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首页> 外文期刊>Mathematical Problems in Engineering >Computation of Trajectories and Displacement Fields in a Three-Dimensional Ternary Diffusion Couple: Parabolic Transform Method
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Computation of Trajectories and Displacement Fields in a Three-Dimensional Ternary Diffusion Couple: Parabolic Transform Method

机译：三维三元扩散对中的轨迹和位移场的计算：抛物线变换法

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摘要

The problem of Kirkendall's trajectories in finite, three-and one-dimensional ternary diffusion couples is studied. By means of the parabolic transformation method, we calculate the solute field, the Kirkendall marker velocity, and displacement fields. The velocity field is generally continuous and can be integrated to obtain a displacement field that is continuous everywhere. Special features observed experimentally and reported in the literature are also studied: (i) multiple Kirkendall's planes where markers placed on an initial compositional discontinuity of the diffusion couple evolve into two locations as a result of the initial distribution, (ii) multiple Kirkendall's planes where markers placed on an initial compositional discontinuity of the diffusion couple move into two locations due to composition dependent mobilities, and (iii) a Kirkendall plane that coincides with the interphase interface. The details of the deformation (material trajectories) in these special situations are given using both methods and are discussed in terms of the stress-free strain rate associated with the Kirkendall effect. Our nonlinear transform generalizes the diagonalization method by Krishtal, Mokrov, Akimov, and Zakharov, whose transform of diffusivities was linear.
机译：研究了有限，三维和一维三元扩散对中柯肯德尔轨道的问题。通过抛物线变换方法，我们计算了溶质场，柯肯德尔速度和位移场。速度场通常是连续的，可以积分以获得在任何地方都是连续的位移场。还对通过实验观察到并在文献中报道的特殊特征进行了研究：（i）多个Kirkendall平面，其中由于初始分布而在扩散对的初始成分不连续性上放置的标记演变为两个位置；（ii）多个Kirkendall平面，其中由于依赖于成分的迁移率，放置在扩散偶的初始成分不连续性上的标记移到两个位置，（iii）与相间界面重合的柯肯德尔平面。两种方法都给出了在这些特殊情况下变形（材料轨迹）的细节，并根据与柯肯德尔效应相关的无应力应变率进行了讨论。我们的非线性变换通过Krishtal，Mokrov，Akimov和Zakharov推广了对角化方法，其扩散系数的变换是线性的。

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