Linköping University | Department of Management and Engineering

Master’s thesis, 30 credits| Mechanical Engineering

Spring 2020 | ISRN LIU-IEI-TEK-A--20/03936--SE

Modelling, evaluation and assessment

of welded joints subjected to fatigue

Author: Prajeet Rajaganesan

Supervisors: Amir Alizadeh

Jari Mäkinen

Carl-Johan Thore

Examiner: Kjell Simonsson

Sigma Industry

Sigma Industry

Linköping University

Linköping University

i

Abstract

Fatigue assessment of welded joints using finite element methods is becoming very common.

Research about new methods is being carried out every day that show a more accurate estimation

of the fatigue life cycle than the previous ones. Some of these methods are investigated in this

thesis for a thorough understanding of the weld fatigue evaluation process.

The thesis study presents several methods as candidates for analysis of selected case studies for

comparison. The sensitivity of methods towards FE model properties was studied. The ease of

implementation for further automatization of the method was highly considered from the early

stages of the project. A comparison study amongst feasible methods was then performed after

analysis.

The selected three case studies provided a wide range of difficulties in terms of geometry and

loading and made them suitable for the methods to be evaluated. It should be noted that case

studies only with fillet welds were considered during the literature study and analysis.

Implementation of some methods on a case study where they have not previously been tested

before gave a challenging task during the analysis phase. The proposed method after comparison

and ranking of the methods based on several criteria such as accuracy, robustness, etc. was the hot

spot stress method. The main advantages of this method are its low computational time, less

complexity during both pre- and post-processing, and the ability to work for both solid and shell

models.

Finally, the report gives a walk-through of several functionalities of the post-processor tool built

to enhance workflow for the hot spot based fatigue assessment of welds. Pseudo-codes for some

functions of the tool are given for clarity. A summary of the workflow is presented as a flowchart.

The outputs of the case studies were then evaluated using the tool and compared with the manual

evaluation to check the effectiveness of the tool on different scenarios. The tool shows flexibility

in handling different types of weld geometry with good agreement to the results obtained manually

but only for welds lying on a flat surface. Some of the advantages of the tool are its capability to

handle multiple welds simultaneously and the flexibility to the user in selecting the way the results

are presented. Most of the postprocessing steps are automatized, while some require user inputs.

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Table of contents Abstract ................................................................................................................................. i

Preface .................................................................................................................................. iv

List of abbreviations ............................................................................................................. v

List of symbols ...................................................................................................................... v

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

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

1.2 Problem definition ...................................................................................................................................... 2

1.3 Methodology ................................................................................................................................................ 2

1.4 Delimitations ................................................................................................................................................ 3

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

2 Theory ............................................................................................................................ 5

2.1 Fatigue in welded joints.............................................................................................................................. 5

2.2 Factors influencing fatigue in welds ......................................................................................................... 6

2.2.1 Fatigue loading ................................................................................................................................... 6

2.2.2 Geometry............................................................................................................................................. 7

2.3 Fatigue resistance curves – S-N curves ................................................................................................... 7

2.4 Stress analysis approaches .......................................................................................................................... 8

2.4.1 Introduction ........................................................................................................................................ 8

2.4.2 Nominal stress approach .................................................................................................................. 9

2.4.3 Structural stress approaches ...........................................................................................................10

2.4.4 Effective notch stress approach ....................................................................................................18

2.5 Summary of approaches ...........................................................................................................................19

3 Finite element analysis ................................................................................................ 21

3.1 Case study 1 ...............................................................................................................................................21

3.1.1 Results ................................................................................................................................................23

3.2 Case study 2 ...............................................................................................................................................29

3.2.1 Results ................................................................................................................................................30

3.3 Case study 3 ...............................................................................................................................................31

3.3.1 Results ................................................................................................................................................32

4 Observations and discussion ....................................................................................... 35

5 A plug-in tool for weld fatigue assessment .................................................................. 39

5.1 Introduction ...............................................................................................................................................39

5.2 User inputs .................................................................................................................................................39

5.3 Methodology ..............................................................................................................................................40

5.3.1 Segregation and classification of welds ........................................................................................41

5.3.2 Determination of type of weld geometry .....................................................................................42

iii

5.3.3 Extraction of stresses ......................................................................................................................48

5.3.4 Reporting the results as plot ...........................................................................................................48

6 Results and comparison study ..................................................................................... 49

6.1 Case study 1 ...............................................................................................................................................49

6.2 Case Study 2 ...............................................................................................................................................50

6.3 Case study 3 ...............................................................................................................................................52

7 Conclusions and summary........................................................................................... 55

7.1 Conclusions – Theory ..............................................................................................................................55

7.2 Conclusions – FEA...................................................................................................................................55

7.3 Summary – Plug-in tool for weld fatigue assessment ..........................................................................56

8 Recommendations ....................................................................................................... 58

References ........................................................................................................................... 59

Appendix A – Method scoring matrix ................................................................................ 61

Appendix B – Workflow summary ...................................................................................... 62

Appendix C – Weld fatigue assessment tool interface ....................................................... 63

Appendix D – Structural stress approaches for further scope ............................................ 64

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Preface

The work presented in this master thesis was conducted at Sigma Industry in Stockholm between

February and October 2020. The project was initiated and carried out within the Technical

Calculation & Testing department of Sigma Industry. This thesis is a part of the requirements for

the master’s degree in Mechanical Engineering at Linköping University, Sweden.

I would like to acknowledge and thank my supervisors at Sigma Industry, Amir Alizadeh and Jari

Mäkinen for their excellent guidance, strong technical support, and helpful discussions throughout

the thesis work. I would also like to express my gratitude to Daniel Tanner at Sigma Industry for

his constant help and encouragement. I gratefully acknowledge everyone at Sigma Industry East

North for providing me with the best learning experience.

I would also like to thank my supervisor at Linköping University, Carl-Johan Thore for thoroughly

studying my work and contributing to the report. I would like to thank my examiner, Kjell

Simonsson for his help and feedback on this thesis.

Finally, I would like to express my profound gratitude to my family and friends for their everlasting

support and patience.

Linköping, October 2020

Prajeet Rajaganesan

v

List of abbreviations

IIW International Institute of Welding FEA Finite Element Analysis FEM Finite Element Method 2D Two Dimensional 3D Three Dimensional GUI Graphical User Interface WIN32COM Python package TTWT Through Thickness at the Weld Toe CAE Computer-Aided Engineering SS Structural stress methods HSS Hot Spot Stress LSE Linear Surface Extrapolation S-N Stress-Life ENS Effective Notch Stress method SAE Society of Automotive Engineers CAFL Constant Amplitude Fatigue Loading VAFL Variable Amplitude Fatigue Loading LEFM Linear Elastic Fracture Mechanics

E2S2 Equilibrium Equivalent Structural Stress

KPI Key Performance Index

List of symbols

∆𝜎 Stress range

R Stress ratio

𝜎𝑚 Mean stress

∆𝜎𝑛𝑜𝑚,𝐻𝑆𝑆 Stress computed from nominal stress or Hot spot method

t Thickness of the welded plate

𝑡𝑟𝑒𝑓 Reference thickness; 25 mm in IIW

n Thickness exponent

∆𝑆𝑒𝑞 Equivalent structural stress parameter

𝜎𝑆 Structural stress

𝜎𝑚 Membrane stress

𝜎𝑏 Bending stress

∆𝑆𝑠 Structural stress parameter

𝑟 Bending ratio

FAT Fatigue strength at 2 ∙ 106 cycles

𝜑𝑄 Coefficient of risk failure

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1 Introduction

This master thesis was initiated and carried out as a co-operation between Sigma Industry East

North and Linköping University and aims for developing standardized methods to assess welded

joints that are subjected to fatigue loading.

1.1 Background

Fatigue is the failure of a structure due to cyclic loading and is one of the important criteria for the

design of a welded structure. Structures involved in transportation such as automobiles, ships,

airplanes, offshore structures, bridges, cranes, etc. that are subject to fluctuating loads are prone to

fatigue failure as time progresses. The phenomenon originates at the microscopic level, where local

damages evolve into a macroscopic crack, and then leads to final failure. It is usual for the damage

to initiate at a location consisting of sudden geometrical change such as a notch where there is

stress concentration or at a material defect such as a material inhomogeneity within the weld [1],

[2].

Fatigue of welds as a process is known to be highly localized as the fatigue life of a structure is

majorly influenced by the local parameters such as geometry, loading, and material characteristics

of the region. Structures under repetitive cyclic loading are known to possess critical locations

prone to fatigue failure at the welded joints due to high stress concentration. The industries should

thus employ a method that accurately estimates the fatigue life of a welded structure regardless of

the geometrical or loading complexities involved [1], [2], [3].

There are two approaches to fatigue assessment in welded structures, viz. global and local methods.

In both of them, the fatigue cycles or the crack growth is determined by the S-N curve approach

or fracture mechanics approach. The S-N curve approach has been focused on this thesis project,

where most of them come under local methods. The local methods provide better results than the

global methods as the fatigue of welds is a localized process. The S-N curve approach branches

into two most used methods that are the focus of this project: the structural stress approaches and

the effective notch stress approach. Both are known for providing a reliable estimation of fatigue

life cycles from the stress results of a Finite Element Analysis (FEA) [1].

IIW recommendations [4] provide the reference classes for both sub-branches of the S-N curve

approaches under several geometries and loading scenarios, based on which the stress from an

FEA can be plugged in to obtain the fatigue life cycle. The reference classes for different geometry

and loading conditions correlate to different stress-life curves. The curves are based on many

fatigue experiments that automatically considers the effect of material defects.

Different methods require different post-processing procedures to arrive at a result, and the

execution of the steps in the right way determines the level of accuracy. Most of them have

straightforward calculations, while a few of them are complex due to the way the results are

extracted from the analysis or due to complicated calculations. Automatizing these repetitive steps

makes the evaluation of multiple welds faster. However, to do that for any weld type, a multiple

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number of times, one requires a plug-in tool in Abaqus1 that can automatize most of the post-

process, which will be the result of this thesis project.

1.2 Problem definition

The fatigue assessment methods presented in this report are stress-based, and almost all of them

are functionally different involving different procedures during both pre- and post-processing.

Even when some methods are computationally cheap, they are still highly time-consuming during

FE-modelling and post-processing of the FE results when complex calculations are involved.

It is the work of the engineer to manually extract the stresses from a read-out point and plug it in

a formula to obtain the stress required to determine fatigue life. For a single weld, this might be

simple, but when there are multiple welds or when a complex weld geometry is involved, it will be

beneficial to automatize the process to minimize the time taken. However, the method for

automatization should be selected based on a combination of several aspects of the method aside

from just the computational time or level of complexity.

The selected methods should be compared based on aspects that influence the performance and

the effectiveness of the tool built for automatization. The resulting method that is ranked higher

among others based on those aspects should be implemented as a program scripted by using

Python for Abaqus. The program should be checked for effectiveness and efficiency through a

comparison of manually obtained results to the automatized results. The re-evaluation of the case

studies using the tool will be used for inspection for possible bugs or flaws inside the tool to be

fixed.

Therefore, the objectives of this thesis can be presented as the following questions:

• Which method outranks other methods based on Key Performance Indexes, KPIs that

makes it suitable for implementation as a post-processing tool for assessing weld fatigue?

• How can the plug-in tool be built in Abaqus and how flexible can it be made to handle

different types of welds and element types i.e., shell, and solid elements?

• How effective is the tool built based on how it is influenced by finite element properties

and how does it compare with the manual way of result extraction?

1.3 Methodology

Methods considered for fatigue assessment in this project are different from each other in several

ways, and the procedure followed in those to arrive at the results must be studied and understood

to avoid mistakes. A literature study was performed to find the existing methods of weld fatigue

assessment and to gain an understanding of the theory and challenges behind those methods. A

preliminary summary from the theoretical study of some major methods was presented, listing all

their advantages and disadvantages. The inaccurate ones were eliminated.

The simulation process was carried out in Abaqus, while the calculation and output analysis were

carried out in MATLAB2. Several case studies consisting of geometries of different levels of

complexity and approaches were used to gather reference data. The case studies were then recreated

1 https://www.3ds.com/products-services/simulia/products/abaqus/ 2 https://www.mathworks.com/products/matlab.html

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in the solver to be compared again based on properties like accuracy, post-processing time, pre-

processing workload, and so on.

The aim of recreating the model, simulating and evaluating it using different methods was to obtain

a good understanding of the procedures followed to correctly apply the methods to different

geometry, to understand the difficulty behind applying the procedures, and to check how the mesh

properties influence the results obtained. This process determined the degree of the

conservativeness of the methods which was essential during the comparison and ranking.

The development of the easy-to-use plug-in tool in Abaqus formed one of the primary objectives

and the result of the thesis project. Python scripting for Abaqus was used to create the plug-in tool.

Several functionalities of a GUI that can be created using Python was studied and explored to

create a versatile, easy-to-use tool.

The final part will show the validation of the tool and its desired properties by reevaluating the case

studies using the tool for fatigue assessment. A thorough comparison of the manual simulation and

the automatized one was done where the possible improvements were identified and implemented.

Further enhancements for the tool in the future were also established as recommendations.

1.4 Delimitations

The welded joints used in this project are As-welded types of joints which imply that after-weld

treatment effects and high strength steels were not considered. Constant amplitude loading was the

type of loading used in the case studies referred to in this project. High cycle fatigue was the only

type of fatigue within the scope of this project as stress-based approaches were considered for

fatigue assessment.

Heat-induced residual stress from welding or metallurgical and heat-affected zones were not

considered in this thesis. Multiaxial fatigue was also not within the scope of this thesis. The effects

of shear stresses are assumed to be minimal hence, only the first principal stress will be used in the

static and fatigue analyses.

One of the limitations involved with Abaqus is related to its Python version and the pre-installed

libraries. As the Python version installed with the software varies with the software version, it is

impossible to implement some functions due to the unavailability of some in-built libraries with

older versions of Python.

1.5 Other considerations

The thesis work does not raise any questions regarding gender, age, ethnicity, sexual identification,

or religious belonging. Furthermore, no sustainability related questions are in focus in this work,

which has been carried out in accordance with the Swedish law.

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5

2 Theory

This Chapter provides an overview of the basic theory behind fatigue in welds through the literature

considered for this project. The Chapter describes theory behind all the methods considered for

preliminary comparison. Also, Appendix D – Structural stress approaches for further scope

includes theory for methods that can be implemented in the future work.

