# The Static Frictional Behaviors of Rubber for Pipe-Laying Operation
## 3 Results
### Deformation of Contact  
A sequence of six frames are demonstrated in Figure 6 to identify the deformation of the contact area in rubber A-PMMA test where the normal load is 30 N and the increasing rate of \(F_{T}\) is 0.062 N/s. Six pen lines which are drawn on the rubber surface beforehand are ordered from 1 to 6 to confirm the scale of deformation of the rubber surface.  
Figure 5: Coefficient of the static friction versus normal load; (**a**) Rubber samples in contact with steel; (**b**) Rubber samples in contact with PMMA.  
As is shown in Figure 6a, contact system sustains the normal load only, the contact area is stable and the black lines are approximately linear. The slight bend of the black lines indicates that the contact area deforms due to the normal loading. As soon as the pipe sample is dragged by the tangential load, the contact area begins to deform from its original shape, the front edge of the contact shrinks to the center with very small scale, while the rear edge expands smoothly (Figure 6b). This phenomenon can be deduced as a result of integral elastic deformation of the rubber sample. The black lines bend distinctly with increasing tangential load, meaning that the surface of the contact moves forward with the pipe surface. A fold appears at the front edge of the contact (Figure 6c 1), and then vanishes due to the re-adhesion of the interfaces (Figure 6d 2). The contact at the rear edge enlarges to beyond the line 1 (Figure 6d 3), this phenomenon illustrates an obvious and continuous attachment between contact surfaces. The red area which is marked in Figure 6e 4 within the apparent contact area represents the estimation of the adhesive zone. The shape of the adhesive zone is deduced from the different bend of the black lines. The black line keeps partially straight at the part of rubber surface which is located at the adhesive zone, whereas it becomes a bend at the partial slip zone. In Figure 6f, most of the apparent contact area is occupied by the partial slip zone; the residual adhesive zone (Figure 6f 5) cannot hold the tangential load, and then the macroscopic slip is emerging.  
The other sequence of six frames illustrating the deformation of the rubber A-PMMA contact are shown in Figure 7, where the normal load is 30 N and the increasing rate of \(F_{T}\) is 1.5 N/s. At the beginning of the test, the deformation of the contact behaves similarly to the deformation which is under the low increasing rate of the \(F_{T}\). However, distinct difference takes place when the tangential load increases quickly. In Figure 7c,d, two folds appear at the front edge of the contact simultaneously (Figure 7c 1 and 2), and then propagate towards the center of the contact (Figure 7d 3 and 4). The propagating speed of the folds slows down when the folds get close to the boundary between the adhesive zone and partial slip zone. The first fold stops at the boundary of the adhesive zone, and the boundary is compressed to the rear edge of the contact due to the subsequent folds (Figure 7e 5). Finally, the displacement between the contact surfaces takes place. Attachment is rarely observed at the rear edge of the contact; this observation indicates that the integral elastic deformation of the rubber sample does not affect to the deformation of the contact area effectively.  
Figure 6: Evolution of the rubber A-PMMA contact area. Normal load: 30 N; increasing rate of \(F_{T}\): 0.062 N/s; (**a**) Stable contact area; (**b**) The contact area deforms due to the tangential load; (**c**) The fold appears as the tangential load increases; (**d**) The contact area deforms with the integral elastic deformation of the rubber sample; (**e**) Shrink of the central adhesive zone; (**f**) The instant of the macroscopic slip. Six black lines are marked from 1–6; the white dotted lines circle the areas which deform distinctly due to the tangential load; the red dotted lines circle the central adhesive zone.