\documentclass[10pt]{article}
\usepackage{fullpage}
\usepackage{setspace}
\usepackage{parskip}
\usepackage{titlesec}
\usepackage[section]{placeins}
\usepackage{xcolor}
\usepackage{breakcites}
\usepackage{lineno}
\usepackage{hyphenat}
\PassOptionsToPackage{hyphens}{url}
\usepackage[colorlinks = true,
linkcolor = blue,
urlcolor = blue,
citecolor = blue,
anchorcolor = blue]{hyperref}
\usepackage{etoolbox}
\makeatletter
\patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{%
\errmessage{\noexpand\@combinedblfloats could not be patched}%
}%
\makeatother
\usepackage{natbib}
\renewenvironment{abstract}
{{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize}
{\bigskip}
\titlespacing{\section}{0pt}{*3}{*1}
\titlespacing{\subsection}{0pt}{*2}{*0.5}
\titlespacing{\subsubsection}{0pt}{*1.5}{0pt}
\usepackage{authblk}
\usepackage{graphicx}
\usepackage[space]{grffile}
\usepackage{latexsym}
\usepackage{textcomp}
\usepackage{longtable}
\usepackage{tabulary}
\usepackage{booktabs,array,multirow}
\usepackage{amsfonts,amsmath,amssymb}
\providecommand\citet{\cite}
\providecommand\citep{\cite}
\providecommand\citealt{\cite}
% You can conditionalize code for latexml or normal latex using this.
\newif\iflatexml\latexmlfalse
\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%
\AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}}
\usepackage[utf8]{inputenc}
\usepackage[ngerman,greek,english]{babel}
\usepackage{float}
\begin{document}
\title{Fatigue analysis of monopile weldments under service loading conditions
using a cyclic deformation modelling approach}
\author[1]{Romali Biswal}%
\author[2]{Abdullah Mamun}%
\author[1]{Ali Mehmanparast}%
\affil[1]{Cranfield University}%
\affil[2]{University of Bristol}%
\vspace{-1em}
\date{\today}
\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup
\selectlanguage{english}
\begin{abstract}
This paper investigates the cyclic deformation behaviour of S355 G10+M
steel which is predominantly used in offshore wind applications. The
thick weldments were identified as regions prone to fatigue crack
initiation due to stress concentration at weld toe as well as weld
residual stress fields. The monopile structure was modelled using a
global-local finite element (FE) method and the weld geometry was
adopted from circumferential weld joints used in offshore wind turbine
monopile foundations. Realistic service loads collected using SCADA and
wave buoy techniques were used in the FE model. A non-linear
isotropic-kinematic hardening model was calibrated using the strain
controlled cyclic deformation results obtained from base metal as well
as cross-weld specimen tests. The tests revealed that the S355 G10+M
base metal and weld metal undergo continuous cyclic stress relaxation.
Fatigue damage over a period of 20 years of operation was predicted
using the total elastic-plastic strain energy accumulated at the root of
the weldments as the life limiting criterion. This study helps in
quantifying the level of conservatism in the current monopile design
approaches and has implications towards making wind energy more
economic.%
\end{abstract}%
\sloppy
\textbf{Abstract}
This paper investigates the cyclic deformation behaviour of S355 G10+M
steel which is predominantly used in offshore wind applications. The
thick weldments were identified as regions prone to fatigue crack
initiation due to stress concentration at weld toe as well as weld
residual stress fields. The monopile structure was modelled using a
global-local finite element (FE) method and the weld geometry was
adopted from circumferential weld joints used in offshore wind turbine
monopile foundations. Realistic service loads collected using SCADA and
wave buoy techniques were used in the FE model. A non-linear
isotropic-kinematic hardening model was calibrated using the strain
controlled cyclic deformation results obtained from base metal as well
as cross-weld specimen tests. The tests revealed that the S355 G10+M
base metal and weld metal undergo continuous cyclic stress relaxation.
Fatigue damage over a period of 20 years of operation was predicted
using the total elastic-plastic strain energy accumulated at the root of
the weldments as the life limiting criterion. This study helps in
quantifying the level of conservatism in the current monopile design
approaches and has implications towards making wind energy more
economic.
Keywords: Service loads; Offshore wind turbine; S355 welds; Finite
element modelling; Fatigue life prediction.
\textbf{Introduction}
Over the last 15 years, constant efforts have been directed towards
promoting renewable energy technologies and the deployment of new
offshore wind farms has rapidly accelerated around the world,
particularly in Europe. A recent example of such efforts is the new
offshore wind farm being constructed by Seimens Gamesa Renewable off the
coast of Yorkshire-UK, (which is the largest project among the current
wind farms) and is approaching completion. It is estimated that by 2024,
this wind farm could result in meeting the energy demand of 1.2 million
households in the UK {[}1{]}. Nevertheless, being a relatively newer
technology as compared to fossil fuels, considerable efforts have been
put towards bringing down the levelised cost of energy (LCOE) for
offshore wind power, which would render the technology commercially
competitive {[}2,3{]}. It has been established that scaling up the
offshore wind turbine (OWT) size, which includes taller mast (thereby
giving access to stronger winds) and larger rotor blades (which
increases the swept area), enhances the efficiency, but requires
advanced designs to withstand greater structural loads {[}4{]}.
Steady efforts have been focused towards development of optimized
features for rotor blades {[}5,6{]}, tower {[}7,8{]}, foundation
{[}9,10{]} and structural health monitoring {[}11,12{]}. In addition to
exploring newer methods, many studies have also been carried out to
enhance the structural integrity of existing designs. Jacob et al.
{[}13{]} investigated the residual stress profile in a typical
circumferential butt weld of OWT monopile made of S355 G10+M and found
compressive residual stresses in the heat affect zone (HAZ). Since, this
would lead to a reduction in the value of stress intensity factor (crack
driving force), such weld residual stresses would be beneficial in life
extension of the OWT. Regardless, residual stress redistribution
phenomenon and interaction of environmental factors with fatigue crack
can significantly alter the material behaviour. Mehmanparast et al.
{[}14{]} studied the effect of environment (i.e. air and seawater) and
microstructure (basemetal and heat affected zone) on the fatigue crack
growth in S355 G8+M and reported that in free corrosion condition, the
crack growth rate was increased by a factor of 2 as compared to tests
conducted in air. Moreover, an independent study was conducted by
Mehmanparast et al. to characterise the mechanical and fracture
properties of monopile weldments to improve the structural integrity
assessment of monopiles {[}15{]}.
Foundation structure acts as a life-limiting component for an OWT as it
is subjected to a spectrum of structural loads, such as weight of the
rotor and nacelle assembly, bending load from wind, wave currents and
vibrations due to rotor blades being some of the significant loads. Most
of the installed OWTs consist of monopile foundations which are built by
stacking 3-7 m diameter cylindrical sections of 30-125 mm thickness and
can cost up to 35\% of the total set up cost of an OWT {[}16--18{]}.
Besides, the circumferential weldments joining the thick monopile
sections, lead to material property variations at the weld
metal-HAZ-base metal interface which turns into a favourable site for
fatigue crack initiation. This is due to difference in microstructure
and chemical segregation as a result of rapid heating and cooling
associated with the submerged arc welding process. Kolios et al.