2.1 Fatigue in welded joints

There are three stages to Fatigue failure:

1. Crack initiation phase

2. Crack propagation phase

3. Final rupture

The micro- and macro-phenomena stages of fatigue can be inferred from [2] as shown in Figure 1.

Figure 1: Micro- and macro- phenomena stages of fatigue, picture redrawn from [2]

The first stage, the crack initiation phase, consists of micro-cracks formed at the surface of a

structure where the initiation time depends on the level of material defects and stress. When welded

joints are considered, this phase has little significance compared to a nonwelded detail where it is

essential in the determination of its fatigue life. The already available weld imperfections result in

early crack initiation, usually in the first loading cycle itself [1], [2].

The locations of imperfections in the welds are more prone to crack initiation than the regions of

the base material. The crack either starts from the weld root or weld toe and propagates through

the thickness of the plate. The amount of penetration of the weld will determine if the failure will

start from the weld toe or root. Usually, weld toe failure occurs when the weld penetration is

complete and root failure when it is incomplete. One of the solutions for increasing the number of

cycles before crack initiation is to conduct a post-weld treatment in the weld toe, which has the

capability of reducing the chances of cracks initiating from the weld toe [1].

The crack propagation phase is the second stage. Here the growth of the crack has progressed to

macroscopic size due to strain occurring in the perpendicular direction of loading. The propagation

of macro cracks in this phase is stable until the crack size reaches a critical limit above which it

tends to become unstable and ultimately leads to the final rupture. This propagation rate is highly

dependent on the material properties in the thickness region, whereas the crack initiation is surface,

material and environment interaction dependent [1], [2], [5].

The crack is most often initiated due to local stress concentration created by a sudden change in

geometry like holes or notches. So, one needs to understand how these properties affect the fatigue

life of a structure, which leads to the next part of the theory.

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2.2 Factors influencing fatigue in welds

Many factors affect the fatigue strength of a structure, including the magnitude and frequency of

loading, geometric details, weld imperfections such as voids, insufficient penetration and notches,

material flaws and discontinuities, surface quality, and environment. However, the two most

important factors are loading and geometry.

2.2.1 Fatigue loading

Fatigue loading is one of the significant factors that affect the fatigue life of the structure. It is the

process of inducing fluctuating stresses through varying the applied load by changing pressure,

vibrations, temperature, or wave loads. There are two types of fatigue loading: Constant Amplitude

Fatigue Loading (CAFL) and Variable Amplitude Fatigue Loading (VAFL). A structure is

commonly under variable amplitude loading. The stress ranges in a VAFL are generated by varying

amplitudes of loads. Other important factors that determine the fatigue life of the structure, such

as the mean stress value and the sequence of loading, are also constantly changing in a VAFL. For

simple design calculations, constant amplitude stress ranges are utilized throughout the thesis work

[6].

As can be inferred from Figure 2, the stress range, ∆𝜎, is one of the important parameters

influencing fatigue life. Another important parameter is the stress ratio, R, which is the ratio of

minimum stress to the maximum stress indicating the effect of mean stresses, 𝜎𝑚. The stress ratio

is considered zero for most of the thesis work except for one case where the stress ratio is -1 due

to fully reversed loading condition.

Figure 2: Constant amplitude fatigue loading, CAFL. Redrawn from [6]

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2.2.2 Geometry

Fatigue is directly influenced by the geometrical aspects of a structure, such as dimensions, crack

location, and complexity of the structure. The main reason for stress concentration is the presence

of a sudden change in geometry. Such changes must thus be reduced during the design phase for

a better fatigue life of the structure [6].

The fatigue strength of a weld joint is highly affected by the thickness of the welded geometry. This

was confirmed by T.R. Gurney, 1968 [1] through experimental results and analysis. He concluded

that the increase in thickness resulted in the decrease of fatigue strength of the weld due to the

increase in residual stress caused by welding process. A so-called thickness correction factor was

introduced in 1995 by T. R. Gurney [6] where the thickness reduction factor for thicker plates is

given by

∆𝜎𝑡 = ∆𝜎𝑛𝑜𝑚,𝐻𝑆𝑆 (𝑡𝑟𝑒𝑓

𝑡)𝑛

where ∆𝜎𝑛𝑜𝑚,𝐻𝑆𝑆 is the fatigue strength from nominal stress or hot spot method, 𝑡𝑟𝑒𝑓 is the

reference thickness, and 𝑛 is the thickness exponent

2.3 Fatigue resistance curves – S-N curves

There are two approaches used for the fatigue assessment during the designing phase [6]:

• Classification approach (also known as the S-N curve approach)

• Fracture mechanics approach based on Linear Elastic Fracture Mechanics (LEFM)

The classification method utilizes S-N curves with fatigue design classes presented as a logarithmic

relationship between stress range and the number of stress cycles to failure, as shown in Figure 3.

These values are obtained through experiments with samples subjected to variable stresses of both

constant and variable amplitudes. This standardized fatigue design method assumes that the

material behavior of the whole structure and the fatigue-critical area is elastic [6], [7].

The welded structure details are divided into fatigue design classes, also known as FAT, along with

a number indicating the nominal stress range at 2 million cycles at a survival probability of 97.7%.

The fatigue strength curve for every standard detail has a knee point, which corresponds to the

fatigue or endurance limit. A specimen with applied stress less than the fatigue limit can work up

to an infinite number of load cycles without failing. The fatigue strength curves that are

recommended by IIW will be used throughout this thesis project [6], [7], [4].

The fracture mechanics approach was introduced by Paris [1] and represents the fatigue crack

propagation by connecting the propagation rate to the stress intensity at the tip of the crack, which

is prone to cyclic stress. The method is one of the basic approaches and is widely used nowadays

as it can describe crack propagation while the S-N curve approach cannot. However, the approach

assumes the size of the initial crack, which is not possible to measure during the design phase and

needs more research in certain other areas [1].

There is another type of S-N curve called the Master S-N curve which is used in structural stress

methods involving stress linearization through the thickness of the weld plate such as Dong’s

approach [8]. The Master S-N curve can be expressed by:

8

𝑙𝑜𝑔𝑁𝑓 = 12.88 − 3.08𝑙𝑜𝑔∆𝑆𝑒𝑞

where ∆𝑆𝑒𝑞 is the equivalent structural stress parameter. This curve can be used for all types of

loading or geometry conditions but the structural stress must be obtained from Dong’s approach

[8].

Figure 3: S-N curve for fatigue classes 100 and 225, normal stress, standard applications; picture redrawn from [6]

2.4 Stress analysis approaches

These methods make use of the stress obtained from an analysis to determine fatigue life or fatigue

strength. Some of these methods are presented in this Section.

2.4.1 Introduction

There are two ways of approaching fatigue life assessment for welded joints:

• Global methods

• Local methods.

Global methods are based on stresses obtained from strength assessments considering the external

forces and moments acting on a critical cross section. The macro geometrical effects are not

considered in this approach. Local methods consider local parameters such as local stresses or

strain from local geometry at a critical location. Variants of both global and local approaches used

within industry are shown in Figure 4 [1].

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Figure 4:Global and local approaches for fatigue life assessments; picture redrawn from [1]

A well-known global method is the nominal stress method which is based on the average stress in

the cross-section where the local effects are neglected. Local methods include structural stress,

notch stress, and notch strain approaches. The different types of stresses in weld fatigue and the

stress distribution along the thickness of the welded plate are shown in Figure 5.

Figure 5: Stress distribution through the thickness of a welded plate and weld fatigue stresses. Redrawn from [6]

2.4.2 Nominal stress approach

The nominal stress approach is the simplest and most widely used method for steel structures and

is also standardized for different types of welds. This method disregards local stress raising effects

such as nonlinear stress peak and residual stress while calculating the average stress from a cross-

section using a linear stress assumption. However, those influencing factors, including

misalignment, are considered in the design codes and recommendations [1], [3].

The nominal stress method is easy to implement for practical applications. However, the limitation

of this method is the required classification of structural details. The welds are classified by their

joint geometry and loading conditions. Selecting a specific S-N curve for an application can lead to

10

an error when there are differences in dimensions or loading in the application compared to the

reference data. The nominal stress method is thus unsuitable for complex geometry or loading

conditions as it might be hard to implement and will result in lower accuracy leading to costlier

errors during design [9].

The fatigue life calculated from this method represents the total fatigue life of the component and

does not differentiate between crack initiation and propagation life. The method does not provide

guidelines on how to use FEA for calculating nominal stress, but it can be assumed that the stress

is obtained at a distance of 1 or 1.5 times the plate thickness away from the weld toe which makes

it mesh dependent. The effect of residual stresses was included by shifting the S-N curves down to

a slope of 2.7 from 3 but still, it does not help to account for the actual residual stress for the

specific weld detail [9].

Considering all the advantages and disadvantages of the nominal stress method, it was decided to

not take this method forward to the next step of comparison with the other methods due to the

compromise in the accuracy which is one of the major criteria in the ranking of the methods.

2.4.3 Structural stress approaches

Structural stress methods have in common the ability to capture the effect of geometrical

discontinuity (unlike nominal stress method) which is desired when the method must capture the

load effect due to geometrical changes. This Section gives a brief description of the basic types of

structural stress methods.

2.4.3.1 Hot spot method

The hot spot method is applicable when the geometry is complex. This method was initially

developed for pressure vessels and tubular structures and was later used for plates or non-tubular

joints in the early 1990s. The reason this method can be applied to complex geometries is that it

takes local stress concentrations and load redistributions into account and that the S-N curve for

most types of loading is available [6].

The hot spot method has become a widely used method for fatigue assessment of welded joints

over the past decade. It has evolved into a method that can provide accurate fatigue life data for a

structure [6].

Hot spots are regions that are prone to fatigue failure, and there exist two types of hot spots: Type

A and B. The types of hot spots are seen in Figure 6. The hot spots exist in the weld toe either at

the edge of the weld or along the weld. The hot spots limit the assessment to failure at the weld

toe only. Type A is present on the weld toe of the plate surface and Type B is on the weld toe of

the plate edge. Both types have their extrapolation distances that differ based on the FE mesh

being coarse or fine [6]. This will be discussed later.

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Figure 6: Types of fatigue critical hot spots, redrawn from [6]

The dimensions and loading conditions of the component near the weld joint affect the value of

hot spot stress obtained. The procedure to determine structural stress for all the methods involve

either extraction of stress values from the surface attached to the weld toe or through linearization

of stress through the thickness of the plate. The hot spot method uses extraction of stress results

from the surface as shown in Figure 7. IIW recommendations suggest that the reference point

closest to the weld toe for stress extrapolation should be at 0.4 times the thickness of the plate to

avoid the influence of nonlinear stress from the weld notch [4].

Figure 7: Mesh and stress extrapolation direction for all hot spot types on shell and solid elements, redrawn from [4]

One of the procedures to derive the hot spot stress from an FEA is reading the stress values at two

reference points and using those to extrapolate for the stress at the weld toe. This will exclude the

notch stress as the reference points are located outside the region that is influenced by the local

weld geometry. Haibach and Oliver [10] suggested that for Type A hot spots, the distance can be

considered as a function of thickness, around 0.3 t from the weld toe. However, this project will

consider the IIW recommendations [4], which suggest 0.4 t. Type B hot spots have fixed

predetermined distances from the weld toe, and it doesn’t vary with the thickness of the welded

plate [4].

There are two major types of stress extrapolation techniques for both Type A and Type B hot

spots: linear and quadratic stress extrapolation. The linear extrapolation for Type A consists of two

subtypes for coarse mesh with higher order elements and fine mesh which is shown in Figure 8,

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while Type B doesn’t have any subtypes. Both Type A and Type B has only one type of quadratic

extrapolation which is shown in Figure 9.

Figure 8: Linear extrapolation for fine and coarse mesh models, redrawn from [6]

Three reference points are required in the quadratic extrapolation method. For a Type A hotspot,

the reference points are located at 0.4t, 0.9t and 1.4t from the weld toe and for a Type B hotspot,

at 4, 8 and 12mm from the weld toe. This requires the model to be finely meshed at the weld toe

vicinity. It can be noted that the distances are not a function of thickness for Type B hot spot

unlike for Type A hot spot.

Figure 9: Quadratic extrapolation of Type A and B hot spots, redrawn from [6], [4]

IIW [4] recommends the following formulas for hot spot stress evaluation.

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Type A hot spot:

• Linear extrapolation

o Fine mesh with element length not more than 0.4t from the hot spot, Figure 8

left:

𝜎𝐻𝑆𝑆 = 1.67 ∙ 𝜎0.4∙𝑡 − 0.67 ∙ 𝜎1.0∙𝑡

o Coarse mesh with higher order elements having lengths equal to plate thickness,

Figure 8 right:

𝜎𝐻𝑆𝑆 = 1.50 ∙ 𝜎0.5∙𝑡 − 0.50 ∙ 𝜎1.5∙𝑡

• Quadratic extrapolation

o Fine mesh and reference points as defined above. Recommended for thick-walled

structures, Figure 9 left.

𝜎𝐻𝑆𝑆 = 2.52 ∙ 𝜎0.4∙𝑡 − 2.24 ∙ 𝜎0.9∙𝑡 + 0.72 ∙ 𝜎1.4∙𝑡

Type B hot spot:

• Coarse mesh with higher order elements with element size of 10 mm at hot spot, Figure 8

right:

𝜎𝐻𝑆𝑆 = 1.50 ∙ 𝜎5 𝑚𝑚 − 0.50 ∙ 𝜎15 𝑚𝑚

• Fine mesh and quadratic extrapolation, Figure 9 right:

𝜎𝐻𝑆𝑆 = 3 ∙ 𝜎4 𝑚𝑚 − 3 ∙ 𝜎8 𝑚𝑚 + 𝜎12 𝑚𝑚

There are two challenges when it comes to the hot spot method. The first one is estimating the

structural hot spot stress by applying the right mesh properties as it is known to be sensitive to

mesh size near the weld toe. The second is selecting the right fatigue design curve for the loading

and geometry conditions. There are nine fatigue design S-N curve groups based on geometry and

loading type in IIW for the hot spot method. It should be noted that the S-N curves include the

tensile residual stresses present in the tested samples. Several experimental studies have confirmed

that the hot spot method provides accurate results in real case scenarios [9], [11].

The hot spot approach in FEA is widely used nowadays and is one of the methods which have

proven to provide results of acceptable accuracy. However, the main drawback of the hot spot

method is that it does not consider the local stress due to the weld itself resulting from the sharp

notch at the weld toe.

