PSI - Issue 13

Koji Uenishi et al. / Procedia Structural Integrity 13 (2018) 670–675 Uenishi et al. / Structural Integrity Procedia 00 (2018) 000–000

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t : time, T : duration and A : amplitude) and 0 (otherwise) is applied to the four elements at the bottom of the sphere (diameter D = 50 mm) that consists of the stacked cubes with the side length  x .

Fig. 1. Snapshots taken by a high-speed digital video camera indicate typical dynamic fracture development with time, from left to right, in ice spheres (diameter D = 50 mm) that are colliding against a transparent polycarbonate plate (side view). The preparation process for ice spheres (a) and (b) is identical. However, the sphere in (a) is fragmented only near the lower surface and the most part remains unbroken (“top”-type fracture pattern) while that in (b) is split into several larger segments of comparable size (“orange segments”-type pattern). The leftmost photographs were taken just after collision. The time elapsed after the leftmost photographs is 40, 500, 2000 and 8000  s (after Uenishi et al., 2016b).

a

10 mm

b

Fig. 2. Experimentally recorded top view of the fracturing ice spheres: (a) “Top”-type fracture pattern (impact speed 4.67 m/s) and (b) “orange segments”-type pattern (speed of impact 5.83 m/s). The spheres (diameter D = 60 mm) do not contain apparent initial inhomogeneities inside. The time elapsed after the leftmost pictures is 4, 8 and 14 ms (from left to right) where the leftmost pictures show the spheres just before dynamic collision (after Uenishi et al., 2017). Figure 3 depicts typical distributions of normalized octahedral shear stress in ice spheres with (a) shorter and (b) longer duration of collision. In Fig. 3(a), surfaces waves with relatively short wavelengths are induced and propagated from the impacted bottom along the free surface to cause regions of larger stress only near the surface and thus the “top”-type fracture pattern is expected. On the contrary, in Fig. 3(b), an area of larger stress is expanding along the central axis of the sphere and in this case the “orange segments”-type fracture pattern is likely to be produced. Together with Figs. 1 and 2, these numerical speculations suggest that the waves propagating three-dimensionally inside the sphere may significantly affect the generation and extent of dynamic fracture. However, this does not necessarily mean that the effect of the crystalline structure of ice, residual stress (if any), etc., on the observed dynamic phenomena is completely negligible.