. The life of the weld is computed with the maximum measured stress range. For

comparison the stress increase compared to the normal weld model also are displayed.

Table 19 - Rounded weld end comparison, effective notch

Load level

Model

Normal weld end

Stress increase

-

Rounded 7.07 mm 1.8 %

100 kN

σ toe

MPa

219

Cycles

4 764 000

200 kN

σ toe

MPa

441

Cycles

300 kN

σ toe

MPa

582 462

666

Cycles

169 000

223

4 510 000

449

551 000

678

160 000

Rounded 10 mm

Rounded 12 mm

1.8 %

2.0 %

223

224

4 510 000

449

4 482 000

450

551 000

678

548 000

680

160 000

159 000

The maximum principal stresses are compared to the normal weld end modelling. As can be seen in

Figure 41 the maximum principal stress is present in the beginning of the rounding at the weld end.

The upper and lower limits of the stress field are set to 0 MPa and 670 MPa.

42

Figure 41 - Stress field comparison between the rounded and normal weld ends at load level

300 kN

The stresses in the rounded weld ends increase with increasing radius and all have higher notch stress

than the normal weld end, Table 19. The maximum principal stresses however show very small

differences between the models. This pattern is also present in load case two, Table 20, but with an

increase in maximum stress.

Table 20 - Rounded weld end comparison for load case 2

Load level

Model

Normal weld end

Stress increase

-

100 kN

σ toe

MPa

4 724

Cycles

475

Rounded 7.07 mm 3 %

Rounded 10 mm

Rounded 12 mm

8 %

9 %

4 885

5 080

5 133

429

382

370

200 kN

σ toe

MPa

Cycles

7 533

120

7 821

8 097

8 168

105

94

92

300 kN

σ toe

MPa

9 798

10 159

10 489

10 572

Cycles

55

48

43

42

43

3.4.2

Concave and convex weld profile

Another way of changing the stress at the weld toe is to change the profile of the weld. Instead of an

isosceles triangle, the weld surface is modelled as an arc with two different radii, see Figure 45.

Figure 42 - Different weld profiles, normal, convex radius 10 mm, convex with radius

7.07 mm and concave with radius 12 mm

The resulting stresses and corresponding life can be seen in Table 21. The profile of the weld clearly

affects the stress in the weld toe, the higher angle between the weld and the plate, the higher the stress becomes. If a concave weld profile is chosen the stresses in the weld toe decreases due to decreased stress concentrations.

Table 21 - Concave and convex weld profile comparison

Load level

Model

Normal weld end

Stress increase

-

Convex 7.07 mm

Convex 10 mm

2.3 %

2.0 %

Concave 12 mm -12.7 %

100 kN

σ toe

MPa

219

224

223

195

Cycles

4 764 000

4 460 000

4 515 000

6 799 000

200 kN

σ toe

MPa

441

451

450

392

Cycles

582 000

544 000

548 000

834 000

300 kN

σ toe

MPa

666

682

680

590

Cycles

169 000

158 000

159 000

243 000

In Figure 43 the stress field can be seen, no big differences are visible more than the higher stresses in

the convex weld profiles.

Figure 43 - Stress field comparison, normal weld end, convex radius 10 mm and convex radius 7.07 mm

44

3.4.3

Changed notch radii

To increase the stress in the weld toe and root, the radii are decreased. The original radius of 1 mm

together with 0.5 mm, 0.4 mm, 0.3 mm and 0.2 mm are compared, see Figure 44. The number of

elements in the meshes are heavily increased due to the decreased element size, thus the partition with refinement around the notches are also decreased in radius. The radius of the partition used for refinement is twice the radius of the hole. The element size is chosen based on the notch radius, π‘’π‘™π‘’π‘šπ‘’π‘›π‘‘ 𝑠𝑖𝑧𝑒 = π‘Ÿ ⁄ 4

stated by (Wolfgang, 2013). The gap between the plates in the weld root is also changed to the same radius as in the notches. A smaller notch radius could cause modelling incompabilities at the weld gap and weld root.

Figure 44 - Different root and toe radii, 1 mm, 0.5 mm, 0.4 mm, 0.3 mm and 0.2 mm

The results are shown in Table 22; the notch radii together with the finer mesh have a great impact on

the stress increment.

Table 22 - Toe radii comparison

Load level

Notch radius mm

1.0

0.5

0.4

0.3

0.2

Stress increase

-

19.3 %

19.8 %

31.4 %

40 %

100 kN

σ toe

MPa

219

270

273

319

363

Cycles

4 764 000

2 510 000

2 463 000

1 537 000

1 049 000

200 kN

σ toe

MPa

Cycles

441

547

550

644

731

582 000

307 000

301 000

188 000

128 000

300 kN

σ toe

MPa

Cycles

666

825

830

972

1 103

169 000

89 000

88 000

46 000

37 000

The stress field around the weld toe looks much the same in the four cases, with the difference that the

stresses in the weld toe are different, Figure 45. The maximum and minimum values of the stress field

are set to 0 and 670 MPa.

Figure 45 - Stress field for different notch radii, 1 mm, 0.4 mm and 0.2 mm

45

3.5

Single fillet weld

In some cases it is impossible to use a fillet weld due to geometric limitations. A single fillet weld is an alternative, but how does the life of the single fillet weld compare to a fillet weld? The weld is compared in the two different load cases at different load levels as stipulated earlier. It is similar to the

fillet weld but only comprises a weld at one side of the plate, see Figure 46. The finite element model

uses symmetry constraints along the specimen, in the YZ-plane as stipulated earlier, and boundary conditions according to boundary condition case 1. Four different modelling weld end models will be tested, normal and rounded with different radii.

Figure 46 - Single fillet weld specimen

3.5.1

Load case 1

The stress ranges are examined in the same way as described before, the only difference is that the maximum stress appear in the root of the weld. This is the stress used for computation of the fatigue

life that can be seen in Table 23.

Table 23 - Comparison single fillet weld models

Load level

Model

Normal weld end

Rounded, 7.07 mm

Rounded, 10 mm

Rounded, 12 mm

Stress increase

-

1 %

1 %

1 %

100 kN

σ root,I

MPa

Cycles

184

2 555 000

186

2 540 000

186

187

2 622 000

2 524 000

200 kN

σ root,I

MPa

369

373

372

374

Cycles

318 000

316 000

327 000

315 000

300 kN

σ root,I

MPa

555

561

559

562

Cycles

94 000

94 000

97 000

93 000

The differences between the cases are very small, and are contained within

±1 %

. The modelling technique used for the weld end, clearly does not matter in this case since the maximum stress occurs in the root of the weld.

