Comparative Study and Limits of Different Level-Set Formulations for the Modeling of Anisotropic Grain Growth
Abstract
:1. Introduction
2. The Numerical Framework
2.1. Crystallographic Definitions
2.2. FE-LS Formulation
3. The Grim Reaper Case
3.1. Description of the Test Case
- The velocity of the triple junction is computed using the relation , where is the y-position of the triple point at time and is the time step.
- The dihedral angles are computed using the methodology presented in [26]: one may define, at each time, a circle of radius with circumference , and divide it into arcs which pass through grain with length . The angle of the arc, , could be approximated thanks to the relation .
3.2. Numerical Strategy
3.3. Results and Analysis
3.4. Conclusions
4. Effect of the Texture and Heterogeneous GB Properties during GG Simulations for a Polycrystalline Microstructure
4.1. Effect of the Heterogeneity
4.1.1. Heterogeneous Grain Boundary Energy
4.1.2. Heterogeneous Grain Boundary Energy and Mobility
4.2. CPU Time
5. Accounting for Mis-Orientation and Inclination Dependence
5.1. Triple Junction
5.2. Coherent and Incoherent Twin Boundary
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
FE | Finite Element |
GB | Grain Boundary |
LS | Level Set |
FE-LS | Finite Element Level-Set |
DDF | Disorientation Distribution Function |
GG | Grain Growth |
Iso | Isotropic formulation |
Het | Heterogeneous formulation |
HetGrad | Heterogeneous with Gradient formulation |
Aniso | Anisotropic formulation |
SUPG | Streamline Upwind Petrov–Galerkin |
BC | Boundary Condition |
RS | Read–Shockley |
S | Sigmoidal |
LAGB | Low-Angle Grain Boundary |
HAGB | High-Angle Grain Boundary |
GBED | Grain Boundary Energy distribution |
GB5DOF | Code to compute the GB energy as a function of the mis-orientation |
and normal orientation [73] | |
CTB | Coherent Twin Boundary |
ICB | Incoherent Twin Boundary |
Appendix A. Grim Reaper Case: Effect of the Boundary Conditions
Appendix B. Large-Scale Simulation: Effect of a Strong Texture
Appendix B.1. Heterogeneous Grain Boundary Energy
Appendix B.2. Heterogeneous Grain Boundary Energy and Mobility
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Case | Iso | Het | HetGrad | Aniso |
---|---|---|---|---|
Random | 5.4 | 5.5 | 5.5 | 5.6 |
Textured | 5.4 | 5.5 | 7.3 | 9.4 |
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Murgas, B.; Florez, S.; Bozzolo, N.; Fausty, J.; Bernacki, M. Comparative Study and Limits of Different Level-Set Formulations for the Modeling of Anisotropic Grain Growth. Materials 2021, 14, 3883. https://doi.org/10.3390/ma14143883
Murgas B, Florez S, Bozzolo N, Fausty J, Bernacki M. Comparative Study and Limits of Different Level-Set Formulations for the Modeling of Anisotropic Grain Growth. Materials. 2021; 14(14):3883. https://doi.org/10.3390/ma14143883
Chicago/Turabian StyleMurgas, Brayan, Sebastian Florez, Nathalie Bozzolo, Julien Fausty, and Marc Bernacki. 2021. "Comparative Study and Limits of Different Level-Set Formulations for the Modeling of Anisotropic Grain Growth" Materials 14, no. 14: 3883. https://doi.org/10.3390/ma14143883