Microstructure Evolution Modeling for AM

State of the art in microstructure evolution models for welding and additive manufacturing: Monte Carlo Potts, cellular automata, Kampmann-Wagner precipitation, and CALPHAD coupling.

Monte Carlo Potts models for grain growth

The MC Potts model maps grain orientations to discrete spin states on a lattice. Grain boundary migration is simulated via Monte Carlo sampling of spin-flip events that reduce interfacial energy.

Key papers

Rodgers, Mitchell & Tikare (2017): First fully 3D MC Potts model for weld grain evolution. Sandia National Labs.

Citation: Rodgers, T.M., Mitchell, J.A. & Tikare, V. (2017). “A Monte Carlo model for 3D grain evolution during welding.” Modelling and Simulation in Materials Science and Engineering, 25(6). Cited 59 times.

Yang, Sista, Elmer & DebRoy (2000): Foundational 3D MC for GTA welding of titanium.

Citation: Yang, Z., Sista, S., Elmer, J.W. & DebRoy, T. (2000). “Three dimensional Monte Carlo simulation of grain growth during GTA welding of titanium.” Acta Materialia, 48(13). Cited 187 times.

Oh & Lee (2026): Extends MC Potts to handle solidification (not just grain growth) within a single framework.

Citation: Oh, S.H. & Lee, B.J. (2026). “A Monte Carlo Potts model for solidification.” Nature Communications.

Limitations

• Require calibration of MC time steps to real time via mobility-temperature relationships
• Struggle with strong texture/anisotropy
• Computationally expensive for large 3D domains (>10^6 cells)

Cellular automata for microstructure in AM

CA models use local rules on a grid to simulate nucleation and growth during solidification. Faster than phase-field, can handle polycrystalline solidification with competitive grain growth.

Key papers

Zinoviev et al. (2016): Foundational CA for laser additive manufacturing.

Citation: Zinoviev, A. et al. (2016). “Evolution of grain structure during laser additive manufacturing. Simulation by a cellular automata method.” Materials & Design, 106. Cited 309 times.

Lian et al. (2019): 3D CA-FV coupling for microstructure evolution.

Citation: Lian, Y. et al. (2019). “A cellular automaton finite volume method for microstructure evolution during additive manufacturing.” Materials & Design, 169. Cited 240 times.

Staroselsky, Voytovych & Acharya (2024): CA model for Ni-based alloy microstructure in WAAM.

Citation: Staroselsky, A., Voytovych, D. & Acharya, R. (2024). “Prediction of Ni-based alloy microstructure in wire arc additive manufacturing from cellular automata model.” Computational Materials Science, 232. Cited 14 times.

Stump, Plotkowski & Nutaro (2024): DECA — Discrete Event inspired Cellular Automata for accelerated grain structure prediction.

Citation: Stump, B.C., Plotkowski, A. & Nutaro, J. (2024). “DECA: Discrete Event inspired Cellular Automata for grain structure prediction in additive manufacturing.” Computational Materials Science, 232. Cited 9 times.

Liang et al. (2025): Multi-level capture algorithm for accelerating CA predictions of grain structure and texture.

Citation: Liang, X., Zhu, J., Popovich, V. & Hermans, M. (2025). “A multi-level capture algorithm for accelerating cellular automata predictions.” Additive Manufacturing. Cited 10 times.

Kampmann-Wagner numerical model for precipitation kinetics

The KWN model tracks the full precipitate size distribution by solving coupled nucleation, growth, and coarsening equations. Standard for multi-component precipitation kinetics.

Key papers

Stechauder & Kozeschnik (2015): Foundational KWN validation for Cu precipitation in alpha-Fe.

Citation: Stechauder, G. & Kozeschnik, E. (2015). “Thermo-kinetic modeling of Cu precipitation in alpha-Fe.” Acta Materialia, 100. Cited 85 times.

Sheng et al. (2021): Assessment of Langer-Schwartz-Kampmann-Wagner models for Cu precipitation in PH stainless steels.

Citation: Sheng, Z. et al. (2021). “Langer-Schwartz-Kampmann- Wagner precipitation simulations.” Journal of Materials Science, 56. Cited 46 times.

Aslam et al. (2025): KWN + CALPHAD for AM IN718 fabricated by DED.

Citation: Aslam, A., Felisardo Cavalcante, T.R. & Avila, J.A. (2025). “CALPHAD-based simulation of precipitation kinetics during heat treatment in IN718 fabricated by DED.” SSRN preprint.

