4. Model ZIRC in Code_Aster

4.1. Internal variables

The internal variables of the “ZIRC” behavior relationship are:

V1*:*

proportion of the alpha phase1,

V2:

proportion of the alpha2 phase,

V3: TP, temperature at the nodes,

V4:

or

Corresponding to

or

, respectively.

The proportion of the phases and is given by:

with the following relationships:

• 
• 

Eventually, the variables V1 and V2 will disappear to store only

in V1.

Note: for the material parameters of the mechanical model, we consider 3 different phases:, and, that is why two phases V1 and V2 are stored. However, the relationships above are not appropriate.

In mechanical model META_LEMA_ANI, the following relationships are considered:

• 
• 
• 
• 
• 

4.2. Using the model

In the case of using the law of mechanical behavior META_LEMA_ANI, the metallurgical phase is an internal variable of the law of behavior. It is therefore determined during the integration of the latter.

For any other law of behavior, the instructions below must be respected.

To activate this model, simply enter the relationship “ZIRC” (COMPORTEMENT =_F (RELATION =” ZIRC “)) in command CALC_META, under the keyword COMPORTEMENT, under the keyword).

Material parameters are entered under the DEFI_MATERIAU keyword factor META_ZIRC.

Finally, the definition of the initial metallurgical state is possible using the command CREA_CHAMP, under the keyword factor ETAT_INIT of the operator CALC_META. It is mandatory to fill in the internal variables V1, V2 and V4.

Note: In principle, the initial metallurgical state is either

, or

and the variable V4 does not need to be entered initially. But, if for some reason, a user wants to perform the following calculation:

initially for

So the moment

will be taken by default to zero if V4 was not mandatory. This is why the variable V4 is mandatory and corresponds to the first moment of the metallurgical calculation (necessarily equal to zero).