Multi-axial fatigue strengthassessment of a turret in a FPSO
Rick Donk
Faculty 3ME; Section Ship and Offshore Structures
Delft University of Technology
Supervisor
Dr.ir. J.H. den Besten, TU DelftDr.ir. J.J. van der Cammen, Bluewater Energy Services
In partial fulfillment of the requirements for the degree of
Master of Science in Offshore Dredging Engineering
October 21, 2019
Acknowledgements
This thesis will present the final graduation research assignment, where mul-
tiaxial fatigue strength of welded details within the turret of a FPSO are
assessed. This assignment is carried out for Bluewater Energy services, a
company that is specialized in turret designs.
Turret structures within FPSO’s are subjected to a variety of repeated loads
during their service live, therefore fatigue is a governing limit state in turret
structural design. Due to the complexity of these structures and their load-
ing, current fatigue design approaches can be non conservative for welded
details subjected to a multiaxial stress state. Within this research these
welded joints are identified and selected for proper multiaxial fatigue evalu-
ation.
During the last few months a lot of knowledge is gained on this topic, there-
fore I would also like to thank Dr.ir. J.H. den Besten, Ir P.S. van Lieshout
and Prof.dr.ir. M.L. Kaminski for their guidance and supervision.
Furthermore, I would like to thank all Bluewater Energy Services engineers
who help me during this assignment, the section head of the structural de-
partment Ir. J. van Nielen who made this graduation research possible and
especially Dr.ir. J.J. van der Cammen who was my daily supervisor for his
feedback and support during this process.
Last but not least I would like to thank my family who supported me during
this process. This process wasn’t always smooth sailing, but together with
the help of my family I’ve pushed the tides to be in my favor.
Rick Donk 21-10-2019
Abstract
Keywords: Multiaxial fatigue, welded joints, out-of-phase, welded struc-
tures, FPSO, turret, maximum load path, Path-Dependent maximum range,
non-conservative, arc-welded joints, service life, cycle counting.
Turret structures within FPSO’s are subjected to a variety of repeated loads,
due to the harsh environment they operate in during their service live, mean-
ing that fatigue is a governing limit state in turret structural design. Turret
structural components are connected by arc-welded joints which are consid-
ered particularly susceptible to fatigue damage. Due to the complexity of
the structure and its loading, welded details may be subjected to a multi-
axial stress state. Currently fatigue design of turret structures is predomi-
nantly based on a uniaxial fatigue criteria assuming governing mode I (i.e
normal stresses). This design approach can be non-conservative for welded
details subjected to a multiaxial stress state, especially when these are non-
proportional (i.e. out of phase). The estimation of multiaxial fatigue live for
details subjected to a multiaxial stress state is still an extremely complex
task. There is still a discrepancy in obtained multiaxial fatigue live between
different design rules (i.e. as presented in ISSC), meaning that future work
on this topic is required.
Due to the size and complexity of turret structures, identification of welded
details (i.e. in the order of hundreds) subjected to a multiaxial (non)-
proportional stress state is a rather complicated and laborious task. This
thesis proposes a new screening method that identifies sensitive locations
where multiaxiality occurs, either geometry or loading induced. Component
stresses (i.e. Mode I and III) are determined from finite element models using
a mesh-insensitive structural stress method. The stress state (i.e. multiax-
iality and proportionality) of these stress components is determined using
the parameters of an ellipse that encloses the stress data (i.e. component
stresses) in 2-dimensional stress space. Making this a practical and efficient
method to identify sensitive locations within the turret where multiaxiality
occurs.
For the multiaxial fatigue damage calculations of welded details subjected
to a non-proportional multiaxial stress state, the accumulative Moment of
Load Path (MLP) concept is used. Within this concept the multiaxial fa-
tigue damage for any given non-proportional load path is assumed to consist
of two parts. The first part can be considered damage due to the effective
stress range Δσe (i.e. stress due to direct path), and the second is the ”load-
path non-proportionality” fatigue damage due to excursion of the reference
load path. By implementing the MLP-based method as part of the path-
dependent maximum range (PRMD) cycle counting procedure, half cycles
and their corresponding MLP-based equivalent stresses ranges are computed.
