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High-fidelity level-set modeling of polycrystalline grain growth

Tianchi Li, Marc Bernacki

Abstract

Accurate modeling of polycrystalline microstructure evolution under strong crystallographic heterogeneities remains a major challenge for full-field numerical methods at the mesoscopic scale. In this work, we present a high-fidelity level-set framework for capillarity-driven grain growth in polycrystals with highly-heterogeneous, disorientation-dependent grain boundary energies. The novel framework represents a polycrystalline extension of our level-set formulation, previously developed and validated using a single triple junction benchmark case. In-depth comparisons with three established level-set models demonstrate that the proposed method yields the most energetically-consistent evolution of grain statistics, disorientation distribution function, and triple junction dihedral angles. Accuracy and robustness are maintained across the entire heterogeneity spectrum. To the best of our knowledge, this approach delivers the highest-fidelity front-capturing level-set modeling of grain growth based on Mullins' mean curvature flow theory, paving the way for state-of-the-art digital twins for annealing applications.

High-fidelity level-set modeling of polycrystalline grain growth

Abstract

Accurate modeling of polycrystalline microstructure evolution under strong crystallographic heterogeneities remains a major challenge for full-field numerical methods at the mesoscopic scale. In this work, we present a high-fidelity level-set framework for capillarity-driven grain growth in polycrystals with highly-heterogeneous, disorientation-dependent grain boundary energies. The novel framework represents a polycrystalline extension of our level-set formulation, previously developed and validated using a single triple junction benchmark case. In-depth comparisons with three established level-set models demonstrate that the proposed method yields the most energetically-consistent evolution of grain statistics, disorientation distribution function, and triple junction dihedral angles. Accuracy and robustness are maintained across the entire heterogeneity spectrum. To the best of our knowledge, this approach delivers the highest-fidelity front-capturing level-set modeling of grain growth based on Mullins' mean curvature flow theory, paving the way for state-of-the-art digital twins for annealing applications.
Paper Structure (3 sections, 12 equations, 5 figures)

This paper contains 3 sections, 12 equations, 5 figures.

Table of Contents

  1. CRediT authorship contribution statement
  2. Declaration of competing interest
  3. Acknowledgements

Figures (5)

  • Figure 1: Capillarity-driven grain growth strongly influenced by grain boundary (GB) heterogeneity. $R_\gamma$ denotes the free-energy ratio between the 4 inner and 4 outer GBs. (a) Initial configuration and (b) evolved grain morphology for $R_\gamma = 100$. (c) Initial configuration and (d) evolved grain morphology for $R_\gamma = 0.5$.
  • Figure 2: Polycrystalline system used for simulations in this work. (a) Grain size distribution. (b) Disorientation angle distribution. (c) Orientation magnitude map.
  • Figure 3: GB energy functions considered in the current work and grain growth statistics measured in the Bumpy case. (a) The analytical forms of $\gamma(\theta)$ and the evolution of (b) number of grains, (c) mean equivalent grain radius, and (d) total normalized GB energy in Bumpy simulations, with comparison to existing level-set models.
  • Figure 4: Disorientation Distribution Function (DDF) weighted by grain boundary (GB) length after 2 hours of grain growth simulation using (a) Iso, (b) RS$^+$, and (c) Bumpy GB energy functions, with comparison against initial DDF. Compared to (d)(e)(f) Het, (g)(h)(i) HetGrad, (j)(k)(l) HetGradProj formulations, (m)(n)(o) the new model gives the most energetically coherent DDF prediction.
  • Figure 5: Statistics of triple junction dihedral angles in Bumpy simulations using (a)(b) Het, (c)(d) HetGrad, (e)(f) HetGradProj, and (g)(h) new model. left column: Measured angles plotted against their theoretical equilibrium values computed using Young's equation. right column: Deviation of measured angles from theoretical predictions.