OWEMES Fatigue Design 2003 Tcm4-29402

8/2/2019 OWEMES Fatigue Design 2003 Tcm4-29402

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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: [email protected]

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

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OWEMES Fatigue Design 2003 Tcm4-29402