Abstract: Fatigue cracks pose threats to the integrity of welded structures and thus need to be addressed in the whole service lives of structures. In-service inspections are important means to decease the probability of failure due to uncertainties that cannot be accounted for in the design stage. To help schedule inspection actions, the decline curve of reliability index with time needs to be known. A predictive tool is normally developed based on crack propagation models neglecting the crack initiation stage, which leads to conservative predictions for fatigue life. Inspection plans built on those predictions are far from optimal, especially for welds with relatively long crack initiation life. This paper proposes to use a fracture mechanics based reliability analysis method that takes the crack initiation stage into account via the concept of Time-To-Crack-Initiation (TTCI). The optimum inspection plan for a fatigue prone ship structural component is derived by the new approach and compared to the commonly-used method that only considers crack propagation life. Two inspection planning approaches are tested to investigate the influence of incorporating crack initiation period: (i) target reliability approach and, (ii) equidistant inspection times approach. With each planning approach, two inspection methods are adopted: close visual and magnetic particle inspection. The paper concludes with recommendations on the inspection method and planning approach to adopt while considering and without considering the crack initiation stage.

1. 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

2.  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

3. 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

4. Inspection planning & FM model
Crack propagation (Paris’s law)
Limit-state function
Strengths:
1. detailed information
2. comparable with inspections
Limitations:
1. 𝑎0 is hard to obtain
2. 𝑇0 is not accounted for
Three stages of crack development
ESREL, 20 Jun, 2017

5. Time-To-Crack-Initiation (𝑁𝐼)
 For critical components, 𝑎0 may be smaller than 𝑎 𝑑, and hard to measure
 𝑁𝐼 may account for a large part of fatigue life of critical components
 Crack size under 𝑎 𝑑 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 + 𝑁 𝑃
𝑁𝐹 = 𝑁𝐼 +
1
𝜋 𝑚 2 𝐶∆𝜎 𝑚
𝑎 𝑑
𝑎 𝑐 𝑑𝑎
𝑎 𝑚 2 𝑌 𝑎 𝑚
𝑎 𝑡
𝑎 𝑑
𝑁𝐼
𝑎0
N
ESREL, 20 Jun, 2017

6. Inspection strategies
 Inspection timing
fixed inspection interval approach vs. target reliability approach
 Inspection method
close visual inspection (CVI) vs. magnetic particle inspection (MPI)
𝑡
𝛽𝑡
𝑡
𝛽𝑡
𝛽
𝛽 𝑇𝑆𝐿
∆𝑇 ∆𝑇 ∆𝑇
𝑇𝑆𝐿𝑇𝑖𝑛𝑠𝑝 1 𝑇𝑖𝑛𝑠𝑝 2
𝑃𝑜𝐷 = 𝐹 𝑎 𝑑 = 1 − exp − 𝑎 𝑑 𝜈 𝑑
Probability of detection curves for CVI & MPI
ESREL, 20 Jun, 2017

7. Illustrative example
 Fatigue-prone welded T joints
 Inspection plans allowing for 𝑁𝐼
 Reliability based & time based inspection
 Visual inspection & MPI
ESREL, 20 Jun, 2017

8. Results(reliability-based plans)
βt = 2.5, CVI βt = 2.5, MPI
βt = 3.5, CVI βt = 3.5, MPI
ESREL, 20 Jun, 2017

9. Results(time-based plans)
ICI, CVI ICI, MPI
NCI, CVI NCI, MPI
ESREL, 20 Jun, 2017

10. 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

11. 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

12. 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

13. 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 𝑁 𝑃, 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

14. 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