# Crack Propagation Behavior of Fused Silica during Cyclic Indentation under Incremental Loads
## 3 Results and Discussion
### Load-Displacement Curve Analysis  
To investigate temporal deformation/fracture behaviors of material during incremental cyclic indentation, load-displacement curve analysis was performed. Figures 11 and 12 are load-displacement curves of indentations made by the Berkovich indenter at maximum loads of 100 mN and 50 mN, respectively. For both figures, the loading curves of multiple cycles overlapped partially, and the slopes of the unloading curves were very similar. No features such as pop-in and pop-out on the curves were observed, indicating that indentation by the Berkovich indenter did not induce significant detachment of a surface layer due to cracks. Figure 7: SEM images of indents generated by a cube-corner indenter at 50 mN: (**a**) single; (**b**) 2 cycles; (**c**) 5 cycles; (**d**) 10 cycles; (**e**) 10 cycles. Figure 8: CCD camera images of indents shown in Figure 6 which were generated by a cube-corner, indenter at 100 mN: (**a**) single; (**b**) 2 cycles; (**c**) 5 cycles; (**d**) 10 cycles. The shining areas and interference fringes indicate lateral crack propagation in the subsurface regions. Figure 9: Incidence of complete spalling for each incremental cyclic indentation condition. Figures 13 and 14 illustrate load displacement curves of incremental cyclic indentations by the cube-corner indenter at maximum loads of 100 mN and 50 mN, respectively. As compared to the curves of the Berkovich indenter in Figures 11 and 12, there are some characteristic features. First, all the unloading curves exhibit elbows, namely, discrete changes in slope, at the last parts of unloading curves. An elbow means promoted displacement decrease by some factors such as phase transformation with volume expansion [26; 27] and detachment of a surface layer like a coating beneath the indenter [28; 29]. The elbows were more clearly observed via the slope changes of the tangential lines on the unloading curves as shown in Figure 15. For the Berkovich indenter, the slope decreases and the decreasing speed becomes faster as unloading progresses ((a) (b)). On the other hand, for the cube-corner indenter, the slope decrease becomes discrete and slower at the end parts (\(\sim\)20 mN for (c) and \(\sim\)6 mN for (d)), which is the evidence of elbows. In this study, the elbow would be caused by surface spalling, i.e., detachment of a surface layer due to lateral crack propagation. This agrees with the result that the incremental-load cyclic indentation significantly promoted lateral crack propagation, as shown by the SEM observations. Due to the occurrence of elbow, the overlapping phenomenon of loading/unloading curves in Figures 11 and 12 was not observed in Figures 13 and 14. The repetitive occurrence of elbow indicates incremental propagation of lateral cracks and surface spalling, as shown in Figure 9.  
Figure 10: Surface topography around the secondary spalling in Figure 6d: (**a**) 2D and (**b**) 3D images; (**c**) cross-sectional profile of the spalling along the dotted line in (**a**). Figure 11: Load–displacement curves recorded during indentations using a Berkovich indenter at 100 mN: (**a**) single; (**b**) 2 cycles; (**c**) 5 cycles; (**d**) 10 cycles, corresponding to the SEM images in Figure 4.  
Figure 12: Load–displacement curves recorded during indentations by a Berkovich indenter at 50 mN: (**a**) single; (**b**) 2 cycles; (**c**) 5 cycles; (**d**) 10 cycles, corresponding to the SEM images in Figure 5.  
Another feature of the load-displacement curve is the occurrence of pop-ins. In Figures 13d and 14d, pop-ins were observed. A pop-in is known as a result of radial crack formation, although radial crack formation does not always result in a pop-in [23]. Pop-ins usually occur during loading. It has been also reported that a cube-corner indenter induces pop-ins during unloading due to the wedging [23; 24]. The big pop-in observed during unloading in Figure 13d might be based on the wedging.