/MAT/LAW80
Block Format Keyword This law allows modeling the ultrahigh 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)  (10)  

/MAT/LAW80/mat_ID/unit_ID  
mat_title  
${\rho}_{i}$  
E  $\nu $  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  Iflag_T  fct_ID_T  
QR2  QR3  QR4  Alpha  T_{ref}  
${\tau}_{1}$  ${\tau}_{3}$  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) 

${\rho}_{i}$  Initial density (Real) 
$\left[\frac{\text{kg}}{{\text{m}}^{3}}\right]$ 
E  Young's modulus (Real) 
$\left[\text{Pa}\right]$ 
$\nu $  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) 
$\left[\text{Pa}\right]$ 
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.
(Integer) 

F_{cut}  Cutoff frequency for strain rate
filtering. Default = 10^{30} (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) 
$\left[\text{Pa}\right]$ 
Yscale_{2}  Scale factor for ordinate (stress) for
tab_ID_{Y2}. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
Yscale_{3}  Scale factor for ordinate (stress) for
tab_ID_{Y3}. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
Yscale_{4}  Scale factor for ordinate (stress) for
tab_ID_{Y4}. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
Yscale_{5}  Scale factor for ordinate (stress) for
tab_ID_{Y5}. Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
Xscale_{1}  Scale factor for third variable strain
rate for tab_ID_{Y1}. Default = 1.0 (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
Xscale_{2}  Scale factor for third variable strain
rate for tab_ID_{Y2}. Default = 1.0 (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
Xscale_{3}  Scale factor for third variable strain
rate for tab_ID_{Y3}. Default = 1.0 (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
Xscale_{4}  Scale factor for third variable strain
rate for tab_ID_{Y4}. Default = 1.0 (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
Xscale_{5}  Scale factor for third variable strain
rate for tab_ID_{Y5}. Default = 1.0 (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
Θ2  Memory coefficient that determines the
fraction of previous straining in the austenite that will be remembered in the newly
formed ferrite.
(Real) 

Θ3  Memory coefficient that determines the
fraction of previous straining in the austenite that will be remembered in the newly
formed pearlite.
(Real) 

Θ4  Memory coefficient that determines the
fraction of previous straining in the austenite that will be remembered in the newly
formed bainite.
(Real) 

Θ5  Memory coefficient that determines the
fraction of previous straining in the austenite that will be remembered in the newly
formed martensite.
(Real) 

Alpha1  Thermal expansion coefficient for austenite (gamma phase)  $\left[\frac{1}{\text{K}}\right]$ 
Alpha2  Thermal expansion coefficient for products (alpha phase).  $\left[\frac{1}{\text{K}}\right]$ 
Iflag_T  Heating process. 5


fct_ID_T  Cooling and heating function identifier.
Only used, if Iflag_T=2. 5
(Integer) 

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) 
$\left[\text{K}\right]$ 
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) 
$\left[\text{K}\right]$ 
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) 
$\left[\text{K}\right]$ 
Alpha  Material constant for martensite phase.
3 (Real) 

T_{ref}  Reference temperature for thermal
expansion. (Real) 
$\left[\text{K}\right]$ 
${\tau}_{1}$  Time necessary to start transformation
during heating at temperature T =
$Ae1$
(starting point of austenization). 6 (Real) 
$\left[\text{s}\right]$ 
${\tau}_{3}$  Time necessary to start transformation
during heating at temperature T =
$Ae3$
(final point of austenization). 6 (Real) 
$\left[\text{s}\right]$ 
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) 
$\left[\frac{\text{J}}{{\text{m}}^{\text{3}}}\right]$ 
Lat2  Latent heat for the decomposition of
austenite to martensite. (Real) 
$\left[\frac{\text{J}}{{\text{m}}^{\text{3}}}\right]$ 
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
#12345678910
/UNIT/1
unit for mat
Mg mm s
#12345678910
# 2. MATERIALS:
#12345678910
/MAT/LAW80/1/1
steel
# RHO_I
7.8E9
# 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 Iflag_T fct_ID_T
2.51E5 1.11E5
# QR2 QR3 QR4 Alpha Tref
13022 15569 15287 .011 298.14999
# tau1 tau3 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
#12345678910
/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
#12345678910
#ENDDATA
/END
#12345678910
Comments
 If Q should be in $\left[\frac{\text{J}}{\text{mol}}\right]$ , then 1 cal =4.1855 J.
 The strain rate dependency when Cowper
Seymonds is used:
(1) $$\sigma ={\sigma}_{y}\left(1+{\left(\frac{\dot{\epsilon}}{{C}_{eps}}\right)}^{\frac{1}{{P}_{eps}}}\right)$$  The martensite volume fraction
${x}_{M}$
equation is:
(2) $${x}_{M}={x}_{\gamma}\left(1\mathrm{exp}\left(\alpha \left(MsT\right)\right)\right)$$Where, $Ms$
 Temperature of martensite transformation
 ${x}_{\gamma}$
 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.
 By default, this law considers dealing
with a cooling process. Iflag_T can be used to define if heating or
cooling is simulated as:
 Iflag_T = 0: Cooling  Austenite transforms to product phase (martensite)
 Iflag_T = 1: Heating  Austenite is formed from ferrite
 Iflag_T = 2: Cooling and heating is flag is defined as a function of time with using fct_ID_T. Cooling occurs when the function is 0 and heating occurs when the function is 1.
 The Austenization model is based on a
modified Leblond model^{1}; where
${x}_{\gamma}$
is the fraction of austenite.
(3) $${\dot{x}}_{\gamma}=\frac{{x}_{eq}\left(T\right){x}_{\gamma}}{\tau \left(T\right)}$$Where,
${x}_{eq}\left(T\right)=\{\begin{array}{l}0,\text{if}T\le A{e}_{1}\\ 1,\text{if}T\ge A{e}_{3}\\ \frac{TA{e}_{1}}{A{e}_{3}A{e}_{1}}\text{,otherwise}\end{array}$
$\tau \left(T\right)=\{\begin{array}{l}{\tau}_{1}\text{,if}T\le A{e}_{1}\\ {\tau}_{3}\text{,if}T\ge A{e}_{3}\\ {\tau}_{1}+\frac{TA{e}_{1}}{A{e}_{3}A{e}_{1}}\left({\tau}_{3}{\tau}_{1}\right)\text{,otherwise}\end{array}$ $T$
 Temperature.
 $A{e}_{1}$
 Starting temperature of austenization.
 $A{e}_{3}$
 Final temperature of austenization.
The starting and final temperatures of austenization are calculated automatically based on the composition of the steel and written to the Starter output file.
 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.