Investigations on the correlation of fatigue crack initiations with numerical calculations for the prediction of the crack initiation process

Kurzfassung

The fatigue strength of steel components is a key challenge in the design of offshore wind turbines. During operation, the turbines are exposed to high dynamic loads from wind or waves. Due to this type of load, fatigue strength verification is crucial and critical areas in the structure must be given special consideration. Particularly critical areas include geometric discontinuities and weld seams. These areas generate stress peaks in the structure due to their notch effect and thus promote crack initiation. Traditionally, crack initiation is not explicitly taken into account in the verification process. Component tests can be used to determine the stress that can be absorbed as a function of the number of load cycles. These tests result in the S-N curve (Wöhler-curve) for the component detail under investigation. Crack initiation and crack propagation are not explicitly determined and are only taken into account experimentally.

In contrast, the crack propagation concept can determine crack propagation mathematically based on crack initiation. The crack depth as a function of the number of load cycles can be used to calculate the service life. Based on this, a fracture surface analysis is performed in this work to approximate the final crack curve. Fracture surface analysis is further combined with digital image correlation (DIC) and numerical stress calculations to investigate correlations. The aim is to be able to predict the crack curve or crack geometry based on the stress distribution. To this end, parameters such as crack depth, crack initiation, and curvature of the approximated crack curve were correlated in the first step. However, no dependencies beyond obvious mathematical relationships were found in this analysis. Using DIC, it was determined that, assuming a symmetrical crack curve, the lowest point of the approximated crack curve corresponds to the crack initiation point. A symmetrical crack curve describes the crack path before reaching the sample edge. As soon as the crack reaches the sample edge, it grows along it, creating asymmetry. Assuming this final asymmetrical crack curve, in many cases the lowest point no longer corresponds to the start of the crack. The numerical calculation of the models is based on the Implicit Gradient Model (IGM), which averages stress peaks caused by notches or geometric changes over an area a. This distribution of stress peaks corresponds to the micro-support effect of steel in reality, ensuring a realistic calculation method in this respect. The results show that in approximately 50 % of the cases considered with a = 0.01 mm², the critical crack initiation can be predicted based on the maximum stress. For specimens where there was no correlation between the maximum stress and the crack initiation, correlations between the stress distribution and the crack propagation could still be found. For example, the symmetry of the stress distribution at 95 – 100 % of the maximum stress can predict the crack propagation direction.

The stress distribution can also be used to predict the crack width. For this purpose, the models with a = 1.0 mm² were examined. The length of the stress distribution at 95 – 100 % of the maximum stress was compared with the actual crack width. In this case, the crack width can be determined with an average deviation of 4.8 mm based on the stress distribution.

The results of this work thus show that combining stress distribution with fracture surface analysis can provide valuable information for predicting the crack curve. In the future, the numerical calculation can be further adapted by explicitly implementing cracks in the calculation. It is conceivable that the agreement between the maximum stress and the critical crack initiation can be further increased.