2.4.3.2 Through Thickness Stress Linearization

The linearization of stress through the thickness of the plate is required for certain cases to obtain

more accurate results. There are many different linearization techniques, but the one that is

commonly used is Through Thickness at Weld Toe (TTWT) [12]. The structural stress in this

method is calculated directly in the weld toe plate cross-section, as shown in Figure 10. When using

a coarse mesh, nodal averaging can cause stress underestimation. This method should thus only

use the elements present in front of the weld toe to avoid nodal averaging by the surrounding

elements [12].

14

Figure 10: Through thickness at weld toe method, redrawn from [12]

The stress distribution under the weld toe is non-linear, as depicted by the arrows inside the trend

in Figure 10. The non-linear stress distribution can be integrated to generate a linear distribution

from which the membrane and bending stress components can be found. It can be inferred from

Figure 11 that the local notch stress is the sum of bending, membrane, and non-linear stress. The

TTWT method does not capture the non-linear stress component caused by the notch, hence, the

structural stress will be the sum of membrane and bending stress [12].

Figure 11: Decomposition of local notch stress, recreated from [1]

There are a few more approaches for estimating the structural stress at the weld toe: Dong’s

approach, Xiao Yamada or 1mm method, and Equilibrium equivalent structural stress method, also

known as 𝐸2𝑆2 (see Appendix D – Structural stress approaches for further scope). All these

methods consider thickness effects during weld fatigue assessment by using the stress distribution

in the thickness of the welded plate during the calculation of the structural stress. As a result, these

methods can give more accurate fatigue assessment than the hot spot method as the latter does not

consider the thickness effect [13].

2.4.3.3 Dong’s Structural Stress or Master S-N curve approach

Dong’s approach utilizes a procedure similar to TTWT to calculate structural stress but at a distance

𝛿 from the weld toe. Dong’s approach is claimed to be insensitive to mesh size and element type

as it takes the stress at a distance from the weld toe [14]. The claim has been proven numerically

for shell elements but is false for solid. This is because the approach fails to capture the effect of

shear forces acting in the lateral direction. Research shows its inability in the case of solid elements

15

through comparison studies but has also proven that for 𝛿=0.4t, the approach gives appropriate

results as the effect of shear stresses is minimal at that distance from the weld toe [14].

Figure 12: Structural stress according to Dong, redrawn from [14]

The structural stress for Dong’s approach has been calculated at 0.4t throughout this project. The

structural stress, 𝜎𝑆 , is obtained as the sum of bending and membrane stress distribution in the

weld plate cross section as shown in Figure 12. The membrane stress, 𝜎𝑚, and the bending stress,

𝜎𝑏, are found by using the equations given below. The membrane stress is found by integrating the

horizontal stress, 𝜎𝑥 , along the direction of thickness, 𝑦. This membrane stress is then plugged into

the second equation to find the corresponding bending stress [8].

𝜎𝑚 =1

𝑡∫ 𝜎𝑥(𝑦)𝑑𝑦𝑡

0

𝜎𝑚 ∙𝑡2

2+ 𝜎𝑏 ∙

𝑡2

6= ∫ 𝜎𝑥(𝑦) ∙ 𝑦 𝑑𝑦 + 𝛿 ∫ 𝜏𝑥𝑦(𝑦)𝑑𝑦

𝑡

0

𝑡

0

𝜎𝑆 = 𝜎𝑚 + 𝜎𝑏

Where 𝑡 is the thickness of the plate and 𝛿 is the distance from the weld toe. The structural stress

is then substituted into the formula given below to find the structural stress parameter, ∆𝑆𝑠, which

can be used with the master S-N curve to find the fatigue life.

∆𝑆𝑠 = ∆𝜎𝑠 ∙ 𝑡𝑚−22𝑚 ∙ 𝐼(𝑟)−

1𝑚

It should be noted that the thickness correction, effect of loading mode and geometrical

discontinuities are already included in this formula. The variable 𝐼(𝑟) is a dimensionless function

of bending ratio, 𝑟, and varies with the loading mode of the model and the crack type. Two cases

are shown below: edge crack, load-controlled (a) and semi-elliptical crack, small detail (b) [8].

𝐼(𝑟)1

𝑚 = −0.0732𝑟6 + 0.2132𝑟5 − 0.2063𝑟4 + 0.091𝑟3 + 0.0193𝑟2 − 0.014𝑟 + 1.102 (a)

𝐼(𝑟)1

𝑚 = 0.0011𝑟6 + 0.0767𝑟5 − 0.0998𝑟4 + 0.0946𝑟3 + 0.0221𝑟2 + 0.014𝑟 + 1.2223 (b)

Here the bending ratio is given by the ratio of bending stress to the sum of bending and membrane

stress and 𝑚 is the exponent in Paris law. The function will be different for semi-elliptical cracks,

16

but only edge-type crack was considered in this project. However, one should note that the crack

is not modelled during the analysis.

2.4.3.4 Xiao and Yamada or 1mm approach

The “1 mm method” is another structural stress method that captures the thickness effect well.

This is an unconventional approach because the structural stress is calculated at 1mm below the

notch tip. This approach is motivated by the assumption that the fatigue crack propagation occurs

1mm below the weld toe. The stress taken 1mm below the weld toe is claimed to capture the

thickness and size effect, thereby avoiding the necessity for a thickness correction factor for weld

plates thicker than 25mm. It is preferred to use first-order finite elements to avoid stress gradients

[15], [13].

Figure 13: Structural stress according to Xiao & Yamada, redrawn from [15]

To capture the stress at 1mm depth with acceptable accuracy, the finite element model must have

fine mesh, which is one of the main drawbacks of this approach. The other drawback is that the

method is not applicable in cases where bending stress is dominant [13]. This method has been

shown to provide results in good agreement with experimental evaluations except in cases when

bending is dominant. However, the 1 mm method tends to underestimate the stress for thin plates

as 1mm point below the weld toe exists close to the neutral axis [15].

2.4.3.5 Modified Structural hot spot stress

According to [16], the stress concentration factor, 𝐾𝑠𝑎, can be found using the following formula,

depending on the difference between weld leg length, 𝑙𝑤, and half thickness of the base plate:

𝐾𝑠𝑎 = 1 +𝜎𝑤𝜎𝑛(1 −

𝑙𝑤𝑡) 𝑓𝑜𝑟 𝑙𝑤 ≤

𝑡

2

𝐾𝑠𝑎 = 1 +𝜎𝑤𝜎𝑛(𝑡

4𝑙𝑤) 𝑓𝑜𝑟 𝑙𝑤 ≥

𝑡

2

where 𝜎𝑤 is the weld stress and 𝜎𝑛 is the nominal stress. The results yield FAT 95 for throat

thickness a = 3 mm, and FAT 83 for a = 7 mm [16], [17]. This method claims a few desirable

properties for increase in flexibility of analysis:

• Simple meshes with various mesh element types and sizes can be used.

• Useful also when root cracks are included

• Applicable with coarse solid, plane, or thin shell element models,

• Thickness correction is not required with wide range of thickness applicability

17

The drawback of this method is that it is applicable only for two-sided fillet lap welds and the study

[16] warns the reader to use this method for other type of welds with caution as the stress

concentration formula might differ.

2.4.3.6 Force equivalent traction stress

The force equivalent traction stress method claims to be able to capture the stress distribution

through the thickness regardless of whether using a coarse or a fine mesh. This method combines

the application of both Hot spot method and Through thickness method by extracting traction

stress at the hot spot point 0.5t and 1.5t and extrapolating it to find the structural stress at the weld

toe.

The study [18] claims that the mesh dependency is minimized by using nodal forces to calculate

sectional force and moments. The formulas below show the summation of axial force and two

bending moments using nodal forces to find the traction stress, 𝑝 , acting on the section. The result

of the summation is shown in Figure 14.

Figure 14: Decomposition of force equivalent traction stress of a section, redrawn from [18]

�̂�1 =∑𝑓𝑖

𝑙𝑡+6∑𝑧𝑖𝑓𝑖

𝑙𝑡2−6∑𝑦𝑖𝑓𝑖

𝑡𝑙2; �̂�2 =

∑𝑓𝑖

𝑙𝑡+6∑𝑧𝑖𝑓𝑖

𝑙𝑡2+6∑𝑦𝑖𝑓𝑖

𝑡𝑙2;

�̂�3 =∑𝑓𝑖

𝑙𝑡−6∑𝑧𝑖𝑓𝑖

𝑙𝑡2+6∑𝑦𝑖𝑓𝑖

𝑡𝑙2; �̂�4 =

∑𝑓𝑖

𝑙𝑡−6∑𝑧𝑖𝑓𝑖

𝑙𝑡2−6∑𝑦𝑖𝑓𝑖

𝑡𝑙2

Here 𝑙 is the length of an element, 𝑡 is the thickness of the plate, 𝑓𝑖 and �̂�𝑖 is the nodal force and

traction stress at i-th node on the cut section and 𝑧𝑖, 𝑦𝑖 are the z and y coordinate, respectively.

The traction stress from the cut section is multiplied with the shape functions for type of elements

used in the analysis. An example with bi-linear element is

𝑁1(𝑟, 𝑠) =1

4(1 − 𝑟)(1 − 𝑠); 𝑁2(𝑟, 𝑠) =

1

4(1 + 𝑟)(1 − 𝑠);

𝑁3(𝑟, 𝑠) =1

4(1 + 𝑟)(1 + 𝑠); 𝑁4(𝑟, 𝑠) =

1

4(1 − 𝑟)(1 + 𝑠)

where 𝑟 and 𝑠 are natural coordinates. The traction stress of the cut section is thus obtained as

𝑝(𝑟, 𝑠) = ∑𝑁𝑖(𝑟, 𝑠)�̂�𝑖

4

𝑖=1

18

2.4.4 Effective notch stress approach

This approach is based on including stress raisers arising from geometrical discontinuities such as

notches, holes, weld defects, joints, etc. from the structural component which are usually not

captured by the methods discussed till now. It is necessary to include the stress due to local

geometry as it determines the realistic fatigue strength of the component based on the stress

concentration.

The basic concept of this method is to model the weld toe or root as a notch of radius 𝜌𝑓 which is

given by Neuber’s micro-support concept for welded joints as shown in Figure 15 where the

maximum principal stress is directly read from the FEA results of the local notch geometry [6].

This approach gives more accurate results compared to the structural stress methods as it gives a

much better representation of fatigue strength by including local geometry effects through the

reference radius or notch radius [19].

The modelling and pre-processing part for this method needs more effort than compared to other

methods. To capture the maximum stress, the model requires a higher element density in the notch

region. A complex geometry would require a sub model of the structure to concentrate only on the

critical location from where the stress should be extracted also resulting in reduction of

computational cost.

Figure 15: Notch rounding with reference radius, 𝜌𝑓 ; redrawn from [19]

The notch radius is usually set to 1mm for plates thicker than 5 mm and 0.05mm for thinner plates.

The notch radius for thin plates was proposed by Zhang, which is based on the relationship

between the stress intensity factor and the notch stress [6]. The element size in the notch region

should be in the range of 1/4th or 1/6th of the radius of the notch so, it is usually set at 0.25 mm.

The method gives non-conservative results for thin butt joints due to small stress concentration

occurring in such joints [20].

One of the main advantages of using this method is that only one Fatigue class curve is used

regardless of the geometry or loading detail. For steel welded joints, IIW recommends the FAT

19

225 curve which will be linked to maximum principal stress found from the analysis to find the

fatigue life. The disadvantage to this method is high computational time and meshing requirements.

2.5 Summary of approaches

Advantages Disadvantages

Nominal Stress approach

Simple, well known method Simple and quick application with guidelines Fatigue classes available

Limited to simple geometrical changes Less compatible and less accurate with complex geometries Only applicable for the tabulated structural details

Hot Spot method

Most widely used FE-modelling effort is less Medium mesh requirements Good accuracy Less number of fatigue classes and S-N curves Applicable for both shell and solid models

Not applicable for weld root failure Mesh dependent Thickness effect is not included Only applicable for the tabulated structural details

Through Thickness Linearization

Fatigue life calculations include thickness effect Good accuracy Applicable in complex geometrical and loading conditions Intermediate mesh requirement

FE-modelling needs more effort to capture stress along thickness Nodal averaging underestimates stress Works only for solid model

Dong’s Structural stress approach

Mesh independent Good accuracy One Master S-N curve

Mesh dependency is observed when solid elements are used Works only for solid model

Xiao Yamada or “1 mm approach”

Post processing is simple Good accuracy Thickness effect included

Fine mesh is required Not applicable for bending stress dominant cases Works only for solid model

Modified structural stress approach

Mesh Independent Best Accuracy Applicable for all Thickness Root crack scenario applicable

Not for every type of weld joint Needs more research for stress concentration on different types of weld joint types Works only for solid model

Force traction stress method

Promising improvement for Hot spot method Good accuracy Mesh insensitive Thickness effect is included

Needs more research to prove applicability Works only for solid model

Effective notch stress approach

Better accuracy than rest of the above One S-N curve Thickness effect is captured Applicable for weld root failure

More FE-modelling effort Requires sub-modelling in case of less computational capability High mesh requirement

20

Section 2.5 presents the summary of all the methods in the form of a table, which has been

collectively obtained from the literature([1] – [25]).

The nominal stress, modified structural stress and force traction methods were decided not to

proceed with because the first two of them were not applicable in every type of weld joint and the

last one required more research for comparison and validation.

21

3 Finite element analysis

This Chapter describes the FEA done on three case studies with information about modelling, pre-

processing steps, and results from postprocessing. Further comparison of results of some methods

from this project that were available in reference literature was done for validation.

3.1 Case study 1

The first case study concerns a geometry obtained from [21], shown in Figure 16. It is a simple

Transverse joint (T-joint) with an incomplete weld along the joint. The reference study [21]

contained an FEA on the model and a comparison between the fatigue life results from the nominal

stress, hot spot, and effective notch stress methods. In the reference study, a so-called coefficient

for risk of failure, 𝜑𝑄, was included in the fatigue life calculation as shown in the formula (a) shown

below which is a formula to calculate the fatigue life from the hot spot stress method. A 50% failure

risk was considered in the reference study to match the fatigue life results obtained from FEA with

experimentally tested fatigue life. Different values of 𝜑𝑄 is shown in Table 1. The risk of failure

taken in this project is 2.3%, which makes 𝜑𝑄 = 1. This is done so that the results are comparable

with the results from the automatized process.