46

Comparing the results from the fillet welds and the single fillet welds shows that the stresses are larger

in the single fillet weld case, Figure 47.

300

200

Rounded 7 mm single

Rounded 10 mm single

Rounded 12 mm single

Normal weld end single

Rounded 7 mm

Rounded 10 mm

Rounded 12 mm

100

10000 100000 1000000 10000000

Cycles

Figure 47 – Comparison between single fillet weld and fillet weld

At any load applied to the specimen, a single fillet weld has higher stresses in the weld than a comparable fillet weld. Also, the single fillet weld is problematic since the higher stress occurs at the weld root making it hard to see possible crack initiations.

47

3.5.2

Load case 2

The single fillet weld is also tested with load case 2, the results displayed in Table 24. The maximum

stresses found are used when computing the life of the weld. Like in load case 1 for the single fillet weld the maximum stress is present in the weld root.

Table 24 - Comparison single fillet weld, load case 2

Load level

Model

Normal weld end

Rounded 7.07 mm

Rounded 10 mm

Rounded 12 mm

Stress increase

-

-1 %

-1 %

0 %

100 kN

σ root,I

MPa

Cycles

4 863

435

4 818

4 826

4 861

447

445

436

200 kN

σ root,I

MPa

7 846

7 803

7 815

7 853

Cycles

104

105

105

103

300 kN

σ root,I

MPa

10 263

10 256

10 242

10 275

Cycles

46

46

47

46

In load case 2 the differences in stresses between the modelling methods are magnified, if present. In

Figure 48 - Single fillet weld modelling comparisonFigure 48 the results are plotted and as can be

seen, there are no big differences in the equations or fatigue life. The rounded weld ends even show lower maximum stresses than the normal weld end model.

300

200

Normal weld end

Rounded 7.07

mm

Rounded 10 mm

Rounded 12 mm

100

10000 100000

Cycles

1000000 10000000

Figure 48 - Single fillet weld modelling comparison

48

3.6

Testing preparation

The testing has been performed on specimens welded according to Figure 5 and loaded according to

load case 1.

3.6.1

Placement of strain gauges

The strain gauges are placed in areas of interests on the specimen. Those are at the weld end, along the weld and at some distance away from the weld, to retrieve comparison for the hot spot method. The nominal stresses are also measured by strain gauges away from the weld where no stress concentrations due to the weld are present. The strain gauges measures 1x4 mm and measure the strain in the middle of the gauge in the longitudinal direction.

A total of 20 strain gauges are placed at the specimen in the areas according to Figure 49. All of the

strain gauge placements can be studied in Appendix B.

Figure 49 - Overview of strain gauge placements

The strain gauges are numbered according to Table 25.

Table 25- List of strain gauges

Area

Upper side

Upper side

Upper side

Upper side

Upper side

Upper side

Upper side

Upper side

Upper side

Upper side

Upper side

Underside

Underside

Placement Strain gauge

Weld toe

Weld toe

Weld toe

Weld toe

Weld toe

Weld toe

Weld, outward

Centred, weld toe

OS-ST-1 (R, L)

OS-ST-2 (R, L)

OS-ST-3 (R, L)

OS-ST-4 (R, L)

OS-ST-5 (R, L)

OS-ST-6 (R, L)

OS-SY-1 (R, L)

OS-C-1

Centred, weld toe

Centred, outward

OS-C-2

OS-C-3

Centred OS-C-4

Centred, middle of plate US-C-1

Centred US-C-2

49

3.6.2

Comparative measurements from FE-analysis

To have comparable results between the fatigue test objects and the FE-analysis, stresses are read from the models from the same points as the strain gauges are placed. It is also conducted at the same load levels as the specimens are fatigue tested at. The maximum or minimum stresses are measured at the same angle as the strain gauges are directed in.

The points where measurements were conducted are meshed with a finer mesh than the global 20 mm element size. An element size of 1.25 is specified in an area of 5x5 mm around the point of interest. At the weld toe a finer mesh are specified up to 5 mm from the toe. Partitioning is used to get fine mesh through the thickness of the specimen. The finer mesh is also used in the weld, with the same

criterions as earlier mentioned, Figure 50. These measurements are conducted in all four types of

models, normal weld end, rounded 7.07 mm, rounded 10 mm and rounded 12 mm.

Figure 50 - Partitioning and mesh for stress measurements at the weld toe

Where the stresses have been measured and the magnitude for all models and load levels can be seen

in Appendix C.

50

4 Testing

4.1

Gluing of strain gauges

The stresses at the locations defined in Appendix B are to be compared between the FE-model and a

real test specimen. According to the placements the strain gauges were glued to one of the test

specimens, see Figure 51. Since the specimen does not have perfect geometry the placements are

differing from the ideal FE-model.

Figure 51 - Strain gauge placements on the real test specimen

4.2

Measuring of specimens

All specimens are measured before testing. Measurements of the thickness of the plates and the length of the welds are performed. Also the misalignments of the transverse plate are measured, and the bending caused by the welding. The way the specimens were measured and all the notations can be

seen in Appendix D. The measurements can be seen in Appendix E. All the data are used to produce a

FE-model with imperfections and to calculate the stress in the tested specimens. Also fatigue life data can be compared to the dimensions to see correlations between lower or higher fatigue life and measurements of the specimen.

51

4.2.1

FE-model with imperfections

The real weld geometry contains imperfections of many kinds and the strain gauges are not placed in the exact same positions as in the FE-model. Therefore an updated model which includes some of the imperfections and the updated strain gauge placements are created. This is done to be able to calibrate the results, and hopefully retrieve better correlation. Both the different radii of the welds and the

angular imperfection of the transverse plate are considered. In Figure 52 the calibrated model and the

points where stress evaluation are performed can be seen. The stresses can be seen in Appendix C.

Figure 52 - Calibrated FE-model with strain gauge placements shown in red

52

4.3

Fatigue testing

All the specimens are put through a fatigue test in a hydraulic fatigue testing machine. The specimen with the glued strain gauges went through some extra steps.

The specimens are tested at four different load levels with the parameters defined in Table 26. At

every load level seven specimens were supposed to be tested. To ensure that the specimens always were under tension the stress ratio

𝑅

are set to 0.1. The number of load levels was chosen due to the chance of getting better results out of the testing than if only three were used. And based on the limits of the fatigue testing machine, the magnitudes of the load levels were chosen.

