强制对流影响凝固微观组织的相场法研究
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摘要
凝固材料在凝固过程中形成的微观组织决定其最终性能,有效地控制凝固过程中微观组织的形成具有重要理论和实际意义。对流作用在凝固过程中不可避免,并通过改变固液界面附近的溶质和温度分布影响凝固微观组织的形成。随着计算科学的发展,耦合流场的相场法模拟已经成为国内外学者研究的热点。枝晶是凝固过程中最常见的微观组织,本文采用耦合流场的相场模型模拟了凝固中的枝晶生长过程,研究了强制对流作用下的枝晶生长机制,定量分析了有无强制对流作用下枝晶尖端生长行为,为有效预测和改善材料性能奠定了良好的理论基础。
本文在Wheeler相场模型的基础上,耦合温度场和流场建立了强制对流作用下纯物质枝晶生长相场模型;进一步耦合溶质场建立了强制对流作用下二元合金枝晶生长相场模型。在数值求解过程中,选用基于均匀网格的有限差分对控制方程进行离散,为了避免时间步长的限制,提高计算效率,温度场控制方程用交替显隐式法求解。采用Visual C++语言实现相关模拟程序的编制,直接将Tecplot可视化程序与相场模型计算程序集成,建立了相场法微观组织模拟的可视化软件系统。
采用强制对流作用下纯物质相场模型,以纯Ni为例,模拟研究了强制对流作用下纯物质单枝晶和多枝晶生长演化过程。结果表明,在单枝晶生长时,逆流枝晶臂生长迅速,顺流枝晶臂生长缓慢,水平枝晶臂逆流侧和顺流侧的生长也存在显著差别;在多枝晶生长时,受强制流动、晶体结构特征和生长空间的共同作用,仅有指向逆流侧外部区域的优先生长方向上的枝晶臂生长受到促进,主枝和侧枝发达,其它优先生长方向的枝晶臂生长均受到抑制,主枝和侧枝退化,模拟结果与重力对流作用下的丁二腈枝晶生长形貌相吻合。
采用强制对流作用下二元合金相场模型,以Ni-Cu合金为例,模拟研究了强制对流作用下二元合金单枝晶和多枝晶生长演化过程。结果表明,在强制对流作用下,逆流枝晶臂受过冷熔体冲刷,枝晶臂尖端溶质浓度和温度低,实际过冷度大,枝晶臂生长迅速;热量和溶质在顺流侧富集,顺流枝晶臂尖端溶质浓度和温度高,实际过冷度小,枝晶臂生长缓慢。多枝晶共同生长时,枝晶间内部区域的枝晶臂生长主要受相邻枝晶控制,远离边界的外部区域的枝晶臂生长主要受流场控制。模拟结果与同步辐射X射线成像观察到的直流电场下Sn-Bi合金枝晶生长形貌一致。
采用适应hcp晶系的二元合金相场模型,模拟研究AZ91D镁合金凝固中纯扩散和强制对流作用下单枝晶和多枝晶生长过程。结果表明,在纯扩散条件下,枝晶表现出明显的六方异性,各方向均衡生长;在强制对流作用下,流体逆流侧3个方向的枝晶臂明显比流体顺流侧3个方向的枝晶臂生长快,各枝晶臂长度存在很大差异。在多晶粒生长初期,各晶粒独立生长,为规则正六边形;随着凝固的进行,正六边形晶粒逐渐发展成枝晶,相向生长的枝晶臂互相影响并竞争生长,不同枝晶的一次枝晶臂彼此抑制,最终形成不对称枝晶形貌。模拟结果与实际枝晶形貌接近。
对σ=σ0[1+εkcos(kθ)]形式的界面能各向异性函数进行修正,建立了修正的相场模型,在对纯扩散情况下Si枝晶生长形貌进行模拟研究并与实验结果对比的基础上,以Ni-Cu合金为例,对纯扩散和强制对流作用下的高界面能各向异性二元合金枝晶生长行为进行预测。结果表明,在高界面能各向异性纯Si枝晶生长中,部分晶向角方向的生长消失,一次枝晶和二次枝晶尖端出现棱角,从而都具有典型的棱角特征,模拟结果与实验结果相符合。在高界面能各向异性Ni-Cu合金枝晶生长中,当界面能各向异性强度ε4<1/15时,随着ε4增加,枝晶尖端速度增大,且在接近1/15处达到最大值;当ε4=1/15时,枝晶尖端速度下降4.34%;进一步增加ε4时,枝晶尖端速度先增到极大值后逐渐减小。引入界面动力学各向异性后,界面仅存在界面动力学各向异性δ时,固相以类矩形方式沿<110>方向生长;界面同时存在δ、ε4和仅存在ε4时,固相以枝晶方式沿<100>方向生长。在流速为6.43 m/s的强制对流作用下,枝晶的逆流侧受过冷熔体冲刷,逆流枝晶臂生长迅速,与纯扩散时相比稳态生长速度增加12.61%;热量和溶质在顺流侧聚集,顺流枝晶臂生长缓慢,与纯扩散时相比稳态生长速度减小14.62%。
The final properties of the solidification material depend on the microstructures established during the solidification process, so to control the formation of the microstructures effectively in solidification has important theoretical and practical significance. Convection is difficult to avoid in solidification processes, it will influence the formation of the microstructures remarkably by altering the distributions of concentration and temperature in the vicinity of the solid/liquid interface. With the development of computational science, coupling with flow filed of phase field simulation for solidification microstructures has become a hot research scholars at home and abroad. Dendrite is common microstructure in solidification process. In this Dissertion, the dendritic growth process in solidification is simulated by the phase field model coupling with flow field, the mechanism of the dendritic growth under forced flow during solidification is discussed, the dendritic growth behavior of tips under without flow and forced flow is quantitatively analysed, and a favorable base for prediction and improvement of mechanical property of material is established.
