input of static anisotropy changed!

technical aspects of .dri file generation (e.g. debug mode ) etc...
jan
Posts: 74
Joined: Thu Jun 19, 2008 2:54 pm

input of static anisotropy changed!

Post by jan » Mon Jun 23, 2008 8:12 am

Dear MICRESS users!

Due to a reprogramming the range of valid inputs for the static anisotropy coefficient in the metallic anisotropy model has changed. The valid input range is now between 0 and 1 corresponding to no anisotropy and maximal anisotropy respectively. Before it has been between 0 and 1/16. Note that values above about 0.7 can introduce numerical problems because the interface stiffness is reduced to less than 30% in the preferred direction, at the maximum value of 1 for the static anisotropy it would vanish completely!
The changes are effective for versions after April 2005 (Version 5.12).

Best wishes

Bernd

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original message from Bernd

jan
Posts: 74
Joined: Thu Jun 19, 2008 2:54 pm

Additional remark

Post by jan » Mon Jun 23, 2008 8:12 am

Dear all,

just to clarify, the above said is true only for metallic anisotropy, not for faceted growth, and has to be specified in the phase interaction data!

Bernd

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original message from Bernd

qiangdu
Posts: 2
Joined: Wed Oct 15, 2008 9:03 pm

Re: input of static anisotropy changed!

Post by qiangdu » Wed Oct 15, 2008 9:16 pm

I am doing a simulation of Al-Cu solidification microstructure with MICRESS. I noticed that in the MICRESS example (AlCu_dri and AlCu_Equiaxed_dir), the static anisotropy coefficient for the phase interaction between liquid and solid is set to 0.5. Is it a realistic value for Al-Cu system? How is this coefficient related to the the static anisotropy coefficnet defined in Eq. (17) of B. Bottger et al Acta Materialia 54 (2006) paper?

Thanks in advance,

Qiang

Bernd
Posts: 1504
Joined: Mon Jun 23, 2008 9:29 pm

Re: input of static anisotropy changed!

Post by Bernd » Tue Oct 21, 2008 4:21 pm

Dear Qiang,

Excuse me for not answering before!

The static anisotropy coefficient which you find in the AlCu examples correspond to the "effective" interfacial energy or interface stiffness. In the Acta Materialia paper this would correspond to sigma^*_alpha,beta in Eq. (18) (if the system were hexagonal and not cubic like it is the case for AlCu). For the cubic system, there is a factor of 15 between the static anisotropy coefficient deta_st (Eq. 17) and the interface stiffness which comes from the second derivative of the fourfold cosinus, i.e., an interface stiffness of 0.5 would correspond to an anisotropy coefficient of about 3%. This order of magnitude for the variation of the interface energy with the direction is realistic for metallic systems.

Bernd

qiangdu
Posts: 2
Joined: Wed Oct 15, 2008 9:03 pm

Re: input of static anisotropy changed!

Post by qiangdu » Thu Oct 23, 2008 7:57 am

Dear Bernd,

Thanks very much! As I told you before in our E-mail communications, I have been trying to simulate a diffusion-controlled solidification (i.e., with large isotropic kinetic coefficient and "reasonable" static anisotropic coefficient). It seems that setting the interface stiffness to 0.5 or 0.6 works well in my calculations. How do you reasoning your pragmatic treatment of the anisotropy in surface energy in 2D case? Do you have a paper with more details describing this issue?

BR,

Qiang

janin
Posts: 39
Joined: Thu Oct 23, 2008 3:06 pm

Re: input of static anisotropy changed!

Post by janin » Thu Oct 23, 2008 4:15 pm

Dear Qiang,

In the present MICRESS version, the anisotroy of the interfacial energy has been introduced in a pragmatic way by direct matching to the modified Gibbs-Thomson equation for anistropic interfaces, which reads
v = mu [dG - sigma* kappa ]
with v being the velocity in normal direction, mu the kinetic coefficient, dG the driving force, kappa the curvature and sigma* the interface stiffness .
The stiffness is defined by
sigma*(phi) = sigma(phi) + sigma''(phi),
where phi describes the local growth direction and '' denotes the second derivative with respect to phi.

