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为改善增材制造过程中由于界面不稳定性引发的晶体结构缺陷问题, 本文基于线性稳定性理论, 系统研究了旋转与强剪切流协同作用对快速凝固中固-液界面形态稳定性的影响机制. 通过对增材制造过程的分析, 构建了包含旋转(泰勒数)与剪切流动参数的数学物理模型, 揭示了多物理场协同作用对界面不稳定性的调控规律. 研究发现强剪切流可有效降低逆临界形态数, 稳定固-液界面; 旋转场的引入则显著缩小了系统的不稳定性区域, 尤其在小波数范围内表现出显著的稳定作用. 此外旋转与流动的耦合效应进一步增强了界面附近溶质的均匀性, 并改善了熔池内的流动形态, 提升了整体的稳定性. 同时高表面能也表现出促进界面稳定的趋势, 旋转场对此效果具有增强作用. 本文的研究结果为实现高质量晶粒结构调控和增材制造工艺的参数优化提供了一定的理论支撑.To address the persistent challenge of morphological instability during laser-based additive manufacturing (AM) of dilute alloys, this study systematically explores the coupled effects of rotation and strong shear flow on the stability of the solid–liquid interface under rapid solidification conditions. A comprehensive multi-physics theoretical model is established based on linear stability analysis, incorporating key dimensionless parameters: Taylor number (${T_a}$), inverse Schmidt number (${\cal{R}}$), dimensionless surface energy ($\Gamma $), and a nonlinear shear velocity profile applied parallel to the interface. The model also accounts for the presence of a solute boundary layer. By solving the resulting perturbation equations, the growth rates of interface disturbances are obtained. The results reveal that strong shear flow markedly increases the critical morphological number, indicating enhanced interfacial stability. When rotation is introduced, the instability region in wavenumber space is significantly compressed, particularly at small wavenumbers, due to the Coriolis-induced stabilization. Figure 3 illustrates how the critical conditions vary with increasing Ta and surface energy, while Figure 7 demonstrates the instantaneous perturbation fields of concentration and velocity in the melt pool, where the Coriolis effect promotes symmetrical recirculation cells and suppresses disturbance penetration in the vertical direction. Moreover, the synergy of rotation and shear flow facilitates a more uniform solute distribution near the interface, mitigates compositional gradients, and supports the formation of ordered laminar flow structures. These effects contribute to suppressing constitutional undercooling and refine the microstructure. The model is dimensionless and general, with key dimensionless groups reflecting process inputs such as solidification velocity, thermal gradients, and material diffusivity. This work provides critical physical insights into rotation–flow coupling mechanisms in AM and offers a quantitative framework for optimizing process parameters to control microstructural evolution. The findings are particularly relevant for AM of symmetric components (e.g., axisymmetric gears or biomedical implants) where rotational auxiliary fields can be practically introduced.
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Keywords:
- additive manufacturing /
- strong shear flow /
- rotation /
- interface stability
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图 1 增材制造中的液体熔池凝固
Fig. 1. Solidification of the molten pool during additive manufacturing.
图 2 不同流速下, 逆临界形态数$ {\cal{M}}_c^{ - 1} $随泰勒数$ {T_a} $的变化曲线, 所用参数取值为$ \beta = 1 $, $ {k_E} = 0.5 $, $ {\cal{R}} = 1 $, $ \Gamma $ = 0.02
Fig. 2. The function of inverse critical morphological number $ {\cal{M}}_c^{ - 1} $ with Taylor number $ {T_a} $ under different flow velocities, with the parameter values set to $ \beta = 1 $, $ {k_E} = 0.5 $, $ {\cal{R}} = 1 $ and $ \Gamma $ = 0.02.
图 3 不同泰勒数$ {T_a} $下, 逆临界形态数$ {\cal{M}}_c^{ - 1} $随$ {v^{ - 1}} $ 变化的函数关系, 所用参数取值为$ \beta = 1 $, $ {k_E} = 0.5 $, $ {\cal{R}} = 1 $, $ \Gamma $ = 0.06
Fig. 3. The functional relationship of the inverse critical morphological number $ {\cal{M}}_c^{ - 1} $ with $ {v^{ - 1}} $ under different Taylor numbers $ {T_a} $, with the parameter values set to $ \beta = 1 $, $ {k_E} = 0.5 $, $ {\cal{R}} = 1 $ and $ \Gamma $ = 0.06.
图 4 不同泰勒数$ {T_a} $下, 逆临界形态数$ {\cal{M}}_c^{ - 1} $随表面能$ \Gamma $的变化函数关系式, 所用参数取值为$ v = 100 $, $ {k_E} = 0.5 $, $ {\cal{R}} = 0.5 $, $ \beta $ = 0.01
Fig. 4. The functional relationship of the inverse critical morphological number $ {\cal{M}}_c^{ - 1} $ with surface energy $ \Gamma $ under different Taylor numbers $ {T_a} $, with the parameter values set to $ v = 100 $, $ {k_E} = 0.5 $, $ {\cal{R}} = 0.5 $ and $ \beta $ = 0.01.
图 5 平面$ (\alpha {\cal{V}}, {{\cal{M}}^{ - 1}}{\cal{V}}) $上的中性稳定性曲线, 所用参数取值为$ {a_2} = 0 $, $ \beta/v = 0.01 $, $ {k_E} = 0.5 $, $ {\cal{R}}$ = 1
Fig. 5. The neutral stability curve on plane $ (\alpha {\cal{V}}, {{\cal{M}}^{ - 1}}{\cal{V}}) $, with the parameter values set to $ {a_2} = 0 $, $ \beta/v = 0.01 $, $ {k_E} = 0.5 $ and $ {\cal{R}}$ = 1.
图 6 当泰勒数$ {T_a} = 10 $时, 不同流速 $ {\cal{V}} $下的中性稳定性曲线, 所用参数取值为$ {a_2} = 0 $, $ \beta = 0.01 $, $ {k_E} = 0.5 $, $ \Gamma = $$ 0.001 $, $ {\cal{R}}$ = 1
Fig. 6. The neutral stability curves under different flow velocities $ {\cal{V}} $ at a Taylor number of $ {T_a} = 10 $ with the parameter values set to $ {a_2} = 0 $, $ \beta = 0.01 $, $ {k_E} = 0.5 $, $ \Gamma = $$ 0.001 $ and $ {\cal{R}}$ = 1.
图 7 当泰勒数$ {T_a} = 10 $时, 熔池内瞬时扰动浓度场与速度场分布图, 所用参数取值为$ {a_1} = 1.6 $, $ {a_2} = 0 $, $ {\cal{R}}$ = 1. 图中彩色背景表示扰动浓度场, 白色箭头表示扰动速度矢量场
Fig. 7. Instantaneous distributions of the perturbation concentration field and velocity field in the melt pool at a Taylor number of $ {T_a} = 10 $, with parameter values set to $ {a_1} = 1.6 $, $ {a_2} = 0 $ and $ {\cal{R}} = 1 $. The colored background represents the perturbation concentration field, while the white arrows indicate the perturbation velocity vector field.
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