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Fatigue design of offshore wind turbines and support structures
Author: Mr. Jan Behrendt Ibs, General Manager, M.Sc., Ph.D.
Company: Det Norske Veritas (DNV), Denmark A/S
Address: Tuborg Parkvej 8, DK-2900 Hellerup, Denmark
Tel. No. : + 45 39 45 48 38
Fax No.: + 45 39 45 48 01
E-mail: jan.ibsoe@dnv.com
Contents:
0. Introduction
1. Deterministic Fatigue Analyses2. Calculation of Stress Concentration Factors (SCFs) by closed form and FE3. Local Joint Flexibility4. Influence from mean stresses on fatigue life, welded and not welded plate structures5. Validity of the Palmgren-Miner Rule6. Conclusions
0. Introduction
The design of offshore wind turbines and their support structures requires mastering of multiple
technical disciplines, e.g. combined wave-wind load calculations, offshore technology and
calculation of the structural dynamics of the integrated system consisting of wind turbine, support
structure (tower and foundation structure) and soil. In order for offshore wind turbines and their
support structures to be economically feasible, optimisation of the design needs to be carried out.
Fatigue is often governing for the structural design of offshore wind turbines and the ir support
structures due to their flexible structural performance and exposure to highly dynamic loads from
wind and waves combined with the corrosive environment at sea. Design of offshore wind turbine
support structures hence requires application of state-of-the-art fatigue rules and calculation
methods.
1. Deterministic Fatigue Analyses
The procedures used today for offshore fatigue inspection planning are closely related to the
procedure adopted for deterministic fatigue analysis. Hence, the fatigue inspection planning are
today based on deterministic fatigue analysis and not spectral analysis. Fatigue calibration studies
performed for the platforms in the Danish part of the North Sea have shown that it is possible to
predict the fatigue loading with a very low scatter using the deterministic approach.
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Wave Load
The analysis is to be based on discrete wave statistics as given for the particular area in question.
Normally, the waves are given in one-meter wave height intervals from 8 compass directions. For
waves between 0 and 1 m, intervals of 0.2 m should be applied to the sensitivity to the fatigueloading in this interval.
The wave theory to be applied for the calculation of wave kinematics very much dependent on the
water depth at the actual location. In shallow waters, i.e. for water depths less than approximately
15 m, higher order stream function theory is to be applied. For deeper water, i.e. for water depths
larger than approximately 30 m, Stokes 5th
order wave theory is to be applied.
For tubular members the following hydrodynamic coefficients apply for water depths larger than
approximately 20 meters:
Nominal diameter less than or equal to 2.2 m: CD = 0.8 and CM = 1.6
Nominal diameter larger that 2.2 m: CD = 0.7 and CM = 2.0
If a standoff type of anodes protects the support structure equally distributed over the structure, the
hydrodynamic coefficients are to be increased by 7 % between MSL and seabed.
Each of the fatigue waves is stepped through the structure over one wave period. The corresponding
stress range in the structure is to be calculated based on at least 8 equidistant points over each wave
period.
Marine growth is to be taken into account by increasing the outer diameter in the wave load
calculations.The following marine growth profile generally applies in the North Sea, see Figure
1.1:
Distance below MSL Design profile
0-10m 50 mm
10-20m 45 mm
20-25m 65 mm25-35m 90 mm
35m to bottom 80 mm
Figure 1.1 Marine growth profile.
Dynamic amplification shall be taken into account.
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If the natural period is less than or equal to 2.5 seconds, a dynamic amplification factor (DAF) may
be included on the wave load using a single degree of freedom DAF as:
Where
Damping ratio (relative to critical damping)
= Relevant natural period/fatigue wave period
If the natural period of the integrated design of wind turbine, support structure and foundation is
above 2.5 seconds, a direct time domain shall be carried out to determine the relevant dynamicamplification factors.
The structural damping ratio for tripod type support structures can generally be chosen as 1 %
relative to the critical damping. The vibration modes relevant for determination of DAFs are
typically the global sway modes, which can be excited by wave loading.
Corrosion Allowance
Steel structure components in the splash zone shall be protected by corrosion protection systems,
which are suitable for resisting the aggressive environment in this zone. Recognised design practice
involves the application of corrosion allowance as main system for corrosion protection in thesplash zone, i.e. the wall thickness is increased due to corrosion. The particular corrosion allowance
for a given location shall be assessed in each particular case. However, as guidance for calculation
of corrosion allowance it can generally be assumed that the rate of corrosion in the splash zone is in
the range of 0.3 0.5 mm/per year, ref./1/. It should be noted that, in general, the rate of corrosion
will increase proportional with the age of the structure.
