13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- σmax and σmin are of path 1 are shown in Fig. 13, where max min ( ) max( (,)), ( ) min( (,)), x x t t x x t x x t σ σ σ σ = = . It is illustrated that the σmax of nodes in region II are larger than the nodes in region I and region III. σmax reaches a maximum value when the contact region moves to the red region in Fig. 11 because of the cumulated effect of contact shear stress and maximum applied load. Δσ= σmax −σmin is shown in Fig. 14. It gives a different property with the stress amplitude of a standard specimen as shown in Fig 15. It may clarify that the crack does not occur at the middle of the contact area where the wear depth reached the maximum, but at the edge of the contact area. Figure 10. The contact pressures of path 1 for different times. Figure 11. The regions on the surface of the tube. Figure 12. Stress of the elements in the three different regions Figure 13. The maximum and minimum stress of nodes on path 1 during one cycle.
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