{[}19{]} performed linear elastic finite element (FE) analysis on
monopile circumferential weldments and observed that depending on the
weld quality, the stress concentration factor at weld toe lies between
1.1 and 1.65. Subsequent fatigue testing {[}19{]} on the large scale
dog-bone samples extracted from 90 mm thick weldments displayed crack
initiation at regions of maximum stress concentration. In {[}20{]}, the
authors studied the stress-strain response at the different sections
(base metal, heat affected zone and weld metal) of a cross-weld specimen
using digital image correlation technique. It was found that the three
regions exhibited comparable strength values, however the elongation to
failure of the weld metal and heat affected zone was reduced by a factor
of 10 with respect to the base metal. As the OWT weldments are not
subjected to any post-weld treatment, a combination of mechanical
properties mismatch (between heat affected zone and the surrounding base
metal), residual stress and stress concentration factor at weld toe make
it a potential site for fatigue crack initiation. Another study {[}21{]}
used down-sized geometries of monopile section to investigate the effect
of bending moment. The stresses were found to be greatest at regions
nearest to the fixed bottom of the monopile, which in an OWT would be
the section just around the sea-bed. However, the loading conditions in
an OWT is governed by multiple factors such as wind (speed and
direction), wave (height and frequency) and rotor speed. Therefore, some
researchers {[}17,22,23{]} used Supervisory Control And Data Acquisition
(SCADA) technique to measure the true service loads acting on an OWT.
Another form of relevant damage mechanism in OWT structures is due to
corrosion. Corrosion-fatigue process is initiated by the formation of
localised corrosion pits at certain parts of the wind turbine structure
which are formed as a result of the breakdown of the thin oxide-layer on
the surface of metals, which then develop into a critical size large
enough to initiate a crack. However, the quantification of
corrosion-fatigue mechanism poses an important challenge as the
pit-to-crack stage of this process is largely unknown, hence in most
instances, the pit itself is often taken as a crack in the fatigue
analysis {[}24--26{]}. Corrosion damage can be accounted for in the
fatigue design process by considering the S-N curves for structural
steels in seawater with and without cathodic protection {[}14{]}.
Nevertheless, such a prediction would have inherent uncertainties due to
the variations in corrosion rate with geometric location as well as the
water depth. This difference is a result of the variations in the
chemical composition of the seawater at different locations. Seawater is
generally considered to be composed of 3.5 wt. \% of sodium chloride
(NaCl) and its pH ranges from 7.8 to 8.3 {[}16{]}. From material loss
due to corrosion perspective, the splash zone (at the free surface of
sea) is considered to undergo maximum uniform corrosion, that could
amount to a yearly thickness reduction of 0.2-0.4 mm in structural
material {[}24{]}. The submerged sections are subjected to a thickness
reduction of 0.1-0.2 mm per year {[}24{]}.
The present study aims to analyse the effect of service loading
conditions on offshore wind monopile foundation structure using a full
scaled FE model to predict the fatigue life of the structure. A
global-local model was used to enable optimized computation of local
stress and strain value at the weld toe of circumferential butt weld
joints located nearest to the sea-bed. The model was calibrated using
strain controlled cyclic test data to improve the prediction accuracy.
Development of reliable fatigue life prediction tools will encourage
design optimizations on OWT structures and therefore make wind energy
harvesting more economic.
\textbf{Material and test methods}
The material considered in this study is S355 G10+M structural steel
since it is commonly employed in fabrication of OWT foundation
structures. In S355 G10+M notation, the letter S indicates that the
material employed in this study is a structural steel with a minimum
yield stress of 355 MPa while G10 indicates the steel grade within the
material groups specified in EN-10225 standard and +M indicates thermo
mechanical rolling process. A 90 mm thick hot rolled plate was welded
using submerged arc welding process and three circular round bar
specimens were extracted from the weld region as shown in Fig. 1(a),
referred to as cross-weld specimens. Details of the welding procedure
can be found in a previous study by Jacob et al. {[}20{]}. The specimen
extraction location was selected such that the 2-3 mm thick heat
affected zone was positioned at the centre of the specimen gauge
section. This configuration allows the interface between weld metal, HAZ
and base metal to be tested under the applied loading condition.
Therefore the test results obtained from the cross-weld specimens would
represent the material properties of the monopile circumferential welded
joint. Further, three more specimens were extracted from the hot rolled
plate in a region far from the weld section to represent the base metal
material properties. All the specimens were designed according to ASTM
E606 design standard {[}27{]} as shown in Fig. 1(b).\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
(a) & (b)\tabularnewline
\bottomrule
\end{longtable}
Fig. 1 Schematic showing (a) extraction location for preparing
cross-weld specimens, (b) specimen geometry (all dimensions are in
millimetres)
Strain controlled cyclic load tests were performed using a 100 kN
Instron servo-hydraulic machine at room temperature condition. Three
strain amplitudes of \selectlanguage{ngerman}±1\%, ±2\% and 0-3\% were selected to capture the
cyclic deformation behaviour of the cross-weld and base metal specimens.
Two tests were performed at each strain amplitude, with one test
capturing the cross-weld material behaviour while the second test giving
the base material behaviour which acts as a reference for comparison
purposes. In each test, the specimen was loaded at a frequency of 0.1 Hz
and the measurements were recorded at 40 Hz to capture the variations in
stress levels in the test specimen. The tests were conducted for 200
cycles or until failure, if the cycles to failure was less than 200
cycles.
For the purpose of determining the service loads acting on an OWT,
online monitoring data for the wind and wave characteristics was taken
from an offshore wind farm located in the North Sea. The data was
collected from a 6 MW capacity OWT which had a rotor diameter of 154 m
and hub height of 106 m. The measurement and recording of the wind
profile was carried out using supervisory control and data acquisition
(SCADA) system. The data was collected for a period of 2 years, from
beginning of 2016 to the end of 2017. The data included main shaft
rotational frequency (RPM), wind speed (minimum, maximum, mean and
standard deviation), wind direction (monitored by the yaw position
sensor), ambient temperature and turbine power generation, recorded
every 10 minutes over the 2-year duration. Similarly, the wave
characteristics including the maximum wave height, wave period, mean
wave spectral direction and water temperature were monitored using a
wave buoy (SEAWATCH midi model) at an interval of every 30 minutes over
the 2-year period. The wind speed and wave height variations exhibited a
random behaviour with respect to time as shown in Fig. 2(a) and Fig.
2(b) respectively.\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
(a) & (b)\tabularnewline
\bottomrule
\end{longtable}
Fig. 2 Two years of online monitoring data showing variation of (a) wind
speeds, (b) wave heights
The variation of the wave speed along the depth of the sea was also
monitored by taking measurements every 3 m from the free surface of
seawater, up to a depth of 33 m below the sea level. Fig. 3 shows that
the wave speed below the sea level remains fairly constant with
increasing depth and undergoes a rapid drop as the depth reaches 24 m.
This value corresponds to a region within few meters of sea floor and
the fall in wave speed can be explained by the obstruction offered by
the sea-bed. It is worth mentioning that this measurement indicates that
the sea waves at the sea-level would have maximum contribution towards
wave loads, therefore the present study uses the height of sea waves at
the surface to compute the wave loads on the monopile foundation.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}
\end{center}
\end{figure}
Fig. 3 Variation of speed of waves with increasing depth from free
surface of sea.