𝑁 = 2 ∙ 106 ∙ (𝜑𝑄∙𝐹𝐴𝑇

𝜎𝐻𝑆𝑆)𝑚

(a),

where FAT is the fatigue strength at 2 million cycle for a 97.7% survival probability S-N curve, 𝑚

is the slope of the S-N curve and 𝜎𝐻𝑆𝑆 is the hot spot stress obtained from FEA postprocessing.

Consequence of failure Approximated risk of failure Coefficient for risk of failure φQ

Testing 50% 1.3

Negligible 2.3% 1.0

Less severe 0.1% 0.87

Severe 0.01% 0.8

Very severe 0.001% 0.74 Table 1: Coefficient for risk of failure for different percentages of failure, referred from [21]

Figure 16: Dimensions of case study 1 geometry (in mm)

The geometry was modeled in Abaqus and the dimensions from the reference study [21] were used,

as shown in Figure 16. The quarter model of the geometry was used in the analysis as the geometry,

loading, and boundary conditions have symmetry as marked with the blue centerline in Figure 16.

The same material properties from the reference study [21] were applied with the isotropic elastic

properties shown along with Figure 17.

22

Figure 17: Meshing with tetrahedral elements

Material properties

𝐸 = 210 𝐺𝑃𝑎

𝜈 = 0.3

The model was meshed with quadratic tetrahedral elements, C3D10I, with improved surface stress

formulation, as shown in Figure 17. The model was partitioned to have the FE mesh nodes at the

points where stress must be extracted for all the methods. For example, the stress should be

extracted from the nodes at 0.4t, 0.9t, 1.0t, and 1.4t distance from weld toe for linear and quadratic

of hot spot method. The model should be partitioned on the thickness to extract stress 1 mm

below the weld toe for the 1 mm approach calculation.

The reference study [21] contained two cases based on how the weld was loaded. Case 1 was for

applying load in the base plate, making it a non-load carrying fillet weld, which is a type of weld

that contains an attachment plate which does not involve in transmitting load to the main or base

plate. Case 2 was for applying load in the attachment plate, making it a load-carrying weld. This

project only uses the loading case 1 from the study for analysis and comparison, as shown in Figure

18.

Figure 18: Loading case

Symmetry boundary conditions were used to constrain x- and z- direction where symmetry exists

in the geometry. The model in this project was given boundary conditions like the reference study,

where it represented the testing scenario as accurately as possible. A reference point was created at

the point shown in Figure 19 as RP-1. A reference point is a point you can create in a part or

assembly in Abaqus. It can be created anywhere in the space and is useful for creating a point where

there is no vertex available. A rigid body constraint is introduced to constrain the motion of the

points present in the highlighted surface in the expanded image, to the motion of the reference

point. This is used to apply a distributed load in Abaqus. A load of 100 kN is applied at the reference

point shown in Figure 19. This case study involves a pulsating load with stress ratio R = 0.

Therefore, the stress obtained from the FE results is directly plugged in the formula for calculating

fatigue life.

23

Figure 19: Boundary conditions of case study 1

3.1.1 Results

• Hot spot stress

The stresses extracted from the predetermined distances are put in Table 2. This was done using

the probe values tool, available in the Abaqus query window.

Distance from weld toe Maximum principal stress [MPa]

0.4t 107.94

0.9t 105.60

1.0t 105.41

1.4t 104.75 Table 2: Stress extracted from the model for hot spot stress calculation

The maximum stress values were extracted from the following path created in Abaqus by defining

a node list. The points shown in Figure 20 are in the order as given in the table.

Figure 20: Nodal points for stress extraction for the hot spot method

As mentioned in Section 2.4.2.1 Hot spot method, hot spot stress can be extrapolated in three ways:

Linear with coarse mesh, linear with fine mesh, and Quadratic. The linear with coarse mesh was

not implemented for this model as the mesh density is fine near the weld toe. The stress results

24

extracted from the points 0.4t and 1.0t will be used for Linear extrapolation with fine mesh and

results from points 0.4t, 0.9t, and 1.4t will be used for quadratic extrapolation. The fatigue strength

class, FAT, was taken as 100 and the fatigue life, N, was calculated and presented in Table 3. The

value of the FAT and the formula shown below are referred from the reference study [21] and can

be referred in the IIW recommendations [4] for a non-load carrying weld type.

𝑁 = 2 ∗ 106 ∙ (𝐹𝐴𝑇

𝜎𝐻𝑆𝑆)3

Type of extrapolation Hot spot stress σHSS [MPa] Fatigue life N [cycles]

Linear 109.64 1517500

Quadratic 110.88 1470000 Table 3: Hot spot stress results for the case study 1 model

It was agreed that the results obtained from this hot spot method is acceptable as the value for hot

spot stress is the same as in reference study [21]. The only variation in results was found in fatigue

life as the coefficient 𝜑𝑄 was assumed to be 1 for this project.

• Through Thickness at weld toe (TTWT) method

Figure 21: Stress extraction for Through thickness method

Figure 21 shows which stress are extracted for the linearization of stress through the thickness.

Here the initial crack length was assumed to be 1 mm. The longitudinal stress values were used to

extract 𝜎𝑚,1 and 𝜎𝑏,1, the vertical stress values were used for 𝜎𝑚,2 and 𝜎𝑏,2, and shear stress acting

on the plane was used to extract values for 𝜏1 and 𝜏2. The crack length was taken as 𝑙 = 1 𝑚𝑚

and the thickness as 𝑡 = 1 𝑚𝑚. One should note that a crack was not modelled during the analysis

but was assumed to have propagated for calculation purposes.

𝐹 = 𝜎𝑚 ∙ 𝑙 ∙ 𝑡

𝑀 = 𝜎𝑏 ∙ 𝑡 ∙𝑙2

6

𝑄 = 𝜏 ∙ 𝑙 ∙ 𝑡

𝜎𝑠 = 𝜎𝑚 + 𝜎𝑏 =𝐹

𝑙𝑡+6𝑀

𝑙𝑡2

25

The structural stress parameter is found using the formula given in Page 15 and is plugged into the

master S-N curve equation given in Page 8 to find the fatigue life. There is no FAT value required

in this case. The results are shown in Table 4.

𝜎𝑚,1 120.956

𝜎𝑚,2 17.677

𝜎𝑏,1 2.013

𝜎𝑏,2 5.15

𝜏1 -8.907

𝜏2 12.07

𝜎𝑠 93.267

Fatigue life, N 1790000

Table 4: Results from TTWT for case study 1 model

• Xiao Yamada or 1 mm method

Figure 22: Xiao Yamada method with 0.5 mm element

This method is based on extracting the stress 1mm below the weld toe which is marked with a red

point in Figure 22. The fatigue life was calculated using the same formula shown in the hot spot

stress section in Page 24 but the stress taken from the red point was used. Element sizes of 1 mm

and 0.5 mm along the thickness were compared to check for stress underestimation and the results

are shown in Table 5.

Element Maximum principal stress (MPa) Fatigue life

1 mm 98.7131 2080000

0.5 mm 100.185 1988900 Table 5: Results from Xiao Yamada or 1 mm method for case study 1 model

• Dong’s structural stress method

A similar procedure like in TTWT was followed except that the stresses were taken at 𝛿 = 0.4 t where the effect of shear stress is minimal. The same force-moment equilibrium approach applied

in TTWT method was used to find the structural stress which was then applied to the master S-N

curve to find the fatigue life. The results are shown in Table 6.

26

Membrane stress, 𝜎𝑚 [MPa] 109.766

Bending stress, 𝜎𝑏 [MPa] -8.319

Structural stress, 𝜎𝑠 [MPa] 101.2317

Fatigue life, N 1934300 Table 6: Results from Dong's approach for case study 1 model

• Effective notch stress approach

The Effective notch stress method, ENS, requires the region of the notch to be meshed finely

enough to capture the notch stress accurately. To reduce the computational cost, the sub modelling

technique was incorporated as shown in Figure 23. The sub model boundary condition was applied

to the highlighted surfaces shown in Figure 24 and the number of nodes on the connecting region

of the global model and sub model was the same. The sub model boundary condition in Abaqus

transfers the displacement obtained from the analysis of a global model to the sub model and hence

there exists no symbol to represent the boundary conditions in Figure 24.

Figure 23: Global model and sub model for effective notch stress approach

Figure 24: Sub model boundary conditions Figure 25: Meshing of the sub model

The element size around the notch region was kept at 0.25 mm which is 1/4th of the notch radius

1 mm. The local seeds in Abaqus are used to assign an edge in the geometry a specific element size

different than the global element size. This function was used to modify the mesh density near the

notch so that a dense mesh was generated in the notch. The resulting mesh is shown in Figure 25.

The model attributes were modified to read the results from the main model and apply it to the

sub-model boundary conditions so that the displacements are transferred to the sub-model.

27

The results from the analysis can be seen in Figure 26 where the maximum principal stress can be

directly read from the analysis. The stress can be used to calculate the fatigue life with FAT value

as 225 as shown in Table 7. This FAT value was referred from both IIW [4], and the reference

study [21], and is constant for all types of geometry and loading scenario unlike the hot spot

method. The formula for calculating fatigue life in this method is the same as in hot spot method

as shown in Page 24, but the stress used in the formula and the FAT value are different.

Figure 26: Maximum principal stress from the analysis

Maximum principal stress (MPa) 223.2

Fatigue life 2048800 Table 7: Results from Effective notch stress for case study 1 model

The results from the ENS and hot spot method shown in Table 8 were in close agreement with

the results from the reference study [21] where only these two methods were implemented in the

same geometry. ENS method was considered to provide the most accurate results as most of the

literature suggests. Therefore, the results from the rest of the methods were compared with ENS

and are represented as percentage of difference in Table 9.

Table 8: Comparison of results between project and reference [21] for case study 1

Method Structural stress [MPa] Fatigue life Percentage of difference (%)

Hot spot Linear 109.64 1553000 24

Quadratic 110.88 1496000 27

TTWT 93.27 1790000 12.6

1 mm method 1 mm element 98.7131 2080000 -1.5

0.5 mm element 100.185 1988900 2.9

Dong’s 101.231 1934300 5.6

Effective notch stress 223.2 2048800 - Table 9: Case study 1 results of methods with their percentage difference compared to the effective notch stress

Method Project stress results [MPa]

Reference paper stress results [MPa]

Error (%)

Hot spot (solid) Linear 109.64 110 0.3

Quadratic 110.88 111 0.1

Effective notch stress 223.2 217 2.7

28

Shell model

The weld geometry can be modelled using shell elements in several ways, one of which is modelling

the weld as an oblique shell element. The mid surface shell model was created as shown in Figure

27 where the dimensions vary with the plate thickness and the weld leg length 𝑙𝑤.

Figure 27: Weld modelled as oblique shell elements

The resulting shell model of the case study is shown in Figure 28 for reference. The plate thickness

was assigned to the specific shell surface and the weld geometry. The material and boundary

conditions were also applied and analysed. The disadvantage of using this model will be the inability

to capture stress along the thickness of the plate. All the methods except the hot spot method

require the thickness of the model in the geometry, so therefore, only the hot spot method was

applicable for shell models.

Figure 28: Shell model of case study 1

The results of the shell model show differences from the solid model due to difference in stiffness

between solid and shell elements. The results from shell element model for the hot spot method

are shown in Table 10.

Table 10: Shell model results for hot spot with the percentage difference compared to the effective notch stress

Method Structural stress [MPa] Fatigue life Percentage of difference (%)

Hot spot Linear 104.94 1731000 15.51

Quadratic 110.88 1705000 16.78

29

3.2 Case study 2

The second case study concerns a longitudinal stiffener welded to a test specimen shown in Figure

29 that is subjected to bending load. This model is taken from a research paper [22] where it was

tested using strain gauges to calculate the structural hot spot stress. Results from the experiment

were then compared with the hot spot stress obtained from numerical analysis.

The reference study [22] dealt with two types of load cases: tensile and bending load on the same

geometry. This project only considers the bending load scenario as tensile loading was already

treated in case study 1. A wider perspective can be obtained from this case study by involving

bending load with longitudinal welds, unlike case study 1, where it was tensile loading with

transverse weld.

Figure 29: Case study-2 geometry

The same methods that were applied in case study 1 were implemented in this case study as well.

This expands the existing research by comparing results from methods other than the hot spot

method to find if the structural stress values agree with the reference study [22]. It should be noted

that the fatigue life was calculated without including misalignment, thickness correction, or risk

factor like in case study 1. The fatigue class for this type of loading is FAT 90, and a survival

probability of 97.7% was assumed in the calculations.

The material property is the same as used in reference study [22], which is from ASTM mild steel

of grade A, with similar isotropic elastic properties as in the previous case study. The loading is a

three-point bending scenario where the load is applied at the bottom of the longitudinal weld, and

the ends of the test specimen are held, as shown in Figure 30.

Figure 30: Case study 2 three-point bending loading case

30

A kinematic coupling between a reference point (RP-1) and a line representing the midline of the

specimen (magenta line) at the bottom surface was created as shown in Figure 31. This coupling

constrains the motion of the nodes on the midline (coupling nodes) to the motion at the reference

point in the user defined degree of freedom. A load of 6.86 kN was applied at the reference point

in the positive y- direction and the coupling nodes on the midline were constrained only in the y-

direction to avoid formation of unwanted stresses as a result of contraction. This is a pulsating load

with stress ratio R = 0. Therefore, the same procedures apply for the calculation of fatigue life as

in case study 1.

Figure 31: Kinematic coupling between reference point and the midline

The element type used in the analysis was hexahedral 20-node brick elements, C3D20R, with R

indicating reduced integration. This element type was used in the reference study [22] and is thus

also used here for comparison purposes.

3.2.1 Results

The procedure followed for all the methods is the same as presented in case study 1. The results

from the case study are presented in Table 11.

Method Structural stress [MPa] Fatigue life Percentage of difference (%)

Hot spot Linear 483.36 12870 21.4

Quadratic 498.2 11790 11.2

TTWT 587.6 12970 22.4

1 mm method 1 mm element 447.6 16260 53.4

0.5 mm element 484.56 12815 20.9

Dong’s 585.14 11820 11.5

Effective notch stress 1291 10600 - Table 11: Case study 2 results with percentage difference compared to the effective notch stress

The fatigue life values from the hot spot method and Dong’s method showed accurate results,

whereas the 1 mm method showed bad accuracy compared to the previous case study. This

inaccuracy from the 1 mm method agrees with the conclusions inferred from [13]. Figure 32 shows

the sub-model showing results for the effective notch stress method.

