PSI - Issue 57

Baran Yeter et al. / Procedia Structural Integrity 57 (2024) 133–143 Baran Yeter & Feargal Brennan/ Structural Integrity Procedia 00 (2023) 000 – 000

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Following the global load analysis, the simulated time histories of overturning bending moments are used to calculate the global and local structural response at the tower base for each sea state. As the overturning bending moment is the predominant source of the stress cycles, the nominal stress is calculated using merely the bending moment. To achieve the local stress, hotspot stress, the nominal stress cycle should be multiplied by the stress concentration factor suitable for welded-tubular joints. In this regard, the present study employs the empirical formulas provided by DNV (2014). = (1) = (2) Before the structural integrity assessment, the final step is to count the relevant stress cycles using the rainflow counting (RFC) technique. For the time history to be comprised only of damage-inducing stress cycles (reversals), smaller interruption cycles (closed loops) need to be extracted. RFC has been used for a long time to transform varying stress into a set of constant amplitudes to calculate fatigue damage through linear damage accumulation or crack growth increment. The time-domain structural response denotes the way in which the principal stresses change in time under a given sea state, which needs to be weighted by the probability of occurrence associated with the sea state to derive the long-term distribution of the stress ranges. Fig. 4 illustrates an example of the rainflow counted stress cycles (8 th sea state) in a multiaxial histogram where amplitude distribution is presented on one axis, and the other axis shows the mean value at which the stress cycle fluctuates. Fig. 4 indicates that the majority of the stress cycles are small amplitude stress cycles, and the number of cycles for those stress amplitudes decreases dramatically as the stress amplitudes increase. Similar attributes are observed for the short-term distributions of other sea states, which infers that the long-term stress range distribution can most likely be explained by a Weibull distribution with a shape factor less than 1.

Fig. 4. An illustration of rainflow counted stress cycles for 8 th sea state

4. Probabilistic Structural Integrity Assessment 4.1. Fatigue Crack Growth Accounting for Load Sequence and Retardation Effects

The structural integrity assessment can be performed using the analytical solutions developed within the scope of the linear-elastic and elastic-plastic fracture mechanics. In this regard, the modified Paris law offers an effective tool to assess fatigue crack growth (FCG) at every stress cycle accounting, assuming that the crack tip conditions can be approximated by the stress intensity factor (SIF). The Paris law has been modified to account for other influencing factors such as stress ratio, load sequence effect, and acceleration or deceleration of crack growth. The modified Paris law can be adapted to investigate FCG under three regions separated by threshold and critical SIFs (crack initiation, stable crack growth and fast fracture) (Anderson, 2005).