\textbf{Modelling Methodology}
\textbf{3.1 Determination of service loads on OWT monopile
structure3.1.1 Hydrodynamic forces due to sea-waves}
As Fig. 2(b) denotes, the waves can vary over a wide spectrum of heights
and periods which are non-linear and stochastic. For modelling purpose,
a linear wave theory was adopted to represent the sea-waves. The
Morison's semi-empirical equations {[}28{]} give the hydrodynamic forces
due to an unsteady, viscous flow acting on a fixed body along the flow
(i.e. wave) direction. The total hydrodynamic force is composed of two
components in this study as shown in Eq. (1). The first term represents
the inertia force due to acceleration of the surrounding fluid while the
second term gives the contribution of the viscous drag force against the
monopile surface. Therefore, Morison's approach was used in this study
with the following critical assumptions:
1. The wave flow is irrotational and incompressible
2. The sea-bed is horizontal, impermeable and provides a fixed support
to the monopile structure
3. Pressure at the sea-surface is constant
4. Force acting on the structure due to undisturbed waves is negligible
5. Wave diffraction and wave splash on the monopile surface is
negligible
6. The mass coefficient and drag coefficient remains constant throughout
the service life
From Fig. 2(b) and Fig. 3 it is evident that wave speed coming across on
a monopile section vary with time and depth. Eq. (1) shows the force
acting on an infinitesimal section of the monopile due to the waves. The
total force on a monopile structure due to sea-waves was therefore
evaluated using an integration shown in Equation (2).\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(\text{dF}\left(z,t\right)=C_{m}\selectlanguage{greek}\frac{\text{ρπ}d^{2}}\selectlanguage{english}{4}\text{\ u}\left(z,t\right)dz+\ C_{d}\selectlanguage{greek}\frac{\text{ρd}}\selectlanguage{english}{2}\text{\ u}\left(z,t\right)\left|u\left(z,t\right)\right|\text{dz}\) & (1)\tabularnewline
\midrule
\endhead
\(F\left(z,t\right)=\int_{z=0}^{z=L}{dF(z,t)}\) & (2)\tabularnewline
\bottomrule
\end{longtable}
where \emph{C\textsubscript{m}} and \emph{C\textsubscript{d}} are the
coefficients of inertia force (referred to as mass coefficient) and
viscous drag force (referred to as drag coefficient), respectively. In
the present study, the values of \emph{C\textsubscript{m}}
and\emph{C\textsubscript{d}} were assumed to be 2 and 0.7 {[}28{]}. The
remaining terms are: density of sea-water \selectlanguage{greek}\emph{ρ} , \selectlanguage{english}diameter of
monopile structure \emph{d} , wave speed \emph{u} which is a function of
height from sea-floor \emph{z} and time \emph{t} . The length of
submerged section of the monopile structure is \emph{L} .
Following this, the wave speed variation recorded over the 2 years of
online monitoring was sorted into six groups using the rainflow counting
algorithm {[}29{]} implemented in MATLAB. Also, the frequency of
occurrence of these wave speeds over the 2 year period was used to
estimate the weight that should be given to each group during fatigue
life analysis. For any given moment in time, one of the load cases (or
wave force) and its corresponding frequency was assumed to be acting on
the OWT structure {[}24{]}.
\textbf{3.1.2 Aerodynamic forces due to wind}
The classical Blade Element Momentum (BEM) approach {[}30{]} was used to
compute the loads acting on the rotor due to coursing wind. The wind
behaviour was modelled with a one dimensional wave theory. Eq. (3) and
Eq. (4) give the lift and drag forces respectively experienced by an
airfoil.\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(F_{L}=\frac{1}{2}C_{L}\rho V_{0}^{2}c\) & (3)\tabularnewline
\midrule
\endhead
\(F_{D}=\frac{1}{2}C_{D}\rho V_{0}^{2}c\) & (4)\tabularnewline
\bottomrule
\end{longtable}
where \emph{C\textsubscript{L}} and \emph{C\textsubscript{D}} are the
coefficients of lift and drag, respectively. The density of air is given
by \selectlanguage{greek}\emph{ρ} , \selectlanguage{english}wind speed \emph{V\textsubscript{0}} and length of
airfoil\emph{c} . For the purpose of simplicity an average angle of
attack was assumed at 30\selectlanguage{ngerman}° and the corresponding values of
\emph{C\textsubscript{L}}and \emph{C\textsubscript{D}} were taken as
0.97 and 0.63 for the calculations {[}30{]}.
The total thrust acting on an infinitesimal section of rotor blade is
given by Eq. (5). Similarly, the moment produced by the incoming wind on
an infinitesimal section of the rotor blade is given by Eq. (6). The
total thrust and moment due to the wind were therefore computed by
integrating Eq. (5) and Eq. (6) over the entire rotor blade. Details of
the derivation of the BEM equations can be found elsewhere {[}30{]}.\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(dT=\frac{1}{2}\selectlanguage{greek}\text{ρB}\selectlanguage{english}\frac{V_{0}^{2}{(1-a)}^{2}}{\sin\phi}cC_{N}\text{\ dr}\) & (5)\tabularnewline
\midrule
\endhead
\(dM=\frac{1}{2}\selectlanguage{greek}\text{ρB}\selectlanguage{english}\frac{V_{0}\left(1-a\right)r\omega(1+a^{{}^{\prime}})}{\sin\phi\cos\phi}cC_{T}\text{\ rdr}\) & (6)\tabularnewline
\bottomrule
\end{longtable}
where \emph{B} is the number of rotor blades in the turbine, \emph{a}the
axial induction factor, a' \selectlanguage{english}the factor to account for any rotational
speed in the wake (non-ideal rotor condition), \selectlanguage{greek}\emph{ϕ} \selectlanguage{english}the flow angle
of incoming wind, \emph{C\textsubscript{N}} the coefficient of normal
component of force, \emph{r} the radial distance from centre of rotation
of rotor blades, \selectlanguage{greek}\emph{ω} \selectlanguage{english}the rotational speed of rotor
and\emph{C\textsubscript{T}} the coefficient of tangential component of
force.
In order to calculate the wind load, the wind velocity profile was
regrouped into six categories using rainflow counting algorithm {[}29{]}
and implemented in MATLAB. Each group of wind speed was characterised by
the frequency of occurrence through the 2 years of monitoring. For each
group of wind speed, the mean wind speed of the group was used to
calculate the corresponding wind loads using Eq. 5 and Eq. 6. For any
given moment in time, one of the load case (or wind speed and its
corresponding frequency) was assumed to be acting on the OWT structure
{[}24{]}.
\textbf{3.2 Finite element modelling3.2.1 Material model}
The elastic properties used in the FE model were taken from a previous
study as shown in Fig. 4(a) {[}20{]}. Further, the stabilised hysteresis
loop obtained for obtained from the cyclic load tests conducted in this
study. The tests were performed on the base metal and cross-weld
specimens as shown in Fig. 4(b-d). The experimentally measured values of
the tensile and cyclic properties of S355 G10+M are given in Table 1.
