Dynamic fragmentation of ice spheres: Two specific fracture patterns

Unexpected, mystifying but simple three-dimensional dynamic fracture phenomena

“…In this case, surface waves with relatively short wavelengths are not generated and the larger-scale ‘orange segments’-type fracture pattern may be more easily found. Together with figures 1 and 6, these numerical speculations may suggest a possible influence of the initial wavelengths relative to the size of the sphere, c P T / a , on ensuing three-dimensional wave evolution and the initiation and extension of dynamic fracture inside the sphere, but this does not necessarily mean that the role played by the crystalline structure of ice, residual stress, if any, etc., is fully negligible [11]. However, additional experiments using a pressure sensor of effective radius 6.35 mm in combination with laser displacement sensors suggest that the rise time, here, the time needed to reach a certain pressure, approximately 40 kPa, upon impact, is generally shorter when the fracture is the ‘orange segments’-type.…”

“…These experimental observations are consistent with our numerical speculations of different wave patterns in figure 7. Also, more rigorous discontinuous Galerkin (DG) simulations, which are based on the second-order numerical scheme and include the dynamic unilateral contact between the sphere and a rigid plate where the normal stress is proportional to the penetration depth through a compliance coefficient 1.7 × 10 4 GPa m −1 , indicate that for the impact speed of 4.67 m s −1 having experimentally given the ‘top’-type fracture pattern, the maximum shear stress τ max (Tresca criterion) seems to be a promising fracture criterion, while for a larger impact speed of 5.83 m s −1 having induced the ‘orange segments’-type fracture pattern, a different criterion, the maximum principal stress σ 1 or Rankine criterion, looks plausible [11]. However, it is hard to directly and visually trace the involved dynamics by looking at these physical quantities τ max and σ 1 only.…”

“…Figure 6 shows the two representative fracture patterns repeatedly recognized: (i) only the sections in the proximity of the free surface of the lower hemisphere are fragmented upon collision and the relatively large top-shaped part remains unbroken (here named ‘top’-type fracture pattern; figure 6 a ); and (ii) the sphere is divided mainly into several large segments of similar size like segments of oranges (named ‘orange segments’-type fracture pattern; figure 6 b and also figure 1). Further laboratory experiments using another different receptacle that makes a more single crystal-like transparent ice sphere of radius 30 mm do support the presence of the two specific, plain fracture patterns, even without the pre-existence of apparent material inhomogeneities like air bubbles and planes of weakness in ice spheres [2,11]. Now the question is how to analytically or numerically express the dynamics of fracture, particularly the mechanical difference between the two patterns.…”

“…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 fracture pattern). In each sequence, the time elapsed after the leftmost photograph taken at the beginning of collision is 40, 500, 2000 and 8000 μs (after [11]). The estimated P and S wave speeds of the ice spheres are c P ≈ 4000 m s −1 and c S ≈ 2000 m s −1 , and, for instance, the time required for an S wave to propagate the distance of the diameter, 50 mm, is about 25 µs.…”

Impact of Comminution Kinetic Energy: First Mathematical Modeling of Fragmentation Dynamic Fractures Per Millimetre of Coal

“…Whereas difference energy impact _ by to geometry part of matter, originate from point energy center impact direct; then the impact of the energy propagates through throughout the material as concussion dynamic fragmentation pattern [28][29][30][31][32][33][34]. By because that's the principal pulverization is the process of material fragmentation, where sample move and stomp self to wall base when the material have kinetic energy.…”