Lagamine

File number = 35 ; Generally called *IN.MET
This *.met file is read in the Prepro by METLAW.F

This file contains all the data necessary to use effectively the laws META, METAMEC, ELAMET, ARBTHMET and THMET. It must always exist to perform a metallurgical thermal analysis. Sections 1 to 8 are repeated with increasing ILAWN if more than one steel is described.

Remark: Some values are already defined in Integer parameters, pay attention to give the same value. Values as NTPCA, NPA, NVM, NTEMP are defined a first time automatically in LAWPRE. If you want to change these values, change also in the FORTRAN source file called LMETA.F.

All the characteristic temperatures are defined on the figure below:

Remark : Some additional parameters can occur depending on the steel and its plasticity transformation formula or the modification of the formula of the shift ($D=C\sigma$). If you want to change, you must adopt:

1. NTPCA (section 2);
2. Subroutine METLAW that read and write with comments the parameters of section 3;
3. Subroutine ARMEA that read the great vector PAMET where are stored the parameters of section 3 and where the formulae of $D$ and $\varepsilon^{pt}$ are implemented.

If IPOLY =1

The conductivity $\lambda$, the mass density $\rho$, the heat capacity C and the hardness$ H_v$ have to be defined for each phase. The latent heat L is defined for each transformation. You can choose the order in which you want to define these parameters:

1. Firstly you give five letters (A5): 'A1^A2' where:
   
   1. A1 defines the thermal parameter
      
      • $\lambda \rightarrow$ LA
      • C$\rightarrow$ CA
      • $\rho \rightarrow$ RO
      • $H_v \rightarrow$ HV
      • L $\rightarrow$ TR
        
   2. $A_2$ defines the phase; For $\lambda, \rho, C, H_v$:
      • Austenite $\rightarrow$ AU
      • Bainite$\rightarrow$ BA
      • Proeutectoïd $\rightarrow$ PR
      • Martensite$\rightarrow$MA
      • Pearlite$\rightarrow$PE
        For L (latent heat) A2 = PR, PE, BA or MA to define in which phase the austenite is transformed.
2. Secondly you give the polynomial coefficient (A(I), I=1,NDPO+1) which defines the following polynomial: $$A(1)+A(2)T+A(3)T^{2}+ … +A(NDPO+1)T^{NDPO}$$
3. Finally the non-defined parameters will be initialized to zero. So if you know that only certain phases will be present you do not need to define the other phase parameters.

If IPOLY = 0
One must write FI followed by a blank card.
If input parameters (temperature dependent) are given as a table, all the tables must have the same length. Otherwise, it does not work properly.

1. Firstly you give five letters : 'A1^A2' and NTER where :
   • A1 defines the mechanical parameter:
     • YOUNG modulus: YO
     • POISSON ratio: NU
     • Thermal dilatation: AC or AP (AC for the $\alpha$ coefficient of classical type and AP for the $\alpha$ coefficient of partial type)
     • Yield stress $\sigma_y$: SY
     • Plastic slope: ET
   • If IPOLY=0:
     • Thermal conductivity: LA
     • Mass density: RO
     • Heat capacity: CA
     • Vickers hardness: HV
     • Latent heat of transformation: TR
   • '^' is a space;
   • A2 defines the phase concerned;
     • Austenite: AU (Except for A1=TR)
     • Proeutectoïd: PR
     • Pearlite: PE
     • Bainite: BA
     • Martensite: MA
   • NTER as the number of temperature used to describe the evolution of the parameter.
     
2. Secondly, ONLY IF AC is chosen:
   (A5,G10.0) 3 spaces and 'TO' or 'T0'
   VALUE: Value of $T_0$ (usually $T_0$ is the room temperature so 20°C or 293K, be careful there is no default value for this parameter, so you should enter a value, otherwise the preprocessor will crash)
3. Thirdly, you repeat NTER times:
   • TEMPE: Temperature
   • VALUE: Value of the parameter

Remarks :

1. No defined tables are initialized to zero
2. A1 = FI followed by a blank card indicates the end of section 5.
3. For the table describing ALPHA, the first temperature must be zero otherwise the integration of $\int_0^{T_{\alpha}} dT$ will not be correct.
   

