RBI Intro & some activities at DNV 19 April 2017 RBI Intro & some activities at DNV Fatigue Workshop

19 April 2017 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 - 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.

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.

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

From API RP 579: Crack depth increment per cycle as a function of log stress intensity factor range

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

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

RBI - Stress intensity factor range magnification 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 Membrane stress range Bending Dependent on crack size, can be determined from FEM

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

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

RBI –If membrane and bending stresses are linearly dependent 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 – 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 worth pursuing!

Flow-induced vibration (FIV) – physical context 19 April 2017 Flow-induced vibration (FIV) – physical context Well fluid: Flow rate Pressure Sub-sea Processing: Bends chokes Flow-meters MEG injection Unsteady pressure distribution Vibration of (flexible) piping system Oscillatory stresses Fatigue

FIV – sample stress time history (A)

FIV – sample stress time history (B)

FIV – sample spectrum (A)

FIV – sample spectrum (B)

FIV – sample probability density – (A)

FIV – sample probability density – (B)

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?

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

LC+HC - Vessel with one longitudinal bulkhead

LC+HC - Operation: Ballast – Full last

LC+HC - Operation: Alternating Half cycles

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

LC+HC - Stress range from wave loading Weibull dstn. nLCF number of loading/unloading cycles during lifetime

LC+HC - Low cycle fatigue loading/unloading Eurocode plasticity correction EN 13445-3 -2002

Safeguarding life, property and the environment 19 April 2017 Safeguarding life, property and the environment www.dnv.com