Following this, an elastic-plastic constitutive equation was used to
simulate the experimental results. Calibrated parameters for the mixed
isotropic-kinematic model is given in Table 1. Further details of the
model can be found in the Abaqus manual {[}31{]}. In the cyclic load
test, it was observed that the stress vs. strain response (hysteresis
loops) were stabilised within the first 20 cycles, nevertheless, the
experiment was conducted for 200 cycles (or until failure if cycles to
failure was less than 200). Therefore, the 20\textsuperscript{th} cycle
from test was used to calibrate the model, where the set parameters
resulted in a good fit between the stress vs. strain response of the
test and FE model in 20 cycles. Fig. 4(b-d) shows the stabilised cyclic
stress vs. strain response obtained for the 20th cycle from experiment
as well as the FE model.\selectlanguage{english}
\begin{longtable}[]{@{}lllllllllllll@{}}
\toprule
(a) & (a) & (a) & (a) & (a) & (a) & (a) & (b) & (b) & (b) & (b) & (b) &
(b)\tabularnewline
\midrule
\endhead
(c) & (c) & (c) & (c) & (c) & (c) & (c) & (d) & (d) & (d) & (d) & (d) &
(d)\tabularnewline
Fig. 4 Results of strain controlled cyclic load tests showing the
stabilised hysteresis loops for cross-weld samples and base metal
samples tested at (a) \selectlanguage{ngerman}±1\% strain, (b) ±2\% strain and (c) 0-3\% strain
& Fig. 4 Results of strain controlled cyclic load tests showing the
stabilised hysteresis loops for cross-weld samples and base metal
samples tested at (a) \selectlanguage{ngerman}±1\% strain, (b) ±2\% strain and (c) 0-3\% strain
& Fig. 4 Results of strain controlled cyclic load tests showing the
stabilised hysteresis loops for cross-weld samples and base metal
samples tested at (a) \selectlanguage{ngerman}±1\% strain, (b) ±2\% strain and (c) 0-3\% strain
& Fig. 4 Results of strain controlled cyclic load tests showing the
stabilised hysteresis loops for cross-weld samples and base metal
samples tested at (a) \selectlanguage{ngerman}±1\% strain, (b) ±2\% strain and (c) 0-3\% strain
& Fig. 4 Results of strain controlled cyclic load tests showing the
stabilised hysteresis loops for cross-weld samples and base metal
samples tested at (a) \selectlanguage{ngerman}±1\% strain, (b) ±2\% strain and (c) 0-3\% strain
& Fig. 4 Results of strain controlled cyclic load tests showing the
stabilised hysteresis loops for cross-weld samples and base metal
samples tested at (a) \selectlanguage{ngerman}±1\% strain, (b) ±2\% strain and (c) 0-3\% strain
& Fig. 4 Results of strain controlled cyclic load tests showing the
stabilised hysteresis loops for cross-weld samples and base metal
samples tested at (a) \selectlanguage{ngerman}±1\% strain, (b) ±2\% strain and (c) 0-3\% strain
& Fig. 4 Results of strain controlled cyclic load tests showing the
stabilised hysteresis loops for cross-weld samples and base metal
samples tested at (a) \selectlanguage{ngerman}±1\% strain, (b) ±2\% strain and (c) 0-3\% strain
& Fig. 4 Results of strain controlled cyclic load tests showing the
stabilised hysteresis loops for cross-weld samples and base metal
samples tested at (a) \selectlanguage{ngerman}±1\% strain, (b) ±2\% strain and (c) 0-3\% strain
& Fig. 4 Results of strain controlled cyclic load tests showing the
stabilised hysteresis loops for cross-weld samples and base metal
samples tested at (a) \selectlanguage{ngerman}±1\% strain, (b) ±2\% strain and (c) 0-3\% strain
& Fig. 4 Results of strain controlled cyclic load tests showing the
stabilised hysteresis loops for cross-weld samples and base metal
samples tested at (a) \selectlanguage{ngerman}±1\% strain, (b) ±2\% strain and (c) 0-3\% strain
& Fig. 4 Results of strain controlled cyclic load tests showing the
stabilised hysteresis loops for cross-weld samples and base metal
samples tested at (a) \selectlanguage{ngerman}±1\% strain, (b) ±2\% strain and (c) 0-3\% strain
& Fig. 4 Results of strain controlled cyclic load tests showing the
stabilised hysteresis loops for cross-weld samples and base metal
samples tested at (a) \selectlanguage{ngerman}±1\% strain, (b) ±2\% strain and (c) 0-3\%
strain\tabularnewline
Table 1. Tensile properties of S355 G10+M from literature {[}20{]} and
calibrated parameters for the cyclic deformation obtained in this study.
Mixed kinematic (\emph{C}\textsubscript{k} (MPa), \selectlanguage{greek}γ\selectlanguage{english}\textsubscript{k} and
isotropic (\emph{Q\textsubscript{[?]}} (MPa), \emph{b}) model parameters
fitted to stabilised hysteresis loops (refer Fig. 4) for S355 G10+M
obtained from cyclic load test. \emph{C}\textsubscript{k} is the
plasticity modulus, \selectlanguage{greek}γ\selectlanguage{english}\textsubscript{k} the rate of change in
\emph{C}\textsubscript{k} with increase in the applied plastic strain.
Similarly, is the change in yield surface with increasing equivalent
plastic strain and the rate of change is controlled by the parameter
\emph{b}. & Table 1. Tensile properties of S355 G10+M from literature
{[}20{]} and calibrated parameters for the cyclic deformation obtained
in this study. Mixed kinematic (\emph{C}\textsubscript{k} (MPa),
\selectlanguage{greek}γ\selectlanguage{english}\textsubscript{k} and isotropic (\emph{Q\textsubscript{[?]}} (MPa),
\emph{b}) model parameters fitted to stabilised hysteresis loops (refer
Fig. 4) for S355 G10+M obtained from cyclic load test.
\emph{C}\textsubscript{k} is the plasticity modulus, \selectlanguage{greek}γ\selectlanguage{english}\textsubscript{k}
the rate of change in \emph{C}\textsubscript{k} with increase in the
applied plastic strain. Similarly, is the change in yield surface with
increasing equivalent plastic strain and the rate of change is
controlled by the parameter \emph{b}. & Table 1. Tensile properties of
S355 G10+M from literature {[}20{]} and calibrated parameters for the
cyclic deformation obtained in this study. Mixed kinematic
(\emph{C}\textsubscript{k} (MPa), \selectlanguage{greek}γ\selectlanguage{english}\textsubscript{k} and isotropic
(\emph{Q\textsubscript{[?]}} (MPa), \emph{b}) model parameters fitted to
stabilised hysteresis loops (refer Fig. 4) for S355 G10+M obtained from
cyclic load test. \emph{C}\textsubscript{k} is the plasticity modulus,
\selectlanguage{greek}γ\selectlanguage{english}\textsubscript{k} the rate of change in \emph{C}\textsubscript{k} with
increase in the applied plastic strain. Similarly, is the change in
yield surface with increasing equivalent plastic strain and the rate of
change is controlled by the parameter \emph{b}. & Table 1. Tensile
properties of S355 G10+M from literature {[}20{]} and calibrated
parameters for the cyclic deformation obtained in this study. Mixed
kinematic (\emph{C}\textsubscript{k} (MPa), \selectlanguage{greek}γ\selectlanguage{english}\textsubscript{k} and
isotropic (\emph{Q\textsubscript{[?]}} (MPa), \emph{b}) model parameters
fitted to stabilised hysteresis loops (refer Fig. 4) for S355 G10+M
obtained from cyclic load test. \emph{C}\textsubscript{k} is the
plasticity modulus, \selectlanguage{greek}γ\selectlanguage{english}\textsubscript{k} the rate of change in
\emph{C}\textsubscript{k} with increase in the applied plastic strain.
Similarly, is the change in yield surface with increasing equivalent
plastic strain and the rate of change is controlled by the parameter
\emph{b}. & Table 1. Tensile properties of S355 G10+M from literature
{[}20{]} and calibrated parameters for the cyclic deformation obtained
in this study. Mixed kinematic (\emph{C}\textsubscript{k} (MPa),
\selectlanguage{greek}γ\selectlanguage{english}\textsubscript{k} and isotropic (\emph{Q\textsubscript{[?]}} (MPa),
\emph{b}) model parameters fitted to stabilised hysteresis loops (refer
Fig. 4) for S355 G10+M obtained from cyclic load test.