Given the MLP-based stress distributions from PDMR cycle counting, the
well know Palmgren-Minor rule is used to determine the accumulation of
fatigue damage considering a proper fatigue resistance curve.
By implementing both the screening and the proposed multiaxial fatigue
damage method onto a relatively simple Tube-to-Flange connection, a com-
parison study is used to determine whether the screening method is capable
of identifying sensitive locations that may be susceptible to multiaxial fa-
tigue. For five considered load scenarios, the screening method showed to
give relatively similar results with respect to the actual fatigue damage cal-
culation, making it a suitable structural screening method. Using the same
Tube-to-Flange connection the multiaxial fatigue damage is calculated based
on DNVGL and compared with those calculated using the MLP-based con-
cept. For uniaxial proportional loading scenarios similar fatigue damages are
observed, however for the non-proportional load scenarios the MLP-based
method gives significantly higher fatigue damage results w.r.t DNVGL.
Performing structural screening on complex structural systems like the turret
considering each load signal during its service live would be very computa-
tionally expensive. Therefore five load scenarios are considered to be suffi-
cient to perform the structural screening. For this thesis a certain domain
of the turret of the Aoka Mizu vessel is screened using the defined screening
load scenarios. Within the scope (i.e. evaluated domain) details resulting in
relative high fatigue damage due to high levels of non-proportionality are not
encountered. Even Though details exist with high non-proportionality fac-
tors the stress ranges of these details are usually relatively small compared
to details subjected to a dominant uni-axial stress state.
Contents
1 Introduction 1
1.1 FPSO fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Problem description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Scope of Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Thesis Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Literature review 10
2.1 Multi-axial fatigue according to codes guidelines and regulations . . . . 11
2.1.1 Multiaxial fatigue from Eurocode 3 . . . . . . . . . . . . . . . . . 11
2.1.2 Multiaxial fatigue from IIW . . . . . . . . . . . . . . . . . . . . . 12
2.1.3 Multiaxial fatigue from DNVGL-C203 . . . . . . . . . . . . . . . 12
2.2 Multi-axial fatigue according to structural stress concept . . . . . . . . . 13
2.2.1 Stress-based calculation methods . . . . . . . . . . . . . . . . . . 13
2.2.1.1 Nominal stress . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.1.2 Hot spot stress . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.1.3 Traction based structural stress . . . . . . . . . . . . . 15
2.2.2 Load path stress based representation . . . . . . . . . . . . . . . 18
2.3 Fatigue Life time Estimation . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.1 Cycle counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.2 Fatigue damage accumulation . . . . . . . . . . . . . . . . . . . . 19
3 Structural Screening 21
3.1 Structural stress analysis of weld seams . . . . . . . . . . . . . . . . . . 22
3.1.1 Structural stress tube-to-flange connection . . . . . . . . . . . . . 23
v
CONTENTS
3.1.1.1 finite element model of the tube-to-flange connection . 23
3.1.1.2 Global nodal forces and moments from weld seams . . . 24
3.1.1.3 Local nodal forces and moments at intersection . . . . . 25
3.1.1.4 Line force and moments at intersection . . . . . . . . . 28
3.2 Proportionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.1 Proportional loading . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2.2 Non-proportional loading . . . . . . . . . . . . . . . . . . . . . . 30
3.3 Level of stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.1 Minimum volume enclosed ellipse . . . . . . . . . . . . . . . . . . 32
3.3.2 Formulation of the level of stress . . . . . . . . . . . . . . . . . . 33
3.4 Screening tube-to-flange model . . . . . . . . . . . . . . . . . . . . . . . 34
3.5 Screening turret structure of the AM FPSO . . . . . . . . . . . . . . . . 37
3.5.1 Finite element modelling of the turret structure . . . . . . . . . . 37
3.5.2 Loads considered for turret screening . . . . . . . . . . . . . . . . 38
3.5.3 Intersections screened within the specified turret domain . . . . . 40