It is recommended to combine the protection system based on corrosion allowance with surface
treatment, e.g. with glass fibre reinforced epoxy paint. It is a normal practice not to take into
consideration that the surface treatment reduces the rate of corrosion, however the beneficial effect
on the fatigue life (i.e. in selection of the relevant SN-curve) is to be taken into account.
Corrosion allowance is to be taken into account by decreasing the nominal wall thickness in the
fatiguecalculations. A corrosion allowance of 6 mm should be applied on all primary steel in the
splash zone for fatigue analyses. For secondary structures, a corrosion allowance of 2 mm in the
splash zone can be applied.
In a zone around the seabed it is recommended to combine the cathodic protection with a corrosion
allowance of 3 mm on e.g. piles, and to calculate with a fatigue life endurance reduced by a factor
of 2, which takes into accountthat a optimal cathodic protection is not obtainable in this area due to
the an-aerobic environment in this zone.
222 211DAF
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2. Calculation of Stress Concentration Factors (SCFs) by closed form and FE
SCFs using Parametric Equations
SCFfor Tubular Joints
Calculations of stress concentration factors (SCF) for simple planar tubular joints can be carried out
applying the equations given in the below Figure 2.1:
Validity Range*3Joint TypeEquation Reference
T & Y Efthymiou 4-40 0.2-1.0 8-32 0.2-1.0 30 -90 NA /8/
DT & X Efthymiou 4-40 0.2-1.0 8-32 0.2-1.0 30 -90 NA /8/
K & KT Lloyd's 4 0.13-1.0 10-35 0.25-1.0 30 -90 0-1 /9/
Figure2.1 Parametric equations for SCF in tubular joints.
A minimum SCF equal to 1.5 should be adopted if no other documentation is available.
For fatigue life calculations, the equations given in above Table are consistent together with the
T SN curve in Ref. /2/:
k
reft
tmaN logloglog
(1) In Air:
log a = 12.164,m = 3 for N = 107
log a = 15.606, m = 5 for N > 107
(2) In Water with adequate Cathodic protection:
log a = 11.764, m = 3 for N = 106
log a = 15.606, m = 5 for N > 106
where
N = Fatigue life in numbers of load/stress cycles
Stress trange in MPa
m = negative inverse slope of the S N curve
log a = intercept of log N axis
tref = For tubular joints the reference thickness is 32 mm.
t = thickness through which a crack will most likely grow. t = tref is used for thickness
less than trefk = 0.25 for tubular joints
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Low
High
DegreeofConservatism
Regarding fatigue life improvement by e.g. weld toe grinding for tubular joints and weld profile
grinding for tubular girth welds and the influence on the SN-curve, reference is made to/1/ and /2/.
For classification of simple tubular joints reference is made to /2/, Annex C, Appendix 2.
If multi-planar effects are not negligible, the following solutions are possible:
Detailed FE Analyses of the multi-planar joint
A complex multi-planar joint may be assessed based taking the largest possible SCF for
each brace considering the connection to be a Y, X or K joint.
If conical stubs are used, the stress concentration may be determined using the cone cross section at
the point where the cone centre line crosses the outer surface of the chord. For gappedjoints with
conical stubs, the true gaps shall be applied.
SCF for Tubular to Tubular Girth Welds
In tubular to tubular girth welds, geometrical stress increases are caused by local bending moments
in the tube wall. The bending moments are created by centreline misalignment (due to tapering and
fabrication tolerances) and differences in hoop stiffness oftubules of different thickness.
The geometrical stress increase is not included in the SN curves applicable for girth welds and
should thus be included in the stress range.
The numerical largest geometrical SCF (hotspot stress) may be estimated using one of the equations
in the below Figure 2.2.
Equation
IDEquation Nomenclature
Tube-A
Tube-B
T: Member thickness
T1 T2
e: Wall midline offset
between tube 1 and
tube 2
Figure 2.2 SCF equations for girth welds.
5.1
1
21
1
161
T
TT
eSCF
1
31
T
eSCF
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Fabrication tolerances on the local wall centreline misalignment (high/low) are to be included in
the determination of the SCF. If the location and size of the fabrication tolerances are unknown (not
measured), the tolerances are to be applied in the direction giving the highest SCF.
Generally, the max fabrication tolerances as given in the below Figure 2.3 can be applied.
Single Sided Full Penetration Welds Double Sided Full Penetration Welds
Figure 2.3 Fabrication tolerances for tubular to tubular girth welds. T1 is the smallest wall
thickness of the adjoining tubes
SCFs using Finite Element Analysis
The finite element method is ideally suited for estimation of stress concentrations in complex
geometry. General-purpose FE programs are available which allow large and complex analyses to
be performed. However, care should be taken that reliable analyses are performed.