Software implementations

• MatCalc (Kozeschnik group)
• TC-PRISMA (Thermo-Calc)
• PanPrecipitation (Pandat)

CALPHAD-coupled simulations with FEM

Integration approaches

• TC-API (Thermo-Calc): Programmatic access to equilibrium/Scheil calculations from external codes
• DICTRA: 1D diffusion-controlled transformation solver, coupled sequentially with FEM thermal histories
• PanEngine (Pandat): Alternative thermodynamic databases
• OpenCalphad: Open-source CALPHAD engine (Sundman et al.)

Key papers

Keller et al. (2017): Landmark multi-scale coupling paper. NIST. Application of FEM, phase-field, and CALPHAD to AM of Ni-based superalloys.

Citation: Keller, T. et al. (2017). “Application of finite element, phase-field, and CALPHAD-based methods to additive manufacturing of Ni-based superalloys.” Acta Materialia, 139. Cited 515 times.

Sargent et al. (2021): DICTRA + FEM coupling for non-equilibrium solidification.

Citation: Sargent, N. et al. (2021). “Integration of processing and microstructure models for non-equilibrium solidification in additive manufacturing.” Metals, 11(1). Cited 45 times.

Smith et al. (2016): CALPHAD embedded directly in FEM for thermodynamically consistent microstructure prediction.

Citation: Smith, J., Xiong, W., Cao, J. & Liu, W.K. (2016). “Thermodynamically consistent microstructure prediction of additively manufactured materials.” Computational Mechanics, 57(3). Cited 88 times.

Texture evolution during WAAM thermal cycles

WAAM thermal cycles cause repeated partial re-austenitization and re-transformation in previously deposited layers. This produces banded microstructures with alternating grain sizes and texture intensities. Columnar-to-equiaxed transitions (CET) are governed by local G/R ratios that vary layer-by-layer.

Key papers

Wang et al. (2018): Grain morphology evolution and texture characterization of WAAM Ti-6Al-4V.

Citation: Wang, J. et al. (2018). “Grain morphology evolution and texture characterization of wire and arc additive manufactured Ti-6Al-4V.” Journal of Alloys and Compounds, 768. Cited 182 times.

Gil Plazas & Amaya Villabon (2026): Influence of interlayer thermal cycling on microstructural evolution in WAAM carbon steel.

Citation: Gil Plazas, A.F. & Amaya Villabon, T.A. (2026). “Influence of interlayer thermal cycling on microstructural evolution in WAAM processed carbon steel.” Welding in the World, 70. Cited 9 times.

Kumar & Jha (2026): FEA thermal-history-guided study of spatial microstructure evolution and mechanical property heterogeneity in robotic WAAM of Al-Cu alloys.

Citation: Kumar, D. & Jha, S. (2026). “FEA thermal-history-guided study of spatial microstructure evolution.” Journal of Manufacturing Processes.

Computational bottlenecks

Scale disparity

FEM thermal models resolve mm-cm scales with ~10^5 to 10^6 elements. Microstructure models need um resolution over the same domain, requiring 10^9 to 10^12 cells. Direct coupling is computationally intractable for part-scale components.

Time scale disparity

WAAM deposition of a 100-layer wall takes hours. Each layer’s solidification occurs in seconds, but microstructure evolution (precipitation, coarsening) continues over the full build time. KWN models must integrate over 10^4 to 10^5 thermal cycles.

CALPHAD lookup cost

Calling Thermo-Calc/DICTRA at each FEM integration point for each time step is prohibitively expensive. A single equilibrium calculation takes ~10 to 100 ms. For 10^6 integration points x 10^4 time steps, this is 10^11 to 10^13 ms of CALPHAD calls.

ML surrogate opportunities

• Replace CALPHAD lookups: Train NNs on Thermo-Calc databases to predict phase fractions, transformation temperatures, and driving forces. Speedup: 10^3 to 10^4x per evaluation.
• Surrogate CA/phase-field models: CNNs trained on phase-field grain evolution data predict grain morphology from thermal gradient and cooling rate inputs in milliseconds (Peivaste et al. 2022, Computational Materials Science, cited 61 times).
• Process-structure-property surrogates: SHAP-interpretable ML maps AM process parameters to microstructure features, bypassing the entire physics simulation chain (Ackermann & Haase 2023, Additive Manufacturing, cited 59 times).
• GNNs for grain structure: Graph neural networks on grain adjacency graphs could replace MC Potts for grain growth prediction.

Connection to TMM surrogate project

See TMM Surrogates. Microstructure evolution models feed the metallurgical stage of the TMM pipeline. The computational bottleneck (scale disparity, CALPHAD cost) is a primary motivation for ML surrogates.

See also JMAK Phase Transformation for the kinetics models that drive phase fraction predictions.