Phase field precipitate aging model
Phase field model for precipitate aging in ternary analogues to Ni-based superalloys. Please cite using the following DOI:
Table of Contents
To capture δ and λ intermetallic precipitates in a γ matrix, I have chosen the ternary Cr-Nb-Ni system. The three-phase three-component model is represented using two composition fields (Cr and Nb) and two phase fields (δ and λ). There is one dependent composition (Ni) and one dependent phase (γ). Based on ASTM F3056, combining Cr with Mo under the assumption that their influences on the alloy are similar, this codebase considers system compositions between (Ni--0.0202 Nb--0.2794 Cr) and (Ni--0.0269 Nb--0.3288 Cr), expressed as molar fractions. Based on DICTRA simulations, this work considers 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 from Du et al. to enable one-to-one mapping of sublattice compositions to system compositions. This modified database is provided. The CALPHAD expressions are further simplified using 2nd-order Taylor series (paraboloid) approximations.
This repository contains Python code to handle the CALPHAD database and C++ code to perform the phase-field simulation. A Python 3 interpreter and C++11 compiler are recommended. You will need to satisfy the following dependencies:
After downloading MMSP, please set the environmental variable
to its location. If you are using
bash, do something similar to
$ echo "MMSP_PATH=~/Downloads/mmsp" >> ~/.bashrc $ . ~/.bashrc
You will also want to build the MMSP utilities, as described in the MMSP documentation.
make. This will compile the source code into a binary,
- Run the code. Since your executable is built against
MMSP.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.*.datto generate VTK visualization files, then use a VTK viewer such as ParaView or Mayavi to see the results.
- Remix, run, and analyze your own variants.
"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." Calphad 29 (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 Science 112 (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 Forum 237-240 (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 E 60 (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 Materialia 139 (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 Explicitly Incorporating Nucleation Events." Scripta Materialia 43 (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 B 47B (2016) 3126–3131. DOI: 10.1007/s11663-016-0726-6.
Zhou, N.; Lv, D.; Zhang, H.; McAllister, D.; Zhang, F.; Mills, M. and Wang, Y. "Computer simulation of phase transformation and plastic deformation in IN718 superalloy: Microstructural evolution during precipitation." Acta Materialia 65 (2014) 270–286. DOI: 10.1016/j.actamat.2013.10.069.
The source files (
.cpp) in this repository
were written by an employee of the United States federal government in the
course of their employment, and are therefore not subject to copyright.
They are public domain. However, the Mesoscale Microstructure Simulation
Project (MMSP) is subject to the General Public License v3.0, and this
#includes major aspects of that work. Therefore, if you are
not an employee of the US government, your derivative works will likely be
subject to the terms and conditions of GPLv3.