31

Figure 32: Effective notch results for case study 2

Table 12: Comparison of results between project and reference paper [22] for case study 2

The hot spot method gave results that were in close agreement to the results from the reference

study [22], as shown in Table 12. For the second case the shell model was not prepared as the

comparison was only made for a solid model.

3.3 Case study 3

The third case concerns a rectangular hollow section joint that was referred from the SAE FD&E

committees’ “Fatigue Challenge” with specifications shown in Figure 33. The model was studied

in [23] using another structural stress approach called the 𝐸2𝑆2 method. The method gave results

close to experimental results.

Figure 33: Case study 3 geometrical details (in mm)

The material is A13R-RC7 steel with the same isotropic elastic properties as in the other case

studies. The loading is applied at the end of the 101.6 × 101.6 mm section through a rigid link

317.5 mm above the center of the 101.6 × 101.6 mm cross-section. This is achieved by giving a

Method Project stress results [MPa]

Reference paper stress results [MPa]

Error (%)

Hot spot Linear 483.36 493.84 2.1

Quadratic 498.2 514.63 3.2

32

rigid link constraint between the center point and the reference point, RP-2, as shown in Figure

34, and the center point is given kinematic coupling to the surface of the cross-section.

The surfaces shown in Figure 35 were fixed in all directions, and a load of 17.8 kN is applied at the

reference point RP-2 in the positive z-direction. However, in this case the type of loading is

alternating which makes the stress ratio R<0. Hence, the stress obtained from the FE results is

doubled when plugged in for fatigue life calculation.

Figure 34: Rigid link and kinematic coupling in the hollow section

Figure 35: Boundary conditions on the rectangular hollow section

The element type used in the analysis was hexahedral 20-node brick elements, C3D20R, with

reduced integration and quadratic wedge elements, C3D15, for the weld geometry.

3.3.1 Results

The possibility of using the hot spot method with quadratic extrapolation and Xiao Yamada with

a 0.5 mm element size was limited due to geometrical and computational limitations. The rest of

33

the methods that are possible for this geometry are performed and listed in Table 13. The hot spot

method using linear extrapolation was performed by creating a path using a node list, as shown in

Figure 36. The location of high hot spot stress is marked in a yellow square, which coincides with

the location of the damage from the experiments conducted in the reference study [23].

Figure 36: Path created using node list for hot spot linear extrapolation on case study 3

The main model and the sub model used in effective notch stress is shown in Figure 37. This is

concentrated at the area where the crack occurred in the reference study [23].

Figure 37: Main model and sub model for effective notch stress on case study 3

Figure 38: Results from effective notch stress for case study 3

34

Method Structural stress [MPa] Fatigue life Percentage of difference (%)

Hot spot Linear 336 52720 16.47

TTWT 421.8 60344 4.39

Xiao Yamada 1 mm element 314 64601 -2.35

Dong’s 356.74 61650 2.32

Effective notch stress 713 63116 - Table 13: Case study 3 results with percentage difference compared to the effective notch stress

Table 14: Comparison of results between project and reference paper [24] for case study 3

The results from effective notch stress of this project agreed with the results from another

reference study [24], in which the effective notch stress method was performed for the same

geometry. Comparison of the results are shown in Table 14. Therefore, the other methods were

compared with the effective notch stress and are represented as a percentage of difference. The

hot spot method, TTWT, and Dong’s method showed conservative results.

Method Project stress results [MPa]

Reference paper stress results [MPa]

Error (%)

Effective notch stress 356.66 360 0.92

35

4 Observations and discussion

The results from the case studies were used to compare the weld fatigue assessment methods and

rank them based on selected key performance indexes, KPIs. This comparison directed the project

work towards the most suitable method to be implemented as a tool.

The first case study was a simple T-joint with the load applied in the transverse direction on a non-

load carrying weld affected indirectly by the load, unlike a load-carrying weld, which is under the

direct influence of the load. This classified the first case study under Fatigue class 100 or FAT-100

curve, and Type A hot spot for hot spot approach. The same fatigue class was applied for the 1

mm method. The other methods included all geometrical and loading conditions in a single

classification.

For the first case, the effective notch stress result was taken as the reference fatigue life, which was

compared with other methods for accuracy. The quadratic hot spot method shows the conservative

result when compared to the linear hot spot, which was not expected. All other methods showed

increased accuracy compared to hot spot except for the 1 mm method with 1mm element size

where fatigue life was overestimated, as shown in Table 9. This suggested the necessity to use a

fine mesh of 0.5 mm or denser near the weld region for the 1 mm method. The shell model was

evaluated for hot spot method in this case to show that the method was applicable in both solid

and shell model.

The second case study was a bending load scenario with a Type A hot spot, which classified it as a

FAT-90 curve. It can be noted in Table 11 that all the methods overestimated the fatigue life when

compared to the results from the effective notch stress, unlike the previous case study. This is

because the bending stress dominates, which increases the bending ratio and affects the structural

stress obtained.

The 1 mm method however showed high variations from the results when the stress was taken

from the point marked in red shown in Figure 39. The results from the red point for 1mm and 0.5

mm element sizes are represented in Table 15, where fatigue life is compared with the result from

the ENS method. The crack was now assumed to propagate under the weld bead like a lamellar

tear so, the 1mm stress was taken in the point marked in yellow, which gives somewhat acceptable

results. This demonstrates the sensitivity of the Xiao Yamada method towards bending stress,

which agrees with the conclusions referred from [13].

Figure 39: Xiao Yamada or 1 mm stress method on case study 2

36

Iteration Element size [mm]

1 mm stress [MPa]

Fatigue life Error (%)

1 (point marked in red)

1 432.92 17970 69.52

0.5 442.7 16805 58.5

2 (point marked in yellow)

1 447.6 16260 53.4

0.5 484.56 12815 20.9 Table 15: Xiao Yamada of case study 2 compared with effective notch stress

The Dong’s method showed mesh dependency when used in solid models as can be inferred from

many research papers ( [12], [14], [15], [19], and [21]) but has been shown to give acceptable results

at the distance of 0.4 times the thickness of the plate from the weld toe as shown in Table 16.

Case study 2

Distance from weld toe 0.4*t 0.9*t

Structural stress [MPa] 585.14 559.12

Fatigue life [cycles] 11820 13493

% difference from ENS 11.6 27.4 Table 16: Dong's method results comparison based on distance from the weld toe

Apart from the mesh dependency and need for partitioning the geometry before analysis, the

calculation involved during post-processing is cumbersome. These are some of the difficulties

associated with through-thickness approaches in addition to the lack of resources for comparison

of results, especially with the TTWT method. It was noticed that this method required an

assumption on the crack length formed in the direction of the thickness during the calculation to

arrive at a result. This can increase the time for analysis when there are multiple welds to be analysed

simultaneously and is difficult to automatize.

The third case study was a complex model with a curved weld attached to a curved surface. Hot

spot quadratic was not performed as the stress at 1.4 t from the weld toe cannot be extracted from

the curved surface due to difficulty in partitioning. Xiao Yamada with a 0.5mm element size was

not performed, because of computational limits. Through thickness methods, TTWT and Dong’s

approach showed a similar accuracy range as shown for previous case studies. The effective notch

stress result from this project was verified with the research study [24], which was used as the

reference fatigue life for comparison with other methods.

The above observations made from the case studies gave a clear view on the methods and made it

easier to differentiate them based on accuracy, computational time, post-processing time, and

robustness for an eventual ranking of methods based on these criteria.

For the case of computational time taken:

• Hot spot method took the least amount of time out of all methods as the mesh density

required in the analysis was intermediate.

• TTWT and Dong’s approach took equal amount of time as hot spot.

• Xiao Yamada was time consuming when the mesh density was high. It was proven that

fine mesh was required for good results from the analysis.

• Effective notch takes the most amount of time out of all methods because of the high-

density mesh present in the notch.

Pre- and Postprocessing time taken:

37

• Hot spot method required partition in the surface where stress is extracted and assignment

of local seeds for the partition. Local seeds indicate the number of elements present on the

surface near the weld toe region. Pre-processing steps were not much time consuming.

Postprocessing was also not time consuming as it only took few calculation steps to get the

fatigue life value.

• TTWT and Dong’s approach took medium amount of time at pre-processing as

partitioning over the thickness of the welded plate was required. Postprocessing involves

creation of local coordinate system based on the weld geometry and lots of calculations

which was time consuming.

• Xiao Yamada required partitioning and mesh refinement near the weld toe but, it has the

least amount of postprocess of all the methods as the structural stress was directly read

from the viewport.

• Effective notch stress method took the most amount of pre-processing time as it required

sub modelling in all the case studies and detailed partitioning and assigning of local seeds

for accurate results. Postprocessing did not take much time as it took one step of calculation

after obtaining maximum stress from the analysis results.

Accuracy of each method:

• Hot spot method showed consistent accuracy and can be the most conservative approach

of all.

• TTWT method also showed consistent accuracy but is sensitive to the assumed initial crack

growth length.

• Dong’s approach showed varying accuracy determined by the distance from the weld toe

and is suggested to have 0.4 t from weld toe to ignore the effect of shear stress.

• Xiao Yamada was second most accurate method of all but is sensitive to bending stress.

• Effective notch stress method is assumed to give the most accurate results of all the

methods and is found to be sensitive with respect to the element size on and near the notch

region.

The average error percentage of each fatigue life prediction methods are presented in Table 17,

Method Error range (%)

Hot spot Linear 20.62

Quadratic 19.1

TTWT 13.13

Dong’s approach 6.47

Xiao Yamada 8.7 Table 17: Average percentage difference of each methods with effective notch stress method

The robustness or flexibility of the methods was highly prioritized as the implementation of a

method as a tool required the method to assess numerous welds of different types simultaneously.

The ease of implementation of the method as a tool also adds to the advantage. Flexibility and ease

of implementation of each method:

• Hot spot method can be easily applicable to numerous welds as the computational time is

less and the minimum mesh size requirement is 0.4 t.

38

• TTWT required partition for all the weld plates along thickness direction and creation of

local coordinate system based on weld orientation to the global axes which makes it tough

to be implemented as a tool.

• Dong’s approach is limited by the dimensionless function of bending ratio, 𝐼(𝑟), as it

changes based on the loading mode. In addition to that, it also requires local coordinate

system which is tough to automatize.

• Xiao Yamada is proven to be sensitive to bending stress which makes it less flexible.

• Effective notch is easy to implement when one is talking about postprocessing only.

However, it required lots of pre-processing work which makes it tough to implement when

there are multiple welds.

Considering all the above observations and discussions regarding all the methods and their

respective advantages and disadvantages, it was decided to proceed with the hot spot method,

which is robust enough and gives acceptable accuracy.

The decision was made easy by implementing a scoring matrix where the methods were scored

against the criteria discussed above with weight functions assigned to the criteria. The methods

were rated on the scale of 1-5 for each of the criteria with 1 being the least and 5 being the highest

score for each criterion. The weighted score of methods for each criterion was obtained by

multiplying the weight functions with the rating and is summed up to obtain the total score for

each method. The methods were then ranked based on the scores. The scoring matrix can be found

in Appendix A – Method scoring matrix.

39

5 A plug-in tool for weld fatigue assessment

This Chapter describes the internal workflow in the developed tool for weld fatigue assessment. It

starts with a brief explanation of the user input requirements and the working to arrive at the result.

A summary of the workflow is represented as a flowchart in Appendix B – Workflow summary.

5.1 Introduction

There are currently several commercial tools available for fatigue evaluation of welds. These

software packages directly read the stresses from the numerical calculations. However, most of

these software packages do not come with an automated post-processing plug-in that is specific

for the fatigue evaluation of welds. Thus, there arises a need for a user interactive plug-in that is

easily accessible in Abaqus. The primary objective for this thesis has been to develop a tool that

can evaluate the fatigue life of multiple welds which makes it convenient for the user to automate

most of the steps in postprocessing.

The hot spot stress method was selected based on its ease of applicability for different loading,

geometrical, and model type scenarios. The computational time is also minimal for the hot spot

method. The combination of this method and the finite element method is widely employed in

postprocessing welded joints. The hot spot method can assess multiple welds simultaneously.

Hence, automatizing the process can reduce the postprocessing time by a significant amount.

The hot spot stress for a welded joint is obtained by extracting the principal stress acting on the

surface perpendicular to the weld. Usually, the surface is partitioned at the place where the stress

is read out at a predetermined distance from the weld toe. The stress is extracted manually for each

hot spot location and finally extrapolated using the formula given for that type of extrapolation.

This increases the time involved when there are multiple welds.

The plug-in tool was developed in Python by using functions from FOX GUI Toolkit and Abaqus

GUI Toolkit. The FEA software has an inbuilt Python library whose contents vary based on the

software’s version. However, it contains the NumPy library, which is very useful for building a tool

for postprocessing. The tool will act as an extension for postprocessing with extra procedures

where the user is required to provide some inputs about the welds, and the results will be plotted

according to the requirement.

A Plug-in tool is either built by using Really Simple GUI (RSG) Dialog Builder or by using the

GUI Toolkit manual, which involves coding the interface from scratch using Python. The RSG

Dialog Builder is an inbuilt Abaqus function used to create a dialog box that can connect an

interface to the commands written in the kernel. Building the tool using the RSG can make the

tool non-updatable based on the version. Hence, in this project the plug-in tool is built using the

Abaqus GUI Toolkit manual so that it is updatable for future needs.

5.2 User inputs

There are some basic user inputs required for the calculation of hot spot stresses for welded

joints. These inputs are defined by the user in the starting dialog box and are

• Weld geometry, in this case, the weld toe edge

• Face adjacent to the weld toe edge where stress is extracted

• Hot spot stress extrapolation type: Type A and B

40

• Fatigue class, design codes: FAT 90 and 100

• Loading type: Pulsating (zero-max-zero) and alternating

The first input required is the weld, which is taken in the form of an edge. thereby making it usable

in cases where there is no weld geometry as well (shown in Figure 40). The user is essentially

selecting the weld toe where a hot spot exists, and to select multiple welds when the critical location

is unknown, the user must select the last edge of the current weld twice. This informs the program

to create a set and separate the weld, and to create a new set for the edges of the next weld.

Figure 40: Edges of weld in solid model with weld geometry and shell model with no weld geometry

This way of surveying the whole weld instead of assuming a spot is done so that the hot spot stress

trend can be calculated for the whole weld. It can help detect the location for a crack to occur,

which is not usually known during the design phase. The secondary input for edges of the weld is

the number of divisions on each weld. It can be given a zero if no division is required and is

assigned ten by default.