\emph{C}\textsubscript{k} is the plasticity modulus, \selectlanguage{greek}γ\selectlanguage{english}\textsubscript{k}
the rate of change in \emph{C}\textsubscript{k} with increase in the
applied plastic strain. Similarly, is the change in yield surface with
increasing equivalent plastic strain and the rate of change is
controlled by the parameter \emph{b}. & Table 1. Tensile properties of
S355 G10+M from literature {[}20{]} and calibrated parameters for the
cyclic deformation obtained in this study. Mixed kinematic
(\emph{C}\textsubscript{k} (MPa), \selectlanguage{greek}γ\selectlanguage{english}\textsubscript{k} and isotropic
(\emph{Q\textsubscript{[?]}} (MPa), \emph{b}) model parameters fitted to
stabilised hysteresis loops (refer Fig. 4) for S355 G10+M obtained from
cyclic load test. \emph{C}\textsubscript{k} is the plasticity modulus,
\selectlanguage{greek}γ\selectlanguage{english}\textsubscript{k} the rate of change in \emph{C}\textsubscript{k} with
increase in the applied plastic strain. Similarly, is the change in
yield surface with increasing equivalent plastic strain and the rate of
change is controlled by the parameter \emph{b}. & Table 1. Tensile
properties of S355 G10+M from literature {[}20{]} and calibrated
parameters for the cyclic deformation obtained in this study. Mixed
kinematic (\emph{C}\textsubscript{k} (MPa), \selectlanguage{greek}γ\selectlanguage{english}\textsubscript{k} and
isotropic (\emph{Q\textsubscript{[?]}} (MPa), \emph{b}) model parameters
fitted to stabilised hysteresis loops (refer Fig. 4) for S355 G10+M
obtained from cyclic load test. \emph{C}\textsubscript{k} is the
plasticity modulus, \selectlanguage{greek}γ\selectlanguage{english}\textsubscript{k} the rate of change in
\emph{C}\textsubscript{k} with increase in the applied plastic strain.
Similarly, is the change in yield surface with increasing equivalent
plastic strain and the rate of change is controlled by the parameter
\emph{b}. & Table 1. Tensile properties of S355 G10+M from literature
{[}20{]} and calibrated parameters for the cyclic deformation obtained
in this study. Mixed kinematic (\emph{C}\textsubscript{k} (MPa),
\selectlanguage{greek}γ\selectlanguage{english}\textsubscript{k} and isotropic (\emph{Q\textsubscript{[?]}} (MPa),
\emph{b}) model parameters fitted to stabilised hysteresis loops (refer
Fig. 4) for S355 G10+M obtained from cyclic load test.
\emph{C}\textsubscript{k} is the plasticity modulus, \selectlanguage{greek}γ\selectlanguage{english}\textsubscript{k}
the rate of change in \emph{C}\textsubscript{k} with increase in the
applied plastic strain. Similarly, is the change in yield surface with
increasing equivalent plastic strain and the rate of change is
controlled by the parameter \emph{b}. & Table 1. Tensile properties of
S355 G10+M from literature {[}20{]} and calibrated parameters for the
cyclic deformation obtained in this study. Mixed kinematic
(\emph{C}\textsubscript{k} (MPa), \selectlanguage{greek}γ\selectlanguage{english}\textsubscript{k} and isotropic
(\emph{Q\textsubscript{[?]}} (MPa), \emph{b}) model parameters fitted to
stabilised hysteresis loops (refer Fig. 4) for S355 G10+M obtained from
cyclic load test. \emph{C}\textsubscript{k} is the plasticity modulus,
\selectlanguage{greek}γ\selectlanguage{english}\textsubscript{k} the rate of change in \emph{C}\textsubscript{k} with
increase in the applied plastic strain. Similarly, is the change in
yield surface with increasing equivalent plastic strain and the rate of
change is controlled by the parameter \emph{b}. & Table 1. Tensile
properties of S355 G10+M from literature {[}20{]} and calibrated
parameters for the cyclic deformation obtained in this study. Mixed
kinematic (\emph{C}\textsubscript{k} (MPa), \selectlanguage{greek}γ\selectlanguage{english}\textsubscript{k} and
isotropic (\emph{Q\textsubscript{[?]}} (MPa), \emph{b}) model parameters
fitted to stabilised hysteresis loops (refer Fig. 4) for S355 G10+M
obtained from cyclic load test. \emph{C}\textsubscript{k} is the
plasticity modulus, \selectlanguage{greek}γ\selectlanguage{english}\textsubscript{k} the rate of change in
\emph{C}\textsubscript{k} with increase in the applied plastic strain.
Similarly, is the change in yield surface with increasing equivalent
plastic strain and the rate of change is controlled by the parameter
\emph{b}. & Table 1. Tensile properties of S355 G10+M from literature
{[}20{]} and calibrated parameters for the cyclic deformation obtained
in this study. Mixed kinematic (\emph{C}\textsubscript{k} (MPa),
\selectlanguage{greek}γ\selectlanguage{english}\textsubscript{k} and isotropic (\emph{Q\textsubscript{[?]}} (MPa),
\emph{b}) model parameters fitted to stabilised hysteresis loops (refer
Fig. 4) for S355 G10+M obtained from cyclic load test.
\emph{C}\textsubscript{k} is the plasticity modulus, \selectlanguage{greek}γ\selectlanguage{english}\textsubscript{k}
the rate of change in \emph{C}\textsubscript{k} with increase in the
applied plastic strain. Similarly, is the change in yield surface with
increasing equivalent plastic strain and the rate of change is
controlled by the parameter \emph{b}. & Table 1. Tensile properties of
S355 G10+M from literature {[}20{]} and calibrated parameters for the
cyclic deformation obtained in this study. Mixed kinematic
(\emph{C}\textsubscript{k} (MPa), \selectlanguage{greek}γ\selectlanguage{english}\textsubscript{k} and isotropic
(\emph{Q\textsubscript{[?]}} (MPa), \emph{b}) model parameters fitted to
stabilised hysteresis loops (refer Fig. 4) for S355 G10+M obtained from
cyclic load test. \emph{C}\textsubscript{k} is the plasticity modulus,
\selectlanguage{greek}γ\selectlanguage{english}\textsubscript{k} the rate of change in \emph{C}\textsubscript{k} with
increase in the applied plastic strain. Similarly, is the change in
yield surface with increasing equivalent plastic strain and the rate of
change is controlled by the parameter \emph{b}. & Table 1. Tensile
properties of S355 G10+M from literature {[}20{]} and calibrated
parameters for the cyclic deformation obtained in this study. Mixed
kinematic (\emph{C}\textsubscript{k} (MPa), \selectlanguage{greek}γ\selectlanguage{english}\textsubscript{k} and
isotropic (\emph{Q\textsubscript{[?]}} (MPa), \emph{b}) model parameters
fitted to stabilised hysteresis loops (refer Fig. 4) for S355 G10+M
obtained from cyclic load test. \emph{C}\textsubscript{k} is the
plasticity modulus, \selectlanguage{greek}γ\selectlanguage{english}\textsubscript{k} the rate of change in
\emph{C}\textsubscript{k} with increase in the applied plastic strain.
