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@PHDTHESIS{Wang:845158,
author = {Wang, Kai},
othercontributors = {Spatschek, Robert and Svendsen, Bob},
title = {{Q}uantitative nondiagonal phase field modeling of phase
transformations},
school = {Rheinisch-Westfälische Technische Hochschule Aachen},
type = {Dissertation},
address = {Aachen},
publisher = {RWTH Aachen University},
reportid = {RWTH-2022-04446},
pages = {1 Online-Ressource : Illustrationen},
year = {2021},
note = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
University 2022; Dissertation, Rheinisch-Westfälische
Technische Hochschule Aachen, 2021},
abstract = {The investigation of phase transformations is of great
interest in various fields. For diffusional transitions,
accurate descriptions of the diffusion processes in the
parent, growing phases and at the interfaces are the
prerequisite to predict the complex growth patterns. In the
last decades, the phase field method has emerged as a
powerful tool to investigate the moving interface problems.
However, the elimination of the artificial enhanced
interface effects is a long-standing unsolved problem in the
phase field community. In the symmetric and the one-sided
cases, the “thin-interface limit” and the anti-trapping
current are proposed by Karma to reproduce the free boundary
conditions. Only recently, the nondiagonal phase field model
has been developed according to Onsager’s relations in the
two-sided case. In this work, we present the capabilities of
the nondiagonal phase field model and extend the binary
nondiagonal phase field model to complex alloys. A four-fold
surface energy anisotropy is incorporated in the binary
nondiagonal phase field model to investigate the
two-dimensional free dendrite growth of pure substances
solidification. In the symmetric and the one-sided cases,
the nondiagonal phase field simulation results are
benchmarked with Green’s function calculations. In the
general two-sided case, the capabilities of nondiagonal
phase field model are compared with the predictions of a
generalized expression. Furthermore, the necessity of the
Onsager cross-coupling term is also evidenced. Based on
Onsager’s principles, the binary nondiagonal phase field
model is ex- tended to three-phase transformations by using
the free energy functional. The two-dimensional nondiagonal
phase field simulations are carried out not only for
eutectic solidification in the one-sided case, but also for
eutectoid transformation in the two-sided case. One the one
hand, the obtained simulation results during eu- tectic
solidification are benchmarked against boundary integral
calculations in the one-sided case. On the other hand,
simulations performed in the two-sided case during eutectoid
transformations reveal that the dimensionless growth
velocities of the lamellae is proportional to the ratio of
diffusion coefficients. Furthermore, in both the one- and
two-sided cases, the necessity of using the cross-coupling
term in the nondiagonal phase field model is verified by
quantitative simulations. Since the free energy based
nondiagonal model is limited for simple symmetric phase
diagrams, we develop a grand potential based nondiagonal
three-phase field model for complex alloy transformations.
The corresponding two-dimensional phase field simulations
are implemented to investigate the growth kinetics of the
pearlite transformation with respect to different diffusion
paths. In the one-sided case, the simulation results are
compared with the Zener-Hillert model, while the simulation
results in the two-sided case are proportional to the
diffusivity ratios, which agrees well wit Ankit’s model.
Additionally, we also point out that diffusion in cementite
has low influence on the growth kinetic of the pearlite
transformation. When the surface diffusion is considered, in
the one-sided case, the growth velocities of the lamellae is
proportional to the surface diffusion coefficient. Finally,
we consider the diffusion in austenite, cementite as well as
the surface diffusion and reproduce the pearlite growth for
different undercoolings. The nondiagonal phase field
simulation results have a convincing agreement with the
experimental observations without adjustable parameters.},
cin = {525820 / 520000},
ddc = {620},
cid = {$I:(DE-82)525820_20160614$ / $I:(DE-82)520000_20140620$},
typ = {PUB:(DE-HGF)11},
doi = {10.18154/RWTH-2022-04446},
url = {https://publications.rwth-aachen.de/record/845158},
}
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