# Fatigue Crack Calculation of Steel Structure Based on the Improved McEvily Model
## 1 Introduction  
Nowadays, orthotropic steel decks have been widely used in modern bridge structures, with outstanding advantages such as high bearing capacity, light weight, and wide application range [1, 2]. However, Orthotropic steel bridge decks are directly loaded by vehicle tires during the service period, easily resulting in the accumulation of fatigue damage and fatigue cracks, which have become an important factor affecting structural safety. Since the first report of fatigue cracks in the Orthotropic steel deck of Severn Bridge in 1971, numbers of fatigue cracking damages have been found in bridges worldwide of Orthotropic steel deck [3]. According to the investigation of [PERSON] et al. [4], the proportion of fatigue damage in the failure of the bridge structure with or without collapse is 13% and 67%, respectively. Therefore, the fatigue life assessment of orthotropic plates is very important for bridge safety [5, 6, 7]. The fatigue crack growth rate curve is the basic material characteristic of steel structures under fatigue load, and a good fatigue crack growth model plays a vital role in fatigue life evaluation [8, 9]. In order to accurately simulate the criterion of fatigue crack growth, some fatigue crack growth models have been proposed. The first crack growth rate based on linear elastic fracture mechanics was introduced by [PERSON] [10], who equated fatigue crack growth rate by using amplitude stress intensity factor. [PERSON] et al. [11] improved on the basis of the Paris model and modified the exponential crack growth model to cover the effects owing to the load ratio and the maximum stress-intensity factor. [PERSON] et al. [12] proposed a modified constitutive model introducing the concept ofcrack closure and effective stress intensity factor \(K_{\textit{eff}}\). While the Paris model is the most extensively utilized at the moment, it has several limitations: First, the Paris model with the same material constant cannot explain the effect of crack growth under different load ratios (\(R=K_{\text{min}}/K_{\text{max}}\)). Second, the Paris model cannot include the entire process of crack growth. Due to the aforementioned limitations, the reliability of the Paris model results in the structural fatigue life prediction in practical engineering remains to be discussed to confirm. As one of the fatigue crack growth models, the McEvily model can be applied to small physical cracks and can explain various metal fatigue phenomena [13; 14; 15]. Due to the superiority of the McEvily model, many scholars used this model to evaluate the fatigue life of materials. [PERSON] et al. [14] used the constitutive relationship of the McEvily model to conduct a series of high and low cycle tests during the fatigue life cycle of the titanium alloy to obtain the function relationship between the crack length and the number of loading cycles, and the test results were in good agreement with the predicted results. [PERSON] et al. [15] used the extended McEvily model to predict the fatigue life of surface cracked deep-water structures. The prediction results were compared with the test results, and it was found that the extended McEvily model had better prediction accuracy results than other models. [PERSON] et al. [16] compared the newly proposed crack growth models; they found that the improved form of the variable slope of different materials can be explained by the McEvily model, it is capable of predicting fatigue for both short and long fatigue cracks because the McEvily model retains the slope \(m\). Nevertheless, the aforementioned research is based on the experiment; the model is challenging to apply to actual bridge engineering because some parameters are impossible to obtain in practice. To facilitate the practical application of the McEvily fatigue crack growth model. Firstly, an improved McEvily fatigue crack growth model was proposed by simplifying the model parameters with reasonable assumptions and empirical formulas.