镁基合金自由枝晶生长的相场模拟研究

Phase-field modeling of free dendritic growth of magnesium based alloy

利用定量相场模型,以Mg-0.5 wt.%Al合金为例模拟了基面((0001)面)内镁基合金的等温自由枝晶生长过程.通过研究该合金体系数值模拟的收敛性,获得了最优化值耦合参数λ=5.5及网格宽度△x/W_0=0.4,并在该参数下系统研究了各向异性强度和过饱和度对枝晶尖端生长速度、尖端曲率半径、Peclet数及稳定性常数σ~*的影响.结果表明,由微观可解性理论得到的稳定性系数σ~*与ε_6拟合值σ~*∝ε_6^(1.81905),更接近理想值σ~*(ε_6)∝ε_6^(1.75).此外,当过饱和度Ω<0.6时,稳定性系数σ~*不随ε_6的变化而变化,而当Ω>0.6时,稳定性系数σ~*随着ε_6的增加而减小.这反映了枝晶的生长由扩散控制向动力学控制的转变.随着过饱和度的增加,枝晶形貌由雪花状枝晶向圆状枝晶转变.

In this paper,the process of the free dendritic growth of Mg-0.5 wt.%Al alloy in the basal plane（0001） is simulated in two-dimensional system by using a quantitative phase-field model.A convergence study is carried out to choose the optimal coupling parameter A and grid width △x/W0 in simulation.Then we systematically discuss the effects of the anisotropic strength e and the supersaturation Ω on dendritical tip growth velocity,radius,Peclet number,and stability parameter σ^＊.Results show that the stability parameter σ^＊ defined by the theory of microscopic solvability is a function of the anisotropy strength ε,i.e.,σ^＊ ∝ε^1.81905,which is obviously closest to σ^＊ε∝ε^1.75 obtained from the analytical solution.Moreover,for Ω 0.6,the stability parameter σ^＊ is approximately a constant while it sharply and monotonically decreases with the augment of the value of e for Ω 0.6.This indicates that there is a transition from solute-controlled dendrite to kinetic dendrite as Ω increases.Furthermore,the transition of the growth pattern from the snow-like to the circle-like patterns occurs as Ω increases.