## 5 Discussion  
Temporal and morphological characteristics are important indicators for revealing dynamic fractures, but their quantitative description is still challenging. In this paper, the incubation time criterion was proposed to present the time-dependence of dynamic fracture. Based on the experimental data, the incubation times of Breccia and Andesite specimens were fitted as 61.5 and 124.3 us, respectively, by Equation (7). However, in the experiments on the two igneous rocks with approximate striking velocity, the high-speed images presented the observable macroscopic cracks at 100 and 230 us, respectively. This discrepancy can be explained on the basis of the physical meaning of the incubation time. Specifically, the incubation time is a fundamental material property associated with the dynamics of the microcracking relaxation processes, which is independent of the loading conditions, whereas the cracking times recorded in the high speed images were the particular times under the specific loading conditions. Obviously, the microscopic preparation time for a particular dynamic fracture is affected by both the loading conditions and the material properties. The experiments of [PERSON] et al. [39] showed that the fracture moment of rocks occurred earlier with the loading rate increase. Therefore, the incubation time was suggested as an indicator of the temporal characteristic of the dynamic fracture. Central cracking is widely acknowledged as a fracture pattern for the Brazilian test [3; 40], and this fracture pattern is dominated by the loading conditions and geometry of the specimen. However, only a qualitative description of the fracture pattern as central cracking is unsatisfactory. The differences in the morphological characteristics of the frag-memtized process resulting from different rock types after the central cracking need further attention. FracPaQ statistically describes the morphological characteristics of fractures by generating and fulfilling fracture traces according to crack binarization. The statistics of fracture trace lengths and angles are consistent with a Gaussian distribution, and the fitted parameters in the Gaussian function can visualize the morphological characteristics of the fragmentized process of the Brazilian test for different rocks. For example, \(y_{0}\) at 0\({}^{\circ}\) or 180\({}^{\circ}\) reflects the opening width of the dynamic cracks, and \(A+y_{0}\) at 90\({}^{\circ}\) reflects the penetration of the dynamic crack. The fitted results of the two igneous rocks shown in Figure 12 indicated the difference tensile fracture responses to the approximate striking velocities. After the observable cracks appeared, the larger \(y_{0}\) of Andesite compared to Breccia presented a larger opening width of the main crack, which was consistent with that illustrated in Figure 8. Furthermore, the larger \(A+y_{0}\) of Andesite reflected the faster penetration of cracks, which implied a more significant brittleness than Breccia. In conclusion, the morphological characteristics of dynamic tensile fracture in the Brazilian tests were statistically and quantitatively described by FracPaQ and Gaussian function.