/MAT/LAW16 (GRAY)

Block Format Keyword This material law is based on Gray EOS and Johnson-Cook yield criteria.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW16/mat_ID or /MAT/GRAY/mat_ID
mat_title
ρiρi ρ0ρ0            
E ν            
a b n εmaxεmax σmaxσmax
P0 C S γγ 0 αe
AW Pmin E0        
c ˙ε0˙ε0 m Tmelt Tmax
γγ 0m αm γγ e ge ΔSΔS
Tm0 Vj Vb        
  Eoh Ay θθ    

Definitions

Field Contents SI Unit Example
mat_ID Material identifier.

(Integer, maximum 10 digits)

 
mat_title Material title.

(Character, maximum 100 characters)

 
ρiρi Initial density.

(Real)

[kgm3][kgm3]
ρ0ρ0 Reference density used in E.O.S (equation of state).

Default = ρ0ρ0 = ρiρi (Real)

[kgm3][kgm3]
E Young's modulus.

(Real)

[Pa][Pa]
ν Poisson's ratio.

(Real)

 
a Plasticity yield stress.

(Real)

[Pa][Pa]
b Plasticity hardening parameter.

(Real)

[Pa][Pa]
n Plasticity hardening exponent.

Default = 1.0001 (Real)

 
εmaxεmax Failure plastic strain.

Default = 1030 (Real)

 
σmaxσmax Plasticity maximum stress.

Default = 1030 (Real)

[Pa][Pa]
P0 Initial pressure.

(Real)

[Pa][Pa]
C Hugoniot parameters.

(Real)

[ms][ms]
S Us=C+SUpUs=C+SUp

(Real)

 
γγ 0 Lattice gamma.

(Real)

 
σσ e γ=γ0axγ=γ0ax

(Real)

 
AW Atomic weight.

(Real)

[kgmole][kgmole]
Pmin Pressure cutoff.

Default = -1030 (Real)

[Pa][Pa]
E0 Initial energy per unit volume.

(Real)

[Jm3][Jm3]
c Strain rate coefficient.
= 0 (Default)
No strain rate effect.

(Real)

 
˙ε0˙ε0 Reference strain rate (time unit)-1.

(Real)

[1s][1s]
m Temperature exponent.

Default = 1.0 (Real)

 
Tmelt Melting temperature.

Default = 1030 (Real)

[K][K]
Tmax For T > Tmax: m =1 is used.

Default = 1030 (Real)

[K][K]
γγ 0m Melting gamma.

Default = γγ 0 (Real)

 
σσ m γm=γ0mamxγm=γ0mamx

Default = a (Real)

 
γγ e Electronic gamma.

Default = 2/3 (Real)

 
ge Electronic energy coefficient.

Default = 0.0 (Real)

[JmoleK2][JmoleK2]
ΔSΔS Entropy of melting.

Default = 9.637e+3 [JkgK][JkgK] (Real)

If blank or 0, default entropy of melting value is automatically translated to the working units.

[JkgK][JkgK]
Tm0 Melting temperature parameter.

Default = 1.3 Tmelt (Real)

[K][K]
Vj Volume where EOS are joined.

(Real)

[m3kg][m3kg]
Vb Excluded volume for vapor phase.

Default = 0.5/r0 (Real)

[m3kg][m3kg]
Eoh Energy at V=V0, T=300K, P=0.

Default = 0.0 (Real)

[J][J]
Ay Coefficient of attractive potential.

(Real)

[Jm3mole2][Jm3mole2]
θθ Join parameter.

Default = 1.0 (Real)

 

Example (Aluminum)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW16/1
Aluminium - GRAY EOS (unit g_cm_mus)
#              RHO_I               RHO_0
                 2.7                   0
#                  E                  Nu
                0.71                 .33
#                  a                   b                   n             Eps_max              sigmax
               0.002             0.00144                0.62                   0                   0
#                 P0                   C                   S             Gamma_0                 a_e
                   0               0.533               1.338                2.18                 1.7
#                 AW               P_min                  E0
               26.98               -5e-3
#                  c           eps_dot_0                   m              T_melt               T_max
                                                           1                1E30
#           Gamma_0m                 a_m             Gamma_e                 g_e             delta_S
                2.18                 1.7              0.6667              8.7e-9             9.637E5
#               T_m0                 V_j                 V_b
                1220             0.47388             0.19025            
#                                   E_0h                 a_y               Theta
                                       0                  47                   1
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comment

  1. The correct moel units must be defined in the /BEGIN card because the default value of ΔSΔS entropy of melting is calculated based on the unit system.
    (1)
    σ=(a+bεpn)(1+cln˙ε˙ε0)(1(T*)m)T*=TT0TmeltT0
1
E. B. Royce, GRAY, a three-phase equation of state, UCRL-51121, Lawrence Livermore Laboratory, 1971