液固界面滞后对凝固初始过渡区溶质再分配的影响

Effect of Hysteresis of Solid-Liquid Interface during Solidification on Initial Transient Solute Redistribution

实际定向凝固过程中,当改变外加速度或凝固刚开始时,液固界面并不是立即跟上外加速度,而是存在一种滞后效应。本文在采用一些近似假设的基础上,研究了这种滞后效应对定向凝固过程初始过渡区溶质再分配的影响,得到一个新的初始过渡区溶质分布公式,证明Tiller的经典结果只是本文结果当△T_0/G→0时的极限情况。理论计算结果还表明,液固界面实际速度对外部控制速度的滞后效应将使凝固初始过渡区溶质分布趋于稳态所需时间和距离增长;不仅外部控制速度V_0和分配系数k,而且温度梯度G,合金平均成分C_0和液相线斜率m都会影响初始过渡区溶质再分配过程,其影响以V_0最大,k、D_L次之,G,C_0,m最小。

Previous research papers on the initial transient solute redistribution during solidification have all been based on the basic assumption that the solid-liquid interface advancing velocity reaches the externally imposed velocity at the very beginning of solidification and remains constant till the end of solidification. Somboonsuk et al [5], later Eshelman et al [6], and the present authors have experimentally found that during solidification, when externally imposed velocity is abruptly changed or at the beginning of solidification, the solid-liquid interface advancing velocity is unable to catch up with the changed external velocity immediately, hence a hysteresis occurs. But Somboonsuk and Eshelman did not go into the theoretical analysis of the experimental finding just mentioned. In the present paper, the authors believe that they find for the first time that the hysteresis of interface velocity reflects the coupling effects of temperature field and concentration field and must be included in the theoretical treatments of the initial transient solute redistribution. Study in the present paper has been focused on the effects of such hysteresis on the solute redistribution in the initial transient stage of directional solidification. New equations for the solute redistribution have been deduced. It has been proved that the classical analysis only corresponds to the extreme case of the current result when ΔT_0/G tends to zero. Theoretical calculations also show that the hysteresis of the real solid-liquid interface velocity relative to the externally imposed velocity makes the time and distance required to reach steady state increased. Not only the external velocity V_0, distribution coefficient k and diffusivity D_L, but the temperature gradient G, the mean concentration of the alloy C_0 and the slope of liquidus m influence the solute redistribution process in the initial transient stage. The six factors may he app roximately placed in three groups: V_0 has the greatest influence, k and D_L are next in importance, and G, C_0, in exert minor influence.