About the input for "volume" and "matrix"

[tatalemon]

Hi,I am now simulating the case that one single grain of B2_Bcc phase precipitates from the matrix Fcc_A1 phase and the elastic strain is considered.
the lattice constant for B2_Bcc phase is a=0.287nm, molar volume is V=7.7746cm3/mol, the lattice constant for fcc_a1 phase is a=0.3552nm,
molar volume is V=6.7446cm3/mol.
As shown in the following, there are some input for "Eigenstrain", the "volume" and "matrix" , I have tried the two input repectly,
...
# Notation for Eigenstrain?
# Options: volume matrix
volume
# Abstraction of the 3D continuum
# Options: plane_stress plane_strain
plane_strain
...
If I choose "volume" , the molar volume of each phase should be input, and the grain will grow up to achieve equilibrium, the chemical driving force and elastic driving force are show in fig.1, their value are all in normal level, and the absolute value of chemical driving force is larger than elastic driving force.


If I choose "matrix" , three lattice misfit value of each phase should be input for "line", the calculated lattice misfit value according to
"(a(precipitate)-a(matrix))/a(matrix)" is " -0.192 " , which value is so large, the grain shrinked,which is not expected, the chemical driving force and elastic driving force are show n in fig.2, their value are abnormal, and the absolute value of chemical driving force is much less than elastic driving force,which lead to the shrinking process.


So my questions are as following,
(1) What's the difference between the two input for "volume" and "matrix",such as the calculating methods , assumption , for what condition they are applied, how can we choose them appropriately?
(2) Could you give me some help or interpretation about the above totally different results for grain growth by choosing "volume" and "matrix"? And for this condition which one do you recommend me to use?
(3) What's the difference between the "plane stress" and "plane strain"?
(4) Another question,we need to determine the number of matrix phase at the beginning, if there are multi-phase in the simulation, there may be one more different matrix phase, as for the present MICRESS code, how could we input two or more matrix phase number??,usually, we can only determine one phase number as Matrix,so if more, how to???

[Bernd]

Dear tatalemon,

Welcome to the MICRESS forum!

I am moderator in this forum and happy about your interesting contibution. Furthermore, I am one of the experts around the MICRESS software, but unfortunately not for your specific questions about stress coupling. But Marcus, who is our stress and strain expert, will certainly do his best to you the answers as soon as he is back to his office!

Meanwhile, I would like to remind you that the two pictures you included in your post seem not to show what you intended. On option is to edit your post and replace them, or just send them in a consecutive post! Before submitting your changes you can use the "Preview" button to check whether they are displayed correctly.

Best wishes

Bernd

[markus]

Dear tatalemon,
indeed we have no explainations about your issues in the MICRESS manual and the MICRESS text messages are not that helpfull, we will improve that in future updates! Let me add a few remarks along your questions:

(1) What's the difference between the two input for "volume" and "matrix",such as the calculating methods , assumption , for what condition they are applied, how can we choose them appropriately?

This input refers to the material data input for the calculation of the "eigenstrain", i.e. how MICRESS handles different molar volumes of the individual phases in the computation of elastic stress and strain. Here I have to issue a first warning: in the driving file the molar volume had been given already before in the section about the thermodynamic properties. In the present versions of MICRESS this first input is completely ignored by the stress/strain solver and one has to specify this quantity again. One reason is the anisotropy in the mechanical behavior which is often not considered in a thermodynamic framework.

For the computation of the Eigenstrain only relative differences are important, thus one has some freedom for the input, e.g.
the molar volume or the sizes of a mechanical unit cell would be possible choices.

# Notation for Eigenstrain?
# Options: volume matrix

For isotropic elastic material behavior the notation "volume" is the most convenient choice and one can give the molar volume (mol atoms!) as an input. MICRESS takes the cubic root from the volume to get the size of a "unit cell" in this case.
"matrix" is the only choice to feed in anisotropic expansions and one has to give the "Eigenstrain matrix" of a unit cell for any phase.

Example:
phase 0, a cubic system
1.0 0.0 0.0
0.0 1.0 0.0
0.0 0.0 1.0

phase 1, a tetragonal distortion
1.0 0.0 0.0
0.0 1.0 0.0
0.0 0.0 1.05

This means phase 1 needs a 5% larger volume in z-direction to be stress free.

(2) Could you give me some help or interpretation about the above totally different results for grain growth by choosing "volume" and "matrix"? And for this condition which one do you recommend me to use?

"volume" and "matrix" should give the same result if the input is consistent. I can't tell you what's going wrong in your case because I do not have your complete input. Anyhow, if your system has a -19% misfit along the x-Axis, the input should be 0.81 0.0 0.0 in the first line. This is already a huge value which brings me to the second warning: MICRESS can only compute in the linear elastic limit. Often large misfits lead to stress levels above the yield strength. As the strain energy usually counteracts the chemical driving force (can be seen in your example by the positive signe of the mechanical driving force), the mechanical effect will be overestimated and the computed stress levels are above the true stress in the material.
One way for a better approximation is to adjust the molar volumes in a way that the max. Eigenstress of a precipitate would be the yield stress, this can be done, e.g. by taking an estimate according to Eshelby's solution for a spherical inclusion.
However, it remains a rough estimation ....


(3) What's the difference between the "plane stress" and "plane strain"?

That denotes the approximation used for 2D stress/strain computations. Please have a look at e.g. wikipedia, plane stress

(4) Another question,we need to determine the number of matrix phase at the beginning, if there are multi-phase in the simulation, there may be one more different matrix phase, as for the present MICRESS code, how could we input two or more matrix phase number??,usually, we can only determine one phase number as Matrix,so if more, how to???

"matrix phase" is maybe a bit misleading. It denotes in this case the reference phase for zero Eigenstrain. In a single domain there can be only one reference for zero strain.

[tatalemon]

Dear markus ,

Thanks for your valuable answers, I think which will be helpful to my simulation.

Best Regards

tatalemon

[tatalemon]

Dear markus ,

Hi, Thanks for your answers last time, now I have a another question about the elasticity calculation,

Actually, I want to know how to distinguish the coherent problem with high elastic energy between

incoherent problem with low elastic energy in MICRESS, you know that both of them have a large difference between

lattice misfits or molar volume for input in MICRESS. So if I want to simulate a incoherent problem with the

parameters I have given last time, in which there is a big difference between the molar volume or lattice misfits, but

the elastic energy should be low, how should I do it ???

I really wander it, hope for your answer!


Best Regards

tatalemon

[markus]

Dear Tatalemon,

unfortunatly, I do not see a clean solution for doing this. The implemented model in MICRESS is still based on the article I.Steinbach, M.Apel, "Multi Phase Field Model for Solid State Transformation with Elastic Strain", Physica D 217 (2006) 153-160.

This model does not distinguish between coherent and incoherent interfaces, even normal and tangential components for the stress and strain at the interface are not discriminated by the model. Thus, the matching conditions at the interfaces are certainly too rigid compared to the real situation.
We are working on model improvements, but this will certainly take some time until it will be included into MICRESS.

A rough approximation for your problem could be to limit the driving force which is acting at the interface. You can enter this in the phase interaction parameter list: DeltaG option: max . The max value sets the limit for the sum of chemical and mechanical contribution, not for both parts seperatly. Nevertheless, by properly setting this limit it is possible to have large elastic stresses and strains, but a small contribution to the driving force.

[tatalemon]

Dear markus ,

Thanks a lot for your help, I think I will give a try as you suggested.

Looking forward to your new model .

Best Regards

tatalemon