Stress Extrapolation
SN curves for welded details are developed from fatigue tests of representative steel specimen. At
the weld root/toe positions a stress singularity is present. i.e. stresses approach infinity. At the same
time it is impossible during testing to measure the strain directly at the weld root/toe location, as
strain gauges can not fitted directlyat the root/toe location due to the presence of the weld. Hence,
the notch stress at the singularity has no meaning as stress reference, as it can not be measured and
as it approaches infinity (see below Figure 2.4 for typical stress distribution in welded details).
efab
efab
efab
efab
12.03min
Tmmofefab
12.0
6minT
mmofefab
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Stress distribution along surface normal to weld
Stress Distributions through the thickness of the plate/tube wall
Notch Stress Zone Geometric stress zone Nominal Stress Zone
Figure 2.4 Definition of stresses in welded structures. The three lower drawings show the
distributions of stress through the thickness of the tube/plate wall in the different stress regions
To overcome this problem and have a unique detail dependent stress reference for welded details,
which is compatible with standard stress sampling, i.e. strain gauges, the so-called hotspot stress
is used as reference for the SN-curves covering welded details. The hot spot stress is an imaginary
reference stress. It is established by extrapolation of stresses form outside the notch zone and into
the singularity at the weld root/toe. During testing (e.g. for establishing the SN-curve) strain gauges
are located in the same extrapolation points and the hot spot stress is established by processing the
measures.
For tubular joints the hot spot stress is found by linear extrapolation as defined in the below Figure
2.5.
Section A-A Section B-B Section C-C
Notch stress
Geometric stress
Nominal stress
A B C
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Stress Extrapolation Points in Brace
Stress Extrapolation Points in Chord
Figure 2.5 Definition of the geometric stress zone in tubular joints. The hotspot stress is
calculated by a linear extrapolation of the stress in the geometric stress zone to
the weld toe
The SN curves for single sided and double-sided full penetration welds in plates and tubules are
also based on the hotspot stress methodology. As no curvature is present in plate structures, the
tubular joint definition of the hot spot stress, see above Figure, cannot be applied for plate
structures.
For plate structures the definition given in Ref. /2/ or /4/ can be applied, see below Figure 2.6.
Chord:
RC = chord radius
TC = chord thickness
Brace:
RB = brace radius
TB = brace thickness
Stress
extrapolation inbrace parallel
to brace axis
Stress
extrapolation in
chord
perpendicular
to weld
Geometric stress
zones:
Brace side
Chord side
SCF Stress
BBTR65.0
BBTR2.0
25.04.0 CCBB TRTR
SCF
Stress
BBTR2.0
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.
Figure 2.6 Stress extrapolation locations for plate structures and girth welds. Distances are
measured from the notch (typically weld toe or weld root). 0.4T/1.0T are recommended inRef./4/
and 0.5T/1.5T are recommended by Ref. /2/. Stress extrapolation always from the plate with the
smallest thickness
The definition of the geometric stress zone given in the above Figure 2.6 is applicable for plates as
well as for girth welds in tubular sections.
When using the FE method for determination of the hot spot stress, the stress extrapolation
philosophy as outlined above is generally to be followed, i.e. the notch stress shall be excluded by
use of extrapolation and SCF directly based on the extrapolated geometric stress.
Welded details Location of Weld Singularity
For a complete 3D FE model completely representing the 3D shape of the actual detail inclusive
weld profiles etc, hotspot stresses can be obtained directly using the relevant stress extrapolation
points given in the above Figures. For simplified models, such as e.g. shell models of thin plate
structures without weld modelling, some modifications to stress extrapolation need to be
1.0T (1.5T)
0.4T (0.5T)
Normal to
Weld Stress
SCF
T
1.0T (1.5T)
0.4T (1.5T)
SCF
Stress singularity at
weld root
Stress singularity at
weld toe
Normal to
Weld Stress
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introduced. The definition of the hotspot (weld toe or root singularity) location in relation to stress
extrapolation for different modelling detail/approach is given in the below Figure 2.7.
Solid elements with weld profile
modelled
Solid elements without weld
profile
Shell elements (no weld profile
included)
Extrapolation to: Extrapolation to: Extrapolation to:
Weld toe Intersection of surfaces Midline intersection
Figure 2.7 Location of weld singularity for hot spot stress extrapolation dependent upon element
types used in tubular joint FE models. The green arrows give the primary positions. The yellow
arrow pointing at the imaginary surface intersection in shell models defines an alternative location,
which may be adopted for shell models if it can be justified. The location of the red arrows may not
be used for extrapolation.