3.5.4 Results Multiaxial Fatigue screening of the Turret . . . . . . . . 41
4 Multiaxial fatigue damage of welded details 44
4.1 Path Dependent Maximum Range cycle counting . . . . . . . . . . . . . 45
4.1.1 PDMR cycle counting procedure . . . . . . . . . . . . . . . . . . 45
4.2 Non-proportional multiaxial loading . . . . . . . . . . . . . . . . . . . . 50
4.2.1 Moment of load path (MLP) concept . . . . . . . . . . . . . . . . 50
4.3 Fatigue resistance curves . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.3.1 Test specimen Setup and Loading . . . . . . . . . . . . . . . . . 53
4.3.2 Data correlation pure Mode I and Mode III . . . . . . . . . . . . 54
4.3.3 Data correlation with mean stress correction . . . . . . . . . . . 56
4.3.4 Data correlation for all loading scenarios . . . . . . . . . . . . . . 58
4.4 Results Multiaxial fatigue damage . . . . . . . . . . . . . . . . . . . . . 59
4.4.1 Multiaxial fatigue damage tube-to-flange model . . . . . . . . . . 60
4.4.2 Multiaxial fatigue damage selected turret details . . . . . . . . . 62
vi
CONTENTS
5 Screening versus Multiaxial fatigue damage 64
5.1 Validation of the structural screening tool . . . . . . . . . . . . . . . . . 65
5.2 Fatigue damage comparison study DNVGL vs MLP-based . . . . . . . . 66
5.2.1 Multiaxial fatigue damage calculations based on DNVGL . . . . 66
5.2.2 Comparison study results and conclusions . . . . . . . . . . . . . 69
6 Conclusions 72
6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
A Proposal final research assignment BES 78
B Verification study 80
B.1 Mesh sensitivity check according to the structural stress method . . . . 80
B.2 PDMR cycle counting algorithm verification . . . . . . . . . . . . . . . . 81
B.3 Fatigue resistance curve for the SLP-based equivalent stress . . . . . . . 83
C Fatigue loading used for structural screening 85
C.0.1 Fatigue loads based on worst case loading direction . . . . . . . . 85
C.0.1.1 Histogram of the buoy and turret fatigue loads . . . . . 86
C.0.1.2 Screening loads . . . . . . . . . . . . . . . . . . . . . . . 87
References 90
vii
List of Figures
1.1 The Aoka Mizu FPSO as designed for the Lancaster field. This Turret
system will serve as case study throughout this thesis. . . . . . . . . . . 2
1.2 High level flowchart of the work which will be performed in this thesis. . 7
1.3 Flow-diagram for the evaluation of welded structural details subjected to
a multiaxial stress state. . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1 Principle stress direction given by the principal angle ϕ . . . . . . . . . 12
2.2 Local stress increase at a structural detail (bracket) . . . . . . . . . . . 14
2.3 Through-thickness structural stress definition: (a) Local stresses from
FE-model; (b) Structural stress or far-field stress; (c) Self equilibrating
stress. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 Definition of three traction-based structural stress components at the
hypothetical crack plane . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5 The structural calculation procedure for an arbitrarily curved weld using
shell/plate element models . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.6 Representation of the load path stresses . . . . . . . . . . . . . . . . . . 18
3.1 Section view of the finite element model of the tube-to-flange, consisting
of a tube welded to a flange by means of a fillet weld. . . . . . . . . . . 23
3.2 Finite element representation of a intersection composed of two elemental
subsets {green and red} along the intersection nodes . . . . . . . . . . . 24
3.3 (a) Nodes sorted based on node numbering from Ansys (b) Nodes sorted
using written Matlab code . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.4 local coordinate for each intersection node individually . . . . . . . . . . 28
viii
LIST OF FIGURES
3.5 Multi-axial stress state due to multiaxial loading . . . . . . . . . . . . . 29
3.6 Load case 1: Proportionality visualization . . . . . . . . . . . . . . . . . 30
3.7 Load case 2: Proportionality visualization . . . . . . . . . . . . . . . . . 30
3.8 MVEE fit over Mode I and III stresses, plotted in a 2 dimensional stress
space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.9 Tube-to-Flange screening results. . . . . . . . . . . . . . . . . . . . . . . 36
3.10 Section view of the finite element model of the turret structure which is
