Page 289 - The Combined Finite-Discrete Element Method

272 FLUID COUPLING

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initial density ρ o = 1600 kg/m = 1/v o
p 0 = 1e + 10 Pa
initial volume of the cut V c v c
, i.e. = = 1.90
initial volume of charge V o v o
Due to the ignition taking place at the bottom of the cut, the initial stress wave is elongated
towards the top edge of the block. At a later stage, the front of the stress wave takes an
almost circular form, with the top end of the wave front reaching the top edge of the
block just before 0.24 ms after ignition. Behind the wave-front radial cracks appear, with
the crack front moving much slower than the wave front. Thus, by the time the wave
front has reached the free edges of the block inner cracks still propagate toward the edges
of the block.
Further propagation of the wave front, leads to the reflection of the stress wave from
the free surface of the block causing outer cracks on the boundary of the block. The
final fracture pattern is a result of the inner cracks propagating outwards and outer cracks
propagating inwards, together with the opening of secondary cracks.
It can be observed that 0.03 kg of explosive, although sufficient to break the block, is
insufficient to cause a substantial fragmentation of the block. Thus, the same problem
was solved with explosive charge being increased to 0.08 kg. Again, initial stress wave
propagation is followed by propagation of inner cracks, and as the stress wave reflects
from the boundary, outer cracks appear. The combined propagation of inner and outer
cracks yields the final fracture pattern. The increased mass of the explosive charge has
resulted in a considerable fragmentation of the block, (Figure 8.8).

Figure 8.8 Stress wave and fracture sequence in a 2 m block at 0.08 ms, 0.24 ms, 0.32 ms, 0.40 ms,
0.48 ms and 0.72 ms after ignition of 0.08 kg explosive charge.