jan mathisen 24 february 2010 rbi intro & some activities at dnv fatigue workshop

Jan Mathisen 24 February 2010

RBI Intro & some activities at DNV

Fatigue Workshop

© Det Norske Veritas AS. All rights reserved.


24 February 2010

2

Contents - tentative

Risk-based inspection planning intro, with emphasis on use of stress processes --- RBI

Flow-induced vibration --- FIV

Low and high cycle fatigue in ships --- LC+HC



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RBI - principle

Plan inspection such that, either

A. the probability of fatigue failure is kept below a target level, or

B. the expected, combined cost of inspections and repairs is minimised.

-6

-5

-4

-3

-2

-1

0

0.0 5.0 10.0 15.0 20.0

Service time (yr)

Lo

g(P

rob

. fa

ilu

re)

No insp.

Insp.at 4.5

Insp.at 9.2

Insp.at 13.4

Target



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RBI - Quantitative

• Non-destructive testing inspection results typically, eitherNo crack was detected (with a certain probability of detection PoD), orA crack was detected with an estimated, uncertain size.

Requires fracture mechanics to handle information about crack sizes- S-N approach is not detailed enough

Probabilistic modelling is important to handle uncertainties in- Inspection method, load model, crack growth model, crack initiation or initial size

Reference- Sigurdsson, G., Lotsberg, I. & Landet, E., (2000), “Risk Based Inspection of FPSOs”, Int.

Conf. on Offshore Mechanics and Arctic Engineering, OMAE'2000, New Orleans.



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Probabilistic crack growth

0)(

0)(

0

taTTP

tAaPtTP

crG

crf

Time offailure

Time forcrack growthto critical depth

Time forcrackinitiation

Criticalcrackdepth

Crack depthat time t

Specifiedtime



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From APIRP 579:

Crack depthincrement per cycle

as a function of log stress intensity factor range



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RBI – fracture mechanics Lacks convenient model for crack initiation or initial crack size

- S-N data includes crack initiation- Calibrate probabilistic FM model against probabilistic S-N model- Fatigue design standards can be used to imply a target probability of failure from the

probabilistic S-N model

Paris equation models crack growth- From initial to critical crack size

Failure assessment diagram models rupture in the presence of a crack- Can give a critical crack size as a function of rupture load

References- BSI, “Guide to methods for assessing the acceptability of flaws in metallic structures,”

BS7910:2005.- API 579-1/ASME FFS-1 2007 Fitness-For-Service



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RBI - Deterministic crack growth – 2-D Paris law

00

00

)(;;)(

)(;;)(

cnckkkcdn

dc

anakkkcdn

da

ThCm

CC

ThAm

AA

Slopeparameterfor crackgrowth

Increments incrack depth a &half-length cper stress cycle

Initial depth

Initial length/2

Interceptparameterfor growthin depth

Stress intensityfactor range atcrack tip on surface

Interceptparameterfor growthin length

Stress intensityfactor thresholdfor crack growth

Stress intensityfactor range atdeepest point



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RBI - Stress intensity factor range

Stressmagnificationfactor forbending stress

Newman-Raju geometry factor formembrane stress

Stress intensityfactor range-Separate geom. factors at the deepest point & the surface tip

Membranestress range

Newman-Raju geometry factor forbending stress

Bendingstress range

amcaymcayk BKBBMKMM ),(),(

Stressmagnificationfactor formembrane stress

Dependent on crack size, can be determined from FEM



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Point location and stress components

q

w

r

y

z

mZ

mY

q

w

r

y

z

mZ

mY

Cross-section through hot-spot

2c

w

r a

M

B

T

Axialstress

0

2c

w

r a

M

B

T

Axialstress

0

Definition of stress components:- membrane stress- bending stress- outer fibre stress



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RBI – handling load process

Assume load-sequence effects negligible

Good if crack growth rate is slow compared to load variability

Then expected crack increment can be expressed in terms of distribution of stress cycles- rM and rB are dependent on crack size but independent of stress processes

mBBMM rrEdn

daE

As written, assumes threshold stress intensity factor range = 0



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RBI –If membrane and bending stresses are linearly dependent

mMm

BM

M

B

Errdn

daE

Familiar expectationfrom S-N analysis

A detail --- If the threshold stress intensity factor range is non-zero- then use conditional expectation- with a corresponding stress threshold- but this stress threshold will be dependent on crack size- and will introduce numerical noise if an empirical stress distribution is used- hence a smooth stress distribution function is desirable to ensure convergence in the reliability analysis