Table 26 - Parameters used for the fatigue testing

R-value

0.1

0.1

0.1

0.1

F mean kN

110

88

66

44

F amp kN

90

72

54

36

F max kN

200

160

120

80

F min kN

20

16

12

8

Frequency

Hz

8

10

10

15

The procedure is described for the specimen with strain gauges; all other specimens are only clamped and then put through the fatigue test at one load level.

Figure 53 - Rigging of the specimen in the fatigue testing machine

Firstly the specimen is clamped in one end, Figure 53, and the strain gauges are connected to the

measuring devices, Figure 54. They are in turn connected to a computer which saves the recorded

strains in a frequency of 500 Hz. The strain gauges are calibrated and reset, before clamping the other end of the specimen. From the recorded strains the clamping stress can be calculated. Since the specimens have been deformed due to welding, stresses will arise in the specimen when it is clamped into the fatigue testing machine.

53

Figure 54 - Computer connected to the measuring devices logging the strains

The strain gauges are now reset once more before starting the measuring. The specimen will be put through all of the four load levels, one at the time, while the strains are recorded. Beginning with 80 kN, 120 kN, 160 kN and the highest load level 200 kN last. After some data has been registered at the first load level the machine is stopped and the strain gauges are reset. And the same procedure is performed at all the load levels. When finished, the strain gauges were reset and the fatigue testing machine was started at the highest load level. Now the machine continued until fracture of the specimen.

4.3.1

Data

The strains recorded are imported into FAMOS, a measuring program used to edit the data. Here, the data of interest are analysed and the strains are also converted to stresses with Hook’s law for

comparison with the FE-model. In Figure 55 the strains from the whole fatigue test at 200 kN can be

seen.

Figure 55 - Strain curves for the whole fatigue test

54

If a small part of the whole recording are shown the cyclic pattern resulting from the pulsating load

can be seen, Figure 56. From this view the maximum, minimum and mean strains can be extracted.

Figure 56 –Typical strain curves showing the cyclic loading pattern

By smoothing the strain curves, the mean strains are seen directly in Figure 57. By looking at this it

could be possible to determine where the crack initiates and how it propagates. When a crack initiates, the strain and consequently the stress drops. Other parts of the specimen then have to take more of the load and the strains at those places increases. One of the strain gauges, OS_ST_6_H is assumed

broken since it acted strange in the beginning of the test and was neglected, the green curve in Figure

57.

Figure 57 - Mean strains registered by some of the strain gauges

55

4.3.2

Crack inspection

The specimens failed at the weld toe in all of the cases, possible crack initiation points are either in the middle of the weld or at one of the weld ends. A weld end crack is very likely due to the higher stresses recorded at these positions. It would also coincide with the FE-analysis where the highest

stresses are at the weld ends. As it is possible to see in Figure 58 and Figure 59, there are no obvious

signs of crack initiation and crack propagation.

Figure 58 - Fracture of specimen 1

Figure 59 - Fracture surface of specimen 1

56

4.3.3

Detection of crack initiation

The specimens failed at the weld toe or in the middle of the weld. To better understand the recorded strains, crack detection was used at the weld that had not failed. The method used was magnetic particle inspection where the specimen is temporarily magnetised and sprayed with a fluorescent fluid containing small iron oxide particles. If there is any crack present the crack disrupts the magnetic field and the particles are gathered at a possible crack. Using a UV light source the crack can be seen as the

thin bright green part at the weld toe in Figure 60.

Figure 60 - Detection of crack initiation at opposite side of the failure

In Figure 60 the small initiation can be seen in the weld toe. It is present from weld end to weld end,

the glue from the strain gauges are possibly blocking the crack from being seen just in front of them. It does not tell anything more about where the crack initiation has occurred.

57

4.4

Results from testing

4.4.1

Fatigue test

The fatigue testing results can be seen in Table 27 for all the specimens tested at a failure probability

of 50 %. These are to be compared with the theoretical calculations made for both the normal weld models and the alternative models with rounded weld ends and changed weld profile. Specimen number five went through 6 500 000 cycles when the fatigue testing machine broke. Thus that test is neglected and only four specimens were successfully tested.

Table 27 - Fatigue life testing results

1

2

3

4

5

Specimen R-value

0.1

0.1

0.1

0.1

0.1

F mean

F amp

F max

F min

S min kN kN kN kN

S max

mm mm

110

110

88

66

44

90

90

72

54

36

200

200

160

120

80

20

20

16

12

8

1.56 2.79

1.87 -0.7

1.55 2.46

2.7 3.39

2.25 2.72

S Cycles mm

1.23 191 190

1.17 222 313

0.91 362 009

0.69 995 076

0.47 -

The fatigue life results are plotted in the S-N diagram Figure 61, also known as a Wöhler diagram. To

retrieve comparable results all of the data gathered are recalculated from a failure probability of

50 % that is used during testing, to the 2.3 % probability which is used when designing welds.

Table 28 - Slope and standard deviation of the S-N curves

Mean curve and characteristic curve

Results curve

Characteristic curve - offset

Slope

3.00

3.05

3.00

Standard deviation

0.038

0.037

0.17

Due to the few numbers of results, the standard deviation would not correspond to a reasonable value.

Therefore it was set to 0.17, in belief that the results corresponds to a normal specimen and are usable,

see Table 28. The characteristic curve 0.17 is thus the design curve which was offset two standard

units form the mean curve. The standard deviation is a measurement of the diffusion of the test results.

A lower value corresponds to a higher conformity of the test results.

58

1,000

100

Mean curve

Results mean curve

Results

Characteristic curve 0.17

10

10,000 100,000

Cycles

1,000,000

Figure 61 - Fatigue life results and results curves

The characteristic curve corresponds to a failure probability of 2.3 % and the results mean curve corresponds to a failure probability of 50 %. The characteristic curve is the curve that the analytical calculations should match.

59

4.4.2

Stress test

The strains recorded at the different load levels where imported into FAMOS where they were analysed. At a point where all the strains where stable the max and min strains were exported from the cyclic strain curves, for all of the strain gauges. The strains are given in πœ‡π‘š π‘š

thus to get the stresses in MPa the strains are multiplied with the Young’s modulus, corresponding to

0.21

GPa, according to

Equation 4.1. 𝜎 = πœ€ βˆ™ 𝐸

Equation (4.1)

The stresses at the different load levels and the clamping stresses occurring due to the imperfections

are shown in Table 29.