Based on the Wheeler model, coupling with the temeperature field and flow field, the phase field model for dendritic growth of pure material under forced flow is developed; Further coupling with concentration field, the phase field model for dendritic growth of alloy under forced flow is developed. The governing equations are discretized on uniform grids using the Finite Difference method. The thermal governing equation is numerically solved using an alternating direct implicit method, which improve the calculating efficiency and avoid the restriction of the time step. The Visual C++ code is used to complete the phase-field simulation program, when visible software Tecplot is integrated with the simulation program, the visible system of the phase-field simulation is established.
Using the pure material dendritic growth phase-field model, taking pure Ni for example, the growth process of the single and multi-dendrites under forced flow are simulated. In the case of single dendrite growth, the upstream arms of dendrite grow fast, the downstream arms of it grow slow, upstream side and downstream side of the lateral principal branches has significant differences. For multi-dendrites growth, the growth of dendrite arms on the preferred directions toward the out of upstream area is promoted, which lead to the principal branches and side branches are developed; The growth of dendrite arms on the other preferred directions is inhibited, principal branches and side branches degenerate. The simulated results show that the solidification features are consistent with those observed based on the dendrite growth in succinonitrile under gravity convection.
Using the alloy dendritic growth phase-field model, taking Ni-Cu alloys for example, the growth process of the single and multi-dendrites under forced flow are simulated. In the case of single dendrite growth, because of fluid flushing, the temperature and the concentration of the upstream dendrite arm are low, the actual supercooling of it is great, which lead to the dendrite grow fast; Heat and solute enrich in the downstream, the temperature and the concentration of the downstream dendrite arm are high, the actual supercooling of it is small, which make the dendrite grow slow. For multi-dendrites growth, the growth of dendrite arms in internal area is mainly controlled by adjacent dendrite and those in external area away from border is mainly controlled by flow field. The simulated results show that the solidification features are consistent with those observed based on the dendrite growth in Sn-Bi alloys under direct current electric field.
