# Notch Fatigue Life Research Based on Critical Distance Theory
## 1 Introduction  
The fatigue of orthotropic anisotropic steel bridge deck panels, as the preferred deck structure for large-span bridges, has been a hot issue to which scholars from various countries have attached great importance [1; 2; 3]. Among them, fatigue cracks in the parent material sprouting from curved cutouts in the diaphragm are one of the major fatigue diseases of orthotropic anisotropic bridge deck panels [4; 5; 6]. Existing studies have shown that different notch geometries and dimensions, such as notch type and arc radius size, have a significant effect on the fatigue performance of curved notch details [7; 8; 9], but these conclusions are mainly drawn using the nominal stress method based on S-N curves or field monitoring [10; 11]. It is worth pointing out that nominal stresses based on S-N curves are mainly used to predict the fatigue life of arcuate cutouts in diaphraggs. The nominal stress method has been widely used by virtue of its advantages of clear definition and easy calculation [12; 13; 14; 15; 16]. The method is indeed convenient and feasible for clearly stressed members. However, the fatigue rating based on the nominal stress method is differentin different design codes, and with complex geometric details, it is difficult to find the corresponding fatigue design detail types in the codes. Although both Eurocode 3 and AASHTO LRFD [17; 18] have proposed a recommended curved cutout type, there is no unified understanding of the fatigue design of this construction detail, and the limitations of its use are large. In contrast, the field monitoring workload is huge, and the influence of traffic flow is significant. At present, there is a lack of accurate and simple methods to study the fatigue life at curved notches under different notch radii. The critical distance theory has been applied to the fatigue analysis of notched components in the mechanical field [19; 20; 21; 22; 23]. The basic concept of the critical distance theory is that the fatigue damage of notches depends not only on the peak point of stress concentration, but also on the stress distribution in a certain distance range near the stress concentration [24]. This distance range is called the \"critical distance L\". The average stress within this distance is defined as the characteristic stress, which is the controlling parameter for fatigue damage of notched members, and fatigue damage occurs when the characteristic stress reaches a threshold value. [PERSON] and [PERSON] [25; 26] made the first attempt to use the critical distance theory to evaluate the fatigue strength of notched members. [PERSON] et al. [27] found that specimens with different geometrical features and notch sizes had different critical distance. [PERSON] et al. extensively tested the efficiency and accuracy of the critical distance theory for the fatigue prediction of notched members and welded joints, verifying the applicability to a wide range of notch geometries [28; 29; 30]. Others have utilized the extended finite element method to analyze the fatigue crack extension, which in turn enables the fatigue life prediction of uncracked structural details [31; 32]. For example, [PERSON] et al. [33; 34] investigated the fatigue of bridge steel wires based on the critical region method and Bayesian Gaussian process combined with the finite element method, and found that there was a good agreement between theoretical predictions and experimental observations. Existing studies have proved the applicability of the critical distance theory. Theoretically, any type of stress concentration problem can be analyzed using the critical distance, but few people have analyzed the fatigue problem of steel box girder diaphragms at the curved cutout with the critical distance theory. Therefore, in this paper, fatigue life tests of notched specimens were carried out with three rectangular plate members with arc notches with different radii as the research object.