Clamping stress

60

29

-10

-10

-14

-10

61

35

MPa

61

81

66

85

74

48

87

55

75

53

-30

-81

The specimens in reality have bent base plates due to the welds. When the specimen was clamped in the fatigue machine, clamping stresses arose. Some of the strain gauges registered compressive strains and some tensile. When the test started, some of the points could have a stress ratio

𝑅 < 0

, due to the compressive clamping stresses.

60

4.5

Comparison FE-model and testing

4.5.1

Fatigue test

The same Wöhler diagram is used to find the analytical method that best matches the results from the fatigue tests. All of the results that are shown, except the results curve and the mean curve have a failure probability of 2.3 %.

1,000

Mean curve

100

Results mean curve

Results

Effective notch

Nominal stress

Hot spot stress

10

10,000 100,000

Cycles

1,000,000

Characteristic curve 0.17

Figure 62 – Wöhler diagram with the calculation method used today

As can be seen in Figure 62, the calculation method used today is heavily overestimating the fatigue

life of the weld for this type of specimen. Since the difference is so big, the first alternative modelling method that will be validated is the ones with changed notch radii.

1,000

100

Mean curve

Results mean curve

Results

Computed life

Characteristic curve 0.17

Notch radii 0.5 mm

Notch radii 0.3 mm

Notch radii 0.2 mm

10

10,000 100,000

Cycles

1,000,000

Figure 63 - Wöhler diagram with the different notch radii compared

In Figure 63 the results from the modelling techniques with different notch radii are compared to the

characteristic curve. The curves that are closest are those with a notch radius of 0.3 mm and 0.2 mm.

To further improve the weld model, the rounded and convex weld end modelling techniques are

compared in Figure 64.

61

1,000

100

10

10,000 100,000

Cycles

1,000,000

Mean curve

Results mean curve

Results

Effective notch

Characteristic curve 0.17

Notch radius 0.2 mm rounded

7.07 mm

Notch radius 0.2 mm rounded

10 mm

Notch radius 0.2 mm rounded

12 mm

Notch radius 0.3 mm convex

7.07 mm

Notch radius 0.3 mm convex

10 mm

Figure 64 - Wöhler diagram with the different modelling techniques compared

From Figure 64 it is possible to see that there are several models that closely match the characteristic

curve with the standard deviation of 0.17. The closest match is the model with a notch radius of 0.3 mm and a convex weld shape with radius 7.07 mm. Using a notch radius of 0.2 mm with a rounding of the weld end is also very suitable.

62

4.5.2

Stress test

The results from the FE-models are compared with the stresses gained from the strain gauge

measurements. In Figure 65 the conformity of the simulation of the normal weld end can be seen at the

load level 120 kN. The green line corresponds to equality between the CAE values and the tested values. And the red lines represent the interval of

±20 %

within which the values are accepted. In

Appendix G all the deviation values are shown.

250.0

200.0

150.0

100.0

50.0

0.0

0.0

50.0

100.0

150.0

CAE Normal weld end [MPa]

200.0

Figure 65 - Normal weld end accuracy compared to measured test values

If the values are placed below the green line, they are conservative in the FE-model. The stress levels in this case are in general a bit low in the model. Also, the difference between the modelling techniques, including the model with imperfections is small. At the weld ends, all of the models have better conformity than the normal weld end. And the imperfection model has the best conformity with the angled strain gauges in the weld end. The strain gauges placed in the weld end parallel to the weld have very bad compliance with the FE-model. The rounded weld end model has more data points

within the accepted range, as can be seen in Figure 66.

250.0

200.0

150.0

100.0

50.0

0.0

0.0

50.0

100.0

150.0

CAE Value rounded 7.07 mm (MPa)

200.0

Figure 66 - Accuracy of rounded weld end, 7.07 mm compared to measured test values

63

In Figure 67 the two other rounded weld end raddi are shown. All of the rounded weld end models

have mostly the same accuracy.

250.0

200.0

150.0

100.0

50.0

250.0

200.0

150.0

100.0

50.0

0.0

0.0

50.0

100.0

150.0

200.0

CAE Value rounded 10 mm (MPa)

0.0

0.0

50.0

100.0

150.0

200.0

CAE Value rounded 12 mm (MPa)

Figure 67 - Accuracy of rounded weld end, 10 and 12 mm compared to measured test values

All of the models shown have a perfect geometry and weld with the same radii on the rounding of all weld ends. In reality the weld ends have different radii in the start and the end of the weld. The model with some imperfections and have taken the geometry of the test specimens into account. The placing of the strain gauges has also been calibrated to the real test specimen. The accuracy of the model can

be seen in Figure 68.

250.0

200.0

150.0

100.0

50.0

0.0

0.0

50.0

100.0

150.0

Calibrated CAE Value (MPa)

200.0

Figure 68 - Accuracy of calibrated, imperfect model

The figure shows an improvement of the stress measurements compared to the other models. There is however still big differences in the measuring points angled parallel to the weld. A model which was shortened to better simulate where the specimen was clamped in the fatigue testing machine was also tested. Showing no big differences compared to the imperfect model.

64

5 Discussion

The aim of this project was to find a new modelling technique that matched to the testing. As the results show there are modelling techniques that closely match the testing results. These modelling techniques are therefore proposed as the new way of assessing the weld ends. However, there are some questions that have to be arisen.

The theory used for the fatigue life calculations are based on that the weld does not have any start or end. Instead it is a continuous weld that has the same fatigue properties along the entire weld. Since the welds in reality are far from continuous, especially at the start and end of the weld, does the theory apply? It has been assumed that so is the case and the focus has been on the modelling. Maybe when enough data are retrieved it could be possible to modify the theory for the weld ends, taking those into account in the fatigue calculations. Due to the fact that the theory only treats continuous welds, there is no transverse contraction around the weld. In reality there is a lot of transverse contraction around the weld ends. This can be seen in the stress test results where the deviations from the finite element model are big. Another cause could be that there was a lot of grinding when the strain gauges where glued, which resulted in thinner material, at those spots. The clamping stresses parallel to the weld, in the weld ends are negative. This causes compressive forces around the weld end, which is mostly a good thing in fatigue.

The three main methods for evaluation of welds have been compared, nominal stress, hot spot and effective notch approach. They produce very different results and the modelling techniques also differ.

From the early tests it was concluded that the hot spot approach actually made the best fatigue life approximations. Nominal stress method was not especially precise but was the only one presenting a conservative result. But since the stress evaluation method should be useful in other applications as well, the effective notch is the most applicable. When increasing the thickness of the material, the hotspot method may become less exact. Since the highest stresses may not appear at the surface of the model, which is where this method evaluates the stresses.

