## 1 Introduction  
In underground mining, it is imperative to safeguard the safety and health of miners' operators from the threats of polluted air and toxic gases [1]. Particular attention must therefore be paid to ventilation to control the underground mining temperatures. However, regarding the challenging loading conditions and the operational surroundings, fan blades are prone to developing cracks and are susceptible to potential fracture failure, resulting in a significant decline in performance [2]. Hence, exploring crack propagation under diverse loading conditions is of great engineering importance in terms of theoretical guidance and practical application to guarantee the proper operation of mining ventilation. With the aim of determining the fatigue crack propagation behavior at the rotary machine's blades containing initial damage, tests and analyses have been conducted on certain models and full-size components with seeded faults under various types of loads. Nevertheless, conducting fatigue crack growth (FCG) prediction for axial-fan blades is complicated owing to the challenging cross-sectional shape and the harsh loading conditions associated with centrifugal and aerodynamic loads. According to previous investigations, two alternative approaches are at hand for predicting FCG. Experiments and engineering fracture models were extensively used to perform FCG prediction for axial-fan blades. These approaches are based on simplification of the geometry and loads. Many studies have been conducted recently on the experimental investigation of crack growth in practical engineering structures under various loads [3; 4; 5]. With the use of servo-hydraulic fatigue testing devices, [PERSON] et al. [6] conducted fatigue tensile tests on aluminum alloy plate specimens with an initial crack. Considering the finite element method, the crack propagation path and the fatigue life were predicted. Making use of a compact tension (CT) specimen, [PERSON] et al. [7] performed crack propagation and evaluated the crack growth life under tensile loading. [PERSON] et al. [3] used a CT specimen to obtain fracture parameters through tensile testing. The aim of their study was to examine crack propagation within a steel marine structure subjected to multiple loading amplitudes. [PERSON] et al. [8] evaluated the process of fracture initiation and propagation on the surface of S355 steel specimens under cyclic bending loads. [PERSON] et al. [9] carried out an experimental investigation of fracture initiation and propagation in a simplified compressor blade subjected to bending resonance. On account of its economic and efficiency advantages, numerical fracture analysis is an effective approach for predicting FCG and lifetime [10; 11]. It accurately calculates the stress intensity factor (SIF), taking into account the actual crack, specific loads, and boundary conditions, constantly updating the structural configuration and re-meshing as the crack grows [12; 13]. In recent years, a growing number of researchers have employed the fracture mechanics tool FRANC3D combined with different finite element packages such as ANSYS and ABAQUS for crack growth analysis [14; 15]. With the intention of determining the fracture geometry. [PERSON] et al. [16] investigated the crack propagation law of nickel aluminide turbine blades subjected to tensile stress. [PERSON] and [PERSON] [17] explored the compressor impeller's crack propagation law at various rotation speeds while taking the centrifugal load into consideration. They also established the direction of the cracks according to the maximum principal stress criterion. [PERSON] et al. [18] predicted the crack growth direction under non-proportional mixed-mode loadings. The results of FRANC3D showed a good agreement compared to CRACKTRACER3D and experimental results. [PERSON] et al. [19] proposed an optimization method for a 3D shrouded fan blade. The crack propagation process was simulated, and the stress intensity factors were calculated using the method of ANSYS and FRANC3D joint simulations.