Bridging the gap between dendrites and gamma'-precipitation in Ni-base superalloys

solid-solid phase transformations, influence of stresses and strains
Bernd
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Bridging the gap between dendrites and gamma'-precipitation in Ni-base superalloys

Post by Bernd » Thu Mar 08, 2018 9:45 pm

Hi all,

A typical way to address the sub-µ gamma' microstructures in Ni-base superalloys would be to model solidification and heat treatments on the scale of the dendrites or grains. Then, picking the local composition in one point of interest, one would set up a simulation on a smaller scale and simulate phenomenae related to gamma' growth and morphology (see here).

However, there are cases where you need to take the effect of gamma' precipitates into account while you are still on the scale of the dendrites or dendrite arms. Then, the difficulty is that for reasons of the local thermodynamic consistency gamma' cannot be neglected, but the precipitates also cannot be displayed properly at that scale.

From a principle point of view, there could be 3 approaches to the problem:

a) Effective Phase Approach
If it were possible to describe 2-phase mixtures of gamma and gamma' as an effective phase, one could just use this phase description instead of gamma in the phase-field simulation. However, theoretical analysis shows that this is possible only for binary systems or those which can be approximated by a pseudo-binary system (see e.g. J. Rudnizki, B. Böttger, U. Prahl, and W. Bleck, "Phase-Field Modeling of Austenite Formation from a Ferrite plus Pearlite Microstructure during Annealing of Cold-Rolled Dual-Phase Steel", METALLURGICAL AND MATERIALS TRANSACTIONS A 42A (2011) 2516).

b) Diffuse Phase Approach
If it is possible to represent the two-phase mixture as a diffuse two-phase region in MICRESS, the thermodynamic consistency problem of an effective phase can be overcome (because there is an extra degree of freedom given by the local phase fractions). This approach can be used in MICRESS for eutectic or eutectoid reactions where a eutectic front, which consists of the two phases, is moving ("unresolved" model, see e.g. here). However, this model is not useful for precipitiation of one solid phase in another one.

c) "Big Particle" Approach
What remains for multicomponent systems (after rejecting a and b) is to accept that - if morphology anyway cannot be correctly represented - the size of the particles also is not relevant. This means, if we accept that the particles, which can be represented at the given resolution, are by a factor of maybe 10 too big, but still cover the whole areas such as to establish the correct local equilibria everywhere, then we can live with that (see e.g. B. Böttger, M. Apel, B.Laux, S. Piegert, "Detached Melt Nucleation during Diffusion Brazing of a Technical Ni-based Superalloy: A Phase-Field Study", 2015 IOP Conf. Ser.: Mater. Sci. Eng. 84 012031, http://dx.doi.org/10.1088/1757-899X/84/1/012031).
While the "Big Particle" approach sounds quite simple at first glance, there are some important difficulties linked to it:
- the particles must be quite regulary distributed in order to fill the whole space (i.e. practically all space should be covered by interface between gamma and gamma'. To obtain that, using "bulk restrictive" and a suitable nucleation distance is essential.
- the number of particles is very high. Thus, it is not possible that each one represents an own grain number. Instead, particles must be "categorized" or already set as several "new sets" in conjunction with the nucleation option "add_to_grain".
- there should be no coalescence which creates few big particles instead of many small ones. Adjacent particls should not have the same grain number, and the gamma'-gamma' interface energy has to be chosen big enough.
- in any case, a lot of interface regions are created which reduce performance. Timestepping and relinearisation schemes need to be optimized to reduce this effect.

Bernd

CharMIC
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Re: Bridging the gap between dendrites and gamma'-precipitation in Ni-base superalloys

Post by CharMIC » Fri Mar 09, 2018 1:03 pm

Hej Bernd,

In the end of first paragraph did you try to put up a link under "see here". If that the case I cannot find a link.

BR
Chamara

Bernd
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Re: Bridging the gap between dendrites and gamma'-precipitation in Ni-base superalloys

Post by Bernd » Sun Mar 11, 2018 11:20 pm

Thanks Chamara!

I wanted to refer to my post prior about simulation of gamma' ripening, and eventually forgot - now the link should work...

Bernd

CharMIC
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Re: Bridging the gap between dendrites and gamma'-precipitation in Ni-base superalloys

Post by CharMIC » Fri Jul 06, 2018 11:22 am

Hej Bernd,

I was wondering this approach could be used to simulate the precipitation γ''. Do you have any experience with this. Since γ'' is non-equilibrium phase.

BR
Chamara

Bernd
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Re: Bridging the gap between dendrites and gamma'-precipitation in Ni-base superalloys

Post by Bernd » Fri Jul 06, 2018 4:08 pm

Hi Chamara,

I don't see why it should not be applicable to gamma'', although I have no experiences with that phase. I also don't see why it should matter whether it is an equilibrium phase or not - gamma' is also often non-equilibrium if tcp-phases are allowed.

What could be a criterion is the phase fraction. If it is too low, it is not easy to approximate evenly distributed fine particles by "big particles" without having too large distances.

Bernd

CharMIC
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Re: Bridging the gap between dendrites and gamma'-precipitation in Ni-base superalloys

Post by CharMIC » Mon Jul 09, 2018 9:51 am

Thanks Bernd for the input. I have another question. When γ'' is kept at high temperature for a long period of time, it will transform it to δ phase. Is this possible to simulate in MICRESS ?

BR
Chamara

Bernd
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Re: Bridging the gap between dendrites and gamma'-precipitation in Ni-base superalloys

Post by Bernd » Thu Jul 12, 2018 7:17 am

Dear Chamara,

If this transformation, as I would assume, is controlled by nucleation and diffusion-controlled growth, it should be a perfect task for MICRESS. The challenges would be to know where it nucleates and to model the correct growth morphology of the delta-phase.

Bernd

CharMIC
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Re: Bridging the gap between dendrites and gamma'-precipitation in Ni-base superalloys

Post by CharMIC » Fri Dec 07, 2018 1:35 pm

Hi Bernd,

What is the exact role of the critical radius in the analytical_curvature model considering the big particle approach?

BR
Chamara

Bernd
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Re: Bridging the gap between dendrites and gamma'-precipitation in Ni-base superalloys

Post by Bernd » Fri Dec 07, 2018 3:35 pm

Dear Chamara,

If a small grain with analytical curvature model gets big, this model is not switched off. The reason is that the critical radius may be bigger than the grid spacing. That means that even if the grain has reached "full size" it may still be much smaller than the critical radius, and still curvature reduction is needed to allow it to grow. This is often the case when working with very fine resolution (essentially this is an important reason for using this model!).

What the analytical curvature model is doing with a big grain is that it still reduces curvature to a value which is given by the critical radius. Of course there is no effect if there is no curvature higher that this critical value.

Bernd

CharMIC
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Re: Bridging the gap between dendrites and gamma'-precipitation in Ni-base superalloys

Post by CharMIC » Fri Dec 07, 2018 4:56 pm

Thanks Bernd for the explanation.

I have the following scenario. I am working with grid resolution of 50nm. The phase that is precipitating has usually maximum size of ~40nm.
So I need to define a critical radius larger than 50nm or am I wrong.

What I noticed was (and may be expected) is that when I use smaller critical radius than 50 nm (eg:5nm) then the minimum undercooling required for the precipitation goes to a value around 170K which is not practical. This is not changing with changing the interfacial energy also.

BR
Chamara

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