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RBI – Not linearly dependent membrane & bending stresses

-120

-80

-40

0

40

80

120

-3 -2 -1 0 1 2 3 4

Time

Str

es

s

Membrane

Bending

Outer fibre

Peak

Trough

Double amplitude

Value at peak

Value at trough

Range

Outer fibre - 93.1 -105.3 198.4

Membrane 200.0 93.4 -97.5 190.9

Bending 20.0 -0.3 -7.8 7.5

Suggest to:- Identify range in outer fibre stress by RFC- Pick off membrane & bending stress ranges from peak & trough- Develop a 2-D histogram for use in crack growth

Maybe a problem worthpursuing!



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Flow-induced vibration (FIV) – physical context

Well fluid:•Flow rate•Pressure

Sub-seaProcessing:•Bends•chokes•Flow-meters•MEG injection

Unsteadypressure

distribution

Vibration of(flexible)

pipingsystem

Oscillatorystresses

Fatigue



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FIV – sample stress time history (A)



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FIV – sample stress time history (B)



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FIV – sample spectrum (A)



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FIV – sample spectrum (B)



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FIV – sample probability density – (A)



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FIV – sample probability density – (B)



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FIV - Comments

Novel application, combining computational fluid dynamics (CFD) and dynamic finite element stress analysis- CFD part is CPU-intensive, only short time series practicable at present- Is the response stationary?- Needs verification

Stochastic stress response- Dominated by some of the many natural frequencies of piping system- Damping is light and uncertain in magnitude- Might tend towards harmonic response, might tend towards Gaussian response- Frequencies around 8 Hz, period of 1/8 s

Fatigue assessment- Rainflow counting applied- High cycle- Low stress ranges- Validity of S-N curves?



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Low and high cycle fatigue in ships

From presentation by Inge Lotsberg- Fatigue Methodology of Offshore Ships- Part 15 Combination of low cycle and high cycle fatigue- 17 July 2009

Some discussion to be given by Inge Lotsberg in- “Background for new revision of DNV-RP-C203 fatigue design of offshore steel structures,”

OMAE2010-20649.

See also:- “Fatigue Assessment of Ship Structures,” DNV Classification Notes, No. 30.7, Oct. 2008.- Joo-Ho Heo, Joong-Kyoo Kang, Yooil Kim, In-Sang Yoo, Kyung-Su Kim, Hang-Sub Urm: “A

Study on the Design Guidance for Low Cycle Fatigue in Ship Structure.”- Urm, H. S., Yoo, I. S., Heo, J. H., Kim, S. C. and Lotsberg, I.: “Low Cycle Fatigue Strength

Assessment for Ship Structures.” PRADS 2004.- [email protected]



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LC+HC - Vessel with one longitudinal bulkhead



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LC+HC - Operation: Ballast – Full last



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LC+HC - Operation: Alternating

Half cycles



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-400

-300

-200

-100

0

100

200

300

400

-0.006 -0.004 -0.002 0 0.002 0.004 0.006

Strain

Str

esse

s [M

Pa]

LC+HC - Non-linear analysisTransverse frame

in double bottom



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LC+HC - Stress range from wave loading

0

50

100

150

200

250

300

1 10 100 1000 10000 100000 1000000 10000000

1E+08

Log n

Str

ess r

an

ge (M

Pa)

h

LCFw n

n/1

00 log

log1

Weibull dstn.

nLCF number of loading/unloadingcycles duringlifetime



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LC+HC - Low cycle fatigue loading/unloading

h

LCFw n

n/1

00 log

log1

ye

yy

ee

fork

fork

20.1

212

4.00.1

HCFLCF DDD

ewLCFe k

EurocodeplasticitycorrectionEN 13445-3-2002



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Safeguarding life, property and the environment

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jan mathisen 24 february 2010 rbi intro & some activities at dnv fatigue workshop

Documents

crack tip

crack growth increments

crack depth increment

crack sizes s

initial crack size s

det norske veritas

growth model

time slide