Similarly, is the change in yield surface with increasing equivalent
plastic strain and the rate of change is controlled by the parameter
\emph{b}.\tabularnewline
Monotonic properties & Monotonic properties & Monotonic properties &
Monotonic properties & \emph{E} & \selectlanguage{greek}\emph{ν} & \selectlanguage{greek}σ\selectlanguage{english}\textsubscript{0.2(BM)} &
\selectlanguage{greek}σ\selectlanguage{english}\textsubscript{0.2(BM)} & \selectlanguage{greek}σ\selectlanguage{english}\textsubscript{0.2(HAZ)} &
\selectlanguage{greek}σ\selectlanguage{english}\textsubscript{0.2(WM)} & \selectlanguage{greek}ε\selectlanguage{english}\textsubscript{f(BM)} &
\selectlanguage{greek}ε\selectlanguage{english}\textsubscript{f(HAZ)} & \selectlanguage{greek}ε\selectlanguage{english}\textsubscript{f(WM)}\tabularnewline
& & & & 196 & 0.3 & 455 & 455 & 469 & 477 & 87.9 & 10.76 &
8.19\tabularnewline
\emph{C}\textsubscript{1} & \selectlanguage{greek}γ\selectlanguage{english}\textsubscript{1} &
\emph{C}\textsubscript{2} & \selectlanguage{greek}γ\selectlanguage{english}\textsubscript{2} &
\emph{C}\textsubscript{3} & \selectlanguage{greek}γ\selectlanguage{english}\textsubscript{3} &
\emph{C}\textsubscript{4} & \emph{C}\textsubscript{4} &
\selectlanguage{greek}γ\selectlanguage{english}\textsubscript{4} & \emph{C}\textsubscript{5} & \selectlanguage{greek}γ\selectlanguage{english}\textsubscript{5} &
\emph{Q}\textsubscript{[?]} & \emph{b}\tabularnewline
204 & 9500 & 120 & 600 & 45 & 565 & 30 & 30 & 420 & 12 & 85 & -300 &
25\tabularnewline
\bottomrule
\end{longtable}
\textbf{3.2.2 Loads and boundary conditions}
A three dimensional finite element (FE) model was used to determine the
peak stresses in the monopile foundation. The separation between two
consecutive circumferential welds in the monopile was assumed to be 6.5m
and the first weld close to the mudline was assumed to be 4m above the
sea-bed. Since the bending stresses on the monopile decrease rapidly
with increasing distance from the fixed end, only the first weld
(assumed at 4m from mudline) was modelled in the FE geometry. Fig. 5
shows the FE model dimensions and weld geometry details. Additionally,
the regions of load application are also included in the figure and the
corresponding values are summarised in Table 2. As discussed in the
previous sections, the loads corresponding to each of the six load cases
were applied to determine the maximum stress in the structure. The
hydrodynamic and aerodynamic forces for the mean wave height and mean
wind speed of each group was calculated from section 3.1.1 and section
3.1.2 respectively. Three regions were selected to apply the
corresponding loads, i.e. (1) the centre of buoyancy of the submerged
section of the monopile was used to apply the wave load, (2) centroid of
the tower geometry was used to apply the horizontal wind force, (3) the
top edge of the tower was used to apply the wind load acting on the
rotor blades and (4) the structural weight consisting of the rotor and
nacelle was applied on the tower vertically.\selectlanguage{english}
\begin{longtable}[]{@{}l@{}}
\toprule
Fig. 5 Schematic of the model geometry and loading conditions. The weld
geometry is shown in the enlarged view on the right. Only the bottom
most weld (shown in solid red line) was included in the model. {[}Note:
Figure is not to scale. HAZ: heat affected zone, WM: weld metal, BM:
base metal{]}.\tabularnewline
\bottomrule
\end{longtable}
Table 2. Aerodynamic and hydrodynamic load cases used in the FE model\selectlanguage{english}
\begin{longtable}[]{@{}lllllllll@{}}
\toprule
Load case & Load case probability & Cycles & Wind load (kN) & Wind load
(kN) & Wind load (kN) & Wave load (kN) & Wave load (kN) & Wave load
(kN)\tabularnewline
\midrule
\endhead
& & & Blade & Tower & Frequency & Inertia & Drag &
Frequency\tabularnewline
1 & 0.6119 & 1286459 & 217 & 2 & 0.0275 & 190 & 1 & 0.225\tabularnewline
2 & 0.2986 & 627777 & 515 & 12 & 0.0225 & 462 & 6 & 0.2\tabularnewline
3 & 0.0733 & 154106 & 826 & 32 & 0.0175 & 773 & 17 &
0.175\tabularnewline
4 & 0.0145 & 30485 & 1145 & 61 & 0.0125 & 1067 & 38 &
0.15\tabularnewline
5 & 0.0017 & 3574 & 1466 & 100 & 0.0075 & 1343 & 72 &
0.13\tabularnewline
6 & 0.0001 & 210 & 1769 & 145 & 0.0035 & 1483 & 105 &
0.12\tabularnewline
\bottomrule
\end{longtable}
Owing to the large difference between the dimensions of the turbine and
the circumferential weldments, a global-local FE model was used in this
study. The global FE model was meshed with elements of sizes varying
between 0.5m and 0.1m, where the mesh was refined at regions closer to
the weldment to keep the element aspect ratio within 0.1. The element
size in the local model was further reduced between 3mm and 20mm as
shown in Fig. 6. A 20-noded quadratic hexahedral (brick) element with
reduced integration (C3D20R) was used to avoid shear locking phenomenon
encountered during bending. In the global model, 2 elements were used
across the thickness of the cylinder so that the total number of
elements in the geometry was 10340. In order to improve the accuracy in
the local model, the same was increased to 5 elements in the local
model, thereby resulting in 61500 elements.\selectlanguage{english}
\begin{longtable}[]{@{}l@{}}
\toprule
Fig. 6 FE model mesh showing the two step modelling approach: stress
distribution from global model was applied as boundary condition in the
local model at the weldment\tabularnewline
\bottomrule
\end{longtable}
\textbf{Results and discussion}
The strain controlled cyclic test results showed that the load carrying
capacity of the cross-weld specimen was comparable to that of the base
metal. Static test results in the literature {[}20{]} presented in Table
1, showed that the strength of weld section and heat affected zone were
both slightly higher than the base metal but such behaviour was not
noticed in the cyclic test performed in this study. This can be
explained by the cyclic softening behaviour (Fig. 7) observed within the
first 20 cycles in this study. Strain controlled test leads to
application of plastic strains to the material, i.e. the material is
deformed well beyond the yield strength. Since a stress plateau region
is characteristic of metals due to work hardening, the difference in the
behaviour of the cross-weld specimen and base metal specimen becomes
negligible. Moreover, the application of cyclic loads causes the stress
to relax in consecutive cycles owing to the Bauschinger effect.
Therefore, the experimental results obtained from this study indicate
that the cyclic deformation behaviour of circumferential welds employed
in OWT structures can be predicted using the base metal material
properties.\selectlanguage{english}
\begin{longtable}[]{@{}l@{}}
\toprule
Fig. 7 Cyclic softening response of S355 G10+M under strain controlled
loading condition obtained from the test\tabularnewline
\bottomrule
\end{longtable}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image13/image13}
\end{center}
\end{figure}
Fig. 8 (a) von Mises stress profile in the OWT structure obtained for
the 6 load cases from Table. 2, (b) sub-model result for load case 6 to
highlight the local stress concentration at the weld toe, (c) axial
stress (in y-direction) vs. axial strain variation at the weld toe for
the (cyclic) load case 6.
The peak local stress values in the OWT structure was obtained from FE
analysis and the results are shown in Fig. 8. As seen in Fig. 8(b), the
higher stress values were found near the weld toe with lower values
found further away from the weld region. Also seen in this figure is
that the maximum stress values at the weld toe was below the yield
stress of the material, indicating zero or limited plastic deformation
during the operational life of the OWT monopile. The deformation in the
OWT caused bending stresses, therefore the stress at the weld toe was
compared to a nearby region instead of the nominal stress further away.
Moreover, since the weld geometry was included in the model, the effect
of stress concentration at the weldment has been considered. It should
be mentioned that the weld geometry used in the FE analysis was taken
from literature where S355 welds were performed on 90mm thick plates as
considered in this study {[}19{]}. The stress concentration factor for
the chosen weld geometry was found to be 1.18 which falls between the
values reported by Kolios et al. {[}19{]}. The maximum stress produced
at the weld toe of the circumferential weld in the monopile was fully
reversed, i.e mean stress was zero. Assuming that the weld is free from
any residual stresses, a null mean stress condition would indicate that
the structure will have better resistance to fatigue crack growth since
only half of the cycle (when stress is tensile in nature) can contribute
towards fatigue crack growth. For all the six load cases (refer Table 2
for values) the stress vs. strain curve showed elastic behaviour similar
to that of shown in Fig. 8(c). This suggests that the stresses in the
monopile are well within the design criterion and the S-N fatigue design
life approach can be employed to estimate the remaining life of the
service exposed monopile. However, this study has not taken the effect
of residual stress and environment interaction which can have
significant effects on the result. Further, the calibrated material
model's contribution was negligible since the stress values were found
be within the elastic regime of the material. However, the proposed
cyclic plasticity material model would be useful for applications
looking into the effect of hammering loads on the monopile during the
installation process in future work as well as the fatigue life
assessment in the case of storm events (i.e. over loads).
