# Fatigue Crack Calculation of Steel Structure Based on the Improved McEvily Model
## 2 Improved McEvily Model
### The Effectiveness of Improved McEvily Model  
In order to prove the effectiveness of the improved McEvily model, the typical steel structure fatigue crack (fatigue crack of butt weld of orthotropic steel deck) was selected for analysis in this study, and the experimental research data of Q345 qD steel were cited. [PERSON] et al. [29] conducted experiments on the fatigue crack growth rate of metallic materials. The different thickness specimens and different stress ratios were used for the experimental research, and the fully automated crack length measurement software was used for collecting data. By means of data processing, the fatigue crack growth rate curves of 6.1 mm, 10.0 mm, and 23.5 mm thickness weld specimens under different stress ratios (R = 0.1, 0.2, 0.5) were obtained. The test specimens were made according to the mechanical standard of GB/T 714-2008 specification [30], in which the schematic diagram of the test specimens is shown in Figure 2a, and the dimensions of the test specimens are shown in Figure 2b. The basic mechanical properties of Q345 qD butt welds were measured by uniaxial tensile test, and the average mechanical properties of Q345 qD butt welds: \(f_{y}\) is 534 MPa, \(f_{u}\) is 596 MPa, \(E\) is 2.51 \(\times\) 10\({}^{5}\) MPa. Figure 2: Geometry of test specimens, (**a**) The schematic diagram of test specimens, (**b**) The dimensions of the test specimens. The improved model was validated numerous times in this paper using the experimental data. Due to the presence of the weld, the test results for the same specimen subjected to the same stress ratio remain somewhat dissimilar. In this study, the above dissimilar is mainly manifested in the change of the material constants (as shown in Table 1 and Figures 3-5). As a result, the establishment of different Paris models is essential to exactly estimate the fatigue crack growth rate for the same specimens with different material constants. Compared to the Paris model, the improved McEvily model has extremely robust against the effects of welds. Just one improved McEvily model for the same specimen is required. The improved McEvily model, based on the same specimen, is only related to stress ratios, which significantly improves computing efficiency and engineering application. The validation procedure is demonstrated here by utilizing a specimen set consisting of 6.1 mm thick nine specimens (as shown in Table 1 and Figure 3). Firstly, the specimen set was divided into three working conditions with stress ratios of 0.1, 0.2, and 0.5, and the average value of material constants was computed for each set of working conditions using experimental data (as shown in Table 1). Second, three Paris models with different material constants were established based on experimental data to predict the fatigue crack growth rate at various stress ratios, respectively. Then, an improved McEvily model was established based on the test data of three specimens with a stress ratio equal to 0.5. The experimental data of the sample set with a stress ratio of 0.5 is the most concentrated, and the accuracy of the established improved McEvily model can be enhanced (as shown in Figure 3c). Finally, the established McEvily model was applied to specimen sets with stress ratios of 0.2 and 0.3. The accuracy of the fitting results was proven by comparing with the fatigue crack growth rate curves of Paris models (as shown in Figure 3).