/MAT/LAW80

Block Format Keyword This law allows modeling the ultra-high strength steel behavior at high temperatures and the phase transformation phenomena from austenite to ferrite, pearlite, bainite and martensite during cooling.

Format

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
/MAT/LAW80/`mat_ID`/`unit_ID`
`mat_title`
$ρ_{i}$
`E`		$ν$		`fct_ID`_E	`Yscale`_E		`Time_unit`
	`F`_smooth	`F`_cut		`C`_eps		`P`_eps
`tab_ID`_Y1	`tab_ID`_Y2	`tab_ID`_Y3	`tab_ID`_Y4	`tab_ID`_Y5
`Yscale`₁		`Yscale`₂		`Yscale`₃		`Yscale`₄		`Yscale`₅
`Xscale`₁		`Xscale`₂		`Xscale`₃		`Xscale`₄		`Xscale`₅
`Θ2`		`Θ3`		`Θ4`		`Θ5`
`Alpha1`		`Alpha2`
`QR2`		`QR3`		`QR4`		`Alpha`		`T`_ref
								`Gsize`
`KF`		`KP`		`Lat1`		`Lat2`		`T`_ini
`B`		`Mo`		`Mn`		`W`		`Al`
`C`		`Cr`		`Si`		`Cu`		`As`
`Co`		`Ni`		`V`		`P`		`Ti`

Definitions

Field	Contents	SI Unit Example
`mat_ID`	Material identifier (Integer, maximum 10 digits)
`unit_ID`	Unit Identifier (Integer, maximum 10 digits)
`mat_title`	Material title (Character, maximum 100 characters)
$ρ_{i}$	Initial density (Real)	$[\frac{kg}{m^{3}}]$
`E`	Young's modulus (Real)	$[Pa]$
$ν$	Poisson's ratio (Real)
`fct_ID`_E	Function identifier for temperature dependent Young's modulus. (Integer)
`Yscale`_E	Scale factor for ordinate (Young) for `fct_ID`_E. Default = 1.0 (Real)	$[Pa]$
`Time_unit`	Number of time units per hour. Default corresponds to seconds, equals 3600 time units per hour. Defaults = 3600 (Real)
`F`_smooth	Smooth strain rate option flag. = 0 (Default) No strain rate smoothing. = 1 Strain rate smoothing active. (Integer)
`F`_cut	Cutoff frequency for strain rate filtering. Default = 10³⁰ (Real)
`C`_eps	Parameter for the effective strain rate dependency (Cowper Symonds relation). 2 (Real)
`P`_eps	Parameter for the effective strain rate dependency (Cowper Symonds relation). 2 (Real)
`tab_ID`_Y1	Table identifier for yield stress, first entry effective plastic strain and second temperature, for austenite. (Integer)
`tab_ID`_Y2	Table identifier of yield stress for ferrite. (Integer)
`tab_ID`_Y3	Table identifier of yield stress for pearlite. (Integer)
`tab_ID`_Y4	Table identifier of yield stress for bainite. (Integer)
`tab_ID`_Y5	Table identifier of yield stress for martensite. (Integer)
`Yscale`₁	Scale factor for ordinate (stress) for `tab_ID`_Y1. Default = 1.0 (Real)	$[Pa]$
`Yscale`₂	Scale factor for ordinate (stress) for `tab_ID`_Y2. Default = 1.0 (Real)	$[Pa]$
`Yscale`₃	Scale factor for ordinate (stress) for `tab_ID`_Y3. Default = 1.0 (Real)	$[Pa]$
`Yscale`₄	Scale factor for ordinate (stress) for `tab_ID`_Y4. Default = 1.0 (Real)	$[Pa]$
`Yscale`₅	Scale factor for ordinate (stress) for `tab_ID`_Y5. Default = 1.0 (Real)	$[Pa]$
`Xscale`₁	Scale factor for third variable strain rate for `tab_ID`_Y1. Default = 1.0 (Real)	$[\frac{1}{s}]$
`Xscale`₂	Scale factor for third variable strain rate for `tab_ID`_Y2. Default = 1.0 (Real)	$[\frac{1}{s}]$
`Xscale`₃	Scale factor for third variable strain rate for `tab_ID`_Y3. Default = 1.0 (Real)	$[\frac{1}{s}]$
`Xscale`₄	Scale factor for third variable strain rate for `tab_ID`_Y4. Default = 1.0 (Real)	$[\frac{1}{s}]$
`Xscale`₅	Scale factor for third variable strain rate for `tab_ID`_Y5. Default = 1.0 (Real)	$[\frac{1}{s}]$
`Θ2`	Memory coefficient that determines the fraction of previous straining in the austenite that will be remembered in the newly formed ferrite. = 1 All the plastic strains are transferred. (Real)
`Θ3`	Memory coefficient that determines the fraction of previous straining in the austenite that will be remembered in the newly formed pearlite. = 1 All the plastic strains are transferred. (Real)
`Θ4`	Memory coefficient that determines the fraction of previous straining in the austenite that will be remembered in the newly formed bainite. = 1 All the plastic strains are transferred. (Real)
`Θ5`	Memory coefficient that determines the fraction of previous straining in the austenite that will be remembered in the newly formed martensite. = 1 All the plastic strains are transferred. (Real)
`Alpha1`	Thermal expansion coefficient for austenite (gamma phase)	$[\frac{1}{K}]$
`Alpha2`	Thermal expansion coefficient for products (alpha phase).	$[\frac{1}{K}]$
`QR2`	Activation energy divided by the universal gas constant (R=8.314472) for the diffusion reaction of the austenite ferrite reaction. 1) Default = 11575 (Real)	$[K]$
`QR3`	Activation energy divided by the universal gas constant (R=8.314472) for the diffusion reaction of the austenite pearlite reaction. 1 Default = 13840 (Real)	$[K]$
`QR4`	Activation energy divided by the universal gas constant (R=8.314472) for the diffusion reaction of the austenite bainite reaction. 1 Default = 13588 (Real)	$[K]$
`Alpha`	Material constant for martensite phase. 3 (Real)
`T`_ref	Reference temperature for thermal expansion. (Real)	$[K]$
`Gsize`	ASTM grain size number for the austenite. (Real)
`KF`	Coefficient of Boron in the composition of ferrite. 4 (Real)
`KP`	Coefficient of Boron in the composition of pearlite. 4 (Real)
`Lat1`	Latent heat for the decomposition of austenite to ferrite, pearlite, and bainite. (Real)	$[\frac{J}{m^{3}}]$
`Lat2`	Latent heat for the decomposition of austenite to martensite. (Real)	$[\frac{J}{m^{3}}]$
`T`_ini	Initial temperature. (Real)
`B`	Boron percentage weight in material (0.0~1.0). (Real)
`Mo`	Molybdenum percentage weight in material (0.0~1.0). (Real)
`Mn`	Manganese percentage weight in material (0.0~1.0). (Real)
`W`	Tungsten percentage weight in material (0.0~1.0). (Real)
`Al`	Aluminum percentage weight in material (0.0~1.0). (Real)
`C`	Carbon percentage weight in material (0.0~1.0). (Real)
`Cr`	Chromium percentage weight in material (0.0~1.0). (Real)
`Si`	Silicon percentage weight in material (0.0~1.0). (Real)
`Cu`	Copper percentage weight in material (0.0~1.0). (Real)
`As`	Arsenic percentage weight in material (0.0~1.0). (Real)
`Co`	Cobalt percentage weight in material (0.0~1.0). (Real)
`V`	Vanadium percentage weight in material (0.0~1.0). (Real)
`P`	Phosphorous percentage weight in material (0.0~1.0). (Real)
`Ti`	Titanium percentage weight in material (0.0~1.0). (Real)
`Ni`	Nickel percentage weight in material (0.0~1.0). (Real)

