150
5 Projectile Penetrations into Coarse Aggregated UHPCC Targets
5.4.2.2 Constitutive Model Parameters of Concrete and Projectile
The projectile deformed and damaged obviously in the test, and thus the
*MAT_JOHNSON_COOK (JC) model (MAT#015) (Hallquist 2007; Johnson and
Cook 1985) and Mie-Gruneisen equation of state are selected as the projectile material model, which can better describe the dynamic mechanics properties of metals
under the large deformation, high strain rate and high temperature. Moreover, JC
model is widely used in the numerical simulation of metal penetration. The corresponding parameters of JC model and Mie-Gruneisen equation of state are listed in
Tables 5.8 and 5.9, respectively.
Similarly, the HJC model is selected as the material model for the mortar and
corundum aggregates, and the corresponding parameters are listed in Table 5.10.
The keyword *Mat_ADD_EROSION is also applied to delete failed elements
according to the maximum principal strain, and the corresponding value of 0.2 derived
by trial and error is given as the failure criterion for the test.
5.4.2.3 Comparisons of Numerical Results with Test Data
The numerical simulation is performed by above 3D mesoscopic UHPC model with
randomly distributed sphere coarse aggregates and the corresponding constitutive
parameters. Meanwhile, the numerical results and test data are listed in Table 5.11,
Table 5.8 Parameters of JC model for projectile (Johnson and Cook 1985)
Parameter
Projectile Parameter
Projectile
Density ρ (kg/m 3 )
5208
Room temperature T r (K)
298
Shear modulus G (GPa)
77
Specific heat C v (J/(g*K))
469
Yield stress constant A (MPa)
792
Quasi-static threshold strain rate
EPS0
1
Strain hardening constant B (MPa) 510
Failure constant D
1
0.05
Strain hardening exponent N
0.26
Failure constant D
2
3.44
Strain rate correlation coefficient C 0.014
Failure constant D
3
−2.12
Temperature correlation index M
1.03
Failure constant D
4
0.002
Melt temperature T m (K)
1793
Failure constant D
5
0.61
Table 5.9 Mie-Gruneisen equation of state (Johnson and Cook 1985)
Parameter
Projectile
Parameter
Projectile
Intercept of the curve C 1 (m/s)
4569
Slope coefficients of curve S 3
0
Slope coefficients of curve S 1
1.49
Grüneisen coefficient γ 0
2.17
Slope coefficients of curve S 2
0
First order volume correction
coefficient α
0.46
5 Projectile Penetrations into Coarse Aggregated UHPCC Targets
5.4.2.2 Constitutive Model Parameters of Concrete and Projectile
The projectile deformed and damaged obviously in the test, and thus the
*MAT_JOHNSON_COOK (JC) model (MAT#015) (Hallquist 2007; Johnson and
Cook 1985) and Mie-Gruneisen equation of state are selected as the projectile material model, which can better describe the dynamic mechanics properties of metals
under the large deformation, high strain rate and high temperature. Moreover, JC
model is widely used in the numerical simulation of metal penetration. The corresponding parameters of JC model and Mie-Gruneisen equation of state are listed in
Tables 5.8 and 5.9, respectively.
Similarly, the HJC model is selected as the material model for the mortar and
corundum aggregates, and the corresponding parameters are listed in Table 5.10.
The keyword *Mat_ADD_EROSION is also applied to delete failed elements
according to the maximum principal strain, and the corresponding value of 0.2 derived
by trial and error is given as the failure criterion for the test.
5.4.2.3 Comparisons of Numerical Results with Test Data
The numerical simulation is performed by above 3D mesoscopic UHPC model with
randomly distributed sphere coarse aggregates and the corresponding constitutive
parameters. Meanwhile, the numerical results and test data are listed in Table 5.11,
Table 5.8 Parameters of JC model for projectile (Johnson and Cook 1985)
Parameter
Projectile Parameter
Projectile
Density ρ (kg/m 3 )
5208
Room temperature T r (K)
298
Shear modulus G (GPa)
77
Specific heat C v (J/(g*K))
469
Yield stress constant A (MPa)
792
Quasi-static threshold strain rate
EPS0
1
Strain hardening constant B (MPa) 510
Failure constant D
1
0.05
Strain hardening exponent N
0.26
Failure constant D
2
3.44
Strain rate correlation coefficient C 0.014
Failure constant D
3
−2.12
Temperature correlation index M
1.03
Failure constant D
4
0.002
Melt temperature T m (K)
1793
Failure constant D
5
0.61
Table 5.9 Mie-Gruneisen equation of state (Johnson and Cook 1985)
Parameter
Projectile
Parameter
Projectile
Intercept of the curve C 1 (m/s)
4569
Slope coefficients of curve S 3
0
Slope coefficients of curve S 1
1.49
Grüneisen coefficient γ 0
2.17
Slope coefficients of curve S 2
0
First order volume correction
coefficient α
0.46