Using the dendritic growth phase-field model for the magnesium alloys with hcp structure, the growth process of the single and multi-dendrites of AZ91D alloys under without flow and forced flow are simulated. These results indicate that the dendrite displays obviously six-fold symmetry anisotropy and the growth is same in each direction under without flow. When dendrite exists in a forced flow, the growth of three directions on the upstream side are much faster than those of three directions on the downstream side, there exists much differences in the length of dendrite arm. In the case of the multi-dendrites, at the early stage, the crystals grow independently and is regular hexagon; With the increase of time, the regular hexagon become to dendrite morphology. The dendrite arms grown face to face influence mutually and grow competitively, the dendrite arms of different dendrite mutually inhibited, ultimately, to form asymmetric dendrite morphology. The simulation results as same as the experimental results.
The function of anisotropic interface energy with the form ofσ=σ0[1+εkcos(kθ)] is regularized, and the regularized phase field model is developed. By comparing the simulation morphology for dendrite growth of pure Si under without flow with experimental results, the dendrite growth behaviours of Ni-Cu alloys with strong surface energy under without flow and forced flow is predicted. The results show that the variation of interface orientation discontinuity and the corners form on the main stem and side branches of dendrite during the dendrite growth process of pure Si with strong interface energy anisotropy, the simulation results is similar to the experimental results. During the dendrite growth process of Ni-Cu alloys with strong interface energy anisotropy (ε4), asε4 increases, the growth velocity of dendrite increases when theε4 is lower than the critical value; As theε4 crossed the critical value, the growth velocity dropped down by about 4.34%; With again increase inε4, the growth velocity reached a maximum value and then tends to decrease. Introducing interface kinetic anisotropy (δ), when there only existsδ, the melt solidifies growth along the <110> orientation and the crystals grow into a square-like. Under the strong interface energy anisotropy or two kinds of anisotropies conditions, the melt solidifies in a dendrite pattern growth along the <100> orientation. Under forced flow with flow velocity of 6.43 m/s, the upstream dendrite arm grows faster because of the undercooled melt flushing, the tip velocity at steady state increases by about 12.61% compared to the case without flow. The heat and solute are congregated in the downstream, which makes the dendrite arm grows slowly, the tip velocity at steady state decreases by about 14.62% compared to the case without flow.
本文在Wheeler相场模型的基础上,耦合温度场和流场建立了强制对流作用下纯物质枝晶生长相场模型;进一步耦合溶质场建立了强制对流作用下二元合金枝晶生长相场模型。在数值求解过程中,选用基于均匀网格的有限差分对控制方程进行离散,为了避免时间步长的限制,提高计算效率,温度场控制方程用交替显隐式法求解。采用Visual C++语言实现相关模拟程序的编制,直接将Tecplot可视化程序与相场模型计算程序集成,建立了相场法微观组织模拟的可视化软件系统。