Example (Steel)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                  Mg                  mm                   s
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW80/1/1
steel
#              RHO_I
              7.8E-9
#                  E                  Nu   Fct_IDE             YscaleE           Time_unit
              210000                  .3         0                   0                3600
#            Fsmooth                Fcut                Ceps                Peps
                   0                   0                   0                   0
# TAB_IDY1  TAB_IDY2  TAB_IDY3  TAB_IDY4  TAB_IDY5
        10        10        10        10        10
#            Yscale1             Yscale2             Yscale3             Yscale4             Yscale5
                   0                   0                   0                   0                   0
#            Xscale1             Xscale2             Xscale3             Xscale4             Xscale5
                   0                   0                   0                   0                   0
#             Theta2              Theta3              Theta4              Theta5
                   0                   0                   0                   0
#             Alpha1              Alpha2
             2.51E-5             1.11E-5
#                QR2                 QR3                 QR4               Alpha                Tref
               13022               15569               15287                .011           298.14999
#                                                                                              Gsize
                                                                                                   8
#                 KF                  KP                Lat1                Lat2                Tini
              190000               31000                 590                 640                1083
#                  B                  Mo                  Mn                   W                  Al
               .0025                   0                1.23                   0                   0
#                  C                  Cr                  Si                  Cu                  As
                .248                 .24                 .29                   0                   0
#                 Co                  Ni                   V                   P                  Ti
                   0                   0                   0                .015                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/TABLE/1/10
table
         3
      2011                           0.0                273.                                       
      2013                          0.02                300.                                       
      2013                          0.04                300.                                       
      2012                           0.0                300.                                       
      2012                          0.02                273.                                       
      2012                          0.04                273.                                       
/FUNCT/2011
1st
                 0.0               185.0
                 0.1               339.0
                 1.0               339.0
/FUNCT/2012
2nd
                 0.0               190.0
                 0.1               344.0
                 1.0               344.0
/FUNCT/2013
3rd
                 0.0               195.0
                 0.1               349.0
                 1.0               349.0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

If Q should be in $[\frac{J}{mol}]$ , then 1 cal =4.1855 J.
The strain rate dependency when Cowper Seymonds is used:(1)
$σ = σ_{y} (1 + {(\frac{\dot{ε}}{C_{e p s}})}^{\frac{1}{P_{e p s}}})$
The martensite volume fraction $x_{M}$ equation is:(2)
$x_{M} = x_{γ} (1 - \exp (- α (M s - T)))$

Where,

$M s$

Temperature of martensite transformation

$x_{γ}$

Fraction of austenite available when the transformation of martensite starts
In order to take into account the Boron added in the composition of the material, the functions of ferrite and pearlite are modified: the coefficients KF and KP, multiplies the weight percentage of Boron (B), respectively in ferrite and pearlite composition functions.
This law can be used with /HEAT/MAT.
This law is compatible with /PROP/TYPE1, /PROP/TYPE9, and /PROP/TYPE10.
List of Animation output (/ANIM/SHELL/USRII/JJ):
- USR 2= Austenite Phase Fraction
- USR 3= Ferrite Phase Fraction
- USR 4= Pearlite Phase Fraction
- USR 5= Bainite Phase Fraction
- USR 6= Martensite Phase Fraction
- USR 7= Hardness
- USR 8= Temperature
- USR 9= Yield
- USR 10= XGAMA in martensite equation
Material phase transformations will occur only during the cooling. There is no material phase transformation due to deformation or heating.