When welding the specimen it is deformed due to the heating before and cooling after the weld is done. These imperfections created causes problems when the object is to be used. When the specimen was clamped in the fatigue machine, clamping stresses arose. The base plate of the specimen was initially bent and when clamped into the machine it was straightened. Some of the strain gauges registered compressive strains and some tensile. When a pulsating load is applied, the stresses in those points will have a mean stress near zero. The stress ratio will be negative. Moreover the tensile clamping stresses help rising the mean stress in that point, in worst case the yield limit could be passed.

If the yield limit is reached, all of a sudden the specimen starts to flow plastically, which is not taken care of in the theory. Not in the linear elastic analysis that has been performed in the FE-program either. It is worth mentioning that since the same loads were used in both load cases the geometry in load case 2 is deformed a lot more than in load case 1. The nonlinear effects in the geometry were taken into account in the analysis and compared to a strictly linear analysis the differences were evident. If those high loads were to be applied to the specimen in load case 2, the effects of nonlinearity should be considered and also further investigated. Different load levels should also be considered since the analysis should be performed within the linear elastic zone.

Without further investigation it is hard to know exactly where the crack has started. Even though the highest stresses are present in the weld ends, it may not be unlikely that the crack has started in the middle of the weld.

65

6 Conclusion

6.1

Weld calculations and parametric study

The fatigue life calculations were tested with three different calculation methods, which are based on different stresses retrieved from the FE-model. The easiest method to use, the nominal stress approach underestimates the life of the weld. The hot spot approach are in this case approximating the life of the weld very well and has to be seen as the most accurate method. However, these two methods are not very applicable in all load cases. The effective notch approach is overestimating the life of the weld.

This is caused not only by lower stresses in the sub model, but lower stresses in the global model as seen in the stress test. Since this is the most used and versatile method, it is the method that was used during the rest of the project.

6.2

Different types of welds

When comparing the fatigue life of the normal weld end with the test results, it is clear that the fatigue life of the welds is too low. By changing the geometry of the weld the stresses could be increased and the fatigue life estimations better coincides with the test results. To replicate a real weld end they were rounded with different radii which increased the stresses by a few per cent. The use of a rounded weld end alone is not enough to get accurate results though. Changing the weld profile from an isosceles triangle to a convex shape also increases the stresses in the notches. With a radius equal to 7.07 mm the angle in the weld transition is increased and are better capturing the geometry of some weld ends.

Another way to increase the stresses is by changing the notch radii used in the effective notch approach. Together with a smaller element size stresses could be increased effectively. By combining the different weld modelling techniques and a changed notch radii models satisfying the test results could be found.

6.3

Testing

As the testing is the main source of results to compare the calculation methods against, it is of great importance that they are correct. Due to unforeseen circumstances and heavily increased production the amount of test specimens that was able to be tested before the end of the thesis was very small.

This causes statistical problems where the results are not especially well substantiated. The results that were obtained could very well represent the normal fatigue life of these welds, but it could likewise be in a slightly different way. Due to the small amount of specimens that were tested, four, the standard deviation calculated would be big. This standard deviation does not at all represent a normal value.

Therefore the decision was made that a normal standard deviation of 0.17 was to be assumed, hopefully a good approximation.

The stress test resulted in very useful data that could explain a lot about the propagation of the crack and where the highest stresses are present. Around the weld and weld ends, the stresses are higher than expected and also higher compared to the FE-model. The overall stress field is however consistent between the two, where the highest stresses appear at the weld ends. The consistency depends a great deal on where the stresses are read in the model, a thoroughly calibrated positioning of the strain gauge is of great importance to retrieve good results in the stress test.

Both the strain data from the 200 kN fatigue test and the fatigue life data from the other tested specimens was of course vital for comparison against the FE-models. The welds did not last as long as suspected, but the results from the four specimens that were put through the test lead to a very good S-

N curve with an incline of 3.05. That is not far from the theoretical value of three that is used in the standards.

66

6.4

Proposed modelling technique

Based on the fatigue test results two new ways of modelling the weld ends are proposed. Since the modelling effort needed differs between the techniques, the best choice is not maybe the most

effective. Based on the results in Figure 64 the best model is the one with a notch radii of 0.2 mm and

a rounded weld end, which would create a conservative model. A radius of 0.2 mm in the notches was also measured by (Kaffenberger, et al., 2012) who calculated the radius based on scanned welds. The radius of the weld end rounding is not the most important variable since the differences in results between them are negligible. Choosing a radius of 10 mm could be recommended based on radii of real welds and ease of modelling. Kaffenberger et al. also proposed that a rounding of the weld end was suitable. Another model that coincides with the results are the model with a convex weld profile with radius 7.07 mm and a notch radii of 0.3 mm, it is however on the anti-conservative side. Seen to the effort needed for modelling, the latter one is preferred. But the first one has the right looks, better

approximating the real weld geometry, Figure 69.

Figure 69- Proposed weld ends for effective notch sub models

6.5

Future work

To statistically ensure the results, more specimens have to be tested at every load level. They also have to be compared to the proposed modelling techniques to see if they are valid even after this has been done. The results are only valid for the tested specimen, at the load direction tested. Also, testing has to be performed in different load directions. Some of them have been investigated in the report, and they all have load transmitting welds, which would reduce the force needed during the testing. It would also be interesting to make a crack initiation analysis during the fatigue testing to see exactly where and how the crack propagates.

At the moment there is no theory or modelling technique available, to calculate the fatigue life of welds loaded in the direction parallel to the weld. Since the theory states that welds have very good fatigue resistance in that direction, it would be a good weld end test. It would be testing the fatigue life of the weld end only, not the whole weld. If the rounded weld end geometry was to be adopted into the calculation methods, it would be possible to find the stresses in the weld toe around the whole weld end.

Instead of changing the model used, when enough data are gathered from testing, the FAT-value for weld ends could be changed. This would be the easiest way of implementing the lower fatigue limit.

67

68

References

Anon., 2012.

Toyota Material Handling Europe AB - History.

[Online]

Available at: http://www.toyota-forklifts.eu/en/company/tmhephilosophy/Pages/History.aspx

[Accessed 2 June 2014].

BSK99 , 2003.

Swedish Regulations for Steel Structures, ,

s.l.: National Board of Housing, Building and Planning.

Dahlberg, T. & Ekberg, A., 2002.

Failure Fracture Fatigue - An Introduction.

