Applications of Solidification Fundamentals: Phase Field Modeling
Sponsored by: TMS Materials Processing and Manufacturing Division, TMS: Solidification Committee
Program Organizers: Andre Phillion, McMaster University; Amber Genau, University of Alabama at Birmingham; Lifeng Zhang, University of Science and Technology Beijing
Tuesday 8:30 AM
February 28, 2017
Location: San Diego Convention Ctr
Session Chair: Ebrahim Asadi, University of Memphis; Damien Tourret, Los Alamos National Laboratory
On the Solidification Kinetics of Metal Alloys: A Study Using 3-D Phase Field Modeling and Synchrotron X-ray Image Techniques: Zhipeng Guo1; Manhong Yang1; Shuo Wang1; Shoumei Xiong1; 1Tsinghua University
To fully understand the microstructure transition during solidification of metal alloys, a 3-D phase field model was developed. An algorithm, namely Para-AMR, comprising of adaptive mesh refinement (AMR) and parallel (Para-) computing capabilities was developed to solve the phase field equations. Results showed that employment of this approach could speed up computational efficiency for about 3 orders magnitude. Synchrotron X-ray image techniques were also applied in this study to (1) reveal the full physics of the solidification phenomena in real space and time scales, and (2) to fully testify the validity of the phase field modeling results. Accordingly, solidification behaviors, including dendrite growth and pattern formation (for both fcc and hcp dendrites), fragmentation (under the influence from electromagnetic forces and ultrasounds), and coarsening were studied and compared with either experiment results or existing theories.
3D Phase-field Simulations of Graphite Growth in Ductile Cast Iron Considering Interaction between Local Expansion and Microsegregation: Janin Eiken1; Bernd Böttger1; 1Access
The solidification of multicomponent ductile cast iron (Fe-C-Si-Mn-Mg) was simulated on the microstructure scale using the Micress multi-phase-field model extended by a new solver which considers volumetric expansion. Thermodynamic and diffusion data were evaluated by online coupling to the Calphad database TCFE8. The simulations were performed in three dimensions to correctly handle the critical volume-to-length ratios. During initial solidification, dendritic austenite and graphite nodules grow as a divorced eutectic. Whenever a graphite nodule gets into direct contact with the austenite, it becomes rapidly encapsulated and isolated from the melt. The subsequent growth of this nodule is then controlled by interstitial diffusion of carbon through the austenitic shell. During this indirect eutectic transition, the volumetric expansion of the graphite causes a pushing of the enveloping austenitic shell, i.e. a local transport of Fe as well as solute atoms. This mechanism has been found to significantly affect growth kinetics and microsegregation.
Dendritic Grain Growth Competition in Directional Solidification of Alloys: A Phase-field Study
: Damien Tourret1; Younggil Song2; Amy Clarke3; Alain Karma2; 1Los Alamos National Laboratory; 2Northeastern University; 3Colorado School of Mines
Grain growth competition in polycrystalline materials is essential to the formation of cast grain structures. Yet, despite numerous experimental observations over the past decades, a comprehensive picture of dendritic grain growth competition is still lacking. Using phase-field simulations, we study the formation of grain boundaries (GBs) during directional solidification. We focus on the GB orientation selection between two competing grains and explore its dependence upon the orientation of the two grains. We identify orientation combinations that behave according to classical theory, and the occurrence of “unusual overgrowth” of favorably oriented dendrites. In three dimensions, we study the effect of the azimuthal crystal orientations in a thin sample. We identify the combinations of orientations yielding a quasi-2D behavior, and the orientations promoting unusual overgrowth events. Resulting insight into dynamical GB formation could yield significant improvements and progress in casting simulations at larger length and time scales.
Phase Field Modelling of Snowflakes Growth: Gilles Demange1; Helena Zapolsky1; Renaud Patte1; Marc Brunel2; 1Université de Rouen/GPM/ERAFEN; 2Université de Rouen/CORIA
In this work, a phase field model was developed to simulate the growth of snowflakes in a supersaturated atmosphere in 3 dimensions. The evolution of the phase field variable is governed by the model A equation, coupled with the diffusion equation for water supersaturation. The 6-fold symmetry of snowflakes was taken into account in the anisotropic surface tension. To perform the simulations, a new semi implicit finite difference scheme in spectral space was developed. In order to take into account the high anisotropy of interface leading to faceting, a 3D regularization algorithm was developed as well. The growth of different morphologies of snowflakes (prism, stellar dendrite, sectored plates etc.) in 3 dimensions has been simulated. The link between snowflakes morphology and atmospheric parameters such as temperature and pressure (or supersaturation) has been established
Quantitative Phase-Field Crystal Model for Coarsening in Pb-Sn Solid-Liquid Mixtures: Ahmad Nourian Avval1; Seyyed Alireza Etesami1; Kyle Moats1; Mohamed Laradji1; Ebrahim Asadi1; 1University of Memphis
Particle coarsening is one of the diffusional material processes wherein larger particles grow at the expense of smaller particles, leading to a reduction in the total surface area, and thus a reduction in the total free energy of the system. In the other hand, phase-field crystal (PFC) is a recently-developed computational model, which has a great potential in simulating solidification and subsequent microstructural evolution with atomistic details. A wide range of phenomena has been studied via PFC including solidification, grain nucleation and growth, segregation, etc. that shows the potential that this model has to study particle coarsening. The goal of this research is to develop a binary one-mode PFC model for coarsening in Pb-Sn solid-liquid mixtures. In addition, the developed PFC model will be quantified based on the coarsening in solid-liquid mixtures at microgravity experiments and MEAM-MD simulations. In this presentation, we will present our progress toward this goal.
