## 5 Tubing Fatigue Precision Fracture Separation Finite Element Simulation
### Crack Propagation Process of Tubing Fatigue Fracture Precision Separation  
Figure 14 shows the PHILSM cloud image of tubing outer surface fatigue crack propagation. According to the crack propagation trajectory, the crack mainly propagates forward along the section where the V-groove is located. In the early stage of fatigue crack propagation, the crack grows along the V-groove section. In addition, the crack propagation direction is shifted toward the loading end side. In the late stage of fatigue crack propagation, the crack propagates toward the bottom of the V-groove.  
Figure 15 shows the STATUSXFEM cloud image of the tubing fatigue fracture precision separation process. Among them, the value of STATUSXFEM is between 0 and 1. STATUSXFEM = 1 means complete break. STATUSXFEM = 0 means no cracking. STATUSXFEM between 0 and 1 indicates different degrees of fragmentation. The fatigue crack propagation is analyzed according to the crack surface propagation process. When loading cycles \(N\) = 0, prefabricated crack appears. When loading cycles \(N\) is 10-100, the crack propagation is stable, and the section is smooth, namely, the stable propagation region. When loading cycles \(N\) is 150-300, the crack propagation fluctuates slightly. Additionally, partially shaded  
Figure 14: PHILSM cloud image of fatigue crack propagation.  
Figure 13: Tubing loading time displacement curve.  
areas and bumps appear. Overall, the extension is relatively complete. When loading cycles \(N\) is 350-450, there is a large deviation in the crack propagation direction, which leads to the unsmooth local expansion, that is, the unsmooth propagation region. When loading cycles \(N\) is 500, the final fracture region occurs. In the later stages of crack propagation, tubing section separation is affected by crack propagation. Due to eccentric load as well as cantilever beam state, the tubing separation is mainly due to the tearing of material, and finally, the instantaneous break occurs. Therefore, the last separated section region does not have the characteristics of stable crack propagation. According to Figure 150, 1 represents the stable propagation region, 2 represents the unsmooth propagation region, and 3 represents the final fracture region. It can be seen from the longitudinal crack surface in Figure 150 that the crack surface in the early stage of fatigue crack propagation is flat, while the crack surface in the later stage of crack propagation is unsmooth.  
According to Figure 15, during the finite element propagation process of the crack in the tubing fatigue fracture precision separation, the propagation speed of the outer ring crack is greater than that of the inner ring. With the increase in loading cycles, the crack surface gradually changes from smooth to undulating, and the overall section is gradually uneven. In the crack propagation process, the time between the crack initiation stage and the instability transient stage is shorter than that in the steady-state propagation stage.  
For the experimental setup, the same type of 304 stainless steel tubing as the simulation is chosen. Finally, the tubing separation section shown in Figure 16 is obtained. There are three main regions in the section, namely, stable propagation region, unsmooth propagation region and final fracture region. The positions of the three regions agree with the section positions obtained from the crack propagation process simulation of tubing fatigue fracture. Therefore, the tube fatigue crack propagation precision separation process is validated.