mainly built using shell-181 elements. . . . . . . . . . . . . . . . . . . . 37
3.11 Load scenarios with (a) Combined envelope mooring loads where a phase
shift of 900 is applied to the mooring horizontal moment (b) Combined en-
velope mooring loads where the mooring horizontal moment has a higher
frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.12 MVEE fit over Mode I and III stresses, plotted in a 2 dimensional stress
space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.13 MVEE fit over Mode I and III stresses, plotted in a 2 dimensional stress
space given loading from selected sea state . . . . . . . . . . . . . . . . . 43
4.1 Illustration definitions: Turning point, Projected Turning point and Vir-
tual path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 PDMR cycle counting for remaining load paths (a - c), (b) second counted
half cycle (d) third counted half cycle. . . . . . . . . . . . . . . . . . . . 49
4.3 MLP based non-proportional damage factor illustration . . . . . . . . . 51
4.4 flange-to-tube joint tested by Yousefi et al. [1] . . . . . . . . . . . . . . . 54
4.5 Experimental results of constant amplitude test; R = -1 for pure Mode I
(pink) and pure Mode III (green) . . . . . . . . . . . . . . . . . . . . . . 55
4.6 Experimental results of constant amplitude test taking load ratio into
account . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.7 Fatigue resistance SN curve for steel, MLP-based equivalent stress . . . 59
4.8 Multiaxial fatigue results for the 5 load scenarios . . . . . . . . . . . . . 61
4.9 Normalized damage comparison given 5 loading scenarios . . . . . . . . 63
ix
LIST OF FIGURES
5.1 Comparison results where the blue dots represent the estimated normal-
ized damage using the screening tool and the red dots the normalized
multiaxial fatigue damage both for load scenario 4 and 5 . . . . . . . . . 65
5.2 DNVGL detail classification as E for stress direction normal to the weld 67
5.3 Signed principle stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.4 Signed principle stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.5 Normalized damage comparison given 5 loading scenarios . . . . . . . . 71
B.1 Tube-to-flange model used for the verification of mesh sensitivity . . . . 80
B.2 Mesh sensitivity study using the mesh insensitivity method . . . . . . . 81
B.3 SAE ”Grapple skidder” variable loading . . . . . . . . . . . . . . . . . . 82
B.4 Comparison of ASTM rainflow and PDMR cycle counting results using
SAE “Grapple skidder” load history . . . . . . . . . . . . . . . . . . . . 82
B.5 Fatigue resistance SN curve for steel, MLP-based equivalent stress . . . 84
C.1 Load histogram from BES fatigue report . . . . . . . . . . . . . . . . . . 86
x
List of Tables
3.1 Finite element model propertiest tube-to-flange . . . . . . . . . . . . . . 24
3.2 Finite element properties of the turret model . . . . . . . . . . . . . . . 38
3.3 Maximum mooring envelope load amplitudes . . . . . . . . . . . . . . . 39
3.4 Finite element properties of the turret model . . . . . . . . . . . . . . . 42
3.5 Screening properties of the three selected details . . . . . . . . . . . . . 43
4.1 PDMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2 Fatigue resistance curve parameters of figure 4.5 . . . . . . . . . . . . . 55
4.3 Mode I and Mode III including correction factor . . . . . . . . . . . . . 57
4.4 Fatigue resistance for VA data . . . . . . . . . . . . . . . . . . . . . . . 59
4.5 Finite element properties of the turret model . . . . . . . . . . . . . . . 62
B.1 Fatigue resistance for VA data . . . . . . . . . . . . . . . . . . . . . . . 84
C.1 Maximum mooring envelope load amplitudes . . . . . . . . . . . . . . . 87
xi
Chapter 1
Introduction
1.1 FPSO fundamentals
A turret moored FPSO is composed of a turret system and a mooring system that
connects the turret column to the seabed. Two types of turret systems are commonly
used for FPSOs - the internal turret system where the turret is mounted within the
FPSOs hull, and an external turret system where the turret is mounted on an extended
structure cantilevered off the vessel bow. Since all the anchor chains of the mooring
system are attached to the turret column, such a system is called a single point mooring
system (SPM). This in contrary to the spread moored system, where the vessel is moored
by anchor legs from the bow and stern of the vessel, usually in a four-group arrangement.