The stresses at the edge of the weld toe are calculated in one direction based on the selected face,

as shown in Figure 40. There can be only one face attached to all the edges of the weld, or each

edge might have a separate face attached so, the tool is made to check if the assigned face is attached

to the edge.

The next step is to select the type of hot spot and the corresponding type of extrapolation for that

hot spot. Type A and Type B hot spot can be selected in the first dialog box, and the interface

makes sure that option from both the types cannot be selected, which is necessary to avoid

semantic errors. The tool at the present state can look at a single type of hot spot weld at one

iteration but can be modified to look at different types of welds at the same iteration in the future.

Finally, the user must specify the fatigue class based on the geometry and loading of the model

being evaluated. Currently, the fatigue classes 100 and 90 are included, but more can be included

based on the model.

5.3 Methodology

The workflow of the fatigue assessment tool is,

• Define the number of welds and their corresponding weld toe (edges) along with the

number of divisions on each weld’s edges

• Determine type of weld geometry; straight weld, slant/oblique weld, and curved weld

41

• Find the normal to the weld toe where the stress read out points exist

• Calculate the coordinate points and create path for stress extraction

• Extract stress and calculate fatigue life based on the extrapolation type and design code

with the given assumptions and delimitations (Heading 1.4).

• Report results in plot with user inputs

5.3.1 Segregation and classification of welds

When the user inputs were provided in the first dialog box, the GUI command (AFXGuiCommand3)

transfers the object information to the kernel, where it will be used for further steps. The kernel

can be considered as the backbone of the tool as it connects all the functions and contains every

step from the beginning to the end.

As of the present state, the important inputs that the kernel receives from the command are the

edge object, which contains the information about all the edges of every welds combined, the face

object, which consists of all the faces selected. In addition to that, the inputs regarding the

extrapolation type, the fatigue design codes, and the loading type are also received by the kernel.

The edge object has all the information about the edges selected, which can be accessed by the

index number. By using the index number, we obtain the vertices of the edge, which directly gives

the coordinates of the weld edge.

--------------------------------------------------------------

Import modules

Start function Hoteval

Get edge object myEdge from AFXGuiCommand

IF length of myEdge > 1 THEN

FOR i in 1 to length of myEdge

Get vertices of current edge

Get coordinates of the vertices

Append into variable Welds at position [t][k]

Add k by 1

IF myEdge index == previous myEdge index

Add t by 1

Append empty array to variable Welds

Position K is zero

End of If statement

End of For loop

Do Coordcheck

Do Postproc_multi

Elif length of edge object == 0

Do Postproc

End of If statement

--------------------------------------------------------------

This Pseudo code snippet shows how the program will segregate welds by checking if an edge is

selected twice. It should be noted that the DO keyword in the code means to perform a function

calling action.

A code in its developing stages is expected to have few bugs or flaws in the functioning, and this

tool had one that was found at the early stages. It was related to the numbering of vertices of an

edge in Abaqus. The FEA software has a convention of assigning a parameter to each edge, which

3 Abaqus GUI Toolkit Reference Manual

42

increases from 0 to 1 from one end to the other. This affects the order in which the user can choose

the edges as the path is created based on the coordinates of the vertices from the selected edge.

Figure 41 shows two examples of how a path is created when the user selects the edges of a weld

in two different orders. The user is selecting the edges in the anti-clockwise direction in the left-

hand side of the picture, which coincides with the parameterization of the vertices from 0 to 1 so

the path is created without any discrepancies. Whereas, in the second case (right-hand side), the

user selects it in the clockwise direction, which does not coincide with the ascending order of

parameterization of the vertices. Therefore, the path starts from the 0th vertex of the smaller edge

and abruptly extends to the 0th vertex of the longer edge and ends at the same point.

Figure 41: Path creation based on order of edge selection

This problem was solved by using the function Coordcheck, which can check the order of the

parametrization of the vertices of an edge and will arrange the vertices in the order of the user’s

selection to avoid the discrepancy. The function also removes the redundant vertex of the

consecutive adjacent edge. This makes the tool insensitive to the order in which the user selects

the edges of a weld, thereby making it more flexible.

5.3.2 Determination of type of weld geometry

After the weld segregation and classification, the post-process function is performed where the

first step is to determine the type of weld geometry. The weld geometry types are differentiated

based on whether the weld edge is straight, curved, or oblique. This is determined and then sent to

another function called Path Creator, which then creates the coordinates for the welds and sends

it in the form of a list for the creation of path.

It should be noted that the limitations of the tool at the present state would be its incapability to

extract stress from a weld lying on a curved surface. This problem can be overcome by projecting

the points onto the surface but requires more time to research the issue. Although the tool is

applicable for the weld geometries mentioned before, it still must be applicable for spline, which

requires more time and study of Bezier curves, control points, and so on.

5.3.2.1 Straight welds

The weld toe is defined by the edge selected and as mentioned before, the tool takes the coordinates

of the vertices present on the edge to the next steps. This is necessary to create a path that requires

43

the start and endpoint coordinates along with the distance from the weld toe and the type of weld

as inputs.

For the first case, which is a straight weld, the vertices coordinate values for a single axis are

supposed to be unequal while the other axes’ values are equal. The program checks for the presence

of a curve or radius by using a software library keyword called getRadius4, which returns the

radius of the edge object in case it is curved. Whenever the weld toe edge is straight, an exception

error is passed by the exception handler (try-except loop from Python) to set the variable to zero

as there is no radius.

--------------------------------------------------------------

Import Pathcreate function as pc

Start function Postproc/postproc_multi

Get coordinates of vertices, radius and face object

Get normal of face object set it to variable gi

Assign to (x1, y1, z1) and (x2, y2, z2)

If radius == 0

If x1 != x2 and y1 == y2 and z1 == z2

If check for y/z normal gi[1/2] is 1 or -1

Set norm as 0/1

Do pc.pathcreatex

...

Check similar If conditions for y and z axis

Do pc.pathcreatey or pc.pathcreatez with norm as 0/1

...

--------------------------------------------------------------

The pseudo-code snippet presents how a straight weld is handled by the program to create the

path. The normal of a selected face which is attached to a weld is obtained by using a software

library keyword called getNormal5, which is specifically for a face object keyword. The normal of

the attached face is checked, and the program will set the variable norm as 0 or 1 based on the

normal direction. This will affect how the path is created by providing the direction at which the

distance from the weld toe will be offset.

Figure 42: Path creation for a quadratic extrapolation of straight weld

4 Abaqus Scripting Reference Manual 5 Abaqus Scripting Reference Manual

44

Figure 42 shows an example of a straight weld that lies on one axis (y-axis) and is perpendicular to

the rest. Here, the coordinate value for the y-axis of points 1 and 2 will not be equal whereas, the

rest will be equal, this will satisfy one of the three if conditions. The normal for the attached face

will be in z-direction which means that the variable gi[2]6 will hold the value 1. This will assign a

value of 1 to the norm and the path is offset to predetermined distances in the x-axis.

5.3.2.2 Slant or Oblique welds

The previous approach cannot be used when the weld toe propagates in a 2-d direction i.e., the

weld toe line lies in the x-z plane but only perpendicular to the y-axis, as shown in Figure 43. This

requires the code to call another function where the corresponding calculation are made to find

the start point, endpoint with the slope of the line, and so on.

Figure 43 : Geometry example for a slanting weld without the weld geometry

The geometry in Figure 43 can be taken as an example for a slant weld where the coordinates of

points 1 and 2 are known. The y-axis coordinate value for the points will be equal while the rest

will not be. This will call a function to create a path in the x-, z- plane with the coordinates and the

distance from the weld toe as the input as the rest of all things required to trace the path are

calculated.

The first step of calculation when a line is slant is finding the slope, which in this case is:

𝑠𝑙𝑜𝑝𝑒,𝑚 =𝑧2 − 𝑧1𝑥2 − 𝑥1

The equation of line is formed with the slope and the constant c which can be found by substituting

the z and x values into the equation and solving for c

𝑧 = 𝑚𝑥 + 𝑐

The first objective is to find the coordinates of the starting point of the offset line of distance, 𝑑 =

𝑛 ∗ 𝑡 where t is the thickness of the weld plate and n is the pre-set distance from the weld toe. To

6 gi is returned in the form of (x,y,z) with values ranging from -1 to 1; gi[2] refers to the index position of z value in the array (0,1,2)

45

find the coordinates, we need the equation of the line perpendicular to the current line which can

be done as follows

𝑧 − 𝑧2 = −1

𝑚(𝑥 − 𝑥2)

And use the distance formula or the equation of circle to form another equation

(𝑥 − 𝑥2)2 + (𝑧 − 𝑧2)

2 = 𝑑2

Now that there are two equations with two variables, it can be solved for x and z

(𝑥 − 𝑥2)2 + (−

1

𝑚(𝑥 − 𝑥2))

2

= 𝑑2

(1 +1

𝑚2) (𝑥 − 𝑥2)

2 = 𝑑2

𝑥 = 𝑥2 ±√𝑑2

1 +1𝑚2

The value of z can be found by plugging in the value of the x in the line equation and solving for

z. Repeating the same steps will give the start point and the endpoint of the offset line of the same

slope of the distance, d, from the weld toe. Now, the offset line can be traced by using the line

equation and the available x values of the offset line. The expected output from the code for a

linear type of extrapolation can be seen.

Figure 44: Path creation for a linear extrapolation of a slant/oblique weld

This path creation shown in Figure 44 is for a linear type extrapolation for a Type A weld where

only two distances from the weld toe are considered and also are divided into 10 equally distanced

points.

46

5.3.2.3 Curved welds

A weld in form of a circular curve presents itself with more challenges as both previous algorithms

are not applicable. The first thing to know about a curve would be its origin or centre coordinates,

which are usually found by solving a couple of equations. The inbuilt software library keyword can

provide the coordinates of the two endpoints of the circular curve, the radius, and the

circumference. Although this seems to be a situation where the values can be easily plugged into

an equation to find the centre, the Python library for Abaqus does not contain all the necessary

libraries for certain functions i.e., one cannot plot separately using Python libraries such as

Matplotlib and SciPy. Depending on the version of the Abaqus, the libraries present in the inbuilt

Python varies along with the Python version.

This appears as a limitation for several upcoming processes but for this case, it would be the

disability of using symbols for solving equations. The process of solving complex equations with

two or more variables required the usage of symbols, and this posed as a challenge as the current

Python version was not able to use symbols in all the versions of Abaqus except for the recent

version7. Keeping the motive of developing a robust tool that is applicable in all versions, the

problem was taken differently, and the centre of the curve was found using just the two endpoint

coordinates and the radius of the curve.

Taking the same geometry used in the previous Section as an example, the coordinates of points 1

and 2 in Figure 45 are known, along with the radius of the curve and the circumference. The code

checks for the radius and sends the user inputs, radius, and the coordinates of the end points to a

function where the calculations occur.

Figure 45: Geometry example of a curved weld without weld geometry

Let the coordinates of the point 1 be (𝑥1, 𝑧1), point 2 (𝑥2, 𝑧2) and the centre of the arc, (𝑥0, 𝑧0). The chord connecting the point 1 and 2 is perpendicular to the bisector from the centre of the arc.

So, by using the point-slope formula and distance formula and solving for the centre coordinates,

we can arrive at the solution. A brief derivation of the problem is shown for reference.

Slope of the line connecting 1 and 2 (line1-2) is 𝑧2−𝑧1

𝑥2−𝑥1 and the perpendicular slope is

𝑥1−𝑥2

𝑧2−𝑧1.

7 3DS SIMULA Abaqus 2020

47

The midpoint of the line 1-2 is given by the midpoint formula (𝑥1+𝑥2

2,𝑧1+𝑧2

2).

The midpoint of line 1-2 and the centre of the arc makes a line and the equation for this line can

be found using point-slope formula.

𝑧0 −𝑧1 + 𝑧22

=𝑥1 − 𝑥2𝑧2 − 𝑧1

(𝑥0 −𝑥1 + 𝑥22

)

As the chord connecting points 1 and 2 and the bisector from the centre of the arc, o, creates a

right-angle triangle as shown in Figure 45, using trigonometry one can arrive at the solution,

tan (|𝜃 − 𝜋|

2) =

2𝑟𝐿𝑙

where 𝑟𝐿 is the distance of the centre from the midpoint of the line 1-2, 𝑙 is the length of the line

connecting points 1 and 2 and 𝜃 is the angle formed by the two arc endpoints as shown in Figure

45.

The distance between the centre of the circle and the midpoint is given by

𝑟𝐿 = √(𝑥0 −𝑥1 + 𝑥22

)2

+ (𝑧0 −𝑧1 + 𝑧22

)2

By substituting 𝑧0 from the point-slope formula and solving for 𝑥0, the formulas for finding the

coordinates of a centre of arc using the end points of an arc and radius was found.

𝑥0 =𝑥1 + 𝑥22

± 𝑧1 + 𝑧22

tan (𝜃 − 𝜋

2)

𝑦0 =𝑧1 + 𝑧22

± 𝑥2 − 𝑥12

tan (𝜃 − 𝜋

2)

After finding the centre of the arc, the starting degree of the arc or the position of point 1 in the

polar coordinate system is found. This gives the starting degree value for the rest of the offset lines.

The total degree of rotation can be obtained from the circumference data, and the divisions are

made on the span of the total rotation in degrees. Figure 46 shows the result of the code with the

curve offset by 0.4t from the weld toe.

Figure 46: Path formation for a curved weld without weld geometry

48

5.3.3 Extraction of stresses

The hot spot stress at the weld toe is found by extrapolating the stresses from the pre-set distances

from the weld toe. Some loss in accuracy can be expected due to nodal averaging and extrapolation

of the nodal stresses. However, the results can be appropriate when the mesh applied is fine

enough. It should be noted that when creating the path using point list, the path is independent of

the mesh formation on the surface and lies fixed in a space irrespective of changes in the model.

So, to avoid errors, only the undeformed model was used while extracting results from the path.

While extracting the stress from the specified path, the required inputs are the points from the

path, a variable indicating the type of results that is to be extracted, which in our case is the max

principal stress, and finally, the type of model output shape, which is undeformed. This changes

slightly when the shell model is evaluated as one needs to specify which normal of the surface is to

be considered for stress extraction. The user is asked to give input regarding the normal for

extraction.

The distinction between solid and shell elements are made automatically by checking the element

type. If the element type is ‘C’ it means continuum stress/displacement element in Abaqus, which

is usually used in three-dimensional solid models, whereas if it is element type ‘S’ then it is a

conventional or continuum shell model which is for displacement or stress calculation in a two-

dimensional or three-dimensional shell model.

