6.4 Discussions
181
Table 6.3 Residual velocities of the bullet in Sovják et al. (2015)
f c (MPa)
V 0 (m/s)
V r (m/s)
Predicted V r (m/s)
Chen et al. (2008)
Wu et al. (2015a)
132
691
260
223.5 (−14.0%)
300.8 (15.7%)
154
705
226
201.1 (−11.0%)
303.1 (34.1%)
149
703
228
209.7 (−8.0%)
304.1 (33.4%)
V r =
Sf c d 3 I r
M
; I r = I 0 − K(I 0 )H /d ;
K(I 0 ) = 1.99 − 1.52 exp(−I 0 /15.11); S = 127.7(f c /10
6
)
−0.675
(6.4)
Also the perforation limit h per could be solved through Eq. (6.4) by setting I r
= 0. Equation (6.3) can be applied for different projectile nosed shapes, including
(truncated-) ogive nose, hemi-spherical nose, conical nose and flat nose. However,
Eq. (6.4) is only suitable for ogive-nosed projectile.
The available small caliber projectile impacting tests on UHP-SFRC are limited.
Sovják et al. (2015) have conducted a set of truncated-ogive nosed bullet impacting
tests on no coarse aggregated UHP-SFRC panels with the thickness of 45 mm, and
the experimental and predicted residual velocities are listed in Table 6.3.
Máca et al. (2014) also obtained the perforation limit of the bullet impacting on no
coarse aggregated UHP-SFRC panels with the striking velocity of 710 m/s, and the
experimental and predicted perforation limits for experiments in Máca et al. (2014)
and present test are listed in the first two rows of Table 6.4.
For predicting the bullet impact resistance of UHP-BASFRC, compared with the
no coarse aggregate UHP-SFRC, it is difficult to study the enhancing degree of the
adding coarse aggregates in tests. By considering the effect of the coarse aggregates,
Whiffen formula (Whiffen 1943) for dimensionless DOP is suggested by British
Road Research Laboratory as
x
d
=
2.61
f c
M
d 3
d
d a,max
0.1
V 0
533.4
97.51
f 0.25
c
(6.5)
where d a,max is the maximum aggregate size. The application ranges are 5.52 MPa <
f c < 68.95 MPa, 0.136 kg < M < 9979.2 kg, 12.7 mm < d < 965.2 mm, 0 <
V 0 < 1127.8 m/s and 0.5 < d/d a,max < 50 for ogival projectile nose shapes with
caliber radius between 0.8 and 3.5. At follows, the influence of coarse aggregates
on the impact resistance is discussed according to Eq. (6.5). It could be derived
from Eq. (6.5) that, with the identical other parameters of both projectile and targets,
the projectile penetration depth of the UHP-BASFRC with basalt coarse aggregates
(d a,max = 10 mm) is nearly 77.7% of that of the UHP-SFRC with only fine sands
(d a,max = 0.8 mm). By considering the above reduction, the corresponding predicted
perforation limits of the present test are listed in the 3rd row of Table 6.4, and the
181
Table 6.3 Residual velocities of the bullet in Sovják et al. (2015)
f c (MPa)
V 0 (m/s)
V r (m/s)
Predicted V r (m/s)
Chen et al. (2008)
Wu et al. (2015a)
132
691
260
223.5 (−14.0%)
300.8 (15.7%)
154
705
226
201.1 (−11.0%)
303.1 (34.1%)
149
703
228
209.7 (−8.0%)
304.1 (33.4%)
V r =
Sf c d 3 I r
M
; I r = I 0 − K(I 0 )H /d ;
K(I 0 ) = 1.99 − 1.52 exp(−I 0 /15.11); S = 127.7(f c /10
6
)
−0.675
(6.4)
Also the perforation limit h per could be solved through Eq. (6.4) by setting I r
= 0. Equation (6.3) can be applied for different projectile nosed shapes, including
(truncated-) ogive nose, hemi-spherical nose, conical nose and flat nose. However,
Eq. (6.4) is only suitable for ogive-nosed projectile.
The available small caliber projectile impacting tests on UHP-SFRC are limited.
Sovják et al. (2015) have conducted a set of truncated-ogive nosed bullet impacting
tests on no coarse aggregated UHP-SFRC panels with the thickness of 45 mm, and
the experimental and predicted residual velocities are listed in Table 6.3.
Máca et al. (2014) also obtained the perforation limit of the bullet impacting on no
coarse aggregated UHP-SFRC panels with the striking velocity of 710 m/s, and the
experimental and predicted perforation limits for experiments in Máca et al. (2014)
and present test are listed in the first two rows of Table 6.4.
For predicting the bullet impact resistance of UHP-BASFRC, compared with the
no coarse aggregate UHP-SFRC, it is difficult to study the enhancing degree of the
adding coarse aggregates in tests. By considering the effect of the coarse aggregates,
Whiffen formula (Whiffen 1943) for dimensionless DOP is suggested by British
Road Research Laboratory as
x
d
=
2.61
f c
M
d 3
d
d a,max
0.1
V 0
533.4
97.51
f 0.25
c
(6.5)
where d a,max is the maximum aggregate size. The application ranges are 5.52 MPa <
f c < 68.95 MPa, 0.136 kg < M < 9979.2 kg, 12.7 mm < d < 965.2 mm, 0 <
V 0 < 1127.8 m/s and 0.5 < d/d a,max < 50 for ogival projectile nose shapes with
caliber radius between 0.8 and 3.5. At follows, the influence of coarse aggregates
on the impact resistance is discussed according to Eq. (6.5). It could be derived
from Eq. (6.5) that, with the identical other parameters of both projectile and targets,
the projectile penetration depth of the UHP-BASFRC with basalt coarse aggregates
(d a,max = 10 mm) is nearly 77.7% of that of the UHP-SFRC with only fine sands
(d a,max = 0.8 mm). By considering the above reduction, the corresponding predicted
perforation limits of the present test are listed in the 3rd row of Table 6.4, and the