Fig. 9(a) shows the maximum stress and strain values for the respective
load cases obtained from the FE model. The selected weld geometry showed
a stress concentration value of 1.18 but it is worth mentioning that
depending on the weld profile, the stress concentration factor for OWT
weldments are reported to vary between 1.1 to 1.6 {[}19{]}. Therefore,
according to the DNVGL-RP-C203 standard {[}32{]} (Eq. 7 for as welded
joints in free corrosion environment which is referred to as D curve),
the number of fatigue cycles to failure corresponding to each load case
was determined.\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(\log{N_{i}=}\ 11.687-3\log\left(\sigma_{i}\left(\frac{t}{t_{\text{ref}}}\right)^{0.2}\right)\) & (7)\tabularnewline
\bottomrule
\end{longtable}
where \emph{[?]σ\textsubscript{i}}\selectlanguage{english} is the stress range corresponding to
which the cycles to failure \emph{N\textsubscript{i}} is calculated.
Further, the monopile structure in this study consists of a weldment of
90mm thickness, therefore a thickness correction is applied according to
the guidelines provided in DNVGL-RP-C203 standard such
that\emph{t\textsubscript{ref}} denotes a thickness of 25mm and \emph{t}
is the corrected weld thickness. Since the plate thickness and weld
width, both affect the local stress field at the weld toe, the effective
thickness of the plate was given by Eq. 8. For the weld geometry
considered in this study, the values of plate thickness \emph{T} and
weld width \emph{L} are 90mm and 54mm, respectively as shown in Fig. 5.\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(t=min[\left(14mm+0.66L\right),T]\) & (8)\tabularnewline
\midrule
\endhead
\(D=\sum_{n=1}^{6}\frac{n_{i}}{N_{i}}\) & (9)\tabularnewline
\bottomrule
\end{longtable}
Following this, the damage \emph{D} for each load case was calculated
using Palmgren-Miner method as shown in Eq. (9). Depending on the load
case probability given by the rainflow algorithm in Table 2, the number
of fatigue cycles to which the monopile structure is subjected to over a
period of 20 years (\emph{n\textsubscript{i}} ) was calculated. Since
the wind and wave characteristics were measured for a period of 2 years,
it was assumed that similar characteristics are applicable for a period
of 20 years, which is the design life of the OWT structure.
Subsequently, the number of fatigue cycles to failure
(\emph{N\textsubscript{i}} ) was calculated from the stress-life
equation given in Eq. (7). Fig. 9(b) shows the number of fatigue cycles
sustained by the OWT in the 20 years of operation
(\emph{n\textsubscript{i}} ) and the number of cycles that the
structural material (S355) can withstand before fatigue failure occurs
(\emph{N\textsubscript{i}} ). Fig. 9(c) shows that at the end of 20
years, the total fatigue damage in the monopile structure caused due to
all the load cases is well within the design limits and the cumulative
damage value was found to be 7.13\%. This shows a sufficiently large
safety margin against failure. It is worth noting that the present study
has been conducted on a monopile weldment geometry with a relatively low
stress concentration factor as the weld toe and in the absence of
welding residual stresses. Therefore, further studies will be conducted
in future work to account for the variation in stress concentration
factors as well as the residual stress profiles to provide a more
accurate estimation of the OWT monopile fatigue life under realistic
operational loading conditions.
This study found that the presently followed design criterion is leading
to over designing of the OWT structure, thereby adding to the CAPEX cost
and impacting the commercial aspect of the wind energy production. The
maximum stress and strain in the structure were found to be within the
elastic regime of S355 G10+M. Plastic deformation was not observed for
any of the load cases, therefore indicating that the monotonic
properties of the material are sufficient for determining the design
limits. The cyclic deformation behaviour of S355 G10+M was studied
experimentally as it is widely used in a number of structural
applications, and can be used to investigate the effect of over loads on
the structure. Further, the proposed parameters for the cyclic
deformation analysis using FE method will be useful for over load
analysis.\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
(a) & (b)\tabularnewline
\midrule
\endhead
(c) Fig. 9 (a) Maximum stress and strain values for the respective load
cases obtained from the FE model, (b) for each load case, the number of
fatigue cycles sustained by the OWT in the 20 years of operation
(\emph{n\textsubscript{i}}) is shown by the marker points and the number
of cycles that the structural material (S355) can withstand before
fatigue failure occurs (\emph{N\textsubscript{i}}) is shown by the
dotted line, (c) fatigue damage caused by individual load cases and the
cumulative fatigue damage according to Minor's method. & (c) Fig. 9 (a)
Maximum stress and strain values for the respective load cases obtained
from the FE model, (b) for each load case, the number of fatigue cycles
sustained by the OWT in the 20 years of operation
(\emph{n\textsubscript{i}}) is shown by the marker points and the number
of cycles that the structural material (S355) can withstand before
fatigue failure occurs (\emph{N\textsubscript{i}}) is shown by the
dotted line, (c) fatigue damage caused by individual load cases and the
cumulative fatigue damage according to Minor's method.\tabularnewline
\bottomrule
\end{longtable}
\textbf{Conclusions}
The aim of this study was to find the fatigue damage accumulated in the
offshore wind turbine (OWT) monopile structure under service loading
conditions. A mixed (isotropic and kinematic) hardening approach was
used to model the non-linear cyclic response of S355 G10+M material. The
findings can be summarised as follows:
(1) Strain controlled cyclic load testing of S355 showed the cyclic
softening behaviour with a 10\% drop in stress level in the stabilised
hysteresis loop for all the tested strain amplitudes.
(2) Realistic service loads were calculated by using the wind speed and
wave height data recorded from an offshore wind farm in the North-sea
using SCADA and wave buoy.
(3) A non-linear constitutive equation was proposed to model the cyclic
deformation behaviour of S355 for large strain applications (upto 3\%
strain). However, the present study showed that the peak stress and
strain values in the structure were within the elastic regime.
(4) The cumulative fatigue damage calculated for the OWT monopile was
7.13\% after 20 years of operation under the realistic service loads.
This indicates that the structural design can be optimised for reducing
the material cost, thereby making wind power generation more economic.
\textbf{Acknowledgements}
This work was supported by grant EP/L016303/1 for Cranfield, Oxford and
Strathclyde Universities, Centre for Doctoral Training in Renewable
Energy Marine Structures - REMS from the UK Engineering and Physical
Sciences Research Council (EPSRC).
\textbf{References}
{[}1{]} Dorrell G, D\selectlanguage{ngerman}íaz V. Siemens Gamesa's flagship 14 MW turbine to
power 1.4 GW Sofia offshore wind power project in the UK. Siemens Gamesa
Renew Energy 2020.
{[}2{]} Johnston B, Foley A, Doran J, Littler T. Levelised cost of
energy, A challenge for offshore wind. Renew Energy 2020;160:876--85.
https://doi.org/https://doi.org/10.1016/j.renene.2020.06.030.
{[}3{]} Sharifzadeh M, Lubiano-Walochik H, Shah N. Integrated renewable
electricity generation considering uncertainties: The UK roadmap to 50\%
power generation from wind and solar energies. Renew Sustain Energy Rev
2017;72:385--98.
https://doi.org/https://doi.org/10.1016/j.rser.2017.01.069.