Remarks about the thermal coefficient $\alpha$:

1. The $\alpha_C$ coefficient of classical type is defined by : \[\alpha_C(T) = \frac{1}{L_0}\frac{L_{(T)}-L_0}{T-T_0}\] where $L_0=L(T_0)$.
   The $\alpha_P$ coefficient of partial type is defined by : \[\alpha_P(T)=\frac{1}{L_{(T)}}\frac{dL}{dT}\] The user could give the classical type or the partial type $\alpha$ coefficient (with AC or AP).
   
2. If $\alpha$ is of classical type ($\alpha_C$) :
   • The unity, chosen by the user, of $T_0$ has to be the same as the unity of the temperatures at which the $\alpha_C$ coefficient is given.
   • The temperatures, at which the $\alpha_C$ coefficient is given, have to be given in increasing order.
   • It is necessary to give at least 2 values of $\alpha_C$ at two temperatures.
   • Each $\alpha_C$ coefficient has to verify the following relation : \[1+\alpha_C(T).(T-T_0)>0\;\text{ and not equal to 0}\]
3. If the user gives the classical type $\alpha_C$ coefficient (AC), the pre-processor will calculate the partial type $\alpha_P$ coefficient. If the user gives the partial one, the pre-processor keeps these values. In the case of the calculus of the partial type $\alpha_P$ coefficient, the following relations are used (see the file ALPHAPARTIEL.F) for given couples ($T_i,\alpha_{Ci}$) with $i=1,\ldots,n$ : \[\alpha_{P1} = \frac{\alpha_{C1}+(T_1-T_0)\frac{\alpha_{C2}-\alpha_{C1}}{T_2-T_1}}{1+\alpha_{C1}(T_1-T_0)}\]\[\alpha_{Pn} = \frac{\alpha_{Cn}+(T_n-T_0)\frac{\alpha_{Cn}-\alpha_{Cn-1}}{T_n-T_{n-1}}}{1+\alpha_{Cn}(T_n-T_0)}\] and for $i$ such as $1<i<n$: \[\alpha_{Pi}=\frac{\alpha_{Ci}+\frac{1}{2}(T_i-T_0)\left(\frac{\alpha_{Ci}-\alpha_{Ci-1}}{T_i-T_{i-1}}+\frac{\alpha_{Ci+1}-\alpha_{Ci}}{T_{i+1}-T_i}\right)}{1+\alpha_{Ci}(T_i-T_0)}\]
4. For more information about the $\alpha$ coefficient of classical and partial type, the reader could see the internal report N° M&S/2002-8 of the 5$^{th}$ December 2002 entitled “Comparaison des coefficients de dilatation thermique classique et partiel”.
5. An example of what the user should give is:

  AC AU    5
      T0       0.0
         0.0   10.E-06
       200.0   12.E-06
       400.0   16.E-06
       700.0   25.E-06
       900.0   30.E-06
  AC PE    2
      T0       0.0
         0.0   10.E-06
       900.0   30.E-06
  AP MA    5
         0.0   30.E-06
       200.0   25.E-06
       400.0   16.E-06
       700.0   12.E-06
       900.0   10.E-06     

The three phases : Proeutectoïd (PROEU). Pearlite (PERLI) and bainite (BAINI) have to be described successively by the sections detailed hereafter. The order PROEU, then PERLI, then BAINI must be respected.

N.B.These data are used to complete n and b coefficients of the Johnson-Mehl-Avrami law
Remark 1: The NTR number must be limited by the data NT1, NT2 or NT3 given in section General data for each phase (PROEU, PEARLI or BAINI)
Remark 2: Do not leave an empty card at the end of the *.met. Otherwise the Prepro will expect for another material.