Reliability-based inspection planning in view of both crack initiation and propagation

· Presenter Guang Zou (research fellow, PhD student)

· Authors Guang Zou (Lloyd’s Register, UK)

Dr Kian Banisoleiman (Lloyd’s Register, UK)

Dr Arturo González (University College Dublin, IR)

The funding from the EU’s Horizon 2020 programme under the Marie Sklodowska-Curie grant agreement No. 642453 is greatly appreciated.

ESREL, 20 Jun, 2017

Serious consequences of fatigue and fracture failure Significant uncertainties associated with wave loads and fatigue

degradation Design assumptions cannot be fully satisfied during operation. Inspection/monitoring results can be utilized to support optimal

decisions on operation and maintenance.

Motivation(Structural integrity management)

Structural Integrity management (SIM) for ships

ESREL, 20 Jun, 2017

Fatigue design & S-N model

One and two-segment characteristic S-N curve

Miner’s Rule

Limit-state function

Long-term stress range

Equivalent stress range

𝑔 = 𝑁 − 𝑁𝑆<0

∆, 𝐴, 𝐵 are variables: ∆ reflect the uncrtainty in damage accumulation

𝐴 reflect the uncrtainty in fatigue capacity

𝐵 reflect the uncrtainty in stress calculation

Limitations: too general, no link with inspection results

ESREL, 20 Jun, 2017

Inspection planning & FM model

Crack propagation (Paris’s law)

Limit-state function

Strengths: 1. detailed information2. comparable with inspectionsLimitations: 1. 𝑎0 is hard to obtain2. 𝑇0 is not accounted for

Three stages of crack development

ESREL, 20 Jun, 2017

Time-To-Crack-Initiation (𝑁𝐼)

For critical components, 𝑎0 may be smaller than 𝑎𝑑 , and hard to measure 𝑁𝐼 may account for a large part of fatigue life of critical components Crack size under 𝑎𝑑 is not important, but 𝑁𝐼 is important for inspection planning Obtain info. on 𝑁𝐼 by specimen test (e.g. Lassen and Sørensen (2002a))

𝑁𝐹 = 𝑁𝐼 + 𝑁𝑃

𝑁𝐹 = 𝑁𝐼 +1

𝜋 𝑚 2𝐶∆𝜎𝑚 𝑎𝑑

𝑎𝑐 𝑑𝑎

𝑎 𝑚 2𝑌 𝑎 𝑚

𝑎𝑡

𝑎𝑑

𝑁𝐼

𝑎0

N

ESREL, 20 Jun, 2017

Inspection strategies

Inspection timingfixed inspection interval approach vs. target reliability approach

Inspection methodclose visual inspection (CVI) vs. magnetic particle inspection (MPI)

𝑡

𝛽𝑡

𝑡

𝛽𝑡

𝛽

𝛽 𝑇𝑆𝐿

∆𝑇 ∆𝑇 ∆𝑇

𝑇𝑆𝐿𝑇𝑖𝑛𝑠𝑝 1 𝑇𝑖𝑛𝑠𝑝 2

𝑃𝑜𝐷 = 𝐹 𝑎𝑑 = 1 − exp − 𝑎𝑑 𝜈𝑑

Probability of detection curves for CVI & MPI

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Illustrative example

Fatigue-prone welded T joints Inspection plans allowing for 𝑁𝐼 Reliability based & time based inspection Visual inspection & MPI

ESREL, 20 Jun, 2017

Results(reliability-based plans)

βt = 2.5, CVI βt = 2.5, MPI

βt = 3.5, CVI βt = 3.5, MPI

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Results(time-based plans)

ICI, CVI ICI, MPI

NCI, CVI NCI, MPI

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Discussions(reliability-based plans)

𝑛𝑖𝑛𝑠𝑝 may be decreased while allowing for 𝑁𝐼. But if 𝛽𝑡 is

high, regular inspections are necessary.

ESREL, 20 Jun, 2017

Discussions(reliability-based plans)

∆𝑇𝑖𝑛𝑠𝑝1 can be prolonged while allowing for 𝑁𝐼. Fail to take this into

account may result in waste of inspection resources. There isn’t much difference in the following inspection intervals ∆𝑇𝑖𝑛𝑠𝑝2, ∆𝑇𝑖𝑛𝑠𝑝3, …, whether considering 𝑁𝐼 or not.

No indication from MPI supports longer inspection interval, compared with no indication from CVI.

ESREL, 20 Jun, 2017

Discussions(time-based plans)

Fixed inspection interval is preferred from the point of logistics. The fixed interval is also be determined based on reliability analysis.

Reliability-based plans are able to keep safety margin above a certain level more even than time-based plans.

ESREL, 20 Jun, 2017

Conclusions

𝑁𝐼 may account for a significant part of 𝑁𝐹 for some critical joints, and should be taken into account in inspection planning.

𝑁𝐼 can be obtained based on specimen tests, and be added to 𝑁𝑃, so that crack initiation life is included, without having to know statistical information on 𝑎0.

Allowing for 𝑁𝐼, ∆𝑇𝑖𝑛𝑠𝑝 1 can be prolonged, but there isn’t much

difference in ∆𝑇𝑖𝑛𝑠𝑝2, ∆𝑇𝑖𝑛𝑠𝑝3, …, .

Allowing for 𝑁𝐼, 𝑛𝑖𝑛𝑠𝑝 may be decreased, depending on 𝛽𝑡.

ESREL, 20 Jun, 2017

Thank you for your attention!

· Presenter Guang Zou (Lloyd’s Register, research fellow)

guang.zou@lr.org

The funding from the EU’s Horizon 2020 programme under the Marie Sklodowska-Curie grant agreement No. 642453 is greatly appreciated.

ESREL, 20 Jun, 2017