/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
ρ i ρ 0            
E ν            
a b n ε max σ max
P0 C S γ 0 αe
AW Pmin E0        
c ε ˙ 0 m Tmelt Tmax
γ 0m αm γ e ge Δ S MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaam 4uaaaa@3834@
Tm0 Vj Vb        
  Eoh Ay θ    

Definitions

Field Contents SI Unit Example
mat_ID Material identifier.

(Integer, maximum 10 digits)

 
mat_title Material title.

(Character, maximum 100 characters)

 
ρ i Initial density.

(Real)

[ kg m 3 ]
ρ 0 Reference density used in E.O.S (equation of state).

Default = ρ 0 = ρ i (Real)

[ kg m 3 ]
E Young's modulus.

(Real)

[ Pa ]
ν Poisson's ratio.

(Real)

 
a Plasticity yield stress.

(Real)

[ Pa ]
b Plasticity hardening parameter.

(Real)

[ Pa ]
n Plasticity hardening exponent.

Default = 1.0001 (Real)

 
ε max Failure plastic strain.

Default = 1030 (Real)

 
σ max Plasticity maximum stress.

Default = 1030 (Real)

[ Pa ]
P0 Initial pressure.

(Real)

[ Pa ]
C Hugoniot parameters.

(Real)

[ m s ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada Wcaaqaaiaab2gaaeaacaqGZbaaaaGaay5waiaaw2faaaaa@39DE@
S U s = C + S U p

(Real)

 
γ 0 Lattice gamma.

(Real)

 
σ e γ = γ 0 a x

(Real)

 
AW Atomic weight.

(Real)

[ k g m o l e ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada WcaaqaaiaadUgacaWGNbaabaGaamyBaiaad+gacaWGSbGaamyzaaaa aiaawUfacaGLDbaaaaa@3D93@
Pmin Pressure cutoff.

Default = -1030 (Real)

[ Pa ]
E0 Initial energy per unit volume.

(Real)

[ J m 3 ]
c Strain rate coefficient.
= 0 (Default)
No strain rate effect.

(Real)

 
ε ˙ 0 Reference strain rate (time unit)-1.

(Real)

[ 1 s ]
m Temperature exponent.

Default = 1.0 (Real)

 
Tmelt Melting temperature.

Default = 1030 (Real)

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

Default = 1030 (Real)

[ K ]
γ 0m Melting gamma.

Default = γ 0 (Real)

 
σ m γ m = γ 0 m a m x

Default = a (Real)

 
γ e Electronic gamma.

Default = 2/3 (Real)

 
ge Electronic energy coefficient.

Default = 0.0 (Real)

[ J m o l e K 2 ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada WcaaqaaiaadQeaaeaacaWGTbGaam4BaiaadYgacaWGLbGaeyyXICTa am4samaaCaaaleqabaGaaGOmaaaaaaaakiaawUfacaGLDbaaaaa@4093@
Δ S MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaam 4uaaaa@3834@ Entropy of melting.

Default = 9.637e+3 [ J kgK ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada WcaaqaaiaabQeaaeaacaqGRbGaae4zaiabgwSixlaabUeaaaaacaGL BbGaayzxaaaaaa@3DB3@ (Real)

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

[ J kgK ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada WcaaqaaiaabQeaaeaacaqGRbGaae4zaiabgwSixlaabUeaaaaacaGL BbGaayzxaaaaaa@3DB3@
Tm0 Melting temperature parameter.

Default = 1.3 Tmelt (Real)

[ K ]
Vj Volume where EOS are joined.

(Real)

[ m 3 kg ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada Wcaaqaaiaac2gadaahaaWcbeqaaiaacodaaaaakeaacaGGRbGaai4z aaaaaiaawUfacaGLDbaaaaa@3BAF@
Vb Excluded volume for vapor phase.

Default = 0.5/r0 (Real)

[ m 3 k g ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada Wcaaqaaiaac2gadaahaaWcbeqaaiaacodaaaaakeaacaGGRbGaai4z aaaaaiaawUfacaGLDbaaaaa@3BAF@
Eoh Energy at V=V0, T=300K, P=0.

Default = 0.0 (Real)

[ J ]
Ay Coefficient of attractive potential.

(Real)

[ J m 3 mole 2 ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbmaadmaapaqaamaalaaabaGaciOsaiaab2gadaahaaWcbeqaaiaa iodaaaaakeaacaqGTbGaae4BaiaabYgacaqGLbWaaWbaaSqabeaaca aIYaaaaaaaaOWdbiaawUfacaGLDbaaaaa@4000@
θ 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 Δ S MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaam 4uaaaa@3834@ entropy of melting is calculated based on the unit system.
    (1)
    σ = ( a + b ε p n ) ( 1 + c ln ε ˙ ε ˙ 0 ) ( 1 ( T * ) m ) T * = T T 0 T melt T 0
1 E. B. Royce, GRAY, a three-phase equation of state, UCRL-51121, Lawrence Livermore Laboratory, 1971