10:10 AM Break
Pattern Formation during In-variant Three-phase Eutectic Growth: Abhik Choudhury1; 1Indian Institute of Science
Eutectic growth offers interesting instances of spontaneous pattern formation, which is therefore of immense interest both for physicists as well as material scientists. In this presentation we will first analyse stable three-phase eutectic growth for different morphologies in three dimensions such as semi-regular brick, lamellar and hexagon arrangement of phases, using both, modified Jackson-Hunt type calculations and phase-field simulations with a comparison of the undercooling vs spacing relationship. Additionally, we will comment on the relative variation of the eutectic length scales between the morphologies with change in properties of the alloy. Thereafter, we will study pattern selection during growth in three dimensions as a function of volume fractions of the solid phases as well as interfacial energies in a model alloy using phase-field simulations. Subsequently, we investigate microstructures observed in a real alloy using coupling with thermodynamic databases and survey the possible range of microstructures during isotropic three-phase growth.
Pattern Formation during Directional Solidification of the Ternary Eutectic Alloy Al-Ag-Cu under Influence of Velocity Changes: Johannes Hötzer1; Philipp Steinmetz2; Michael Kellner2; Anne Dennstedt3; Amber Genau4; Britta Nestler2; 1University of Applied Science Karlsruhe; 2KIT; 3 Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR) ; 4University of Alabama at Birmingham
During the directional solidification of ternary eutectic alloys a wide range of different patterns in the microstructure form. These patterns directly influence the later mechanical properties of the component. Especially the effect of changing process conditions on the microstructure evolution is of high industrial and scientific interest. To investigate the microstructure evolution in 3D, large scale and massive parallel phase-field simulations based on the Grand potential approach are conducted. For the ternary eutectic system Al-Ag-Cu the pattern formation is studied, applying different but constant velocities. The results show a good visual and quantitative accordance with experimental micrographs. Subsequently the effect of velocity changes on the evolving microstructure is investigated and compared to experimental results from 3D synchrotron tomography. The microstructure is analyzed over the growth height with statistical methods and a novel approach based on a graph analysis is applied.
Pattern Formation during the Directional Solidification of Ternary Eutectic Alloys and the Influence of the Average Front Undercooling: Philipp Steinmetz1; Johannes Hötzer1; Michael Kellner1; Britta Nestler1; 1Karlsruhe Institute of Technology
During the directional solidification of ternary eutectic alloys, the three evolving solid phases form a wide range of different patterns, depending on the physical parameters, which strongly influence the mechanical properties of the component. To gain a better understanding of this pattern formation process in ternary eutectic alloys, phase-field simulations based on the minimization of the grand potential difference are used. Through a systematical variation of the simulation domain size, a dependence of the average front undercooling on the arising patterns can be demonstrated in 3D phase-field simulations of an ideal ternary eutectic system. The simulation results are in good quantitative accordance with a three dimensional, ternary eutectic Jackson-Hunt analysis. Also concentration variations in the melt and their influence on the arising patterns as well as the average front undercooling are studied with large-scale 3D phase-field simulations for the ternary eutectic system Al-Ag-Cu.
Three Dimensional Eutectic Colony Morphologies in Multi-component, Multi-phase Alloys: Arka Lahiri1; Abhik Choudhury1; 1Indian Institute Of Science
During two phase eutectic growth in directionally solidified ternary alloys, the volume fractions of the individual solid phases are not constants but are determined by the growth conditions in conjunction with the interfacial undercoolings and the lamellar widths. In this study, we present an analytical Jackson-Hunt type calculation in such mono-variant systems for arbitrary diffusivities and compare the derived undercooling vs spacing relationships with phase-field simulations. Secondly, such two-phase growth in ternary alloys are also known to show Mullins-Sekerka type destabilization of the solid-liquid interface during directional solidification, giving rise to colonies. In this presentation, we highlight the influence of solid-solid and solid-liquid interfacial energy anisotropy on the colony morphology during thin-film solidification. Finally, we extend the study to 3D investigating the stability and formation of two-phase spiraling fingers termed as “eutectic spirals”. References: 1.S. Akamatsu, M. Perrut, S. Bottin-Rousseau, G. Faivre, Phys. Rev. Lett. 104 (2010) p.056101