The turret system contains a bearing system that allows the vessel to rotate freely
around the fixed geostatic part of the turret (also known as weathervane). The 360-
degree weathervaning feature of a turret moored FPSO significantly reduces the loads
on the mooring system. Also, vessel motions, particularly rolling motions, are typically
reduced thus allowing more operating uptime during inclement weather conditions. This
weathervaning ability is very important for the offloading operation as the headings of
the FPSO and the export tanker are both into the predominant sea or winds, thus
creating safer approaches and alignments during offloading operations. As the risers are
contained within the turret structure, offloading operations are simplified as the FPSO
hull is uncluttered with risers or exposed mooring lines.
1
1.1 FPSO fundamentals
For offshore areas of the world subjected to harsh environments and where seasonal
cyclonic weather systems are predominant but with characteristically mild environments
throughout the remainder of the year disconnectable turret are preferred. While the
turret enables the vessel to freely weathervane in normal to severe conditions, this
type of internal system allow the vessel to disconnect to avoid typhoons, hurricanes,
icebergs, and other extreme dangerous conditions. The Aoka Mizo vessel is equipped
with a disconnetable turret as shown in Figure 1.1. It should be noted that even thought
this FPSO is equipped with a disconnectable turret, it doesn’t mean that it currently
opperates in a area which might be subjected to seasonal cyclonic weather.
Figure 1.1: The Aoka Mizu FPSO as designed for the Lancaster field. This Turretsystem will serve as case study throughout this thesis.
FPSOs can be a conversion of an oil tanker or can be a vessel built specially for
the application. Although there has been a shift toward newbuild FPSO, especially for
developments in harsh environments, very large crude carrier tanker conversions remain
the basis for projects in areas where benign environmental conditions (mild sea waves
and swells) are predominant, such as off west Africa, southeast Asia, Australia, and
Brazil. Providing flexibility and mobility, tanker conversions in some cases offer quicker
production of first oil. There are, however, certain drawbacks to converting old tankers,
the most important of which is the restriction on the weather conditions and water
2
1.2 Problem description
depth. For these conditions, the demands for integrating the turret into the hull can
become quite elaborate and is therefore usually not economically feasible. With the
development of turret mooring and new-build ship-shaped hulls the number of FPSOs
operating in very deep water and harsh weather conditions has grown substantially.
1.2 Problem description
FPSOs are being recognized as one of the most economical systems to exploit marginal
and (ultra) deep-water areas. Due to the world’s increasing demand for energy, oil and
gas companies continue to move into new and increasingly harsh and remote environ-
ment to meet this demand. FPSOs are therefore a important way to accommodate this
need in a cost effective, flexible way. Due to the fact that these FPSOs and in particular
the turret mooring systems have to operate in harsher environment they increase in size
and complexity. The emphasis therefore lies on the optimization of design, building
and operations in order to achieve high levels of integrity in term of safety, health and
environmental factors, and life-cycle capital (CAPEX) and operational (OPEX) expen-
ditures.
Presently turret mooring system design, construction and operational practices are
largely influenced by high-cycle fatigue as a primary degradation parameter. Empirical
(inspection) practices are deployed as the key instrument to identify and mitigate sys-
tem anomalies and unanticipated defects. Current inspection, maintenance and repair
are time consuming and quite expensive.
Due to harsher operating environments the loading on the turret becomes higher and
more complex. Conventional calculation method using high contingencies may no longer
be economically justifiable. BES currently started a in-house FPSO integrity project
’AMON’, which stands for Aoka Mizu monitoring. The intension is to gain more insight
in the loading and structural response, based on actual measured data from the FPSO.
Timely identifying deviations from design conditions allows to take action in case for ex-
ample the fatigue life is being consumed too fast. Furthermore BES also participates in
the 4D fatigue JIP which focuses more on the fatigue capacity of welded joints subjected
3
1.2 Problem description
to multiaxial (non)-proportional loading. This assignment also mainly focusses on the
fatigue capacity of welded joints subjected to multiaxial (non)-proportional loading, but
taking into account more realistic loading conditions rather then just theoretical loading
conditions.
