RBI Intro & some activities at DNV
Fatigue Workshop
Jan Mathisen
24 February 2010
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
RBI Intro & some activities at DNV
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RBI - principle

Plan inspection
such that, either
0
B. the expected,
combined cost of
inspections and
repairs is
minimised.
-1
-2
Log(Prob. failure)
A. the probability of
fatigue failure is
kept below a target
level, or
No insp.
Insp.at 4.5
-3
Insp.at 9.2
Insp.at 13.4
Target
-4
-5
-6
0.0
5.0
10.0
Service time (yr)
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15.0
20.0
RBI - Quantitative
• Non-destructive testing inspection results typically, either
No crack was detected (with a certain probability of detection PoD), or
A 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.
RBI Intro & some activities at DNV
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Probabilistic crack growth
Time of
failure
Specified
time


Critical
crack
depth
Crack depth
at time t
P T f  t  Pacr  A(t )  0
 PT0  TG (acr )  t  0
Time for
crack
initiation
Time for
crack growth
to critical depth
RBI Intro & some activities at DNV
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From API
RP 579:
Crack depth
increment
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
Intercept
parameter
for growth
in depth
Increments in
crack depth a &
half-length c
per stress cycle
Stress intensity
factor range at
deepest point
da
 c A (k A ) m ; k A  k Th ; a (n0 )  a 0
dn
dc
 cC (k C ) m ; k C  k Th ; c(n0 )  c0
dn
Intercept
parameter
for growth
in length
Stress intensity
factor range at
crack tip on
surface
RBI Intro & some activities at DNV
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Slope
parameter
for crack
growth
8
Stress intensity
factor threshold
for crack growth
Initial depth
Initial length/2
RBI - Stress intensity factor range
Newman-Raju
geometry factor for
bending stress
Newman-Raju
geometry factor for
membrane stress
Stress intensity
factor range
-Separate geom.
factors at the
deepest point &
the surface tip
k   yM (a, c)  mKM   M  y B (a, c)  mKB   B  a
Bending
stress range
Membrane
stress range
Stress
magnification
factor for
membrane stress
Stress
magnification
factor for
bending stress
Dependent on crack size, can be determined from FEM
RBI Intro & some activities at DNV
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Point location and stress components
y
Axial
stress
mY
B
T
M
0
r
q
w
mZ

z
w
r
a
2c
Cross-section through hot-spot
Definition of stress components:
- membrane stress
- bending stress
- outer fibre stress
RBI Intro & some activities at DNV
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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

 da 
m
E    E rM   M  rB   B 
 dn 

As written, assumes threshold stress intensity factor range = 0
RBI Intro & some activities at DNV
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RBI –If membrane and bending stresses are linearly dependent
   B 
M

 da 
m
m
E    rM  rB     E  M 
 dn 

Familiar expectation
from 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
RBI Intro & some activities at DNV
24 February 2010
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RBI – Not linearly dependent membrane & bending stresses
120
80
Stress
40
Membrane
Bending
0
Outer fibre
Peak
Trough
-40
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 worth
pursuing!
-80
-120
-3
-2
-1
0
1
2
3
4
Time
Outer fibre
Membrane
Bending
Double
amplitude
200.0
20.0
Value at
peak
93.1
93.4
-0.3
Value at
trough
-105.3
-97.5
-7.8
Range
198.4
190.9
7.5
RBI Intro & some activities at DNV
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Flow-induced vibration (FIV) – physical context
Well fluid:
•Flow rate
•Pressure
Sub-sea
Processing:
•Bends
•chokes
•Flow-meters
•MEG injection
Vibration of
(flexible)
piping
system
Unsteady
pressure
distribution
Oscillatory
stresses
Fatigue
RBI Intro & some activities at DNV
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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)
RBI Intro & some activities at DNV
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FIV – sample spectrum (B)
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FIV – sample probability density – (A)
RBI Intro & some activities at DNV
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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?
RBI Intro & some activities at DNV
24 February 2010
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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.
- Hang.Sub.Urm@dnv.com
RBI Intro & some activities at DNV
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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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LC+HC - Non-linear analysis
400
300
Stresses [MPa]
200
100
0
-0.006
-0.004
-0.002
0
0.002
0.004
0.006
-100
-200
-300
-400
RBI Intro & some activities at DNV
Strain
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Transverse frame
in double bottom
LC+HC - Stress range from wave loading
 log nLCF
 w   0 1 
log n0

1/ h



300
Weibull dstn.
Stress range (MPa)
250
nLCF number of
loading/unloading
cycles during
lifetime
200
150
100
50
0
1
10
100
1000
10000
Log n
100000
1000000 1000000
0
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1E+08
LC+HC - Low cycle fatigue loading/unloading
 log n LCF
 w   0 1 
log n0




1/ h
 e   LCF   w  k e

  e



ke  1.0  0.4
 1 
 2


 y


ke  1.0
D  DLCF  DHCF
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for
for
  2  y
  2 y
Eurocode
plasticity
correction
EN 13445-3
-2002
Safeguarding life, property
and the environment
www.dnv.com
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