采用强制对流作用下纯物质相场模型,以纯Ni为例,模拟研究了强制对流作用下纯物质单枝晶和多枝晶生长演化过程。结果表明,在单枝晶生长时,逆流枝晶臂生长迅速,顺流枝晶臂生长缓慢,水平枝晶臂逆流侧和顺流侧的生长也存在显著差别;在多枝晶生长时,受强制流动、晶体结构特征和生长空间的共同作用,仅有指向逆流侧外部区域的优先生长方向上的枝晶臂生长受到促进,主枝和侧枝发达,其它优先生长方向的枝晶臂生长均受到抑制,主枝和侧枝退化,模拟结果与重力对流作用下的丁二腈枝晶生长形貌相吻合。
采用强制对流作用下二元合金相场模型,以Ni-Cu合金为例,模拟研究了强制对流作用下二元合金单枝晶和多枝晶生长演化过程。结果表明,在强制对流作用下,逆流枝晶臂受过冷熔体冲刷,枝晶臂尖端溶质浓度和温度低,实际过冷度大,枝晶臂生长迅速;热量和溶质在顺流侧富集,顺流枝晶臂尖端溶质浓度和温度高,实际过冷度小,枝晶臂生长缓慢。多枝晶共同生长时,枝晶间内部区域的枝晶臂生长主要受相邻枝晶控制,远离边界的外部区域的枝晶臂生长主要受流场控制。模拟结果与同步辐射X射线成像观察到的直流电场下Sn-Bi合金枝晶生长形貌一致。
采用适应hcp晶系的二元合金相场模型,模拟研究AZ91D镁合金凝固中纯扩散和强制对流作用下单枝晶和多枝晶生长过程。结果表明,在纯扩散条件下,枝晶表现出明显的六方异性,各方向均衡生长;在强制对流作用下,流体逆流侧3个方向的枝晶臂明显比流体顺流侧3个方向的枝晶臂生长快,各枝晶臂长度存在很大差异。在多晶粒生长初期,各晶粒独立生长,为规则正六边形;随着凝固的进行,正六边形晶粒逐渐发展成枝晶,相向生长的枝晶臂互相影响并竞争生长,不同枝晶的一次枝晶臂彼此抑制,最终形成不对称枝晶形貌。模拟结果与实际枝晶形貌接近。
对σ=σ0[1+εkcos(kθ)]形式的界面能各向异性函数进行修正,建立了修正的相场模型,在对纯扩散情况下Si枝晶生长形貌进行模拟研究并与实验结果对比的基础上,以Ni-Cu合金为例,对纯扩散和强制对流作用下的高界面能各向异性二元合金枝晶生长行为进行预测。结果表明,在高界面能各向异性纯Si枝晶生长中,部分晶向角方向的生长消失,一次枝晶和二次枝晶尖端出现棱角,从而都具有典型的棱角特征,模拟结果与实验结果相符合。在高界面能各向异性Ni-Cu合金枝晶生长中,当界面能各向异性强度ε4<1/15时,随着ε4增加,枝晶尖端速度增大,且在接近1/15处达到最大值;当ε4=1/15时,枝晶尖端速度下降4.34%;进一步增加ε4时,枝晶尖端速度先增到极大值后逐渐减小。引入界面动力学各向异性后,界面仅存在界面动力学各向异性δ时,固相以类矩形方式沿<110>方向生长;界面同时存在δ、ε4和仅存在ε4时,固相以枝晶方式沿<100>方向生长。在流速为6.43 m/s的强制对流作用下,枝晶的逆流侧受过冷熔体冲刷,逆流枝晶臂生长迅速,与纯扩散时相比稳态生长速度增加12.61%;热量和溶质在顺流侧聚集,顺流枝晶臂生长缓慢,与纯扩散时相比稳态生长速度减小14.62%。
The final properties of the solidification material depend on the microstructures established during the solidification process, so to control the formation of the microstructures effectively in solidification has important theoretical and practical significance. Convection is difficult to avoid in solidification processes, it will influence the formation of the microstructures remarkably by altering the distributions of concentration and temperature in the vicinity of the solid/liquid interface. With the development of computational science, coupling with flow filed of phase field simulation for solidification microstructures has become a hot research scholars at home and abroad. Dendrite is common microstructure in solidification process. In this Dissertion, the dendritic growth process in solidification is simulated by the phase field model coupling with flow field, the mechanism of the dendritic growth under forced flow during solidification is discussed, the dendritic growth behavior of tips under without flow and forced flow is quantitatively analysed, and a favorable base for prediction and improvement of mechanical property of material is established.
Based on the Wheeler model, coupling with the temeperature field and flow field, the phase field model for dendritic growth of pure material under forced flow is developed; Further coupling with concentration field, the phase field model for dendritic growth of alloy under forced flow is developed. The governing equations are discretized on uniform grids using the Finite Difference method. The thermal governing equation is numerically solved using an alternating direct implicit method, which improve the calculating efficiency and avoid the restriction of the time step. The Visual C++ code is used to complete the phase-field simulation program, when visible software Tecplot is integrated with the simulation program, the visible system of the phase-field simulation is established.
