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Phase field model for precipitate aging in ternary analogues to Ni-basedsuperalloys. This is WORK IN PROGRESS with unresolved performance,implementation, and design flaws. It is posted publicly as the output of along-term, ongoing, federally funded research project, for reference anddifferential analysis only.

This work has not yet been published in a refereed journal. If you would like torefer to it in a publication of your own, please cite using the following DOI:

• Background
• Install
• Usage
• Details
• Contribute
• References
• License

This repository contains a phase-field model for solid-statetransformations in Inconel 625 based onZhouet al., whichinvolves a ternary generalization of the binaryKKS model.

To capture δ and λ intermetallic precipitates in a γ matrix, I have chosen theternary Cr-Nb-Ni system. The three-phase three-component model is representedusing two composition fields (Cr and Nb) and two phase fields (δ and λ). Thereis one dependent composition (Ni) and one dependent phase (γ). Based onASTM F3056, combining Cr with Mo under the assumption that theirinfluences on the alloy are similar, this codebase considers system compositionsbetween (Ni--0.0202 Nb--0.2794 Cr) and (Ni--0.0269 Nb--0.3288 Cr), expressed asmolar fractions. Based onDICTRA simulations, this workconsiders enrichment of interdendritic regions to compositions between(Ni--0.1659 Nb--0.2473 Cr) and (Ni--0.1726 Nb--0.2967 Cr).

Free energies for each constituent phase are computed using a CALPHAD database,simplified fromDuet al. to enable one-to-one mapping ofsublattice compositions to system compositions. This modified database isprovided. The CALPHAD expressions are furthersimplified using 2^nd-order Taylor series (paraboloid) approximations.

Further details are provided insrc/README andthermo/README.

This repository contains Python code to handle the CALPHAD database and C++ codeto perform the phase-field simulation. A Python 3 interpreter and C++11 compilerare recommended. You will need to satisfy the following dependencies:

• Python

  • Cloudpickle
  • Dill
  • NumPy
  • PyCALPHAD
  • SymPy
  • TinyDB
  • Xarray

• C++

  • CUDA
  • MMSP
  • matplotlib-cpp (submodule)

After downloading MMSP, please set the environmental variableMMSP_PATHto its location. If you are usingbash, do something similar to

$echo"MMSP_PATH=~/Downloads/mmsp">>~/.bashrc$.~/.bashrc

You will also want to build the MMSP utilities, as described in the MMSPdocumentation.

2. make. This will compile the source code into a binary,src/alloy625.
3. Run the code. Since your executable is built againstMMSP.main.hpp,the options of that program apply to your binary. For usage suggestions,run./alloy625 --help. A typical MMSP run comprises two steps:initialization and update loops. So you would normally do:
   • ./alloy625 --example 2 data.dat
   • ./alloy625 data.dat 10000000 1000000
   • mmsp2pvd data.dat data.*.dat to generate VTK visualizationfiles, then use a VTK viewer such as ParaView or Mayavi to see theresults.
4. Remix, run, and analyze your own variants.

Pull requests are welcome! Comments are also appreciated viaissuesande-mail.

"Standard Specification for Additive Manufacturing Nickel Alloy (UNS N06625)with Powder Bed Fusion."URL:https://www.astm.org/Standards/F3056.htm

Du, Y.; Liu, S.; Chang, Y. and Yang, Y."A thermodynamic modeling of the Cr–Nb–Ni system."Calphad29 (2005) 140–148.DOI:10.1016/j.calphad.2005.06.001.

Jokisaari, A.M.; Permann, C.; Thornton, K."A nucleation algorithm for the coupled conserved-nonconserved phase field model."Computational Materials Science112 (2016) 128–138.DOI:10.1016/j.commatsci.2015.10.009.

Karunaratne, M. S. A. and Reed, R. C."Interdiffusion of Niobium and Molybdenum in Nickel between 900 - 1300°C."Defect and Diffusion Forum237-240 (2005) 420–425.DOI:10.4028/www.scientific.net/DDF.237-240.420

Kim, S. G.; Kim, W. T. and Suzuki, T."Phase-field model for binary alloys."Physical Review E60 (1999) 7186–7197.DOI:10.1103/PhysRevE.60.7186.

Keller, T.; Lindwall, G.; Ghosh, S.; Ma, L.; Lane, B.; Zhang, F.; Kattner, U.; Lass, E.; Heigel, J.; Idell, Y.; Williams, M.; Allen, A.; Guyer, J.; and Levine, L."Application of finite element, phase-field, and CALPHAD-based methods to additive manufacturing of Ni-based superalloys."Acta Materialia139 (2018) 244-253.DOI:10.1016/j.actamat.2017.05.003.

Provatas, N. and Elder, K.Phase-Field Methods in Materials Science and Engineering.Wiley-VCH: Weinheim, 2010. ISBN: 978-3-527-40747-7.

Simmons, J.P. and Shen, C. and Wang, Y."Phase Field Modeling of Simultaneous Nucleation and Growth by ExplicitlyIncorporating Nucleation Events."Scripta Materialia43 (2000) 935–942.DOI:10.1016/S1359-6462(00)00517-0.

Xu, G.; Liu, Y. and Kang, Z."Atomic Mobilities and Interdiffusivities for fcc Ni-Cr-Nb Alloys."Metallurgical Transactions B47B (2016) 3126–3131.DOI:10.1007/s11663-016-0726-6.

Zhou, N.; Lv, D.; Zhang, H.; McAllister, D.; Zhang, F.; Mills, M. andWang, Y. "Computer simulation of phase transformation and plasticdeformation in IN718 superalloy: Microstructural evolution duringprecipitation."Acta Materialia65 (2014) 270–286. DOI:10.1016/j.actamat.2013.10.069.

SeeLICENSE.

The source files (.py,.hpp, and.cpp) in this repositorywere written by an employee of the United States federal government in thecourse of their employment, and are therefore not subject to copyright.They are public domain. However, the Mesoscale Microstructure SimulationProject (MMSP) is subject to the General Public License v3.0, and thissoftware#includes major aspects of that work. Therefore, if you arenot an employee of the US government, your derivative works will likely besubject to the terms and conditions of GPLv3.