{[}4{]} Barutha P, Nahvi A, Cai B, Jeong HD, Sritharan S. Evaluating
commercial feasibility of a new tall wind tower design concept using a
stochastic levelized cost of energy model. J Clean Prod 2019;240:118001.
https://doi.org/https://doi.org/10.1016/j.jclepro.2019.118001.
{[}5{]} MacPhee DW, Beyene A. Experimental and Fluid Structure
Interaction analysis of a morphing wind turbine rotor. Energy
2015;90:1055--65.
https://doi.org/https://doi.org/10.1016/j.energy.2015.08.016.
{[}6{]} Regodeseves PG, Morros CS. Unsteady numerical investigation of
the full geometry of a horizontal axis wind turbine: Flow through the
rotor and wake. Energy 2020;202:117674.
https://doi.org/https://doi.org/10.1016/j.energy.2020.117674.
{[}7{]} Jin Q, Li VC. Structural and durability assessment of
ECC/concrete dual-layer system for tall wind turbine towers. Eng Struct
2019;196:109338.
https://doi.org/https://doi.org/10.1016/j.engstruct.2019.109338.
{[}8{]} Yadav KK, Gerasimidis S. Imperfection insensitive thin
cylindrical shells for next generation wind turbine towers. J Constr
Steel Res 2020;172:106228.
https://doi.org/https://doi.org/10.1016/j.jcsr.2020.106228.
{[}9{]} Lin K, Xiao S, Zhou A, Liu H. Experimental study on long-term
performance of monopile-supported wind turbines (MWTs) in sand by using
wind tunnel. Renew Energy 2020;159:1199--214.
https://doi.org/https://doi.org/10.1016/j.renene.2020.06.034.
{[}10{]} Ma H, Yang J. A novel hybrid monopile foundation for offshore
wind turbines. Ocean Eng 2020;198:106963.
https://doi.org/https://doi.org/10.1016/j.oceaneng.2020.106963.
{[}11{]} Long L, Mai QA, Morato PG, Sørensen JD, Thöns S. Information
value-based optimization of structural and environmental monitoring for
offshore wind turbines support structures. Renew Energy
2020;159:1036--46.
https://doi.org/https://doi.org/10.1016/j.renene.2020.06.038.
{[}12{]} Farrar CR, Worden K. Structural Health Monitoring: A Machine
Learning Perspective. Struct Heal Monit A Mach Learn Perspect 2012.
https://doi.org/10.1002/9781118443118.
{[}13{]} Jacob A, Mehmanparast A, D'Urzo R, Kelleher J. Experimental and
numerical investigation of residual stress effects on fatigue crack
growth behaviour of S355 steel weldments. Int J Fatigue 2019;128.
https://doi.org/10.1016/j.ijfatigue.2019.105196.
{[}14{]} Mehmanparast A, Brennan F, Tavares I. Fatigue crack growth
rates for offshore wind monopile weldments in air and seawater: SLIC
inter-laboratory test results. Mater Des 2017.
https://doi.org/10.1016/j.matdes.2016.10.070.
{[}15{]} Mehmanparast A, Taylor J, Brennan F, Tavares I. Experimental
investigation of mechanical and fracture properties of offshore wind
monopile weldments: SLIC interlaboratory test results. Fatigue Fract Eng
Mater Struct 2018;41:2485--501. https://doi.org/10.1111/ffe.12850.
{[}16{]} Arany L, Bhattacharya S, Macdonald J, Hogan SJ. Design of
monopiles for offshore wind turbines in 10 steps. Soil Dyn Earthq Eng
2017;92:126--52.
https://doi.org/https://doi.org/10.1016/j.soildyn.2016.09.024.
{[}17{]} Biswal R, Mehmanparast A. Fatigue damage analysis of offshore
wind turbine monopile weldments. Procedia Struct. Integr., 2019.
https://doi.org/10.1016/j.prostr.2019.08.086.
{[}18{]} Bocher M, Mehmanparast A, Braithwaite J, Shafiee M. New shape
function solutions for fracture mechanics analysis of offshore wind
turbine monopile foundations. Ocean Eng 2018;160:264--75.
https://doi.org/https://doi.org/10.1016/j.oceaneng.2018.04.073.
{[}19{]} Kolios A, Wang L, Mehmanparast A, Brennan F. Determination of
stress concentration factors in offshore wind welded structures through
a hybrid experimental and numerical approach. Ocean Eng 2019;178:38--47.
https://doi.org/https://doi.org/10.1016/j.oceaneng.2019.02.073.
{[}20{]} Jacob A, Oliveira J, Mehmanparast A, Hosseinzadeh F, Kelleher
J, Berto F. Residual stress measurements in offshore wind monopile
weldments using neutron diffraction technique and contour method. Theor
Appl Fract Mech 2018. https://doi.org/10.1016/j.tafmec.2018.06.001.
{[}21{]} Yeter B, Garbatov Y, Guedes Soares C. Numerical and
experimental study of the ultimate strength of a monopile structure. Eng
Struct 2019;194:290--9.
https://doi.org/https://doi.org/10.1016/j.engstruct.2019.05.074.
{[}22{]} Mai QA, Weijtjens W, Devriendt C, Morato PG, Rigo P, Sørensen
JD. Prediction of remaining fatigue life of welded joints in wind
turbine support structures considering strain measurement and a joint
distribution of oceanographic data. Mar Struct 2019;66:307--22.
https://doi.org/https://doi.org/10.1016/j.marstruc.2019.05.002.
{[}23{]} Ambühl S, Kofoed JP, Sørensen JD. Determination of wave model
uncertainties used for probabilistic reliability assessments of wave
energy devices. Proc Int Offshore Polar Eng Conf 2014;2:508--15.
{[}24{]} Moghaddam BT, Hamedany AM, Taylor J, Mehmanparast A, Brennan F,
Davies CM, et al. Structural integrity assessment of floating offshore
wind turbine support structures. Ocean Eng 2020;208:107487.
https://doi.org/10.1016/j.oceaneng.2020.107487.
{[}25{]} Igwemezie V, Mehmanparast A, Kolios A. Materials selection for
XL wind turbine support structures: A corrosion-fatigue perspective. Mar
Struct 2018. https://doi.org/10.1016/j.marstruc.2018.06.008.
{[}26{]} Igwemezie V, Mehmanparast A. Waveform and frequency effects on
corrosion-fatigue crack growth behaviour in modern marine steels. Int J
Fatigue 2020;134:105484.
https://doi.org/10.1016/j.ijfatigue.2020.105484.
{[}27{]} Modulus T, Modulus C, Rates S. Strain-Controlled Fatigue
Testing 1. ASTM Stand E606 2013;92:1--16.
https://doi.org/10.1520/E0606-04E01.Copyright.
{[}28{]} Zhao D, Han N, Goh E, Cater J, Reinecke A. Offshore wind
turbine aerodynamics modelling and measurements. Wind Turbines Aerodyn
Energy Harvest 2019:373--400.
https://doi.org/10.1016/b978-0-12-817135-6.00005-3.
{[}29{]} ASTM E1049. Standard practices for cycle counting in fatigue
analysis. ASTM Stand 2017;85:1--10.
https://doi.org/10.1520/E1049-85R17.2.
{[}30{]} Hansen MO. Chapter 6:The classical blade element momentum
method. 3rd ed. Taylor Francis Group; 2015.
https://doi.org/10.1049/ip-a-1.1983.0080.
{[}31{]} Models for metals subjected to cyclic loading. Abaqus Anal.
User's Guid., vol. 6.14, Dassault Systèmes; 2014.
{[}32{]} Norske Veritas D. RECOMMENDED PRACTICE DET NORSKE VERITAS AS
Fatigue Design of Offshore Steel Structures. 2011.
\selectlanguage{english}
\FloatBarrier
\end{document}