Simulating growth of porosity during solidification of Ni base superalloy

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Simulating growth of porosity during solidification of Ni base superalloy

Post by yzn12 » Thu Feb 08, 2018 1:58 pm

Dear Bernd,

Recently, I am thinking about to simulation the growth of porosity during the solidification of Ni base superalloy. Can we take the porosity holes as a distinctive phase, compared with liquid and gamma phase? For Thermocalc, there are 'voids' , and I do not know if it is approporiate to link it with the growth of porosity. On the other hand, the molar volume of liquid, gamma and gamma prime are different, but there would be no porosity formation for the standard example of CMSX-4. How does MICRess software treat the difference of molar volume during simulation?

Best regards!

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Re: Simulating growth of porosity during solidification of Ni base superalloy

Post by Bernd » Thu Feb 08, 2018 5:00 pm

Dear Yang,

The concept of "voids" or "vacancies" in Thermo-Calc cannot be easily used for description of pores, because vacancies are empty places inside a defined lattice of a crystalline phase, and there are no phases which have only vacancies.

The general problem associated with different molar volumes of phases in MICRESS was already addressed as answer to "how to simulate the evolution of voids in a material" in this board. The basic problem is that matter has to be moved if there is a phase transformation between phases of different molar volume. Workaround solutions of this basic problem have been indicated in this mentioned thread.

Now, with the new version MICRESS 6.4, a new "expansion" mode has been released which, in principle, addresses this problem. Moving matter in materials, in reality, is connected with a lot of different complex physical phenomena (elasticity, plasticity, visco-plasticity, fluid flow, ...). However, what we are interested in is mainly the volume balance, especially if liquid phase is present. Therefore, the assumption of the expansion mode (which is activated using the "volume_change" keyword in "Flags and Settings") is sort of "viscous" expansion which bring each phase to its correct molar volume by use of an explicit "matter flow" solver.

Of course, such an "expansion solver" increases complexity and numerical challenges. As the approach is quite new, we still do not have sufficient experience and cannot recommend to use it as default, even though it could guarantee getting correct phase volumes in any kind of simulation. The only application case assessed in detail by now was the simulation of growth of globular graphite in cast iron, which was designed by Janin and which is available as standard application example "A003_CastIronDendriteNodules_dri".

With porosity, however, we have not yet made any experiences using the new "volume change" functionality. Some years ago, using an unofficial precursor model, we made an approach to gas porosity, which can be regarded as growth of a gas phase with strongly reduced molar volume (A. Carré, B. Böttger, M. Apel, "Phase-field modelling of gas porosity formation during the solidification of aluminium", International Journal of Materials Research 2010/04, Page 510-514). In this model, a variable total pressure and a simple ideal gas approach for molar volume had been included which is still not present in the current implementation of MICRESS Version 6.4.

In any case, when using a constant pressure and a constant molar volume for the gas phase, it should in principle be already possible to simulate nucleation and growth of gas pores (e.g N2) in a Ni-base alloy. The way to get there could be done in 3 steps:

1.) Include gas phase and gas elements in an normal simulation without expansion mode. The gas phase should already appear with the correct composition and at the correct temperature, only the volume of the pores will be much too small.
2.) Now use the new expansion model, using an only slightly bigger molar volume for the gas phase. This step should help to get the simulation numerically stable.
3.) Increase the molar volume of gas step-wise up to the correct value, adjusting numerical parameters as necessary.

Thus, gas pores should already be within the possibilities of the new version. However, for shrinkage porosity, the time when pores will form depends on the pressure inside the entrapped liquid. This effect cannot be simulated correctly without a variable pressure and a model for the pressure dependency of the molar volume.


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