# Residual Stress Relaxation of DRWDs in OSDs under Constant/Variable Amplitude Cyclic Loading
## 1 Introduction  
Orthotropic steel decks (OSDs) have been widely used as main girders in long-span bridges as a result of their high load-loading capacity, light weight, excellent aerodynamic, and speedy construction [1, 2]. Recently, many fatigue cracks have been reported in OSDs in China and other countries. For instance, three types of fatigue cracks were found in the rib-to-deck welds on the Severn Bridge in the UK after the bridge was open to traffic for five years. Numerous fatigue cracks were observed in OSDs on the Second Van Brienenenoord Bridge in Denmark after it was in service for seven years, which resulted in the bridge beingdifficult to repair. Fifteen years after the Rio-Niteroi Bridge was built in Brazil and opened to traffic, it was found that serious cracks of OSDs had developed, mainly distributed in deck-to-rib welding details (DRWDs). Serious fatigue issues have occurred in the Humen Bridge, the first bridge with OSDs in China, after it was in service for only five years. The Jiangyin Yangtze River Bridge, located in the Yangtze River Delta, the busiest transportation region in China, also had fatigue cracks nine years after construction [3,4]. Numerous cases indicated that the fatigue behavior of OSDs under long-term train loading is an important concern. The fatigue cracks in DRWDs appear most frequently among the various types of cracks in OSDs [5, 6, 7]. Moreover, it is difficult to repair and detect such cracks, which seriously affects the durability and safe operation of bridges. The welding residual stress plays a vital role in the fatigue assessment of DRWDs. Welding, as a steel structure connection method, is widely used in the fabrication of OSDs. Therefore, it is inevitable that it will produce welding residual stresses owing to the local plastic deformation induced by the local high temperature during the welding process. The existence of high residual stress at the welding details will result in a significant decrease in the fatigue strength bearing capacity of the structure [8, 9, 10]. However, the initial welding residual stress in the structure might be relaxed under cyclic vehicle loading, which resulted in the variation of distribution and magnitude of residual stress around the welded joints [11,12]. Hence, the real stresses at the welding heat-affected zone under the coupling effect of residual stress induced by welding and mechanical stress caused by external loading cannot be determined, but they produce a lot of resistance to the fatigue damage assessment and life prediction of the pivotal welding details of OSDs. As a result, the relaxation effect of welding residual stress under cyclic loading should be taken into account in the fatigue strength analysis of OSDs. Researchers have studied the release behavior of residual stress in a simple welded structure under constant amplitude cyclic loading by experimental methods, and determined the calculation release formula of residual stress based on the experimental data [13]. Due to the high cost of experimental methods, the finite element (FE) method is introduced to analyze the relaxation behavior of residual stress. [PERSON] et al. [14] and [PERSON] et al. [15] simulated the release behavior of residual stress under constant amplitude cyclic loading by the 3D heat conduction elastic-plastic method. In recent years, Chinese scholars carried out research on the influence of the welding residual stress on the fatigue life of OSDs [16,17, 17], but few focused on the relaxation effect of residual stress. [PERSON] et al. [18] studied transverse residual stress relaxation in innovative both-side welded rib-to-deck joints of OSDs under constant amplitude cyclic loading. Numerous studies have shown that the relaxation behavior of residual stress is a complicated process [19,20] affected by multiple variables, such as the stress amplitude, stress ratio, loading cycles, material properties, etc. However, it is worth noting that the vehicle loading is often a cyclic loading with variable amplitude.