1:7 ed. s.l.:Studentlitteratur AB.

Eriksson, Å., Lignell, A.-M., Spennare, H. & Olsson, C., 2002.

Svetsutvärdering med FEM.

Göteborg: s.n.

Hobbacher, A., 2008.

Recommendations for Fatigue Design of Welded Joints and Components,

Paris:

International Institute of Welding.

Hobbacher, A. F., 2009. The new IIW recommendations for fatigue assessment of welded joints and components – A comprehensive code recently updated.

International Journal of Fatigue,

Volume 31, pp. 50-58.

Introduction week

(2014).

Kaffenberger, M., Malikoutsakis, M., Savaidis, G. & Vormwald, M., 2012. Fatigue resistance of weld ends.

Computational Materials Science,

01 02, 52(1), pp. 287-292.

Kaffenberger, M. & Vormwald, M., 2011. Fatigue resistance of weld ends - Analysis of the notch stress using real geometry.

Materialwissenschaft Und Werkstofftechnik,

01 10, 42(10), pp. 874-880.

Karolczuk, A. & Macha, E., 2005. A review of critical plane orientations in multiaxial fatigue failure.

International Journal of Fracture

, Volume 134, pp. 267-304.

Malikoutsakis, M. & Savaidis, G., 2011. Modeling and fatigue assessment of weld start-end locations.

Materialwissenschaft Und Werkstofftechnik,

01 04, 42(4), pp. 298-56.

Olsson, C., 2005.

Konstruktionshandbok för svetsade produkter.

3 ed. Lidingö: Industrilitteratur.

Olsson, C., 2014.

Konstruktionshandbok för svetsade produkter.

5 ed. Onsala: Techstrat Publishing.

Osgood, W. R. & Ramberg, W., 1943. Description of stress-strain curves by three parameters. In:

Technical Note No. 902.

Washington: National Advisory Committee For Aeronautics.

Ranganathan, N., 2014. The Energy Based Approach to Fatigue.

Advanced Materials Research

, 12

Mar, Volume 891-892, pp. 821-826.

SSAB, 2011.

Plåthandboken, att konstruera och tillverka i höghållfast stål..

s.l.:s.n.

Wolfgang, F., 2003. Fatigue analysis of welded joints: state of development.

Marine Structures,

Volume 16, pp. 185-200.

Wolfgang, F., 2013. IIW guideline for the assessment of weld root fatigue.

Weld World

, Issue 57, pp.

753-791.

69

Appendix

Appendix A

71

(Olsson, 2005)