Finally, after obtaining the stress results from the path as x-y data, based on the selected fatigue

design class and the extrapolation type the results are calculated and stored as x-y data with respect

to true distance. All hot spot stress values and fatigue values of each point at the weld toe are stored

and are visible from the postprocessor. Modification can be made to be able to segregate the data

to store as a text file in the future.

5.3.4 Reporting the results as plot

The user is given the flexibility to produce several plots in the post-processor module. The results

on hot spot stress along weld lines and the fatigue life along the weld line can be plotted. Although

the fatigue life and stress can be plotted for separate welds, the incapability to create a good

comparison of the fatigue lives of all the welds as bar plots in the same viewport was considered

as a limitation of the Abaqus solver. This was tackled by externally calling Microsoft Excel from

the program.

Microsoft Excel is called from the kernel code after storing the fatigue life of all the welds in a

separate variable, which can be sent to excel to be plotted as a bar plot. This is achieved in Python

by using a library called win32com, which can call Microsoft applications available in the working

environment. It is an obvious requirement for the working environment to have Microsoft Excel,

which is checked and is given the warning to ensure if it is installed in case of its unavailability. This

is required in the case of multiple welds to get the bar plots of fatigue life of all the welds as a

comparison.

49

6 Results and comparison study

The case studies were evaluated for hot spot stress using different choices of extrapolation, fatigue

design classes, and mesh sizes using the tool to compare the manual and automatized process of

evaluation.

6.1 Case study 1

The geometry was tested with different extrapolation types and mesh types for determining the

level of accuracy of the tool under different extrapolation types and to check the mesh

independence, which in turn determines the robustness of the tool.

Case study 1 is a Type A hot spot and, therefore, can be applied with three types of extrapolation:

Linear with coarse mesh, Linear with fine mesh, and quadratic. The results for both manual and

automatized were obtained for a 0.1*t mesh size and the element type being tetrahedral.

Extrapolation type Manual Automatized Error %

Linear with coarse mesh 1620140 1620534 2.4e-4

Linear with fine mesh 1517500 1529985 0.0082

Quadratic 1470000 1450797 0.013 Table 18: Comparison of fatigue life from manual and automatized process for case study 1

It can be seen in Table 18 that the results from the automatized process agree well with the manual

extrapolation techniques even though the path has been created based on the input coordinates

and doesn’t necessarily coincide with the mesh nodes. However, it must be checked on how the

mesh size influences the results and how much variance it causes, which might give a limitation on

the tool. Hence, five sizes of mesh were tested using the automatized process including a manual

extrapolation from 10 points on a 0.1*t mesh size to check the accuracy of the results.

Figure 47: Mesh sensitivity analysis with different element sizes obtained from case study 1

50

The graph in Figure 47 shows how the mesh size affects the results obtained from the analysis. It

can be noted that the results start to converge at 0.4*t, which is the suggested mesh size for a hot

spot evaluation by IIW [4]. The red square markers on the graph represent the location of the

lowest fatigue life because of the high hot spot stress value obtained in the respective element size

iteration. This seems to shift location on the 0.5*t iteration suggesting inaccuracy. It should be

noted that the hot spot stress comparison graph is the exact mirror of the fatigue life graph in the

x-axis perspective.

Figure 48: Result plot annotation with weld detail and fatigue life in case study – 1

The result for a quadratic extrapolation of the case study with 0.1*t mesh size is shown in Figure

48. Annotation of the weld detail with fatigue life at that point is given in the viewport to show the

point of high hot spot stress, which suggests the possible point of crack propagation. This is helpful

when there are multiple edges on a weld.

6.2 Case Study 2

The first case study gave us the necessary knowledge for conducting a reasonable evaluation for a

single weld with one weld edge, whereas this case study will extend that knowledge to applying for

cases with multiple edges on a single weld and applying for different types of hot spots. The hot

spot stress from manual and automatized processes for single weld toe considered for the manual

was validated at the start.

The analysis results were obtained with hexahedral brick elements, and only the edge where the

manual results were taken was evaluated using the tool as a weld with a single weld toe. The results

for three extrapolation types were taken and compared with the manual extrapolation results in

Table 19.

51

Extrapolation type Manual Automatized Error %

Linear with coarse mesh 14220 12423 0.126

Linear with fine mesh 12870 11172 0.131

Quadratic 11790 9974 0.154 Table 19: Comparison of fatigue life from manual and automatized process for case study 2

The next evaluation was done for a single weld with multiple weld toe edges using quadratic

extrapolation for which the continuous path was created as shown in Figure 49. This evaluation

gave us a thorough perspective of the welds. It can be seen in the figure that the annotation is on

the same side of the weld toe that was evaluated on the previous iteration with single edge criteria,

which suggests an overall evaluation of the weld geometry is preferred for a reasonable output

from the assessment.

Figure 49: Continuous path creation for multiple weld edges and fatigue life details

The final evaluation for this model was for the Type B hot spots at the top of the weld as marked

by red lines in Figure 50. The evaluation was done for fine and coarse mesh and compared in Table

20.

Figure 50: Type B welds in the case study 2 weld geometry

Extrapolation type Manual Automatized Error %

Coarse mesh 37540 37447 0.002

Fine mesh 47843 47156 0.014 Table 20: Difference between results from automatized and manual Type B hot spot evaluation in case study 2

52

The evaluation of this case study gave a proof that the tool can work for welds with multiple

edges/weld toes and for a Type B hotspot meshed coarsely or finely. The tool in its current state

can calculate the fatigue life for a weld or multiple welds belonging to a single type of hot spot. The

freedom of choosing a different type of hot spot for different welds in the same iteration must be

included in the future for certain cases.

6.3 Case study 3

The complexity of weld geometry in this case study will help determine if the tool is robust enough

to evaluate welds with both straight and curved edge geometry. The analysis was carried out with

the same elemental properties except for some refinement near the weld area as the tool shows

acceptable accuracy with 0.3*t or smaller element size.

The original geometry that was analysed in Section 3.3 was not applicable for evaluation because

of the limitation of the tool not being able to create a path on a curved surface. However, with

future modifications and improvements, this problem might be overcome by projecting the path

points onto the surface. For now, the existing geometry was modified by extending the flat surface

such that stress readout points are accessible by the tool. The first iteration was just for the weld

shown in Figure 51.

Figure 51: First iteration of case study 3 using the tool. Weld_1_path_04 is shown in the figure

In the results, a shift in the position of high hot spot stress when compared to what was obtained

in Section 3.3 is seen as shown in Figure 51 with the annotation and arrow. The point of high stress

was expected to be in the region of top curved weld marked with a yellow rectangle as suggested

by the reference study but, due to the geometrical changes, has shifted to the top corner of the

weld.

To compare with the manual linear extrapolation method applied to the original geometry, a linear

extrapolation was implemented with the tool on the modified geometry. The results obtained from

both manual and automatized in the yellow rectangle region is presented in Table 21. It should be

noted that the comparison, in this case, is done between the original geometry used in Section 3.3

and the modified geometry, but the difference is less.

53

Type Fatigue life (cycles)

Manual (original geometry) 52720

Automatized (modified geometry) 53850 Table 21: Comparison of results from manual and automatized process for case study 3

Figure 52: Hot spot stress comparison between automatized and manual extraction

The graph in Figure 52 shows the comparison of linear extrapolation from manual and automatized

in the modified geometry where the stress peak obtained in the top weld. The graph in Figure 53

is a comparison of the fatigue.

Figure 53: Fatigue life comparison between automatized and reference method

The next iteration was done for both welds on the geometry and the results are obtained, as shown

in Figure 54. An option to choose between stress and fatigue plots in the post-processing

visualization module was added. The tool showed that it works for a curved weld and can handle

multiple welds with ease. The amount of work done for a hot spot evaluation during post-

processing was substantially reduced by using the tool automatization.

54

Figure 54: Second iteration with evaluation of both welds

When there are multiple welds during an evaluation, the tool automatically gives a comparison of

the fatigue life of all the welds as a bar plot in Excel. Figure 55 shows the bar plot automatically

plotted at the last step of the evaluation using the tool. This can be used to check which welds go

beneath a certain amount of expected fatigue life and can give an overall perspective of the model.

Figure 55: Welds comparative chart for case study 3

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

l1 r1

Fati

gue

Lif

e

Weld number

Welds Fatigue Life Comparison Chart

Series1

55

7 Conclusions and summary

Several conclusions were drawn from the theory and FEA and are presented in this report. A

summary of points highlighted during the making of the plug-in tool is also included.

7.1 Conclusions – Theory

The theoretical study on fatigue assessment of welds gave a wide variety of methods to examine

and understand the procedures involved in them to arrive at the results. This preliminary

comparison revealed several important points that helped filter the methods before moving on to

the next step. The Nominal stress method was eliminated first because of its incapability to work

with complex geometries and loading conditions.

Structural stress methods, SS, are continuously improving and are highly considered when FEM is

involved because of their capability to work with complex geometries. These methods consider

membrane and bending stresses eliminating the non-linear peak stress. This results in a relatively

less realistic fatigue strength value. In addition to that, most of these methods are applied only for

a failure occurring at the weld toe. The SS methods applicable for failure at weld root are reserved

for future work as it requires more research.

The study concluded that the effective notch stress method, ENS, gave the most accurate results

of all the methods according to several papers. This method takes the stress raiser due to the local

notch into account, unlike the SS methods. Regardless of the geometry or loading conditions, the

ENS method requires only one S-N curve. These are some of the desirable properties of the

method.

7.2 Conclusions – FEA

Three case studies were selected from the literature for the implementation of the methods. The

process of implementation gave a basic understanding of the procedures involved in each of them.

The results and the trend observed from these methods during analysis coincided with their

corresponding theory from reference papers. This part of the project resulted in the ranking of

methods based on selected criteria or key performance indexes, KPIs.

The hot spot method showed sensitivity towards the mesh size near the vicinity of weld toe. It

gave good results when the mesh was very fine (<0.4*t). Fatigue classes are available for all types

of geometries and loadings, and there were no difficulties faced while finding one for the selected

case studies. An average error of 19% was observed for the hot spot method when compared with

results from ENS, which was assumed to give the most accurate results out of all methods.

The methods TTWT and Dongs gave results with good accuracy for all the case studies. The results

are mesh-sensitive for solid elements but are appropriate at 0.4 t from the weld toe, which agrees

with [14]. When the weld was inclined at an angle to the global coordinate system, the local

coordinate system was used to obtain stress normal to the cross-section. Both methods consider

the thickness effect very well and require only one master S-N curve, unlike the hot spot method.

The 1 mm method gave good results only when there was tensile loading and showed high

deviations when bending stress is dominant, thereby agreeing with the conclusions in [13]. It also

required high mesh density in the vicinity of the weld toe, which increased computation time based

56

on the weld geometry. The postprocessing time was less as the structural stress is obtained directly

from the viewport.

ENS method gave an accurate and conservative fatigue life values for all the case studies. The

analysis results from this project for case studies 1 and 3 agreed with the results from the reference

paper [21] and [24]. This gave the results from this project credibility and when combined with the

conclusion from theory, it bolstered the decision of using the results from this method as the

reference value for comparing with other methods.

The FEA concluded with hot spot method being selected as the method to move forward with for

implementation as the plug-in tool. The reasons for that are:

• Applicable for both solid and shell models.

• Multiple welds can be considered simultaneously because of low computational time

• Easy pre-processing and post-processing as it required less partitioning during the former

and as stresses can be read directly from the results in the latter.

• FAT classes are available for all geometries and loading conditions

• No need for assuming critical spot as the whole weld can be evaluated

• No need for sub modelling or creating local coordinate system

The hot spot method gave less accurate fatigue life values compared to other methods but was

consistent in accuracy for all cases. This trade-off between accuracy and computational time/effort

was found to be inevitable but, the collective compromise involved in the hot spot method was

relatively low, which was the motivation behind the conclusion derived from the points.

7.3 Summary – Plug-in tool for weld fatigue assessment

The project resulted in a fully developed GUI- plugin tool capable of handling multiple welds in a

detailed manner with various options and flexibility given to the user. The fatigue assessment tool

is currently written using Python for Abaqus and enables fatigue assessment based on design codes

from IIW recommendation.

This tool for fatigue life assessment is an advanced add-on for post-processing that is capable of

substantially reducing the workload, time taken, and can be extended to further capabilities based

on the necessity. It is capable of assessing a single weld with the capability to give a detailed stress

trend throughout the weld length to assessing multiple welds in the same manner with an additional

comparison of fatigue life of all the welds as an Excel sheet chart. It is applicable for both shell and

solid models for any shape of weld geometry regardless of the orientation of it to the global

coordinate axis but only with a limitation of applicability for welds attached to a flat surface.

One of the main goals of this project was to build a plugin GUI that can be updated and changed

in the future, which can suit specific requirements of a project. Building the interface from the

scratch gave a clear idea of how the software connects the interface to the kernel code where the

calculations happen. This can be used by any engineer with basic knowledge in Python and Abaqus

classes while trying to modify the code to develop a plug-in for a similar method or while updating

the existing code. This program can act as the base for building a more robust tool applicable for

all kinds of welds on all surfaces and to make it assess fatigue due to failure at the weld root.

Summary from the analysis of the case studies,

57

• Mesh dependency was not totally out of the equation. There was a minimum mesh size

requirement near the weld for acceptable accuracy. However, partitioning the surface

according to the extrapolation type was not necessary.

• The tool can handle straight welds oriented parallel to single axis, oblique welds inclined at

an angle to two global axes and circular curved welds perpendicular to a single global axis.

This implies one limitation, namely that, the weld should be lying in a flat surface.

• To get a good representation of stress trend along the weld, the provision of giving

divisions on each edge of weld was included.

• Applicable to both Type A and B Hot spot welds but only single type of welds can be

evaluated together.

• To represent the critical spot on a weld, the highest hot spot stress location is marked by

using an arrow and an annotation.

This plug-in can be made more robust and more automatized with updates and has the

potential to increase work-flow efficiency in a substantial manner.

58

8 Recommendations

The execution of the tool on the case studies gave a clear idea of what was missed out while building

the tool and what could be modified to obtain better results and make work-flow easier. Some bugs

or flaws exist in a newly built tool, which can be optimized in several ways. But due to limited

experience in the language and limited time, the optimization process was skipped. With more

analysis on different types of models and geometries, one can search for errors within the tool.

This can be solved easily as the code is built clearly with separate functions for different aspects

making it clear where the error might be present.

