The stress coupled

[sunny]

Hi, Bernd,

I am now simulating the case that one phase precipitates from the matrix phase and the elastic strain is considered.

As shown in the following, there are some input for "line". If my understanding is right, "lattice misfit" should be inputed here. However, there exist three definitions of "lattice misfit" available in the literature, i.e. (x(precipitate)-x(matrix))/x(matrix), (x(precipitate)-x(matrix))/x(precipitate), 2*(x(precipitate)-x(matrix))/(x(precipitate)+x(matrix)). Which one do you suggest? I know that when the lattice parameters for the two phase are close to each other, the three definitions can lead to almost the same results.

...
# phase 2
# ---------------------------------------
# line? (real) (real) (real)
0.00907 0 0
# line? (real) (real) (real)
0 0.00907 0
# line? (real) (real) (real)
0 0 0.00907
...

Thank you in advance!

BG/sunny

[markus]

OK, MICRESS behaves at present a bit silent in this point ....

As input you should give for each phase a tensor for the definition of the lattice symmetry. The lattice misfit is calculated according to your first definition. The identifier (number) for the matrix phase is the one MICRESS is asking for.

e.g.

Matrix:
1. 0. 0.
0. 1. 0.
0. 0. 1.

Precipitate:
1.05 0. 0.
0. 1. 0.
0. 0. 0.95

would result in a +/-5% mismatch in the x/z principle lattice directions between matrix and particle. According to the definition, the stress free strain of the matrix is always 0.

[sunny]

Hi, Markus,

Thank you for your reply!

According to your reply, we should enter 1 for the matrix by default. Thus, I should define my case (3D) in this way:

Matrix:
1. 0. 0.
0. 1. 0.
0. 0. 1.

Precipitate:
1.907 0. 0.
0. 1.907 0
0. 0. 1.907

because (x(precipitate)-x(matrix))/x(matrix)=0.00907=0.907% for my calculation. Then, I can enter c_ij considering the phases are both FCC crystal structure and isotropic. Am I right?

One more thing is that I just treat my simulation in 2D case now. Is it necessary to modify the above tensor for the lattice symmetry as follows?

Matrix:
1. 0. 0.
0. 1. 0.
0. 0. 1.

Precipitate:
1.907 0. 0.
0. 1 0
0. 0. 1.907



BG/sunny

[markus]

?????

I would suggest 1.0097 for a +0.97% mismatch. Just try it out and look at the output for the displacement *uxCV, *uzCV.

The definition of the elastic material properties has to be defined always in 3D. MICRESS takes into account 3D rotations of grains even for a 2D calculation. This leads sometimes to unexpected results for low symmetry systems if the grains are rotated.

[sunny]

Thank you so much for your reply.

Another question: Does it make some differences between the following two cases in MICRESS simulation?

Case 1:
Matrix:
1. 0. 0.
0. 1. 0.
0. 0. 1.
Precipitate:
1.00907 0. 0.
0. 1.00907 0
0. 0. 1.00907

Case 2:
Matrix:
0. 0. 0.
0. 0. 0.
0. 0. 0.
Precipitate:
0.00907 0. 0.
0. 0.00907 0
0. 0. 0.00907