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Grain boundary grooving in a bicrystal with passivation coating
Continuum Mechanics and Thermodynamics ( IF 2.6 ) Pub Date : 2021-07-27 , DOI: 10.1007/s00161-021-01040-0
H. Kalantarova 1 , L. Klinger 1 , E. Rabkin 1
Affiliation  

We use the sixth-order linear parabolic equation

$$\begin{aligned} \frac{\partial y}{\partial t}=B\left( \alpha \frac{\partial ^{6}y}{\partial x^{6}}-\frac{\partial ^{4}y}{\partial x^{4}}\right) ,\ x\in {\mathbb {R}}_{+},\ t>0, \end{aligned}$$

proposed by Rabkin and describing the evolution of a solid surface covered with a thin, inert and fully elastic passivation layer, to analyze the grain boundary groove formation on initially flat surface. We derive the corresponding boundary conditions and construct an asymptotic representation of the solution to this initial boundary value problem when \(\alpha \) is small, by applying the theory of singular perturbation. We illustrate the effect of passivation film near and far from a grain boundary groove.



中文翻译:

具有钝化涂层的双晶中的晶界开槽

我们使用六阶线性抛物线方程

$$\begin{对齐} \frac{\partial y}{\partial t}=B\left( \alpha \frac{\partial ^{6}y}{\partial x^{6}}-\frac{ \partial ^{4}y}{\partial x^{4}}\right) ,\ x\in {\mathbb {R}}_{+},\ t>0, \end{aligned}$$

由 Rabkin 提出并描述了覆盖有薄的、惰性的和完全弹性的钝化层的固体表面的演变,以分析最初平坦表面上晶界凹槽的形成。通过应用奇异摄动理论,我们推导出相应的边界条件,并在\(\alpha \)很小时构造该初始边界值问题的解的渐近表示。我们说明了靠近和远离晶界凹槽的钝化膜的影响。

更新日期:2021-07-27
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