# The Static Frictional Behaviors of Rubber for Pipe-Laying Operation
## 4 Discussion
### Tangential Load Condition
#### 4.2.2 Increasing Rate of the Tangential Load  
Figure 10 illustrates schematic cutaway views of rubber-PMMA contact during a whole test run for the increasing rate of \(F_{T}\) at 1.5 N/s. As the tangential load begins to increase, the apparent contact area becomes smaller and loses its original symmetric shape, and the front edge of the contact area shrinks remarkably (Figure 10a,b). The fold appears at the front edge of the contact area (Figure 10b 1), and the schematic cutaway views of formation of the fold are shown in Figure 10b. Even though there is no slipping within the central adhesive zone, the partial slip zone increases with increasing of the normal load. Relative displacement has taken place in the apparent contact area, and this situation can be seen as a quasi-sliding stage of contact. According to the former studies [9; 10], the fold or detachment wave forms at the front edge results from the strong adhesive junction between the interfaces and the discrepancy of rubber deformation and pipe motion. The fold or detachment wave never slips on the pipe surface, but propagates on the surface of rubber. In sliding contact, the detachment wave can propagate across the contact zone when the motion of the pipe is high enough. However, in the static contact, the motion of the pipe cannot allow the fold propagating from the leading edge to the rear. Even the speed of the fold is distinctly higher than the relative displacement velocity between the interfaces. The fold slows down when it comes close to the boundary of the adhesive zone (Figure 10c 2) and finally stops adjacent to the boundary (Figure 10d 4). It is deduced that the fold is resisted by the bulking of the rubber surface which is under extremely high compression and shear stress within the central adhesive zone. This phenomenon can also be described by fracture mechanics. The fold is commonly regarded as an air tunnel between the interfaces, the leading edge of the fold is the side part which is close to the boundary of the central adhesive zone, whereas the opposite side part is the rearedge of the fold. When the fold is propagating across the contact area, the leading edge of the fold can be regarded as a crack tip which opens the adhesive junction between the interfaces. On the contrary, the rear edge of the fold closes the crack and the interfaces re-adhere together. The propagating mechanism of the fold is also observed at the front edge of the contact area. As is shown in Figure 10c 3, a small fold forms and moves to the rear edge of the contact for a little distance, and then being stopped by the bulking of rubber surface which is in front of the fold (Figure 10d 5). The fold vanishes because that the apparent contact area is shrinking with the increasing tangential load. Finally, the central adhesive zone is squeezed by two sides (Figure 10e 6 and 7) and replaced by the partial slip zone. The relative displacement takes place at the whole apparent contact area. We have known that the strain of the rubber surface can be relaxed by the propagation of the detachment wave in sliding conditions [10], so that it is easy to deduce that the propagation of the fold can also release the extremely high shear stress which is caused by the increasing tangential load. It means that the partial slip zone can convert to the adhesive zone for a moment when the folds pass through. Typically, the partial slip zone holds more shear stress due to the successive propagation of the folds, and it leads an increasing of the critical value of the tangential load which triggers macroscopic slip. Figure 10: Schematic cutaway views of the rubber A-PMMA contact during a whole test run. Normal load: 30 N; Increasing rate of the \(F_{T}\): 1.5 N/s; (**a**) Stable contact area without tangential load; (**b**) The folds appear as the tangential load increases; (**c**) The propagation of the folds; (**d**) The folds is stopped adjacent the boundary of the central adhesive zone; (**e**) The instant of the macroscopic slip.