But with regards to general functionality some of the possible improvements for the tool would

be,

• To be able to extract stresses from a curved and oblique surface getting it one step closer

to a robust tool

• More fatigue design codes from different recommendations can be included for various

industrial applications

• Multiaxial stress states should be included for evaluation of complex structures

• To be able to evaluate different types of hot spots simultaneously.

• Decrease the number of user inputs in between the first dialog box and the results

reporting; to automatize all the possible processes.

• To be able to find the normal for a curved or slant weld automatically.

• To make it applicable for more types of welds geometries i.e., spline

• The tool should be able to find which normal of a shell surface to extract stress from,

automatically.

Further research on other methods and all the scope for developments will results in a much

more efficient, robust, and advanced tool capable of providing results with improved accuracy.

59

References

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Welded Steel Structures,” Advances in Civil Engineering, vol. 2018, p. 16, 2018.

[2] D. Radaj, C. M. Sonsino and W. Fricke, “Fatigue Assessment of Welded Joints by Local

Approaches,” vol. 2nd edition, 2006.

[3] W. Fricke, “Recent developments and future challenges in fatigue strength assessment of

welded joints,” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical

Engineering Science, 229(7),, vol. 229, no. 7, 2015.

[4] A. F. Hobbacher, “Recommendations for Fatigue Design of Welded Joints and

Components,” IIW collection, 2016.

[5] J. Schijve, Fatigue of Structures and Materials, Springer, Dordrecht, 2009.

[6] M. Aygül, Fatigue evaluation of welded details - using finite element method, Gothenburg:

Chalmers University of Technology, 2013.

[7] S. Bakhtiari, Fatigue behaviour of welded components undervariable amplitude loading,

KTH Industrial Engineering and Management, Machine Design, 2013.

[8] M. H. Kim, . S. M. Kim , J. M. Lee and S. W. Kang, “Fatigue Assessment of Ship Structures

using Hot Spot Stress and Structural Stress Approaches with Experimental Validation,”

2008.

[9] R. K. Goyal, A stress analysis method for fatigue life prediction of welded structures,

UWSpace, 2015.

[10] H. Erwin and O. Rainer, “Fatigue investigation of higher strength structural steels in

notched and in welded condition,” 1974.

[11] E. Subramanian, Estimation of fatigue life of welded joint using vibration-fatigue

computational model, University of Manitoba, Department of Mechanical and

Manufacturing Engineering, 2015.

[12] I. Poutiainen, P. Tanskanen and G. Marquis, “"Finite element methods for structural hot

spot stress determination - A comparison of procedures",” International Journal of Fatigue ,

vol. 26, no. 11, 2004.

[13] G. Li and Y. Wu, “A study of the thickness effect in fatigue design using the hot spot stress

method,” 2010.

[14] M. Heshmati, M. Al-Emrani and B. Edlund, “Fatigue Assessment of Weld Terminations in

Welded Cover-Plate Details,” Oslo, Norway, 2012.

[15] H. Remes and W. Fricke, “Influencing factors on fatigue strength of welded thin plates

based on structural stress assessment,” Weld World 58, p. 915–923, 2014.

60

[16] I. Poutiainen, “A modified structural stress method for fatigue assessment of welded

structures,” 2006.

[17] W. Fricke and O. Feltz, “"Fatigue Tests and Numerical Analyses of Partial-Load and Full-

Load Carrying Fillet Welds at Cover Plates and Lap Joints",” Weld World 54, p. R225–R233,

2010.

[18] Y. Kim, J.-S. Oh and S.-H. Jeon, “Novel hot spot stress calculations for welded joints using

3D solid finite elements,” Marine Structures, vol. 44, pp. 1-18, 2015.

[19] D. E. Djavit and S. Erik, Fatigue failure analysis of fillet welded joints used in offshore

structures, Chalmers University of Technology Department of Shipping and Marine

Technology, 2013.

[20] M. R. Pradana, X. Qian and S. Swaddiwudhipong, “A Revisit to the Effective Notch Stress

S-N Curve for Welded Circular Hollow Section Joints,” 2016.

[21] A. Göransson, Fatigue life analysis of weld ends, Linköping University, Department of

Management and Engineering, Division of Solid Mechanics, 2012.

[22] J.-M. Lee, J.-K. Seo, M.-H. Kim, S.-B. Shin, M.-S. Han, J.-S. Park and M. Mahendran,

“Comparison of hot spot stress evaluation methods for welded structures,” International

Journal of Naval Architecture and Ocean Engineering, vol. 2, no. 4, pp. 200-210, 2010.

[23] H. Kyuba and P. Dong, “Equilibrium-equivalent structural stress approach to fatigue

analysis of a rectangular hollow section joint,” International Journal of Fatigue, vol. 27, no. 1,

pp. 85-94, 2005.

[24] W. Fricke, “Round-Robin Study on Stress Analysis for the Effective Notch Stress

Approach,” Weld World 51, p. 68–79, 2007.

[25] W. Fricke, A. Kahl and R. H. Paetzold, “Fatigue Assessment of Root Cracking of Fillet

Welds Subject to Throat Bending using the Structural Stress Approach,” Weld World 50, p.

64–74, 2006.

61

Appendix A – Method scoring matrix

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62

Appendix B – Workflow summary

63

Appendix C – Weld fatigue assessment tool interface

64

Appendix D – Structural stress approaches for further scope

Here are some structural stress methods with a brief introduction that can be considered for future

implementation as a plug-in tool.

Equilibrium-equivalent Structural stress (𝑬𝟐𝑺𝟐 ) method

This method is like the through thickness linearization, but the structural stresses are calculated

along the weld line. The direction at which stress is calculated is perpendicular to the theoretical

plane of crack propagation along a weld line. The stress distribution over a plate thickness is non-

linear near the notch tip or weld toe due to presence of non-linear peak stress. But upon integration

through the thickness by considering self-equilibrium condition, the non-linear peak stress is

cancelled out thus the remaining bending stress, 𝜎𝑚 and membrane stress, 𝜎𝑏 contribute to the

structural stress of the weld [23].

The equilibrium condition excluding the non-linear stress peak is given by the equations below

where 𝜎𝑥(𝑦) is the stress distribution and 𝑦 corresponds to a point in thickness axis direction:

𝜎𝑚 =1

𝑡∫ 𝜎𝑥(𝑦)𝑑𝑦𝑡

0

𝜎𝑏 =6

𝑡2 ∫ 𝜎𝑥(𝑦) ∙ (

𝑡

2− 𝑦) 𝑑𝑦

𝑡

0

𝜎𝑆 = 𝜎𝑚 + 𝜎𝑏

The 𝐸2𝑆2 is a stress index that is obtained after calculations of the results from an FEA by

considering equilibrium conditions at the weld toe. The calculated 𝐸2𝑆2 is then plugged into a

master S-N curve to find the fatigue life of the model. This method yields the best results for shell

or plate element models and only requires the nodal forces due to elements obtained from the

command NFORC in ABAQUS.

Firstly, the nodal forces obtained with respect to global coordinate system is converted to local

coordinate system [23]. This nodal force, 𝐹𝑥 is further used to calculate the line force, 𝑓𝑥 and line

moment, 𝑚𝑦 using the shape function matrix where the variables 𝑙1,𝑙2…𝑙𝑛−1 are the length of the

corresponding ith (i = 1 to n-1) element along the weld line. The inverse of the shape matrix is

found and multiplied to the nodal force matrix to find the line force. The shape matrix and the

procedures followed are same for finding the line moment as well.

{

𝐹1𝐹2𝐹3⋮⋮𝐹𝑛}

=

[ 𝑙13

𝑙16

0 0 ⋯ 0

𝑙16

𝑙1 + 𝑙23

𝑙26

0 ⋯ 0

0𝑙26

𝑙2 + 𝑙33

𝑙36

0 0

0 0 ⋱ ⋱ ⋱ 0

⋮ ⋱ ⋱ ⋱𝑙𝑛−2 + 𝑙𝑛−1

3

𝑙𝑛−16

0 ⋯ ⋯ 0𝑙𝑛−16

𝑙𝑛−13 ]

{

𝑓1𝑓2𝑓3⋮⋮𝑓𝑛}

65

The line force and line moments are further divided by the thickness and section modulus to

obtain the bending stress and membrane stress which gives the structural stress when combined:

𝜎𝑠 = 𝜎𝑚 + 𝜎𝑏 =𝑓𝑥′

𝑡+6𝑚𝑦′

𝑡2

The equivalent 𝐸2𝑆2 parameter, 𝑆𝑠 can be calculated by substituting the structural stress into:

𝑆𝑠 =𝜎𝑠

𝑡2−𝑚′

2𝑚′ ∙ 𝐼(𝑟)1𝑚′

where 𝑡 is plate thickness, 𝑚′ is the slope and 𝐼(𝑟) is a dimensionless function of bending ratio, 𝑟

that varies with the type of element and loading mode used in the analysis, and is generally given

by:

𝐼(𝑟) = 0.294𝑟2 + 0.846𝑟 + 24.815

𝑟 =𝜎𝑏

𝜎𝑏 + 𝜎𝑚

The fatigue life 𝑁 can now be found by using the equation

𝑙𝑜𝑔𝑁 = 𝐵. 𝑙𝑜𝑔∆𝑆𝑆 + 𝐴,

where A and B are constants given in the table below.

Statistical basis A B

Mean curve 12.185448 -3.055853

Upper 95% prediction 12.9285869

Lower 95% Prediction 11.4423091

Upper 99% prediction 13.166404

Lower 99% prediction 11.24044912

Structural stress at the weld throat for root failure

Wolfgang Fricke (2006) [25] proposed methods based on linearization of stress through thickness

for fillet welds subjected to throat bending where the structural stress acting along a weld leg must

be determined. The linearized structural stress across the weld leg can be obtained through several

ways based on the type of model being used:

• Linearization of stresses or forces directly in the leg section

• Linearization of stresses or forces in the throat section to the leg section

• Linearization of stresses or forces in the attached plate to the leg section

Linearization of stresses or forces in the weld leg section utilizes from the weld leg of the base plate

which is welded to the attached plate. The stress distribution or nodal forces from the weld leg

section is applied to the formula given below to find the structural stress.

𝜎𝑚,𝑤 = (1

𝜆)∫ 𝜎(𝑧)𝑑𝑧; 𝜎𝑏,𝑤 = (

6

𝜆2)∫ 𝜎(𝑧) ((

𝜆

2) − 𝑧)𝑑𝑧

𝜆

0

𝜆

0

66

𝜎𝑠,𝑤 = 𝜎𝑏,𝑤 + 𝜎𝑚,𝑤

where 𝜎(𝑧) is the stress normal to leg section, 𝑧 is the coordinate along the weld leg line, 𝜆 is the

leg length, 𝜎𝑚,𝑤 is the membrane portion of structural stress in weld leg section and, 𝜎𝑏,𝑤 is the

bending portion of structural stress in weld leg section

When nodal forces are used, the formula becomes

𝜎𝑚,𝑤 = (1

𝑏 ∙ 𝜆)∑𝑃𝑥,𝑖 ; 𝜎𝑏,𝑤 = (

6

𝑏 ∙ 𝜆2) ∑[𝑃𝑥,𝑖 ((

𝜆

2) − 𝑍𝑖)]

where 𝑃𝑥,𝑖 is the nodal force perpendicular to the weld leg section, 𝑍𝑖 is the nodal point

coordinate and, 𝑏 is the distance of the nodal position in weld direction

Linearization of stress at weld throat to weld leg section takes place in the mid-plane between two

weld leg or otherwise known as weld throat. Weld throat is defined by the smallest distance between

the weld root and the surface of the weld. The corresponding perpendicular to the mentioned

section will be used in the formula to find the structural stress at the throat to weld leg section:

𝜎𝑚,𝑤 = (1

𝜆)∫ 𝜎⊥ ∙ 𝑐𝑜𝑠𝜃 + 𝜏⊥𝑠𝑖𝑛𝜃 𝑑𝑠 ; 𝜎𝑏,𝑤 = (

6

𝜆2)∫ [𝜎⊥ ((

𝜆

2𝑐𝑜𝑠𝜃) − 𝑠) + 𝜏⊥

𝜆

2𝑠𝑖𝑛𝜃]𝑑𝑠

𝑎

0

𝑎

0

𝜏𝑤 = (1

𝜆) ∫ 𝜎⊥ ∙ 𝑠𝑖𝑛𝜃 + 𝜏⊥𝑐𝑜𝑠𝜃 𝑑𝑠

𝑎

0

where, 𝑎 is the throat thickness, 𝑠 is the coordinate along the throat section and 𝜃 is the weld

flank angle. When using nodal force for finding stress the formula is:

𝜎𝑚,𝑤 = (1

𝑏 ∙ 𝜆)∑𝑃𝑥,𝑖 ; 𝜎𝑏,𝑤 = (

6

𝑏 ∙ 𝜆2) ∑[𝑃𝑥,𝑖 ((

𝜆

2) − 𝑍𝑖) + 𝑃𝑧,𝑖 ∙ 𝑥𝑖]

𝜏𝑤 = (1

𝑏 ∙ 𝜆)∑𝑃𝑧,𝑖

where 𝑃𝑥,𝑖, 𝑃𝑧,𝑖 , 𝑥 and 𝑧 are nodal x-force and z-force at (𝑥𝑖, 𝑧𝑖) where 𝑥 and 𝑧 are coordinates.

Linearization of stress using stress or force in the attached plate are categorized into two based

on whether the attached plate is perpendicular or parallel to the main plate.

The formulas for the two types:

a) Attached plate perpendicular to main plate

𝜎𝑚,𝑤 = 𝜎𝑚 (𝑡

𝜆)

𝜎𝑏,𝑤 = 𝜎𝑚 [3 (𝑡

𝜆) + 6 (

𝑡

𝜆2)(𝑔 − (

𝑡

2))] − 𝜎𝑏 [(

𝑡2

𝜆2) − 6𝜏 (

𝑡 ∙ 𝛿

𝜆2)]

𝜏𝑤 = 𝜏𝑡

𝜆

b) Attached plate parallel to main plate

67

𝜎𝑚,𝑤 = 𝜏𝑡

𝜆

𝜎𝑏,𝑤 = −3𝜎𝑚𝑡2

𝜆2+ 𝜎𝑏

𝑡2

𝜆2+ 6𝜏

𝑡

𝜆((𝛿

𝜆) + (

1

2))

𝜏𝑤 = 𝜎𝑚 (𝑡

𝜆)