# Crack Propagation Behavior of Fused Silica during Cyclic Indentation under Incremental Loads
## 3 Results and Discussion
### Crack Generation/Propagation Mechanisms  
Based on the above-mentioned results and analysis, the mechanisms of cracking behaviors in incremental-load cyclic indentation are discussed as follows. First, the load-displacement curves showed repetitive elbows during unloading, which indicates occurrence of multiple lateral cracks. A lateral crack initiates beneath the plastic region beneath an indenter [11; 30; 31]. During incremental-load cyclic indentation, the plastic region expands with increasing maximum load and indentation depth. Therefore, new lateral cracks may initiate and propagate beneath the expanded plastic region during later cycles. As schematically illustrated in Figure 17, the newly formed lateral crack in the \(n_{2}\)th cycle will be deeper than the that formed in an early \(n_{1}\)th cycle. An early lateral crack causes shallow spalling while a crack occurring in the later stage leads to deep spalling. In addition, the generation of multiple lateral cracks may result in spalling inside the indents. As the inden  
Figure 14: Load–displacement curves recorded during indentations by a cube-corner indenter at 50 mN: (**a**) single; (**b**) 2 cycles; (**c**) 5 cycles; (**d**) 10 cycles; (**e**) 10 cycles, corresponding to the SEM images in Figure 7.  
tation depth increases, the shallow lateral cracks are affected by the plastic deformation caused by the later indentation cycles. The loading-induced densification and unloading-induced elastic spring-back become significant in the indentation of silica glass [32]. Due to these cyclic deformations, internal spalling occurs, as observed in Figures 6c,d and 7d. Another characteristic brittle fracture induced by incremental-load cyclic indentation is secondary spalling as shown in Figures 6d and 7d. As the secondary spalling occurs at a distant region from the indent, the direct cause of it may not be the indenter itself. Instead, it might be caused by the fragment of deep spalling which behaves as an expanding core under compression from the indenter. As illustrated in Figure 18, in later cycles, the fragment piece generated by a deep spalling is compressed by the indenter and pushed toward the outer area. The lateral compression force from the indenter is transferred by the fragment to the crater edge step of the deep spalling, causing the occurrence of secondary spalling. Such a situation is similar to loading a blunt indenter to the outer material, which induces new lateral crack initiation along spreading direction, and in turn, a secondary spalling. Figure 15: Change in slope of unloading curve during single indentations: (**a**) 100 mN, Berkovich (Figure 11a); (**b**) 50 mN, Berkovich (Figure 12a); (**c**) 100 mN, cube-corner (Figure 13a); (**d**) 50 mN, cube-corner (Figure 14a). Based on the aforementioned analysis, a schematic diagram of temporal cracking/spalling behavior during incremental-load cyclic indentation using a cube-corner indenter is illustrated in Figure 19. On loading of early cycles, median/radial cracks initiate and propagate, and a plastic region is also formed beneath the indenter (Figure 19a). On unloading, lateral cracks initiate and propagate beneath the plastic region (Figure 19b). In a single Vickers indentation, lateral cracks propagate in semicircular median/radial cracks [10] or along the bottom of semielliptical medial/radial cracks with interrupting further median/radial crack propagation to the depth direction [8]. The lateral crack propagates on unloading, but enough large load can induce lateral cracking even on loading [11]. In such a case, the lateral crack can interrupt further propagation of radial/median cracks  
Figure 16: Ratio of \(P^{\prime}\) and \(P\) (\(P^{\prime}\): load at the intersection between two cycles; \(P\): the maximum load of the previous cycle) in incremental cyclic indentation by a cube-corner indenter at maximum loads of (**a**) 100 mN and (**b**) 50 mN. The subfigure in (**a**) explains the definition of \(P^{\prime}\) and \(P\).