Fatigue Life Time Estimates of Welded Joints in Maritime Structures

Abstract

Ships at sea encounter wave-induced cyclic loading, meaning fatigue is a governing limit state. The structural response introduces stress concentrations, hotspots, at notch geometry like welded joints locations. At the same time, the welding process typically introduces defects, meaning welded joints are typically the governing fatigue-sensitive details. Accurate predictions of the fatigue lifetime are paramount for ensuring safety and economic viability in the maritime sector.

Because of the welding-induced defects, the fatigue lifetime of welded joints is growth rather than initiation-dominated; adopting a cracked geometry-based fatigue damage criterion like the stress intensity factor seems straightforward. Weld notch characteristic crack growth behaviour, however, becomes crucial. Since both short and long crack growth are considered important, a typical one-stage Paris relation-based long crack model must be extended, particularly since most of the welded joint fatigue lifetime is spent in the notch-affected short crack growth region. The short crack growth behaviour can be both non-monotonic as well as monotonically increasing, depending on the elastoplastic response conditions. A two-stage crack growth model, incorporating both short crack growth behaviour and the long crack growth characteristic, has already been proposed in a different project based on compact tension (CT) specimen crack growth testing results obtained using potential drop measurements. However, the corresponding strain/stress field possibly explaining the crack growth behaviour in terms of elastoplasticity is not part of the output. Images have been captured, which can be analyzed with Digital Image Correlation (DIC) to provide the field measurements.
\noindent The first aim of the research has been to explore dedicated displacement field formulations to capture the crack tip location and corresponding stress intensity factor simultaneously by developing a one-step DIC approach. The expected benefits of this approach over other DIC methods consist of an expected increase in accuracy and the elimination of a post-processing step. Current DIC methods generally exist out of a two-step approach. First, a DIC procedure is employed with a generalized kinematic basis. Secondly, a post-processing step is employed to determine the crack tip location and stress intensity factor (SIF). Specifically for the crack tip, the post-processing step generally assumes a dedicated kinematic basis function describing the field around the crack. Directly incorporating the dedicated function into the DIC procedure allows for the intermediate generalized kinematic assumptions to be eliminated.
The resulting crack size and SIF from this approach can be used to determine the crack growth relationship. This relationship can be used for the second aim of this thesis, which has been to determine the material parameters of the proposed two-stage crack growth model and validate its ability to capture the short crack growth behaviour.
However, the SIF values obtained with the developed one-step DIC do not align with the analytically obtained values. Regarding the crack growth relationship, this difference in loading introduces a mean shift. Nevertheless, the observed crack growth behaviour aligns with the trends established in prior investigations, which combined potential drop crack size results with analytically determined SIF values.
A three-step approach has been adopted to investigate the accuracy of the SIF determination:
Step 1: A direct approach using a finite element formulation based on global rather than local DIC, enforcing displacement field continuity as required for a crack path-independent SIF calculation. \par
Step 2: An indirect approach using the global DIC-based displacement field (step 1) and Williams' crack tip displacement field formulation to obtain the crack tip location and SIF at the same time.
Step 3: A direct approach using Williams' crack tip displacement field formulation to obtain the crack tip location and the SIF simultaneously.
Analyses showed that involving Williams' asymptotic solution (steps 2 and 3) for long cracks in a simple far-field stress condition is beneficial. Accurate crack tip location and SIF estimates have been obtained. However, for complex stress fields at notched geometries additionally containing geometry boundaries in the same region, higher order terms are required to obtain a converged displacement field. An accuracy improvement has been observed when adopting a direct approach (step 3) rather than an indirect one (step 2) approach. A global FEM-based direct approach (step 1) allows for describing complex displacement fields and obtaining SIF estimates independent of the Williams' formulation. The resulting estimates from this approach agree with the Williams-based estimations (steps 2 and 3). From this, it can be concluded that the obtained difference in the SIF follows from a fundamental difference in the load obtained by analytical determination and the DIC approaches. This conclusion is supported by the difference in the structural stress obtained from the DIC approaches compared to the analytical estimate.
The second aim of this thesis requires further investigation into the loading discrepancy before the total life model can undoubtedly be validated. Nevertheless, preliminary usage remains possible with the usage of consistent SIF determination. Resulting in the establishment of model parameters using likelihood regression for the CT and as-welded joint specimens. \par
For the final aim of this thesis, the total life fatigue strength criterion is obtained by integrating the two-stage crack growth model. This criterion is applied in a case study to estimate the total fatigue lifetime of a critical welded joint in a general cargo carrier. In order to determine the estimated lifetime of the critical joint, the fatigue loading is required. While knowledge of the cargo load is available, the impact of wave-induced loading requires investigation. Two distinct approaches have been used to determine the wave loading. Initially, Four representative wave loading scenarios established by Bureau Veritas regulations are considered. The cumulative fatigue damage resulting from these scenarios is then extrapolated to encompass the entirety of loading conditions experienced by the ship.
Secondly, a wave spectrum approach is undertaken to address uncertainties in loading analysis. A hydro-structural solver is utilized to calculate loading across various sea states. The total fatigue damage is based on a weighted average of a representative sea spectrum. The fatigue lifetimes derived from these methodologies are compared to the hot spot structural stress concept as typically adopted in industry for reference purposes. A comparison of the results shows that the hot spot structural stress concept underestimates the fatigue lifetime due to the increased conservatism required in this model.