Analysis of Fatigue Crack Propagation of an Orthotropic Bridge Deck Based on the Extended Finite Element Method

As one of the most fatigue-sensitive parts of an orthotropic steel bridge deck, the weld between the U-rib and the top deck is prone to fatigue cracking under the actions of the stress concentration, welding residual stress, and vehicle load. To investigate the mechanism of fatigue crack propagation and the influence of the welding residual stress on the propagation patterns of fatigue cracks, a multiscale modeling method was proposed, and the static analysis and the dynamic propagation analysis of fatigue crack were carried out in this paper. First, a multiscale finite element model was established, including whole bridge models with a scale feature of 10² m, orthotropic bridge deck models with a scale feature of 10⁰ m, and crack models with a scale feature of 10⁻³ m. Then, a segmental model of the bridge deck was extracted, which is regarded as a critical location of the bridge, and the shell-solid coupling method is adopted in the segmental model in order to further analyze the crack propagation rule. Moreover, based on the extended finite element method (XFEM), the static crack and dynamic crack propagation in this critical position were analyzed. Finally, thermoelastoplastic analysis was carried out on the connection of the U-rib and deck with a length of 500 mm to obtain the residual stress, and then the results of residual stress were introduced into the segmental model to further study its influence on the evolution of fatigue crack propagation. The analysis of the welding process shows that near the weld region of the connection of the U-rib and deck, the peak value of the residual tensile stress can reach the material yield strength. The static analysis of fatigue cracks shows that under the single action of a standard fatigue vehicle load, the fatigue details at the weld toe of the deck cannot reach the tensile stress required for fatigue crack propagation, and only the fatigue details at the weld toe of the U-rib can meet the requirements of fatigue crack propagation. The dynamic analysis of fatigue cracks reveals that the crack in the weld toe of the U-rib is a mixed-mode crack with modes I, II, and III. The propagation of a fatigue crack without a residual stress field will be terminated until the crack length is extended to a certain length. Nevertheless, when the residual stress field was introduced, the growth angle and size of the fatigue crack would increase, and no crack closure occurs. For the crack in the weld toe of the deck, the crack is in the closed state under the standard fatigue vehicle load. When the residual stress field is introduced, the tensile stress of the fatigue details increases. Meanwhile, the fatigue crack will become a mixed-mode crack with modes I, II, and III that will be dominated by mode I and extend toward the weld at a slight deflection angle. The results of various initial crack sizes at the weld toes of the top deck are analyzed, which shows that the initial crack size has a certain effect on the fatigue crack growth rate, especially the initial crack depth.

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