## 2 Numerical Investigations
### Quasi-Static Bending Fatigue Simulation Analysis  
The establishment of the shaft tube model refers to GB/T 1449-2005 while taking into account the preparation conditions of the test piece and the size of the three-point bending fixture of the fatigue testing machine. The shaft tube's inner diameter is 51 mm, the outer diameter is 59.8 mm, and the length is 400 mm. According to the common lay-up principle of carbon fiber composites, four lay-up angles of \(0^{\circ}\), \(\pm 45^{\circ}\), and \(90^{\circ}\) were selected, and the lay-up method was symmetric lay-up. The final laying scheme of the CFRP shaft tube is \([0/90/45/02/\pm 45/0/-45/0/90]\) s, with a total of 22 layers and a thickness of 0.2 mm in one layer. The carbon fiber composite material shaft tube test piece used in this paper is FAW200 RC38 prepreg produced by Zhongfu Shenying Carbon Fiber Co., Ltd. (China Jiangsu). Its main components are T700 carbon fiber and epoxy resin. Table 1 shows the material properties of FAW200 RC38 prepreg. In Table 1, \(E_{1}\), \(E_{2}\), \(E_{3}\) are the elastic modulus in the three main directions respectively, and \(V_{12}\), \(V_{23}\), \(V_{13}\) are the Poisson's ratios in the 12, 23, and 13 directions. \(G_{12}\), \(G_{23}\), \(G_{13}\) are the shear modulus in the 1-2, 2-3, and 1-3 planes respectively, and \(X_{t}\), \(Y_{t}\), \(Z_{t}\) are the tensile strengths in the three main directions respectively. \(X_{c}\), \(Y_{c}\), \(Z_{c}\) represent the compressive strength in the three main directions,\(S_{12}\), \(S_{13}\), \(S_{23}\) are the shear strength in the 1-2, 1-3, and 2-3 planes, respectively, and \(G_{LT}\), \(G_{TT}\) are the fiber longitudinal directions. And transverse tensile fracture toughness, \(G_{LC}\), \(G_{TC}\) are the fiber longitudinal and transverse compressive fracture toughness respectively, and \(\rho\) is the density. The material properties of the prepreg interface elements are shown in Table 2.  
In the table, \(E_{n}\), \(E_{s}\) and \(E_{t}\) represent the longitudinal, transverse, and out-of-plane stiffness of the prepreg interface element, respectively; \(\sigma_{n}^{0}\), \(\sigma_{s}^{0}\) and \(\sigma_{t}^{0}\) represent the maximum nominal stress corresponding to type I, type II, and type III failures, respectively; \(G_{n}^{c}\), \(G_{s}^{c}\), \(G_{t}^{c}\) is the fracture toughness corresponding to the failure modes I, II and III, respectively, and \(\eta\) is the power exponent. In the property module of ABAQUS, we define the layup according to the predetermined layup scheme, assign the material parameters in Table 1 to the fiber layer of the shaft tube, and set the physical thickness of the fiber layer to 0.19 mm; set the material parameters in Table 2 to the adhesive layer assigned to the shaft tube, and set the physical thickness of the adhesive layer to 0.01 mm. There is contact between the CFRP shaft tube, the loading head, and the support seat, and the corresponding contact properties should be set in the simulation analysis software for the places where there is contact. Regarding the friction properties between the shaft tube, the indenter, and the support seat, in this paper, a set of control tests are designed in the simulation, and the tests with no friction and a friction coefficient of 0.1 are adopted respectively. Under the same model information, the maximum load of the output shaft tube is the same, so the simulation contact property in this paper is set to frictionless. The type of contact pair used in this paper is face-to-face contact, the contact property is set to hard contact, and it is considered that there is no friction between the contact pairs,