Fatigue design and evaluation of welded joints are typically carried out by weld clas-
sification approach in which a family of parallel nominal stress based S-N curves are
used according to joint types and loading modes [2]. Therefore the accuracy of the
stress range is very important for assessing the fatigue life. The form of the S-N curve
indicates that a small change in the estimate of the stress range results in a much larger
change in the life because of the equation for the S-N curve, S = CN−1/m. For example
if the stress range were increased by only 20%, the computed life would be reduced by
42% for m= 3. Therefore, an accurate estimate of stress range is required for fatigue
evaluation of a given welded structure. As discussed before this method makes use of
several empirical S-N curves that are associated with detail categories and on corrective
factors. The selection of a detail class for a welded joint type and loading mode is
often subjective and, in many common situations, even skilled engineers might have a
hard time choosing a suitable detail class. This is especially true when the geometry
of the structure is complex or when the stress state is not reducible to a simple main
component. Moreover it must be added that the real structures can develop cracks in
locations different to those indicated in the details present in the standards, resulting
in several limitations.
The structural members of the TMS are Generally evaluated using finite element anal-
ysis, due to it’s complexity. From these analysis it is usually difficult to evaluate what
is ”nominal stress” to be used together with the S-N curves, as some of the local stress
due to a detail is accounted for in the S-N curve. In many cases it may therefore be
more convenient to use an alternative / extrapolation-based hot spot stress approach.
For this approach the hot spot is determined using finite elements calculations at prede-
fined reference points and extrapolated to the fatigue hot spot. The fatigue capacity is
described by the D-curve, which can be considered as the hot spot S-N curve. Accord-
ing to [3], the stress at the fatigue hot spot consists of a nominal stress times a stress
4
1.3 Scope of Work
concentration factor (SCF). With FEA model widely used nowadays, this method gains
a lot of attention, making it a widely used method in several design codes. Even though
this method is considered a widely used method, the hot spot stress calculated by using
different extrapolation procedures and element types varies a lot and besides this the
method is also mesh insensitive [4].
To this very moment, the fundamental references in the design of ship and offshore
structures and the inherent fatigue resistance are directed from uni-axial and constant
amplitude testing ref. Furthermore fatigue design of TMS is predominantly based on
uni-axial fatigue criteria assuming a governing ”Mode I” normal stress. These criteria
are then used in combination with damage accumulation hypothesis (e.g. Miner’s rule)
and cycle counting method (e.g. rain flow counting) or Rayleigh distributed to deter-
mine the fatigue life. Nonetheless, during real-life conditions, structures are subjected
to multi-axial, variable-amplitude loading including non-proportional characteristics for
specific details. Unfortunately, the usability of current multi-axial practices are re-
strained due to limited validation efforts and finite academic scope in testing, which
can be reverted to the general engineering perception that uni-axial loading is the pre-
dominant factor [5]. Recent research has shown that conventional uni-axial methods
significantly overestimate the fatigue lifetime, and lifetime predictions of multi-axial
methods show significant differences [1].
Although all of the above potentially pose relevant and significant problems using cur-
rent evaluation methods, this research will mainly address the latter (weld details sub-
jected to multiaxial non-proportional loading).
1.3 Scope of Work
Within BES the structural department is responsible for the structural design and struc-
tural integrity of structures like the turret within a FPSO. Due to the increasing size
of the turret structures, conventional methods may be too conservative or in case of
details subjected to a multiaxial non-proportional stress state the conventional method
may result in higher fatigue then actually would be the case.
5
1.3 Scope of Work
The focus of this thesis will mainly be on welded structural details which are subjected
to a multiaxial (non)-proportional stress state. Conventional methods can’t properly
estimate the fatigue life of these details. Within design codes a attempt has been made
to account for the fatigue of details subjected to a multiaxial stress state. The meth-
ods from the design codes will be reviewed, determining if these would produce reliable
results or if a more advance methods is required to determine the fatigue life of these
details.
In addition to the design codes, a literature study is performed on newly developed
methods that are not covered by the design codes ”yet”. Its aim is to provide an
understanding of the challenges that still need to be overcome. Also several fatigue
experiments are well documented and used for both validation and further research.
