Facet Model in MICRESS

Exchange about the physics background, diffuse interface theory, etc..
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Bernd
Posts: 1144
Joined: Mon Jun 23, 2008 9:29 pm

Facet Model in MICRESS

Post by Bernd » Thu Jan 08, 2009 8:08 pm

Hi all,

MICRESS gives the possibility to use a facet model for the anisotropy. In the phase data input, the user has to specify all individual Normal vectors of the facets in the local coordinate system, which can consist of different types and thus have different properties, and which can be further optionally mirrored using cubic or hexagonal symmetry. Furthermore one has to specify the parameter kappa, which defines the broadness of the anisotropy factor. Up to MICRESS version 5.4 only one value of kappa is allowed for all phases, an improved beta-version is already available.

...
# Is phase 01 anisotrop?
# Options: isotropic anisotropic faceted antifaceted
faceted
# Crystal symmetry of the phase?
# Options: none xyz_axis cubic hexagonal
none
# Number of type of facets in phase 01
1
# kin. anisotropy parameter Kappa?
# only one value for all facets/phases
# 0 < kappa <= 1
0.5000000
# Number of possible orientations of a facet 1
4
# 1 -th normal vector facet 1 ? 3*
1.000000
1.000000
1.000000
# 2 -th normal vector facet 1 ? 3*
1.000000
1.000000
-1.000000
# 3 -th normal vector facet 1 ? 3*
1.000000
-1.000000
1.000000
# 4 -th normal vector facet 1 ? 3*
-1.000000
1.000000
1.000000
...

In the phase interaction input, a static and kinetic anisotropy coefficient has to be specified for each facet type, if one of the two interacting phases is faceted:

...
# Is interaction isotropic?
# Options: isotropic anisotropic
anisotropic
# static anisotropy coefficient of facet 1 (< 1. <0.1>)
0.10000
# kinetic anisotropy coefficient of facet 1 (< 1. <0.1>)
0.10000
...

the static anisotropy function is defined as

sigma = sigma0 * kSt ^2 * ( kSt^2 * cos(theta)^2 + sin(theta)^2) ^(-1.5)

where kSt is the static anisotropy coefficient of the facet and theta is the misorientation of the normal vector of the interface to the normal vector of the nearest facet and sigma is the surface stiffness. A value of 1 for kSt means no anisotropy, 0 means maximal anisotropy. Kappa has no influence on the static anisotropy.

The kinetic anisotropy is calculated as

mue = mue0 * (kKin + (1-kKin) * tanh(kappa/tan(theta)) * tan(theta)/kappa)

where kKin is the kinetic anisotropy coefficient of the facet and theta as stated above. Effectively, kappa determines the sharpness of the facet (in theta) and kKin gives the factor by which the mobility is reduced in direction of the facet. This is illustrated in the attached figure. Again, a value of 1 for kKin means no anisotropy and 0 maximal anisotropy.
ForenbildLR.png
ForenbildLR.png (14.59 KiB) Viewed 2781 times

salarniknafs
Posts: 2
Joined: Wed Mar 11, 2009 5:11 am

Re: Facet Model in MICRESS

Post by salarniknafs » Fri Apr 29, 2011 2:29 am

Hi Brend,

The static anisotropy function for faceded structures is defined as Eq 1:

Eq1: sigma = sigma0 * kSt ^2 * ( kSt^2 * cos(theta)^2 + sin(theta)^2) ^(-1.5)

Does the same equation apply for cubic structures (ie bcc)?

Also, could you kindly reference Eq1 in the literature.

Bernd
Posts: 1144
Joined: Mon Jun 23, 2008 9:29 pm

Re: Facet Model in MICRESS

Post by Bernd » Fri Apr 29, 2011 2:48 pm

Hi salarniknafs,

welcome to the MICRESS forum!

If you need a cubic faceted anisotropy, you would just define one facet vector and apply cubic symmetry. Then, the anisotropy function displayed above would be used only in the range -45° to 45°, always with respect to the nearest facet.

If you need a "normal" bcc anisotropy like in steels, use metallic anisotropy, which is invoked in the phase data input by choosing "anisotropic" and "cubic" symmetry. Then, anisotropy is defined with a standard 4-folded cosinus fuction, as has been explained in this thread.

Unfortunately, our anisotropy functions for the faceted case are not very well documented in literature. You can find an old reference here:

Steinbach I, Pezzolla F, Prieler R, Modelling of casting, welding and advanced solidification processes VII, Warrendale (PA): TMS; 1995 p. 695.

For hexagonal metallic isotropy, there are a few of publications from Janin, like

J.Eiken, Phase-Field Simulations of Dendritic Orientation Selection in Mg-Alloys with Hexagonal Anisotropy,
Materials Science Forum 649 (2010) pp 199-204

J.Eiken, Phase-field simulation of microstructure formation in technical magnesium alloys,
International Journal of Materials Research 2010/04, Page 503-509

Bernd

J.-Y
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Joined: Fri May 13, 2016 2:20 am
anti_bot: 333

Re: Facet Model in MICRESS

Post by J.-Y » Fri May 13, 2016 2:25 am

Hi Bernd,

I am using faceted anisotropy to simulate phase transformation during cooling. Is that possible to introduce anisotropy coefficients (static and kinetic anisotropy coefficient of the facet) changing as a function of the temperature (for example provided from a text file as for the interface mobility)? That would be great to be able to implement that, e.g. to obtain isotropic grains at high temperature and anisotropic grains at lower temperature.

Regards,
JY

Bernd
Posts: 1144
Joined: Mon Jun 23, 2008 9:29 pm

Re: Facet Model in MICRESS

Post by Bernd » Fri May 13, 2016 3:56 pm

Dear JY,

Welcome to the MICRESS forum!

Up to now, nobody requested temperature-dependent anisotropy coefficients, but, in principle, it could be done. We will discuss that in our development group, and we will come back to you later.

Thank you for your suggestion.

Bernd

Bernd
Posts: 1144
Joined: Mon Jun 23, 2008 9:29 pm

Re: Facet Model in MICRESS

Post by Bernd » Tue May 24, 2016 6:12 pm

Dear JY,

we have discussed your suggestion, and in principle have agreed that such an implementation could be done, although there are some open questions about the input format. Additional input should not make the input too lengthy, and backward compatibility of the driving files would be an issue.

But there are also concerns about the question whether the changes in morphology which you described are really an effect of anisotropy. In many cases, morphology may change just due to different growth conditions which lead to a different interplay of kinetik and static anisotropy. Then, it would be a better approach to define different values for the kinetik and static anisotropy coefficient and perhaps use also a temperature dependent interface mobility.
Can you give us a bit more information about the system of your interest? Is it really anisotropy which changes with temperature in your case?

Bernd

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