表面张力各向异性对深胞晶生长的影响

发布时间：2018-01-17 17:38

本文关键词：表面张力各向异性对深胞晶生长的影响　出处：《北京科技大学》2017年博士论文　论文类型：学位论文

【摘要】：本文系统的介绍了深胞晶生长理论的发展过程,这是材料科学中的重大理论课题之一,研究了材料科学和加工过程中的固-液界面微结构斑图这一问题。利用匹配渐近展开法和多变量展开法,得到了在定向凝固过程中,当表面张力和界面动力学同为各向异性时,深胞晶生长的一致有效的渐近解,揭示了各向异性对定向凝固中深胞晶生长界面的影响。论文包括深胞晶生长的全局性理论和全局稳定性理论两部分工作:(1)深胞晶生长的全局性理论:在考虑表面张力和界面动力学同为各向异性的情况下,研究了它们的共同作用对定向凝固中深胞晶生长的影响,得到问题的解析解以及该解所对应的界面形状。研究表明,各向异性界面动力学与各向异性表面张力的优选方向不一定相同,假设它们之间相差的角度θ0。当两种各向异性优选方向相同,即θ0为0时,随着各向异性系数的增大,深胞晶的指状界面全长增大,根部底端的曲率半径会减小,即根部底端的曲率增大,且各向异性表面张力系数对深胞晶生长界面形状的影响更为显著。当0≤θ0≤π/4时,随着θ0增大,深胞晶的指状界面全长减小,根部底端的曲率半径会减小,即根部底端的曲率增大;当π/4≤θ0≤π/2时,随着θ0增大,深胞晶的指状界面全长增大,根部底端的曲率半径会增大,即根部底端的曲率减少。(2)深胞晶生长的全局稳定性理论:通过对表面张力为各向异性的定常深胞晶生长的整体稳定性的研究发现,与表面张力为各向同性的定向凝固系统中深胞晶界面形态稳定性比较,表面张力各向异性的定向凝固中深胞晶生长界面形态也有两种整体不稳定性机制:整体波动不稳定性(GTW)和低频不稳定性(IF)。随着表面张力各向异性的增加,中性模式产生强振荡的枝晶结构的整体波动不稳定性的不稳定区域减小,而中性模式产生弱振荡的胞晶结构的低频不稳定性的不稳定区域增加。
[Abstract]:This paper introduces the development process of deep cellular crystal growth theory, which is one of the major problems in material science, material science and research in the process of solid-liquid interface micro structure pattern of this problem. By using the matched asymptotic expansion method and multi variable expansion method, obtained during directional solidification and when the surface tension and interface dynamics with anisotropic, deep cellular crystal growth of the uniformly valid asymptotic solution, to reveal the effect of anisotropy on the growth interface in directional solidification of deep cellular crystal. The thesis consists of two parts of the global theory of deep cellular growth and global stability theory: (1) deep cellular crystal the growth of the global Theory: in consideration of surface tension and interface dynamics with anisotropic, studied their common effects on the growth of directional solidification of deep cellular crystal, obtained the analytical solution of the problem and its solution The corresponding interface shape. The research results show that the preferred orientation of anisotropic interface dynamics and anisotropic surface tension is not necessarily the same, the difference between them is that the angle of 0. when the two kinds of anisotropic preferably the same direction, namely is 0 to 0, with the increase of anisotropy, deep cellular crystal finger length increase interface the radius of curvature, the root ends will decrease, which is at the bottom of the root curvature increases, and the effect of anisotropic surface tension coefficient of deep cellular crystal growth interface shape is more significant. When less than 0 and less than 0 theta PI /4, with about 0 increase of deep cellular crystal finger interface length decreases, the radius of curvature the root of the bottom will decrease, which is at the bottom of the root curvature increases; when /4 = 0 = Pi Pi theta theta /2, with 0 increase of deep cellular crystal finger interface length increases, the radius of curvature of the root of the bottom will increase, which is at the bottom of the root curvature decreases. (2) deep cellular crystal the growth of global Stability theory: through the research on the overall stability of surface tension anisotropy constant deep cellular crystal growth was found, compared with the surface tension of the stability of directional solidification system deep cellular crystal interface shape is isotropic, the directional solidification of deep cellular crystal surface tension anisotropy growth interface morphology also has two kinds: overall instability mechanism the overall fluctuation (GTW) and low frequency instability (IF). With the increase of surface tension anisotropy, the unstable region overall volatility model produces strong oscillations of neutral dendrite structure instability decreases, the unstable region of low frequency and mode of neutral cellular crystal structure and weak oscillation instability increases.

【学位授予单位】：北京科技大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：TB30

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