Based on the definition of weld singularity location, see the above Figure, and the extent of the
geometric stress zone, the relevant locations/elements in the model for extrapolation can be
selected.
It should be noted, that for FE models which do not include a detailed model of the weld, the
extrapolation point distances is measured from the Hotspot Stress Location as given by the green
arrows in the above Figure, i.e. not from the location of the imaginary weld toe (red arrows in the
above Figure).
The extrapolation shall be based on the surface stress, i.e. not the midline stress for shell models.The most correct stress is the normal to weld stress. The surface stress is to be based on averaged
nodal stresses.
3. Local Joint Flexibility
The main reason why the stiffness of the joints is interesting is that normally the design of offshore
structures is based in an analysis assuming rigid beam connections at the joints, which is not in
accordance with the actual design. Joint flexibility will change the static and dynamic behaviour of
the structure, and thus also the fatigue life.
Solid element model
with weld profileSolid element model
without weld profile
Shell element model (no
weld modelled)
OK OKOK
Maybe
No No
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Traditionally, a node to node beam modelling is adopted for analysis ofspace frame jacket
structures. The beam elements are rigidly connected in the centre line intersections. The sectional
forces used to derive the stress range are collected at the intersection points (nodes). This procedure
generally yields conservative results for fatigue analyses as the sectional moments in the brace ends
are predicted too high.
Inclusion of the local joint flex modelling at the nodes, see Figure 3.1 reduces the moments in the
member ends. Furthermore, a local flex model allows that sectional forces are retrieved at the
correct location (at the surface footprint of the brace to chord connection). Implementation of local
joint flexibility in the model will give a more correct force flow in the structure. Inclusion of LJF in
the global frame model will change the force flow in the structure (lower bending moments in
joints, higher member normal forces). Therefore, it is generally not acceptable to include LJF
springs in joint only. Springs shall also be included in joints influencing the force distribution to the
joint being analysed; i.e. isolated or separate parts of the structure may include LJF.
Figure. 3.1 Traditional node to node modelling in jacket space frame structures (left) and
refined node modelling with local joint flexibility (right) Note that the LJF spring nodes are
to be coincident. The nodes are only separated in the figure for illustrative purposes.
Parametric equations for LJF
The Buitrago parametric equations given in ref./3/ can generally be applied.
Preferable joint classification should be dependent upon force flow (for joints with more than one
brace in each plane). This will generally need an iterative procedure to be applied. However, a
simple joint classification may be acceptable, i.e. all joints are considered as T/Y joints when
determining LJF.
LJF in Multi-Planar Joints
The parametric equations are primarily based on planar joints and do in principle not cover
Rotational and/or axial
LJF spring
Stiff offset elementBeam element
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multi-planar joints. However, from FE studies carried through it is concluded that out-of-plane
braces have a negligible influence on the local joint flexibility for the bending moment loading, and
generally some effect for axial loading. As it is the rotational flexibility, which influences the
fatigue life, it is thus concluded that the planar joint LJFs may be applied for multi-planar joints as
well. This conclusion is based on non-stiffened and non-overlapping joints within a traditionallybraced jacket structure.
Implementation of LJF in Global Finite Element Model
Based on the above, the following should be implemented in the global support structure finite
element model regarding Local Joint Flexibility:
1. Automatic implementation of Local Joint Flexibility in all joints according to Buitrago
parametric formula
2. Automatic calculation of sectional forces at the surface footprint of the brace to chord connection3. Classification of joints (T/Y/X/XT joints) dependent on load path (i.e. not from geometry)
4. Influence from mean stresses on fatigue life, welded and not welded plate structures
For structural details where the magnitude of the welding residual stresses and stress concentration
are relatively small, such as plate stiffener details in a wind turbine tower, some reduction in the
fatigue damage can credited when parts of stress range are in compression.It should be emphasised
that the below formulas do not apply to tubular joints due the presence of high concentration factors
and high, long range welding residual stresses (which are not easily relaxed due to loading) in
tubular joints.
Non-welded structures details
For fatigue analysis of regions in base material not significantly affected by residual stresses due to
welding, the stress range may be reduced dependent whether mean cycling stress is tension or
compression. This is due to the fact that fatigue cracks will close at least partly and at the crack tip
under compression and also under tension loading, if the mean stress (including possible residual
stresses) is relatively low. This reduction may e.g. be carried out for cut-outs in the base material.
