We investigate the plane problem of an edge dislocation inside a bilayer elastic film in which an elastic film of infinite thickness is perfectly bonded to one of finite thickness fixed on a rigid substrate. The two elastic films have identical shear moduli but distinct Poisson's ratios. Under this assumption, analytical expressions of the two pairs of analytic functions (characterizing the corresponding stress and displacement fields) in the bilayer elastic film are derived. In addition, an explicit expression of the image force acting on the edge dislocation is obtained. We find that the mismatch in Poisson's ratios makes it possible for an unstable equilibrium position for the edge dislocation to emerge. The analytical solution developed here can be expediently employed as a Green's function in the analysis of a nanocrack via an enhanced continuum-based model of fracture which incorporates surface effects in the bilayer elastic film.

中文翻译：

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双层弹性薄膜中的边缘位错

我们研究了双层弹性薄膜内的边缘位错的平面问题，其中无限厚度的弹性薄膜与固定在刚性基板上的有限厚度的弹性薄膜完美结合。两个弹性薄膜具有相同的剪切模量但不同的泊松比。在此假设下，导出了双层弹性膜中两对解析函数（表征相应的应力场和位移场）的解析表达式。此外，得到了作用在边缘位错上的像力的明确表达式。我们发现泊松比的不匹配使得边缘位错出现不稳定的平衡位置成为可能。这里开发的分析解决方案可以方便地用作 Green'