8.4 Calibration of K&C Model Parameters for UHPCC
253
Fig. 8.14 Meridian plane, reprinted from Wu et al. (2019), copyright 2020, with permission from
Elsevier
Table 8.6 Strength parameters of K&C model for UHPCC
Parameters
a 0
a 1
a 2
a 1f
a 2f
a 0y
a 1y
a 2y
Calibrated
37.50 0.43 5.87e-04 0.41 7.82e-04 30.26 0.60 1.80e-03
Auto-generated 39.31 0.45 6.08e-04 0.44 8.90e-04 29.69 0.63 1.94e-03
by conducting the split Hopkinson pressure bar (SHPB) compression and spalling
tests, we have obtained the empirical DIF relations for dynamic compressive (DIF c )
and tensile (DIF t ) strengths of UHPCC, as given in Eqs. (8.13, 8.14) and illustrated
in Fig. 8.15.
DIF c =
(˙ ε/˙ ε 0 )
0.014
for ˙
ε ≤ 62s
−1
0.587(log ˙
ε)
2
− 1.435log ˙
ε + 1.911 for ˙
ε > 62s
−1
(8.13)
DIF t =
(˙ ε/˙ ε 0 )
0.018
for ˙
ε ≤ 10.3s
−1
9.959log ˙
ε − 8.718 for ˙
ε > 10.3s
−1
(8.14)
(3) Equation of state parameters
The relationship between pressure and volumetric strain can be described as the
equation of state, and the change in the volumetric strain will induced the change in
pressure. As shown in Sect. 8.4.1, the *EOS #8 (LS-DYNA Keyword User’s Manual,
2014) which can be determined by the triaxial compressive test and fly plate impact
test is used in K&C model. The auto-generated EOS parameters of K&C model are
253
Fig. 8.14 Meridian plane, reprinted from Wu et al. (2019), copyright 2020, with permission from
Elsevier
Table 8.6 Strength parameters of K&C model for UHPCC
Parameters
a 0
a 1
a 2
a 1f
a 2f
a 0y
a 1y
a 2y
Calibrated
37.50 0.43 5.87e-04 0.41 7.82e-04 30.26 0.60 1.80e-03
Auto-generated 39.31 0.45 6.08e-04 0.44 8.90e-04 29.69 0.63 1.94e-03
by conducting the split Hopkinson pressure bar (SHPB) compression and spalling
tests, we have obtained the empirical DIF relations for dynamic compressive (DIF c )
and tensile (DIF t ) strengths of UHPCC, as given in Eqs. (8.13, 8.14) and illustrated
in Fig. 8.15.
DIF c =
(˙ ε/˙ ε 0 )
0.014
for ˙
ε ≤ 62s
−1
0.587(log ˙
ε)
2
− 1.435log ˙
ε + 1.911 for ˙
ε > 62s
−1
(8.13)
DIF t =
(˙ ε/˙ ε 0 )
0.018
for ˙
ε ≤ 10.3s
−1
9.959log ˙
ε − 8.718 for ˙
ε > 10.3s
−1
(8.14)
(3) Equation of state parameters
The relationship between pressure and volumetric strain can be described as the
equation of state, and the change in the volumetric strain will induced the change in
pressure. As shown in Sect. 8.4.1, the *EOS #8 (LS-DYNA Keyword User’s Manual,
2014) which can be determined by the triaxial compressive test and fly plate impact
test is used in K&C model. The auto-generated EOS parameters of K&C model are