For cubic ansitropy in 2D, sigma is defined by:
sigma(phi) = sigma0 (1 + delta cos (4 phi))
where delta is the static anisotropy coefficient From this, the effective stiffness can be derived to be:
sigma*(phi) = sigma0 (1 - 15 delta cos (4 phi))
= sigma0 (1 - delta* cos (4 phi))
As Bernd already explained, this effective anisotropy coefficient delta*= 15 delta is read in the present MICRESS version.

The implemented static anisotropy treatment gives good results for 2D-simulations with optimized numerical parameters. Strange artifical effects may occur if the the phase-field profile is already deformed e.g. due to an insufficient grid resolution. The major problem of this approach is that it cannot be easily extended to 3D and therefore it will probably be replaced by a more comprehensive solution I'm currently testing in a beta-Micress version.

Regards,

Janin

zhubq
Posts: 84
Joined: Mon Jun 22, 2009 7:33 pm

Re: input of static anisotropy changed!

Post by zhubq » Thu Jul 02, 2009 9:00 pm

what about the grain boudary? The energy and mobility anisotropy formula used is MICRESS.
they are also the same as you mentioned above, x=x0*(1-k*cos(n*t)), where x is energy or mobility, k is the static or kinetic coefficient, n is symmetry, t is the angle?

if so, what the exact meaning of t, the misorientation between the two adjacent grains or the angle between the grain boudary and global system or else?

By the way, when indicate the symmetry, 'none' 'cubic' and 'hexagonal' is clearly understood, what about 'xyz_axis'?

Besides, when we use random grain input, for random size and orientation of grains, the randomness is uniform or following some distribution?
Thank you.

Bernd
Posts: 1504
Joined: Mon Jun 23, 2008 9:29 pm

Re: input of static anisotropy changed!

Post by Bernd » Thu Jul 02, 2009 9:27 pm

Dear zhubq,

The anisotropy description for the mobility in principle is the same as for the interfacial energy as you said. In both cases, such a description makes only sense if one of the two phases is isotropic, otherwise the situation would be more complicated. The angle then is the relative orientation of the interface normal to the anisotropic grain.

Unfortunately, I cannot tell you right now what xyz_axis means. Let's hope that Janin will give us this information...

With respect to the randomness of the orientation distributions, I think we did our best to achieve a uniform orientation distribution - did you experience problems with that?

Bernd

Bernd
Posts: 1504
Joined: Mon Jun 23, 2008 9:29 pm

Re: input of static anisotropy changed!

Post by Bernd » Fri Jul 03, 2009 9:57 am

Hi,

Janin gave me the following information:

With xyz_axis symmetry the anisotropy function has the same shape as cubic, but with a preferred direction (i.e. tetragonal)!

Bernd

janin
Posts: 39
Joined: Thu Oct 23, 2008 3:06 pm

Re: input of static anisotropy changed!

Post by janin » Mon Mar 08, 2010 5:49 pm

The xyz_axis option represents a pragmatic approach to define cubic anisotropy, but with different values for x,y and z axis. It's long ago that I programmed it and I don't know whether anyone has ever used it. Therefore, I would be glad if I could get some feedback, if this feature shall still be supported in future releases.

The present formulation just stretches the classic cubic formula in the given directions.
E.g. in 2D, the user can specify two values delta1 and delta2 in the input file.
Delta1 refers to the standard function:
a = a0 * (1-delta1 * cos(n*theta))
This value is then multiplied by an elongation factor:
elongation_factor = cos(theta)**2 + delta2 * sin(theta)**2
leading to:
a_elongated_z = elongation_factor * a0 * (1-delta1 * cos(n*theta))

The following figures illustrates this for
a) delta1 = 0.2 and delta2 = 1
4fold_anisotropy.jpg
4fold_anisotropy.jpg (15.21 KiB) Viewed 29284 times
and b) delta1 = 0.2 and delta2 = 1.5
4fold_anisotropy_e.jpg
4fold_anisotropy_e.jpg (16.04 KiB) Viewed 29272 times
Regards,

Janin

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