Using the pure material dendritic growth phase-field model, taking pure Ni for example, the growth process of the single and multi-dendrites under forced flow are simulated. In the case of single dendrite growth, the upstream arms of dendrite grow fast, the downstream arms of it grow slow, upstream side and downstream side of the lateral principal branches has significant differences. For multi-dendrites growth, the growth of dendrite arms on the preferred directions toward the out of upstream area is promoted, which lead to the principal branches and side branches are developed; The growth of dendrite arms on the other preferred directions is inhibited, principal branches and side branches degenerate. The simulated results show that the solidification features are consistent with those observed based on the dendrite growth in succinonitrile under gravity convection.
Using the alloy dendritic growth phase-field model, taking Ni-Cu alloys for example, the growth process of the single and multi-dendrites under forced flow are simulated. In the case of single dendrite growth, because of fluid flushing, the temperature and the concentration of the upstream dendrite arm are low, the actual supercooling of it is great, which lead to the dendrite grow fast; Heat and solute enrich in the downstream, the temperature and the concentration of the downstream dendrite arm are high, the actual supercooling of it is small, which make the dendrite grow slow. For multi-dendrites growth, the growth of dendrite arms in internal area is mainly controlled by adjacent dendrite and those in external area away from border is mainly controlled by flow field. The simulated results show that the solidification features are consistent with those observed based on the dendrite growth in Sn-Bi alloys under direct current electric field.
Using the dendritic growth phase-field model for the magnesium alloys with hcp structure, the growth process of the single and multi-dendrites of AZ91D alloys under without flow and forced flow are simulated. These results indicate that the dendrite displays obviously six-fold symmetry anisotropy and the growth is same in each direction under without flow. When dendrite exists in a forced flow, the growth of three directions on the upstream side are much faster than those of three directions on the downstream side, there exists much differences in the length of dendrite arm. In the case of the multi-dendrites, at the early stage, the crystals grow independently and is regular hexagon; With the increase of time, the regular hexagon become to dendrite morphology. The dendrite arms grown face to face influence mutually and grow competitively, the dendrite arms of different dendrite mutually inhibited, ultimately, to form asymmetric dendrite morphology. The simulation results as same as the experimental results.
The function of anisotropic interface energy with the form ofσ=σ0[1+εkcos(kθ)] is regularized, and the regularized phase field model is developed. By comparing the simulation morphology for dendrite growth of pure Si under without flow with experimental results, the dendrite growth behaviours of Ni-Cu alloys with strong surface energy under without flow and forced flow is predicted. The results show that the variation of interface orientation discontinuity and the corners form on the main stem and side branches of dendrite during the dendrite growth process of pure Si with strong interface energy anisotropy, the simulation results is similar to the experimental results. During the dendrite growth process of Ni-Cu alloys with strong interface energy anisotropy (ε4), asε4 increases, the growth velocity of dendrite increases when theε4 is lower than the critical value; As theε4 crossed the critical value, the growth velocity dropped down by about 4.34%; With again increase inε4, the growth velocity reached a maximum value and then tends to decrease. Introducing interface kinetic anisotropy (δ), when there only existsδ, the melt solidifies growth along the <110> orientation and the crystals grow into a square-like. Under the strong interface energy anisotropy or two kinds of anisotropies conditions, the melt solidifies in a dendrite pattern growth along the <100> orientation. Under forced flow with flow velocity of 6.43 m/s, the upstream dendrite arm grows faster because of the undercooled melt flushing, the tip velocity at steady state increases by about 12.61% compared to the case without flow. The heat and solute are congregated in the downstream, which makes the dendrite arm grows slowly, the tip velocity at steady state decreases by about 14.62% compared to the case without flow.
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