# Crack Propagation Behavior of Fused Silica during Cyclic Indentation under Incremental Loads
## 1 Introduction  
Fused silica possesses various excellent optical properties and is utilized for a wide range of applications including high-resolution imaging lenses for photolithography devices, laser communication, and space telescopes [1, 2]. Fused silica optics are usually shaped by ultraprecision grinding and finished by polishing [3, 4]. As fused silica is highly hard and brittle, cracks easily occur during grinding [5]. It takes a very long time to remove the grinding-induced cracks by subsequent polishing, and if the residual cracks cannot be completely removed, they will greatly affect the surface optical quality and the service life of the final products. Hence, clarification of the behavior and mechanism of crack initiation and propagation in fused silica is an extremely important step.  
For investigating brittle fractures of materials in grinding processes, indentation experiments have been performed by various researchers attributed to the geometrical similarity between an indenter and an abrasive grain. It is well known that in indentation, brittle materials exhibit a characteristic crack system including median cracks, radial cracks, lateral cracks, and cone cracks [6, 7]. The crack system in glass was confirmed by cross-sectional observation along the median/radial cracks [8, 9, 10]. Real-time observation of crack evolution during loading/unloading was also accomplished [6, 11]. Furthermore, the indentation-induced crack generation mechanism has been used for understanding the subsurface damaging behaviors during abrasive machining processes [12, 13, 14].  
The material removal model by grinding is schematically illustrated in Figure 1. Machining always starts from a subsurface damaged layer generated by the previous passof the abrasive grain, rather than from a fresh bulk region. As the depth of the preexisting cracks is usually deeper than the thickness of material removed by a single cut of an abrasive grain [15], the cracked layer is subjected to incrementally accumulated cyclic loads as the grinding wheel rotates. This situation causes a kind of accumulative historical effect in subsurface damage formation. However, most previous indentation studies focused on individual indentations, thus the effects of incremental-load cyclic loading/unloading still remains unknown. In recent years, cyclic indentation has been attempted on brittle single-crystalline materials such as silicon [16; 17] and germanium [18; 19], and it was demonstrated that multi-cyclic indentation induced completely different mechanical responses from that of individual indentations. For optical glasses, multi-cyclic indentation tests were performed by using Vickers indenters [20] and spherical indenters [21] to investigate fatigue properties, and the evolution of indentation-induced cracks during cyclic bending tests was also investigated [22]. However, all those experiments were performed under a constant maximum load; thus, the effect of incrementally increasing loads, which is closer to the actual grinding process, has not been clarified.  
In this study, multi-cyclic indentations with incrementally increasing maximum loads were performed on fused silica to investigate the material responses to cyclic loading/unloading, and the mechanisms of crack initiation and propagation were analyzed in detail. This study will deepen the understanding of cyclic load-induced subsurface damaging behaviors of high-hardness optical glass materials and other brittle solids in the micro/nanoscale, which is important for clarifying the ultraprecision grinding mechanisms and improving the machined surface quality.