Eigenstrain

[Jane]

Dear Bernd,

I coupled the phase field and stress in MICRESS. I would like to ask you some questions.

1. What should I do with Eigenstrain? If I want to study the eutectoid phase transformation of Fe-0.77C% alloy: γ→α+θ, here I can take γ Eigenstrain as a function of concentration, then how to determine α and θ Eigenstrain?

2. How to add stress in a single direction to MICRESS to influence the phase transformation?

3. Besides Eigenstrain, how are the extra stresses/strains added in the software?

I am looking forward to your reply. I wish you a smooth work and good health.

Jane

[Bernd]

Hi Jane,

I try to answer one by one:

1.) For incorporating concentration dependent eigenstrains you must use "mechano_chemical" as type of mechanical contribution. Then, if you use a database with volume data, you should use "volume" for the notation of eigenstrains, and "database" for "(mechanical relevant) molar volume input" for each phase. Then, MICRESS will automatically calculate concentration and temperature dependent eigenstrains using the database.

2.) Use "fix_normal_pressure" as boundary condition, and specify the corresponding stress in each direction.

3.) I don't know which "extra stresses" you mean - elastic stresses and strains will be calculated automatically.

Bernd

[Jane]

Dear Bernd,

First of all, thank you for your answer. Regarding the first question, I want to adjust the Eigenstrain of each phase through the "matrix". Still taking the γ→α+θ in the Fe-0.77C% alloy as an example, how should I define their Eigenstrain ? Is there any basis?
Another problem I have encountered is, after I add strain through "matrix", why does it not inhibit the phase transition?
Thank you again.

Jane

[Bernd]

Dear Jane,

As far as I know, eigenstrains are always formulated relative to a reference phase which the user has to define in MICRESS. Thus, there is no need to worry about the absolute values. If you do not want to assume isotropic eigenstrain (then you could simply define them by volume), then you need to have detailed crystallographic information like lattice-parameters which allow you defining the eigenstrains. To be honest, I never did that...
Defining eigenstrains in whichever way does not "impede" phase transformations, it just creates an extra driving-force (.dGsp) which acts on the interface and adds up with the chemical driving force to the total driving force (.driv). In case there is no difference in the eigenstrains of two interacting phases, then there will be no effect on the driving-force, as long as concentration dependency is neglected (chemo-elastic case).

Bernd

[Jane]

Dear Bernd,

My first simulation condition is: I coupled the stress field and defined eigenstrains. My current requirement is to suppress the phase transformation. What should I do? Hope to get your advice.
The eigenstrain I'm using here is in this form. But it doesn't inhibit phase transitions.

Jane

[Bernd]

Dear Jane,

Eigenstrain is a required input parameter for any simulation with stress coupling. It can only disfavor a phase transition if it is higher for the forming phase than for the vanishing. I would advise you to use volume notation and use respective molar volumes.

Btw, you have a typo in the 3rd line of your eigenstrain input.

Bernd

[Jane]

Dear Bernd,

Yes, what you said is that I have solved this problem through the volume as you said, but the problem of the "matrix" module has not been solved. If there is a chance, I very much hope that you can explain about the "matrix" " related questions. Thank you very much.
wish you a happy life.

Jane

[Jane]

Dear Bernd,

Following your guidance, I am defining Eigenstrain in terms of "Volume", but there are still some basic questions I would like to ask you:
1. What is the difference between “# Value of molar volume ?” and “# Value of molar volume ?”? How should I define them?
2. How does "Volume" represent Eigenstrain, and how should I define the relationship between them?
3. Can I use "Volume" to express the degree of mismatch?

Jane

[Bernd]

Hi Jane,

1.) There is none

2.) Volume is transformed in the following way to obtain the eigenstrain ε of phase α. Here a is a lattice constant, and β is the reference phase.

a = ( Vm ) ^1/3

ε(α) = [a(α) /a(β)] - 1

However, if you are using direct input of eigenstrains, you should essentially specify the lattice constant a for each phase. As you can see the units don't matter here, just the relative values.

3.) Yes, because different values of Vm lead to a difference in the lattice constant a.

Bernd

[Jane]

Dear Bernd,

After coupling the stress, the Eigenstrain is represented by Volume, and there will be two molar volumes shown in the red box, one is related to mechanical, how should I distinguish between the two?

Jane