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116 Ch a p t e r F o u r

cross-section identifications. There are some special cases that might confuse the detec-
th
th
tion. As was shown in Figure 4.15, particle a in the j slice disappeared in the (j+1) slice;
th
and particle b in the (j+1) slice appears in almost the same position as particle c in the
th
j slice. The above two conditions might also give a minimum SI, but the particles de-
tected did not belong to the same particle in the adjacent slices. Therefore, computer
intelligence and human judgment were interactively used to implement the particle
recognition decisions. A FORTRAN program was developed to automatically execute
the above steps with consideration of the above special cases.
The second procedure involves finding matching particles before and after testing.
Since the particles were treated as rigid bodies, the volumes of the particles would re-
main the same before and after testing. The procedure to identify the particles before
and after testing is briefly described as follows.
The first step is to compare the mass center coordinates of the particles. For bonded
material, the displacement inside the mixture is relatively small, which means the
mass center of the particle before and after testing will not change much. Therefore,
the SI based on the mass center coordinates was used as the criterion to identify the
particles. The second step is to compare the volumes of the particles before and after
testing. The particles, which have the closest location and volume, belong to the same
particle. The mass center (X mc , Y mc , Z mc ) and volume (V i ) of particle i are calculated us-
ing the following equations:
i ∑
V ≈ A j−1 + A j H j−−1 j (4-16)
2

∑ ( A j−1 + A H j− −1 j x ( j−1 + x )/4
)
j
j
X ≈ (4-17a)
mc V
i
∑ ( A j−1 + A H j− −1 j y ( j−1 + y )/ 4
)
j
j
Y ≈ (4-17b)
mc V
i
∑ ( A j−1 + A H j− −1 j z ( j−1 + z )/ 4
)
j
j
Z ≈ (4-17c)
mc V
i
FIGURE 4.15 Special cases Particle a Particle c Particle c
for particle identifi cation.
Particle b

th
th
j slice ( j + 1) slice