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Keyword: Stochastic

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Studies in the Fatigue Lives of Offshore Welded Joints considering Non­-Proportionality and Stochastic Effects

Mikkel Løvenskjold Larsen

Offshore jacket foundations for wind turbine generators are in risk of metal fatigue at the weldedjoints due to the highly dynamic wind and wave loading. The complex multiaxial stresses occurringat the welded joints can be non­proportional and lead to increased fatigue damage as compared toproportional stresses. Furthermore, several random effects influence the response of the offshorestructures and the fatigue lives of the welded joints.

In this thesis, the fatigue response of welded joints in offshore jacket structures is assessed. The influence of non­proportional stress states on the fatigue life has been examined using experimental fatigue data from literature by modelling the published experiments using the finite element method (FEM) and assessing the stress states using the notch stress approach. The results show that a nonzero phase­shift between the governing normal and shear stress at the weld toe leads to increased damages at the weld. An approach for determining the non­proportionality penalty factors for obtaining correct fatigue life estimations has been proposed.

To quantify the level of non­proportionality in the stress states at welds a new quantification approach has been developed based on the principal component analysis (PCA). The approach is easy to implement and simple to interpret, which is often difficult for many of the already published methods. The PCA­based approach is furthermore extended to be used with variable amplitude stress states. By implementing the developed quantification approaches in the fatigue life calculation framework, it is possible to determine if non­proportionality occurs and to account for this in the fatigue life estimation automatically using the estimated penalty factors.

The stochastic finite element method (SFEM) has been used to implement approaches for considering the spatial variability occurring in the jacket structures and welds. Closed­form solutions to the stochastic stiffness and stress stiffness matrices have been proposed, making it possible to easily implement the spatial variability of the bending rigidity and other parameters in beam FE models. The matrices have been developed for both classical Euler­Bernoulli and Timoshenko beam theory and are based on the Karhunen­Loéve (KL) expansion for random field discretization. The KL expansion is then further used to formulate a stochastic size effect that takes into account that longer welds tend to fail earlier than shorter welds when considering fatigue. Other approaches for taking into account the size effect are often based on statistical evaluation of fatigue experiments which is used to determine a deterministic calibration factor. The stochastic size effect makes it possible to simulate the randomness in a full weld independently of the highest stressed zones. Using this method, the quality of the welding can be simulated and used to predict more accurate fatigue lives.

In order to design more fatigue resistant welded joints in offshore jacket structures, automatic optimization of the welded joints is required. Already published approaches to do so, often focus on only a few simple fatigue criteria. For an optimization framework to be efficient it has to take into account the complex multiaxial non­proportional fatigue and the stochastic effects of the welds. In the thesis, an optimization framework for fatigue life estimation using the developed PCA­based quantifier and the stochastic size effect has been developed. The framework is easy to use and based on simple formulations, making it possible to implement many types of fatigue criteria without having to reformulate the optimization procedure. The framework has been used to optimize the weld locations in a cast steel jacket insert and shows that considerable mass savings can be achieved by automatic
optimization.

University of Southern Denmark / 2022
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