Mean stress means the static notch stress including stress concentration factors. The calculated
stress range obtained may be multiplied by the reduction factor fm as obtained from the below
Figure 4.1 before entering the SN-curve.
Figure 4.1 Stress range reduction factor that may be used with SN-curves forbase material..
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Weldedstructural details
Residual stresses due to welding and construction are reduced over time as the structure is subjected
to loading. If a hot spot region is subjected to a tension force implying local yielding at theconsidered region, the effective stress range for fatigue analysis can be reduced due to the mean
stress effect also for regions affected by residual stresses from welding. Mean stress means the
static notch stress including stress concentration factors. The following reduction factor on the
derived stress range may be applied, see below figure 4.2.
fm = reduction factor due to mean stress effects
= 1.0 for tension over the whole stress cycle
= 0.85 for mean stress equal to zero
= 0.7 for compression over the whole stress cycle
Figure 4.2 Stress range reduction factor that may be used with SN-curves for welded structural
details (plate structures)..
5. Validity of the Palmgren-Miner Rule
The development of fatigue damage under variable amplitude loading or random loading is in
general termed cumulative damage. Several theories for calculating cumulative damage from
SN-data may be found in the literature. The far most popular method to assess cumulative damage
is to use the so-called Palmgren-Miner or Minersrule, Refs. [5] and [6]. The Palmgren-Miner Rule
and the equivalent constant amplitude stress range approach can be shown to conform with fracturemechanics analysis using the Paris-Erdogan crack growth equation and neglecting the stress
interaction or load sequence effects. In spite of the fact, that the Palmgren-Miner summation does
not take account of stress interaction or load sequence effects, it is often being used for calculating
damage in design. Comparisons with test results have shown that the Palmgren-Miner rule is no
worse thanother damage accumulation rules, and it is very simple to use.As the Palmgren Miner
rule do not account for stress interaction effects (e.g. crack growth retardation following tensile
loads and crack growth acceleration following compressive underload) , however it may in many
application be biased, see e.g. Ref. [7], leading to large uncertainties in the fatigue strength
calculations. Analytical results [7] also clearly show that conclusions about the damaging effect of
a given load spectrum may change as conditions of geometry, loading (type and level), welding
residual stresses (distribution and level) and material properties change. The conclusion is that the
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Palmgren-Miner or Miners Rule can be applied for variable amplitude loading as for offshore wind
turbines and their support structures and that when using this rule is within acceptable accuracy.
6. Conclusions
The present paper focuses on presenting state-of-art methods, recommendations, standards and rules
for design of wind turbine support structures with respect to fatigue based on recent theoretical and
experimental research and development results.During the past approximately 10 years significant
theoretical and experimental research and development has been carried through in order to
establish a more rational basis for calculation of fatigue behaviour under variable (spectrum)
loading and in corrosive environments. Significant results form this research and development
program are now available which allows for more precise calculation of fatigue problems, e.g. in
order to take into account the influence from mean stresses (influence from crack closure). These
results have also been applied as basis for testing the validity of the widely used Palmgren-Miner or
Miners damage accumulation rule. The present papers summaries the above and makes references
to state-of-the art standards and rules for the design of offshore wind turbine structures.
Ref. /1/:
DNV Rules for Classification of Fixed Offshore Installations, 2000
Ref. /2/:
NORSOK Standard N-004 Design of Steel Structures, Rev. 1, Dec. 1998
Ref. /3/:
"Local Joint Flexibility of Tubular Joints", OMAE Article 1993 by J. Buitrago, B. Healy and T.Chang
Ref. /4/:
IIW94 Recommendations on Fatigue of Welded Components, International Institute of Welding,
IIW document XIII-1539-94/XV-845-94 by A. Hobbacher
Ref. /5/:
Palmgren, A., Die Lebensdauer von Kugellagern, Zeitschrift des Vereines Deutscher Ingenieure,
Vol. 68, No. 14, 1924.
Ref. /6/:
Miner, M.A:, Cumulative Damage in Fatigue, Journal of Applied Mechanics Trans., ASME, Vol.
12, No. 3, pp. 154-164, 1945.
Ref. /7/:
J.B.Ibs, An Analytical Model for Fatigue Life Prediction Based on Fracture Mechanics and
Crack Closure, Journal ofConstructional Steel Research, Vol. 37, No. 3, pp. 229-261.
Ref. /8/:
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M. Efthymiou, Development of SCF Formulae and Generalised Influence Functions for Use in
Fatigue Analysis, Proceedings of Offshore Tubular Joint Conference, Surrey, UK October 1988.
Ref. /9/:
P. Smedley and P. Fischer, Stress Contration Factors for Simple Tubular Joints, ISOPE 1991