RBI Intro & some activities at DNV

1. RBI Intro & some activities at DNV Fatigue Workshop

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

3. RBI - principle • Plan inspection such that, either • the probability of fatigue failure is kept below a target level, or • the expected, combined cost of inspections and repairs is minimised.

4. 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.

5. Time of failure Specified time Critical crack depth Crack depth at time t Time for crack initiation Time for crack growth to critical depth Probabilistic crack growth

6. From APIRP 579: Crack depthincrement per cycle as a function of log stress intensity factor range

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

8. Intercept parameter for growth in depth Stress intensity factor range at deepest point Slope parameter for crack growth Increments in crack depth a & half-length c per stress cycle Initial depth Initial length/2 Intercept parameter for growth in length Stress intensity factor range at crack tip on surface Stress intensity factor threshold for crack growth RBI - Deterministic crack growth – 2-D Paris law

9. Newman-Raju geometry factor for membrane stress Newman-Raju geometry factor for bending stress • Stress intensity • factor range • Separate geom. • factors at the • deepest point & • the surface tip Membrane stress range Bending stress range Stress magnification factor for bending stress Stress magnification factor for membrane stress RBI - Stress intensity factor range Dependent on crack size, can be determined from FEM

10. Point location and stress components Cross-section through hot-spot • Definition of stress components: • membrane stress • bending stress • outer fibre stress

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 As written, assumes threshold stress intensity factor range = 0

12. RBI –If membrane and bending stresses are linearly dependent 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

13. RBI – Not linearly dependent membrane & bending stresses • 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!

14. Unsteady pressure distribution Vibration of (flexible) piping system Oscillatory stresses • Sub-sea • Processing: • Bends • chokes • Flow-meters • MEG injection Flow-induced vibration (FIV) – physical context • Well fluid: • Flow rate • Pressure Fatigue

15. FIV – sample stress time history (A)

16. FIV – sample stress time history (B)

17. FIV – sample spectrum (A)

18. FIV – sample spectrum (B)

19. FIV – sample probability density – (A)

20. FIV – sample probability density – (B)

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?

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. • Hang.Sub.Urm@dnv.com

23. LC+HC - Vessel with one longitudinal bulkhead

24. LC+HC - Operation: Ballast – Full last

25. LC+HC - Operation: Alternating Half cycles

26. LC+HC - Non-linear analysis Transverse frame in double bottom

27. LC+HC - Stress range from wave loading Weibull dstn. nLCF number of loading/unloadingcycles duringlifetime

28. LC+HC - Low cycle fatigue loading/unloading EurocodeplasticitycorrectionEN 13445-3-2002

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