###### Abstract  
In order to study the fatigue performance of the initial crack between the CFRP reinforced deck and the U-rib weld after considering the residual stress, the welding residual stress of the deck and the U-rib weld was analyzed by the welding subprogram of ABAQUS, and then the segment model of the deck and the U-rib of the steel bridge deck was established by using the interaction technology of FRANC 3D-ABAQUS, and the stress intensity factor of the crack between the deck and the U-rib weld under the vehicle-only, vehicle-residual stress combined loads, and CFRP-strengthened combined loads were analyzed. The growth analysis of cracks before and after reinforcement was carried out. The results show that the amplitude of the stress intensity factor of the crack tip is less than the threshold when only the vehicle is applied, and the crack will not spread. After considering the residual stress, the maximum K\({}_{\text{I}}\) value of the crack at the welding toe is increased by 6.9 times compared with the maximum value of the vehicle only, and the maximum K\({}_{\text{I}}\) value at the welding root is increased by 10.7 times; the reinforcement method of CFRP pasted on the lower surface has a reinforcement effect on the fatigue crack at the welding toe, but the fatigue crack at the welding root has no reinforcement effect; the reinforcement effect of the welded to crack increases with the increase of the number of CFRP layers, length, and width. When the weld toe crack after reinforcement extends to half the thickness of the deck, the number of car-residual stress combined load cycles increases by 43% compared to when it is not reinforced.  
steel bridge deck; residual stress; stress intensity factor; CFRP reinforcement; crack growth 2023131  
improve the fatigue performance of members. It has advantages that other methods cannot compare to, that is, it does not need to drill holes in the damaged parts to avoid new stress concentration areas. It has high research and use value for improving the fatigue life of steel members [13; 14; 15]. [PERSON] et al. conducted fatigue tests and analysis of CFRP reinforcement on cross-shaped specimens containing K-shaped welds, while [PERSON] et al. and [PERSON] et al. conducted reinforcement studies on fatigue cracks at the arc notch of the transverse partition of orthotropic steel bridges using CFRP material. The results showed that pasting the CFRP sheet shared the stress at the weld toe and improved the fatigue performance of the weld toe [16; 17; 18]. Therefore, adopting CFRP materials to improve the fatigue problem of orthotropic steel bridge decks will be a future research focus.  
FRANC 3D 7.5.5 version is a software specifically designed for analyzing crack growth, which simplifies some of the tedious steps of crack growth compared to non-professional software such as ABAQUS (2020 version) and ANSYS. However, due to the inability of FRANC 3D to perform model preprocessing work, it is necessary to combine ABAQUS and other finite element software when analyzing cracks using FRANC 3D. FRANC 3D uses the M-integral method to solve the stress intensity factor. Its mathematical expression is similar to the J-integral, but it can consider the influence of temperature, crack surface contact, crack surface traction, residual stress, etc., on the stress intensity factor. When analyzing cracks in FRANC 3D, the front edge of the crack is divided into unit ring grids to refine the grid, thereby reducing calculation errors and improving the accuracy of the calculation results. Refs. [19; 20; 21; 22] compared the calculation results of FRANC 3D with the standard formula, and the validation results showed that FRANC 3D has high accuracy. The interaction process between FRANC 3D and ABAQUS is shown in Figure 1.