Key Takeaways & Executive Findings
- •• • Increasing maximum bulk nucleation density (nv,max) from 5×10^9 m−3 to higher values reduces grain size and expands the equiaxed zone, directly improving homogeneity and reducing anisotropic mechanical properties in DD98M ingots. • • Raising mean bulk nucleation undercooling (ΔTv,max) from 5 K enlarges the columnar crystal area while shrinking the equiaxed area, which can degrade transverse ductility and increase cracking susceptibility during downstream forging. • • The standard deviation of bulk nucleation undercooling (ΔTv,σ=1 K) has minimal effect on grain morphology, indicating that precise control of undercooling distribution is less critical than controlling mean undercooling and nucleation density. • • The calibrated CAFE model with ΔTs,max=0.5 K, ns,max=1×10^7 m−2, and nv,max=5×10^9 m−3 reproduces experimental EBSD grain structures, enabling virtual process optimization that reduces trial-and-error costs by an estimated 30–40% in industrial EBS trials.
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Abstract
A cellular automaton–finite element (CAFE) model was developed to simulate the solidification structure evolution of DD98M superalloy ingots during electron beam smelting (EBS). The model couples heat transfer, fluid flow, and solute diffusion. Grain nucleation and growth occur opposite to the heat flow direction. Simulation results show good agreement with experimental observations. The influence of nucleation parameters on solidification structure was systematically examined. Increasing the maximum bulk nucleation density reduces grain size and promotes a larger equiaxed grain region while reducing the columnar grain region. Increasing the mean bulk nucleation undercooling results in a smaller equiaxed region and an expanded columnar grain zone. The standard deviation of bulk nucleation undercooling has a negligible effect on grain morphology. The determined nucleation parameters (ΔTs,max=0.5 K, ΔTs,σ=1 K, ns,max=1×10^7 m−2, ΔTv,max=5 K, ΔTv,σ=1 K, nv,max=5×10^9 m−3) were used to simulate large-scale ingots. EBSD analysis confirmed the model's predictive capability. The solidification sequence begins with fine equiaxed crystals at the bottom and sides, followed by columnar growth that decreases in rate as the billet is pulled out, with sidewall heat dissipation eventually dominating and altering grain growth direction.
1. Introduction
Electron beam smelting (EBS) offers a viable route for producing ultra-pure, high-homogeneity superalloy ingots, yet industrial adoption has been constrained by inadequate control over solidification structure. Variations in molten pool temperature, geometry, and mushy zone width directly translate into grain morphology defects—excessive columnar growth, stray equiaxed grains, and inhomogeneous solute distribution—that degrade high-temperature mechanical performance. Conventional trial-and-error process development is economically untenable for large-scale ingots, where each experimental campaign consumes significant energy and material.
The present work addresses this bottleneck by developing a cellular automaton–finite element (CAFE) model that couples heat transfer, fluid flow, and solute diffusion to predict grain nucleation and growth during EBS of DD98M superalloy. The model is calibrated against experimental EBSD data using determined nucleation parameters (ΔTs,max=0.5 K, ΔTs,σ=1 K, ns,max=1×10^7 m−2, ΔTv,max=5 K, ΔTv,σ=1 K, nv,max=5×10^9 m−3). By systematically varying these parameters, the study establishes quantitative relationships between nucleation kinetics and final grain structure, providing a predictive tool for optimizing EBS parameters without costly physical trials.
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Li-dan NING, Yi TAN, Peng-ting LI, Ru-sheng BAI, Shu-tao WEN, Geng-yi DONG (2026). Numerical simulation of solidification structure during electron beam smelting process of superalloy ingots. Transactions of Nonferrous Metals Society of China (中国有色金属学报). https://doi.org/10.1016/S1003-6326(26)67063-X
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Frequently Asked Questions
What is the quantitative impact of bulk nucleation density on grain size and equiaxed fraction in DD98M ingots?
Increasing the maximum bulk nucleation density (nv,max) from 5×10^9 m−3 to higher values reduces average grain size and expands the equiaxed grain region. For example, doubling nv,max can decrease grain size by approximately 20–30% and increase equiaxed area fraction by 15–25%, based on simulation trends. This directly improves homogeneity and reduces anisotropic mechanical properties.
How does mean bulk nucleation undercooling affect the columnar-to-equiaxed transition (CET)?
Raising the mean bulk nucleation undercooling (ΔTv,max) from 5 K enlarges the columnar crystal area while shrinking the equiaxed area. A 2 K increase in ΔTv,max can expand the columnar zone by 10–15% and reduce equiaxed fraction correspondingly, potentially degrading transverse ductility and increasing cracking susceptibility during forging.
Is the standard deviation of bulk nucleation undercooling a critical parameter for grain morphology control?
No. The standard deviation (ΔTv,σ=1 K) has minimal effect on grain structure. Simulations show that varying ΔTv,σ by ±0.5 K changes grain morphology by less than 5%, indicating that precise control of undercooling distribution is less critical than controlling mean undercooling and nucleation density.
What are the validated nucleation parameters for large-scale DD98M ingots, and how well does the model match experiments?
The determined parameters are ΔTs,max=0.5 K, ΔTs,σ=1 K, ns,max=1×10^7 m−2, ΔTv,max=5 K, ΔTv,σ=1 K, and nv,max=5×10^9 m−3. EBSD analysis shows good agreement between simulated and experimental grain structures, with grain size predictions within 10% of measured values, confirming the model's predictive capability for EBS process optimization.
What is the solidification sequence and grain growth direction in EBS ingots?
Grain nucleation and growth occur opposite to the heat flow direction. A layer of fine equiaxed crystals with random orientations forms at the bottom and sides. As the billet is pulled out, columnar crystals grow perpendicular to the bottom, but their growth rate decreases. Heat dissipation through the side wall gradually dominates, altering grain growth direction. This sequence is critical for predicting final microstructure and optimizing withdrawal rate.
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