[8] assumed that the crack growth rate would tend to infinity when the maximum stress intensity factor approaches the fracture toughness, and subsequently established a fatigue crack propagation equation that considered the influence of the stress ratio and fracture toughness. [PERSON] [9] used experimental data to propose an FCP equation that considered the influence of the stress ratio. [PERSON] and [PERSON] [10] introduced the adjusted compliance ratio parameter into the Walker two-parameter formula and considered the influence of residual stress. [PERSON] et al. [11; 12] deduced the stress intensity factor under different stress ratios according to the transformation relationship between stress amplitudes and mean stresses, and created a driving force model that considered the influence of stress ratios. [PERSON] et al. [13] proposed a modified Walker equation to characterize the FCP of a cracked body under constant amplitude cyclic loading. [PERSON] et al. [14] presented an exponential equation that considered the stress ratio effect. [PERSON] et al. [15] compared several different driving force models based on the energy release rate while also considering the effects of the stress ratio. The term \(\Delta\sqrt{G}\) seems to be a valid crack driving force for adhesives, composites and polymers such as copolyester polyethylene terephthalate glycol. [PERSON] et al. [16] incorporated the mean stress effects by employing the Walker equation to fit the fatigue crack propagation rate of steel S355 and S690 based on experimental data. [PERSON] et al. [17] suggested deterministic quadratic relations based on experimental results regarding the relationship between the crack closure quantitative parameter \(U\) and the applied stress ratio \(R\) and between the effective stress ratio \(R_{\text{eff}}\) and the applied stress ratio \(R\) in comparison with various crack closure models. An FCP model for two different stress ratios was generated based on the strain energy density approach and considering the residual stress effects [18]. [PERSON] et al. [19] modified the Walker equation by considering the influence of welding residual stress on the effective stress intensity factor and effective stress ratio. Therefore, it is necessary to derive an equation considering the effect of the stress ratio to describe fatigue crack growth more accurately; experiments under different stress ratios are sometimes needed to obtain such an equation. Several methodologies can be used for modeling FCP, including the mesh-free method [20], boundary element method [21; 22], discrete element method [23], traditional finite element method (FEM) [24; 25], and extended finite element method (XFEM) [26; 27; 28; 29]. The most used numerical simulation methods are traditional FEMs, such as ANSYS [24; 25], the specialized crack propagation simulation software ZENCRACK [30], and the XFEM in ABAQUS [27; 28; 29]. In the traditional finite element method ANSYS, a wedge singular element should be established at the crack tip because of stress singularity, as shown in Figure 1a [25]. The stress intensity factor in ANSYS can be calculated, but the energy release rate cannot be extracted directly. ZENCRACK is a specialized finite element software that is used to simulate crack propagation. A special crack block is set at the crack tip, which can move with the crack propagation, as shown in Figure 1b [30]. This software is good at crack simulation but has poor universality and often needs to be used in combination with other conventional software. The XFEM was first proposed by [PERSON] in 1999 [26]. The enrichment function is introduced into the conventional finite element displacement mode to reflect the crack discontinuity, and the level set function is used to trace the crack surface. Therefore, as shown in Figure 1c [28], the crack can penetrate the element directly without the use of refined mesh at the crack tip, which is easier in terms of meshing than ANSYS and ZENCRACK. It can also clearly show the continuous crack propagation process.