The basis of this research is formed by the development of a multiaxial fatigue impor-
tance screening tool, which would allow engineers to quickly screen complex structures,
selecting only those details subjected to a multiaxial stress state. The structural screen-
ing can be performed using the semi-automated post-processing tool, This tool is to be
developed within this assignment. Validation of the developed screening tool, will be
done using a multiaxial fatigue damage criteria which is capable of properly estimating
the fatigue damage of welded details subjected to a multiaxial stress state. This would
be done in Phase I of this assignment, as shown in flow-diagram 1.3
As described above a multiaxial fatigue damage criteria should be selected which prop-
erly calculates the fatigue life of details subjected to multiaxial stress state. For this
a multiaxial fatigue damage criteria from literature is used. Since this is still under
development, usually only the mathematical description can be found in papers. Com-
mercial programs are not yet available, and therefore development of a algorithm should
also be done in this assignment. This work has been done in phase II, as shown in the
flow-diagram 1.3
Validation of the screening tool and the algorithm developed for multiaxial fatigue cal-
culation is done using a simple tube to flange model from which data is available in
literature. Furthermore a comparative study is performed to show difference between
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1.4 Thesis Structure
the results from the screening tool and that of the actual fatigue damage. Also a compar-
ative study has been performed to show the differences between conventional methods
and newly proposed methods.
Validation using measured loading data and actual multiaxial fatigue testing may be
optional, in case data and machine’s are available.
A flow chart is presented in figure 1.2, which gives a better overview of the different
steps which will be involved in this assignment.
Figure 1.2: High level flowchart of the work which will be performed in this thesis.
1.4 Thesis Structure
The structure of this thesis follows similar steps required for the analysis of welded
structural details subjected to a multiaxial (non)-proportional stress state, at least that
was intended. Some effort will be made now to describe the outline of this thesis; how
it will attempt to achieve the objectives described in section 1.3. Two main parts can
be distinguish namely: Phase I ”Structural screening” and Phase II ”Multiaxial fatigue
damage calculation for welded joints”. The flow diagram shown in 1.3 represents the
steps required to perform a structural screening, the results from the screening are later
compared to the considered multiaxial fatigue damage method.
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1.4 Thesis Structure
Figure 1.3: Flow-diagram for the evaluation of welded structural details subjected to amultiaxial stress state.
The layout of the thesis is setup as follows:
� Chapter 2 focuses on the literature study. Over the last few decades intensive
effort have been made to develop multiaxial fatigue approaches which are able to
deal with difficulties such as (random) variable amplitude (VA) loading and non-
proportionality. With is available in engineering codes and guideline’s along with
that what is available in open literates will be discussed briefly in this chapter.
Special emphasis will be on the methods used for this thesis.
� Chapter 3 focuses on Phase I: ”Structural screening” following the flow-diagram
presented in figure 1.3. The section start with a small introduction, explaining
what will be achieved in more details for Phase I. It will then be followed by
some subsection explaining the fundamentals of multiaxial fatigue. Further the
developed screening method will be described extensively. In order to properly
understand and explain the developed screening method, a ”Tube to Flange”
model is used. All the steps, as shown in the flow-diagram figure 1.3, will be
explained in details. This same procedure will be applied to the turret structure,
the findings and the results are then presented in the last sections of this chapter.
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1.4 Thesis Structure
� Chapter 4 This chapter is a follow-up on the previous chapter. In this chapter
the focus will be more on the multiaxial fatigue ”Damage” of welded components.
The same ”Tube to Flange” model is used in this chapter, to explain the con-
sidered/ developed methods. This will also provide a in-depth overview of the
cycle counting method, which is programmed enabling to count cycles in a stress
space, which accounts for multiaxial fatigue. The developed algorithm will the
be used to determine the fatigue damage of the selected details from section 3.
The development of the required SN-curves is also explained, The results are also
presented in the end.
� Chapter 5 will introduce a review, which is performed to validate the screening
method with actual fatigue damage (basically a combination of section 2
and 3). The validation in the sense of structural response and Model validation
will be described briefly. This chapter can be seen as a result section, presenting a
lot of comparative study results, enabling the author to draw enhance the drawn
conclusion and recommendation described in section 6.
� Chapter 6 will present conclusion and recommendation of this study. Some time
will also be spend on some short of reflection (looking back), where the set of goals
are evaluated.
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