72

Appendix B

73

Appendix C

Stress comparison

Normal weld end model - EN

Load level 80

Strain gauge

MPa

OS-C-1

OS-C-2

88

88

MPa

100

OS-C-3

OS-C-4

OS-ST-1

OS-ST-2

OS-ST-3

OS-ST-4

OS-ST-5

OS-ST-6

OS-SY-1

US-C-1

US-C-2

80

98

79

-9

40

81

84

82

81

40

-9

-11

50

102

101

122

99

110

110

106

102

102

50

-11

Rounded weld end model r7- EN

Load level

Strain gauge

MPa

80

OS-C-1

OS-C-2

OS-C-3

OS-C-4

OS-ST-1

OS-ST-2

OS-ST-3

OS-ST-4

82

90

40

89

89

84

-9

-9

OS-ST-5

OS-ST-6

OS-SY-1

US-C-1

US-C-2

40

90

82

98

79

MPa

100

51

112

103

122

99

111

111

106

102

112

51

-11

-11

Rounded weld end model r10- EN

OS-C-1

Load level

Strain gauge

MPa

80

89

OS-C-2

OS-C-3

OS-C-4

OS-ST-1

OS-ST-2

89

85

82

90

43

OS-ST-3

OS-ST-4

OS-ST-5

OS-ST-6

OS-SY-1

US-C-1

US-C-2

90

82

98

-8

-8

43

79

MPa

100

-11

-11

54

113

103

122

99

111

111

106

102

113

54

MPa

120

-13

-13

65

136

124

146

119

134

134

127

123

136

65

MPa

120

61

135

123

146

119

134

134

127

123

135

61

-13

-13

120

MPa

-14

60

122

121

147

119

133

133

127

123

122

60

-14

MPa

160

81

181

165

194

159

179

179

170

163

181

81

-18

-18

160

MPa

-18

81

163

162

195

159

177

177

169

164

163

81

-18

MPa

160

-17

-17

87

182

166

194

159

179

179

170

163

182

87

300

MPa

-34

152

309

305

364

298

335

335

320

306

309

152

-34

MPa

300

154

341

311

363

298

338

338

320

306

341

154

-33

-33

MPa

300

-32

-32

164

344

313

363

298

338

338

321

306

344

164

MPa

200

-21

-21

109

228

208

243

199

224

224

213

204

228

109

MPa

200

102

226

206

243

199

224

224

213

204

226

102

-22

-22

200

MPa

-23

101

205

202

244

198

222

222

212

204

205

101

-23

74

Rounded weld end model r12- EN

Load level

Strain gauge

MPa

80

OS-C-1

OS-C-2

OS-C-3

OS-C-4

OS-ST-1

89

89

85

82

91

OS-ST-2

OS-ST-3

OS-ST-4

OS-ST-5

OS-ST-6

OS-SY-1

US-C-1

US-C-2

44

-8

-8

44

91

83

97

79

MPa

100

55

-10

-10

55

112

112

106

102

114

114

104

122

99

MPa

120

66

-12

-12

66

134

134

128

123

137

137

124

146

119

Copy of real specimen #2 with some imperfections

Load level

Strain gauge

OS-C-1

OS-C-2

OS-C-3

OS-C-4

OS-ST-1-H

OS-ST-1-V

OS-ST-2-H

OS-ST-2-V

OS-ST-3-H

OS-ST-3-V

OS-ST-4-H

OS-ST-4-V

OS-ST-5-H

OS-ST-5-V

OS-ST-6-H

OS-ST-6-V

OS-SY-1-H

OS-SY-1-V

US-C-1

US-C-2

MPa

80

47

53

91

91

-5

-5

-5

-5

83

83

97

79

90

90

58

56

89

89

85

82

MPa

100

58

66

114

113

-7

-6

-6

-6

103

104

121

99

113

113

72

71

111

112

106

102

MPa

120

70

79

136

136

-8

-7

-7

-8

124

125

145

119

136

136

87

85

133

134

127

122

Copy of real specimen #2 with some imperfections and short plate

Load level

Strain gauge

OS-C-1

OS-C-2

OS-C-3

OS-C-4

OS-ST-1-H

OS-ST-1-V

OS-ST-2-H

OS-ST-2-V

OS-ST-3-H

OS-ST-3-V

OS-ST-4-H

OS-ST-4-V

OS-ST-5-H

OS-ST-5-V

OS-ST-6-H

OS-ST-6-V

OS-SY-1-H

OS-SY-1-V

US-C-1

US-C-2

MPa

80

60

78

91

91

-5

-5

-6

-5

83

83

97

80

91

91

67

59

89

90

85

83

MPa

100

72

98

114

114

-6

-7

-7

-6

104

104

121

100

113

114

84

73

112

112

107

104

MPa

120

90

118

137

137

-7

-8

-9

-7

125

125

145

121

136

136

101

88

134

135

128

125

MPa

160

121

157

183

183

-9

-10

-12

-10

167

167

193

161

182

182

135

118

179

180

171

166

MPa

160

94

105

182

182

-10

-10

-9

-10

166

166

193

159

181

182

116

113

178

179

170

163

75

MPa

160

88

-17

-17

88

179

179

170

163

183

183

166

194

159

MPa

200

111

-21

-21

111

225

225

213

204

229

229

208

242

199

MPa

200

118

133

229

228

-13

-12

-11

-13

208

208

242

199

227

228

146

142

224

225

213

204

MPa

200

151

197

229

229

-11

-13

-15

-12

208

209

241

201

228

228

169

147

225

225

214

208

300

MPa

337,1

339,0

320,1

305,9

342,3

343,2

219,5

214,3

-19,6

-18,3

-17,1

-19,2

177,4

204,6

344,6

344,2

312,8

313,7

361,2

298,5

MPa

300

167

-31

-31

167

339

339

321

306

345

345

313

362

298

300

228

297

346

345

-17

-19

-22

-18

313

314

361

302

343

344

254

222

338

339

322

311

76

Appendix D

77

78

Appendix E

100,05

100,24

100,11

100,24

100,06

100,14

100,15

100,11

100,22

100,21

100,19

100,1

100,23

100,14

100,24

100,16

100,29

100,06

100,26

100,12

100,27

LB

Width

99,72

99,76

99,60

99,73

100,24

100,20

100,22

100,13

100,13

100,19

100,11

100,23

100,19

100,13

100,14

T

100,14

100,22

100,12

100,25

100,23

100,13

100,13

100,22

100,19

100,2

100,09

100,24

100,11

99,67

99,78

99,57

99,79

100,24

100,13

100,19

100,12

100,07

100,25

100,14

100,26

100,1

100,11

100,18

100,25

100,16

100,29

100,07

100,26

100,1

100,27

100,08

33

34

35

29

30

31

32

36

23

24

25

26

27

28

17

18

19

20

21

22

Specimen: LA

1

2

14

15

16

10

11

12

13

7

8

9

5

6

3

4

100,13

100,19

100,17

100,27

100,26

100,11

100,34

100,26

100,25

100,25

100,24

100,31

100,33

100,15

100,05

99,70

100,10

100,16

99,54

100,22

100,2

100,28

100,23

100,25

100,26

100,21

100,25

100,26

100,29

100,26

100,19

100,19

100,28

100,29

100,08

100,25

LHA

10,15

10,1

10,11

10,11

10,13

10,12

10,09

10,1

10,1

10,09

10,06

10,08

10,09

10,08

10,05

10,02

10,02

10,08

10,07

10,12

10,1

10,08

10,08

10,09

10,13

10,07

10,08

10,11

10,08

10,09

10,08

10,06

10,09

10,07

10,07

10,08

LHB

10,1

10,09

10,11

10,1

10,14

10,11

10,1

10,07

10,1

10,06

10,06

10,08

10,09

10,08

10,03

10,04

10,02

10,06

10,05

10,09

10,12

10,07

10,05

10,09

10,12

10,08

10,08

10,07

10,1

10,09

10,05

10,07

10,08

10,07

10,06

10,09

LAV

Thickness

LBV

10,01

10,04

10,09

10,03

10,08

10,09

10,09

10,07

