206
7 Impact Resistance of Armor Steel/Ceramic/UHPCC Layered …
loadings. Based on a number of static and dynamic mechanical tests, the HJC constitutive model parameters for NSC and UHPCC materials were calibrated by Ren et al.
(2016, 2017), respectively. In the present study, parameters from Refs. (Woolsey
1990; LSTC, LS-DYNA 2001) are adopted due to the close mixing proportions and
summarized in Table 7.10.
Moreover, JC constitutive model is also employed to represent the response of
10CrNi3MoV21A armor steel plate. At follows, the detailed parameters are calibrated comprehensively by performing the systematic static and dynamic mechanical
tests.
(1) Brief introduction of JC constitutive model
Johnson and Cook (1983) proposed an empirically based constitutive model to
describe the response of metallic material subjected to large strains, high strain rates
and high temperatures. In JC constitutive model, the effects of the strain, strain rate,
and temperature on the flow stress σ of the metallic material are incorporated as a
multiplication form as
σ =
A+Bε
n
1 + C ln ˙
ε
∗
1 − T
∗m
(7.3)
where ε is the equivalent plastic strain; ˙
ε
∗
=˙ ε/˙ ε 0 represents the dimensionless strain
rate with the current strain rate ˙
ε and the reference strain rate ˙
ε 0 . A is the yield stress
at reference strain rate and reference temperature, B and n are the coefficient and
exponent of strain hardening effect, respectively. C and m are the constants which
represent the coefficient of strain rate hardening and exponent of thermal softening,
respectively. Besides, T
∗
=
T − T re f
/
T m − T re f
is the homologous temperature
Table 7.10 Parameters of HJC model for NSC and UHPCC (Ren et al. 2016, 2017)
Parameter
NSC
UHPCC Parameter
NSC UHPCC
Density (g/cm 3 )
2.32
2.5
Maximum tensile hydrostatic
pressure (MPa)
6
6
Shear modulus (GPa) 15.3
17.4
Normalized maximum
strength S max
15
7
Normalized cohesive
strength A
0.28
0.30
Pressure constant K 1 (GPa)
12
116
Normalized pressure
hardening B
1.85
1.73
Pressure constant K 2 (GPa)
135
−243
Pressure hardening
exponent N
0.84
0.79
Pressure constant K 3 (GPa)
698
506
Strain rate coefficient
C
0.006
0.005 Damage constant D 1 (GPa)
0.04
0.04
Uniaxial compressive
strength (MPa)
35
135.1
Damage constant D 2 (GPa)
1.0
1.0
7 Impact Resistance of Armor Steel/Ceramic/UHPCC Layered …
loadings. Based on a number of static and dynamic mechanical tests, the HJC constitutive model parameters for NSC and UHPCC materials were calibrated by Ren et al.
(2016, 2017), respectively. In the present study, parameters from Refs. (Woolsey
1990; LSTC, LS-DYNA 2001) are adopted due to the close mixing proportions and
summarized in Table 7.10.
Moreover, JC constitutive model is also employed to represent the response of
10CrNi3MoV21A armor steel plate. At follows, the detailed parameters are calibrated comprehensively by performing the systematic static and dynamic mechanical
tests.
(1) Brief introduction of JC constitutive model
Johnson and Cook (1983) proposed an empirically based constitutive model to
describe the response of metallic material subjected to large strains, high strain rates
and high temperatures. In JC constitutive model, the effects of the strain, strain rate,
and temperature on the flow stress σ of the metallic material are incorporated as a
multiplication form as
σ =
A+Bε
n
1 + C ln ˙
ε
∗
1 − T
∗m
(7.3)
where ε is the equivalent plastic strain; ˙
ε
∗
=˙ ε/˙ ε 0 represents the dimensionless strain
rate with the current strain rate ˙
ε and the reference strain rate ˙
ε 0 . A is the yield stress
at reference strain rate and reference temperature, B and n are the coefficient and
exponent of strain hardening effect, respectively. C and m are the constants which
represent the coefficient of strain rate hardening and exponent of thermal softening,
respectively. Besides, T
∗
=
T − T re f
/
T m − T re f
is the homologous temperature
Table 7.10 Parameters of HJC model for NSC and UHPCC (Ren et al. 2016, 2017)
Parameter
NSC
UHPCC Parameter
NSC UHPCC
Density (g/cm 3 )
2.32
2.5
Maximum tensile hydrostatic
pressure (MPa)
6
6
Shear modulus (GPa) 15.3
17.4
Normalized maximum
strength S max
15
7
Normalized cohesive
strength A
0.28
0.30
Pressure constant K 1 (GPa)
12
116
Normalized pressure
hardening B
1.85
1.73
Pressure constant K 2 (GPa)
135
−243
Pressure hardening
exponent N
0.84
0.79
Pressure constant K 3 (GPa)
698
506
Strain rate coefficient
C
0.006
0.005 Damage constant D 1 (GPa)
0.04
0.04
Uniaxial compressive
strength (MPa)
35
135.1
Damage constant D 2 (GPa)
1.0
1.0