# Simulation Study of Thermal-Mechanical Coupling Fretting Wear of Ti-6 Al-4V Alloy
## 4 Results and Discussion
### Effect of Number of Cycles on Wear and Temperature Rise  
Simulation results at different cycle counts were extracted to further investigate the wear problem under thermal-mechanical coupling. Figure 9 depicts the contact pressure and wear distribution for different numbers of cycles. As can be seen in Figure 9a, the contact pressure distribution without fretting slip (N = 0) is Hertzian in shape. The distribution of contact pressure becomes wider with the increase in the number of cycles. The difference between the contact pressure at the contact center and contact edge decreases. As the contact before the fretting is cylinder-flat contact, the contact after the wear becomes flat-flat contact. The contact pressure decreases due to the increased contact area as the amount of wear increases. The evolution of wear depth with the number of cycles is depicted in Figure 9b. Wear depth and width increase with the number of cycles. There  
Figure 8: Effect of temperature on contact pressure and wear depth. (**a**) Contact pressure; (**b**) wear depth.  
is a large depression in the wear profile near x = 0.15 (mutation point). It is observed that the difference of the mutation point is weakened with an increase in the number of cycles. That is, the difference in depth between the mutation point and the wear center becomes smaller. This is the result of the stress concentration at the mutation point being reduced and the normal pressure being shared due to the increase in wear area. Additionally, the gap between adjacent wear curves decreases with the number of cycles, which means that the growth rate of the wear depth decreases. The reason for this is that the coefficient of friction between the surfaces continues to decrease due to the increase in temperature. The decrease in the friction coefficient leads to a reduction in the shear stress, which results in a reduction in the growth rate of the wear depth.  
Figure 10 shows the pattern of temperature distribution of the contact surface with the number of cycles. From the figure, it can be found that the larger temperature values are distributed to the left or right of the contact center. It is because the applied tangential load is a cyclic displacement. In one complete cycle, the cylinder specimen moves from the contact center to the right and then returns to the center position. After that, it returns to the center position again after moving from the contact center to the left. Furthermore, due to the ongoing buildup of heat caused by frictional wear, the surface temperature rises with the number of cycles. The temperature difference between the contact area and the non-contact area decreases. As the heat generated in the contact area is transferred to the non-contact area, the temperature of the non-contact area increases. Consequently, the temperature also spreads continuously to the non-contact area.  
Figure 10: Variation pattern of temperature distribution with the number of cycles.  
Figure 9: Variation of contact pressure and wear depth with the number of cycles. (**a**) Contact pressure; (**b**) wear depth.