Jan Mathisen 24 February 2010
RBI Intro & some activities at DNV
Fatigue Workshop
© Det Norske Veritas AS. All rights reserved.
RBI Intro & some activities at DNV
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
© Det Norske Veritas AS. All rights reserved.
RBI Intro & some activities at DNV
24 February 2010
3
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
© Det Norske Veritas AS. All rights reserved.
RBI Intro & some activities at DNV
24 February 2010
4
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.
© Det Norske Veritas AS. All rights reserved.
RBI Intro & some activities at DNV
24 February 2010
5
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
© Det Norske Veritas AS. All rights reserved.
RBI Intro & some activities at DNV
24 February 2010
6
From APIRP 579:
Crack depthincrement per cycle
as a function of log stress intensity factor range
© Det Norske Veritas AS. All rights reserved.
RBI Intro & some activities at DNV
24 February 2010
7
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
© Det Norske Veritas AS. All rights reserved.
RBI Intro & some activities at DNV
24 February 2010
8
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
© Det Norske Veritas AS. All rights reserved.
RBI Intro & some activities at DNV
24 February 2010
9
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
© Det Norske Veritas AS. All rights reserved.
RBI Intro & some activities at DNV
24 February 2010
10
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
© Det Norske Veritas AS. All rights reserved.
RBI Intro & some activities at DNV
24 February 2010
11
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
© Det Norske Veritas AS. All rights reserved.
RBI Intro & some activities at DNV
24 February 2010
12
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
© Det Norske Veritas AS. All rights reserved.
RBI Intro & some activities at DNV
24 February 2010
13
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!
© Det Norske Veritas AS. All rights reserved.
RBI Intro & some activities at DNV
24 February 2010
14
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
© Det Norske Veritas AS. All rights reserved.
RBI Intro & some activities at DNV
24 February 2010
15
FIV – sample stress time history (A)
© Det Norske Veritas AS. All rights reserved.
RBI Intro & some activities at DNV
24 February 2010
16
FIV – sample stress time history (B)
© Det Norske Veritas AS. All rights reserved.
RBI Intro & some activities at DNV
24 February 2010
17
FIV – sample spectrum (A)
© Det Norske Veritas AS. All rights reserved.
RBI Intro & some activities at DNV
24 February 2010
18
FIV – sample spectrum (B)
© Det Norske Veritas AS. All rights reserved.
RBI Intro & some activities at DNV
24 February 2010
19
FIV – sample probability density – (A)
© Det Norske Veritas AS. All rights reserved.
RBI Intro & some activities at DNV
24 February 2010
20
FIV – sample probability density – (B)
© Det Norske Veritas AS. All rights reserved.
RBI Intro & some activities at DNV
24 February 2010
21
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?
© Det Norske Veritas AS. All rights reserved.
RBI Intro & some activities at DNV
24 February 2010
22
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]
© Det Norske Veritas AS. All rights reserved.
RBI Intro & some activities at DNV
24 February 2010
23
LC+HC - Vessel with one longitudinal bulkhead
© Det Norske Veritas AS. All rights reserved.
RBI Intro & some activities at DNV
24 February 2010
24
LC+HC - Operation: Ballast – Full last
© Det Norske Veritas AS. All rights reserved.
RBI Intro & some activities at DNV
24 February 2010
25
LC+HC - Operation: Alternating
Half cycles
© Det Norske Veritas AS. All rights reserved.
RBI Intro & some activities at DNV
24 February 2010
26
-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
© Det Norske Veritas AS. All rights reserved.
RBI Intro & some activities at DNV
24 February 2010
27
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
© Det Norske Veritas AS. All rights reserved.
RBI Intro & some activities at DNV
24 February 2010
28
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
© Det Norske Veritas AS. All rights reserved.
RBI Intro & some activities at DNV
24 February 2010
29
Safeguarding life, property and the environment
www.dnv.com
Top Related