## 5 Numerical Results and Discussion
### The Effect of the Clearance on the Ratcheting Response of the Pipe with Assembly Parts  
Figure 10 shows the effect of different clearance between the sleeve and the pipe on the ratcheting response of the pipe with assembly parts at the three selected positions under the internal pressure of 21 MPa during 45 cycles. The average hoop ratcheting strain rates are listed in Table 3.  
In Figure 10a, it can be seen that the hoop ratcheting strain increases as the clearance increases from 0 mm to 0.07 mm at Position 1, with the corresponding average strain rate also increasing (Table 3). The ratcheting response for different clearances at Position 2 was similar to that at Position 1, as displayed in Figure 10b and Table 3. From Figure 10a,b, it can be deduced that as the clearance increases, the assembly contact effect on the ratcheting response gradually declines, leading to the ratcheting strain and average strain rate increasing as the cycles increase. However, the ratcheting response at Position 3 was different from the first two positions. When the clearance between the sleeve and the pipe increased, the hoop ratcheting strain and the corresponding average ratcheting strain rate decreased at Position 3, as presented in Figure 10c and Table 3. Under the same displacement load, an increase in the clearance resulted in a weakening of the assembly contact inhibition effect, and the part of the pipe inside the sleeve was able to be subjected to more deformation, which made the deformation at Position 3 decrease. This indicates that the bending moment at Position 3 decreased. Thus, when the clearance increases, the ratcheting response at Position 3 reduces due to a smaller bending moment, as exhibited in Figure 10c. When the clearance was 0 mm, the average ratcheting strain rate at Position 1, Position 2 and Position 3 increased (as shown in Table 3) because the assembly contact inhibition effect decreased from Position 1 to Position 3. When the clearance was 0.025 mm and 0.035 mm, the average ratcheting strain rate at the selected positions had the same trend, with the average ratcheting strain rate at Position 3 being the largest, at Position 1 being the second largest and at Position 2 being the smallest. Position 1 was located inside the sleeve and the assembly contact effect enhanced gradually at Position 1 during the loading cycles. Position 2 was closest to the assembly contact area and the assembly contact effect was found to be the largest at Position 2. This means that the assembly contact effect on the ratcheting response at Position 1 was smaller than that at Position 2. Thus, the average ratcheting strain rate at Position 1 was larger than that at Position 2. Position 3, located outside the assembly contact area, was the least affected by assembly contact. Hence, the average ratcheting strain rate at Position 3 was the largest. When the clearance was 0.07 mm, the ratcheting responses at the selected positions were mainly dominated by the bending moment, and the average ratcheting strain rate decreased due to the increase of the bending moment from Position 1 to Position 3. Similar trends for the hoop ratcheting strain from Position 1 to Position 4 under different internal pressures were observed over the clearances used, as shown in Figure 11. The assembly contact appeared \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Positions**} & \multicolumn{3}{c}{**Clearance between the Sleeve and the Pipe (mm)**} \\ \cline{2-5}  & **0.000** & **0.025** & **0.035** & **0.07** \\ \hline Position 1 & 0.00524\%/cycle & 0.02056\%/cycle & 0.02544\%/cycle & 0.03135\%/cycle \\ Position 2 & 0.00929\%/cycle & 0.01911\%/cycle & 0.02240\%/cycle & 0.02823\%/cycle \\ Position 3 & 0.03144\%/cycle & 0.02833\%/cycle & 0.02711\%/cycle & 0.02571\%/cycle \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The average hoop ratcheting strain rate at different positions for different clearance under internal pressure of 21 MPa.