10,08

10,08

10,06

10,07

10,09

10,08

10,08

10,1

10,05

10,08

10,09

10,09

10,11

10,08

10,11

10,09

10,14

10,08

10,12

10,08

10,07

10,06

10,09

10,09

10,05

10,03

10,07

10,05

10,06

10,11

10,08

10,1

10,09

10,08

10,08

10,07

10,05

10,07

10,08

10,08

10,07

10,1

10,05

10,06

10,08

10,1

10,11

10,07

10,11

10,08

10,09

10,09

10,1

10,09

10,08

10,08

10,1

10,09

10,04

10,02

10,07

10,06

10,06

10,1

TH

10,12

10,09

10,09

10,11

10,07

10,08

10,09

10,09

10,1

10,14

10,08

10,08

10,08

10,04

10,04

10,00

10,01

10,04

10,05

10,14

10,08

10,06

10,09

10,08

10,07

10,13

10,04

10,07

10,09

10,09

10,08

10,08

10,09

10,05

10,08

10,09

TV

10,1

10,1

10,1

10,1

10,08

10,09

10,1

10,09

10,1

10,06

10,09

10,1

10,09

10,06

10,05

10,01

10,03

10,02

10,05

10,09

10,08

10,08

10,1

10,08

10,12

10,09

10,09

10,11

10,08

10,09

10,08

10,05

10,07

10,1

10,08

10,07

A

72,34

71,13

72,63

72,61

72,59

69,99

70,88

71,69

70,28

70,27

73,32

72,99

72,44

72,23

74,13

72,61

70,09

69,25

71,53

69,84

71,54

Lengt of weld

B

71,98

70,47

72,25

70,72

70,38

69,77

70,72

71,73

67,44

65,99

69,78

71,20

71,00

72,29

71,14

72,13

72,07

69,54

69,43

69,22

69,39

67,06

65,29

68,17

72,09

70,66

71,90

70,75

72,89

72,51

73,6

75,54

73,14

73,27

72,42

72,88

70,12

74,04

71,72

71,14

71,69

72,66

72,92

73,01

71,4

68,67

73,33

69,78

71,07

70,27

70,38

1,06

1,61

1,16

0,75

1,16

0,87

0,87

1,05

1,66

-1,38

-0,95

-1,17

-1,69

-1,65

0

-0,96

1,05

0,99

1

0

0,89

-0,89

-0,9

-0,7

-0,98

-1,1

-0,93

-1,51

Imperfections

πœ‘ 𝛼

0,3

-1

0,048

0,036

-1,1

-0,9

0,5

-0,7

0,93

-1,49

0,054

0,054

0,044

0,071

0,062

0,044

0,055

0,072

0,043

0,055

0,028

0,062

0,068

0,046

0,046

0,081

0,052

0,060

0,064

0,056

0,053

0,055

0,051

0,048

0,056

0,042

0,070

0,062

0,055

0,044

0,042

0,046

0,066

0,055

0,920

0,914

0,703

1,000

0,777

0,634

0,876

0,778

1,024

0,891

0,886

0,761

0,708 πœƒ

1,013

0,836

0,672

0,830

0,818

0,685

1,218

0,944

0,526

0,623

0,914

0,714

0,783

0,572

0,251

0,691

0,909

0,675

0,000

0,714

0,497

0,968

0,720

0,061

0,078

0,048

0,053

0,033

0,058

0,066

0,058

0,047

0,082

0,055

0,069

0,066 𝛽

0,047

0,036

0,054

0,057

0,052

0,064

0,062

0,045

0,052

0,051

0,061

0,054

0,045

0,066

0,039

0,057

0,071

0,059

0,041

0,042

0,055

0,067

0,058

e

16,4

17,96

14,88

15,51

13,36

16,01

16,73

15,86

14,82

18,4

15,65

17,13

17,03

14,67

13,52

15,35

15,64

15,22

16,365

16,54

14,64

15,94

17,1

16,29

14,180

14,300

15,550

16,930

15,380

15,240

16,430

15,560

14,620

16,720

14,180

16,070

t

A

15,73

17,51

14,36

15,84

12,81

16,22

17,12

14,99

14,8

18,21

15,29

16,22

16,61

14,74

13,51

15,30

15,27

14,43

17,02

16,23

14,53

15,79

15,43

15,82

15,4

14,91

16,1

14,25

17,04

16,4

15,65

14,62

14,27

14,75

16,92

15,74

h

B

1,61

1,6

1,23

1,75

1,36

1,11

1,53

1,36

1,79

1,56

1,55

1,33

1,24

1,77

1,46

1,17

1,45

1,43

1,19

2,13

1,65

0,920

1,090

1,600

1,250

1,370

1,000

0,440

1,21

1,59

1,18

0,000

1,250

0,870

1,690

1,260

h

A

10,28

10,29

10,11

10,30

10,03

10,07

10,30

10,35

10,21

10,10

10,12

10,19

10,23

9,99

9,91

9,93

9,89

10,03

9,96

10,08

10,11

10,17

10,14

10,29

10,33

10,12

10,49

10,08

10,20

10,11

10,18

10,12

10,17

10,32

10,10

10,25

t

B

10,34

10,12

10,13

10,25

10,02

10,18

10,18

10,09

10,08

10,24

10,14

10,26

10,40

9,99

9,90

9,95

9,97

9,99

10,00

10,30

10,11

10,23

10,16

10,33

10,18

10,15

10,16

10,21

10,05

10,38

10,05

10,10

10,05

10,22

10,30

10,26

f

A

5,45

7,22

4,25

5,54

2,78

6,15

6,82

4,64

4,59

8,11

5,17

6,03

6,38

4,75

3,60

5,37

5,38

4,40

7,06

6,15

4,42

5,62

5,29

5,53

5,07

4,79

5,61

6,96

6,20

5,54

4,44

4,15

4,58

6,60

4,15

5,49

f

B

6,06

7,84

4,75

5,26

3,34

5,83

6,55

5,77

4,74

8,16

5,51

6,87

6,63

4,68

3,62

5,40

5,67

5,23

6,37

6,24

4,53

5,15

5,08

6,10

5,38

4,47

6,56

5,73

7,05

5,91

4,13

4,20

5,50

6,71

3,88

5,81

= Weld where fracture occurred

79

Appendix F

Normal weld end global model Convex radius 7 global model

Convex radius 10 global model Rounded weld end radius 7 mm global model

Rounded weld end radius 10 global model Rounded weld end radius 12 global model

80

Sub model of normal weld end Submodel of convex weld end with radius 7.07 mm

Convex weld end with radius 10 mm Rounded weld end with radius 7 mm

Rounded weld end with radius 10 mm Rounded weld end with radius 12 mm

81

Appendix G - FEM-error in per cent at load level 120kN

Strain gauge

OS-C-1

OS-C-2

OS-C-3

OS-C-4

OS-ST-1-H

OS-ST-1-V

OS-ST-2-H

OS-ST-2-V

OS-ST-3-H

OS-ST-3-V

OS-ST-4-H

OS-ST-4-V

OS-ST-5-H

OS-ST-5-V

OS-ST-6-H

OS-ST-6-V

OS-SY-1-H

OS-SY-1-V

US-C-1

US-C-2

Normal weld end

-14 %

-9 %

-5 %

23 %

-25 %

-34 %

-105 %

-108 %

-91 %

-181 %

-125 %

-159 %

-108 %

-138 %

-29 %

-26 %

-5 %

-10 %

17 %

-4 %

Rounded

7.07 mm

-13 %

-8 %

-5 %

23 %

-13 %

-21 %

-103 %

-106 %

-95 %

-187 %

-129 %

-164 %

-107 %

-136 %

-17 %

-14 %

-3 %

-8 %

17 %

-4 %

Rounded

10 mm

-13 %

-8 %

-5 %

23 %

-12 %

-20 %

-90 %

-94 %

-103 %

-199 %

-139 %

-176 %

-94 %

-121 %

-16 %

-13 %

-2 %

-7 %

17 %

-4 %

Rounded

12 mm

-13 %

-8 %

-4 %

23 %

-12 %

-20 %

-87 %

-90 %

-109 %

-207 %

-145 %

-183 %

-90 %

-117 %

-15 %

-13 %

-2 %

-7 %

17 %

-4 %

Imperfection model

-14 %

-8 %

-5 %

23 %

-12 %

-20 %

-42 %

-48 %

-231 %

-423 %

-345 %

-358 %

-79 %

-82 %

-16 %

-13%

-2 %

-7 %

16 %

-4 %

Imperfection model - short

-13 %

-7 %

-4 %

25 %

-12 %

-20%

-22 %

-43 %

-278 %

-390 %

-242 %

-375 %

-39 %

-22 %

-15 %

-12 %

-1 %

-6 %

16 %

-3 %

82

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