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本文针对非对称双边扩散条件下的二元合金枝晶生长,建立了一个包含溶质截流项的定量相场模型.本模型耦合了非线性热力学函数并采用化学势相等的界面条件.通过对相场方程进行二阶的薄界面渐进分析,并结合溶质拖拽模型,推导出相场迁移率和溶质截流项.随后将模型简化为二元稀溶液合金等温枝晶生长的相场模型以对其进行理论验证.通过在各种相场界面厚度条件下进行数值模拟,测试了本模型的数值收敛性.用所建立的模型模拟了Fe-0.15mol%C合金的等温枝晶生长,将相场模拟结果和经典Gibbs-Thomson关系,线性可解性理论以及改进的Lipton-Glicksman-Kurz(LGK)解析模型进行比较,取得了良好的符合.模拟结果表明本模型能有效地消除延拓的界面厚度所导致的界面异常效应,具有良好的定量模拟能力.而且,本模型能够定量地描述从单边扩散到对称扩散的各种固相扩散迁移率条件下的枝晶生长.
Aiming at the dendritic growth of binary alloys under asymmetric bilateral diffusion conditions, a quantitative phase field model is established, which includes the solute cutoff term.The model is coupled with a nonlinear thermodynamic function and adopts an interface condition with equal chemical potential.By analyzing the phase field The second-order thin-walled interfacial evolution analysis and the solute drag model are combined to deduce the phase field mobility and the solute-cutoff term. The model is then simplified to a phase field model of isothermal dendritic growth of binary dilute solution alloys Theoretical validation.The numerical convergence of this model was tested by numerical simulations at various phase-boundary interfacial thicknesses.The isothermal dendritic growth of Fe-0.15mol% C alloy was simulated with the established model, and the phase-field simulation The results are in good agreement with the classical Gibbs-Thomson relation, the linear solvability theory and the improved Lipton-Glicksman-Kurz (LGK) analytical model.The simulation results show that this model can effectively eliminate the extended interface thickness Lead to the abnormal interface effect, with good quantitative simulation ability.Moreover, the model can quantitatively describe all kinds of solid-phase diffusion migration from unilateral diffusion to symmetric diffusion Rate of dendritic growth.